TPTP Axioms File: MSC001-1.ax
%------------------------------------------------------------------------------
% File : MSC001-1 : TPTP v8.2.0. Released v3.2.0.
% Domain : Miscellaneous
% Axioms : Sets, numbers, lists, etc, that make up the Isabelle/HOL library
% Version : [Pau06] axioms.
% English : The files MSC001-[012].ax .ax are really about everything: sets,
% numbers, lists and all the other things that make up the basic
% Isabelle/HOL library. Also, many of the axioms in MSC001-0.ax
% describe the Isabelle/HOL type class hierarchy.
% Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source : [Pau06]
% Names : simp.ax [Pau06]
% Status : Satisfiable
% Syntax : Number of clauses : 1568 ( 485 unt; 231 nHn; 853 RR)
% Number of literals : 3799 (1241 equ;2056 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 42 ( 41 usr; 0 prp; 1-3 aty)
% Number of functors : 193 ( 193 usr; 43 con; 0-18 aty)
% Number of variables : 4320 (1087 sgn)
% SPC :
% Comments : Requires MSC001-0.ax
%------------------------------------------------------------------------------
cnf(cls_Binomial_Obinomial__0__Suc_0,axiom,
c_Binomial_Obinomial(c_0,c_Suc(V_k)) = c_0 ).
cnf(cls_Binomial_Obinomial__1_0,axiom,
c_Binomial_Obinomial(V_y,c_Suc(c_0)) = V_y ).
cnf(cls_Binomial_Obinomial__Suc__Suc_0,axiom,
c_Binomial_Obinomial(c_Suc(V_n),c_Suc(V_k)) = c_plus(c_Binomial_Obinomial(V_n,V_k),c_Binomial_Obinomial(V_n,c_Suc(V_k)),tc_nat) ).
cnf(cls_Binomial_Obinomial__Suc__n_0,axiom,
c_Binomial_Obinomial(c_Suc(V_n),V_n) = c_Suc(V_n) ).
cnf(cls_Binomial_Obinomial__n__0_0,axiom,
c_Binomial_Obinomial(V_n,c_0) = c_1 ).
cnf(cls_Binomial_Obinomial__n__n_0,axiom,
c_Binomial_Obinomial(V_n,V_n) = c_1 ).
cnf(cls_Datatype_Oelem__o2s_0,axiom,
( ~ c_in(V_x,c_Datatype_Oo2s(V_xo,T_a),T_a)
| V_xo = c_Datatype_Ooption_OSome(V_x,T_a) ) ).
cnf(cls_Datatype_Oelem__o2s_1,axiom,
c_in(V_x,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(V_x,T_a),T_a),T_a) ).
cnf(cls_Datatype_Onot__None__eq_0,axiom,
( V_x = c_Datatype_Ooption_ONone
| V_x = c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(V_x,T_a),T_a) ) ).
cnf(cls_Datatype_Onot__Some__eq_0,axiom,
( V_x = c_Datatype_Ooption_ONone
| V_x = c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(V_x,T_a),T_a) ) ).
cnf(cls_Datatype_Oo2s_Osimps__2_0,axiom,
c_Datatype_Oo2s(c_Datatype_Ooption_OSome(V_x,T_a__1),T_a__1) = c_insert(V_x,c_emptyset,T_a__1) ).
cnf(cls_Datatype_Oo2s__empty__eq_0,axiom,
( c_Datatype_Oo2s(V_xo,T_a) != c_emptyset
| V_xo = c_Datatype_Ooption_ONone ) ).
cnf(cls_Datatype_Oo2s__empty__eq_1,axiom,
c_Datatype_Oo2s(c_Datatype_Ooption_ONone,T_a) = c_emptyset ).
cnf(cls_Datatype_Ooption_Odistinct__1_0,axiom,
c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(V_a_H,T_a) ).
cnf(cls_Datatype_Ooption_Odistinct__2_0,axiom,
c_Datatype_Ooption_OSome(V_a_H,T_a) != c_Datatype_Ooption_ONone ).
cnf(cls_Datatype_Ooption_Oinject_0,axiom,
( c_Datatype_Ooption_OSome(V_a,T_a) != c_Datatype_Ooption_OSome(V_a_H,T_a)
| V_a = V_a_H ) ).
cnf(cls_Datatype_Ooption_Osize__1_0,axiom,
c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(T_a)) = c_0 ).
cnf(cls_Datatype_Ooption_Osize__2_0,axiom,
c_Nat_Osize(c_Datatype_Ooption_OSome(V_a,T_a),tc_Datatype_Ooption(T_a)) = c_0 ).
cnf(cls_Datatype_Oprod_Osize_0,axiom,
c_Nat_Osize(c_Pair(V_a,V_b,T_a,T_b),tc_prod(T_a,T_b)) = c_0 ).
cnf(cls_Datatype_Osum_Osize__1_0,axiom,
c_Nat_Osize(c_Sum__Type_OInl(V_a,T_a,T_b),tc_sum(T_a,T_b)) = c_0 ).
cnf(cls_Datatype_Osum_Osize__2_0,axiom,
c_Nat_Osize(c_Sum__Type_OInr(V_b,T_b,T_a),tc_sum(T_a,T_b)) = c_0 ).
cnf(cls_Datatype_Othe_Osimps_0,axiom,
c_Datatype_Othe(c_Datatype_Ooption_OSome(V_y,T_a),T_a) = V_y ).
cnf(cls_Datatype_Ounit_Ocases_0,axiom,
c_Datatype_Ounit_Ounit__case(V_y,c_Product__Type_OUnity,T_a) = V_y ).
cnf(cls_Datatype_Ounit_Orecs_0,axiom,
c_Datatype_Ounit_Ounit__rec(V_y,c_Product__Type_OUnity,T_a) = V_y ).
cnf(cls_Datatype_Ounit_Osize_0,axiom,
c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0 ).
cnf(cls_Datatype__Universe_OAtom__Atom__eq_0,axiom,
( c_Datatype__Universe_OAtom(V_a,T_a,T_b) != c_Datatype__Universe_OAtom(V_b,T_a,T_b)
| V_a = V_b ) ).
cnf(cls_Datatype__Universe_OAtom__not__Scons_0,axiom,
c_Datatype__Universe_OAtom(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) ).
cnf(cls_Datatype__Universe_ODomain__dprod_0,axiom,
c_Relation_ODomain(c_Datatype__Universe_Odprod(V_r,V_s,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(V_r,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),c_Relation_ODomain(V_s,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),T_a,T_b) ).
cnf(cls_Datatype__Universe_ODomain__dsum_0,axiom,
c_Relation_ODomain(c_Datatype__Universe_Odsum(V_r,V_s,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(V_r,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),c_Relation_ODomain(V_s,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),T_a,T_b) ).
cnf(cls_Datatype__Universe_OIn0__eq_0,axiom,
( c_Datatype__Universe_OIn0(V_M,T_a,T_b) != c_Datatype__Universe_OIn0(V_N,T_a,T_b)
| V_M = V_N ) ).
cnf(cls_Datatype__Universe_OIn0__not__In1_0,axiom,
c_Datatype__Universe_OIn0(V_M,T_a,T_b) != c_Datatype__Universe_OIn1(V_N,T_a,T_b) ).
cnf(cls_Datatype__Universe_OIn1__eq_0,axiom,
( c_Datatype__Universe_OIn1(V_M,T_a,T_b) != c_Datatype__Universe_OIn1(V_N,T_a,T_b)
| V_M = V_N ) ).
cnf(cls_Datatype__Universe_OIn1__not__In0_0,axiom,
c_Datatype__Universe_OIn1(V_N,T_a,T_b) != c_Datatype__Universe_OIn0(V_M,T_a,T_b) ).
cnf(cls_Datatype__Universe_OLeaf__not__Numb_0,axiom,
c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b) ).
cnf(cls_Datatype__Universe_OLeaf__not__Scons_0,axiom,
c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) ).
cnf(cls_Datatype__Universe_ONumb__not__Leaf_0,axiom,
c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b) ).
cnf(cls_Datatype__Universe_ONumb__not__Scons_0,axiom,
c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) ).
cnf(cls_Datatype__Universe_OScons__Scons__eq_0,axiom,
( c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OScons(V_M_H,V_N_H,T_a,T_b)
| V_M = V_M_H ) ).
cnf(cls_Datatype__Universe_OScons__Scons__eq_1,axiom,
( c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OScons(V_M_H,V_N_H,T_a,T_b)
| V_N = V_N_H ) ).
cnf(cls_Datatype__Universe_OScons__not__Atom_0,axiom,
c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OAtom(V_a,T_a,T_b) ).
cnf(cls_Datatype__Universe_OScons__not__Leaf_0,axiom,
c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b) ).
cnf(cls_Datatype__Universe_OScons__not__Numb_0,axiom,
c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b) ).
cnf(cls_Datatype__Universe_Ontrunc__0_0,axiom,
c_Datatype__Universe_Ontrunc(c_0,V_M,T_a,T_b) = c_emptyset ).
cnf(cls_Datatype__Universe_Ontrunc__Atom_0,axiom,
c_Datatype__Universe_Ontrunc(c_Suc(V_k),c_Datatype__Universe_OAtom(V_a,T_a,T_b),T_a,T_b) = c_Datatype__Universe_OAtom(V_a,T_a,T_b) ).
cnf(cls_Datatype__Universe_Ontrunc__In0_0,axiom,
c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(V_k)),c_Datatype__Universe_OIn0(V_M,T_a,T_b),T_a,T_b) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(V_k),V_M,T_a,T_b),T_a,T_b) ).
cnf(cls_Datatype__Universe_Ontrunc__In1_0,axiom,
c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(V_k)),c_Datatype__Universe_OIn1(V_M,T_a,T_b),T_a,T_b) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(V_k),V_M,T_a,T_b),T_a,T_b) ).
cnf(cls_Datatype__Universe_Ontrunc__Leaf_0,axiom,
c_Datatype__Universe_Ontrunc(c_Suc(V_k),c_Datatype__Universe_OLeaf(V_a,T_a,T_b),T_a,T_b) = c_Datatype__Universe_OLeaf(V_a,T_a,T_b) ).
cnf(cls_Datatype__Universe_Ontrunc__Numb_0,axiom,
c_Datatype__Universe_Ontrunc(c_Suc(V_k),c_Datatype__Universe_ONumb(V_i,T_a,T_b),T_a,T_b) = c_Datatype__Universe_ONumb(V_i,T_a,T_b) ).
cnf(cls_Datatype__Universe_Ontrunc__Scons_0,axiom,
c_Datatype__Universe_Ontrunc(c_Suc(V_k),c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),T_a,T_b) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(V_k,V_M,T_a,T_b),c_Datatype__Universe_Ontrunc(V_k,V_N,T_a,T_b),T_a,T_b) ).
cnf(cls_Datatype__Universe_Ontrunc__one__In0_0,axiom,
c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(V_M,T_a,T_b),T_a,T_b) = c_emptyset ).
cnf(cls_Datatype__Universe_Ontrunc__one__In1_0,axiom,
c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(V_M,T_a,T_b),T_a,T_b) = c_emptyset ).
cnf(cls_Divides_ODIVISION__BY__ZERO__DIV_0,axiom,
c_div(V_a,c_0,tc_nat) = c_0 ).
cnf(cls_Divides_ODIVISION__BY__ZERO__MOD_0,axiom,
c_Divides_Oop_Amod(V_y,c_0,tc_nat) = V_y ).
cnf(cls_Divides_Odiv__0_0,axiom,
c_div(c_0,V_m,tc_nat) = c_0 ).
cnf(cls_Divides_Odiv__1_0,axiom,
c_div(V_y,c_Suc(c_0),tc_nat) = V_y ).
cnf(cls_Divides_Odiv__le__dividend_0,axiom,
c_lessequals(c_div(V_m,V_n,tc_nat),V_m,tc_nat) ).
cnf(cls_Divides_Odiv__less_0,axiom,
( ~ c_less(V_m,V_n,tc_nat)
| c_div(V_m,V_n,tc_nat) = c_0 ) ).
cnf(cls_Divides_Odiv__less__dividend_0,axiom,
( ~ c_less(c_0,V_m,tc_nat)
| ~ c_less(c_1,V_n,tc_nat)
| c_less(c_div(V_m,V_n,tc_nat),V_m,tc_nat) ) ).
cnf(cls_Divides_Odiv__mult__mult1_0,axiom,
( ~ c_less(c_0,V_c,tc_nat)
| c_div(c_times(V_c,V_a,tc_nat),c_times(V_c,V_b,tc_nat),tc_nat) = c_div(V_a,V_b,tc_nat) ) ).
cnf(cls_Divides_Odiv__mult__mult2_0,axiom,
( ~ c_less(c_0,V_c,tc_nat)
| c_div(c_times(V_a,V_c,tc_nat),c_times(V_b,V_c,tc_nat),tc_nat) = c_div(V_a,V_b,tc_nat) ) ).
cnf(cls_Divides_Odiv__mult__self1_0,axiom,
( ~ c_less(c_0,V_n,tc_nat)
| c_div(c_plus(V_m,c_times(V_k,V_n,tc_nat),tc_nat),V_n,tc_nat) = c_plus(V_k,c_div(V_m,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Divides_Odiv__mult__self1__is__m_0,axiom,
( ~ c_less(c_0,V_n,tc_nat)
| c_div(c_times(V_n,V_y,tc_nat),V_n,tc_nat) = V_y ) ).
cnf(cls_Divides_Odiv__mult__self2_0,axiom,
( ~ c_less(c_0,V_n,tc_nat)
| c_div(c_plus(V_m,c_times(V_n,V_k,tc_nat),tc_nat),V_n,tc_nat) = c_plus(V_k,c_div(V_m,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Divides_Odiv__mult__self__is__m_0,axiom,
( ~ c_less(c_0,V_n,tc_nat)
| c_div(c_times(V_y,V_n,tc_nat),V_n,tc_nat) = V_y ) ).
cnf(cls_Divides_Odiv__self_0,axiom,
( ~ c_less(c_0,V_n,tc_nat)
| c_div(V_n,V_n,tc_nat) = c_1 ) ).
cnf(cls_Divides_Odvd__0__left__iff_0,axiom,
( ~ c_Divides_Oop_Advd(c_0,V_m,tc_nat)
| V_m = c_0 ) ).
cnf(cls_Divides_Odvd__0__left__iff_1,axiom,
c_Divides_Oop_Advd(c_0,c_0,tc_nat) ).
cnf(cls_Divides_Odvd__1__iff__1_0,axiom,
( ~ c_Divides_Oop_Advd(V_m,c_Suc(c_0),tc_nat)
| V_m = c_Suc(c_0) ) ).
cnf(cls_Divides_Odvd__1__iff__1_1,axiom,
c_Divides_Oop_Advd(c_Suc(c_0),c_Suc(c_0),tc_nat) ).
cnf(cls_Divides_Odvd__refl_0,axiom,
c_Divides_Oop_Advd(V_m,V_m,tc_nat) ).
cnf(cls_Divides_Omod__0_0,axiom,
c_Divides_Oop_Amod(c_0,V_m,tc_nat) = c_0 ).
cnf(cls_Divides_Omod__1_0,axiom,
c_Divides_Oop_Amod(V_m,c_Suc(c_0),tc_nat) = c_0 ).
cnf(cls_Divides_Omod__add__self1_0,axiom,
c_Divides_Oop_Amod(c_plus(V_n,V_m,tc_nat),V_n,tc_nat) = c_Divides_Oop_Amod(V_m,V_n,tc_nat) ).
cnf(cls_Divides_Omod__add__self2_0,axiom,
c_Divides_Oop_Amod(c_plus(V_m,V_n,tc_nat),V_n,tc_nat) = c_Divides_Oop_Amod(V_m,V_n,tc_nat) ).
cnf(cls_Divides_Omod__le__divisor_0,axiom,
( ~ c_less(c_0,V_n,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(V_m,V_n,tc_nat),V_n,tc_nat) ) ).
cnf(cls_Divides_Omod__less_0,axiom,
( ~ c_less(V_y,V_n,tc_nat)
| c_Divides_Oop_Amod(V_y,V_n,tc_nat) = V_y ) ).
cnf(cls_Divides_Omod__less__divisor_0,axiom,
( ~ c_less(c_0,V_n,tc_nat)
| c_less(c_Divides_Oop_Amod(V_m,V_n,tc_nat),V_n,tc_nat) ) ).
cnf(cls_Divides_Omod__mult__self1_0,axiom,
c_Divides_Oop_Amod(c_plus(V_m,c_times(V_k,V_n,tc_nat),tc_nat),V_n,tc_nat) = c_Divides_Oop_Amod(V_m,V_n,tc_nat) ).
cnf(cls_Divides_Omod__mult__self1__is__0_0,axiom,
c_Divides_Oop_Amod(c_times(V_n,V_m,tc_nat),V_n,tc_nat) = c_0 ).
cnf(cls_Divides_Omod__mult__self2_0,axiom,
c_Divides_Oop_Amod(c_plus(V_m,c_times(V_n,V_k,tc_nat),tc_nat),V_n,tc_nat) = c_Divides_Oop_Amod(V_m,V_n,tc_nat) ).
cnf(cls_Divides_Omod__mult__self__is__0_0,axiom,
c_Divides_Oop_Amod(c_times(V_m,V_n,tc_nat),V_n,tc_nat) = c_0 ).
cnf(cls_Divides_Omod__self_0,axiom,
c_Divides_Oop_Amod(V_n,V_n,tc_nat) = c_0 ).
cnf(cls_Divides_Onat__mod__div__trivial_0,axiom,
c_div(c_Divides_Oop_Amod(V_m,V_n,tc_nat),V_n,tc_nat) = c_0 ).
cnf(cls_Divides_Onat__mod__mod__trivial_0,axiom,
c_Divides_Oop_Amod(c_Divides_Oop_Amod(V_m,V_n,tc_nat),V_n,tc_nat) = c_Divides_Oop_Amod(V_m,V_n,tc_nat) ).
cnf(cls_Equiv__Relations_Oquotient__is__empty2_0,axiom,
( c_emptyset != c_Equiv__Relations_Oquotient(V_A,V_r,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Equiv__Relations_Oquotient__is__empty2_1,axiom,
c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,V_r,T_a) ).
cnf(cls_Equiv__Relations_Oquotient__is__empty_0,axiom,
( c_Equiv__Relations_Oquotient(V_A,V_r,T_a) != c_emptyset
| V_A = c_emptyset ) ).
cnf(cls_Equiv__Relations_Oquotient__is__empty_1,axiom,
c_Equiv__Relations_Oquotient(c_emptyset,V_r,T_a) = c_emptyset ).
cnf(cls_Extraction_Osumbool_Ocases__1_0,axiom,
c_Extraction_Osumbool_Osumbool__case(V_y,V_f2,c_Extraction_Osumbool_OLeft,T_a) = V_y ).
cnf(cls_Extraction_Osumbool_Ocases__2_0,axiom,
c_Extraction_Osumbool_Osumbool__case(V_f1,V_y,c_Extraction_Osumbool_ORight,T_a) = V_y ).
cnf(cls_Extraction_Osumbool_Odistinct__1_0,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight ).
cnf(cls_Extraction_Osumbool_Odistinct__2_0,axiom,
c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft ).
cnf(cls_Extraction_Osumbool_Orecs__1_0,axiom,
c_Extraction_Osumbool_Osumbool__rec(V_y,V_f2,c_Extraction_Osumbool_OLeft,T_a) = V_y ).
cnf(cls_Extraction_Osumbool_Orecs__2_0,axiom,
c_Extraction_Osumbool_Osumbool__rec(V_f1,V_y,c_Extraction_Osumbool_ORight,T_a) = V_y ).
cnf(cls_Extraction_Osumbool_Osize__1_0,axiom,
c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) = c_0 ).
cnf(cls_Extraction_Osumbool_Osize__2_0,axiom,
c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) = c_0 ).
cnf(cls_Finite__Set_OMax__ge_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_lessequals(V_x,c_Finite__Set_OMax(V_A,T_a),T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMax__in_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_Finite__Set_OMax(V_A,T_a),V_A,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMax__insert_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_b))
| V_A = c_emptyset
| c_Finite__Set_OMax(c_insert(V_x,V_A,T_b),T_b) = c_Orderings_Omax(V_x,c_Finite__Set_OMax(V_A,T_b),T_b) ) ).
cnf(cls_Finite__Set_OMax__le__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_U,V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_lessequals(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| c_lessequals(V_U,V_x,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMax__le__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_Main_OMax__le__iff__1(V_A,V_x,T_a),V_A,T_a)
| c_lessequals(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMax__le__iff_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_lessequals(c_Main_OMax__le__iff__1(V_A,V_x,T_a),V_x,T_a)
| c_lessequals(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMax__less__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_U,V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_less(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| c_less(V_U,V_x,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMax__less__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_Main_OMax__less__iff__1(V_A,V_x,T_a),V_A,T_a)
| c_less(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMax__less__iff_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_less(c_Main_OMax__less__iff__1(V_A,V_x,T_a),V_x,T_a)
| c_less(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMax__singleton_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_Finite__Set_OMax(c_insert(V_y,c_emptyset,T_a),T_a) = V_y ) ).
cnf(cls_Finite__Set_OMin__ge__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_U,V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_lessequals(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| c_lessequals(V_x,V_U,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMin__ge__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_Main_OMin__ge__iff__1(V_A,V_x,T_a),V_A,T_a)
| c_lessequals(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMin__ge__iff_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_lessequals(V_x,c_Main_OMin__ge__iff__1(V_A,V_x,T_a),T_a)
| c_lessequals(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMin__gr__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_U,V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_less(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| c_less(V_x,V_U,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMin__gr__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_Main_OMin__gr__iff__1(V_A,V_x,T_a),V_A,T_a)
| c_less(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMin__gr__iff_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_less(V_x,c_Main_OMin__gr__iff__1(V_A,V_x,T_a),T_a)
| c_less(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMin__in_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_Finite__Set_OMin(V_A,T_a),V_A,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMin__insert_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_b))
| V_A = c_emptyset
| c_Finite__Set_OMin(c_insert(V_x,V_A,T_b),T_b) = c_Orderings_Omin(V_x,c_Finite__Set_OMin(V_A,T_b),T_b) ) ).
cnf(cls_Finite__Set_OMin__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_lessequals(c_Finite__Set_OMin(V_A,T_a),V_x,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_OMin__singleton_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_Finite__Set_OMin(c_insert(V_y,c_emptyset,T_a),T_a) = V_y ) ).
cnf(cls_Finite__Set_Ocard__0__eq_0,axiom,
( ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_Finite__Set_Ocard(V_A,T_a) != c_0
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_Ocard__0__eq_1,axiom,
( ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(T_a))
| c_Finite__Set_Ocard(c_emptyset,T_a) = c_0 ) ).
cnf(cls_Finite__Set_Ocard__empty_0,axiom,
c_Finite__Set_Ocard(c_emptyset,T_a) = c_0 ).
cnf(cls_Finite__Set_Ocard__infinite_0,axiom,
( c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_Finite__Set_Ocard(V_A,T_a) = c_0 ) ).
cnf(cls_Finite__Set_Ocard__insert__disjoint_0,axiom,
( ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_in(V_x,V_A,T_a)
| c_Finite__Set_Ocard(c_insert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ).
cnf(cls_Finite__Set_Ofinite__Diff_0,axiom,
( ~ c_in(V_B,c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_minus(V_B,V_Ba,tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a)) ) ).
cnf(cls_Finite__Set_Ofinite__Diff__insert_0,axiom,
( ~ c_in(c_minus(V_A,c_insert(V_a,V_B,T_a),tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_minus(V_A,V_B,tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a)) ) ).
cnf(cls_Finite__Set_Ofinite__Diff__insert_1,axiom,
( ~ c_in(c_minus(V_A,V_B,tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_minus(V_A,c_insert(V_a,V_B,T_a),tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a)) ) ).
cnf(cls_Finite__Set_Ofinite__Pow__iff_0,axiom,
( ~ c_in(c_Pow(V_A,T_a),c_Finite__Set_OFinites,tc_set(tc_set(T_a)))
| c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ) ).
cnf(cls_Finite__Set_Ofinite__Pow__iff_1,axiom,
( ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_Pow(V_A,T_a),c_Finite__Set_OFinites,tc_set(tc_set(T_a))) ) ).
cnf(cls_Finite__Set_Ofinite__Un_0,axiom,
( ~ c_in(c_union(V_F,V_G,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| c_in(V_F,c_Finite__Set_OFinites,tc_set(T_a)) ) ).
cnf(cls_Finite__Set_Ofinite__Un_1,axiom,
( ~ c_in(c_union(V_F,V_G,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| c_in(V_G,c_Finite__Set_OFinites,tc_set(T_a)) ) ).
cnf(cls_Finite__Set_Ofinite__Un_2,axiom,
( ~ c_in(V_G,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_F,c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_union(V_F,V_G,T_a),c_Finite__Set_OFinites,tc_set(T_a)) ) ).
cnf(cls_Finite__Set_Ofinite__converse_0,axiom,
( ~ c_in(c_Relation_Oconverse(V_r,T_b,T_a),c_Finite__Set_OFinites,tc_set(tc_prod(T_a,T_b)))
| c_in(V_r,c_Finite__Set_OFinites,tc_set(tc_prod(T_b,T_a))) ) ).
cnf(cls_Finite__Set_Ofinite__converse_1,axiom,
( ~ c_in(V_r,c_Finite__Set_OFinites,tc_set(tc_prod(T_b,T_a)))
| c_in(c_Relation_Oconverse(V_r,T_b,T_a),c_Finite__Set_OFinites,tc_set(tc_prod(T_a,T_b))) ) ).
cnf(cls_Finite__Set_Ofinite__insert_0,axiom,
( ~ c_in(c_insert(V_a,V_A,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ) ).
cnf(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_b))
| c_lessequals(c_Finite__Set_OMin(V_A,T_b),c_Finite__Set_OMax(V_A,T_b),T_b)
| V_A = c_emptyset ) ).
cnf(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_in(V_y,V_A,T_b)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_b))
| V_A = c_emptyset
| c_Orderings_Omin(V_y,c_Finite__Set_OMax(V_A,T_b),T_b) = V_y ) ).
cnf(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_in(V_y,V_A,T_b)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_b))
| V_A = c_emptyset
| c_Orderings_Omax(V_y,c_Finite__Set_OMin(V_A,T_b),T_b) = V_y ) ).
cnf(cls_Finite__Set_Oof__nat__id_0,axiom,
c_NatArith_Oof__nat(V_y,tc_nat) = V_y ).
cnf(cls_Fun_Oid__apply_0,axiom,
c_Fun_Oid(V_y,T_a) = V_y ).
cnf(cls_GCD_Ogcd__0_0,axiom,
c_GCD_Ogcd(c_Pair(V_y,c_0,tc_nat,tc_nat)) = V_y ).
cnf(cls_GCD_Ogcd__0__left_0,axiom,
c_GCD_Ogcd(c_Pair(c_0,V_y,tc_nat,tc_nat)) = V_y ).
cnf(cls_GCD_Ogcd__1_0,axiom,
c_GCD_Ogcd(c_Pair(V_m,c_Suc(c_0),tc_nat,tc_nat)) = c_1 ).
cnf(cls_GCD_Ogcd__1__left_0,axiom,
c_GCD_Ogcd(c_Pair(c_Suc(c_0),V_m,tc_nat,tc_nat)) = c_1 ).
cnf(cls_GCD_Ogcd__add1_0,axiom,
c_GCD_Ogcd(c_Pair(c_plus(V_m,V_n,tc_nat),V_n,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(V_m,V_n,tc_nat,tc_nat)) ).
cnf(cls_GCD_Ogcd__add2_0,axiom,
c_GCD_Ogcd(c_Pair(V_m,c_plus(V_m,V_n,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(V_m,V_n,tc_nat,tc_nat)) ).
cnf(cls_GCD_Ogcd__add2_H_0,axiom,
c_GCD_Ogcd(c_Pair(V_m,c_plus(V_n,V_m,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(V_m,V_n,tc_nat,tc_nat)) ).
cnf(cls_GCD_Ogcd__greatest__iff_0,axiom,
( ~ c_Divides_Oop_Advd(V_k,c_GCD_Ogcd(c_Pair(V_m,V_n,tc_nat,tc_nat)),tc_nat)
| c_Divides_Oop_Advd(V_k,V_m,tc_nat) ) ).
cnf(cls_GCD_Ogcd__greatest__iff_1,axiom,
( ~ c_Divides_Oop_Advd(V_k,c_GCD_Ogcd(c_Pair(V_m,V_n,tc_nat,tc_nat)),tc_nat)
| c_Divides_Oop_Advd(V_k,V_n,tc_nat) ) ).
cnf(cls_GCD_Ogcd__greatest__iff_2,axiom,
( ~ c_Divides_Oop_Advd(V_k,V_n,tc_nat)
| ~ c_Divides_Oop_Advd(V_k,V_m,tc_nat)
| c_Divides_Oop_Advd(V_k,c_GCD_Ogcd(c_Pair(V_m,V_n,tc_nat,tc_nat)),tc_nat) ) ).
cnf(cls_GCD_Ogcd__mult_0,axiom,
c_GCD_Ogcd(c_Pair(V_y,c_times(V_y,V_n,tc_nat),tc_nat,tc_nat)) = V_y ).
cnf(cls_GCD_Ogcd__self_0,axiom,
c_GCD_Ogcd(c_Pair(V_y,V_y,tc_nat,tc_nat)) = V_y ).
cnf(cls_Infinite__Set_Onat__infinite_0,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ).
cnf(cls_IntArith_Oabs__minus__one_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),T_a) = c_1 ) ).
cnf(cls_IntArith_Oabs__power__minus__one_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),V_n,T_a),T_a) = c_1 ) ).
cnf(cls_IntArith_Oarith__special__10_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_y,T_a),T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(V_y)),T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__10_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(V_y)),T_a),T_a)
| c_less(c_0,c_Numeral_Onumber__of(V_y,T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__11_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_1,c_Numeral_Onumber__of(V_y,T_a),T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(V_y)),T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__11_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(V_y)),T_a),T_a)
| c_less(c_1,c_Numeral_Onumber__of(V_y,T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__12_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_Numeral_Onumber__of(V_x,T_a),c_0,T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(c_Numeral_OPls)),T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__12_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(c_Numeral_OPls)),T_a),T_a)
| c_less(c_Numeral_Onumber__of(V_x,T_a),c_0,T_a) ) ).
cnf(cls_IntArith_Oarith__special__13_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_Numeral_Onumber__of(V_x,T_a),c_1,T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__13_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),T_a),T_a)
| c_less(c_Numeral_Onumber__of(V_x,T_a),c_1,T_a) ) ).
cnf(cls_IntArith_Oarith__special__14_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_y,c_Numeral_Obin__minus(c_Numeral_OPls)),T_a),T_a)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_y,T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__14_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_y,c_Numeral_Obin__minus(c_Numeral_OPls)),T_a),T_a)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_y,T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__15_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_y,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),T_a),T_a)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(V_y,T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__15_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_y,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),T_a),T_a)
| c_lessequals(c_1,c_Numeral_Onumber__of(V_y,T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__16_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(V_x)),T_a),T_a)
| ~ c_lessequals(c_Numeral_Onumber__of(V_x,T_a),c_0,T_a) ) ).
cnf(cls_IntArith_Oarith__special__16_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(V_x)),T_a),T_a)
| c_lessequals(c_Numeral_Onumber__of(V_x,T_a),c_0,T_a) ) ).
cnf(cls_IntArith_Oarith__special__17_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(V_x)),T_a),T_a)
| ~ c_lessequals(c_Numeral_Onumber__of(V_x,T_a),c_1,T_a) ) ).
cnf(cls_IntArith_Oarith__special__17_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(V_x)),T_a),T_a)
| c_lessequals(c_Numeral_Onumber__of(V_x,T_a),c_1,T_a) ) ).
cnf(cls_IntArith_Oarith__special__1_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_plus(c_1,c_1,T_a) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),T_a) ) ).
cnf(cls_IntArith_Oarith__special__2_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_plus(c_1,c_Numeral_Onumber__of(V_w,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),V_w),T_a) ) ).
cnf(cls_IntArith_Oarith__special__3_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_plus(c_Numeral_Onumber__of(V_v,T_a),c_1,T_a) = c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),T_a) ) ).
cnf(cls_IntArith_Oarith__special__4_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_minus(c_1,c_Numeral_Onumber__of(V_w,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(V_w)),T_a) ) ).
cnf(cls_IntArith_Oarith__special__5_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_minus(c_Numeral_Onumber__of(V_v,T_a),c_1,T_a) = c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),T_a) ) ).
cnf(cls_IntArith_Oarith__special__6_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_0 != c_Numeral_Onumber__of(V_y,T_a)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(V_y)),T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__6_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(V_y)),T_a),T_a)
| c_0 = c_Numeral_Onumber__of(V_y,T_a) ) ).
cnf(cls_IntArith_Oarith__special__7_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_1 != c_Numeral_Onumber__of(V_y,T_a)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(V_y)),T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__7_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(V_y)),T_a),T_a)
| c_1 = c_Numeral_Onumber__of(V_y,T_a) ) ).
cnf(cls_IntArith_Oarith__special__8_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_Numeral_Onumber__of(V_x,T_a) != c_0
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(c_Numeral_OPls)),T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__8_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(c_Numeral_OPls)),T_a),T_a)
| c_Numeral_Onumber__of(V_x,T_a) = c_0 ) ).
cnf(cls_IntArith_Oarith__special__9_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_Numeral_Onumber__of(V_x,T_a) != c_1
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),T_a),T_a) ) ).
cnf(cls_IntArith_Oarith__special__9_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),T_a),T_a)
| c_Numeral_Onumber__of(V_x,T_a) = c_1 ) ).
cnf(cls_IntArith_Oint__eq__iff__number__of_0,axiom,
( c_IntDef_Oint(V_m) != c_Numeral_Onumber__of(V_v,tc_IntDef_Oint)
| V_m = c_IntDef_Onat(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint)) ) ).
cnf(cls_IntArith_Oint__eq__iff__number__of_1,axiom,
( c_IntDef_Oint(V_m) != c_Numeral_Onumber__of(V_v,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_IntArith_Oint__eq__iff__number__of_2,axiom,
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint))) = c_Numeral_Onumber__of(V_v,tc_IntDef_Oint) ) ).
cnf(cls_IntArith_Onat__1_0,axiom,
c_IntDef_Onat(c_1) = c_Suc(c_0) ).
cnf(cls_IntArith_Oof__int__m1_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),T_a) = c_Numeral_Onumber__of(c_Numeral_OMin,T_a) ) ).
cnf(cls_IntArith_Oone__less__nat__eq_0,axiom,
( ~ c_less(c_Suc(c_0),c_IntDef_Onat(V_z),tc_nat)
| c_less(c_1,V_z,tc_IntDef_Oint) ) ).
cnf(cls_IntArith_Oone__less__nat__eq_1,axiom,
( ~ c_less(c_1,V_z,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(V_z),tc_nat) ) ).
cnf(cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0,axiom,
c_plus(V_z,c_uminus(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(V_z,V_w,tc_IntDef_Oint) ).
cnf(cls_IntArith_Ozabs__less__one__iff_0,axiom,
( ~ c_less(c_HOL_Oabs(V_z,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| V_z = c_0 ) ).
cnf(cls_IntArith_Ozabs__less__one__iff_1,axiom,
c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ).
cnf(cls_IntArith_Ozle__add1__eq__le_0,axiom,
( ~ c_less(V_w,c_plus(V_z,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(V_w,V_z,tc_IntDef_Oint) ) ).
cnf(cls_IntArith_Ozle__add1__eq__le_1,axiom,
( ~ c_lessequals(V_w,V_z,tc_IntDef_Oint)
| c_less(V_w,c_plus(V_z,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_IntArith_Ozle__diff1__eq_0,axiom,
( ~ c_lessequals(V_w,c_minus(V_z,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(V_w,V_z,tc_IntDef_Oint) ) ).
cnf(cls_IntArith_Ozle__diff1__eq_1,axiom,
( ~ c_less(V_w,V_z,tc_IntDef_Oint)
| c_lessequals(V_w,c_minus(V_z,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_IntDef_OInteg_OAbs__Integ__inject_0,axiom,
( ~ c_in(V_y,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(V_x,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| c_IntDef_OAbs__Integ(V_x) != c_IntDef_OAbs__Integ(V_y)
| V_x = V_y ) ).
cnf(cls_IntDef_OInteg_OAbs__Integ__inverse_0,axiom,
( ~ c_in(V_y,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(V_y)) = V_y ) ).
cnf(cls_IntDef_OInts__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_in(c_0,c_IntDef_OInts,T_a) ) ).
cnf(cls_IntDef_OInts__1_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_in(c_1,c_IntDef_OInts,T_a) ) ).
cnf(cls_IntDef_OInts__add_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ c_in(V_b,c_IntDef_OInts,T_a)
| ~ c_in(V_a,c_IntDef_OInts,T_a)
| c_in(c_plus(V_a,V_b,T_a),c_IntDef_OInts,T_a) ) ).
cnf(cls_IntDef_OInts__diff_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ c_in(V_b,c_IntDef_OInts,T_a)
| ~ c_in(V_a,c_IntDef_OInts,T_a)
| c_in(c_minus(V_a,V_b,T_a),c_IntDef_OInts,T_a) ) ).
cnf(cls_IntDef_OInts__minus_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ c_in(V_a,c_IntDef_OInts,T_a)
| c_in(c_uminus(V_a,T_a),c_IntDef_OInts,T_a) ) ).
cnf(cls_IntDef_OInts__mult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ c_in(V_b,c_IntDef_OInts,T_a)
| ~ c_in(V_a,c_IntDef_OInts,T_a)
| c_in(c_times(V_a,V_b,T_a),c_IntDef_OInts,T_a) ) ).
cnf(cls_IntDef_ONats__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a)
| c_in(c_0,c_IntDef_ONats,T_a) ) ).
cnf(cls_IntDef_ONats__1_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a)
| c_in(c_1,c_IntDef_ONats,T_a) ) ).
cnf(cls_IntDef_ONats__add_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a)
| ~ c_in(V_b,c_IntDef_ONats,T_a)
| ~ c_in(V_a,c_IntDef_ONats,T_a)
| c_in(c_plus(V_a,V_b,T_a),c_IntDef_ONats,T_a) ) ).
cnf(cls_IntDef_ONats__mult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a)
| ~ c_in(V_b,c_IntDef_ONats,T_a)
| ~ c_in(V_a,c_IntDef_ONats,T_a)
| c_in(c_times(V_a,V_b,T_a),c_IntDef_ONats,T_a) ) ).
cnf(cls_IntDef_Oabs__int__eq_0,axiom,
c_HOL_Oabs(c_IntDef_Oint(V_m),tc_IntDef_Oint) = c_IntDef_Oint(V_m) ).
cnf(cls_IntDef_Oequiv__intrel__iff_0,axiom,
( c_Relation_OImage(c_IntDef_Ointrel,c_insert(V_x,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(V_y,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(V_x,V_y,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ).
cnf(cls_IntDef_Oequiv__intrel__iff_1,axiom,
( ~ c_in(c_Pair(V_x,V_y,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(V_x,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(V_y,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ) ).
cnf(cls_IntDef_Oint__0__neq__1_0,axiom,
c_0 != c_1 ).
cnf(cls_IntDef_Oint__1_0,axiom,
c_IntDef_Oint(c_1) = c_1 ).
cnf(cls_IntDef_Oint__Suc_0,axiom,
c_IntDef_Oint(c_Suc(V_m)) = c_plus(c_1,c_IntDef_Oint(V_m),tc_IntDef_Oint) ).
cnf(cls_IntDef_Oint__eq__0__conv_0,axiom,
( c_IntDef_Oint(V_n) != c_0
| V_n = c_0 ) ).
cnf(cls_IntDef_Oint__eq__0__conv_1,axiom,
c_IntDef_Oint(c_0) = c_0 ).
cnf(cls_IntDef_Oint__int__eq_0,axiom,
( c_IntDef_Oint(V_m) != c_IntDef_Oint(V_n)
| V_m = V_n ) ).
cnf(cls_IntDef_Oint__le__0__conv_0,axiom,
( ~ c_lessequals(c_IntDef_Oint(V_n),c_0,tc_IntDef_Oint)
| V_n = c_0 ) ).
cnf(cls_IntDef_Oint__le__0__conv_1,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint) ).
cnf(cls_IntDef_Oint__less__0__conv_0,axiom,
~ c_less(c_IntDef_Oint(V_k),c_0,tc_IntDef_Oint) ).
cnf(cls_IntDef_Oint__nat__eq_0,axiom,
( ~ c_lessequals(c_0,V_z,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(V_z)) = V_z ) ).
cnf(cls_IntDef_Oint__nat__eq_1,axiom,
( c_lessequals(c_0,V_z,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(V_z)) = c_0 ) ).
cnf(cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0,axiom,
c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(V_x,V_y,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ).
cnf(cls_IntDef_Ointrel__iff_0,axiom,
( ~ c_in(c_Pair(c_Pair(V_x,V_y,tc_nat,tc_nat),c_Pair(V_u,V_v,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_plus(V_x,V_v,tc_nat) = c_plus(V_u,V_y,tc_nat) ) ).
cnf(cls_IntDef_Ointrel__iff_1,axiom,
( c_plus(V_x,V_v,tc_nat) != c_plus(V_u,V_y,tc_nat)
| c_in(c_Pair(c_Pair(V_x,V_y,tc_nat,tc_nat),c_Pair(V_u,V_v,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ).
cnf(cls_IntDef_Onat__int_0,axiom,
c_IntDef_Onat(c_IntDef_Oint(V_y)) = V_y ).
cnf(cls_IntDef_Onat__le__0_0,axiom,
( ~ c_lessequals(V_z,c_0,tc_IntDef_Oint)
| c_IntDef_Onat(V_z) = c_0 ) ).
cnf(cls_IntDef_Onat__zero_0,axiom,
c_IntDef_Onat(c_0) = c_0 ).
cnf(cls_IntDef_Onat__zminus__int_0,axiom,
c_IntDef_Onat(c_uminus(c_IntDef_Oint(V_n),tc_IntDef_Oint)) = c_0 ).
cnf(cls_IntDef_Oneg__zminus__int_0,axiom,
c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(V_n)),tc_IntDef_Oint),tc_IntDef_Oint) ).
cnf(cls_IntDef_Onegative__eq__positive_0,axiom,
( c_uminus(c_IntDef_Oint(V_n),tc_IntDef_Oint) != c_IntDef_Oint(V_m)
| V_n = c_0 ) ).
cnf(cls_IntDef_Onegative__eq__positive_1,axiom,
( c_uminus(c_IntDef_Oint(V_n),tc_IntDef_Oint) != c_IntDef_Oint(V_m)
| V_m = c_0 ) ).
cnf(cls_IntDef_Onegative__eq__positive_2,axiom,
c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint) = c_IntDef_Oint(c_0) ).
cnf(cls_IntDef_Onot__int__zless__negative_0,axiom,
~ c_less(c_IntDef_Oint(V_n),c_uminus(c_IntDef_Oint(V_m),tc_IntDef_Oint),tc_IntDef_Oint) ).
cnf(cls_IntDef_Onot__neg__int_0,axiom,
~ c_IntDef_Oneg(c_IntDef_Oint(V_n),tc_IntDef_Oint) ).
cnf(cls_IntDef_Onot__zle__0__negative_0,axiom,
~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(V_n)),tc_IntDef_Oint),tc_IntDef_Oint) ).
cnf(cls_IntDef_Oof__int__0__eq__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_0 != c_IntDef_Oof__int(V_z,T_a)
| c_0 = V_z ) ).
cnf(cls_IntDef_Oof__int__0__eq__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_0 = c_IntDef_Oof__int(c_0,T_a) ) ).
cnf(cls_IntDef_Oof__int__0__le__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(V_z,T_a),T_a)
| c_lessequals(c_0,V_z,tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Oof__int__0__le__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(c_0,V_z,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(V_z,T_a),T_a) ) ).
cnf(cls_IntDef_Oof__int__0__less__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_0,c_IntDef_Oof__int(V_z,T_a),T_a)
| c_less(c_0,V_z,tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Oof__int__0__less__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_0,V_z,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(V_z,T_a),T_a) ) ).
cnf(cls_IntDef_Oof__int__1_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_IntDef_Oof__int(c_1,T_a) = c_1 ) ).
cnf(cls_IntDef_Oof__int__add_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_IntDef_Oof__int(c_plus(V_w,V_z,tc_IntDef_Oint),T_a) = c_plus(c_IntDef_Oof__int(V_w,T_a),c_IntDef_Oof__int(V_z,T_a),T_a) ) ).
cnf(cls_IntDef_Oof__int__diff_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_IntDef_Oof__int(c_minus(V_w,V_z,tc_IntDef_Oint),T_a) = c_minus(c_IntDef_Oof__int(V_w,T_a),c_IntDef_Oof__int(V_z,T_a),T_a) ) ).
cnf(cls_IntDef_Oof__int__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_IntDef_Oof__int(V_w,T_a) != c_0
| V_w = c_0 ) ).
cnf(cls_IntDef_Oof__int__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_IntDef_Oof__int(c_0,T_a) = c_0 ) ).
cnf(cls_IntDef_Oof__int__eq__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_IntDef_Oof__int(V_w,T_a) != c_IntDef_Oof__int(V_z,T_a)
| V_w = V_z ) ).
cnf(cls_IntDef_Oof__int__int__eq_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_IntDef_Oof__int(c_IntDef_Oint(V_n),T_a) = c_NatArith_Oof__nat(V_n,T_a) ) ).
cnf(cls_IntDef_Oof__int__le__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(c_IntDef_Oof__int(V_w,T_a),c_0,T_a)
| c_lessequals(V_w,c_0,tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Oof__int__le__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(V_w,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(V_w,T_a),c_0,T_a) ) ).
cnf(cls_IntDef_Oof__int__le__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(c_IntDef_Oof__int(V_w,T_a),c_IntDef_Oof__int(V_z,T_a),T_a)
| c_lessequals(V_w,V_z,tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Oof__int__le__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(V_w,V_z,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(V_w,T_a),c_IntDef_Oof__int(V_z,T_a),T_a) ) ).
cnf(cls_IntDef_Oof__int__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_IntDef_Oof__int(V_w,T_a),c_0,T_a)
| c_less(V_w,c_0,tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Oof__int__less__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(V_w,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(V_w,T_a),c_0,T_a) ) ).
cnf(cls_IntDef_Oof__int__less__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_IntDef_Oof__int(V_w,T_a),c_IntDef_Oof__int(V_z,T_a),T_a)
| c_less(V_w,V_z,tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Oof__int__less__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(V_w,V_z,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(V_w,T_a),c_IntDef_Oof__int(V_z,T_a),T_a) ) ).
cnf(cls_IntDef_Oof__int__minus_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_IntDef_Oof__int(c_uminus(V_z,tc_IntDef_Oint),T_a) = c_uminus(c_IntDef_Oof__int(V_z,T_a),T_a) ) ).
cnf(cls_IntDef_Oof__int__mult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_IntDef_Oof__int(c_times(V_w,V_z,tc_IntDef_Oint),T_a) = c_times(c_IntDef_Oof__int(V_w,T_a),c_IntDef_Oof__int(V_z,T_a),T_a) ) ).
cnf(cls_IntDef_Oof__int__of__nat__eq_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_IntDef_Oof__int(c_NatArith_Oof__nat(V_n,tc_IntDef_Oint),T_a) = c_NatArith_Oof__nat(V_n,T_a) ) ).
cnf(cls_IntDef_Oof__nat__in__Nats_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a)
| c_in(c_NatArith_Oof__nat(V_n,T_a),c_IntDef_ONats,T_a) ) ).
cnf(cls_IntDef_Ozero__less__int__conv_0,axiom,
( ~ c_less(c_0,c_IntDef_Oint(V_n),tc_IntDef_Oint)
| c_less(c_0,V_n,tc_nat) ) ).
cnf(cls_IntDef_Ozero__less__int__conv_1,axiom,
( ~ c_less(c_0,V_n,tc_nat)
| c_less(c_0,c_IntDef_Oint(V_n),tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Ozero__less__nat__eq_0,axiom,
( ~ c_less(c_0,c_IntDef_Onat(V_z),tc_nat)
| c_less(c_0,V_z,tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Ozero__less__nat__eq_1,axiom,
( ~ c_less(c_0,V_z,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(V_z),tc_nat) ) ).
cnf(cls_IntDef_Ozero__zle__int_0,axiom,
c_lessequals(c_0,c_IntDef_Oint(V_n),tc_IntDef_Oint) ).
cnf(cls_IntDef_Ozle__int_0,axiom,
( ~ c_lessequals(c_IntDef_Oint(V_m),c_IntDef_Oint(V_n),tc_IntDef_Oint)
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_IntDef_Ozle__int_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_IntDef_Oint(V_m),c_IntDef_Oint(V_n),tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Ozless__int_0,axiom,
( ~ c_less(c_IntDef_Oint(V_m),c_IntDef_Oint(V_n),tc_IntDef_Oint)
| c_less(V_m,V_n,tc_nat) ) ).
cnf(cls_IntDef_Ozless__int_1,axiom,
( ~ c_less(V_m,V_n,tc_nat)
| c_less(c_IntDef_Oint(V_m),c_IntDef_Oint(V_n),tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Ozless__nat__conj_0,axiom,
( ~ c_less(c_IntDef_Onat(V_w),c_IntDef_Onat(V_z),tc_nat)
| c_less(c_0,V_z,tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Ozless__nat__conj_1,axiom,
( ~ c_less(c_IntDef_Onat(V_w),c_IntDef_Onat(V_z),tc_nat)
| c_less(V_w,V_z,tc_IntDef_Oint) ) ).
cnf(cls_IntDef_Ozless__nat__conj_2,axiom,
( ~ c_less(V_w,V_z,tc_IntDef_Oint)
| ~ c_less(c_0,V_z,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(V_w),c_IntDef_Onat(V_z),tc_nat) ) ).
cnf(cls_IntDiv_ODIVISION__BY__ZERO_0,axiom,
c_Divides_Oop_Amod(V_y,c_0,tc_IntDef_Oint) = V_y ).
cnf(cls_IntDiv_Odiv__neg__neg__number__of_0,axiom,
( ~ c_less(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Odiv__neg__pos__number__of_0,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Odiv__pos__neg__1__number__of_0,axiom,
( ~ c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Odiv__pos__neg__number__of_0,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Odiv__pos__pos__1__number__of_0,axiom,
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Odiv__pos__pos__number__of_0,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Odvd__zminus__iff_0,axiom,
( ~ c_Divides_Oop_Advd(V_z,c_uminus(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(V_z,V_w,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Odvd__zminus__iff_1,axiom,
( ~ c_Divides_Oop_Advd(V_z,V_w,tc_IntDef_Oint)
| c_Divides_Oop_Advd(V_z,c_uminus(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Omod__div__trivial_0,axiom,
c_div(c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),V_b,tc_IntDef_Oint) = c_0 ).
cnf(cls_IntDiv_Omod__mod__trivial_0,axiom,
c_Divides_Oop_Amod(c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),V_b,tc_IntDef_Oint) = c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint) ).
cnf(cls_IntDiv_Omod__neg__neg__number__of_0,axiom,
( ~ c_less(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Omod__neg__pos__number__of_0,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Omod__pos__neg__1__number__of_0,axiom,
( ~ c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Omod__pos__neg__number__of_0,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Omod__pos__pos__1__number__of_0,axiom,
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Omod__pos__pos__number__of_0,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_OnegDivAlg__eqn__1__number__of_0,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_OnegDivAlg__eqn__1__number__of_1,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ) ).
cnf(cls_IntDiv_OnegDivAlg__eqn__number__of_0,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_OnegDivAlg__eqn__number__of_1,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ) ).
cnf(cls_IntDiv_OnegDivAlg__minus1_0,axiom,
c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),V_b,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(V_b,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ).
cnf(cls_IntDiv_Oneg__mod__bound_0,axiom,
( ~ c_less(V_b,c_0,tc_IntDef_Oint)
| c_less(V_b,c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Oneg__mod__sign_0,axiom,
( ~ c_less(V_b,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_OnegateSnd__eq_0,axiom,
c_IntDiv_OnegateSnd(c_Pair(V_q,V_r,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(V_q,c_uminus(V_r,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ).
cnf(cls_IntDiv_OposDivAlg__0_0,axiom,
c_IntDiv_OposDivAlg(c_Pair(c_0,V_b,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint) ).
cnf(cls_IntDiv_OposDivAlg__eqn__1__number__of_0,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_OposDivAlg__eqn__1__number__of_1,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ) ).
cnf(cls_IntDiv_OposDivAlg__eqn__number__of_0,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_OposDivAlg__eqn__number__of_1,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ) ).
cnf(cls_IntDiv_Opos__mod__bound_0,axiom,
( ~ c_less(c_0,V_b,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),V_b,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Opos__mod__sign_0,axiom,
( ~ c_less(c_0,V_b,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Opower_Osimps__1_0,axiom,
c_Nat_Opower(V_p,c_0,tc_IntDef_Oint) = c_1 ).
cnf(cls_IntDiv_Opower_Osimps__2_0,axiom,
c_Nat_Opower(V_p,c_Suc(V_n),tc_IntDef_Oint) = c_times(V_p,c_Nat_Opower(V_p,V_n,tc_IntDef_Oint),tc_IntDef_Oint) ).
cnf(cls_IntDiv_Ozdiv__1_0,axiom,
c_div(V_y,c_1,tc_IntDef_Oint) = V_y ).
cnf(cls_IntDiv_Ozdiv__minus1__right_0,axiom,
c_div(V_a,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(V_a,tc_IntDef_Oint) ).
cnf(cls_IntDiv_Ozdiv__number__of__BIT_0,axiom,
c_div(c_Numeral_Onumber__of(c_Numeral_OBit(V_v,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(V_w,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ).
cnf(cls_IntDiv_Ozdiv__number__of__BIT_1,axiom,
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(V_v,V_b),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(V_w,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Ozdiv__number__of__BIT_2,axiom,
( c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| V_b = c_Numeral_Obit_OB0
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(V_v,V_b),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(V_w,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Ozdiv__self_0,axiom,
( V_a = c_0
| c_div(V_a,V_a,tc_IntDef_Oint) = c_1 ) ).
cnf(cls_IntDiv_Ozdiv__zadd__self1_0,axiom,
( V_a = c_0
| c_div(c_plus(V_a,V_b,tc_IntDef_Oint),V_a,tc_IntDef_Oint) = c_plus(c_div(V_b,V_a,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Ozdiv__zadd__self2_0,axiom,
( V_a = c_0
| c_div(c_plus(V_b,V_a,tc_IntDef_Oint),V_a,tc_IntDef_Oint) = c_plus(c_div(V_b,V_a,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Ozdiv__zero_0,axiom,
c_div(c_0,V_b,tc_IntDef_Oint) = c_0 ).
cnf(cls_IntDiv_Ozdiv__zminus__zminus_0,axiom,
c_div(c_uminus(V_a,tc_IntDef_Oint),c_uminus(V_b,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(V_a,V_b,tc_IntDef_Oint) ).
cnf(cls_IntDiv_Ozdiv__zmult__self1_0,axiom,
( V_b = c_0
| c_div(c_times(V_y,V_b,tc_IntDef_Oint),V_b,tc_IntDef_Oint) = V_y ) ).
cnf(cls_IntDiv_Ozdiv__zmult__self2_0,axiom,
( V_b = c_0
| c_div(c_times(V_b,V_y,tc_IntDef_Oint),V_b,tc_IntDef_Oint) = V_y ) ).
cnf(cls_IntDiv_Ozdvd__0__left_0,axiom,
( ~ c_Divides_Oop_Advd(c_0,V_m,tc_IntDef_Oint)
| V_m = c_0 ) ).
cnf(cls_IntDiv_Ozdvd__0__left_1,axiom,
c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint) ).
cnf(cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0,axiom,
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(V_x,tc_IntDef_Oint),c_Numeral_Onumber__of(V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_y,tc_IntDef_Oint),c_Numeral_Onumber__of(V_x,tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ) ).
cnf(cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1,axiom,
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_y,tc_IntDef_Oint),c_Numeral_Onumber__of(V_x,tc_IntDef_Oint),tc_IntDef_Oint) != c_0
| c_Divides_Oop_Advd(c_Numeral_Onumber__of(V_x,tc_IntDef_Oint),c_Numeral_Onumber__of(V_y,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Ozdvd__refl_0,axiom,
c_Divides_Oop_Advd(V_m,V_m,tc_IntDef_Oint) ).
cnf(cls_IntDiv_Ozero__le__zpower__abs_0,axiom,
c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(V_x,tc_IntDef_Oint),V_n,tc_IntDef_Oint),tc_IntDef_Oint) ).
cnf(cls_IntDiv_Ozero__less__zpower__abs__iff_0,axiom,
( ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),V_n,tc_IntDef_Oint),tc_IntDef_Oint)
| V_n = c_0 ) ).
cnf(cls_IntDiv_Ozero__less__zpower__abs__iff_1,axiom,
( c_less(c_0,c_Nat_Opower(c_HOL_Oabs(V_x,tc_IntDef_Oint),V_n,tc_IntDef_Oint),tc_IntDef_Oint)
| V_x = c_0 ) ).
cnf(cls_IntDiv_Ozero__less__zpower__abs__iff_2,axiom,
c_less(c_0,c_Nat_Opower(c_HOL_Oabs(V_x,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint) ).
cnf(cls_IntDiv_Ozminus__dvd__iff_0,axiom,
( ~ c_Divides_Oop_Advd(c_uminus(V_z,tc_IntDef_Oint),V_w,tc_IntDef_Oint)
| c_Divides_Oop_Advd(V_z,V_w,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Ozminus__dvd__iff_1,axiom,
( ~ c_Divides_Oop_Advd(V_z,V_w,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(V_z,tc_IntDef_Oint),V_w,tc_IntDef_Oint) ) ).
cnf(cls_IntDiv_Ozmod__1_0,axiom,
c_Divides_Oop_Amod(V_a,c_1,tc_IntDef_Oint) = c_0 ).
cnf(cls_IntDiv_Ozmod__minus1__right_0,axiom,
c_Divides_Oop_Amod(V_a,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ).
cnf(cls_IntDiv_Ozmod__self_0,axiom,
c_Divides_Oop_Amod(V_a,V_a,tc_IntDef_Oint) = c_0 ).
cnf(cls_IntDiv_Ozmod__zadd__self1_0,axiom,
c_Divides_Oop_Amod(c_plus(V_a,V_b,tc_IntDef_Oint),V_a,tc_IntDef_Oint) = c_Divides_Oop_Amod(V_b,V_a,tc_IntDef_Oint) ).
cnf(cls_IntDiv_Ozmod__zadd__self2_0,axiom,
c_Divides_Oop_Amod(c_plus(V_b,V_a,tc_IntDef_Oint),V_a,tc_IntDef_Oint) = c_Divides_Oop_Amod(V_b,V_a,tc_IntDef_Oint) ).
cnf(cls_IntDiv_Ozmod__zero_0,axiom,
c_Divides_Oop_Amod(c_0,V_b,tc_IntDef_Oint) = c_0 ).
cnf(cls_IntDiv_Ozmod__zminus__zminus_0,axiom,
c_Divides_Oop_Amod(c_uminus(V_a,tc_IntDef_Oint),c_uminus(V_b,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),tc_IntDef_Oint) ).
cnf(cls_IntDiv_Ozmod__zmult__self1_0,axiom,
c_Divides_Oop_Amod(c_times(V_a,V_b,tc_IntDef_Oint),V_b,tc_IntDef_Oint) = c_0 ).
cnf(cls_IntDiv_Ozmod__zmult__self2_0,axiom,
c_Divides_Oop_Amod(c_times(V_b,V_a,tc_IntDef_Oint),V_b,tc_IntDef_Oint) = c_0 ).
cnf(cls_LOrder_Ojoin__idempotent_0,axiom,
( ~ class_LOrder_Ojoin__semilorder(T_a)
| c_LOrder_Ojoin(V_y,V_y,T_a) = V_y ) ).
cnf(cls_LOrder_Omeet__idempotent_0,axiom,
( ~ class_LOrder_Omeet__semilorder(T_a)
| c_LOrder_Omeet(V_y,V_y,T_a) = V_y ) ).
cnf(cls_List_OCons__in__lex_0,axiom,
( ~ c_in(c_Pair(c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))
| c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| V_x = V_y ) ).
cnf(cls_List_OCons__in__lex_1,axiom,
( ~ c_in(c_Pair(c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))
| c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_xs,V_ys,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ) ).
cnf(cls_List_OCons__in__lex_2,axiom,
( ~ c_in(c_Pair(c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))
| V_x = V_y
| c_Nat_Osize(V_xs,tc_List_Olist(T_a)) = c_Nat_Osize(V_ys,tc_List_Olist(T_a)) ) ).
cnf(cls_List_OCons__in__lex_3,axiom,
( ~ c_in(c_Pair(c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))
| c_in(c_Pair(V_xs,V_ys,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))
| c_Nat_Osize(V_xs,tc_List_Olist(T_a)) = c_Nat_Osize(V_ys,tc_List_Olist(T_a)) ) ).
cnf(cls_List_OCons__in__lex_4,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_ys,tc_List_Olist(T_a))
| c_in(c_Pair(c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ) ).
cnf(cls_List_OCons__in__lex_5,axiom,
( ~ c_in(c_Pair(V_xs,V_ys,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))
| c_in(c_Pair(c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_x,V_ys,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ) ).
cnf(cls_List_ONil2__notin__lex_0,axiom,
~ c_in(c_Pair(V_xs,c_List_Olist_ONil,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ).
cnf(cls_List_ONil__eq__concat__conv_0,axiom,
( ~ c_in(V_U,c_List_Oset(V_xss,tc_List_Olist(T_a)),tc_List_Olist(T_a))
| c_List_Olist_ONil != c_List_Oconcat(V_xss,T_a)
| V_U = c_List_Olist_ONil ) ).
cnf(cls_List_ONil__eq__concat__conv_1,axiom,
( c_in(c_Main_ONil__eq__concat__conv__1(V_xss,T_a),c_List_Oset(V_xss,tc_List_Olist(T_a)),tc_List_Olist(T_a))
| c_List_Olist_ONil = c_List_Oconcat(V_xss,T_a) ) ).
cnf(cls_List_ONil__eq__concat__conv_2,axiom,
( c_Main_ONil__eq__concat__conv__1(V_xss,T_a) != c_List_Olist_ONil
| c_List_Olist_ONil = c_List_Oconcat(V_xss,T_a) ) ).
cnf(cls_List_ONil__is__append__conv_0,axiom,
( c_List_Olist_ONil != c_append(V_xs,V_ys,T_a)
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_ONil__is__append__conv_1,axiom,
( c_List_Olist_ONil != c_append(V_xs,V_ys,T_a)
| V_ys = c_List_Olist_ONil ) ).
cnf(cls_List_ONil__is__append__conv_2,axiom,
c_List_Olist_ONil = c_append(c_List_Olist_ONil,c_List_Olist_ONil,T_a) ).
cnf(cls_List_ONil__is__rev__conv_0,axiom,
( c_List_Olist_ONil != c_List_Orev(V_xs,T_a)
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_ONil__is__rev__conv_1,axiom,
c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,T_a) ).
cnf(cls_List_ONil__notin__lex_0,axiom,
~ c_in(c_Pair(c_List_Olist_ONil,V_ys,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ).
cnf(cls_List_Oappend1__eq__conv_0,axiom,
( c_append(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a),T_a) != c_append(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil,T_a),T_a)
| V_xs = V_ys ) ).
cnf(cls_List_Oappend1__eq__conv_1,axiom,
( c_append(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a),T_a) != c_append(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil,T_a),T_a)
| V_x = V_y ) ).
cnf(cls_List_Oappend__assoc_0,axiom,
c_append(c_append(V_xs,V_ys,T_a),V_zs,T_a) = c_append(V_xs,c_append(V_ys,V_zs,T_a),T_a) ).
cnf(cls_List_Oappend__butlast__last__id_0,axiom,
( V_y = c_List_Olist_ONil
| c_append(c_List_Obutlast(V_y,T_a),c_List_Olist_OCons(c_List_Olast(V_y,T_a),c_List_Olist_ONil,T_a),T_a) = V_y ) ).
cnf(cls_List_Oappend__eq__append__conv_0,axiom,
( c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_ys,tc_List_Olist(T_a))
| c_append(V_xs,V_us,T_a) != c_append(V_ys,V_vs,T_a)
| V_xs = V_ys ) ).
cnf(cls_List_Oappend__eq__append__conv_1,axiom,
( c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_ys,tc_List_Olist(T_a))
| c_append(V_xs,V_us,T_a) != c_append(V_ys,V_vs,T_a)
| V_us = V_vs ) ).
cnf(cls_List_Oappend__eq__append__conv_2,axiom,
( c_Nat_Osize(V_us,tc_List_Olist(T_a)) != c_Nat_Osize(V_vs,tc_List_Olist(T_a))
| c_append(V_xs,V_us,T_a) != c_append(V_ys,V_vs,T_a)
| V_xs = V_ys ) ).
cnf(cls_List_Oappend__eq__append__conv_3,axiom,
( c_Nat_Osize(V_us,tc_List_Olist(T_a)) != c_Nat_Osize(V_vs,tc_List_Olist(T_a))
| c_append(V_xs,V_us,T_a) != c_append(V_ys,V_vs,T_a)
| V_us = V_vs ) ).
cnf(cls_List_Oappend__in__lists__conv_0,axiom,
( ~ c_in(c_append(V_xs,V_ys,T_a),c_List_Olists(V_A,T_a),tc_List_Olist(T_a))
| c_in(V_xs,c_List_Olists(V_A,T_a),tc_List_Olist(T_a)) ) ).
cnf(cls_List_Oappend__in__lists__conv_1,axiom,
( ~ c_in(c_append(V_xs,V_ys,T_a),c_List_Olists(V_A,T_a),tc_List_Olist(T_a))
| c_in(V_ys,c_List_Olists(V_A,T_a),tc_List_Olist(T_a)) ) ).
cnf(cls_List_Oappend__in__lists__conv_2,axiom,
( ~ c_in(V_ys,c_List_Olists(V_A,T_a),tc_List_Olist(T_a))
| ~ c_in(V_xs,c_List_Olists(V_A,T_a),tc_List_Olist(T_a))
| c_in(c_append(V_xs,V_ys,T_a),c_List_Olists(V_A,T_a),tc_List_Olist(T_a)) ) ).
cnf(cls_List_Oappend__is__Nil__conv_0,axiom,
( c_append(V_xs,V_ys,T_a) != c_List_Olist_ONil
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Oappend__is__Nil__conv_1,axiom,
( c_append(V_xs,V_ys,T_a) != c_List_Olist_ONil
| V_ys = c_List_Olist_ONil ) ).
cnf(cls_List_Oappend__is__Nil__conv_2,axiom,
c_append(c_List_Olist_ONil,c_List_Olist_ONil,T_a) = c_List_Olist_ONil ).
cnf(cls_List_Oappend__same__eq_0,axiom,
( c_append(V_ys,V_xs,T_a) != c_append(V_zs,V_xs,T_a)
| V_ys = V_zs ) ).
cnf(cls_List_Oappend__self__conv2_0,axiom,
( c_append(V_xs,V_ys,T_a) != V_ys
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Oappend__self__conv2_1,axiom,
c_append(c_List_Olist_ONil,V_ys,T_a) = V_ys ).
cnf(cls_List_Oappend__self__conv_0,axiom,
( c_append(V_xs,V_ys,T_a) != V_xs
| V_ys = c_List_Olist_ONil ) ).
cnf(cls_List_Oappend__self__conv_1,axiom,
c_append(V_xs,c_List_Olist_ONil,T_a) = V_xs ).
cnf(cls_List_Oappend__take__drop__id_0,axiom,
c_append(c_List_Otake(V_n,V_y,T_a),c_List_Odrop(V_n,V_y,T_a),T_a) = V_y ).
cnf(cls_List_Obutlast_Osimps__1_0,axiom,
c_List_Obutlast(c_List_Olist_ONil,T_a__1) = c_List_Olist_ONil ).
cnf(cls_List_Obutlast_Osimps__2_0,axiom,
c_List_Obutlast(c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a__1),T_a__1) = c_List_Olist_ONil ).
cnf(cls_List_Obutlast_Osimps__2_1,axiom,
( V_xs = c_List_Olist_ONil
| c_List_Obutlast(c_List_Olist_OCons(V_x,V_xs,T_a__1),T_a__1) = c_List_Olist_OCons(V_x,c_List_Obutlast(V_xs,T_a__1),T_a__1) ) ).
cnf(cls_List_Obutlast__snoc_0,axiom,
c_List_Obutlast(c_append(V_y,c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a),T_a),T_a) = V_y ).
cnf(cls_List_Ochar_Oinject_0,axiom,
( c_List_Ochar_OChar(V_nibble1,V_nibble2) != c_List_Ochar_OChar(V_nibble1_H,V_nibble2_H)
| V_nibble1 = V_nibble1_H ) ).
cnf(cls_List_Ochar_Oinject_1,axiom,
( c_List_Ochar_OChar(V_nibble1,V_nibble2) != c_List_Ochar_OChar(V_nibble1_H,V_nibble2_H)
| V_nibble2 = V_nibble2_H ) ).
cnf(cls_List_Ochar_Osize_0,axiom,
c_Nat_Osize(c_List_Ochar_OChar(V_nibble1,V_nibble2),tc_List_Ochar) = c_0 ).
cnf(cls_List_Oconcat_Osimps__1_0,axiom,
c_List_Oconcat(c_List_Olist_ONil,T_a__1) = c_List_Olist_ONil ).
cnf(cls_List_Oconcat_Osimps__2_0,axiom,
c_List_Oconcat(c_List_Olist_OCons(V_x,V_xs,tc_List_Olist(T_a__1)),T_a__1) = c_append(V_x,c_List_Oconcat(V_xs,T_a__1),T_a__1) ).
cnf(cls_List_Oconcat__append_0,axiom,
c_List_Oconcat(c_append(V_xs,V_ys,tc_List_Olist(T_a)),T_a) = c_append(c_List_Oconcat(V_xs,T_a),c_List_Oconcat(V_ys,T_a),T_a) ).
cnf(cls_List_Oconcat__eq__Nil__conv_0,axiom,
( ~ c_in(V_U,c_List_Oset(V_xss,tc_List_Olist(T_a)),tc_List_Olist(T_a))
| c_List_Oconcat(V_xss,T_a) != c_List_Olist_ONil
| V_U = c_List_Olist_ONil ) ).
cnf(cls_List_Oconcat__eq__Nil__conv_1,axiom,
( c_in(c_Main_Oconcat__eq__Nil__conv__1(V_xss,T_a),c_List_Oset(V_xss,tc_List_Olist(T_a)),tc_List_Olist(T_a))
| c_List_Oconcat(V_xss,T_a) = c_List_Olist_ONil ) ).
cnf(cls_List_Oconcat__eq__Nil__conv_2,axiom,
( c_Main_Oconcat__eq__Nil__conv__1(V_xss,T_a) != c_List_Olist_ONil
| c_List_Oconcat(V_xss,T_a) = c_List_Olist_ONil ) ).
cnf(cls_List_Odistinct1__rotate_0,axiom,
( ~ c_List_Odistinct(c_List_Orotate1(V_xs,T_a),T_a)
| c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_List_Odistinct1__rotate_1,axiom,
( ~ c_List_Odistinct(V_xs,T_a)
| c_List_Odistinct(c_List_Orotate1(V_xs,T_a),T_a) ) ).
cnf(cls_List_Odistinct_Osimps__1_0,axiom,
c_List_Odistinct(c_List_Olist_ONil,T_a__1) ).
cnf(cls_List_Odistinct_Osimps__2_0,axiom,
( ~ c_List_Odistinct(c_List_Olist_OCons(V_x,V_xs,T_a__1),T_a__1)
| ~ c_in(V_x,c_List_Oset(V_xs,T_a__1),T_a__1) ) ).
cnf(cls_List_Odistinct_Osimps__2_1,axiom,
( ~ c_List_Odistinct(c_List_Olist_OCons(V_x,V_xs,T_a__1),T_a__1)
| c_List_Odistinct(V_xs,T_a__1) ) ).
cnf(cls_List_Odistinct_Osimps__2_2,axiom,
( ~ c_List_Odistinct(V_xs,T_a__1)
| c_List_Odistinct(c_List_Olist_OCons(V_x,V_xs,T_a__1),T_a__1)
| c_in(V_x,c_List_Oset(V_xs,T_a__1),T_a__1) ) ).
cnf(cls_List_Odistinct__append_0,axiom,
( ~ c_List_Odistinct(c_append(V_xs,V_ys,T_a),T_a)
| c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_List_Odistinct__append_1,axiom,
( ~ c_List_Odistinct(c_append(V_xs,V_ys,T_a),T_a)
| c_List_Odistinct(V_ys,T_a) ) ).
cnf(cls_List_Odistinct__append_2,axiom,
( ~ c_List_Odistinct(c_append(V_xs,V_ys,T_a),T_a)
| c_inter(c_List_Oset(V_xs,T_a),c_List_Oset(V_ys,T_a),T_a) = c_emptyset ) ).
cnf(cls_List_Odistinct__append_3,axiom,
( ~ c_List_Odistinct(V_ys,T_a)
| ~ c_List_Odistinct(V_xs,T_a)
| c_inter(c_List_Oset(V_xs,T_a),c_List_Oset(V_ys,T_a),T_a) != c_emptyset
| c_List_Odistinct(c_append(V_xs,V_ys,T_a),T_a) ) ).
cnf(cls_List_Odistinct__drop_0,axiom,
( ~ c_List_Odistinct(V_xs,T_a)
| c_List_Odistinct(c_List_Odrop(V_i,V_xs,T_a),T_a) ) ).
cnf(cls_List_Odistinct__remove1_0,axiom,
( ~ c_List_Odistinct(V_xs,T_a)
| c_List_Odistinct(c_List_Oremove1(V_x,V_xs,T_a),T_a) ) ).
cnf(cls_List_Odistinct__rev_0,axiom,
( ~ c_List_Odistinct(c_List_Orev(V_xs,T_a),T_a)
| c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_List_Odistinct__rev_1,axiom,
( ~ c_List_Odistinct(V_xs,T_a)
| c_List_Odistinct(c_List_Orev(V_xs,T_a),T_a) ) ).
cnf(cls_List_Odistinct__rotate_0,axiom,
( ~ c_List_Odistinct(c_List_Orotate(V_n,V_xs,T_a),T_a)
| c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_List_Odistinct__rotate_1,axiom,
( ~ c_List_Odistinct(V_xs,T_a)
| c_List_Odistinct(c_List_Orotate(V_n,V_xs,T_a),T_a) ) ).
cnf(cls_List_Odistinct__sublistI_0,axiom,
( ~ c_List_Odistinct(V_xs,T_a)
| c_List_Odistinct(c_List_Osublist(V_xs,V_I,T_a),T_a) ) ).
cnf(cls_List_Odistinct__take_0,axiom,
( ~ c_List_Odistinct(V_xs,T_a)
| c_List_Odistinct(c_List_Otake(V_i,V_xs,T_a),T_a) ) ).
cnf(cls_List_Odistinct__upt_0,axiom,
c_List_Odistinct(c_List_Oupt(V_i,V_j),tc_nat) ).
cnf(cls_List_Odrop_Odrop__Nil_0,axiom,
c_List_Odrop(V_n,c_List_Olist_ONil,T_a__1) = c_List_Olist_ONil ).
cnf(cls_List_Odrop__0_0,axiom,
c_List_Odrop(c_0,V_y,T_a) = V_y ).
cnf(cls_List_Odrop__Cons__number__of_0,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) != c_0
| c_List_Odrop(c_Numeral_Onumber__of(V_v,tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ) ).
cnf(cls_List_Odrop__Cons__number__of_1,axiom,
( c_List_Odrop(c_Numeral_Onumber__of(V_v,tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(V_v,tc_nat),c_1,tc_nat),V_xs,T_a)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_0 ) ).
cnf(cls_List_Odrop__Suc__Cons_0,axiom,
c_List_Odrop(c_Suc(V_n),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Odrop(V_n,V_xs,T_a) ).
cnf(cls_List_Odrop__append_0,axiom,
c_List_Odrop(V_n,c_append(V_xs,V_ys,T_a),T_a) = c_append(c_List_Odrop(V_n,V_xs,T_a),c_List_Odrop(c_minus(V_n,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_ys,T_a),T_a) ).
cnf(cls_List_Odrop__drop_0,axiom,
c_List_Odrop(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a) = c_List_Odrop(c_plus(V_n,V_m,tc_nat),V_xs,T_a) ).
cnf(cls_List_Odrop__eq__Nil_0,axiom,
( c_List_Odrop(V_n,V_xs,T_a) != c_List_Olist_ONil
| c_lessequals(c_Nat_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ) ).
cnf(cls_List_Odrop__eq__Nil_1,axiom,
( ~ c_lessequals(c_Nat_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat)
| c_List_Odrop(V_n,V_xs,T_a) = c_List_Olist_ONil ) ).
cnf(cls_List_Odrop__replicate_0,axiom,
c_List_Odrop(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oreplicate(c_minus(V_k,V_i,tc_nat),V_x,T_a) ).
cnf(cls_List_Odrop__upt_0,axiom,
c_List_Odrop(V_m,c_List_Oupt(V_i,V_j),tc_nat) = c_List_Oupt(c_plus(V_i,V_m,tc_nat),V_j) ).
cnf(cls_List_Ohd_Osimps_0,axiom,
c_List_Ohd(c_List_Olist_OCons(V_y,V_xs,T_a),T_a) = V_y ).
cnf(cls_List_Ohd__Cons__tl_0,axiom,
( V_y = c_List_Olist_ONil
| c_List_Olist_OCons(c_List_Ohd(V_y,T_a),c_List_Otl(V_y,T_a),T_a) = V_y ) ).
cnf(cls_List_Ohd__append2_0,axiom,
( V_xs = c_List_Olist_ONil
| c_List_Ohd(c_append(V_xs,V_ys,T_a),T_a) = c_List_Ohd(V_xs,T_a) ) ).
cnf(cls_List_Ohd__in__set_0,axiom,
( c_in(c_List_Ohd(V_xs,T_a),c_List_Oset(V_xs,T_a),T_a)
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Ohd__replicate_0,axiom,
( V_n = c_0
| c_List_Ohd(c_List_Oreplicate(V_n,V_y,T_a),T_a) = V_y ) ).
cnf(cls_List_Ohd__upt_0,axiom,
( ~ c_less(V_y,V_j,tc_nat)
| c_List_Ohd(c_List_Oupt(V_y,V_j),tc_nat) = V_y ) ).
cnf(cls_List_Oitrev_0,axiom,
c_List_Oitrev(V_xs,V_x,T_a) = c_append(c_List_Orev(V_xs,T_a),V_x,T_a) ).
cnf(cls_List_Oitrev_Osimps__1_0,axiom,
c_List_Oitrev(c_List_Olist_ONil,V_y,T_a__1) = V_y ).
cnf(cls_List_Oitrev_Osimps__2_0,axiom,
c_List_Oitrev(c_List_Olist_OCons(V_x,V_xs,T_a__1),V_ys,T_a__1) = c_List_Oitrev(V_xs,c_List_Olist_OCons(V_x,V_ys,T_a__1),T_a__1) ).
cnf(cls_List_Olast_Osimps_0,axiom,
c_List_Olast(c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a),T_a) = V_x ).
cnf(cls_List_Olast_Osimps_1,axiom,
( V_xs = c_List_Olist_ONil
| c_List_Olast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olast(V_xs,T_a) ) ).
cnf(cls_List_Olast__appendL_0,axiom,
c_List_Olast(c_append(V_xs,c_List_Olist_ONil,T_a),T_a) = c_List_Olast(V_xs,T_a) ).
cnf(cls_List_Olast__appendR_0,axiom,
( V_ys = c_List_Olist_ONil
| c_List_Olast(c_append(V_xs,V_ys,T_a),T_a) = c_List_Olast(V_ys,T_a) ) ).
cnf(cls_List_Olast__drop_0,axiom,
( ~ c_less(V_n,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat)
| c_List_Olast(c_List_Odrop(V_n,V_xs,T_a),T_a) = c_List_Olast(V_xs,T_a) ) ).
cnf(cls_List_Olast__in__set_0,axiom,
( c_in(c_List_Olast(V_as,T_a),c_List_Oset(V_as,T_a),T_a)
| V_as = c_List_Olist_ONil ) ).
cnf(cls_List_Olast__replicate_0,axiom,
( V_n = c_0
| c_List_Olast(c_List_Oreplicate(V_n,V_y,T_a),T_a) = V_y ) ).
cnf(cls_List_Olast__snoc_0,axiom,
c_List_Olast(c_append(V_xs,c_List_Olist_OCons(V_y,c_List_Olist_ONil,T_a),T_a),T_a) = V_y ).
cnf(cls_List_Olast__upt_0,axiom,
( ~ c_less(V_i,V_j,tc_nat)
| c_List_Olast(c_List_Oupt(V_i,V_j),tc_nat) = c_minus(V_j,c_1,tc_nat) ) ).
cnf(cls_List_Olength__0__conv_0,axiom,
( c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_0
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Olength__0__conv_1,axiom,
c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(T_a)) = c_0 ).
cnf(cls_List_Olength__append_0,axiom,
c_Nat_Osize(c_append(V_xs,V_ys,T_a),tc_List_Olist(T_a)) = c_plus(c_Nat_Osize(V_xs,tc_List_Olist(T_a)),c_Nat_Osize(V_ys,tc_List_Olist(T_a)),tc_nat) ).
cnf(cls_List_Olength__butlast_0,axiom,
c_Nat_Osize(c_List_Obutlast(V_xs,T_a),tc_List_Olist(T_a)) = c_minus(c_Nat_Osize(V_xs,tc_List_Olist(T_a)),c_1,tc_nat) ).
cnf(cls_List_Olength__drop_0,axiom,
c_Nat_Osize(c_List_Odrop(V_n,V_xs,T_a),tc_List_Olist(T_a)) = c_minus(c_Nat_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ).
cnf(cls_List_Olength__greater__0__conv_0,axiom,
~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(T_a)),tc_nat) ).
cnf(cls_List_Olength__greater__0__conv_1,axiom,
( c_less(c_0,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat)
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Olength__list__update_0,axiom,
c_Nat_Osize(c_List_Olist__update(V_xs,V_i,V_x,T_a),tc_List_Olist(T_a)) = c_Nat_Osize(V_xs,tc_List_Olist(T_a)) ).
cnf(cls_List_Olength__remdups__eq_0,axiom,
( c_Nat_Osize(c_List_Oremdups(V_xs,T_a),tc_List_Olist(T_a)) != c_Nat_Osize(V_xs,tc_List_Olist(T_a))
| c_List_Oremdups(V_xs,T_a) = V_xs ) ).
cnf(cls_List_Olength__remdups__eq_1,axiom,
( c_List_Oremdups(V_xs,T_a) != V_xs
| c_Nat_Osize(c_List_Oremdups(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize(V_xs,tc_List_Olist(T_a)) ) ).
cnf(cls_List_Olength__replicate_0,axiom,
c_Nat_Osize(c_List_Oreplicate(V_y,V_x,T_a),tc_List_Olist(T_a)) = V_y ).
cnf(cls_List_Olength__rev_0,axiom,
c_Nat_Osize(c_List_Orev(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize(V_xs,tc_List_Olist(T_a)) ).
cnf(cls_List_Olength__rotate1_0,axiom,
c_Nat_Osize(c_List_Orotate1(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize(V_xs,tc_List_Olist(T_a)) ).
cnf(cls_List_Olength__rotate_0,axiom,
c_Nat_Osize(c_List_Orotate(V_n,V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize(V_xs,tc_List_Olist(T_a)) ).
cnf(cls_List_Olength__take_0,axiom,
c_Nat_Osize(c_List_Otake(V_n,V_xs,T_a),tc_List_Olist(T_a)) = c_Orderings_Omin(c_Nat_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ).
cnf(cls_List_Olength__tl_0,axiom,
c_Nat_Osize(c_List_Otl(V_xs,T_a),tc_List_Olist(T_a)) = c_minus(c_Nat_Osize(V_xs,tc_List_Olist(T_a)),c_1,tc_nat) ).
cnf(cls_List_Olength__upt_0,axiom,
c_Nat_Osize(c_List_Oupt(V_i,V_j),tc_List_Olist(tc_nat)) = c_minus(V_j,V_i,tc_nat) ).
cnf(cls_List_Olength__zip_0,axiom,
c_Nat_Osize(c_List_Ozip(V_xs,V_ys,T_a,T_b),tc_List_Olist(tc_prod(T_a,T_b))) = c_Orderings_Omin(c_Nat_Osize(V_xs,tc_List_Olist(T_a)),c_Nat_Osize(V_ys,tc_List_Olist(T_b)),tc_nat) ).
cnf(cls_List_Olexn_Osimps__1_0,axiom,
c_List_Olexn(V_r,c_0,T_a__1) = c_emptyset ).
cnf(cls_List_Olexord__Nil__left_0,axiom,
( ~ c_in(c_Pair(c_List_Olist_ONil,V_y,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olexord(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))
| V_y = c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(V_y,T_a),c_Main_Olexord__Nil__left__2(V_y,T_a),T_a) ) ).
cnf(cls_List_Olexord__Nil__left_1,axiom,
c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(V_U,V_V,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olexord(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ).
cnf(cls_List_Olexord__Nil__right_0,axiom,
~ c_in(c_Pair(V_x,c_List_Olist_ONil,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olexord(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ).
cnf(cls_List_Olexord__cons__cons_0,axiom,
( ~ c_in(c_Pair(c_List_Olist_OCons(V_a,V_x,T_a),c_List_Olist_OCons(V_b,V_y,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olexord(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))
| c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| V_a = V_b ) ).
cnf(cls_List_Olexord__cons__cons_1,axiom,
( ~ c_in(c_Pair(c_List_Olist_OCons(V_a,V_x,T_a),c_List_Olist_OCons(V_b,V_y,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olexord(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))
| c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,V_y,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olexord(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ) ).
cnf(cls_List_Olexord__cons__cons_2,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(c_List_Olist_OCons(V_a,V_x,T_a),c_List_Olist_OCons(V_b,V_y,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olexord(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ) ).
cnf(cls_List_Olexord__cons__cons_3,axiom,
( ~ c_in(c_Pair(V_xa,V_y,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olexord(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))
| c_in(c_Pair(c_List_Olist_OCons(V_x,V_xa,T_a),c_List_Olist_OCons(V_x,V_y,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olexord(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ) ).
cnf(cls_List_Olist_Odistinct__1_0,axiom,
c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ).
cnf(cls_List_Olist_Odistinct__2_0,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil ).
cnf(cls_List_Olist_Oinject_0,axiom,
( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
| V_a = V_a_H ) ).
cnf(cls_List_Olist_Oinject_1,axiom,
( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
| V_list = V_list_H ) ).
cnf(cls_List_Olist_Osize__2_0,axiom,
c_Nat_Osize(c_List_Olist_OCons(V_a,V_list,T_a),tc_List_Olist(T_a)) = c_plus(c_Nat_Osize(V_list,tc_List_Olist(T_a)),c_Suc(c_0),tc_nat) ).
cnf(cls_List_Olist__inter_Osimps__1_0,axiom,
c_List_Olist__inter(c_List_Olist_ONil,V_bs,T_a__1) = c_List_Olist_ONil ).
cnf(cls_List_Olist__inter_Osimps__2_0,axiom,
( ~ c_in(V_a,c_List_Oset(V_bs,T_a__1),T_a__1)
| c_List_Olist__inter(c_List_Olist_OCons(V_a,V_as,T_a__1),V_bs,T_a__1) = c_List_Olist_OCons(V_a,c_List_Olist__inter(V_as,V_bs,T_a__1),T_a__1) ) ).
cnf(cls_List_Olist__inter_Osimps__2_1,axiom,
( c_in(V_a,c_List_Oset(V_bs,T_a__1),T_a__1)
| c_List_Olist__inter(c_List_Olist_OCons(V_a,V_as,T_a__1),V_bs,T_a__1) = c_List_Olist__inter(V_as,V_bs,T_a__1) ) ).
cnf(cls_List_Olist__update_Osimps__1_0,axiom,
c_List_Olist__update(c_List_Olist_ONil,V_i,V_v,T_a__1) = c_List_Olist_ONil ).
cnf(cls_List_Olist__update__beyond_0,axiom,
( ~ c_lessequals(c_Nat_Osize(V_y,tc_List_Olist(T_a)),V_i,tc_nat)
| c_List_Olist__update(V_y,V_i,V_x,T_a) = V_y ) ).
cnf(cls_List_Olist__update__id_0,axiom,
( ~ c_less(V_i,c_Nat_Osize(V_y,tc_List_Olist(T_a)),tc_nat)
| c_List_Olist__update(V_y,V_i,c_List_Onth(V_y,V_i,T_a),T_a) = V_y ) ).
cnf(cls_List_Olist__update__length_0,axiom,
c_List_Olist__update(c_append(V_xs,c_List_Olist_OCons(V_x,V_ys,T_a),T_a),c_Nat_Osize(V_xs,tc_List_Olist(T_a)),V_y,T_a) = c_append(V_xs,c_List_Olist_OCons(V_y,V_ys,T_a),T_a) ).
cnf(cls_List_Olist__update__overwrite_0,axiom,
( ~ c_less(V_i,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i,V_y,T_a) = c_List_Olist__update(V_xs,V_i,V_y,T_a) ) ).
cnf(cls_List_Olistrel__Nil_0,axiom,
c_Relation_OImage(c_List_Olistrel(V_r,T_a),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(T_a)),tc_List_Olist(T_a),tc_List_Olist(T_a)) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(T_a)) ).
cnf(cls_List_Olists__Int__eq_0,axiom,
c_List_Olists(c_inter(V_A,V_B,T_a),T_a) = c_inter(c_List_Olists(V_A,T_a),c_List_Olists(V_B,T_a),tc_List_Olist(T_a)) ).
cnf(cls_List_Olists__UNIV_0,axiom,
c_List_Olists(c_UNIV,T_a) = c_UNIV ).
cnf(cls_List_Olistset_Osimps__1_0,axiom,
c_List_Olistset(c_List_Olist_ONil,T_a__1) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(T_a__1)) ).
cnf(cls_List_Olistset_Osimps__2_0,axiom,
c_List_Olistset(c_List_Olist_OCons(V_A,V_As,tc_set(T_a__1)),T_a__1) = c_List_Oset__Cons(V_A,c_List_Olistset(V_As,T_a__1),T_a__1) ).
cnf(cls_List_Onibble_Ocases__10_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_y,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble9,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__11_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_y,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibbleA,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__12_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_y,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibbleB,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__13_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_y,V_f14,V_f15,V_f16,c_List_Onibble_ONibbleC,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__14_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_y,V_f15,V_f16,c_List_Onibble_ONibbleD,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__15_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_y,V_f16,c_List_Onibble_ONibbleE,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__16_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_y,c_List_Onibble_ONibbleF,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__1_0,axiom,
c_List_Onibble_Onibble__case(V_y,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble0,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__2_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_y,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble1,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__3_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_y,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble2,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__4_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_y,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble3,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__5_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_y,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble4,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__6_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_y,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble5,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__7_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_y,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble6,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__8_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_y,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble7,T_a) = V_y ).
cnf(cls_List_Onibble_Ocases__9_0,axiom,
c_List_Onibble_Onibble__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_y,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble8,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__10_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_y,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble9,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__11_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_y,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibbleA,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__12_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_y,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibbleB,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__13_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_y,V_f14,V_f15,V_f16,c_List_Onibble_ONibbleC,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__14_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_y,V_f15,V_f16,c_List_Onibble_ONibbleD,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__15_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_y,V_f16,c_List_Onibble_ONibbleE,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__16_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_y,c_List_Onibble_ONibbleF,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__1_0,axiom,
c_List_Onibble_Onibble__rec(V_y,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble0,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__2_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_y,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble1,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__3_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_y,V_f4,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble2,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__4_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_y,V_f5,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble3,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__5_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_y,V_f6,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble4,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__6_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_y,V_f7,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble5,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__7_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_y,V_f8,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble6,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__8_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_y,V_f9,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble7,T_a) = V_y ).
cnf(cls_List_Onibble_Orecs__9_0,axiom,
c_List_Onibble_Onibble__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_y,V_f10,V_f11,V_f12,V_f13,V_f14,V_f15,V_f16,c_List_Onibble_ONibble8,T_a) = V_y ).
cnf(cls_List_Onibble_Osize__10_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__11_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__12_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__13_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__14_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__15_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__16_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__1_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__2_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__3_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__4_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__5_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__6_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__7_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__8_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onibble_Osize__9_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) = c_0 ).
cnf(cls_List_Onot__Cons__self_0,axiom,
V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ).
cnf(cls_List_Onotin__set__remove1_0,axiom,
( ~ c_in(V_x,c_List_Oset(c_List_Oremove1(V_y,V_xs,T_a),T_a),T_a)
| c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_List_Onotin__set__sublistI_0,axiom,
( ~ c_in(V_x,c_List_Oset(c_List_Osublist(V_xs,V_I,T_a),T_a),T_a)
| c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_List_Onth__Cons__0_0,axiom,
c_List_Onth(c_List_Olist_OCons(V_y,V_xs,T_a),c_0,T_a) = V_y ).
cnf(cls_List_Onth__Cons__Suc_0,axiom,
c_List_Onth(c_List_Olist_OCons(V_x,V_xs,T_a),c_Suc(V_n),T_a) = c_List_Onth(V_xs,V_n,T_a) ).
cnf(cls_List_Onth__Cons__number__of_0,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) != c_0
| c_List_Onth(c_List_Olist_OCons(V_x,V_xs,T_a),c_Numeral_Onumber__of(V_v,tc_nat),T_a) = V_x ) ).
cnf(cls_List_Onth__Cons__number__of_1,axiom,
( c_List_Onth(c_List_Olist_OCons(V_x,V_xs,T_a),c_Numeral_Onumber__of(V_v,tc_nat),T_a) = c_List_Onth(V_xs,c_minus(c_Numeral_Onumber__of(V_v,tc_nat),c_1,tc_nat),T_a)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_0 ) ).
cnf(cls_List_Onth__append__length_0,axiom,
c_List_Onth(c_append(V_xs,c_List_Olist_OCons(V_y,V_ys,T_a),T_a),c_Nat_Osize(V_xs,tc_List_Olist(T_a)),T_a) = V_y ).
cnf(cls_List_Onth__append__length__plus_0,axiom,
c_List_Onth(c_append(V_xs,V_ys,T_a),c_plus(c_Nat_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat),T_a) = c_List_Onth(V_ys,V_n,T_a) ).
cnf(cls_List_Onth__drop_0,axiom,
( ~ c_lessequals(c_plus(V_n,V_i,tc_nat),c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat)
| c_List_Onth(c_List_Odrop(V_n,V_xs,T_a),V_i,T_a) = c_List_Onth(V_xs,c_plus(V_n,V_i,tc_nat),T_a) ) ).
cnf(cls_List_Onth__list__update__eq_0,axiom,
( ~ c_less(V_i,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat)
| c_List_Onth(c_List_Olist__update(V_xs,V_i,V_y,T_a),V_i,T_a) = V_y ) ).
cnf(cls_List_Onth__list__update__neq_0,axiom,
( V_i = V_j
| c_List_Onth(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_j,T_a) = c_List_Onth(V_xs,V_j,T_a) ) ).
cnf(cls_List_Onth__mem_0,axiom,
( ~ c_less(V_n,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat)
| c_in(c_List_Onth(V_xs,V_n,T_a),c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_List_Onth__replicate_0,axiom,
( ~ c_less(V_i,V_n,tc_nat)
| c_List_Onth(c_List_Oreplicate(V_n,V_y,T_a),V_i,T_a) = V_y ) ).
cnf(cls_List_Onth__take_0,axiom,
( ~ c_less(V_i,V_n,tc_nat)
| c_List_Onth(c_List_Otake(V_n,V_xs,T_a),V_i,T_a) = c_List_Onth(V_xs,V_i,T_a) ) ).
cnf(cls_List_Onth__upt_0,axiom,
( ~ c_less(c_plus(V_i,V_k,tc_nat),V_j,tc_nat)
| c_List_Onth(c_List_Oupt(V_i,V_j),V_k,tc_nat) = c_plus(V_i,V_k,tc_nat) ) ).
cnf(cls_List_Onth__zip_0,axiom,
( ~ c_less(V_i,c_Nat_Osize(V_ys,tc_List_Olist(T_b)),tc_nat)
| ~ c_less(V_i,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat)
| c_List_Onth(c_List_Ozip(V_xs,V_ys,T_a,T_b),V_i,tc_prod(T_a,T_b)) = c_Pair(c_List_Onth(V_xs,V_i,T_a),c_List_Onth(V_ys,V_i,T_b),T_a,T_b) ) ).
cnf(cls_List_Onull_Osimps__1_0,axiom,
c_List_Onull(c_List_Olist_ONil,T_a__1) ).
cnf(cls_List_Onull_Osimps__2_0,axiom,
~ c_List_Onull(c_List_Olist_OCons(V_x,V_xs,T_a__1),T_a__1) ).
cnf(cls_List_Oop_A_64_Oappend__Cons_0,axiom,
c_append(c_List_Olist_OCons(V_x,V_xs,T_a__1),V_ys,T_a__1) = c_List_Olist_OCons(V_x,c_append(V_xs,V_ys,T_a__1),T_a__1) ).
cnf(cls_List_Oop_Amem_Osimps__1_0,axiom,
~ c_List_Oop_Amem(V_x,c_List_Olist_ONil,T_a__1) ).
cnf(cls_List_Oop_Amem_Osimps__2_0,axiom,
( ~ c_List_Oop_Amem(V_x,c_List_Olist_OCons(V_y,V_ys,T_a__1),T_a__1)
| c_List_Oop_Amem(V_x,V_ys,T_a__1)
| V_y = V_x ) ).
cnf(cls_List_Oop_Amem_Osimps__2_1,axiom,
c_List_Oop_Amem(V_x,c_List_Olist_OCons(V_x,V_ys,T_a),T_a) ).
cnf(cls_List_Oop_Amem_Osimps__2_2,axiom,
( ~ c_List_Oop_Amem(V_x,V_ys,T_a__1)
| c_List_Oop_Amem(V_x,c_List_Olist_OCons(V_y,V_ys,T_a__1),T_a__1) ) ).
cnf(cls_List_Oremdups_Osimps__2_0,axiom,
( ~ c_in(V_x,c_List_Oset(V_xs,T_a__1),T_a__1)
| c_List_Oremdups(c_List_Olist_OCons(V_x,V_xs,T_a__1),T_a__1) = c_List_Oremdups(V_xs,T_a__1) ) ).
cnf(cls_List_Oremdups_Osimps__2_1,axiom,
( c_in(V_x,c_List_Oset(V_xs,T_a__1),T_a__1)
| c_List_Oremdups(c_List_Olist_OCons(V_x,V_xs,T_a__1),T_a__1) = c_List_Olist_OCons(V_x,c_List_Oremdups(V_xs,T_a__1),T_a__1) ) ).
cnf(cls_List_Oremdups__eq__nil__iff_0,axiom,
( c_List_Oremdups(V_x,T_a) != c_List_Olist_ONil
| V_x = c_List_Olist_ONil ) ).
cnf(cls_List_Oremdups__eq__nil__iff_1,axiom,
c_List_Oremdups(c_List_Olist_ONil,T_a) = c_List_Olist_ONil ).
cnf(cls_List_Oremdups__eq__nil__right__iff_0,axiom,
( c_List_Olist_ONil != c_List_Oremdups(V_x,T_a)
| V_x = c_List_Olist_ONil ) ).
cnf(cls_List_Oremdups__eq__nil__right__iff_1,axiom,
c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,T_a) ).
cnf(cls_List_Oremove1_Osimps__1_0,axiom,
c_List_Oremove1(V_x,c_List_Olist_ONil,T_a__1) = c_List_Olist_ONil ).
cnf(cls_List_Oremove1_Osimps__2_0,axiom,
c_List_Oremove1(V_x,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_xs ).
cnf(cls_List_Oremove1_Osimps__2_1,axiom,
( V_x = V_y
| c_List_Oremove1(V_x,c_List_Olist_OCons(V_y,V_xs,T_a__1),T_a__1) = c_List_Olist_OCons(V_y,c_List_Oremove1(V_x,V_xs,T_a__1),T_a__1) ) ).
cnf(cls_List_Oreplicate_Oreplicate__0_0,axiom,
c_List_Oreplicate(c_0,V_x,T_a__1) = c_List_Olist_ONil ).
cnf(cls_List_Oreplicate_Oreplicate__Suc_0,axiom,
c_List_Oreplicate(c_Suc(V_n),V_x,T_a__1) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_n,V_x,T_a__1),T_a__1) ).
cnf(cls_List_Orev_Osimps__2_0,axiom,
c_List_Orev(c_List_Olist_OCons(V_x,V_xs,T_a__1),T_a__1) = c_append(c_List_Orev(V_xs,T_a__1),c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a__1),T_a__1) ).
cnf(cls_List_Orev__append_0,axiom,
c_List_Orev(c_append(V_xs,V_ys,T_a),T_a) = c_append(c_List_Orev(V_ys,T_a),c_List_Orev(V_xs,T_a),T_a) ).
cnf(cls_List_Orev__eq__Cons__iff_0,axiom,
( c_List_Orev(V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
| V_xs = c_append(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil,T_a),T_a) ) ).
cnf(cls_List_Orev__eq__Cons__iff_1,axiom,
c_List_Orev(c_append(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil,T_a),T_a),T_a) = c_List_Olist_OCons(V_y,V_ys,T_a) ).
cnf(cls_List_Orev__is__Nil__conv_0,axiom,
( c_List_Orev(V_xs,T_a) != c_List_Olist_ONil
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Orev__is__Nil__conv_1,axiom,
c_List_Orev(c_List_Olist_ONil,T_a) = c_List_Olist_ONil ).
cnf(cls_List_Orev__is__rev__conv_0,axiom,
( c_List_Orev(V_xs,T_a) != c_List_Orev(V_ys,T_a)
| V_xs = V_ys ) ).
cnf(cls_List_Orev__replicate_0,axiom,
c_List_Orev(c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Oreplicate(V_n,V_x,T_a) ).
cnf(cls_List_Orev__rev__ident_0,axiom,
c_List_Orev(c_List_Orev(V_y,T_a),T_a) = V_y ).
cnf(cls_List_Orev__singleton__conv_0,axiom,
( c_List_Orev(V_xs,T_a) != c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a)
| V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a) ) ).
cnf(cls_List_Orev__singleton__conv_1,axiom,
c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a) ).
cnf(cls_List_Orotate1__is__Nil__conv_0,axiom,
( c_List_Orotate1(V_xs,T_a) != c_List_Olist_ONil
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Orotate1__is__Nil__conv_1,axiom,
c_List_Orotate1(c_List_Olist_ONil,T_a) = c_List_Olist_ONil ).
cnf(cls_List_Orotate1__length01_0,axiom,
( ~ c_lessequals(c_Nat_Osize(V_y,tc_List_Olist(T_a)),c_1,tc_nat)
| c_List_Orotate1(V_y,T_a) = V_y ) ).
cnf(cls_List_Orotate__Suc_0,axiom,
c_List_Orotate(c_Suc(V_n),V_xs,T_a) = c_List_Orotate1(c_List_Orotate(V_n,V_xs,T_a),T_a) ).
cnf(cls_List_Orotate__id_0,axiom,
( c_Divides_Oop_Amod(V_n,c_Nat_Osize(V_y,tc_List_Olist(T_a)),tc_nat) != c_0
| c_List_Orotate(V_n,V_y,T_a) = V_y ) ).
cnf(cls_List_Orotate__is__Nil__conv_0,axiom,
( c_List_Orotate(V_n,V_xs,T_a) != c_List_Olist_ONil
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Orotate__is__Nil__conv_1,axiom,
c_List_Orotate(V_n,c_List_Olist_ONil,T_a) = c_List_Olist_ONil ).
cnf(cls_List_Orotate__length01_0,axiom,
( ~ c_lessequals(c_Nat_Osize(V_y,tc_List_Olist(T_a)),c_1,tc_nat)
| c_List_Orotate(V_n,V_y,T_a) = V_y ) ).
cnf(cls_List_Osame__append__eq_0,axiom,
( c_append(V_xs,V_ys,T_a) != c_append(V_xs,V_zs,T_a)
| V_ys = V_zs ) ).
cnf(cls_List_Oself__append__conv2_0,axiom,
( V_ys != c_append(V_xs,V_ys,T_a)
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Oself__append__conv2_1,axiom,
V_ys = c_append(c_List_Olist_ONil,V_ys,T_a) ).
cnf(cls_List_Oself__append__conv_0,axiom,
( V_xs != c_append(V_xs,V_ys,T_a)
| V_ys = c_List_Olist_ONil ) ).
cnf(cls_List_Oself__append__conv_1,axiom,
V_xs = c_append(V_xs,c_List_Olist_ONil,T_a) ).
cnf(cls_List_Oset_Osimps__2_0,axiom,
c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a__1),T_a__1) = c_insert(V_x,c_List_Oset(V_xs,T_a__1),T_a__1) ).
cnf(cls_List_Oset__append_0,axiom,
c_List_Oset(c_append(V_xs,V_ys,T_a),T_a) = c_union(c_List_Oset(V_xs,T_a),c_List_Oset(V_ys,T_a),T_a) ).
cnf(cls_List_Oset__empty2_0,axiom,
( c_emptyset != c_List_Oset(V_xs,T_a)
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Oset__empty2_1,axiom,
c_emptyset = c_List_Oset(c_List_Olist_ONil,T_a) ).
cnf(cls_List_Oset__empty_0,axiom,
( c_List_Oset(V_xs,T_a) != c_emptyset
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Oset__empty_1,axiom,
c_List_Oset(c_List_Olist_ONil,T_a) = c_emptyset ).
cnf(cls_List_Oset__remdups_0,axiom,
c_List_Oset(c_List_Oremdups(V_xs,T_a),T_a) = c_List_Oset(V_xs,T_a) ).
cnf(cls_List_Oset__remove1__eq_0,axiom,
( ~ c_List_Odistinct(V_xs,T_a)
| c_List_Oset(c_List_Oremove1(V_x,V_xs,T_a),T_a) = c_minus(c_List_Oset(V_xs,T_a),c_insert(V_x,c_emptyset,T_a),tc_set(T_a)) ) ).
cnf(cls_List_Oset__replicate_0,axiom,
( V_n = c_0
| c_List_Oset(c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_insert(V_x,c_emptyset,T_a) ) ).
cnf(cls_List_Oset__rev_0,axiom,
c_List_Oset(c_List_Orev(V_xs,T_a),T_a) = c_List_Oset(V_xs,T_a) ).
cnf(cls_List_Oset__rotate1_0,axiom,
c_List_Oset(c_List_Orotate1(V_xs,T_a),T_a) = c_List_Oset(V_xs,T_a) ).
cnf(cls_List_Oset__rotate_0,axiom,
c_List_Oset(c_List_Orotate(V_n,V_xs,T_a),T_a) = c_List_Oset(V_xs,T_a) ).
cnf(cls_List_Osingleton__rev__conv_0,axiom,
( c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a) != c_List_Orev(V_xs,T_a)
| V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a) ) ).
cnf(cls_List_Osingleton__rev__conv_1,axiom,
c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a) = c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a),T_a) ).
cnf(cls_List_Osublist__empty_0,axiom,
c_List_Osublist(V_xs,c_emptyset,T_a) = c_List_Olist_ONil ).
cnf(cls_List_Osublist__nil_0,axiom,
c_List_Osublist(c_List_Olist_ONil,V_A,T_a) = c_List_Olist_ONil ).
cnf(cls_List_Osublist__singleton_0,axiom,
( ~ c_in(c_0,V_A,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a),V_A,T_a) = c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a) ) ).
cnf(cls_List_Osublist__singleton_1,axiom,
( c_in(c_0,V_A,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a),V_A,T_a) = c_List_Olist_ONil ) ).
cnf(cls_List_Osublist__upt__eq__take_0,axiom,
c_List_Osublist(V_l,c_SetInterval_OlessThan(V_n,tc_nat),T_a) = c_List_Otake(V_n,V_l,T_a) ).
cnf(cls_List_Otake__Cons__number__of_0,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) != c_0
| c_List_Otake(c_Numeral_Onumber__of(V_v,tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_ONil ) ).
cnf(cls_List_Otake__Cons__number__of_1,axiom,
( c_List_Otake(c_Numeral_Onumber__of(V_v,tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Otake(c_minus(c_Numeral_Onumber__of(V_v,tc_nat),c_1,tc_nat),V_xs,T_a),T_a)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_0 ) ).
cnf(cls_List_Otake__Suc__Cons_0,axiom,
c_List_Otake(c_Suc(V_n),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Otake(V_n,V_xs,T_a),T_a) ).
cnf(cls_List_Otake__all_0,axiom,
( ~ c_lessequals(c_Nat_Osize(V_y,tc_List_Olist(T_a)),V_n,tc_nat)
| c_List_Otake(V_n,V_y,T_a) = V_y ) ).
cnf(cls_List_Otake__append_0,axiom,
c_List_Otake(V_n,c_append(V_xs,V_ys,T_a),T_a) = c_append(c_List_Otake(V_n,V_xs,T_a),c_List_Otake(c_minus(V_n,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_ys,T_a),T_a) ).
cnf(cls_List_Otake__eq__Nil_0,axiom,
( c_List_Otake(V_n,V_xs,T_a) != c_List_Olist_ONil
| V_n = c_0
| V_xs = c_List_Olist_ONil ) ).
cnf(cls_List_Otake__eq__Nil_1,axiom,
c_List_Otake(c_0,V_xs,T_a) = c_List_Olist_ONil ).
cnf(cls_List_Otake__eq__Nil_2,axiom,
c_List_Otake(V_n,c_List_Olist_ONil,T_a) = c_List_Olist_ONil ).
cnf(cls_List_Otake__replicate_0,axiom,
c_List_Otake(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oreplicate(c_Orderings_Omin(V_i,V_k,tc_nat),V_x,T_a) ).
cnf(cls_List_Otake__take_0,axiom,
c_List_Otake(V_n,c_List_Otake(V_m,V_xs,T_a),T_a) = c_List_Otake(c_Orderings_Omin(V_n,V_m,tc_nat),V_xs,T_a) ).
cnf(cls_List_Otake__upt_0,axiom,
( ~ c_lessequals(c_plus(V_i,V_m,tc_nat),V_n,tc_nat)
| c_List_Otake(V_m,c_List_Oupt(V_i,V_n),tc_nat) = c_List_Oupt(V_i,c_plus(V_i,V_m,tc_nat)) ) ).
cnf(cls_List_Otl_Osimps__1_0,axiom,
c_List_Otl(c_List_Olist_ONil,T_a__1) = c_List_Olist_ONil ).
cnf(cls_List_Otl_Osimps__2_0,axiom,
c_List_Otl(c_List_Olist_OCons(V_x,V_y,T_a__1),T_a__1) = V_y ).
cnf(cls_List_Otl__append2_0,axiom,
( V_xs = c_List_Olist_ONil
| c_List_Otl(c_append(V_xs,V_ys,T_a),T_a) = c_append(c_List_Otl(V_xs,T_a),V_ys,T_a) ) ).
cnf(cls_List_Otl__replicate_0,axiom,
( V_n = c_0
| c_List_Otl(c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Oreplicate(c_minus(V_n,c_1,tc_nat),V_x,T_a) ) ).
cnf(cls_List_Oupt_Oupt__Suc_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_List_Oupt(V_i,c_Suc(V_j)) = c_append(c_List_Oupt(V_i,V_j),c_List_Olist_OCons(V_j,c_List_Olist_ONil,tc_nat),tc_nat) ) ).
cnf(cls_List_Oupt_Oupt__Suc_1,axiom,
( c_lessequals(V_i,V_j,tc_nat)
| c_List_Oupt(V_i,c_Suc(V_j)) = c_List_Olist_ONil ) ).
cnf(cls_List_Oupt__eq__Nil__conv_0,axiom,
( c_List_Oupt(V_i,V_j) != c_List_Olist_ONil
| c_lessequals(V_j,V_i,tc_nat)
| V_j = c_0 ) ).
cnf(cls_List_Oupt__eq__Nil__conv_1,axiom,
c_List_Oupt(V_i,c_0) = c_List_Olist_ONil ).
cnf(cls_List_Oupt__eq__Nil__conv_2,axiom,
( ~ c_lessequals(V_j,V_i,tc_nat)
| c_List_Oupt(V_i,V_j) = c_List_Olist_ONil ) ).
cnf(cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0,axiom,
c_List_Olist_OCons(V_x,V_t,T_a) != V_t ).
cnf(cls_List_Ozip_Osimps__1_0,axiom,
c_List_Ozip(V_xs,c_List_Olist_ONil,T_a__1,T_b__1) = c_List_Olist_ONil ).
cnf(cls_List_Ozip__Cons__Cons_0,axiom,
c_List_Ozip(c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b) = c_List_Olist_OCons(c_Pair(V_x,V_y,T_a,T_b),c_List_Ozip(V_xs,V_ys,T_a,T_b),tc_prod(T_a,T_b)) ).
cnf(cls_List_Ozip__Nil_0,axiom,
c_List_Ozip(c_List_Olist_ONil,V_ys,T_a,T_b) = c_List_Olist_ONil ).
cnf(cls_List_Ozip__append_0,axiom,
( c_Nat_Osize(V_ys,tc_List_Olist(T_a)) != c_Nat_Osize(V_vs,tc_List_Olist(T_b))
| c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_us,tc_List_Olist(T_b))
| c_List_Ozip(c_append(V_xs,V_ys,T_a),c_append(V_us,V_vs,T_b),T_a,T_b) = c_append(c_List_Ozip(V_xs,V_us,T_a,T_b),c_List_Ozip(V_ys,V_vs,T_a,T_b),tc_prod(T_a,T_b)) ) ).
cnf(cls_List_Ozip__replicate_0,axiom,
c_List_Ozip(c_List_Oreplicate(V_i,V_x,T_a),c_List_Oreplicate(V_j,V_y,T_b),T_a,T_b) = c_List_Oreplicate(c_Orderings_Omin(V_i,V_j,tc_nat),c_Pair(V_x,V_y,T_a,T_b),tc_prod(T_a,T_b)) ).
cnf(cls_Map_Omap__of__zip__is__None_0,axiom,
( ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a)
| c_Map_Omap__of(c_List_Ozip(V_xs,V_ys,T_a,T_b),V_x,T_a,T_b) != c_Datatype_Ooption_ONone
| c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_ys,tc_List_Olist(T_b)) ) ).
cnf(cls_Map_Omap__of__zip__is__None_1,axiom,
( c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_ys,tc_List_Olist(T_b))
| c_in(V_x,c_List_Oset(V_xs,T_a),T_a)
| c_Map_Omap__of(c_List_Ozip(V_xs,V_ys,T_a,T_b),V_x,T_a,T_b) = c_Datatype_Ooption_ONone ) ).
cnf(cls_NatArith_Oadd__diff__assoc2_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_plus(c_minus(V_j,V_k,tc_nat),V_i,tc_nat) = c_minus(c_plus(V_j,V_i,tc_nat),V_k,tc_nat) ) ).
cnf(cls_NatArith_Oadd__diff__assoc_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_plus(V_i,c_minus(V_j,V_k,tc_nat),tc_nat) = c_minus(c_plus(V_i,V_j,tc_nat),V_k,tc_nat) ) ).
cnf(cls_NatArith_Odiff__Suc__diff__eq1_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_minus(V_m,c_Suc(c_minus(V_j,V_k,tc_nat)),tc_nat) = c_minus(c_plus(V_m,V_k,tc_nat),c_Suc(V_j),tc_nat) ) ).
cnf(cls_NatArith_Odiff__Suc__diff__eq2_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_minus(c_Suc(c_minus(V_j,V_k,tc_nat)),V_m,tc_nat) = c_minus(c_Suc(V_j),c_plus(V_k,V_m,tc_nat),tc_nat) ) ).
cnf(cls_NatArith_Odiff__diff__cancel_0,axiom,
( ~ c_lessequals(V_y,V_n,tc_nat)
| c_minus(V_n,c_minus(V_n,V_y,tc_nat),tc_nat) = V_y ) ).
cnf(cls_NatArith_Odiff__diff__right_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_minus(V_i,c_minus(V_j,V_k,tc_nat),tc_nat) = c_minus(c_plus(V_i,V_k,tc_nat),V_j,tc_nat) ) ).
cnf(cls_NatArith_Odiff__less_0,axiom,
( ~ c_less(c_0,V_m,tc_nat)
| ~ c_less(c_0,V_n,tc_nat)
| c_less(c_minus(V_m,V_n,tc_nat),V_m,tc_nat) ) ).
cnf(cls_NatArith_Oof__nat_Oof__nat__Suc_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a__1)
| c_NatArith_Oof__nat(c_Suc(V_m),T_a__1) = c_plus(c_NatArith_Oof__nat(V_m,T_a__1),c_1,T_a__1) ) ).
cnf(cls_NatArith_Oof__nat__0__eq__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_0 != c_NatArith_Oof__nat(V_n,T_a)
| c_0 = V_n ) ).
cnf(cls_NatArith_Oof__nat__0__eq__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_0 = c_NatArith_Oof__nat(c_0,T_a) ) ).
cnf(cls_NatArith_Oof__nat__0__le__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_0,c_NatArith_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_NatArith_Oof__nat__0__less__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_less(c_0,c_NatArith_Oof__nat(V_n,T_a),T_a)
| c_less(c_0,V_n,tc_nat) ) ).
cnf(cls_NatArith_Oof__nat__0__less__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_less(c_0,V_n,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_NatArith_Oof__nat__1_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a)
| c_NatArith_Oof__nat(c_1,T_a) = c_1 ) ).
cnf(cls_NatArith_Oof__nat__add_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a)
| c_NatArith_Oof__nat(c_plus(V_m,V_n,tc_nat),T_a) = c_plus(c_NatArith_Oof__nat(V_m,T_a),c_NatArith_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_NatArith_Oof__nat__diff_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| c_NatArith_Oof__nat(c_minus(V_m,V_n,tc_nat),T_a) = c_minus(c_NatArith_Oof__nat(V_m,T_a),c_NatArith_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_NatArith_Oof__nat__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_NatArith_Oof__nat(V_m,T_a) != c_0
| V_m = c_0 ) ).
cnf(cls_NatArith_Oof__nat__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_NatArith_Oof__nat(c_0,T_a) = c_0 ) ).
cnf(cls_NatArith_Oof__nat__eq__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_NatArith_Oof__nat(V_m,T_a) != c_NatArith_Oof__nat(V_n,T_a)
| V_m = V_n ) ).
cnf(cls_NatArith_Oof__nat__le__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_lessequals(c_NatArith_Oof__nat(V_m,T_a),c_0,T_a)
| V_m = c_0 ) ).
cnf(cls_NatArith_Oof__nat__le__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_NatArith_Oof__nat(c_0,T_a),c_0,T_a) ) ).
cnf(cls_NatArith_Oof__nat__le__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_lessequals(c_NatArith_Oof__nat(V_m,T_a),c_NatArith_Oof__nat(V_n,T_a),T_a)
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_NatArith_Oof__nat__le__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(V_m,T_a),c_NatArith_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_NatArith_Oof__nat__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_less(c_NatArith_Oof__nat(V_m,T_a),c_0,T_a) ) ).
cnf(cls_NatArith_Oof__nat__less__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_less(c_NatArith_Oof__nat(V_m,T_a),c_NatArith_Oof__nat(V_n,T_a),T_a)
| c_less(V_m,V_n,tc_nat) ) ).
cnf(cls_NatArith_Oof__nat__less__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_less(V_m,V_n,tc_nat)
| c_less(c_NatArith_Oof__nat(V_m,T_a),c_NatArith_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_NatArith_Oof__nat__mult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a)
| c_NatArith_Oof__nat(c_times(V_m,V_n,tc_nat),T_a) = c_times(c_NatArith_Oof__nat(V_m,T_a),c_NatArith_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_NatBin_OSuc__nat__number__of_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_Numeral_Onumber__of(V_v,tc_nat)) = c_1 ) ).
cnf(cls_NatBin_OSuc__nat__number__of_1,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_Numeral_Onumber__of(V_v,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(V_v),tc_nat) ) ).
cnf(cls_NatBin_Oadd__nat__number__of_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat) ) ).
cnf(cls_NatBin_Oadd__nat__number__of_1,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_Numeral_Onumber__of(V_v,tc_nat) ) ).
cnf(cls_NatBin_Oadd__nat__number__of_2,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,V_v_H),tc_nat) ) ).
cnf(cls_NatBin_Odiv__nat__number__of_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_0 ) ).
cnf(cls_NatBin_Odiv__nat__number__of_1,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)) ) ).
cnf(cls_NatBin_Odvd__eq__mod__eq__0__number__of_0,axiom,
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(V_x,tc_nat),c_Numeral_Onumber__of(V_y,tc_nat),tc_nat)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_y,tc_nat),c_Numeral_Onumber__of(V_x,tc_nat),tc_nat) = c_0 ) ).
cnf(cls_NatBin_Odvd__eq__mod__eq__0__number__of_1,axiom,
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_y,tc_nat),c_Numeral_Onumber__of(V_x,tc_nat),tc_nat) != c_0
| c_Divides_Oop_Advd(c_Numeral_Onumber__of(V_x,tc_nat),c_Numeral_Onumber__of(V_y,tc_nat),tc_nat) ) ).
cnf(cls_NatBin_Oeq__0__number__of_0,axiom,
( c_0 != c_Numeral_Onumber__of(V_v,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_NatBin_Oeq__0__number__of_1,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(V_v,tc_nat) ) ).
cnf(cls_NatBin_Oeq__0__number__of_2,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(V_v,tc_nat) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) != c_Numeral_Onumber__of(V_v_H,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_1,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) != c_Numeral_Onumber__of(V_v_H,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_10,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_11,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_12,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(V_v_H)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_2,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) != c_Numeral_Onumber__of(V_v_H,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(V_v_H)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_3,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(V_v_H)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_4,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_5,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(V_v_H)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_6,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_7,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(V_v_H)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_8,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat) ) ).
cnf(cls_NatBin_Oeq__nat__number__of_9,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(V_v_H)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat) ) ).
cnf(cls_NatBin_Oeq__number__of__0_0,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) != c_0
| c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_NatBin_Oeq__number__of__0_1,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_0 ) ).
cnf(cls_NatBin_Oeq__number__of__0_2,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(V_v,tc_nat) = c_0 ) ).
cnf(cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0,axiom,
c_IntDef_Oint(c_plus(V_m,V_n,tc_nat)) = c_plus(c_IntDef_Oint(V_m),c_IntDef_Oint(V_n),tc_IntDef_Oint) ).
cnf(cls_NatBin_Oint__nat__number__of_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oint(c_Numeral_Onumber__of(V_v,tc_nat)) = c_0 ) ).
cnf(cls_NatBin_Oint__nat__number__of_1,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oint(c_Numeral_Onumber__of(V_v,tc_nat)) = c_Numeral_Onumber__of(V_v,tc_IntDef_Oint) ) ).
cnf(cls_NatBin_Oless__0__number__of_0,axiom,
( ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(V_v),tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_NatBin_Oless__0__number__of_1,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(V_v),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(V_v,tc_nat),tc_nat) ) ).
cnf(cls_NatBin_Oless__nat__number__of_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(V_v_H),tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_NatBin_Oless__nat__number__of_1,axiom,
( ~ c_less(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(V_v_H)),tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_NatBin_Oless__nat__number__of_2,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(V_v_H)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) ) ).
cnf(cls_NatBin_Oless__nat__number__of_3,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(V_v_H),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) ) ).
cnf(cls_NatBin_Oless__nat__number__of_4,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(V_v_H)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(V_v_H),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) ) ).
cnf(cls_NatBin_Omod__nat__number__of_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_0 ) ).
cnf(cls_NatBin_Omod__nat__number__of_1,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_Numeral_Onumber__of(V_v,tc_nat) ) ).
cnf(cls_NatBin_Omod__nat__number__of_2,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)) ) ).
cnf(cls_NatBin_Omult__nat__number__of_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_0 ) ).
cnf(cls_NatBin_Omult__nat__number__of_1,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(V_v,V_v_H),tc_nat) ) ).
cnf(cls_NatBin_Onat__number__of_0,axiom,
c_IntDef_Onat(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint)) = c_Numeral_Onumber__of(V_w,tc_nat) ).
cnf(cls_NatBin_Onat__numeral__0__eq__0_0,axiom,
c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0 ).
cnf(cls_NatBin_Onat__numeral__1__eq__1_0,axiom,
c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) = c_1 ).
cnf(cls_NatBin_Oof__nat__number__of__eq_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_NatArith_Oof__nat(c_Numeral_Onumber__of(V_v,tc_nat),T_a) = c_0 ) ).
cnf(cls_NatBin_Oof__nat__number__of__eq_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_NatArith_Oof__nat(c_Numeral_Onumber__of(V_v,tc_nat),T_a) = c_Numeral_Onumber__of(V_v,T_a) ) ).
cnf(cls_NatBin_Oone__div__nat__number__of_0,axiom,
c_div(c_Suc(c_0),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)) ).
cnf(cls_NatBin_Oone__mod__nat__number__of_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_Suc(c_0) ) ).
cnf(cls_NatBin_Oone__mod__nat__number__of_1,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)) ) ).
cnf(cls_NatBin_Oone__power2_0,axiom,
( ~ class_Power_Orecpower(T_a)
| c_Nat_Opower(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),T_a) = c_1 ) ).
cnf(cls_NatBin_Opower2__eq__square__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Power_Orecpower(T_b)
| c_Nat_Opower(c_Numeral_Onumber__of(V_w,T_b),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),T_b) = c_times(c_Numeral_Onumber__of(V_w,T_b),c_Numeral_Onumber__of(V_w,T_b),T_b) ) ).
cnf(cls_NatBin_Opower__minus__even_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_Nat_Opower(c_uminus(V_a,T_a),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),V_n,tc_nat),T_a) = c_Nat_Opower(V_a,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),V_n,tc_nat),T_a) ) ).
cnf(cls_NatBin_Opower__nat__number__of__number__of_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_w,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(V_w,tc_nat),tc_nat) ) ).
cnf(cls_NatBin_Opower__nat__number__of__number__of_1,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_w,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(V_w,tc_nat),tc_IntDef_Oint)) ) ).
cnf(cls_NatBin_Ozero__power2_0,axiom,
( ~ class_Power_Orecpower(T_a)
| c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),T_a) = c_0 ) ).
cnf(cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0,axiom,
c_div(c_Suc(c_Suc(c_Suc(V_m))),c_Numeral_Onumber__of(V_v,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),V_m,tc_nat),c_Numeral_Onumber__of(V_v,tc_nat),tc_nat) ).
cnf(cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0,axiom,
c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(V_m))),c_Numeral_Onumber__of(V_v,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),V_m,tc_nat),c_Numeral_Onumber__of(V_v,tc_nat),tc_nat) ).
cnf(cls_NatSimprocs_Oadd__2__eq__Suc_0,axiom,
c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),V_n,tc_nat) = c_Suc(c_Suc(V_n)) ).
cnf(cls_NatSimprocs_Oadd__2__eq__Suc_H_0,axiom,
c_plus(V_n,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_Suc(V_n)) ).
cnf(cls_NatSimprocs_Oadd__self__div__2_0,axiom,
c_div(c_plus(V_y,V_y,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = V_y ).
cnf(cls_NatSimprocs_Odiv2__Suc__Suc_0,axiom,
c_div(c_Suc(c_Suc(V_m)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(V_m,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)) ).
cnf(cls_NatSimprocs_Odiv__Suc__eq__div__add3_0,axiom,
c_div(V_m,c_Suc(c_Suc(c_Suc(V_n))),tc_nat) = c_div(V_m,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),V_n,tc_nat),tc_nat) ).
cnf(cls_NatSimprocs_Odivide__eq__eq__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Ofield(T_b)
| V_b = c_times(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_Numeral_Onumber__of(V_w,T_b) = c_0 ) ).
cnf(cls_NatSimprocs_Odivide__eq__eq__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Ofield(T_b)
| c_Numeral_Onumber__of(V_w,T_b) != c_0
| c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b) = c_0 ) ).
cnf(cls_NatSimprocs_Odivide__eq__eq__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Ofield(T_b)
| c_Numeral_Onumber__of(V_w,T_b) = c_0
| c_divide(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),c_Numeral_Onumber__of(V_w,T_b),T_b) = V_a ) ).
cnf(cls_NatSimprocs_Odivide__eq__eq__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Ofield(T_b)
| c_divide(c_times(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b),c_Numeral_Onumber__of(V_w,T_b),T_b) = c_0 ) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| c_lessequals(c_0,V_b,T_b)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| c_lessequals(V_b,c_0,T_b)
| c_lessequals(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| c_lessequals(V_b,c_0,T_b)
| c_lessequals(c_0,V_b,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(V_b,c_0,T_b)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_0,V_b,T_b)
| ~ c_lessequals(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_lessequals(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b)
| c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_lessequals(c_0,V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_0,V_a,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_0,V_a,T_b)
| ~ c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_6,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_7,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_lessequals(c_0,V_a,T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_8,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_9,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_lessequals(c_0,V_a,T_b)
| ~ c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| c_less(c_0,V_b,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| c_less(V_b,c_0,T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| c_less(V_b,c_0,T_b)
| c_less(c_0,V_b,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_b,c_0,T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,V_b,T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b)
| c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b)
| c_less(c_0,V_a,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,V_a,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_less(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,V_a,T_b)
| ~ c_less(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_6,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_7,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_less(c_0,V_a,T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_8,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_less(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_9,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_less(c_0,V_a,T_b)
| ~ c_less(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Odivide__minus1_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(V_x,c_Numeral_Onumber__of(c_Numeral_OMin,T_a),T_a) = c_uminus(V_x,T_a) ) ).
cnf(cls_NatSimprocs_Oeq__divide__eq__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Ofield(T_b)
| c_Numeral_Onumber__of(V_w,T_b) = c_0
| c_times(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),c_Numeral_Onumber__of(V_w,T_b),T_b) = V_b ) ).
cnf(cls_NatSimprocs_Oeq__divide__eq__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Ofield(T_b)
| c_Numeral_Onumber__of(V_w,T_b) != c_0
| c_0 = c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oeq__divide__eq__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Ofield(T_b)
| V_a = c_divide(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_Numeral_Onumber__of(V_w,T_b) = c_0 ) ).
cnf(cls_NatSimprocs_Oeq__divide__eq__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Ofield(T_b)
| c_0 = c_divide(c_times(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b),c_Numeral_Onumber__of(V_w,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oequation__minus__iff__1_0,axiom,
( ~ class_HOL_Oone(T_b)
| ~ class_OrderedGroup_Oab__group__add(T_b)
| c_uminus(V_b,T_b) != c_1
| V_b = c_uminus(c_1,T_b) ) ).
cnf(cls_NatSimprocs_Oequation__minus__iff__1_1,axiom,
( ~ class_HOL_Oone(T_b)
| ~ class_OrderedGroup_Oab__group__add(T_b)
| c_uminus(c_uminus(c_1,T_b),T_b) = c_1 ) ).
cnf(cls_NatSimprocs_Oequation__minus__iff__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Oab__group__add(T_b)
| c_Numeral_Onumber__of(V_v,T_b) != c_uminus(V_b,T_b)
| V_b = c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oequation__minus__iff__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Oab__group__add(T_b)
| c_Numeral_Onumber__of(V_v,T_b) = c_uminus(c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ohalf__gt__zero_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_r,T_a)
| c_less(c_0,c_divide(V_r,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),T_a),T_a),T_a) ) ).
cnf(cls_NatSimprocs_Oinverse__eq__divide__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Ofield(T_b)
| c_HOL_Oinverse(c_Numeral_Onumber__of(V_w,T_b),T_b) = c_divide(c_1,c_Numeral_Onumber__of(V_w,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ c_lessequals(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b) ) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_lessequals(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_lessequals(V_a,c_0,T_b) ) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(V_a,c_0,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_lessequals(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(V_a,c_0,T_b)
| ~ c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_6,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_lessequals(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_7,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(V_a,c_0,T_b)
| ~ c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_lessequals(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_8,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_lessequals(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_9,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(V_a,c_0,T_b)
| ~ c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_lessequals(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__minus__iff__1_0,axiom,
( ~ class_HOL_Oone(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_lessequals(c_1,c_uminus(V_b,T_b),T_b)
| c_lessequals(V_b,c_uminus(c_1,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__minus__iff__1_1,axiom,
( ~ class_HOL_Oone(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_lessequals(V_b,c_uminus(c_1,T_b),T_b)
| c_lessequals(c_1,c_uminus(V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__minus__iff__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_uminus(V_b,T_b),T_b)
| c_lessequals(V_b,c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ole__minus__iff__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_lessequals(V_b,c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),T_b)
| c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_uminus(V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oleft__diff__distrib__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oring(T_b)
| c_times(c_minus(V_a,V_b,T_b),c_Numeral_Onumber__of(V_v,T_b),T_b) = c_minus(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oleft__distrib__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Osemiring(T_b)
| c_times(c_plus(V_a,V_b,T_b),c_Numeral_Onumber__of(V_v,T_b),T_b) = c_plus(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b) ) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_less(V_a,c_0,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_a,c_0,T_b)
| c_less(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_a,c_0,T_b)
| ~ c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_less(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_6,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ c_less(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_less(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_7,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_a,c_0,T_b)
| ~ c_less(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_less(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_8,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_less(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_less(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_9,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_a,c_0,T_b)
| ~ c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_less(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| c_less(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oless__minus__iff__1_0,axiom,
( ~ class_HOL_Oone(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_less(c_1,c_uminus(V_b,T_b),T_b)
| c_less(V_b,c_uminus(c_1,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oless__minus__iff__1_1,axiom,
( ~ class_HOL_Oone(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_less(V_b,c_uminus(c_1,T_b),T_b)
| c_less(c_1,c_uminus(V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oless__minus__iff__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_less(c_Numeral_Onumber__of(V_v,T_b),c_uminus(V_b,T_b),T_b)
| c_less(V_b,c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oless__minus__iff__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_less(V_b,c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_v,T_b),c_uminus(V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ominus1__divide_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),V_x,T_a) = c_uminus(c_divide(c_1,V_x,T_a),T_a) ) ).
cnf(cls_NatSimprocs_Ominus__equation__iff__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Oab__group__add(T_b)
| c_uminus(V_a,T_b) != c_Numeral_Onumber__of(V_v,T_b)
| c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b) = V_a ) ).
cnf(cls_NatSimprocs_Ominus__equation__iff__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Oab__group__add(T_b)
| c_uminus(c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) = c_Numeral_Onumber__of(V_v,T_b) ) ).
cnf(cls_NatSimprocs_Ominus__le__iff__1_0,axiom,
( ~ class_HOL_Oone(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_lessequals(c_uminus(V_a,T_b),c_1,T_b)
| c_lessequals(c_uminus(c_1,T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Ominus__le__iff__1_1,axiom,
( ~ class_HOL_Oone(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_lessequals(c_uminus(c_1,T_b),V_a,T_b)
| c_lessequals(c_uminus(V_a,T_b),c_1,T_b) ) ).
cnf(cls_NatSimprocs_Ominus__le__iff__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_lessequals(c_uminus(V_a,T_b),c_Numeral_Onumber__of(V_v,T_b),T_b)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Ominus__le__iff__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),V_a,T_b)
| c_lessequals(c_uminus(V_a,T_b),c_Numeral_Onumber__of(V_v,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ominus__less__iff__1_0,axiom,
( ~ class_HOL_Oone(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_less(c_uminus(V_a,T_b),c_1,T_b)
| c_less(c_uminus(c_1,T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Ominus__less__iff__1_1,axiom,
( ~ class_HOL_Oone(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_less(c_uminus(c_1,T_b),V_a,T_b)
| c_less(c_uminus(V_a,T_b),c_1,T_b) ) ).
cnf(cls_NatSimprocs_Ominus__less__iff__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_less(c_uminus(V_a,T_b),c_Numeral_Onumber__of(V_v,T_b),T_b)
| c_less(c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),V_a,T_b) ) ).
cnf(cls_NatSimprocs_Ominus__less__iff__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),V_a,T_b)
| c_less(c_uminus(V_a,T_b),c_Numeral_Onumber__of(V_v,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omod2__Suc__Suc_0,axiom,
c_Divides_Oop_Amod(c_Suc(c_Suc(V_m)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Divides_Oop_Amod(V_m,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) ).
cnf(cls_NatSimprocs_Omod2__gr__0_0,axiom,
( ~ c_less(c_0,c_Divides_Oop_Amod(V_m,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
| c_Divides_Oop_Amod(V_m,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_1 ) ).
cnf(cls_NatSimprocs_Omod2__gr__0_1,axiom,
( c_Divides_Oop_Amod(V_m,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) != c_1
| c_less(c_0,c_Divides_Oop_Amod(V_m,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ) ).
cnf(cls_NatSimprocs_Omod__Suc__eq__mod__add3_0,axiom,
c_Divides_Oop_Amod(V_m,c_Suc(c_Suc(c_Suc(V_n))),tc_nat) = c_Divides_Oop_Amod(V_m,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),V_n,tc_nat),tc_nat) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b)
| c_lessequals(V_a,V_b,T_b) ) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b)
| c_lessequals(V_b,V_a,T_b) ) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| c_lessequals(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_lessequals(V_b,V_a,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| c_lessequals(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_lessequals(V_a,V_b,T_b)
| c_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| c_lessequals(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_lessequals(V_b,V_a,T_b)
| ~ c_lessequals(V_a,V_b,T_b)
| c_lessequals(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| ~ c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b)
| c_lessequals(V_a,V_b,T_b) ) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| ~ c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b)
| c_lessequals(V_b,V_a,T_b) ) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_lessequals(V_b,V_a,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_lessequals(V_a,V_b,T_b)
| c_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_lessequals(V_b,V_a,T_b)
| ~ c_lessequals(V_a,V_b,T_b)
| c_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| c_less(V_a,V_b,T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b)
| ~ c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| c_less(V_b,V_a,T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| c_less(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(V_b,V_a,T_b)
| c_less(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(V_a,V_b,T_b)
| c_less(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b)
| c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(V_b,V_a,T_b)
| ~ c_less(V_a,V_b,T_b)
| c_less(c_times(c_Numeral_Onumber__of(V_v,T_b),V_a,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| c_less(V_a,V_b,T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b)
| ~ c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| c_less(V_b,V_a,T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| c_less(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(V_b,V_a,T_b)
| c_less(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(V_a,V_b,T_b)
| c_less(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b)
| c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ c_less(V_b,V_a,T_b)
| ~ c_less(V_a,V_b,T_b)
| c_less(c_times(V_a,c_Numeral_Onumber__of(V_v,T_b),T_b),c_times(V_b,c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oright__diff__distrib__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Oring(T_b)
| c_times(c_Numeral_Onumber__of(V_v,T_b),c_minus(V_b,V_c,T_b),T_b) = c_minus(c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_c,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Oright__distrib__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Osemiring(T_b)
| c_times(c_Numeral_Onumber__of(V_v,T_b),c_plus(V_b,V_c,T_b),T_b) = c_plus(c_times(c_Numeral_Onumber__of(V_v,T_b),V_b,T_b),c_times(c_Numeral_Onumber__of(V_v,T_b),V_c,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| c_lessequals(V_b,c_0,T_b)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| c_lessequals(c_0,V_b,T_b)
| c_lessequals(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| c_lessequals(V_b,c_0,T_b)
| c_lessequals(c_0,V_b,T_b) ) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(c_0,V_b,T_b)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_lessequals(V_b,c_0,T_b)
| ~ c_lessequals(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_0,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_1,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| c_less(V_b,c_0,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_2,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| c_less(c_0,V_b,T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b) ) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_3,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| c_less(V_b,c_0,T_b)
| c_less(c_0,V_b,T_b) ) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_4,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(c_0,V_b,T_b)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b) ) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_5,axiom,
( ~ class_Numeral_Onumber(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ c_less(V_b,c_0,T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b) ) ).
cnf(cls_Nat_OOne__nat__def_0,axiom,
c_1 = c_Suc(c_0) ).
cnf(cls_Nat_OSuc__Suc__eq_0,axiom,
( c_Suc(V_m) != c_Suc(V_n)
| V_m = V_n ) ).
cnf(cls_Nat_OSuc__diff__diff_0,axiom,
c_minus(c_minus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat) = c_minus(c_minus(V_m,V_n,tc_nat),V_k,tc_nat) ).
cnf(cls_Nat_OSuc__le__mono_0,axiom,
( ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat)
| c_lessequals(V_n,V_m,tc_nat) ) ).
cnf(cls_Nat_OSuc__le__mono_1,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) ).
cnf(cls_Nat_OSuc__less__eq_0,axiom,
( ~ c_less(c_Suc(V_m),c_Suc(V_n),tc_nat)
| c_less(V_m,V_n,tc_nat) ) ).
cnf(cls_Nat_OSuc__less__eq_1,axiom,
( ~ c_less(V_m,V_n,tc_nat)
| c_less(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ).
cnf(cls_Nat_OSuc__not__Zero_0,axiom,
c_Suc(V_m) != c_0 ).
cnf(cls_Nat_OSuc__pred_0,axiom,
( ~ c_less(c_0,V_y,tc_nat)
| c_Suc(c_minus(V_y,c_Suc(c_0),tc_nat)) = V_y ) ).
cnf(cls_Nat_OZero__not__Suc_0,axiom,
c_0 != c_Suc(V_m) ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
c_plus(V_y,c_0,tc_nat) = V_y ).
cnf(cls_Nat_Oadd__Suc__right_0,axiom,
c_plus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_plus(V_m,V_n,tc_nat)) ).
cnf(cls_Nat_Oadd__gr__0_0,axiom,
( ~ c_less(c_0,c_plus(V_m,V_n,tc_nat),tc_nat)
| c_less(c_0,V_n,tc_nat)
| c_less(c_0,V_m,tc_nat) ) ).
cnf(cls_Nat_Oadd__gr__0_1,axiom,
( ~ c_less(c_0,V_m,tc_nat)
| c_less(c_0,c_plus(V_m,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Oadd__gr__0_2,axiom,
( ~ c_less(c_0,V_n,tc_nat)
| c_less(c_0,c_plus(V_m,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Oadd__is__0_0,axiom,
( c_plus(V_m,V_n,tc_nat) != c_0
| V_m = c_0 ) ).
cnf(cls_Nat_Oadd__is__0_1,axiom,
( c_plus(V_m,V_n,tc_nat) != c_0
| V_n = c_0 ) ).
cnf(cls_Nat_Oadd__is__0_2,axiom,
c_plus(c_0,c_0,tc_nat) = c_0 ).
cnf(cls_Nat_Odiff__0__eq__0_0,axiom,
c_minus(c_0,V_n,tc_nat) = c_0 ).
cnf(cls_Nat_Odiff__Suc__Suc_0,axiom,
c_minus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_minus(V_m,V_n,tc_nat) ).
cnf(cls_Nat_Odiff__Suc__less_0,axiom,
( ~ c_less(c_0,V_n,tc_nat)
| c_less(c_minus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat) ) ).
cnf(cls_Nat_Odiff__diff__left_0,axiom,
c_minus(c_minus(V_i,V_j,tc_nat),V_k,tc_nat) = c_minus(V_i,c_plus(V_j,V_k,tc_nat),tc_nat) ).
cnf(cls_Nat_Odiff__is__0__eq_0,axiom,
( c_minus(V_m,V_n,tc_nat) != c_0
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_Nat_Odiff__is__0__eq_H_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_minus(V_m,V_n,tc_nat) = c_0 ) ).
cnf(cls_Nat_Odiff__le__self_0,axiom,
c_lessequals(c_minus(V_m,V_n,tc_nat),V_m,tc_nat) ).
cnf(cls_Nat_Odiff__self__eq__0_0,axiom,
c_minus(V_m,V_m,tc_nat) = c_0 ).
cnf(cls_Nat_Ole__0__eq_0,axiom,
( ~ c_lessequals(V_i,c_0,tc_nat)
| V_i = c_0 ) ).
cnf(cls_Nat_Ole__0__eq_1,axiom,
c_lessequals(c_0,c_0,tc_nat) ).
cnf(cls_Nat_Ole__add__diff__inverse2_0,axiom,
( ~ c_lessequals(V_n,V_y,tc_nat)
| c_plus(c_minus(V_y,V_n,tc_nat),V_n,tc_nat) = V_y ) ).
cnf(cls_Nat_Ole__add__diff__inverse_0,axiom,
( ~ c_lessequals(V_n,V_y,tc_nat)
| c_plus(V_n,c_minus(V_y,V_n,tc_nat),tc_nat) = V_y ) ).
cnf(cls_Nat_Oless__Suc0_0,axiom,
( ~ c_less(V_n,c_Suc(c_0),tc_nat)
| V_n = c_0 ) ).
cnf(cls_Nat_Oless__Suc0_1,axiom,
c_less(c_0,c_Suc(c_0),tc_nat) ).
cnf(cls_Nat_Oless__one_0,axiom,
( ~ c_less(V_n,c_1,tc_nat)
| V_n = c_0 ) ).
cnf(cls_Nat_Oless__one_1,axiom,
c_less(c_0,c_1,tc_nat) ).
cnf(cls_Nat_Omax__0L_0,axiom,
c_Orderings_Omax(c_0,V_y,tc_nat) = V_y ).
cnf(cls_Nat_Omax__0R_0,axiom,
c_Orderings_Omax(V_y,c_0,tc_nat) = V_y ).
cnf(cls_Nat_Omax__Suc__Suc_0,axiom,
c_Orderings_Omax(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Omax(V_m,V_n,tc_nat)) ).
cnf(cls_Nat_Omin__0L_0,axiom,
c_Orderings_Omin(c_0,V_n,tc_nat) = c_0 ).
cnf(cls_Nat_Omin__0R_0,axiom,
c_Orderings_Omin(V_n,c_0,tc_nat) = c_0 ).
cnf(cls_Nat_Omin__Suc__Suc_0,axiom,
c_Orderings_Omin(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Omin(V_m,V_n,tc_nat)) ).
cnf(cls_Nat_Omult__0__right_0,axiom,
c_times(V_m,c_0,tc_nat) = c_0 ).
cnf(cls_Nat_Omult__Suc__right_0,axiom,
c_times(V_m,c_Suc(V_n),tc_nat) = c_plus(V_m,c_times(V_m,V_n,tc_nat),tc_nat) ).
cnf(cls_Nat_Omult__cancel1_0,axiom,
( c_times(V_k,V_m,tc_nat) != c_times(V_k,V_n,tc_nat)
| V_m = V_n
| V_k = c_0 ) ).
cnf(cls_Nat_Omult__cancel1_1,axiom,
c_times(c_0,V_m,tc_nat) = c_times(c_0,V_n,tc_nat) ).
cnf(cls_Nat_Omult__cancel2_0,axiom,
( c_times(V_m,V_k,tc_nat) != c_times(V_n,V_k,tc_nat)
| V_m = V_n
| V_k = c_0 ) ).
cnf(cls_Nat_Omult__cancel2_1,axiom,
c_times(V_m,c_0,tc_nat) = c_times(V_n,c_0,tc_nat) ).
cnf(cls_Nat_Omult__eq__1__iff_0,axiom,
( c_times(V_m,V_n,tc_nat) != c_Suc(c_0)
| V_m = c_1 ) ).
cnf(cls_Nat_Omult__eq__1__iff_1,axiom,
( c_times(V_m,V_n,tc_nat) != c_Suc(c_0)
| V_n = c_1 ) ).
cnf(cls_Nat_Omult__eq__1__iff_2,axiom,
c_times(c_1,c_1,tc_nat) = c_Suc(c_0) ).
cnf(cls_Nat_Omult__is__0_0,axiom,
( c_times(V_m,V_n,tc_nat) != c_0
| V_n = c_0
| V_m = c_0 ) ).
cnf(cls_Nat_Omult__le__cancel1_0,axiom,
( ~ c_less(c_0,V_k,tc_nat)
| ~ c_lessequals(c_times(V_k,V_m,tc_nat),c_times(V_k,V_n,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_Nat_Omult__le__cancel1_1,axiom,
( c_less(c_0,V_k,tc_nat)
| c_lessequals(c_times(V_k,V_m,tc_nat),c_times(V_k,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Omult__le__cancel1_2,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_times(V_k,V_m,tc_nat),c_times(V_k,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Omult__le__cancel2_0,axiom,
( ~ c_less(c_0,V_k,tc_nat)
| ~ c_lessequals(c_times(V_m,V_k,tc_nat),c_times(V_n,V_k,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_Nat_Omult__le__cancel2_1,axiom,
( c_less(c_0,V_k,tc_nat)
| c_lessequals(c_times(V_m,V_k,tc_nat),c_times(V_n,V_k,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Omult__le__cancel2_2,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_times(V_m,V_k,tc_nat),c_times(V_n,V_k,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Omult__less__cancel1_0,axiom,
( ~ c_less(c_times(V_k,V_m,tc_nat),c_times(V_k,V_n,tc_nat),tc_nat)
| c_less(c_0,V_k,tc_nat) ) ).
cnf(cls_Nat_Omult__less__cancel1_1,axiom,
( ~ c_less(c_times(V_k,V_m,tc_nat),c_times(V_k,V_n,tc_nat),tc_nat)
| c_less(V_m,V_n,tc_nat) ) ).
cnf(cls_Nat_Omult__less__cancel1_2,axiom,
( ~ c_less(V_m,V_n,tc_nat)
| ~ c_less(c_0,V_k,tc_nat)
| c_less(c_times(V_k,V_m,tc_nat),c_times(V_k,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Omult__less__cancel2_0,axiom,
( ~ c_less(c_times(V_m,V_k,tc_nat),c_times(V_n,V_k,tc_nat),tc_nat)
| c_less(c_0,V_k,tc_nat) ) ).
cnf(cls_Nat_Omult__less__cancel2_1,axiom,
( ~ c_less(c_times(V_m,V_k,tc_nat),c_times(V_n,V_k,tc_nat),tc_nat)
| c_less(V_m,V_n,tc_nat) ) ).
cnf(cls_Nat_Omult__less__cancel2_2,axiom,
( ~ c_less(V_m,V_n,tc_nat)
| ~ c_less(c_0,V_k,tc_nat)
| c_less(c_times(V_m,V_k,tc_nat),c_times(V_n,V_k,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Onat__0__less__mult__iff_0,axiom,
( ~ c_less(c_0,c_times(V_m,V_n,tc_nat),tc_nat)
| c_less(c_0,V_m,tc_nat) ) ).
cnf(cls_Nat_Onat__0__less__mult__iff_1,axiom,
( ~ c_less(c_0,c_times(V_m,V_n,tc_nat),tc_nat)
| c_less(c_0,V_n,tc_nat) ) ).
cnf(cls_Nat_Onat__0__less__mult__iff_2,axiom,
( ~ c_less(c_0,V_n,tc_nat)
| ~ c_less(c_0,V_m,tc_nat)
| c_less(c_0,c_times(V_m,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Onat__add__left__cancel_0,axiom,
( c_plus(V_k,V_m,tc_nat) != c_plus(V_k,V_n,tc_nat)
| V_m = V_n ) ).
cnf(cls_Nat_Onat__add__left__cancel__le_0,axiom,
( ~ c_lessequals(c_plus(V_k,V_m,tc_nat),c_plus(V_k,V_n,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_Nat_Onat__add__left__cancel__le_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_plus(V_k,V_m,tc_nat),c_plus(V_k,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Onat__add__left__cancel__less_0,axiom,
( ~ c_less(c_plus(V_k,V_m,tc_nat),c_plus(V_k,V_n,tc_nat),tc_nat)
| c_less(V_m,V_n,tc_nat) ) ).
cnf(cls_Nat_Onat__add__left__cancel__less_1,axiom,
( ~ c_less(V_m,V_n,tc_nat)
| c_less(c_plus(V_k,V_m,tc_nat),c_plus(V_k,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Onat__add__right__cancel_0,axiom,
( c_plus(V_m,V_k,tc_nat) != c_plus(V_n,V_k,tc_nat)
| V_m = V_n ) ).
cnf(cls_Nat_Onot__add__less1_0,axiom,
~ c_less(c_plus(V_i,V_j,tc_nat),V_i,tc_nat) ).
cnf(cls_Nat_Onot__add__less2_0,axiom,
~ c_less(c_plus(V_j,V_i,tc_nat),V_i,tc_nat) ).
cnf(cls_Nat_Onot__gr0_0,axiom,
( c_less(c_0,V_n,tc_nat)
| V_n = c_0 ) ).
cnf(cls_Nat_Onot__gr0_1,axiom,
~ c_less(c_0,c_0,tc_nat) ).
cnf(cls_Nat_Onot__less0_0,axiom,
~ c_less(V_n,c_0,tc_nat) ).
cnf(cls_Nat_Oone__eq__mult__iff_0,axiom,
( c_Suc(c_0) != c_times(V_m,V_n,tc_nat)
| V_m = c_1 ) ).
cnf(cls_Nat_Oone__eq__mult__iff_1,axiom,
( c_Suc(c_0) != c_times(V_m,V_n,tc_nat)
| V_n = c_1 ) ).
cnf(cls_Nat_Oone__eq__mult__iff_2,axiom,
c_Suc(c_0) = c_times(c_1,c_1,tc_nat) ).
cnf(cls_Nat_Oone__le__mult__iff_0,axiom,
( ~ c_lessequals(c_Suc(c_0),c_times(V_m,V_n,tc_nat),tc_nat)
| c_lessequals(c_1,V_m,tc_nat) ) ).
cnf(cls_Nat_Oone__le__mult__iff_1,axiom,
( ~ c_lessequals(c_Suc(c_0),c_times(V_m,V_n,tc_nat),tc_nat)
| c_lessequals(c_1,V_n,tc_nat) ) ).
cnf(cls_Nat_Oone__le__mult__iff_2,axiom,
( ~ c_lessequals(c_1,V_n,tc_nat)
| ~ c_lessequals(c_1,V_m,tc_nat)
| c_lessequals(c_Suc(c_0),c_times(V_m,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Nat_Oop_A_K_Omult__0_0,axiom,
c_times(c_0,V_n,tc_nat) = c_0 ).
cnf(cls_Nat_Oop_A_K_Omult__Suc_0,axiom,
c_times(c_Suc(V_m),V_n,tc_nat) = c_plus(V_n,c_times(V_m,V_n,tc_nat),tc_nat) ).
cnf(cls_Nat_Oop_A_L_Oadd__0_0,axiom,
c_plus(c_0,V_y,tc_nat) = V_y ).
cnf(cls_Nat_Oop_A_L_Oadd__Suc_0,axiom,
c_plus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_plus(V_m,V_n,tc_nat)) ).
cnf(cls_Nat_Oop_A_N_Odiff__0_0,axiom,
c_minus(V_y,c_0,tc_nat) = V_y ).
cnf(cls_Nat_Ozero__less__diff_0,axiom,
( ~ c_less(c_0,c_minus(V_n,V_m,tc_nat),tc_nat)
| c_less(V_m,V_n,tc_nat) ) ).
cnf(cls_Nat_Ozero__less__diff_1,axiom,
( ~ c_less(V_m,V_n,tc_nat)
| c_less(c_0,c_minus(V_n,V_m,tc_nat),tc_nat) ) ).
cnf(cls_Numeral_OMin__1__eq_0,axiom,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_OMin ).
cnf(cls_Numeral_OPls__0__eq_0,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_OPls ).
cnf(cls_Numeral_Oadd__number__of__diff2_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_plus(c_Numeral_Onumber__of(V_v,T_a),c_minus(V_c,c_Numeral_Onumber__of(V_w,T_a),T_a),T_a) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(V_w)),T_a),V_c,T_a) ) ).
cnf(cls_Numeral_Oadd__number__of__left_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_plus(c_Numeral_Onumber__of(V_v,T_a),c_plus(c_Numeral_Onumber__of(V_w,T_a),V_z,T_a),T_a) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,V_w),T_a),V_z,T_a) ) ).
cnf(cls_Numeral_Obin__add__BIT__0_0,axiom,
c_Numeral_Obin__add(c_Numeral_OBit(V_v,c_Numeral_Obit_OB0),c_Numeral_OBit(V_w,V_y)) = c_Numeral_OBit(c_Numeral_Obin__add(V_v,V_w),V_y) ).
cnf(cls_Numeral_Obin__add__BIT__10_0,axiom,
c_Numeral_Obin__add(c_Numeral_OBit(V_v,c_Numeral_Obit_OB1),c_Numeral_OBit(V_w,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(V_v,V_w),c_Numeral_Obit_OB1) ).
cnf(cls_Numeral_Obin__add__BIT__11_0,axiom,
c_Numeral_Obin__add(c_Numeral_OBit(V_v,c_Numeral_Obit_OB1),c_Numeral_OBit(V_w,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(V_v,c_Numeral_Obin__succ(V_w)),c_Numeral_Obit_OB0) ).
cnf(cls_Numeral_Obin__add__Min_0,axiom,
c_Numeral_Obin__add(c_Numeral_OMin,V_w) = c_Numeral_Obin__pred(V_w) ).
cnf(cls_Numeral_Obin__add__Min__right_0,axiom,
c_Numeral_Obin__add(V_w,c_Numeral_OMin) = c_Numeral_Obin__pred(V_w) ).
cnf(cls_Numeral_Obin__add__Pls_0,axiom,
c_Numeral_Obin__add(c_Numeral_OPls,V_y) = V_y ).
cnf(cls_Numeral_Obin__add__Pls__right_0,axiom,
c_Numeral_Obin__add(V_y,c_Numeral_OPls) = V_y ).
cnf(cls_Numeral_Obin__arith__extra__simps__1_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_plus(c_Numeral_Onumber__of(V_v,T_a),c_Numeral_Onumber__of(V_w,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,V_w),T_a) ) ).
cnf(cls_Numeral_Obin__arith__extra__simps__2_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_uminus(c_Numeral_Onumber__of(V_w,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(V_w),T_a) ) ).
cnf(cls_Numeral_Obin__arith__extra__simps__3_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_uminus(c_1,T_a) = c_Numeral_Onumber__of(c_Numeral_OMin,T_a) ) ).
cnf(cls_Numeral_Obin__arith__extra__simps__4_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_times(c_Numeral_Onumber__of(V_v,T_a),c_Numeral_Onumber__of(V_w,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(V_v,V_w),T_a) ) ).
cnf(cls_Numeral_Obin__arith__extra__simps__5_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_minus(c_Numeral_Onumber__of(V_v,T_a),c_Numeral_Onumber__of(V_w,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_Obin__add(V_v,c_Numeral_Obin__minus(V_w)),T_a) ) ).
cnf(cls_Numeral_Obin__arith__extra__simps__6_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_Numeral_Onumber__of(V_x,T_a),c_0,T_a)
| c_HOL_Oabs(c_Numeral_Onumber__of(V_x,T_a),T_a) = c_uminus(c_Numeral_Onumber__of(V_x,T_a),T_a) ) ).
cnf(cls_Numeral_Obin__arith__extra__simps__6_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_less(c_Numeral_Onumber__of(V_x,T_a),c_0,T_a)
| c_HOL_Oabs(c_Numeral_Onumber__of(V_x,T_a),T_a) = c_Numeral_Onumber__of(V_x,T_a) ) ).
cnf(cls_Numeral_Obin__minus__0_0,axiom,
c_Numeral_Obin__minus(c_Numeral_OBit(V_w,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(V_w),c_Numeral_Obit_OB0) ).
cnf(cls_Numeral_Obin__minus__1_0,axiom,
c_Numeral_Obin__minus(c_Numeral_OBit(V_w,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(V_w)),c_Numeral_Obit_OB1) ).
cnf(cls_Numeral_Obin__minus__Min_0,axiom,
c_Numeral_Obin__minus(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) ).
cnf(cls_Numeral_Obin__minus__Pls_0,axiom,
c_Numeral_Obin__minus(c_Numeral_OPls) = c_Numeral_OPls ).
cnf(cls_Numeral_Obin__mult__0_0,axiom,
c_Numeral_Obin__mult(c_Numeral_OBit(V_v,c_Numeral_Obit_OB0),V_w) = c_Numeral_OBit(c_Numeral_Obin__mult(V_v,V_w),c_Numeral_Obit_OB0) ).
cnf(cls_Numeral_Obin__mult__1_0,axiom,
c_Numeral_Obin__mult(c_Numeral_OBit(V_v,c_Numeral_Obit_OB1),V_w) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(V_v,V_w),c_Numeral_Obit_OB0),V_w) ).
cnf(cls_Numeral_Obin__mult__Min_0,axiom,
c_Numeral_Obin__mult(c_Numeral_OMin,V_w) = c_Numeral_Obin__minus(V_w) ).
cnf(cls_Numeral_Obin__mult__Pls_0,axiom,
c_Numeral_Obin__mult(c_Numeral_OPls,V_w) = c_Numeral_OPls ).
cnf(cls_Numeral_Obin__pred__0_0,axiom,
c_Numeral_Obin__pred(c_Numeral_OBit(V_w,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(V_w),c_Numeral_Obit_OB1) ).
cnf(cls_Numeral_Obin__pred__1_0,axiom,
c_Numeral_Obin__pred(c_Numeral_OBit(V_w,c_Numeral_Obit_OB1)) = c_Numeral_OBit(V_w,c_Numeral_Obit_OB0) ).
cnf(cls_Numeral_Obin__pred__Min_0,axiom,
c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) ).
cnf(cls_Numeral_Obin__pred__Pls_0,axiom,
c_Numeral_Obin__pred(c_Numeral_OPls) = c_Numeral_OMin ).
cnf(cls_Numeral_Obin__rel__simps__10_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a)
| ~ c_IntDef_Oiszero(c_1,T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__11_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__12_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(V_w,V_x),T_a),T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__12_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_w,T_a),T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(V_w,V_x),T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__13_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_y,c_Numeral_Obin__minus(V_x)),T_a),T_a)
| ~ c_lessequals(c_Numeral_Onumber__of(V_x,T_a),c_Numeral_Onumber__of(V_y,T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__13_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_y,c_Numeral_Obin__minus(V_x)),T_a),T_a)
| c_lessequals(c_Numeral_Onumber__of(V_x,T_a),c_Numeral_Onumber__of(V_y,T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__1_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_Numeral_Onumber__of(V_x,T_a) != c_Numeral_Onumber__of(V_y,T_a)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(V_y)),T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__1_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(V_y)),T_a),T_a)
| c_Numeral_Onumber__of(V_x,T_a) = c_Numeral_Onumber__of(V_y,T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__2_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__3_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__4_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(V_w,c_Numeral_Obit_OB0),T_a),T_a)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__4_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_w,T_a),T_a)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(V_w,c_Numeral_Obit_OB0),T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__5_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(V_w,c_Numeral_Obit_OB1),T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__6_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_Numeral_Onumber__of(V_x,T_a),c_Numeral_Onumber__of(V_y,T_a),T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(V_y)),T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__6_1,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_x,c_Numeral_Obin__minus(V_y)),T_a),T_a)
| c_less(c_Numeral_Onumber__of(V_x,T_a),c_Numeral_Onumber__of(V_y,T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__7_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,T_a),T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__8_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_0,T_a) ) ).
cnf(cls_Numeral_Obin__rel__simps__9_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_IntDef_Oneg(c_1,T_a) ) ).
cnf(cls_Numeral_Obin__succ__0_0,axiom,
c_Numeral_Obin__succ(c_Numeral_OBit(V_w,c_Numeral_Obit_OB0)) = c_Numeral_OBit(V_w,c_Numeral_Obit_OB1) ).
cnf(cls_Numeral_Obin__succ__1_0,axiom,
c_Numeral_Obin__succ(c_Numeral_OBit(V_w,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(V_w),c_Numeral_Obit_OB0) ).
cnf(cls_Numeral_Obin__succ__Min_0,axiom,
c_Numeral_Obin__succ(c_Numeral_OMin) = c_Numeral_OPls ).
cnf(cls_Numeral_Obin__succ__Pls_0,axiom,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) ).
cnf(cls_Numeral_Obit_Ocases__1_0,axiom,
c_Numeral_Obit_Obit__case(V_y,V_f2,c_Numeral_Obit_OB0,T_a) = V_y ).
cnf(cls_Numeral_Obit_Ocases__2_0,axiom,
c_Numeral_Obit_Obit__case(V_f1,V_y,c_Numeral_Obit_OB1,T_a) = V_y ).
cnf(cls_Numeral_Obit_Odistinct__1_0,axiom,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1 ).
cnf(cls_Numeral_Obit_Odistinct__2_0,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0 ).
cnf(cls_Numeral_Obit_Orecs__1_0,axiom,
c_Numeral_Obit_Obit__rec(V_y,V_f2,c_Numeral_Obit_OB0,T_a) = V_y ).
cnf(cls_Numeral_Obit_Orecs__2_0,axiom,
c_Numeral_Obit_Obit__rec(V_f1,V_y,c_Numeral_Obit_OB1,T_a) = V_y ).
cnf(cls_Numeral_Obit_Osize__1_0,axiom,
c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) = c_0 ).
cnf(cls_Numeral_Obit_Osize__2_0,axiom,
c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) = c_0 ).
cnf(cls_Numeral_Ominus__number__of__mult_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_times(c_uminus(c_Numeral_Onumber__of(V_w,T_a),T_a),V_z,T_a) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(V_w),T_a),V_z,T_a) ) ).
cnf(cls_Numeral_Omult__minus1_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),V_z,T_a) = c_uminus(V_z,T_a) ) ).
cnf(cls_Numeral_Omult__minus1__right_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_times(V_z,c_Numeral_Onumber__of(c_Numeral_OMin,T_a),T_a) = c_uminus(V_z,T_a) ) ).
cnf(cls_Numeral_Omult__number__of__left_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_times(c_Numeral_Onumber__of(V_v,T_a),c_times(c_Numeral_Onumber__of(V_w,T_a),V_z,T_a),T_a) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(V_v,V_w),T_a),V_z,T_a) ) ).
cnf(cls_Numeral_Onumeral__0__eq__0_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_Numeral_Onumber__of(c_Numeral_OPls,T_a) = c_0 ) ).
cnf(cls_Numeral_Onumeral__1__eq__1_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),T_a) = c_1 ) ).
cnf(cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_plus(c_uminus(V_a,T_a),V_a,T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Oabs__0__eq_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_0 != c_HOL_Oabs(V_a,T_a)
| V_a = c_0 ) ).
cnf(cls_OrderedGroup_Oabs__0__eq_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_0 = c_HOL_Oabs(c_0,T_a) ) ).
cnf(cls_OrderedGroup_Oabs__add__abs_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_HOL_Oabs(c_plus(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),T_a) = c_plus(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oabs__eq__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_HOL_Oabs(V_a,T_a) != c_0
| V_a = c_0 ) ).
cnf(cls_OrderedGroup_Oabs__eq__0_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_HOL_Oabs(c_0,T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oabs__idempotent_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_HOL_Oabs(c_HOL_Oabs(V_a,T_a),T_a) = c_HOL_Oabs(V_a,T_a) ) ).
cnf(cls_OrderedGroup_Oabs__le__zero__iff_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_HOL_Oabs(V_a,T_a),c_0,T_a)
| V_a = c_0 ) ).
cnf(cls_OrderedGroup_Oabs__le__zero__iff_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_HOL_Oabs(c_0,T_a),c_0,T_a) ) ).
cnf(cls_OrderedGroup_Oabs__minus__cancel_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_HOL_Oabs(c_uminus(V_a,T_a),T_a) = c_HOL_Oabs(V_a,T_a) ) ).
cnf(cls_OrderedGroup_Oabs__not__less__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_less(c_HOL_Oabs(V_a,T_a),c_0,T_a) ) ).
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_0,V_y,T_a)
| c_HOL_Oabs(V_y,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Oabs__of__nonpos_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(V_a,c_0,T_a)
| c_HOL_Oabs(V_a,T_a) = c_uminus(V_a,T_a) ) ).
cnf(cls_OrderedGroup_Oadd__0__right_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_plus(V_y,c_0,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Oadd__le__cancel__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_lessequals(c_plus(V_c,V_a,T_a),c_plus(V_c,V_b,T_a),T_a)
| c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_OrderedGroup_Oadd__le__cancel__left_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_plus(V_c,V_a,T_a),c_plus(V_c,V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oadd__le__cancel__right_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_OrderedGroup_Oadd__le__cancel__right_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oadd__left__cancel_0,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
| c_plus(V_a,V_b,T_a) != c_plus(V_a,V_c,T_a)
| V_b = V_c ) ).
cnf(cls_OrderedGroup_Oadd__less__cancel__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_less(c_plus(V_c,V_a,T_a),c_plus(V_c,V_b,T_a),T_a)
| c_less(V_a,V_b,T_a) ) ).
cnf(cls_OrderedGroup_Oadd__less__cancel__left_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_less(V_a,V_b,T_a)
| c_less(c_plus(V_c,V_a,T_a),c_plus(V_c,V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oadd__less__cancel__right_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_less(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| c_less(V_a,V_b,T_a) ) ).
cnf(cls_OrderedGroup_Oadd__less__cancel__right_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_less(V_a,V_b,T_a)
| c_less(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oadd__right__cancel_0,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
| c_plus(V_b,V_a,T_a) != c_plus(V_c,V_a,T_a)
| V_b = V_c ) ).
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_plus(c_0,V_y,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Odiff__0_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_minus(c_0,V_a,T_a) = c_uminus(V_a,T_a) ) ).
cnf(cls_OrderedGroup_Odiff__0__right_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_minus(V_y,c_0,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Odiff__eq__0__iff__eq_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_minus(V_a,V_b,T_a) != c_0
| V_a = V_b ) ).
cnf(cls_OrderedGroup_Odiff__le__0__iff__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_OrderedGroup_Odiff__le__0__iff__le_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a) ) ).
cnf(cls_OrderedGroup_Odiff__less__0__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a)
| c_less(V_a,V_b,T_a) ) ).
cnf(cls_OrderedGroup_Odiff__less__0__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(V_a,V_b,T_a)
| c_less(c_minus(V_a,V_b,T_a),c_0,T_a) ) ).
cnf(cls_OrderedGroup_Odiff__minus__eq__add_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) ).
cnf(cls_OrderedGroup_Odiff__self_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_minus(V_a,V_a,T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| ~ c_lessequals(c_plus(V_a,V_a,T_a),c_0,T_a)
| c_lessequals(V_a,c_0,T_a) ) ).
cnf(cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| ~ c_lessequals(V_a,c_0,T_a)
| c_lessequals(c_plus(V_a,V_a,T_a),c_0,T_a) ) ).
cnf(cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ class_Orderings_Olinorder(T_a)
| ~ c_less(c_plus(V_a,V_a,T_a),c_0,T_a)
| c_less(V_a,c_0,T_a) ) ).
cnf(cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ class_Orderings_Olinorder(T_a)
| ~ c_less(V_a,c_0,T_a)
| c_less(c_plus(V_a,V_a,T_a),c_0,T_a) ) ).
cnf(cls_OrderedGroup_Ojoin__0__eq__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| c_LOrder_Ojoin(V_a,c_uminus(V_a,T_a),T_a) != c_0
| V_a = c_0 ) ).
cnf(cls_OrderedGroup_Ojoin__0__eq__0_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| c_LOrder_Ojoin(c_0,c_uminus(c_0,T_a),T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Omeet__0__eq__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| c_LOrder_Omeet(V_a,c_uminus(V_a,T_a),T_a) != c_0
| V_a = c_0 ) ).
cnf(cls_OrderedGroup_Omeet__0__eq__0_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| c_LOrder_Omeet(c_0,c_uminus(c_0,T_a),T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Ominus__add__distrib_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Ominus__diff__eq_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) ).
cnf(cls_OrderedGroup_Ominus__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) ).
cnf(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_times(c_1,V_y,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_times(V_y,c_1,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Oneg__0__equal__iff__equal_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_0 != c_uminus(V_a,T_a)
| c_0 = V_a ) ).
cnf(cls_OrderedGroup_Oneg__0__equal__iff__equal_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_0 = c_uminus(c_0,T_a) ) ).
cnf(cls_OrderedGroup_Oneg__0__le__iff__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_0,c_uminus(V_a,T_a),T_a)
| c_lessequals(V_a,c_0,T_a) ) ).
cnf(cls_OrderedGroup_Oneg__0__le__iff__le_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_0,T_a)
| c_lessequals(c_0,c_uminus(V_a,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oneg__0__less__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_0,c_uminus(V_a,T_a),T_a)
| c_less(V_a,c_0,T_a) ) ).
cnf(cls_OrderedGroup_Oneg__0__less__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(V_a,c_0,T_a)
| c_less(c_0,c_uminus(V_a,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oneg__equal__0__iff__equal_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_uminus(V_a,T_a) != c_0
| V_a = c_0 ) ).
cnf(cls_OrderedGroup_Oneg__equal__0__iff__equal_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_uminus(c_0,T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Oneg__equal__iff__equal_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_uminus(V_a,T_a) != c_uminus(V_b,T_a)
| V_a = V_b ) ).
cnf(cls_OrderedGroup_Oneg__join__eq__meet_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| c_uminus(c_LOrder_Ojoin(V_a,V_b,T_a),T_a) = c_LOrder_Omeet(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oneg__le__0__iff__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_uminus(V_a,T_a),c_0,T_a)
| c_lessequals(c_0,V_a,T_a) ) ).
cnf(cls_OrderedGroup_Oneg__le__0__iff__le_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_uminus(V_a,T_a),c_0,T_a) ) ).
cnf(cls_OrderedGroup_Oneg__le__iff__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a)
| c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_OrderedGroup_Oneg__le__iff__le_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oneg__less__0__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_uminus(V_a,T_a),c_0,T_a)
| c_less(c_0,V_a,T_a) ) ).
cnf(cls_OrderedGroup_Oneg__less__0__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_0,V_a,T_a)
| c_less(c_uminus(V_a,T_a),c_0,T_a) ) ).
cnf(cls_OrderedGroup_Oneg__less__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a)
| c_less(V_a,V_b,T_a) ) ).
cnf(cls_OrderedGroup_Oneg__less__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(V_a,V_b,T_a)
| c_less(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oneg__meet__eq__join_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| c_uminus(c_LOrder_Omeet(V_a,V_b,T_a),T_a) = c_LOrder_Ojoin(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Onprt__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| c_OrderedGroup_Onprt(c_0,T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Onprt__eq__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| ~ c_lessequals(c_0,V_x,T_a)
| c_OrderedGroup_Onprt(V_x,T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Onprt__eq__id_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| ~ c_lessequals(V_y,c_0,T_a)
| c_OrderedGroup_Onprt(V_y,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Onprt__le__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| c_lessequals(c_OrderedGroup_Onprt(V_a,T_a),c_0,T_a) ) ).
cnf(cls_OrderedGroup_Onprt__mono_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_OrderedGroup_Onprt(V_a,T_a),c_OrderedGroup_Onprt(V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Opprt__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| c_OrderedGroup_Opprt(c_0,T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Opprt__eq__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| ~ c_lessequals(V_x,c_0,T_a)
| c_OrderedGroup_Opprt(V_x,T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Opprt__eq__id_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| ~ c_lessequals(c_0,V_y,T_a)
| c_OrderedGroup_Opprt(V_y,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Opprt__mono_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_OrderedGroup_Opprt(V_a,T_a),c_OrderedGroup_Opprt(V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oright__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| ~ c_lessequals(c_0,c_plus(V_a,V_a,T_a),T_a)
| c_lessequals(c_0,V_a,T_a) ) ).
cnf(cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_plus(V_a,V_a,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Ozero__le__pprt_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group(T_a)
| c_lessequals(c_0,c_OrderedGroup_Opprt(V_a,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Ozero__less__abs__iff_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_less(c_0,c_HOL_Oabs(c_0,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Ozero__less__abs__iff_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_less(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| V_a = c_0 ) ).
cnf(cls_Orderings_Omax__less__iff__conj_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_less(c_Orderings_Omax(V_x,V_y,T_a),V_z,T_a)
| c_less(V_x,V_z,T_a) ) ).
cnf(cls_Orderings_Omax__less__iff__conj_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_less(c_Orderings_Omax(V_x,V_y,T_a),V_z,T_a)
| c_less(V_y,V_z,T_a) ) ).
cnf(cls_Orderings_Omax__less__iff__conj_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_less(V_y,V_z,T_a)
| ~ c_less(V_x,V_z,T_a)
| c_less(c_Orderings_Omax(V_x,V_y,T_a),V_z,T_a) ) ).
cnf(cls_Orderings_Omin__less__iff__conj_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_less(V_z,c_Orderings_Omin(V_x,V_y,T_a),T_a)
| c_less(V_z,V_x,T_a) ) ).
cnf(cls_Orderings_Omin__less__iff__conj_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_less(V_z,c_Orderings_Omin(V_x,V_y,T_a),T_a)
| c_less(V_z,V_y,T_a) ) ).
cnf(cls_Orderings_Omin__less__iff__conj_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_less(V_z,V_y,T_a)
| ~ c_less(V_z,V_x,T_a)
| c_less(V_z,c_Orderings_Omin(V_x,V_y,T_a),T_a) ) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,c_Orderings_Omin(V_y,V_z,T_b),T_b)
| c_lessequals(V_x,V_y,T_b) ) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,c_Orderings_Omin(V_y,V_z,T_b),T_b)
| c_lessequals(V_x,V_z,T_b) ) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_x,V_y,T_b)
| c_lessequals(V_x,c_Orderings_Omin(V_y,V_z,T_b),T_b) ) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| c_Orderings_Omin(V_y,V_y,T_b) = V_y ) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| c_Orderings_Omin(V_x,c_Orderings_Omin(V_x,V_y,T_b),T_b) = c_Orderings_Omin(V_x,V_y,T_b) ) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| c_lessequals(V_x,V_z,T_b) ) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| c_lessequals(V_y,V_z,T_b) ) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| c_Orderings_Omax(V_y,V_y,T_b) = V_y ) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| c_Orderings_Omax(V_x,c_Orderings_Omax(V_x,V_y,T_b),T_b) = c_Orderings_Omax(V_x,V_y,T_b) ) ).
cnf(cls_Orderings_Oorder__less__irrefl_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_x,T_a) ) ).
cnf(cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0,axiom,
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(V_v,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(V_v,tc_nat)),tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1,axiom,
( ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(V_v,tc_nat)),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(V_v,tc_nat),tc_nat) ) ).
cnf(cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0,axiom,
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ) ).
cnf(cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1,axiom,
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0
| c_Parity_Oeven(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__difference_0,axiom,
( ~ c_Parity_Oeven(V_y,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(V_x,tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__difference_1,axiom,
( ~ c_Parity_Oeven(V_x,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(V_y,tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__difference_2,axiom,
( ~ c_Parity_Oeven(V_y,tc_IntDef_Oint)
| ~ c_Parity_Oeven(V_x,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__difference_3,axiom,
( c_Parity_Oeven(V_y,tc_IntDef_Oint)
| c_Parity_Oeven(V_x,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__nat__Suc_0,axiom,
( ~ c_Parity_Oeven(V_x,tc_nat)
| ~ c_Parity_Oeven(c_Suc(V_x),tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__Suc_1,axiom,
( c_Parity_Oeven(V_x,tc_nat)
| c_Parity_Oeven(c_Suc(V_x),tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__power_0,axiom,
( ~ c_Parity_Oeven(c_Nat_Opower(V_x,V_y,tc_nat),tc_nat)
| c_Parity_Oeven(V_x,tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__power_1,axiom,
( ~ c_Parity_Oeven(c_Nat_Opower(V_x,V_y,tc_nat),tc_nat)
| c_less(c_0,V_y,tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__power_2,axiom,
( ~ c_Parity_Oeven(V_x,tc_nat)
| ~ c_less(c_0,V_y,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(V_x,V_y,tc_nat),tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__product_0,axiom,
( ~ c_Parity_Oeven(c_times(V_x,V_y,tc_nat),tc_nat)
| c_Parity_Oeven(V_y,tc_nat)
| c_Parity_Oeven(V_x,tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__product_1,axiom,
( ~ c_Parity_Oeven(V_x,tc_nat)
| c_Parity_Oeven(c_times(V_x,V_y,tc_nat),tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__product_2,axiom,
( ~ c_Parity_Oeven(V_y,tc_nat)
| c_Parity_Oeven(c_times(V_x,V_y,tc_nat),tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__sum_0,axiom,
( ~ c_Parity_Oeven(V_y,tc_nat)
| ~ c_Parity_Oeven(c_plus(V_x,V_y,tc_nat),tc_nat)
| c_Parity_Oeven(V_x,tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__sum_1,axiom,
( ~ c_Parity_Oeven(V_x,tc_nat)
| ~ c_Parity_Oeven(c_plus(V_x,V_y,tc_nat),tc_nat)
| c_Parity_Oeven(V_y,tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__sum_2,axiom,
( ~ c_Parity_Oeven(V_y,tc_nat)
| ~ c_Parity_Oeven(V_x,tc_nat)
| c_Parity_Oeven(c_plus(V_x,V_y,tc_nat),tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__sum_3,axiom,
( c_Parity_Oeven(V_y,tc_nat)
| c_Parity_Oeven(V_x,tc_nat)
| c_Parity_Oeven(c_plus(V_x,V_y,tc_nat),tc_nat) ) ).
cnf(cls_Parity_Oeven__nat__zero_0,axiom,
c_Parity_Oeven(c_0,tc_nat) ).
cnf(cls_Parity_Oeven__neg_0,axiom,
( ~ c_Parity_Oeven(c_uminus(V_x,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(V_x,tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__neg_1,axiom,
( ~ c_Parity_Oeven(V_x,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(V_x,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__power_0,axiom,
( ~ c_Parity_Oeven(c_Nat_Opower(V_x,V_n,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(V_x,tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__power_1,axiom,
( ~ c_Parity_Oeven(c_Nat_Opower(V_x,V_n,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,V_n,tc_nat) ) ).
cnf(cls_Parity_Oeven__power_2,axiom,
( ~ c_Parity_Oeven(V_x,tc_IntDef_Oint)
| ~ c_less(c_0,V_n,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(V_x,V_n,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__product_0,axiom,
( ~ c_Parity_Oeven(c_times(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(V_y,tc_IntDef_Oint)
| c_Parity_Oeven(V_x,tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__product_1,axiom,
( ~ c_Parity_Oeven(V_x,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__product_2,axiom,
( ~ c_Parity_Oeven(V_y,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__sum_0,axiom,
( ~ c_Parity_Oeven(V_y,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(V_x,tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__sum_1,axiom,
( ~ c_Parity_Oeven(V_x,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(V_y,tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__sum_2,axiom,
( ~ c_Parity_Oeven(V_y,tc_IntDef_Oint)
| ~ c_Parity_Oeven(V_x,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__sum_3,axiom,
( c_Parity_Oeven(V_y,tc_IntDef_Oint)
| c_Parity_Oeven(V_x,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint) ) ).
cnf(cls_Parity_Oeven__zero_0,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint) ).
cnf(cls_Parity_Ominus__one__even__power_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ c_Parity_Oeven(V_x,tc_nat)
| c_Nat_Opower(c_uminus(c_1,T_a),V_x,T_a) = c_1 ) ).
cnf(cls_Parity_Ominus__one__odd__power_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_Parity_Oeven(V_x,tc_nat)
| c_Nat_Opower(c_uminus(c_1,T_a),V_x,T_a) = c_uminus(c_1,T_a) ) ).
cnf(cls_Parity_Oneg__one__even__power_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Power_Orecpower(T_a)
| ~ c_Parity_Oeven(V_x,tc_nat)
| c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),V_x,T_a) = c_1 ) ).
cnf(cls_Parity_Oneg__one__odd__power_0,axiom,
( ~ class_Numeral_Onumber__ring(T_a)
| ~ class_Power_Orecpower(T_a)
| c_Parity_Oeven(V_x,tc_nat)
| c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),V_x,T_a) = c_Numeral_Onumber__of(c_Numeral_OMin,T_a) ) ).
cnf(cls_Parity_Oneq__one__mod__two_0,axiom,
( c_Divides_Oop_Amod(V_x,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0
| c_Divides_Oop_Amod(V_x,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_1 ) ).
cnf(cls_Parity_Oneq__one__mod__two_1,axiom,
( c_Divides_Oop_Amod(V_x,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0
| c_Divides_Oop_Amod(V_x,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_1 ) ).
cnf(cls_Parity_Oodd__one_0,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint) ).
cnf(cls_Parity_Opower__0__left__number__of_0,axiom,
( ~ class_Power_Orecpower(T_a)
| c_Numeral_Onumber__of(V_w,tc_nat) != c_0
| c_Nat_Opower(c_0,c_Numeral_Onumber__of(V_w,tc_nat),T_a) = c_1 ) ).
cnf(cls_Parity_Opower__0__left__number__of_1,axiom,
( ~ class_Power_Orecpower(T_a)
| c_Nat_Opower(c_0,c_Numeral_Onumber__of(V_w,tc_nat),T_a) = c_0
| c_Numeral_Onumber__of(V_w,tc_nat) = c_0 ) ).
cnf(cls_Parity_Opower__eq__0__iff__number__of_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Nat_Opower(V_a,c_Numeral_Onumber__of(V_w,tc_nat),T_a) != c_0
| V_a = c_0 ) ).
cnf(cls_Parity_Opower__eq__0__iff__number__of_1,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Nat_Opower(V_a,c_Numeral_Onumber__of(V_w,tc_nat),T_a) != c_0
| c_less(c_0,c_Numeral_Onumber__of(V_w,tc_nat),tc_nat) ) ).
cnf(cls_Parity_Opower__eq__0__iff__number__of_2,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_Nat_Opower(c_0,c_Numeral_Onumber__of(V_w,tc_nat),T_a) = c_0 ) ).
cnf(cls_Parity_Opower__even__abs__number__of_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(V_x,T_a),c_Numeral_Onumber__of(V_w,tc_nat),T_a) = c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a) ) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a)
| c_Numeral_Onumber__of(V_w,tc_nat) != c_0 ) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_1,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a)
| V_x = c_0 ) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_2,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a)
| c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_lessequals(V_x,c_0,T_a) ) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_3,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a)
| c_lessequals(V_x,c_0,T_a)
| V_x = c_0 ) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_4,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(V_x,c_0,T_a)
| c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a)
| c_Numeral_Onumber__of(V_w,tc_nat) = c_0 ) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_5,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a)
| c_Numeral_Onumber__of(V_w,tc_nat) = c_0 ) ).
cnf(cls_Parity_Opower__less__zero__eq__number__of_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a) ) ).
cnf(cls_Parity_Opower__less__zero__eq__number__of_1,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a)
| c_less(V_x,c_0,T_a) ) ).
cnf(cls_Parity_Opower__less__zero__eq__number__of_2,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(V_x,c_0,T_a)
| c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_less(c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a) ) ).
cnf(cls_Parity_Opower__minus__even_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ c_Parity_Oeven(V_n,tc_nat)
| c_Nat_Opower(c_uminus(V_x,T_a),V_n,T_a) = c_Nat_Opower(V_x,V_n,T_a) ) ).
cnf(cls_Parity_Opower__minus__odd_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_Parity_Oeven(V_n,tc_nat)
| c_Nat_Opower(c_uminus(V_x,T_a),V_n,T_a) = c_uminus(c_Nat_Opower(V_x,V_n,T_a),T_a) ) ).
cnf(cls_Parity_Ozero__le__power__eq__number__of_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),T_a)
| c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_lessequals(c_0,V_x,T_a) ) ).
cnf(cls_Parity_Ozero__le__power__eq__number__of_1,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),T_a) ) ).
cnf(cls_Parity_Ozero__le__power__eq__number__of_2,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_lessequals(c_0,V_x,T_a)
| c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),T_a) ) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),T_a)
| c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_less(c_0,V_x,T_a)
| c_Numeral_Onumber__of(V_w,tc_nat) = c_0 ) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_1,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(V_w,tc_nat),T_a),T_a)
| c_Numeral_Onumber__of(V_w,tc_nat) = c_0 ) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_2,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(V_w,tc_nat),T_a),T_a)
| c_less(c_0,c_0,T_a)
| c_Numeral_Onumber__of(V_w,tc_nat) = c_0 ) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_3,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Numeral_Onumber__of(V_w,tc_nat) != c_0
| c_less(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),T_a) ) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_4,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),T_a)
| V_x = c_0 ) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_5,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_0,V_x,T_a)
| c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),T_a) ) ).
cnf(cls_Parity_Ozero__less__power__nat__eq__number__of_0,axiom,
( ~ c_less(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),tc_nat),tc_nat)
| c_less(c_0,V_x,tc_nat)
| c_Numeral_Onumber__of(V_w,tc_nat) = c_0 ) ).
cnf(cls_Parity_Ozero__less__power__nat__eq__number__of_1,axiom,
( c_Numeral_Onumber__of(V_w,tc_nat) != c_0
| c_less(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),tc_nat),tc_nat) ) ).
cnf(cls_Parity_Ozero__less__power__nat__eq__number__of_2,axiom,
( ~ c_less(c_0,V_x,tc_nat)
| c_less(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),tc_nat),tc_nat) ) ).
cnf(cls_Power_Onat__one__le__power_0,axiom,
( ~ c_lessequals(c_1,V_i,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(V_i,V_n,tc_nat),tc_nat) ) ).
cnf(cls_Power_Onat__zero__less__power__iff_0,axiom,
( ~ c_less(c_0,c_Nat_Opower(c_0,V_n,tc_nat),tc_nat)
| V_n = c_0 ) ).
cnf(cls_Power_Onat__zero__less__power__iff_1,axiom,
( c_less(c_0,c_Nat_Opower(V_x,V_n,tc_nat),tc_nat)
| V_x = c_0 ) ).
cnf(cls_Power_Onat__zero__less__power__iff_2,axiom,
c_less(c_0,c_Nat_Opower(V_x,c_0,tc_nat),tc_nat) ).
cnf(cls_Power_Opower_Osimps__1_0,axiom,
c_Nat_Opower(V_p,c_0,tc_nat) = c_1 ).
cnf(cls_Power_Opower_Osimps__2_0,axiom,
c_Nat_Opower(V_p,c_Suc(V_n),tc_nat) = c_times(V_p,c_Nat_Opower(V_p,V_n,tc_nat),tc_nat) ).
cnf(cls_Power_Opower__0__Suc_0,axiom,
( ~ class_Power_Orecpower(T_a)
| c_Nat_Opower(c_0,c_Suc(V_n),T_a) = c_0 ) ).
cnf(cls_Power_Opower__eq__0__iff_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Nat_Opower(V_a,V_n,T_a) != c_0
| V_a = c_0 ) ).
cnf(cls_Power_Opower__eq__0__iff_1,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Nat_Opower(V_a,V_n,T_a) != c_0
| c_less(c_0,V_n,tc_nat) ) ).
cnf(cls_Power_Opower__eq__0__iff_2,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_0,V_n,tc_nat)
| c_Nat_Opower(c_0,V_n,T_a) = c_0 ) ).
cnf(cls_Power_Opower__increasing__iff_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_less(c_1,V_b,T_a)
| ~ c_lessequals(c_Nat_Opower(V_b,V_x,T_a),c_Nat_Opower(V_b,V_y,T_a),T_a)
| c_lessequals(V_x,V_y,tc_nat) ) ).
cnf(cls_Power_Opower__increasing__iff_1,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_less(c_1,V_b,T_a)
| ~ c_lessequals(V_x,V_y,tc_nat)
| c_lessequals(c_Nat_Opower(V_b,V_x,T_a),c_Nat_Opower(V_b,V_y,T_a),T_a) ) ).
cnf(cls_Power_Opower__inject__exp_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_less(c_1,V_a,T_a)
| c_Nat_Opower(V_a,V_m,T_a) != c_Nat_Opower(V_a,V_n,T_a)
| V_m = V_n ) ).
cnf(cls_Power_Opower__one_0,axiom,
( ~ class_Power_Orecpower(T_a)
| c_Nat_Opower(c_1,V_n,T_a) = c_1 ) ).
cnf(cls_Power_Opower__one__right_0,axiom,
( ~ class_Power_Orecpower(T_a)
| c_Nat_Opower(V_y,c_1,T_a) = V_y ) ).
cnf(cls_Power_Opower__strict__increasing__iff_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_less(c_1,V_b,T_a)
| ~ c_less(c_Nat_Opower(V_b,V_x,T_a),c_Nat_Opower(V_b,V_y,T_a),T_a)
| c_less(V_x,V_y,tc_nat) ) ).
cnf(cls_Power_Opower__strict__increasing__iff_1,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_less(V_x,V_y,tc_nat)
| ~ c_less(c_1,V_b,T_a)
| c_less(c_Nat_Opower(V_b,V_x,T_a),c_Nat_Opower(V_b,V_y,T_a),T_a) ) ).
cnf(cls_Power_Orecpower__class_Oaxioms__1_0,axiom,
( ~ class_Power_Orecpower(T_a)
| c_Nat_Opower(V_a,c_0,T_a) = c_1 ) ).
cnf(cls_Power_Ozero__le__power__abs_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(V_a,T_a),V_n,T_a),T_a) ) ).
cnf(cls_Power_Ozero__less__power__abs__iff_0,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,T_a),V_n,T_a),T_a)
| V_n = c_0 ) ).
cnf(cls_Power_Ozero__less__power__abs__iff_1,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(V_a,T_a),V_n,T_a),T_a)
| V_a = c_0 ) ).
cnf(cls_Power_Ozero__less__power__abs__iff_2,axiom,
( ~ class_Power_Orecpower(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(V_a,T_a),c_0,T_a),T_a) ) ).
cnf(cls_Product__Type_OPair__eq_0,axiom,
( c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b)
| V_a = V_a_H ) ).
cnf(cls_Product__Type_OPair__eq_1,axiom,
( c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b)
| V_b = V_b_H ) ).
cnf(cls_Product__Type_Ofst__conv_0,axiom,
c_fst(c_Pair(V_y,V_b,T_a,T_b),T_a,T_b) = V_y ).
cnf(cls_Product__Type_Opair__collapse_0,axiom,
c_Pair(c_fst(V_y,T_a,T_b),c_snd(V_y,T_a,T_b),T_a,T_b) = V_y ).
cnf(cls_Product__Type_Osnd__conv_0,axiom,
c_snd(c_Pair(V_a,V_y,T_b,T_a),T_b,T_a) = V_y ).
cnf(cls_Product__Type_Osurj__pair_0,axiom,
V_z = c_Pair(c_Main_Osurj__pair__1(V_z,T_a,T_b),c_Main_Osurj__pair__2(V_z,T_a,T_b),T_a,T_b) ).
cnf(cls_Relation_ODomain__Id_0,axiom,
c_Relation_ODomain(c_Relation_OId,T_a,T_a) = c_UNIV ).
cnf(cls_Relation_ODomain__diag_0,axiom,
c_Relation_ODomain(c_Relation_Odiag(V_y,T_a),T_a,T_a) = V_y ).
cnf(cls_Relation_ODomain__empty_0,axiom,
c_Relation_ODomain(c_emptyset,T_a,T_b) = c_emptyset ).
cnf(cls_Relation_OId__O__R_0,axiom,
c_Relation_Orel__comp(c_Relation_OId,V_y,T_b,T_b,T_a) = V_y ).
cnf(cls_Relation_OImage__Id_0,axiom,
c_Relation_OImage(c_Relation_OId,V_y,T_a,T_a) = V_y ).
cnf(cls_Relation_OImage__diag_0,axiom,
c_Relation_OImage(c_Relation_Odiag(V_A,T_a),V_B,T_a,T_a) = c_inter(V_A,V_B,T_a) ).
cnf(cls_Relation_OImage__empty_0,axiom,
c_Relation_OImage(V_R,c_emptyset,T_b,T_a) = c_emptyset ).
cnf(cls_Relation_OImage__singleton__iff_0,axiom,
( ~ c_in(V_b,c_Relation_OImage(V_r,c_insert(V_a,c_emptyset,T_b),T_b,T_a),T_a)
| c_in(c_Pair(V_a,V_b,T_b,T_a),V_r,tc_prod(T_b,T_a)) ) ).
cnf(cls_Relation_OImage__singleton__iff_1,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(V_b,c_Relation_OImage(V_r,c_insert(V_a,c_emptyset,T_b),T_b,T_a),T_a) ) ).
cnf(cls_Relation_OR__O__Id_0,axiom,
c_Relation_Orel__comp(V_y,c_Relation_OId,T_a,T_b,T_a) = V_y ).
cnf(cls_Relation_ORange__Id_0,axiom,
c_Relation_ORange(c_Relation_OId,T_a,T_a) = c_UNIV ).
cnf(cls_Relation_ORange__diag_0,axiom,
c_Relation_ORange(c_Relation_Odiag(V_y,T_a),T_a,T_a) = V_y ).
cnf(cls_Relation_ORange__empty_0,axiom,
c_Relation_ORange(c_emptyset,T_b,T_a) = c_emptyset ).
cnf(cls_Relation_Oconverse__Id_0,axiom,
c_Relation_Oconverse(c_Relation_OId,T_a,T_a) = c_Relation_OId ).
cnf(cls_Relation_Oconverse__converse_0,axiom,
c_Relation_Oconverse(c_Relation_Oconverse(V_y,T_a,T_b),T_b,T_a) = V_y ).
cnf(cls_Relation_Oconverse__diag_0,axiom,
c_Relation_Oconverse(c_Relation_Odiag(V_A,T_a),T_a,T_a) = c_Relation_Odiag(V_A,T_a) ).
cnf(cls_Relation_Oconverse__iff_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) ) ).
cnf(cls_Relation_Oconverse__iff_1,axiom,
( ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b)) ) ).
cnf(cls_Relation_Odiag__empty_0,axiom,
c_Relation_Odiag(c_emptyset,T_a) = c_emptyset ).
cnf(cls_Relation_Opair__in__Id__conv_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a))
| V_a = V_b ) ).
cnf(cls_Relation_Opair__in__Id__conv_1,axiom,
c_in(c_Pair(V_x,V_x,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)) ).
cnf(cls_Relation__Power_Orel__pow__1_0,axiom,
c_Nat_Opower(V_y,c_1,tc_set(tc_prod(T_a,T_a))) = V_y ).
cnf(cls_Relation__Power_Orelpow_Osimps__1_0,axiom,
c_Nat_Opower(V_R,c_0,tc_set(tc_prod(T_a__1,T_a__1))) = c_Relation_OId ).
cnf(cls_Relation__Power_Orelpow_Osimps__2_0,axiom,
c_Nat_Opower(V_R,c_Suc(V_n),tc_set(tc_prod(T_a__1,T_a__1))) = c_Relation_Orel__comp(V_R,c_Nat_Opower(V_R,V_n,tc_set(tc_prod(T_a__1,T_a__1))),T_a__1,T_a__1,T_a__1) ).
cnf(cls_Ring__and__Field_Oabs__divide_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oabs(c_divide(V_a,V_b,T_a),T_a) = c_divide(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oabs__inverse_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oabs(c_HOL_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse(c_HOL_Oabs(V_a,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oabs__one_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oabs(c_1,T_a) = c_1 ) ).
cnf(cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0,axiom,
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(T_a)
| c_0 != c_1 ) ).
cnf(cls_Ring__and__Field_Odivide__1_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(V_y,c_1,T_a) = V_y ) ).
cnf(cls_Ring__and__Field_Odivide__cancel__left_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(V_c,V_a,T_a) != c_divide(V_c,V_b,T_a)
| V_a = V_b
| V_c = c_0 ) ).
cnf(cls_Ring__and__Field_Odivide__cancel__left_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_0,V_a,T_a) = c_divide(c_0,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__cancel__right_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(V_a,V_c,T_a) != c_divide(V_b,V_c,T_a)
| V_a = V_b
| V_c = c_0 ) ).
cnf(cls_Ring__and__Field_Odivide__cancel__right_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(V_a,c_0,T_a) = c_divide(V_b,c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__divide__eq__left_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_divide(V_a,V_b,T_a),V_c,T_a) = c_divide(V_a,c_times(V_b,V_c,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__divide__eq__right_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(V_a,c_divide(V_b,V_c,T_a),T_a) = c_divide(c_times(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(V_a,V_b,T_a) != c_0
| V_b = c_0
| V_a = c_0 ) ).
cnf(cls_Ring__and__Field_Odivide__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_0,V_b,T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Odivide__eq__0__iff_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(V_a,c_0,T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Odivide__eq__1__iff_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(V_a,V_b,T_a) != c_1
| V_a = V_b ) ).
cnf(cls_Ring__and__Field_Odivide__eq__eq__1_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| c_divide(V_b,c_0,T_a) != c_1 ) ).
cnf(cls_Ring__and__Field_Odivide__eq__eq__1_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| c_divide(V_b,V_a,T_a) != c_1
| V_a = V_b ) ).
cnf(cls_Ring__and__Field_Odivide__eq__eq__1_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| V_x = c_0
| c_divide(V_x,V_x,T_a) = c_1 ) ).
cnf(cls_Ring__and__Field_Odivide__le__0__1__iff_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_lessequals(c_divide(c_1,V_b,T_a),c_0,T_a)
| c_lessequals(V_b,c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__le__0__1__iff_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_lessequals(V_b,c_0,T_a)
| c_lessequals(c_divide(c_1,V_b,T_a),c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__le__eq__1__neg_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_lessequals(c_divide(V_b,V_a,T_a),c_1,T_a)
| c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__le__eq__1__neg_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_divide(V_b,V_a,T_a),c_1,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__le__eq__1__pos_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_lessequals(c_divide(V_b,V_a,T_a),c_1,T_a)
| c_lessequals(V_b,V_a,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__le__eq__1__pos_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| c_lessequals(c_divide(V_b,V_a,T_a),c_1,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__less__0__1__iff_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_divide(c_1,V_b,T_a),c_0,T_a)
| c_less(V_b,c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__less__0__1__iff_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_b,c_0,T_a)
| c_less(c_divide(c_1,V_b,T_a),c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__less__eq__1__neg_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_less(c_divide(V_b,V_a,T_a),c_1,T_a)
| c_less(V_a,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__less__eq__1__neg_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_a,V_b,T_a)
| ~ c_less(V_a,c_0,T_a)
| c_less(c_divide(V_b,V_a,T_a),c_1,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__less__eq__1__pos_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_less(c_divide(V_b,V_a,T_a),c_1,T_a)
| c_less(V_b,V_a,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__less__eq__1__pos_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_b,V_a,T_a)
| ~ c_less(c_0,V_a,T_a)
| c_less(c_divide(V_b,V_a,T_a),c_1,T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__minus__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_uminus(V_a,T_a),V_b,T_a) = c_uminus(c_divide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__minus__right_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(V_a,c_uminus(V_b,T_a),T_a) = c_uminus(c_divide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Odivide__self__if_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_0,c_0,T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Oeq__divide__eq__1_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| c_1 != c_divide(V_b,c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Oeq__divide__eq__1_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| c_1 != c_divide(V_b,V_a,T_a)
| V_a = V_b ) ).
cnf(cls_Ring__and__Field_Oeq__divide__eq__1_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| V_x = c_0
| c_1 = c_divide(V_x,V_x,T_a) ) ).
cnf(cls_Ring__and__Field_Ofield__class_Oaxioms__1_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_a = c_0
| c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 ) ).
cnf(cls_Ring__and__Field_Ofield__mult__cancel__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_times(V_c,V_a,T_a) != c_times(V_c,V_b,T_a)
| V_a = V_b
| V_c = c_0 ) ).
cnf(cls_Ring__and__Field_Ofield__mult__cancel__left_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_times(c_0,V_a,T_a) = c_times(c_0,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Ofield__mult__cancel__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_times(V_a,V_c,T_a) != c_times(V_b,V_c,T_a)
| V_a = V_b
| V_c = c_0 ) ).
cnf(cls_Ring__and__Field_Ofield__mult__cancel__right_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_times(V_a,c_0,T_a) = c_times(V_b,c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__divide_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse(c_divide(V_a,V_b,T_a),T_a) = c_divide(V_b,V_a,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__eq__1__iff_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse(V_x,T_a) != c_1
| V_x = c_1 ) ).
cnf(cls_Ring__and__Field_Oinverse__eq__1__iff_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse(c_1,T_a) = c_1 ) ).
cnf(cls_Ring__and__Field_Oinverse__eq__iff__eq_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse(V_a,T_a) != c_HOL_Oinverse(V_b,T_a)
| V_a = V_b ) ).
cnf(cls_Ring__and__Field_Oinverse__inverse__eq_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse(c_HOL_Oinverse(V_y,T_a),T_a) = V_y ) ).
cnf(cls_Ring__and__Field_Oinverse__le__iff__le_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_b,T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_lessequals(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a)
| c_lessequals(V_b,V_a,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__le__iff__le_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_b,T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| c_lessequals(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__le__iff__le__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_b,c_0,T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_lessequals(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a)
| c_lessequals(V_b,V_a,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__le__iff__le__neg_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_b,c_0,T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| c_lessequals(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__less__iff__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_b,T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_less(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a)
| c_less(V_b,V_a,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__less__iff__less_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_b,V_a,T_a)
| ~ c_less(c_0,V_b,T_a)
| ~ c_less(c_0,V_a,T_a)
| c_less(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__less__iff__less__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_b,c_0,T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_less(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a)
| c_less(V_b,V_a,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__less__iff__less__neg_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_b,V_a,T_a)
| ~ c_less(V_b,c_0,T_a)
| ~ c_less(V_a,c_0,T_a)
| c_less(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__minus__eq_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse(c_uminus(V_a,T_a),T_a) = c_uminus(c_HOL_Oinverse(V_a,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__mult__distrib_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__negative__iff__negative_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_HOL_Oinverse(V_a,T_a),c_0,T_a)
| c_less(V_a,c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__negative__iff__negative_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_a,c_0,T_a)
| c_less(c_HOL_Oinverse(V_a,T_a),c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_lessequals(c_0,c_HOL_Oinverse(V_a,T_a),T_a)
| c_lessequals(c_0,V_a,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_HOL_Oinverse(V_a,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_lessequals(c_HOL_Oinverse(V_a,T_a),c_0,T_a)
| c_lessequals(V_a,c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_lessequals(V_a,c_0,T_a)
| c_lessequals(c_HOL_Oinverse(V_a,T_a),c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse(V_a,T_a) != c_0
| V_a = c_0 ) ).
cnf(cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse(c_0,T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Oinverse__positive__iff__positive_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,c_HOL_Oinverse(V_a,T_a),T_a)
| c_less(c_0,V_a,T_a) ) ).
cnf(cls_Ring__and__Field_Oinverse__positive__iff__positive_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_a,T_a)
| c_less(c_0,c_HOL_Oinverse(V_a,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Ole__divide__eq__1__neg_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_lessequals(c_1,c_divide(V_b,V_a,T_a),T_a)
| c_lessequals(V_b,V_a,T_a) ) ).
cnf(cls_Ring__and__Field_Ole__divide__eq__1__neg_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| c_lessequals(c_1,c_divide(V_b,V_a,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Ole__divide__eq__1__pos_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_lessequals(c_1,c_divide(V_b,V_a,T_a),T_a)
| c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Ole__divide__eq__1__pos_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_1,c_divide(V_b,V_a,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oless__divide__eq__1__neg_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_less(c_1,c_divide(V_b,V_a,T_a),T_a)
| c_less(V_b,V_a,T_a) ) ).
cnf(cls_Ring__and__Field_Oless__divide__eq__1__neg_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_b,V_a,T_a)
| ~ c_less(V_a,c_0,T_a)
| c_less(c_1,c_divide(V_b,V_a,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oless__divide__eq__1__pos_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_less(c_1,c_divide(V_b,V_a,T_a),T_a)
| c_less(V_a,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Oless__divide__eq__1__pos_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(V_a,V_b,T_a)
| ~ c_less(c_0,V_a,T_a)
| c_less(c_1,c_divide(V_b,V_a,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Ominus__divide__divide_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) = c_divide(V_a,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Ominus__mult__minus_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| c_times(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) = c_times(V_a,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Omult__cancel__left1_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| V_c != c_times(V_c,V_b,T_a)
| V_c = c_0
| V_b = c_1 ) ).
cnf(cls_Ring__and__Field_Omult__cancel__left1_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_0 = c_times(c_0,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Omult__cancel__left1_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| V_c = c_times(V_c,c_1,T_a) ) ).
cnf(cls_Ring__and__Field_Omult__cancel__left2_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_times(V_c,V_a,T_a) != V_c
| V_c = c_0
| V_a = c_1 ) ).
cnf(cls_Ring__and__Field_Omult__cancel__right1_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| V_c != c_times(V_b,V_c,T_a)
| V_c = c_0
| V_b = c_1 ) ).
cnf(cls_Ring__and__Field_Omult__cancel__right1_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_0 = c_times(V_b,c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Omult__cancel__right1_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| V_c = c_times(c_1,V_c,T_a) ) ).
cnf(cls_Ring__and__Field_Omult__cancel__right2_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_times(V_a,V_c,T_a) != V_c
| V_c = c_0
| V_a = c_1 ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if1_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_0,c_times(c_0,V_b,T_a),T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if1_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_0
| c_divide(V_c,c_times(V_c,V_b,T_a),T_a) = c_divide(c_1,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if2_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_times(c_0,V_a,T_a),c_0,T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if2_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_0
| c_divide(c_times(V_c,V_a,T_a),V_c,T_a) = V_a ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_times(c_0,V_a,T_a),c_times(c_0,V_b,T_a),T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_0
| c_divide(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) = c_divide(V_a,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if1_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_0,c_times(V_b,c_0,T_a),T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if1_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_0
| c_divide(V_c,c_times(V_b,V_c,T_a),T_a) = c_divide(c_1,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if2_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_times(V_a,c_0,T_a),c_0,T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if2_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_0
| c_divide(c_times(V_a,V_c,T_a),V_c,T_a) = V_a ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_divide(c_times(V_a,c_0,T_a),c_times(V_b,c_0,T_a),T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_0
| c_divide(c_times(V_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a) = c_divide(V_a,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Omult__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_times(V_a,V_b,T_a) != c_0
| V_b = c_0
| V_a = c_0 ) ).
cnf(cls_Ring__and__Field_Omult__minus__left_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| c_times(c_uminus(V_a,T_a),V_b,T_a) = c_uminus(c_times(V_a,V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Omult__minus__right_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| c_times(V_a,c_uminus(V_b,T_a),T_a) = c_uminus(c_times(V_a,V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Omult__zero__left_0,axiom,
( ~ class_Ring__and__Field_Osemiring__0__cancel(T_a)
| c_times(c_0,V_a,T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Omult__zero__right_0,axiom,
( ~ class_Ring__and__Field_Osemiring__0__cancel(T_a)
| c_times(V_a,c_0,T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Onot__one__le__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_lessequals(c_1,c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Onot__one__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_less(c_1,c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Oone__divide__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| c_divide(c_1,V_a,T_a) != c_0
| V_a = c_0 ) ).
cnf(cls_Ring__and__Field_Oone__divide__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| c_divide(c_1,c_0,T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Oone__eq__divide__iff_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_1 != c_divide(V_a,V_b,T_a)
| V_a = V_b ) ).
cnf(cls_Ring__and__Field_Oone__neq__zero_0,axiom,
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(T_a)
| c_1 != c_0 ) ).
cnf(cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_less(c_0,c_1,T_a) ) ).
cnf(cls_Ring__and__Field_Oright__inverse_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_a = c_0
| c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) ).
cnf(cls_Ring__and__Field_Otimes__divide__eq__1_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_times(V_a,c_divide(V_b,V_c,T_a),T_a) = c_divide(c_times(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_Ring__and__Field_Otimes__divide__eq__2_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_times(c_divide(V_b,V_c,T_a),V_a,T_a) = c_divide(c_times(V_b,V_a,T_a),V_c,T_a) ) ).
cnf(cls_Ring__and__Field_Otimes__divide__self__left_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_times(c_divide(V_b,c_0,T_a),c_0,T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Otimes__divide__self__left_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| V_a = c_0
| c_times(c_divide(V_b,V_a,T_a),V_a,T_a) = V_b ) ).
cnf(cls_Ring__and__Field_Otimes__divide__self__right_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| c_times(c_0,c_divide(V_b,c_0,T_a),T_a) = c_0 ) ).
cnf(cls_Ring__and__Field_Otimes__divide__self__right_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| V_a = c_0
| c_times(V_a,c_divide(V_b,V_a,T_a),T_a) = V_b ) ).
cnf(cls_Ring__and__Field_Ozero__eq__1__divide__iff_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| c_0 != c_divide(c_1,V_a,T_a)
| V_a = c_0 ) ).
cnf(cls_Ring__and__Field_Ozero__eq__1__divide__iff_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| c_0 = c_divide(c_1,c_0,T_a) ) ).
cnf(cls_Ring__and__Field_Ozero__le__divide__1__iff_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_lessequals(c_0,c_divide(c_1,V_b,T_a),T_a)
| c_lessequals(c_0,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Ozero__le__divide__1__iff_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| c_lessequals(c_0,c_divide(c_1,V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Ozero__le__one_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_0,c_1,T_a) ) ).
cnf(cls_Ring__and__Field_Ozero__less__divide__1__iff_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,c_divide(c_1,V_b,T_a),T_a)
| c_less(c_0,V_b,T_a) ) ).
cnf(cls_Ring__and__Field_Ozero__less__divide__1__iff_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ c_less(c_0,V_b,T_a)
| c_less(c_0,c_divide(c_1,V_b,T_a),T_a) ) ).
cnf(cls_SetInterval_OCompl__atLeast_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_uminus(c_SetInterval_OatLeast(V_k,T_a),tc_set(T_a)) = c_SetInterval_OlessThan(V_k,T_a) ) ).
cnf(cls_SetInterval_OCompl__atMost_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_uminus(c_SetInterval_OatMost(V_k,T_a),tc_set(T_a)) = c_SetInterval_OgreaterThan(V_k,T_a) ) ).
cnf(cls_SetInterval_OCompl__greaterThan_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_uminus(c_SetInterval_OgreaterThan(V_k,T_a),tc_set(T_a)) = c_SetInterval_OatMost(V_k,T_a) ) ).
cnf(cls_SetInterval_OCompl__lessThan_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_uminus(c_SetInterval_OlessThan(V_k,T_a),tc_set(T_a)) = c_SetInterval_OatLeast(V_k,T_a) ) ).
cnf(cls_SetInterval_OatLeastAtMost__empty_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_n,V_m,T_a)
| c_SetInterval_OatLeastAtMost(V_m,V_n,T_a) = c_emptyset ) ).
cnf(cls_SetInterval_OatLeastAtMost__iff_0,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatLeastAtMost(V_l,V_u,T_a),T_a)
| c_lessequals(V_l,V_i,T_a) ) ).
cnf(cls_SetInterval_OatLeastAtMost__iff_1,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatLeastAtMost(V_l,V_u,T_a),T_a)
| c_lessequals(V_i,V_u,T_a) ) ).
cnf(cls_SetInterval_OatLeastAtMost__iff_2,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_i,V_u,T_a)
| ~ c_lessequals(V_l,V_i,T_a)
| c_in(V_i,c_SetInterval_OatLeastAtMost(V_l,V_u,T_a),T_a) ) ).
cnf(cls_SetInterval_OatLeastAtMost__singleton_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_OatLeastAtMost(V_a,V_a,T_a) = c_insert(V_a,c_emptyset,T_a) ) ).
cnf(cls_SetInterval_OatLeastLessThan__empty_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_n,V_m,T_a)
| c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset ) ).
cnf(cls_SetInterval_OatLeastLessThan__iff_0,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatLeastLessThan(V_l,V_u,T_a),T_a)
| c_lessequals(V_l,V_i,T_a) ) ).
cnf(cls_SetInterval_OatLeastLessThan__iff_1,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatLeastLessThan(V_l,V_u,T_a),T_a)
| c_less(V_i,V_u,T_a) ) ).
cnf(cls_SetInterval_OatLeastLessThan__iff_2,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_less(V_i,V_u,T_a)
| ~ c_lessequals(V_l,V_i,T_a)
| c_in(V_i,c_SetInterval_OatLeastLessThan(V_l,V_u,T_a),T_a) ) ).
cnf(cls_SetInterval_OatLeastLessThan__singleton_0,axiom,
c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) ).
cnf(cls_SetInterval_OatLeast__0_0,axiom,
c_SetInterval_OatLeast(c_0,tc_nat) = c_UNIV ).
cnf(cls_SetInterval_OatLeast__eq__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_SetInterval_OatLeast(V_x,T_a) != c_SetInterval_OatLeast(V_y,T_a)
| V_x = V_y ) ).
cnf(cls_SetInterval_OatLeast__iff_0,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| c_lessequals(V_k,V_i,T_a) ) ).
cnf(cls_SetInterval_OatLeast__iff_1,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a)
| c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a) ) ).
cnf(cls_SetInterval_OatLeast__subset__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_SetInterval_OatLeast__subset__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a)) ) ).
cnf(cls_SetInterval_OatMost__0_0,axiom,
c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ).
cnf(cls_SetInterval_OatMost__eq__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_SetInterval_OatMost(V_x,T_a) != c_SetInterval_OatMost(V_y,T_a)
| V_x = V_y ) ).
cnf(cls_SetInterval_OatMost__iff_0,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| c_lessequals(V_i,V_k,T_a) ) ).
cnf(cls_SetInterval_OatMost__iff_1,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_i,V_k,T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) ) ).
cnf(cls_SetInterval_OatMost__subset__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a))
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_SetInterval_OatMost__subset__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) ) ).
cnf(cls_SetInterval_Ocard__atLeastAtMost_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(V_l,V_u,tc_nat),tc_nat) = c_minus(c_Suc(V_u),V_l,tc_nat) ).
cnf(cls_SetInterval_Ocard__atLeastAtMost__int_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(V_l,V_u,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(V_u,V_l,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) ).
cnf(cls_SetInterval_Ocard__atLeastLessThan_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(V_l,V_u,tc_nat),tc_nat) = c_minus(V_u,V_l,tc_nat) ).
cnf(cls_SetInterval_Ocard__atLeastLessThan__int_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(V_l,V_u,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(V_u,V_l,tc_IntDef_Oint)) ).
cnf(cls_SetInterval_Ocard__atMost_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OatMost(V_u,tc_nat),tc_nat) = c_Suc(V_u) ).
cnf(cls_SetInterval_Ocard__greaterThanAtMost_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(V_l,V_u,tc_nat),tc_nat) = c_minus(V_u,V_l,tc_nat) ).
cnf(cls_SetInterval_Ocard__greaterThanAtMost__int_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(V_l,V_u,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(V_u,V_l,tc_IntDef_Oint)) ).
cnf(cls_SetInterval_Ocard__greaterThanLessThan_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(V_l,V_u,tc_nat),tc_nat) = c_minus(V_u,c_Suc(V_l),tc_nat) ).
cnf(cls_SetInterval_Ocard__greaterThanLessThan__int_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(V_l,V_u,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(V_u,c_plus(V_l,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) ).
cnf(cls_SetInterval_Ocard__lessThan_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OlessThan(V_y,tc_nat),tc_nat) = V_y ).
cnf(cls_SetInterval_OgreaterThanAtMost__empty_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_l,V_k,T_a)
| c_SetInterval_OgreaterThanAtMost(V_k,V_l,T_a) = c_emptyset ) ).
cnf(cls_SetInterval_OgreaterThanAtMost__iff_0,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OgreaterThanAtMost(V_l,V_u,T_a),T_a)
| c_less(V_l,V_i,T_a) ) ).
cnf(cls_SetInterval_OgreaterThanAtMost__iff_1,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OgreaterThanAtMost(V_l,V_u,T_a),T_a)
| c_lessequals(V_i,V_u,T_a) ) ).
cnf(cls_SetInterval_OgreaterThanAtMost__iff_2,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_less(V_l,V_i,T_a)
| ~ c_lessequals(V_i,V_u,T_a)
| c_in(V_i,c_SetInterval_OgreaterThanAtMost(V_l,V_u,T_a),T_a) ) ).
cnf(cls_SetInterval_OgreaterThanLessThan__iff_0,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OgreaterThanLessThan(V_l,V_u,T_a),T_a)
| c_less(V_l,V_i,T_a) ) ).
cnf(cls_SetInterval_OgreaterThanLessThan__iff_1,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OgreaterThanLessThan(V_l,V_u,T_a),T_a)
| c_less(V_i,V_u,T_a) ) ).
cnf(cls_SetInterval_OgreaterThanLessThan__iff_2,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_less(V_i,V_u,T_a)
| ~ c_less(V_l,V_i,T_a)
| c_in(V_i,c_SetInterval_OgreaterThanLessThan(V_l,V_u,T_a),T_a) ) ).
cnf(cls_SetInterval_OgreaterThan__eq__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_SetInterval_OgreaterThan(V_x,T_a) != c_SetInterval_OgreaterThan(V_y,T_a)
| V_x = V_y ) ).
cnf(cls_SetInterval_OgreaterThan__iff_0,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OgreaterThan(V_k,T_a),T_a)
| c_less(V_k,V_i,T_a) ) ).
cnf(cls_SetInterval_OgreaterThan__iff_1,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_less(V_k,V_i,T_a)
| c_in(V_i,c_SetInterval_OgreaterThan(V_k,T_a),T_a) ) ).
cnf(cls_SetInterval_OgreaterThan__subset__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(c_SetInterval_OgreaterThan(V_x,T_a),c_SetInterval_OgreaterThan(V_y,T_a),tc_set(T_a))
| c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_SetInterval_OgreaterThan__subset__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OgreaterThan(V_x,T_a),c_SetInterval_OgreaterThan(V_y,T_a),tc_set(T_a)) ) ).
cnf(cls_SetInterval_Oivl__diff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_i,V_n,T_a)
| c_minus(c_SetInterval_OatLeastLessThan(V_i,V_m,T_a),c_SetInterval_OatLeastLessThan(V_i,V_n,T_a),tc_set(T_a)) = c_SetInterval_OatLeastLessThan(V_n,V_m,T_a) ) ).
cnf(cls_SetInterval_Oivl__subset_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(V_i,V_j,T_a),c_SetInterval_OatLeastLessThan(V_m,V_n,T_a),tc_set(T_a))
| c_lessequals(V_m,V_i,T_a)
| c_lessequals(V_j,V_i,T_a) ) ).
cnf(cls_SetInterval_Oivl__subset_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(V_i,V_j,T_a),c_SetInterval_OatLeastLessThan(V_m,V_n,T_a),tc_set(T_a))
| c_lessequals(V_j,V_n,T_a)
| c_lessequals(V_j,V_i,T_a) ) ).
cnf(cls_SetInterval_Oivl__subset_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_j,V_i,T_a)
| c_lessequals(c_SetInterval_OatLeastLessThan(V_i,V_j,T_a),c_SetInterval_OatLeastLessThan(V_m,V_n,T_a),tc_set(T_a)) ) ).
cnf(cls_SetInterval_Oivl__subset_3,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_j,V_n,T_a)
| ~ c_lessequals(V_m,V_i,T_a)
| c_lessequals(c_SetInterval_OatLeastLessThan(V_i,V_j,T_a),c_SetInterval_OatLeastLessThan(V_m,V_n,T_a),tc_set(T_a)) ) ).
cnf(cls_SetInterval_OlessThan__0_0,axiom,
c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset ).
cnf(cls_SetInterval_OlessThan__eq__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_SetInterval_OlessThan(V_x,T_a) != c_SetInterval_OlessThan(V_y,T_a)
| V_x = V_y ) ).
cnf(cls_SetInterval_OlessThan__iff_0,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OlessThan(V_k,T_a),T_a)
| c_less(V_i,V_k,T_a) ) ).
cnf(cls_SetInterval_OlessThan__iff_1,axiom,
( ~ class_Orderings_Oord(T_a)
| ~ c_less(V_i,V_k,T_a)
| c_in(V_i,c_SetInterval_OlessThan(V_k,T_a),T_a) ) ).
cnf(cls_SetInterval_OlessThan__subset__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(c_SetInterval_OlessThan(V_x,T_a),c_SetInterval_OlessThan(V_y,T_a),tc_set(T_a))
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_SetInterval_OlessThan__subset__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OlessThan(V_x,T_a),c_SetInterval_OlessThan(V_y,T_a),tc_set(T_a)) ) ).
cnf(cls_SetInterval_Osingle__Diff__lessThan_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_minus(c_insert(V_k,c_emptyset,T_a),c_SetInterval_OlessThan(V_k,T_a),tc_set(T_a)) = c_insert(V_k,c_emptyset,T_a) ) ).
cnf(cls_Set_OCompl__Diff__eq_0,axiom,
c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) ).
cnf(cls_Set_OCompl__Int_0,axiom,
c_uminus(c_inter(V_A,V_B,T_a),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),c_uminus(V_B,tc_set(T_a)),T_a) ).
cnf(cls_Set_OCompl__UNIV__eq_0,axiom,
c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset ).
cnf(cls_Set_OCompl__Un_0,axiom,
c_uminus(c_union(V_A,V_B,T_a),tc_set(T_a)) = c_inter(c_uminus(V_A,tc_set(T_a)),c_uminus(V_B,tc_set(T_a)),T_a) ).
cnf(cls_Set_OCompl__disjoint2_0,axiom,
c_inter(c_uminus(V_A,tc_set(T_a)),V_A,T_a) = c_emptyset ).
cnf(cls_Set_OCompl__disjoint_0,axiom,
c_inter(V_A,c_uminus(V_A,tc_set(T_a)),T_a) = c_emptyset ).
cnf(cls_Set_OCompl__empty__eq_0,axiom,
c_uminus(c_emptyset,tc_set(T_a)) = c_UNIV ).
cnf(cls_Set_OCompl__eq__Compl__iff_0,axiom,
( c_uminus(V_A,tc_set(T_a)) != c_uminus(V_B,tc_set(T_a))
| V_A = V_B ) ).
cnf(cls_Set_OCompl__iff_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a) ) ).
cnf(cls_Set_OCompl__iff_1,axiom,
( c_in(V_c,V_A,T_a)
| c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a) ) ).
cnf(cls_Set_OCompl__subset__Compl__iff_0,axiom,
( ~ c_lessequals(c_uminus(V_A,tc_set(T_a)),c_uminus(V_B,tc_set(T_a)),tc_set(T_a))
| c_lessequals(V_B,V_A,tc_set(T_a)) ) ).
cnf(cls_Set_OCompl__subset__Compl__iff_1,axiom,
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| c_lessequals(c_uminus(V_A,tc_set(T_a)),c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) ) ).
cnf(cls_Set_ODiff__Compl_0,axiom,
c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) ).
cnf(cls_Set_ODiff__UNIV_0,axiom,
c_minus(V_A,c_UNIV,tc_set(T_a)) = c_emptyset ).
cnf(cls_Set_ODiff__cancel_0,axiom,
c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset ).
cnf(cls_Set_ODiff__disjoint_0,axiom,
c_inter(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_emptyset ).
cnf(cls_Set_ODiff__empty_0,axiom,
c_minus(V_y,c_emptyset,tc_set(T_a)) = V_y ).
cnf(cls_Set_ODiff__eq__empty__iff_0,axiom,
( c_minus(V_A,V_B,tc_set(T_a)) != c_emptyset
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_ODiff__eq__empty__iff_1,axiom,
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_minus(V_A,V_B,tc_set(T_a)) = c_emptyset ) ).
cnf(cls_Set_ODiff__idemp_0,axiom,
c_minus(c_minus(V_A,V_B,tc_set(T_a)),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ).
cnf(cls_Set_ODiff__iff_0,axiom,
( ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| c_in(V_c,V_A,T_a) ) ).
cnf(cls_Set_ODiff__iff_1,axiom,
( ~ c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ) ).
cnf(cls_Set_ODiff__iff_2,axiom,
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ) ).
cnf(cls_Set_ODiff__insert0_0,axiom,
( c_in(V_x,V_A,T_a)
| c_minus(V_A,c_insert(V_x,V_B,T_a),tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_OInt__UNIV_0,axiom,
( c_inter(V_A,V_B,T_a) != c_UNIV
| V_A = c_UNIV ) ).
cnf(cls_Set_OInt__UNIV_1,axiom,
( c_inter(V_A,V_B,T_a) != c_UNIV
| V_B = c_UNIV ) ).
cnf(cls_Set_OInt__UNIV_2,axiom,
c_inter(c_UNIV,c_UNIV,T_a) = c_UNIV ).
cnf(cls_Set_OInt__UNIV__left_0,axiom,
c_inter(c_UNIV,V_y,T_a) = V_y ).
cnf(cls_Set_OInt__UNIV__right_0,axiom,
c_inter(V_y,c_UNIV,T_a) = V_y ).
cnf(cls_Set_OInt__absorb_0,axiom,
c_inter(V_y,V_y,T_a) = V_y ).
cnf(cls_Set_OInt__empty__left_0,axiom,
c_inter(c_emptyset,V_B,T_a) = c_emptyset ).
cnf(cls_Set_OInt__empty__right_0,axiom,
c_inter(V_A,c_emptyset,T_a) = c_emptyset ).
cnf(cls_Set_OInt__iff_0,axiom,
( ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| c_in(V_c,V_A,T_a) ) ).
cnf(cls_Set_OInt__iff_1,axiom,
( ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| c_in(V_c,V_B,T_a) ) ).
cnf(cls_Set_OInt__iff_2,axiom,
( ~ c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ) ).
cnf(cls_Set_OInt__subset__iff_0,axiom,
( ~ c_lessequals(V_C,c_inter(V_A,V_B,T_a),tc_set(T_a))
| c_lessequals(V_C,V_A,tc_set(T_a)) ) ).
cnf(cls_Set_OInt__subset__iff_1,axiom,
( ~ c_lessequals(V_C,c_inter(V_A,V_B,T_a),tc_set(T_a))
| c_lessequals(V_C,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_OInt__subset__iff_2,axiom,
( ~ c_lessequals(V_C,V_B,tc_set(T_a))
| ~ c_lessequals(V_C,V_A,tc_set(T_a))
| c_lessequals(V_C,c_inter(V_A,V_B,T_a),tc_set(T_a)) ) ).
cnf(cls_Set_OInter__UNIV_0,axiom,
c_Inter(c_UNIV,T_a) = c_emptyset ).
cnf(cls_Set_OInter__UNIV__conv__1_0,axiom,
( ~ c_in(V_U,V_A,tc_set(T_a))
| c_Inter(V_A,T_a) != c_UNIV
| V_U = c_UNIV ) ).
cnf(cls_Set_OInter__UNIV__conv__1_1,axiom,
( c_in(c_Main_OInter__UNIV__conv__1__1(V_A,T_a),V_A,tc_set(T_a))
| c_Inter(V_A,T_a) = c_UNIV ) ).
cnf(cls_Set_OInter__UNIV__conv__1_2,axiom,
( c_Main_OInter__UNIV__conv__1__1(V_A,T_a) != c_UNIV
| c_Inter(V_A,T_a) = c_UNIV ) ).
cnf(cls_Set_OInter__UNIV__conv__2_0,axiom,
( ~ c_in(V_U,V_A,tc_set(T_a))
| c_UNIV != c_Inter(V_A,T_a)
| V_U = c_UNIV ) ).
cnf(cls_Set_OInter__UNIV__conv__2_1,axiom,
( c_in(c_Main_OInter__UNIV__conv__2__1(V_A,T_a),V_A,tc_set(T_a))
| c_UNIV = c_Inter(V_A,T_a) ) ).
cnf(cls_Set_OInter__UNIV__conv__2_2,axiom,
( c_Main_OInter__UNIV__conv__2__1(V_A,T_a) != c_UNIV
| c_UNIV = c_Inter(V_A,T_a) ) ).
cnf(cls_Set_OInter__empty_0,axiom,
c_Inter(c_emptyset,T_a) = c_UNIV ).
cnf(cls_Set_OInter__iff_0,axiom,
( ~ c_in(V_U,V_C,tc_set(T_a))
| ~ c_in(V_A,c_Inter(V_C,T_a),T_a)
| c_in(V_A,V_U,T_a) ) ).
cnf(cls_Set_OInter__iff_1,axiom,
( c_in(V_A,c_Inter(V_C,T_a),T_a)
| c_in(c_Main_OInter__iff__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ) ).
cnf(cls_Set_OInter__iff_2,axiom,
( ~ c_in(V_A,c_Main_OInter__iff__1(V_A,V_C,T_a),T_a)
| c_in(V_A,c_Inter(V_C,T_a),T_a) ) ).
cnf(cls_Set_OInter__insert_0,axiom,
c_Inter(c_insert(V_a,V_B,tc_set(T_a)),T_a) = c_inter(V_a,c_Inter(V_B,T_a),T_a) ).
cnf(cls_Set_OPow__Int__eq_0,axiom,
c_Pow(c_inter(V_A,V_B,T_a),T_a) = c_inter(c_Pow(V_A,T_a),c_Pow(V_B,T_a),tc_set(T_a)) ).
cnf(cls_Set_OPow__UNIV_0,axiom,
c_Pow(c_UNIV,T_a) = c_UNIV ).
cnf(cls_Set_OPow__empty_0,axiom,
c_Pow(c_emptyset,T_a) = c_insert(c_emptyset,c_emptyset,tc_set(T_a)) ).
cnf(cls_Set_OPow__iff_0,axiom,
( ~ c_in(V_A,c_Pow(V_B,T_a),tc_set(T_a))
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_OPow__iff_1,axiom,
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_A,c_Pow(V_B,T_a),tc_set(T_a)) ) ).
cnf(cls_Set_OUNIV__not__empty_0,axiom,
c_UNIV != c_emptyset ).
cnf(cls_Set_OUn__Diff__cancel2_0,axiom,
c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) ).
cnf(cls_Set_OUn__Diff__cancel_0,axiom,
c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ).
cnf(cls_Set_OUn__UNIV__left_0,axiom,
c_union(c_UNIV,V_B,T_a) = c_UNIV ).
cnf(cls_Set_OUn__UNIV__right_0,axiom,
c_union(V_A,c_UNIV,T_a) = c_UNIV ).
cnf(cls_Set_OUn__absorb_0,axiom,
c_union(V_y,V_y,T_a) = V_y ).
cnf(cls_Set_OUn__empty_0,axiom,
( c_union(V_A,V_B,T_a) != c_emptyset
| V_A = c_emptyset ) ).
cnf(cls_Set_OUn__empty_1,axiom,
( c_union(V_A,V_B,T_a) != c_emptyset
| V_B = c_emptyset ) ).
cnf(cls_Set_OUn__empty_2,axiom,
c_union(c_emptyset,c_emptyset,T_a) = c_emptyset ).
cnf(cls_Set_OUn__empty__left_0,axiom,
c_union(c_emptyset,V_y,T_a) = V_y ).
cnf(cls_Set_OUn__empty__right_0,axiom,
c_union(V_y,c_emptyset,T_a) = V_y ).
cnf(cls_Set_OUn__iff_0,axiom,
( ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a) ) ).
cnf(cls_Set_OUn__iff_1,axiom,
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ).
cnf(cls_Set_OUn__iff_2,axiom,
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ).
cnf(cls_Set_OUn__insert__left_0,axiom,
c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) ).
cnf(cls_Set_OUn__insert__right_0,axiom,
c_union(V_A,c_insert(V_a,V_B,T_a),T_a) = c_insert(V_a,c_union(V_A,V_B,T_a),T_a) ).
cnf(cls_Set_OUn__subset__iff_0,axiom,
( ~ c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) ) ).
cnf(cls_Set_OUn__subset__iff_1,axiom,
( ~ c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| c_lessequals(V_B,V_C,tc_set(T_a)) ) ).
cnf(cls_Set_OUn__subset__iff_2,axiom,
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a)) ) ).
cnf(cls_Set_OUnion__Pow__eq_0,axiom,
c_Union(c_Pow(V_y,T_a),T_a) = V_y ).
cnf(cls_Set_OUnion__UNIV_0,axiom,
c_Union(c_UNIV,T_a) = c_UNIV ).
cnf(cls_Set_OUnion__Un__distrib_0,axiom,
c_Union(c_union(V_A,V_B,tc_set(T_a)),T_a) = c_union(c_Union(V_A,T_a),c_Union(V_B,T_a),T_a) ).
cnf(cls_Set_OUnion__empty_0,axiom,
c_Union(c_emptyset,T_a) = c_emptyset ).
cnf(cls_Set_OUnion__empty__conv_0,axiom,
( ~ c_in(V_U,V_A,tc_set(T_a))
| c_Union(V_A,T_a) != c_emptyset
| V_U = c_emptyset ) ).
cnf(cls_Set_OUnion__empty__conv_1,axiom,
( c_in(c_Main_OUnion__empty__conv__1(V_A,T_a),V_A,tc_set(T_a))
| c_Union(V_A,T_a) = c_emptyset ) ).
cnf(cls_Set_OUnion__empty__conv_2,axiom,
( c_Main_OUnion__empty__conv__1(V_A,T_a) != c_emptyset
| c_Union(V_A,T_a) = c_emptyset ) ).
cnf(cls_Set_OUnion__iff_0,axiom,
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnion__iff__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ) ).
cnf(cls_Set_OUnion__iff_1,axiom,
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnion__iff__1(V_A,V_C,T_a),T_a) ) ).
cnf(cls_Set_OUnion__iff_2,axiom,
( ~ c_in(V_A,V_U,T_a)
| ~ c_in(V_U,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a) ) ).
cnf(cls_Set_OUnion__insert_0,axiom,
c_Union(c_insert(V_a,V_B,tc_set(T_a)),T_a) = c_union(V_a,c_Union(V_B,T_a),T_a) ).
cnf(cls_Set_Oall__not__in__conv_0,axiom,
( c_in(c_Main_Oall__not__in__conv__1(V_A,T_a),V_A,T_a)
| V_A = c_emptyset ) ).
cnf(cls_Set_Ocontents__eq_0,axiom,
c_Set_Ocontents(c_insert(V_y,c_emptyset,T_a),T_a) = V_y ).
cnf(cls_Set_Odisjoint__insert__1_0,axiom,
( ~ c_in(V_a,V_B,T_a)
| c_inter(V_B,c_insert(V_a,V_A,T_a),T_a) != c_emptyset ) ).
cnf(cls_Set_Odisjoint__insert__1_1,axiom,
( c_inter(V_B,c_insert(V_a,V_A,T_a),T_a) != c_emptyset
| c_inter(V_B,V_A,T_a) = c_emptyset ) ).
cnf(cls_Set_Odisjoint__insert__1_2,axiom,
( c_inter(V_B,V_A,T_a) != c_emptyset
| c_in(V_a,V_B,T_a)
| c_inter(V_B,c_insert(V_a,V_A,T_a),T_a) = c_emptyset ) ).
cnf(cls_Set_Odisjoint__insert__2_0,axiom,
( ~ c_in(V_b,V_A,T_a)
| c_emptyset != c_inter(V_A,c_insert(V_b,V_B,T_a),T_a) ) ).
cnf(cls_Set_Odisjoint__insert__2_1,axiom,
( c_emptyset != c_inter(V_A,c_insert(V_b,V_B,T_a),T_a)
| c_emptyset = c_inter(V_A,V_B,T_a) ) ).
cnf(cls_Set_Odisjoint__insert__2_2,axiom,
( c_emptyset != c_inter(V_A,V_B,T_a)
| c_in(V_b,V_A,T_a)
| c_emptyset = c_inter(V_A,c_insert(V_b,V_B,T_a),T_a) ) ).
cnf(cls_Set_Odouble__complement_0,axiom,
c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y ).
cnf(cls_Set_Oempty__Diff_0,axiom,
c_minus(c_emptyset,V_A,tc_set(T_a)) = c_emptyset ).
cnf(cls_Set_Oempty__Union__conv_0,axiom,
( ~ c_in(V_U,V_A,tc_set(T_a))
| c_emptyset != c_Union(V_A,T_a)
| V_U = c_emptyset ) ).
cnf(cls_Set_Oempty__Union__conv_1,axiom,
( c_in(c_Main_Oempty__Union__conv__1(V_A,T_a),V_A,tc_set(T_a))
| c_emptyset = c_Union(V_A,T_a) ) ).
cnf(cls_Set_Oempty__Union__conv_2,axiom,
( c_Main_Oempty__Union__conv__1(V_A,T_a) != c_emptyset
| c_emptyset = c_Union(V_A,T_a) ) ).
cnf(cls_Set_Oempty__iff_0,axiom,
~ c_in(V_c,c_emptyset,T_a) ).
cnf(cls_Set_Oempty__not__insert_0,axiom,
c_emptyset != c_insert(V_a,V_A,T_a) ).
cnf(cls_Set_Oinsert__Diff1_0,axiom,
( ~ c_in(V_x,V_B,T_a)
| c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_Oinsert__Diff__single_0,axiom,
c_insert(V_a,c_minus(V_A,c_insert(V_a,c_emptyset,T_a),tc_set(T_a)),T_a) = c_insert(V_a,V_A,T_a) ).
cnf(cls_Set_Oinsert__absorb2_0,axiom,
c_insert(V_x,c_insert(V_x,V_A,T_a),T_a) = c_insert(V_x,V_A,T_a) ).
cnf(cls_Set_Oinsert__disjoint__1_0,axiom,
( ~ c_in(V_a,V_B,T_a)
| c_inter(c_insert(V_a,V_A,T_a),V_B,T_a) != c_emptyset ) ).
cnf(cls_Set_Oinsert__disjoint__1_1,axiom,
( c_inter(c_insert(V_a,V_A,T_a),V_B,T_a) != c_emptyset
| c_inter(V_A,V_B,T_a) = c_emptyset ) ).
cnf(cls_Set_Oinsert__disjoint__1_2,axiom,
( c_inter(V_A,V_B,T_a) != c_emptyset
| c_in(V_a,V_B,T_a)
| c_inter(c_insert(V_a,V_A,T_a),V_B,T_a) = c_emptyset ) ).
cnf(cls_Set_Oinsert__disjoint__2_0,axiom,
( ~ c_in(V_a,V_B,T_a)
| c_emptyset != c_inter(c_insert(V_a,V_A,T_a),V_B,T_a) ) ).
cnf(cls_Set_Oinsert__disjoint__2_1,axiom,
( c_emptyset != c_inter(c_insert(V_a,V_A,T_a),V_B,T_a)
| c_emptyset = c_inter(V_A,V_B,T_a) ) ).
cnf(cls_Set_Oinsert__disjoint__2_2,axiom,
( c_emptyset != c_inter(V_A,V_B,T_a)
| c_in(V_a,V_B,T_a)
| c_emptyset = c_inter(c_insert(V_a,V_A,T_a),V_B,T_a) ) ).
cnf(cls_Set_Oinsert__iff_0,axiom,
( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| V_a = V_b ) ).
cnf(cls_Set_Oinsert__iff_1,axiom,
c_in(V_x,c_insert(V_x,V_A,T_a),T_a) ).
cnf(cls_Set_Oinsert__iff_2,axiom,
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ).
cnf(cls_Set_Oinsert__inter__insert_0,axiom,
c_inter(c_insert(V_a,V_A,T_a),c_insert(V_a,V_B,T_a),T_a) = c_insert(V_a,c_inter(V_A,V_B,T_a),T_a) ).
cnf(cls_Set_Oinsert__not__empty_0,axiom,
c_insert(V_a,V_A,T_a) != c_emptyset ).
cnf(cls_Set_Oinsert__subset_0,axiom,
( ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| c_in(V_x,V_B,T_a) ) ).
cnf(cls_Set_Oinsert__subset_1,axiom,
( ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_Oinsert__subset_2,axiom,
( ~ c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ) ).
cnf(cls_Set_Onot__psubset__empty_0,axiom,
~ c_less(V_A,c_emptyset,tc_set(T_a)) ).
cnf(cls_Set_Osingleton__insert__inj__eq_0,axiom,
( c_insert(V_b,c_emptyset,T_a) != c_insert(V_a,V_A,T_a)
| V_a = V_b ) ).
cnf(cls_Set_Osingleton__insert__inj__eq_1,axiom,
( c_insert(V_b,c_emptyset,T_a) != c_insert(V_a,V_A,T_a)
| c_lessequals(V_A,c_insert(V_b,c_emptyset,T_a),tc_set(T_a)) ) ).
cnf(cls_Set_Osingleton__insert__inj__eq_2,axiom,
( ~ c_lessequals(V_A,c_insert(V_x,c_emptyset,T_a),tc_set(T_a))
| c_insert(V_x,c_emptyset,T_a) = c_insert(V_x,V_A,T_a) ) ).
cnf(cls_Set_Osingleton__insert__inj__eq_H_0,axiom,
( c_insert(V_a,V_A,T_a) != c_insert(V_b,c_emptyset,T_a)
| V_a = V_b ) ).
cnf(cls_Set_Osingleton__insert__inj__eq_H_1,axiom,
( c_insert(V_a,V_A,T_a) != c_insert(V_b,c_emptyset,T_a)
| c_lessequals(V_A,c_insert(V_b,c_emptyset,T_a),tc_set(T_a)) ) ).
cnf(cls_Set_Osingleton__insert__inj__eq_H_2,axiom,
( ~ c_lessequals(V_A,c_insert(V_x,c_emptyset,T_a),tc_set(T_a))
| c_insert(V_x,V_A,T_a) = c_insert(V_x,c_emptyset,T_a) ) ).
cnf(cls_Set_Osubset__UNIV_0,axiom,
c_lessequals(V_A,c_UNIV,tc_set(T_a)) ).
cnf(cls_Set_Osubset__empty_0,axiom,
( ~ c_lessequals(V_A,c_emptyset,tc_set(T_a))
| V_A = c_emptyset ) ).
cnf(cls_Set_Osubset__empty_1,axiom,
c_lessequals(c_emptyset,c_emptyset,tc_set(T_a)) ).
cnf(cls_Sum__Type_OInl__eq_0,axiom,
( c_Sum__Type_OInl(V_x,T_a,T_b) != c_Sum__Type_OInl(V_y,T_a,T_b)
| V_x = V_y ) ).
cnf(cls_Sum__Type_OInl__not__Inr_0,axiom,
c_Sum__Type_OInl(V_a,T_a,T_b) != c_Sum__Type_OInr(V_b,T_b,T_a) ).
cnf(cls_Sum__Type_OInr__eq_0,axiom,
( c_Sum__Type_OInr(V_x,T_b,T_a) != c_Sum__Type_OInr(V_y,T_b,T_a)
| V_x = V_y ) ).
cnf(cls_Sum__Type_OInr__not__Inl_0,axiom,
c_Sum__Type_OInr(V_b,T_b,T_a) != c_Sum__Type_OInl(V_a,T_a,T_b) ).
cnf(cls_Sum__Type_OUNIV__Plus__UNIV_0,axiom,
c_Sum__Type_OPlus(c_UNIV,c_UNIV,T_a,T_b) = c_UNIV ).
cnf(cls_Transitive__Closure_ODomain__rtrancl_0,axiom,
c_Relation_ODomain(c_Transitive__Closure_Ortrancl(V_R,T_a),T_a,T_a) = c_UNIV ).
cnf(cls_Transitive__Closure_ORange__rtrancl_0,axiom,
c_Relation_ORange(c_Transitive__Closure_Ortrancl(V_R,T_a),T_a,T_a) = c_UNIV ).
cnf(cls_Transitive__Closure_Oreflcl__trancl_0,axiom,
c_union(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId,tc_prod(T_a,T_a)) = c_Transitive__Closure_Ortrancl(V_r,T_a) ).
cnf(cls_Transitive__Closure_Ortrancl__empty_0,axiom,
c_Transitive__Closure_Ortrancl(c_emptyset,T_a) = c_Relation_OId ).
cnf(cls_Transitive__Closure_Ortrancl__idemp_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a) ).
cnf(cls_Transitive__Closure_Ortrancl__idemp__self__comp_0,axiom,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),T_a,T_a,T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).
cnf(cls_Transitive__Closure_Ortrancl__reflcl_0,axiom,
c_Transitive__Closure_Ortrancl(c_union(V_R,c_Relation_OId,tc_prod(T_a,T_a)),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).
cnf(cls_Transitive__Closure_Otrancl__domain_0,axiom,
c_Relation_ODomain(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ODomain(V_r,T_a,T_a) ).
cnf(cls_Transitive__Closure_Otrancl__empty_0,axiom,
c_Transitive__Closure_Otrancl(c_emptyset,T_a) = c_emptyset ).
cnf(cls_Transitive__Closure_Otrancl__range_0,axiom,
c_Relation_ORange(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ORange(V_r,T_a,T_a) ).
cnf(cls_Transitive__Closure_Otrancl__reflcl_0,axiom,
c_Transitive__Closure_Otrancl(c_union(V_r,c_Relation_OId,tc_prod(T_a,T_a)),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a) ).
cnf(cls_Wellfounded__Recursion_Oacyclic__converse_0,axiom,
( ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(V_r,T_a,T_a),T_a)
| c_Wellfounded__Recursion_Oacyclic(V_r,T_a) ) ).
cnf(cls_Wellfounded__Recursion_Oacyclic__converse_1,axiom,
( ~ c_Wellfounded__Recursion_Oacyclic(V_r,T_a)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ).
cnf(cls_Wellfounded__Recursion_Oacyclic__insert_0,axiom,
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| c_Wellfounded__Recursion_Oacyclic(V_r,T_a) ) ).
cnf(cls_Wellfounded__Recursion_Oacyclic__insert_1,axiom,
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).
cnf(cls_Wellfounded__Recursion_Oacyclic__insert_2,axiom,
( ~ c_Wellfounded__Recursion_Oacyclic(V_r,T_a)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).
cnf(cls_Wellfounded__Recursion_Owf__insert_0,axiom,
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| c_Wellfounded__Recursion_Owf(V_r,T_a) ) ).
cnf(cls_Wellfounded__Recursion_Owf__insert_1,axiom,
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).
cnf(cls_Wellfounded__Recursion_Owf__insert_2,axiom,
( ~ c_Wellfounded__Recursion_Owf(V_r,T_a)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).
cnf(cls_Wellfounded__Recursion_Owf__not__refl_0,axiom,
( ~ c_Wellfounded__Recursion_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ).
cnf(cls_Wellfounded__Relations_Oless__than__iff_0,axiom,
( ~ c_in(c_Pair(V_x,V_y,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
| c_less(V_x,V_y,tc_nat) ) ).
cnf(cls_Wellfounded__Relations_Oless__than__iff_1,axiom,
( ~ c_less(V_x,V_y,tc_nat)
| c_in(c_Pair(V_x,V_y,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ).
%------------------------------------------------------------------------------