%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV341-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 09:03:26 AM UTC 2026
% Result : Unsatisfiable 150.25s 150.55s
% Output : Proof 150.35s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Datatype__Universe_OLeaf__inject__dest_0,axiom,
( V_x = V_y
| c_Datatype__Universe_OLeaf(V_x,T_a,T_b) != c_Datatype__Universe_OLeaf(V_y,T_a,T_b) ),
file('MSC001-0.ax',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
cnf(cls_Datatype__Universe_ONumb__inject__dest_0,axiom,
( V_x = V_y
| c_Datatype__Universe_ONumb(V_x,T_a,T_b) != c_Datatype__Universe_ONumb(V_y,T_a,T_b) ),
file('MSC001-0.ax',cls_Datatype__Universe_ONumb__inject__dest_0) ).
cnf(cls_Datatype__Universe_OdprodE_0,axiom,
( V_c = c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(V_c,V_r,V_s,T_a,T_b),c_Main_OdprodE__2(V_c,V_r,V_s,T_a,T_b),T_a,T_b),c_Datatype__Universe_OScons(c_Main_OdprodE__3(V_c,V_r,V_s,T_a,T_b),c_Main_OdprodE__4(V_c,V_r,V_s,T_a,T_b),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_in(V_c,c_Datatype__Universe_Odprod(V_r,V_s,T_a,T_b),tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OdprodE_0) ).
cnf(cls_Datatype__Universe_OdprodE_1,axiom,
( c_in(c_Pair(c_Main_OdprodE__2(V_c,V_r,V_s,T_a,T_b),c_Main_OdprodE__4(V_c,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))),V_s,tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))))
| ~ c_in(V_c,c_Datatype__Universe_Odprod(V_r,V_s,T_a,T_b),tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OdprodE_1) ).
cnf(cls_Datatype__Universe_OdprodE_2,axiom,
( c_in(c_Pair(c_Main_OdprodE__1(V_c,V_r,V_s,T_a,T_b),c_Main_OdprodE__3(V_c,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))),V_r,tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))))
| ~ c_in(V_c,c_Datatype__Universe_Odprod(V_r,V_s,T_a,T_b),tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OdprodE_2) ).
cnf(cls_Datatype__Universe_OdprodI_0,axiom,
( c_in(c_Pair(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),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),c_Datatype__Universe_Odprod(V_r,V_s,T_a,T_b),tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))))
| ~ c_in(c_Pair(V_M,V_M_H,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),V_r,tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))))
| ~ c_in(c_Pair(V_N,V_N_H,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),V_s,tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OdprodI_0) ).
cnf(cls_Datatype__Universe_OdsumE_0,axiom,
( V_w = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(V_s,V_w,T_a,T_b),T_a,T_b),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(V_s,V_w,T_a,T_b),T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))
| V_w = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(V_r,V_w,T_a,T_b),T_a,T_b),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(V_r,V_w,T_a,T_b),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_in(V_w,c_Datatype__Universe_Odsum(V_r,V_s,T_a,T_b),tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OdsumE_0) ).
cnf(cls_Datatype__Universe_OdsumE_1,axiom,
( V_w = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(V_r,V_w,T_a,T_b),T_a,T_b),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(V_r,V_w,T_a,T_b),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_in(c_Pair(c_Main_OdsumE__3(V_s,V_w,T_a,T_b),c_Main_OdsumE__4(V_s,V_w,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),V_s,tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))))
| ~ c_in(V_w,c_Datatype__Universe_Odsum(V_r,V_s,T_a,T_b),tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OdsumE_1) ).
cnf(cls_Datatype__Universe_OdsumE_2,axiom,
( V_w = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(V_s,V_w,T_a,T_b),T_a,T_b),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(V_s,V_w,T_a,T_b),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_in(c_Pair(c_Main_OdsumE__1(V_r,V_w,T_a,T_b),c_Main_OdsumE__2(V_r,V_w,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),V_r,tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))))
| ~ c_in(V_w,c_Datatype__Universe_Odsum(V_r,V_s,T_a,T_b),tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OdsumE_2) ).
cnf(cls_Datatype__Universe_OdsumE_3,axiom,
( c_in(c_Pair(c_Main_OdsumE__3(V_s,V_w,T_a,T_b),c_Main_OdsumE__4(V_s,V_w,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),V_s,tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))))
| c_in(c_Pair(c_Main_OdsumE__1(V_r,V_w,T_a,T_b),c_Main_OdsumE__2(V_r,V_w,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),V_r,tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))))
| ~ c_in(V_w,c_Datatype__Universe_Odsum(V_r,V_s,T_a,T_b),tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OdsumE_3) ).
cnf(cls_Datatype__Universe_Odsum__In0I_0,axiom,
( c_in(c_Pair(c_Datatype__Universe_OIn0(V_M,T_a,T_b),c_Datatype__Universe_OIn0(V_M_H,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_Odsum(V_r,V_s,T_a,T_b),tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))))
| ~ c_in(c_Pair(V_M,V_M_H,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),V_r,tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))) ),
file('MSC001-0.ax',cls_Datatype__Universe_Odsum__In0I_0) ).
cnf(cls_Datatype__Universe_Odsum__In1I_0,axiom,
( c_in(c_Pair(c_Datatype__Universe_OIn1(V_N,T_a,T_b),c_Datatype__Universe_OIn1(V_N_H,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_Odsum(V_r,V_s,T_a,T_b),tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))))
| ~ c_in(c_Pair(V_N,V_N_H,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))),V_s,tc_prod(tc_set(tc_Datatype__Universe_Onode(T_a,T_b)),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))) ),
file('MSC001-0.ax',cls_Datatype__Universe_Odsum__In1I_0) ).
cnf(cls_Datatype__Universe_OuprodE_0,axiom,
( V_c = c_Datatype__Universe_OScons(c_Main_OuprodE__1(V_A,V_B,V_c,T_a,T_b),c_Main_OuprodE__2(V_A,V_B,V_c,T_a,T_b),T_a,T_b)
| ~ c_in(V_c,c_Datatype__Universe_Ouprod(V_A,V_B,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OuprodE_0) ).
cnf(cls_Datatype__Universe_OuprodE_1,axiom,
( c_in(c_Main_OuprodE__2(V_A,V_B,V_c,T_a,T_b),V_B,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))
| ~ c_in(V_c,c_Datatype__Universe_Ouprod(V_A,V_B,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OuprodE_1) ).
cnf(cls_Datatype__Universe_OuprodE_2,axiom,
( c_in(c_Main_OuprodE__1(V_A,V_B,V_c,T_a,T_b),V_A,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))
| ~ c_in(V_c,c_Datatype__Universe_Ouprod(V_A,V_B,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OuprodE_2) ).
cnf(cls_Datatype__Universe_OuprodI_0,axiom,
( c_in(c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),c_Datatype__Universe_Ouprod(V_A,V_B,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))
| ~ c_in(V_M,V_A,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))
| ~ c_in(V_N,V_B,tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OuprodI_0) ).
cnf(cls_Datatype__Universe_OusumE_0,axiom,
( V_u = c_Datatype__Universe_OIn1(c_Main_OusumE__2(V_B,V_u,T_a,T_b),T_a,T_b)
| V_u = c_Datatype__Universe_OIn0(c_Main_OusumE__1(V_A,V_u,T_a,T_b),T_a,T_b)
| ~ c_in(V_u,c_Datatype__Universe_Ousum(V_A,V_B,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OusumE_0) ).
cnf(cls_Datatype__Universe_OusumE_1,axiom,
( V_u = c_Datatype__Universe_OIn0(c_Main_OusumE__1(V_A,V_u,T_a,T_b),T_a,T_b)
| c_in(c_Main_OusumE__2(V_B,V_u,T_a,T_b),V_B,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))
| ~ c_in(V_u,c_Datatype__Universe_Ousum(V_A,V_B,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OusumE_1) ).
cnf(cls_Datatype__Universe_OusumE_2,axiom,
( V_u = c_Datatype__Universe_OIn1(c_Main_OusumE__2(V_B,V_u,T_a,T_b),T_a,T_b)
| c_in(c_Main_OusumE__1(V_A,V_u,T_a,T_b),V_A,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))
| ~ c_in(V_u,c_Datatype__Universe_Ousum(V_A,V_B,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OusumE_2) ).
cnf(cls_Datatype__Universe_OusumE_3,axiom,
( c_in(c_Main_OusumE__2(V_B,V_u,T_a,T_b),V_B,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))
| c_in(c_Main_OusumE__1(V_A,V_u,T_a,T_b),V_A,tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))
| ~ c_in(V_u,c_Datatype__Universe_Ousum(V_A,V_B,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) ),
file('MSC001-0.ax',cls_Datatype__Universe_OusumE_3) ).
cnf(cls_Datatype__Universe_Ousum__In0I_0,axiom,
( c_in(c_Datatype__Universe_OIn0(V_M,T_a,T_b),c_Datatype__Universe_Ousum(V_A,V_B,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))
| ~ c_in(V_M,V_A,tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) ),
file('MSC001-0.ax',cls_Datatype__Universe_Ousum__In0I_0) ).
cnf(cls_Datatype__Universe_Ousum__In1I_0,axiom,
( c_in(c_Datatype__Universe_OIn1(V_N,T_a,T_b),c_Datatype__Universe_Ousum(V_A,V_B,T_a,T_b),tc_set(tc_Datatype__Universe_Onode(T_a,T_b)))
| ~ c_in(V_N,V_B,tc_set(tc_Datatype__Universe_Onode(T_a,T_b))) ),
file('MSC001-0.ax',cls_Datatype__Universe_Ousum__In1I_0) ).
cnf(cls_Divides_Odvd__0__right_0,axiom,
c_Divides_Oop_Advd(V_m,c_0,tc_nat),
file('MSC001-0.ax',cls_Divides_Odvd__0__right_0) ).
cnf(cls_Divides_Odvd__1__left_0,axiom,
c_Divides_Oop_Advd(c_Suc(c_0),V_k,tc_nat),
file('MSC001-0.ax',cls_Divides_Odvd__1__left_0) ).
cnf(cls_Divides_Odvd__triv__left_0,axiom,
c_Divides_Oop_Advd(V_k,c_times(V_k,V_m,tc_nat),tc_nat),
file('MSC001-0.ax',cls_Divides_Odvd__triv__left_0) ).
cnf(cls_Divides_Odvd__triv__right_0,axiom,
c_Divides_Oop_Advd(V_k,c_times(V_m,V_k,tc_nat),tc_nat),
file('MSC001-0.ax',cls_Divides_Odvd__triv__right_0) ).
cnf(cls_Divides_Omod__eq__0D__dest_0,axiom,
( V_m = c_times(V_d,c_Main_Omod__eq__0D__dest__1(V_d,V_m),tc_nat)
| c_Divides_Oop_Amod(V_m,V_d,tc_nat) != c_0 ),
file('MSC001-0.ax',cls_Divides_Omod__eq__0D__dest_0) ).
cnf(cls_Finite__Set_OFinites_OemptyI_0,axiom,
c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(T_a)),
file('MSC001-0.ax',cls_Finite__Set_OFinites_OemptyI_0) ).
cnf(cls_Finite__Set_OFinites_OinsertI_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)) ),
file('MSC001-0.ax',cls_Finite__Set_OFinites_OinsertI_0) ).
cnf(cls_Finite__Set_Ofinite__Int_0,axiom,
( c_in(c_inter(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)) ),
file('MSC001-0.ax',cls_Finite__Set_Ofinite__Int_0) ).
cnf(cls_Finite__Set_Ofinite__Int_1,axiom,
( c_in(c_inter(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)) ),
file('MSC001-0.ax',cls_Finite__Set_Ofinite__Int_1) ).
cnf(cls_Finite__Set_Ofinite__Union_0,axiom,
( c_in(c_Union(V_A,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| c_in(c_Main_Ofinite__Union__1(V_A,T_a),V_A,tc_set(T_a))
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(tc_set(T_a))) ),
file('MSC001-0.ax',cls_Finite__Set_Ofinite__Union_0) ).
cnf(cls_Finite__Set_Ofinite__Union_1,axiom,
( c_in(c_Union(V_A,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(c_Main_Ofinite__Union__1(V_A,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(tc_set(T_a))) ),
file('MSC001-0.ax',cls_Finite__Set_Ofinite__Union_1) ).
cnf(cls_GCD_Ogcd__dvd1_0,axiom,
c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(V_m,V_n,tc_nat,tc_nat)),V_m,tc_nat),
file('MSC001-0.ax',cls_GCD_Ogcd__dvd1_0) ).
cnf(cls_GCD_Ogcd__dvd2_0,axiom,
c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(V_m,V_n,tc_nat,tc_nat)),V_n,tc_nat),
file('MSC001-0.ax',cls_GCD_Ogcd__dvd2_0) ).
cnf(cls_Infinite__Set_Oatmost__one__unique_0,axiom,
( V_y = V_x
| ~ c_in(V_x,V_S,T_a)
| ~ c_in(V_y,V_S,T_a)
| ~ c_Infinite__Set_Oatmost__one(V_S,T_a) ),
file('MSC001-0.ax',cls_Infinite__Set_Oatmost__one__unique_0) ).
cnf(cls_IntDef_Onegative__zle_0,axiom,
c_lessequals(c_uminus(c_IntDef_Oint(V_n),tc_IntDef_Oint),c_IntDef_Oint(V_m),tc_IntDef_Oint),
file('MSC001-0.ax',cls_IntDef_Onegative__zle_0) ).
cnf(cls_IntDef_Onegative__zless_0,axiom,
c_less(c_uminus(c_IntDef_Oint(c_Suc(V_n)),tc_IntDef_Oint),c_IntDef_Oint(V_m),tc_IntDef_Oint),
file('MSC001-0.ax',cls_IntDef_Onegative__zless_0) ).
cnf(cls_IntDiv_Ozdvd__0__right_0,axiom,
c_Divides_Oop_Advd(V_m,c_0,tc_IntDef_Oint),
file('MSC001-0.ax',cls_IntDiv_Ozdvd__0__right_0) ).
cnf(cls_IntDiv_Ozdvd__1__left_0,axiom,
c_Divides_Oop_Advd(c_1,V_m,tc_IntDef_Oint),
file('MSC001-0.ax',cls_IntDiv_Ozdvd__1__left_0) ).
cnf(cls_IntDiv_Ozdvd__triv__left_0,axiom,
c_Divides_Oop_Advd(V_k,c_times(V_k,V_m,tc_IntDef_Oint),tc_IntDef_Oint),
file('MSC001-0.ax',cls_IntDiv_Ozdvd__triv__left_0) ).
cnf(cls_IntDiv_Ozdvd__triv__right_0,axiom,
c_Divides_Oop_Advd(V_k,c_times(V_m,V_k,tc_IntDef_Oint),tc_IntDef_Oint),
file('MSC001-0.ax',cls_IntDiv_Ozdvd__triv__right_0) ).
cnf(cls_IntDiv_Ozmod__eq__0D__dest_0,axiom,
( V_m = c_times(V_d,c_Main_Ozmod__eq__0D__dest__1(V_d,V_m),tc_IntDef_Oint)
| c_Divides_Oop_Amod(V_m,V_d,tc_IntDef_Oint) != c_0 ),
file('MSC001-0.ax',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
cnf(cls_List_Odistinct__remdups_0,axiom,
c_List_Odistinct(c_List_Oremdups(V_xs,T_a),T_a),
file('MSC001-0.ax',cls_List_Odistinct__remdups_0) ).
cnf(cls_List_Ofinite__set_0,axiom,
c_in(c_List_Oset(V_xs,T_a),c_Finite__Set_OFinites,tc_set(T_a)),
file('MSC001-0.ax',cls_List_Ofinite__set_0) ).
cnf(cls_List_Oin__listsD__dest_0,axiom,
( c_in(V_U,V_A,T_a)
| ~ c_in(V_U,c_List_Oset(V_xs,T_a),T_a)
| ~ c_in(V_xs,c_List_Olists(V_A,T_a),tc_List_Olist(T_a)) ),
file('MSC001-0.ax',cls_List_Oin__listsD__dest_0) ).
cnf(cls_List_Oin__listsI_0,axiom,
( c_in(c_Main_Oin__listsI__1(V_A,V_xs,T_a),c_List_Oset(V_xs,T_a),T_a)
| c_in(V_xs,c_List_Olists(V_A,T_a),tc_List_Olist(T_a)) ),
file('MSC001-0.ax',cls_List_Oin__listsI_0) ).
cnf(cls_List_Oin__listsI_1,axiom,
( c_in(V_xs,c_List_Olists(V_A,T_a),tc_List_Olist(T_a))
| ~ c_in(c_Main_Oin__listsI__1(V_A,V_xs,T_a),V_A,T_a) ),
file('MSC001-0.ax',cls_List_Oin__listsI_1) ).
cnf(cls_List_Olength__remdups__leq_0,axiom,
c_lessequals(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)),tc_nat),
file('MSC001-0.ax',cls_List_Olength__remdups__leq_0) ).
cnf(cls_List_Olistrel__Cons1_0,axiom,
( V_xs = c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(V_r,V_xs,V_y,V_ys,T_a),c_Main_Olistrel__Cons1__2(V_r,V_xs,V_y,V_ys,T_a),T_a)
| ~ c_in(c_Pair(c_List_Olist_OCons(V_y,V_ys,T_a),V_xs,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ),
file('MSC001-0.ax',cls_List_Olistrel__Cons1_0) ).
cnf(cls_List_Olistrel__Cons1_1,axiom,
( c_in(c_Pair(V_ys,c_Main_Olistrel__Cons1__2(V_r,V_xs,V_y,V_ys,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel(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_y,V_ys,T_a),V_xs,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ),
file('MSC001-0.ax',cls_List_Olistrel__Cons1_1) ).
cnf(cls_List_Olistrel__Cons1_2,axiom,
( c_in(c_Pair(V_y,c_Main_Olistrel__Cons1__1(V_r,V_xs,V_y,V_ys,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(c_List_Olist_OCons(V_y,V_ys,T_a),V_xs,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ),
file('MSC001-0.ax',cls_List_Olistrel__Cons1_2) ).
cnf(cls_List_Olistrel__Cons2_0,axiom,
( V_xs = c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(V_r,V_xs,V_y,V_ys,T_a),c_Main_Olistrel__Cons2__2(V_r,V_xs,V_y,V_ys,T_a),T_a)
| ~ c_in(c_Pair(V_xs,c_List_Olist_OCons(V_y,V_ys,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ),
file('MSC001-0.ax',cls_List_Olistrel__Cons2_0) ).
cnf(cls_List_Olistrel__Cons2_1,axiom,
( c_in(c_Pair(c_Main_Olistrel__Cons2__2(V_r,V_xs,V_y,V_ys,T_a),V_ys,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))
| ~ c_in(c_Pair(V_xs,c_List_Olist_OCons(V_y,V_ys,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ),
file('MSC001-0.ax',cls_List_Olistrel__Cons2_1) ).
cnf(cls_List_Olistrel__Cons2_2,axiom,
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(V_r,V_xs,V_y,V_ys,T_a),V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_xs,c_List_Olist_OCons(V_y,V_ys,T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ),
file('MSC001-0.ax',cls_List_Olistrel__Cons2_2) ).
cnf(cls_List_Olistrel__Nil1_0,axiom,
( V_xs = c_List_Olist_ONil
| ~ c_in(c_Pair(c_List_Olist_ONil,V_xs,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ),
file('MSC001-0.ax',cls_List_Olistrel__Nil1_0) ).
cnf(cls_List_Olistrel__Nil2_0,axiom,
( V_xs = c_List_Olist_ONil
| ~ c_in(c_Pair(V_xs,c_List_Olist_ONil,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))) ),
file('MSC001-0.ax',cls_List_Olistrel__Nil2_0) ).
cnf(cls_List_OlistsE_0,axiom,
( c_in(V_l,c_List_Olists(V_A,T_a),tc_List_Olist(T_a))
| ~ c_in(c_List_Olist_OCons(V_x,V_l,T_a),c_List_Olists(V_A,T_a),tc_List_Olist(T_a)) ),
file('MSC001-0.ax',cls_List_OlistsE_0) ).
cnf(cls_List_OlistsE_1,axiom,
( c_in(V_x,V_A,T_a)
| ~ c_in(c_List_Olist_OCons(V_x,V_l,T_a),c_List_Olists(V_A,T_a),tc_List_Olist(T_a)) ),
file('MSC001-0.ax',cls_List_OlistsE_1) ).
cnf(cls_List_Olists_OCons_0,axiom,
( c_in(c_List_Olist_OCons(V_a,V_l,T_a),c_List_Olists(V_A,T_a),tc_List_Olist(T_a))
| ~ c_in(V_l,c_List_Olists(V_A,T_a),tc_List_Olist(T_a))
| ~ c_in(V_a,V_A,T_a) ),
file('MSC001-0.ax',cls_List_Olists_OCons_0) ).
cnf(cls_List_Olists_ONil_0,axiom,
c_in(c_List_Olist_ONil,c_List_Olists(V_A,T_a),tc_List_Olist(T_a)),
file('MSC001-0.ax',cls_List_Olists_ONil_0) ).
cnf(cls_List_Owf__lenlex_0,axiom,
( c_Wellfounded__Recursion_Owf(c_List_Olenlex(V_r,T_a),tc_List_Olist(T_a))
| ~ c_Wellfounded__Recursion_Owf(V_r,T_a) ),
file('MSC001-0.ax',cls_List_Owf__lenlex_0) ).
cnf(cls_List_Owf__lex_0,axiom,
( c_Wellfounded__Recursion_Owf(c_List_Olex(V_r,T_a),tc_List_Olist(T_a))
| ~ c_Wellfounded__Recursion_Owf(V_r,T_a) ),
file('MSC001-0.ax',cls_List_Owf__lex_0) ).
cnf(cls_Nat_Ole0_0,axiom,
c_lessequals(c_0,V_n,tc_nat),
file('MSC001-0.ax',cls_Nat_Ole0_0) ).
cnf(cls_Nat_OlessI_0,axiom,
c_less(V_n,c_Suc(V_n),tc_nat),
file('MSC001-0.ax',cls_Nat_OlessI_0) ).
cnf(cls_Nat_Oless__irrefl_0,axiom,
~ c_less(V_n,V_n,tc_nat),
file('MSC001-0.ax',cls_Nat_Oless__irrefl_0) ).
cnf(cls_Nat_Ozero__less__Suc_0,axiom,
c_less(c_0,c_Suc(V_n),tc_nat),
file('MSC001-0.ax',cls_Nat_Ozero__less__Suc_0) ).
cnf(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('MSC001-0.ax',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
cnf(cls_Relation_ODomainE_0,axiom,
( c_in(c_Pair(V_a,c_Main_ODomainE__1(V_a,V_r,T_a,T_b),T_a,T_b),V_r,tc_prod(T_a,T_b))
| ~ c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a) ),
file('MSC001-0.ax',cls_Relation_ODomainE_0) ).
cnf(cls_Relation_ODomainI_0,axiom,
( c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b)) ),
file('MSC001-0.ax',cls_Relation_ODomainI_0) ).
cnf(cls_Relation_OIdE_0,axiom,
( V_p = c_Pair(c_Main_OIdE__1(V_p,T_a),c_Main_OIdE__1(V_p,T_a),T_a,T_a)
| ~ c_in(V_p,c_Relation_OId,tc_prod(T_a,T_a)) ),
file('MSC001-0.ax',cls_Relation_OIdE_0) ).
cnf(cls_Relation_OImageE_0,axiom,
( c_in(c_Main_OImageE__1(V_A,V_b,V_r,T_b,T_a),V_A,T_b)
| ~ c_in(V_b,c_Relation_OImage(V_r,V_A,T_b,T_a),T_a) ),
file('MSC001-0.ax',cls_Relation_OImageE_0) ).
cnf(cls_Relation_OImageE_1,axiom,
( c_in(c_Pair(c_Main_OImageE__1(V_A,V_b,V_r,T_b,T_a),V_b,T_b,T_a),V_r,tc_prod(T_b,T_a))
| ~ c_in(V_b,c_Relation_OImage(V_r,V_A,T_b,T_a),T_a) ),
file('MSC001-0.ax',cls_Relation_OImageE_1) ).
cnf(cls_Relation_OImageI_0,axiom,
( c_in(V_b,c_Relation_OImage(V_r,V_A,T_a,T_b),T_b)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| ~ c_in(V_a,V_A,T_a) ),
file('MSC001-0.ax',cls_Relation_OImageI_0) ).
cnf(cls_Relation_ORangeE_0,axiom,
( c_in(c_Pair(c_Main_ORangeE__1(V_b,V_r,T_a,T_b),V_b,T_b,T_a),V_r,tc_prod(T_b,T_a))
| ~ c_in(V_b,c_Relation_ORange(V_r,T_b,T_a),T_a) ),
file('MSC001-0.ax',cls_Relation_ORangeE_0) ).
cnf(cls_Relation_ORangeI_0,axiom,
( c_in(V_b,c_Relation_ORange(V_r,T_a,T_b),T_b)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b)) ),
file('MSC001-0.ax',cls_Relation_ORangeI_0) ).
cnf(cls_Relation_OconverseE_0,axiom,
( c_in(c_Pair(c_Main_OconverseE__1(V_r,V_yx,T_b,T_a),c_Main_OconverseE__2(V_r,V_yx,T_b,T_a),T_b,T_a),V_r,tc_prod(T_b,T_a))
| ~ c_in(V_yx,c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b)) ),
file('MSC001-0.ax',cls_Relation_OconverseE_0) ).
cnf(cls_Relation_OconverseE_1,axiom,
( V_yx = c_Pair(c_Main_OconverseE__2(V_r,V_yx,T_b,T_a),c_Main_OconverseE__1(V_r,V_yx,T_b,T_a),T_a,T_b)
| ~ c_in(V_yx,c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b)) ),
file('MSC001-0.ax',cls_Relation_OconverseE_1) ).
cnf(cls_Relation_OdiagE_0,axiom,
( V_c = c_Pair(c_Main_OdiagE__1(V_A,V_c,T_a),c_Main_OdiagE__1(V_A,V_c,T_a),T_a,T_a)
| ~ c_in(V_c,c_Relation_Odiag(V_A,T_a),tc_prod(T_a,T_a)) ),
file('MSC001-0.ax',cls_Relation_OdiagE_0) ).
cnf(cls_Relation_OdiagE_1,axiom,
( c_in(c_Main_OdiagE__1(V_A,V_c,T_a),V_A,T_a)
| ~ c_in(V_c,c_Relation_Odiag(V_A,T_a),tc_prod(T_a,T_a)) ),
file('MSC001-0.ax',cls_Relation_OdiagE_1) ).
cnf(cls_Relation_OdiagI_0,axiom,
( c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_Odiag(V_A,T_a),tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a) ),
file('MSC001-0.ax',cls_Relation_OdiagI_0) ).
cnf(cls_Relation_Orel__compE_0,axiom,
( c_in(c_Pair(c_Main_Orel__compE__2(V_r,V_s,V_xz,T_c,T_b,T_a),c_Main_Orel__compE__3(V_r,V_s,V_xz,T_c,T_b,T_a),T_c,T_b),V_r,tc_prod(T_c,T_b))
| ~ c_in(V_xz,c_Relation_Orel__comp(V_r,V_s,T_c,T_b,T_a),tc_prod(T_a,T_b)) ),
file('MSC001-0.ax',cls_Relation_Orel__compE_0) ).
cnf(cls_Relation_Orel__compE_1,axiom,
( c_in(c_Pair(c_Main_Orel__compE__1(V_r,V_s,V_xz,T_c,T_b,T_a),c_Main_Orel__compE__2(V_r,V_s,V_xz,T_c,T_b,T_a),T_a,T_c),V_s,tc_prod(T_a,T_c))
| ~ c_in(V_xz,c_Relation_Orel__comp(V_r,V_s,T_c,T_b,T_a),tc_prod(T_a,T_b)) ),
file('MSC001-0.ax',cls_Relation_Orel__compE_1) ).
cnf(cls_Relation_Orel__compE_2,axiom,
( V_xz = c_Pair(c_Main_Orel__compE__1(V_r,V_s,V_xz,T_c,T_b,T_a),c_Main_Orel__compE__3(V_r,V_s,V_xz,T_c,T_b,T_a),T_a,T_b)
| ~ c_in(V_xz,c_Relation_Orel__comp(V_r,V_s,T_c,T_b,T_a),tc_prod(T_a,T_b)) ),
file('MSC001-0.ax',cls_Relation_Orel__compE_2) ).
cnf(cls_Relation_Orel__compI_0,axiom,
( c_in(c_Pair(V_a,V_c,T_a,T_c),c_Relation_Orel__comp(V_r,V_s,T_b,T_c,T_a),tc_prod(T_a,T_c))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_s,tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_c,T_b,T_c),V_r,tc_prod(T_b,T_c)) ),
file('MSC001-0.ax',cls_Relation_Orel__compI_0) ).
cnf(cls_SetInterval_Ofinite__atLeastAtMost_0,axiom,
c_in(c_SetInterval_OatLeastAtMost(V_l,V_u,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('MSC001-0.ax',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
cnf(cls_SetInterval_Ofinite__atLeastAtMost__int_0,axiom,
c_in(c_SetInterval_OatLeastAtMost(V_l,V_u,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('MSC001-0.ax',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
cnf(cls_SetInterval_Ofinite__atLeastLessThan_0,axiom,
c_in(c_SetInterval_OatLeastLessThan(V_l,V_u,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('MSC001-0.ax',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
cnf(cls_SetInterval_Ofinite__atLeastLessThan__int_0,axiom,
c_in(c_SetInterval_OatLeastLessThan(V_l,V_u,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('MSC001-0.ax',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
cnf(cls_SetInterval_Ofinite__atMost_0,axiom,
c_in(c_SetInterval_OatMost(V_k,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('MSC001-0.ax',cls_SetInterval_Ofinite__atMost_0) ).
cnf(cls_SetInterval_Ofinite__greaterThanAtMost_0,axiom,
c_in(c_SetInterval_OgreaterThanAtMost(V_l,V_u,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('MSC001-0.ax',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
cnf(cls_SetInterval_Ofinite__greaterThanAtMost__int_0,axiom,
c_in(c_SetInterval_OgreaterThanAtMost(V_l,V_u,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('MSC001-0.ax',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
cnf(cls_SetInterval_Ofinite__greaterThanLessThan_0,axiom,
c_in(c_SetInterval_OgreaterThanLessThan(V_l,V_u,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('MSC001-0.ax',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
cnf(cls_SetInterval_Ofinite__greaterThanLessThan__int_0,axiom,
c_in(c_SetInterval_OgreaterThanLessThan(V_l,V_u,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('MSC001-0.ax',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
cnf(cls_SetInterval_Ofinite__lessThan_0,axiom,
c_in(c_SetInterval_OlessThan(V_k,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('MSC001-0.ax',cls_SetInterval_Ofinite__lessThan_0) ).
cnf(cls_Set_OInterI_0,axiom,
( c_in(c_Main_OInterI__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_in(V_A,c_Inter(V_C,T_a),T_a) ),
file('MSC001-0.ax',cls_Set_OInterI_0) ).
cnf(cls_Set_OInterI_1,axiom,
( c_in(V_A,c_Inter(V_C,T_a),T_a)
| ~ c_in(V_A,c_Main_OInterI__1(V_A,V_C,T_a),T_a) ),
file('MSC001-0.ax',cls_Set_OInterI_1) ).
cnf(cls_Set_OUNIV__I_0,axiom,
c_in(V_x,c_UNIV,T_a),
file('MSC001-0.ax',cls_Set_OUNIV__I_0) ).
cnf(cls_Set_OUnionE_0,axiom,
( c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('MSC001-0.ax',cls_Set_OUnionE_0) ).
cnf(cls_Set_OUnionE_1,axiom,
( c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a)
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('MSC001-0.ax',cls_Set_OUnionE_1) ).
cnf(cls_Set_Oempty__subsetI_0,axiom,
c_lessequals(c_emptyset,V_A,tc_set(T_a)),
file('MSC001-0.ax',cls_Set_Oempty__subsetI_0) ).
cnf(cls_Set_OpsubsetE_0,axiom,
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_less(V_A,V_B,tc_set(T_a)) ),
file('MSC001-0.ax',cls_Set_OpsubsetE_0) ).
cnf(cls_Set_OpsubsetE_1,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_less(V_A,V_B,tc_set(T_a)) ),
file('MSC001-0.ax',cls_Set_OpsubsetE_1) ).
cnf(cls_Set_OpsubsetI_0,axiom,
( V_A = V_B
| c_less(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
file('MSC001-0.ax',cls_Set_OpsubsetI_0) ).
cnf(cls_Set_OsingletonD__dest_0,axiom,
( V_b = V_a
| ~ c_in(V_b,c_insert(V_a,c_emptyset,T_a),T_a) ),
file('MSC001-0.ax',cls_Set_OsingletonD__dest_0) ).
cnf(cls_Set_OsingletonI_0,axiom,
c_in(V_a,c_insert(V_a,c_emptyset,T_a),T_a),
file('MSC001-0.ax',cls_Set_OsingletonI_0) ).
cnf(cls_Set_Osingleton__inject__dest_0,axiom,
( V_a = V_b
| c_insert(V_a,c_emptyset,T_a) != c_insert(V_b,c_emptyset,T_a) ),
file('MSC001-0.ax',cls_Set_Osingleton__inject__dest_0) ).
cnf(cls_Set_OsubsetD_0,axiom,
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
file('MSC001-0.ax',cls_Set_OsubsetD_0) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
file('MSC001-0.ax',cls_Set_OsubsetI_0) ).
cnf(cls_Set_OsubsetI_1,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
file('MSC001-0.ax',cls_Set_OsubsetI_1) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
file('MSC001-0.ax',cls_Set_Osubset__antisym_0) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_set(T_a)),
file('MSC001-0.ax',cls_Set_Osubset__refl_0) ).
cnf(cls_Sum__Type_OInlI_0,axiom,
( c_in(c_Sum__Type_OInl(V_a,T_a,T_b),c_Sum__Type_OPlus(V_A,V_B,T_a,T_b),tc_sum(T_a,T_b))
| ~ c_in(V_a,V_A,T_a) ),
file('MSC001-0.ax',cls_Sum__Type_OInlI_0) ).
cnf(cls_Sum__Type_OInrI_0,axiom,
( c_in(c_Sum__Type_OInr(V_b,T_a,T_b),c_Sum__Type_OPlus(V_A,V_B,T_b,T_a),tc_sum(T_b,T_a))
| ~ c_in(V_b,V_B,T_a) ),
file('MSC001-0.ax',cls_Sum__Type_OInrI_0) ).
cnf(cls_Sum__Type_OPlusE_0,axiom,
( V_u = c_Sum__Type_OInr(c_Main_OPlusE__2(V_B,V_u,T_b,T_a),T_b,T_a)
| V_u = c_Sum__Type_OInl(c_Main_OPlusE__1(V_A,V_u,T_a,T_b),T_a,T_b)
| ~ c_in(V_u,c_Sum__Type_OPlus(V_A,V_B,T_a,T_b),tc_sum(T_a,T_b)) ),
file('MSC001-0.ax',cls_Sum__Type_OPlusE_0) ).
cnf(cls_Sum__Type_OPlusE_1,axiom,
( V_u = c_Sum__Type_OInl(c_Main_OPlusE__1(V_A,V_u,T_a,T_b),T_a,T_b)
| c_in(c_Main_OPlusE__2(V_B,V_u,T_b,T_a),V_B,T_b)
| ~ c_in(V_u,c_Sum__Type_OPlus(V_A,V_B,T_a,T_b),tc_sum(T_a,T_b)) ),
file('MSC001-0.ax',cls_Sum__Type_OPlusE_1) ).
cnf(cls_Sum__Type_OPlusE_2,axiom,
( V_u = c_Sum__Type_OInr(c_Main_OPlusE__2(V_B,V_u,T_b,T_a),T_b,T_a)
| c_in(c_Main_OPlusE__1(V_A,V_u,T_a,T_b),V_A,T_a)
| ~ c_in(V_u,c_Sum__Type_OPlus(V_A,V_B,T_a,T_b),tc_sum(T_a,T_b)) ),
file('MSC001-0.ax',cls_Sum__Type_OPlusE_2) ).
cnf(cls_Sum__Type_OPlusE_3,axiom,
( c_in(c_Main_OPlusE__2(V_B,V_u,T_b,T_a),V_B,T_b)
| c_in(c_Main_OPlusE__1(V_A,V_u,T_a,T_b),V_A,T_a)
| ~ c_in(V_u,c_Sum__Type_OPlus(V_A,V_B,T_a,T_b),tc_sum(T_a,T_b)) ),
file('MSC001-0.ax',cls_Sum__Type_OPlusE_3) ).
cnf(cls_Transitive__Closure_Or__into__rtrancl_0,axiom,
( c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(V_p,V_r,tc_prod(T_a,T_a)) ),
file('MSC001-0.ax',cls_Transitive__Closure_Or__into__rtrancl_0) ).
cnf(cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0,axiom,
c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)),
file('MSC001-0.ax',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
cnf(cls_Transitive__Closure_Otrancl_Or__into__trancl_0,axiom,
( c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('MSC001-0.ax',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
cnf(cls_Transitive__Closure_Otrancl__into__rtrancl_0,axiom,
( c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('MSC001-0.ax',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
cnf(cls_Wellfounded__Recursion_Owf__empty_0,axiom,
c_Wellfounded__Recursion_Owf(c_emptyset,T_a),
file('MSC001-0.ax',cls_Wellfounded__Recursion_Owf__empty_0) ).
cnf(cls_Wellfounded__Relations_Otrans__less__than_0,axiom,
c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
file('MSC001-0.ax',cls_Wellfounded__Relations_Otrans__less__than_0) ).
cnf(cls_Wellfounded__Relations_Otrans__lex__prod_0,axiom,
( c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(V_R1,V_R2,T_a,T_b),tc_prod(T_a,T_b))
| ~ c_Relation_Otrans(V_R1,T_a)
| ~ c_Relation_Otrans(V_R2,T_b) ),
file('MSC001-0.ax',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
cnf(cls_Wellfounded__Relations_Owf__less__than_0,axiom,
c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
file('MSC001-0.ax',cls_Wellfounded__Relations_Owf__less__than_0) ).
cnf(cls_Wellfounded__Relations_Owf__lex__prod_0,axiom,
( c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(V_ra,V_rb,T_a,T_b),tc_prod(T_a,T_b))
| ~ c_Wellfounded__Recursion_Owf(V_ra,T_a)
| ~ c_Wellfounded__Recursion_Owf(V_rb,T_b) ),
file('MSC001-0.ax',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
cnf(clsarity_Datatype__Ooption_0,axiom,
( ~ class_Finite__Set_Ofinite(T_1)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(T_1)) ),
file('MSC001-0.ax',clsarity_Datatype__Ooption_0) ).
cnf(clsarity_IntDef__Oint_0,axiom,
class_HOL_Ominus(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_0) ).
cnf(clsarity_IntDef__Oint_1,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_1) ).
cnf(clsarity_IntDef__Oint_10,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_10) ).
cnf(clsarity_IntDef__Oint_11,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_11) ).
cnf(clsarity_IntDef__Oint_12,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_12) ).
cnf(clsarity_IntDef__Oint_13,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_13) ).
cnf(clsarity_IntDef__Oint_14,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_14) ).
cnf(clsarity_IntDef__Oint_15,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_15) ).
cnf(clsarity_IntDef__Oint_16,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_16) ).
cnf(clsarity_IntDef__Oint_17,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_17) ).
cnf(clsarity_IntDef__Oint_18,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_18) ).
cnf(clsarity_IntDef__Oint_19,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_19) ).
cnf(clsarity_IntDef__Oint_2,axiom,
class_HOL_Oplus(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_2) ).
cnf(clsarity_IntDef__Oint_20,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_20) ).
cnf(clsarity_IntDef__Oint_21,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_21) ).
cnf(clsarity_IntDef__Oint_22,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_22) ).
cnf(clsarity_IntDef__Oint_23,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_23) ).
cnf(clsarity_IntDef__Oint_24,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_24) ).
cnf(clsarity_IntDef__Oint_25,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_25) ).
cnf(clsarity_IntDef__Oint_26,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_26) ).
cnf(clsarity_IntDef__Oint_27,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_27) ).
cnf(clsarity_IntDef__Oint_28,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_28) ).
cnf(clsarity_IntDef__Oint_29,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_29) ).
cnf(clsarity_IntDef__Oint_3,axiom,
class_HOL_Otimes(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_3) ).
cnf(clsarity_IntDef__Oint_30,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_30) ).
cnf(clsarity_IntDef__Oint_31,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_31) ).
cnf(clsarity_IntDef__Oint_32,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_32) ).
cnf(clsarity_IntDef__Oint_33,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_33) ).
cnf(clsarity_IntDef__Oint_34,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_34) ).
cnf(clsarity_IntDef__Oint_35,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_35) ).
cnf(clsarity_IntDef__Oint_36,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_36) ).
cnf(clsarity_IntDef__Oint_37,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_37) ).
cnf(clsarity_IntDef__Oint_38,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_38) ).
cnf(clsarity_IntDef__Oint_39,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_39) ).
cnf(clsarity_IntDef__Oint_4,axiom,
class_HOL_Ozero(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_4) ).
cnf(clsarity_IntDef__Oint_40,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_40) ).
cnf(clsarity_IntDef__Oint_41,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_41) ).
cnf(clsarity_IntDef__Oint_42,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_42) ).
cnf(clsarity_IntDef__Oint_43,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_43) ).
cnf(clsarity_IntDef__Oint_44,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_44) ).
cnf(clsarity_IntDef__Oint_45,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_45) ).
cnf(clsarity_IntDef__Oint_46,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_46) ).
cnf(clsarity_IntDef__Oint_47,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_47) ).
cnf(clsarity_IntDef__Oint_48,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_48) ).
cnf(clsarity_IntDef__Oint_49,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_49) ).
cnf(clsarity_IntDef__Oint_5,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_5) ).
cnf(clsarity_IntDef__Oint_50,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_50) ).
cnf(clsarity_IntDef__Oint_51,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_51) ).
cnf(clsarity_IntDef__Oint_52,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_52) ).
cnf(clsarity_IntDef__Oint_53,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_53) ).
cnf(clsarity_IntDef__Oint_54,axiom,
class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_54) ).
cnf(clsarity_IntDef__Oint_55,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_55) ).
cnf(clsarity_IntDef__Oint_56,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_56) ).
cnf(clsarity_IntDef__Oint_57,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_57) ).
cnf(clsarity_IntDef__Oint_58,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_58) ).
cnf(clsarity_IntDef__Oint_59,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_59) ).
cnf(clsarity_IntDef__Oint_6,axiom,
class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_6) ).
cnf(clsarity_IntDef__Oint_60,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_60) ).
cnf(clsarity_IntDef__Oint_61,axiom,
class_Divides_Odiv(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_61) ).
cnf(clsarity_IntDef__Oint_62,axiom,
class_Nat_Opower(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_62) ).
cnf(clsarity_IntDef__Oint_63,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_63) ).
cnf(clsarity_IntDef__Oint_64,axiom,
class_Parity_Oeven__odd(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_64) ).
cnf(clsarity_IntDef__Oint_7,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_7) ).
cnf(clsarity_IntDef__Oint_8,axiom,
class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_8) ).
cnf(clsarity_IntDef__Oint_9,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
file('MSC001-0.ax',clsarity_IntDef__Oint_9) ).
cnf(clsarity_Product____Type__Ounit_0,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('MSC001-0.ax',clsarity_Product____Type__Ounit_0) ).
cnf(clsarity_bool_0,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('MSC001-0.ax',clsarity_bool_0) ).
cnf(clsarity_fun_0,axiom,
( ~ class_Finite__Set_Ofinite(T_2)
| ~ class_Finite__Set_Ofinite(T_1)
| class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ),
file('MSC001-0.ax',clsarity_fun_0) ).
cnf(clsarity_fun_1,axiom,
class_Nat_Opower(tc_fun(T_2,T_1)),
file('MSC001-0.ax',clsarity_fun_1) ).
cnf(clsarity_nat_0,axiom,
class_HOL_Oone(tc_nat),
file('MSC001-0.ax',clsarity_nat_0) ).
cnf(clsarity_nat_1,axiom,
class_HOL_Ozero(tc_nat),
file('MSC001-0.ax',clsarity_nat_1) ).
cnf(clsarity_nat_10,axiom,
class_HOL_Oplus(tc_nat),
file('MSC001-0.ax',clsarity_nat_10) ).
cnf(clsarity_nat_11,axiom,
class_HOL_Otimes(tc_nat),
file('MSC001-0.ax',clsarity_nat_11) ).
cnf(clsarity_nat_12,axiom,
class_Nat_Opower(tc_nat),
file('MSC001-0.ax',clsarity_nat_12) ).
cnf(clsarity_nat_13,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('MSC001-0.ax',clsarity_nat_13) ).
cnf(clsarity_nat_14,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('MSC001-0.ax',clsarity_nat_14) ).
cnf(clsarity_nat_15,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('MSC001-0.ax',clsarity_nat_15) ).
cnf(clsarity_nat_16,axiom,
class_OrderedGroup_Osemigroup__mult(tc_nat),
file('MSC001-0.ax',clsarity_nat_16) ).
cnf(clsarity_nat_17,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('MSC001-0.ax',clsarity_nat_17) ).
cnf(clsarity_nat_18,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('MSC001-0.ax',clsarity_nat_18) ).
cnf(clsarity_nat_19,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('MSC001-0.ax',clsarity_nat_19) ).
cnf(clsarity_nat_2,axiom,
class_Orderings_Oord(tc_nat),
file('MSC001-0.ax',clsarity_nat_2) ).
cnf(clsarity_nat_20,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('MSC001-0.ax',clsarity_nat_20) ).
cnf(clsarity_nat_21,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('MSC001-0.ax',clsarity_nat_21) ).
cnf(clsarity_nat_22,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('MSC001-0.ax',clsarity_nat_22) ).
cnf(clsarity_nat_23,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('MSC001-0.ax',clsarity_nat_23) ).
cnf(clsarity_nat_24,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('MSC001-0.ax',clsarity_nat_24) ).
cnf(clsarity_nat_25,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('MSC001-0.ax',clsarity_nat_25) ).
cnf(clsarity_nat_26,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('MSC001-0.ax',clsarity_nat_26) ).
cnf(clsarity_nat_27,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('MSC001-0.ax',clsarity_nat_27) ).
cnf(clsarity_nat_28,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('MSC001-0.ax',clsarity_nat_28) ).
cnf(clsarity_nat_29,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('MSC001-0.ax',clsarity_nat_29) ).
cnf(clsarity_nat_3,axiom,
class_Orderings_Oorder(tc_nat),
file('MSC001-0.ax',clsarity_nat_3) ).
cnf(clsarity_nat_30,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('MSC001-0.ax',clsarity_nat_30) ).
cnf(clsarity_nat_31,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('MSC001-0.ax',clsarity_nat_31) ).
cnf(clsarity_nat_32,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('MSC001-0.ax',clsarity_nat_32) ).
cnf(clsarity_nat_33,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('MSC001-0.ax',clsarity_nat_33) ).
cnf(clsarity_nat_34,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('MSC001-0.ax',clsarity_nat_34) ).
cnf(clsarity_nat_35,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('MSC001-0.ax',clsarity_nat_35) ).
cnf(clsarity_nat_36,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('MSC001-0.ax',clsarity_nat_36) ).
cnf(clsarity_nat_37,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('MSC001-0.ax',clsarity_nat_37) ).
cnf(clsarity_nat_38,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('MSC001-0.ax',clsarity_nat_38) ).
cnf(clsarity_nat_39,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('MSC001-0.ax',clsarity_nat_39) ).
cnf(clsarity_nat_4,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('MSC001-0.ax',clsarity_nat_4) ).
cnf(clsarity_nat_40,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('MSC001-0.ax',clsarity_nat_40) ).
cnf(clsarity_nat_41,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('MSC001-0.ax',clsarity_nat_41) ).
cnf(clsarity_nat_42,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('MSC001-0.ax',clsarity_nat_42) ).
cnf(clsarity_nat_43,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('MSC001-0.ax',clsarity_nat_43) ).
cnf(clsarity_nat_44,axiom,
class_Divides_Odiv(tc_nat),
file('MSC001-0.ax',clsarity_nat_44) ).
cnf(clsarity_nat_45,axiom,
class_Power_Orecpower(tc_nat),
file('MSC001-0.ax',clsarity_nat_45) ).
cnf(clsarity_nat_46,axiom,
class_Numeral_Onumber(tc_nat),
file('MSC001-0.ax',clsarity_nat_46) ).
cnf(clsarity_nat_47,axiom,
class_Parity_Oeven__odd(tc_nat),
file('MSC001-0.ax',clsarity_nat_47) ).
cnf(clsarity_nat_5,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('MSC001-0.ax',clsarity_nat_5) ).
cnf(clsarity_nat_6,axiom,
class_LOrder_Olorder(tc_nat),
file('MSC001-0.ax',clsarity_nat_6) ).
cnf(clsarity_nat_7,axiom,
class_Orderings_Olinorder(tc_nat),
file('MSC001-0.ax',clsarity_nat_7) ).
cnf(clsarity_nat_8,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('MSC001-0.ax',clsarity_nat_8) ).
cnf(clsarity_nat_9,axiom,
class_HOL_Ominus(tc_nat),
file('MSC001-0.ax',clsarity_nat_9) ).
cnf(clsarity_prod_0,axiom,
( ~ class_Finite__Set_Ofinite(T_2)
| ~ class_Finite__Set_Ofinite(T_1)
| class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ),
file('MSC001-0.ax',clsarity_prod_0) ).
cnf(clsarity_set_0,axiom,
class_HOL_Ominus(tc_set(T_1)),
file('MSC001-0.ax',clsarity_set_0) ).
cnf(clsarity_set_1,axiom,
class_Orderings_Oord(tc_set(T_1)),
file('MSC001-0.ax',clsarity_set_1) ).
cnf(clsarity_set_2,axiom,
class_Orderings_Oorder(tc_set(T_1)),
file('MSC001-0.ax',clsarity_set_2) ).
cnf(clsarity_set_3,axiom,
( ~ class_Finite__Set_Ofinite(T_1)
| class_Finite__Set_Ofinite(tc_set(T_1)) ),
file('MSC001-0.ax',clsarity_set_3) ).
cnf(clsarity_set_4,axiom,
class_Nat_Opower(tc_set(T_1)),
file('MSC001-0.ax',clsarity_set_4) ).
cnf(clsarity_sum_0,axiom,
( ~ class_Finite__Set_Ofinite(T_2)
| ~ class_Finite__Set_Ofinite(T_1)
| class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ),
file('MSC001-0.ax',clsarity_sum_0) ).
cnf(clsrel_LOrder_Ojoin__semilorder_0,axiom,
( class_Orderings_Oord(T)
| ~ class_LOrder_Ojoin__semilorder(T) ),
file('MSC001-0.ax',clsrel_LOrder_Ojoin__semilorder_0) ).
cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( class_Orderings_Oorder(T)
| ~ class_LOrder_Ojoin__semilorder(T) ),
file('MSC001-0.ax',clsrel_LOrder_Ojoin__semilorder_1) ).
cnf(clsrel_LOrder_Olorder_0,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_LOrder_Olorder(T) ),
file('MSC001-0.ax',clsrel_LOrder_Olorder_0) ).
cnf(clsrel_LOrder_Olorder_1,axiom,
( class_Orderings_Oord(T)
| ~ class_LOrder_Olorder(T) ),
file('MSC001-0.ax',clsrel_LOrder_Olorder_1) ).
cnf(clsrel_LOrder_Olorder_2,axiom,
( class_Orderings_Oorder(T)
| ~ class_LOrder_Olorder(T) ),
file('MSC001-0.ax',clsrel_LOrder_Olorder_2) ).
cnf(clsrel_LOrder_Olorder_3,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_LOrder_Olorder(T) ),
file('MSC001-0.ax',clsrel_LOrder_Olorder_3) ).
cnf(clsrel_LOrder_Omeet__semilorder_0,axiom,
( class_Orderings_Oord(T)
| ~ class_LOrder_Omeet__semilorder(T) ),
file('MSC001-0.ax',clsrel_LOrder_Omeet__semilorder_0) ).
cnf(clsrel_LOrder_Omeet__semilorder_1,axiom,
( class_Orderings_Oorder(T)
| ~ class_LOrder_Omeet__semilorder(T) ),
file('MSC001-0.ax',clsrel_LOrder_Omeet__semilorder_1) ).
cnf(clsrel_Numeral_Onumber__ring_0,axiom,
( class_HOL_Oplus(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_0) ).
cnf(clsrel_Numeral_Onumber__ring_1,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_1) ).
cnf(clsrel_Numeral_Onumber__ring_10,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_10) ).
cnf(clsrel_Numeral_Onumber__ring_11,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_11) ).
cnf(clsrel_Numeral_Onumber__ring_12,axiom,
( class_HOL_Ominus(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_12) ).
cnf(clsrel_Numeral_Onumber__ring_13,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_13) ).
cnf(clsrel_Numeral_Onumber__ring_14,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_14) ).
cnf(clsrel_Numeral_Onumber__ring_15,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_15) ).
cnf(clsrel_Numeral_Onumber__ring_16,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_16) ).
cnf(clsrel_Numeral_Onumber__ring_17,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_17) ).
cnf(clsrel_Numeral_Onumber__ring_18,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_18) ).
cnf(clsrel_Numeral_Onumber__ring_19,axiom,
( class_Ring__and__Field_Ocomm__ring(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_19) ).
cnf(clsrel_Numeral_Onumber__ring_2,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_2) ).
cnf(clsrel_Numeral_Onumber__ring_20,axiom,
( class_HOL_Oone(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_20) ).
cnf(clsrel_Numeral_Onumber__ring_21,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_21) ).
cnf(clsrel_Numeral_Onumber__ring_22,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_22) ).
cnf(clsrel_Numeral_Onumber__ring_23,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_23) ).
cnf(clsrel_Numeral_Onumber__ring_24,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_24) ).
cnf(clsrel_Numeral_Onumber__ring_25,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_25) ).
cnf(clsrel_Numeral_Onumber__ring_26,axiom,
( class_Ring__and__Field_Osemiring__1__cancel(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_26) ).
cnf(clsrel_Numeral_Onumber__ring_27,axiom,
( class_Ring__and__Field_Oring__1(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_27) ).
cnf(clsrel_Numeral_Onumber__ring_28,axiom,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_28) ).
cnf(clsrel_Numeral_Onumber__ring_29,axiom,
( class_Ring__and__Field_Ocomm__ring__1(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_29) ).
cnf(clsrel_Numeral_Onumber__ring_3,axiom,
( class_HOL_Otimes(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_3) ).
cnf(clsrel_Numeral_Onumber__ring_30,axiom,
( class_Numeral_Onumber(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_30) ).
cnf(clsrel_Numeral_Onumber__ring_4,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_4) ).
cnf(clsrel_Numeral_Onumber__ring_5,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_5) ).
cnf(clsrel_Numeral_Onumber__ring_6,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_6) ).
cnf(clsrel_Numeral_Onumber__ring_7,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_7) ).
cnf(clsrel_Numeral_Onumber__ring_8,axiom,
( class_HOL_Ozero(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_8) ).
cnf(clsrel_Numeral_Onumber__ring_9,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Numeral_Onumber__ring(T) ),
file('MSC001-0.ax',clsrel_Numeral_Onumber__ring_9) ).
cnf(clsrel_OrderedGroup_Oab__group__add_0,axiom,
( class_HOL_Ominus(T)
| ~ class_OrderedGroup_Oab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__group__add_0) ).
cnf(clsrel_OrderedGroup_Oab__group__add_1,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_OrderedGroup_Oab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__group__add_1) ).
cnf(clsrel_OrderedGroup_Oab__group__add_2,axiom,
( class_HOL_Ozero(T)
| ~ class_OrderedGroup_Oab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__group__add_2) ).
cnf(clsrel_OrderedGroup_Oab__group__add_3,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Oab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__group__add_3) ).
cnf(clsrel_OrderedGroup_Oab__group__add_4,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Oab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__group__add_4) ).
cnf(clsrel_OrderedGroup_Oab__group__add_5,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Oab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__group__add_5) ).
cnf(clsrel_OrderedGroup_Oab__group__add_6,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Oab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__group__add_6) ).
cnf(clsrel_OrderedGroup_Oab__group__add_7,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_OrderedGroup_Oab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__group__add_7) ).
cnf(clsrel_OrderedGroup_Oab__semigroup__add_0,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Oab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__semigroup__add_0) ).
cnf(clsrel_OrderedGroup_Oab__semigroup__add_1,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Oab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__semigroup__add_1) ).
cnf(clsrel_OrderedGroup_Oab__semigroup__mult_0,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_OrderedGroup_Oab__semigroup__mult(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).
cnf(clsrel_OrderedGroup_Oab__semigroup__mult_1,axiom,
( class_HOL_Otimes(T)
| ~ class_OrderedGroup_Oab__semigroup__mult(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).
cnf(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).
cnf(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).
cnf(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).
cnf(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
cnf(clsrel_OrderedGroup_Ocancel__semigroup__add_0,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Ocancel__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).
cnf(clsrel_OrderedGroup_Ocancel__semigroup__add_1,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Ocancel__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).
cnf(clsrel_OrderedGroup_Ocomm__monoid__add_0,axiom,
( class_HOL_Ozero(T)
| ~ class_OrderedGroup_Ocomm__monoid__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).
cnf(clsrel_OrderedGroup_Ocomm__monoid__add_1,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Ocomm__monoid__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).
cnf(clsrel_OrderedGroup_Ocomm__monoid__add_2,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Ocomm__monoid__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).
cnf(clsrel_OrderedGroup_Ocomm__monoid__add_3,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Ocomm__monoid__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).
cnf(clsrel_OrderedGroup_Ocomm__monoid__mult_0,axiom,
( class_HOL_Oone(T)
| ~ class_OrderedGroup_Ocomm__monoid__mult(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
cnf(clsrel_OrderedGroup_Ocomm__monoid__mult_1,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_OrderedGroup_Ocomm__monoid__mult(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
cnf(clsrel_OrderedGroup_Ocomm__monoid__mult_2,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_OrderedGroup_Ocomm__monoid__mult(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).
cnf(clsrel_OrderedGroup_Ocomm__monoid__mult_3,axiom,
( class_HOL_Otimes(T)
| ~ class_OrderedGroup_Ocomm__monoid__mult(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).
cnf(clsrel_OrderedGroup_Ocomm__monoid__mult_4,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_OrderedGroup_Ocomm__monoid__mult(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_0,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_0) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_1,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_1) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_10,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_10) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_11,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_11) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_12,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_12) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_13,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_13) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_14,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_14) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_15,axiom,
( class_LOrder_Olorder(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_15) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_16,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_16) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_17,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_17) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_2,axiom,
( class_HOL_Ominus(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_2) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_3,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_3) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_4,axiom,
( class_HOL_Ozero(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_4) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_5,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_5) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_6,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_6) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_7,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_7) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_8,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_8) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_9,axiom,
( class_Orderings_Oord(T)
| ~ class_OrderedGroup_Olordered__ab__group(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group_9) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_0,axiom,
( class_OrderedGroup_Olordered__ab__group(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_10,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_11,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_12,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_13,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_14,axiom,
( class_LOrder_Olorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_15,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_16,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_18,axiom,
( class_Orderings_Oord(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_2,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_3,axiom,
( class_HOL_Ominus(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_4,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_5,axiom,
( class_HOL_Ozero(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_6,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_7,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_8,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_9,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_0,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_1,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_10,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_11,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_12,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_13,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_14,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_15,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_16,axiom,
( class_OrderedGroup_Olordered__ab__group(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_17,axiom,
( class_LOrder_Olorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_18,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_2,axiom,
( class_HOL_Ominus(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_3,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_4,axiom,
( class_HOL_Ozero(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_5,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_6,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_7,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_8,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__join_9,axiom,
( class_Orderings_Oord(T)
| ~ class_OrderedGroup_Olordered__ab__group__join(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_0,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_1,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_10,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_11,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_12,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_13,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_14,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_15,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_16,axiom,
( class_OrderedGroup_Olordered__ab__group(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_17,axiom,
( class_LOrder_Olorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_18,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_2,axiom,
( class_HOL_Ominus(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_3,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_4,axiom,
( class_HOL_Ozero(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_5,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_6,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_7,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_8,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__meet_9,axiom,
( class_Orderings_Oord(T)
| ~ class_OrderedGroup_Olordered__ab__group__meet(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
cnf(clsrel_OrderedGroup_Omonoid__mult_0,axiom,
( class_HOL_Oone(T)
| ~ class_OrderedGroup_Omonoid__mult(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Omonoid__mult_0) ).
cnf(clsrel_OrderedGroup_Omonoid__mult_1,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_OrderedGroup_Omonoid__mult(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Omonoid__mult_1) ).
cnf(clsrel_OrderedGroup_Omonoid__mult_2,axiom,
( class_HOL_Otimes(T)
| ~ class_OrderedGroup_Omonoid__mult(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Omonoid__mult_2) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10,axiom,
( class_LOrder_Olorder(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3,axiom,
( class_Orderings_Oord(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9,axiom,
( class_Orderings_Olinorder(T)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_0,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_1,axiom,
( class_HOL_Ominus(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_10,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_11,axiom,
( class_Orderings_Oord(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_12,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_13,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_2,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_3,axiom,
( class_HOL_Ozero(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_4,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_5,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_6,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_7,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_8,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_9,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1,axiom,
( class_Orderings_Oord(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add_2,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add_4,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3,axiom,
( class_Orderings_Oord(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).
cnf(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).
cnf(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
cnf(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
cnf(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2,axiom,
( class_Orderings_Oord(T)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
cnf(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).
cnf(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).
cnf(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).
cnf(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
cnf(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
cnf(clsrel_OrderedGroup_Osemigroup__add_0,axiom,
( class_HOL_Oplus(T)
| ~ class_OrderedGroup_Osemigroup__add(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Osemigroup__add_0) ).
cnf(clsrel_OrderedGroup_Osemigroup__mult_0,axiom,
( class_HOL_Otimes(T)
| ~ class_OrderedGroup_Osemigroup__mult(T) ),
file('MSC001-0.ax',clsrel_OrderedGroup_Osemigroup__mult_0) ).
cnf(clsrel_Orderings_Olinorder_0,axiom,
( class_LOrder_Olorder(T)
| ~ class_Orderings_Olinorder(T) ),
file('MSC001-0.ax',clsrel_Orderings_Olinorder_0) ).
cnf(clsrel_Orderings_Olinorder_1,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Orderings_Olinorder(T) ),
file('MSC001-0.ax',clsrel_Orderings_Olinorder_1) ).
cnf(clsrel_Orderings_Olinorder_2,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_Orderings_Olinorder(T) ),
file('MSC001-0.ax',clsrel_Orderings_Olinorder_2) ).
cnf(clsrel_Orderings_Olinorder_3,axiom,
( class_Orderings_Oord(T)
| ~ class_Orderings_Olinorder(T) ),
file('MSC001-0.ax',clsrel_Orderings_Olinorder_3) ).
cnf(clsrel_Orderings_Olinorder_4,axiom,
( class_Orderings_Oorder(T)
| ~ class_Orderings_Olinorder(T) ),
file('MSC001-0.ax',clsrel_Orderings_Olinorder_4) ).
cnf(clsrel_Orderings_Oorder_0,axiom,
( class_Orderings_Oord(T)
| ~ class_Orderings_Oorder(T) ),
file('MSC001-0.ax',clsrel_Orderings_Oorder_0) ).
cnf(clsrel_Power_Orecpower_0,axiom,
( class_Nat_Opower(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_0) ).
cnf(clsrel_Power_Orecpower_1,axiom,
( class_HOL_Ozero(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_1) ).
cnf(clsrel_Power_Orecpower_10,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_10) ).
cnf(clsrel_Power_Orecpower_11,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_11) ).
cnf(clsrel_Power_Orecpower_12,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_12) ).
cnf(clsrel_Power_Orecpower_13,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_13) ).
cnf(clsrel_Power_Orecpower_14,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_14) ).
cnf(clsrel_Power_Orecpower_15,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_15) ).
cnf(clsrel_Power_Orecpower_16,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_16) ).
cnf(clsrel_Power_Orecpower_17,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_17) ).
cnf(clsrel_Power_Orecpower_18,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_18) ).
cnf(clsrel_Power_Orecpower_19,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_19) ).
cnf(clsrel_Power_Orecpower_2,axiom,
( class_HOL_Oone(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_2) ).
cnf(clsrel_Power_Orecpower_20,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_20) ).
cnf(clsrel_Power_Orecpower_21,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_21) ).
cnf(clsrel_Power_Orecpower_22,axiom,
( class_Ring__and__Field_Osemiring__1__cancel(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_22) ).
cnf(clsrel_Power_Orecpower_23,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_23) ).
cnf(clsrel_Power_Orecpower_24,axiom,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_24) ).
cnf(clsrel_Power_Orecpower_3,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_3) ).
cnf(clsrel_Power_Orecpower_4,axiom,
( class_HOL_Oplus(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_4) ).
cnf(clsrel_Power_Orecpower_5,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_5) ).
cnf(clsrel_Power_Orecpower_6,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_6) ).
cnf(clsrel_Power_Orecpower_7,axiom,
( class_HOL_Otimes(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_7) ).
cnf(clsrel_Power_Orecpower_8,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_8) ).
cnf(clsrel_Power_Orecpower_9,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Power_Orecpower(T) ),
file('MSC001-0.ax',clsrel_Power_Orecpower_9) ).
cnf(clsrel_Ring__and__Field_Oaxclass__0__neq__1_0,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oaxclass__0__neq__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).
cnf(clsrel_Ring__and__Field_Oaxclass__0__neq__1_1,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Oaxclass__0__neq__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
cnf(clsrel_Ring__and__Field_Oaxclass__abs__if_0,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Oaxclass__abs__if(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
cnf(clsrel_Ring__and__Field_Oaxclass__abs__if_1,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Oaxclass__abs__if(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
cnf(clsrel_Ring__and__Field_Oaxclass__abs__if_2,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oaxclass__abs__if(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).
cnf(clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).
cnf(clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_0) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_1,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_1) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_10,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_10) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_11,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_11) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_12,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_12) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_13,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_13) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_14,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_14) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_15,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_15) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_16,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_16) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_17,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_17) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_18,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_18) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_2,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_2) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_3,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_3) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_4,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_4) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_5,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_5) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_6,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_6) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_7,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_7) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_8,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_8) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring_9,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring_9) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_0,axiom,
( class_Ring__and__Field_Ocomm__ring(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_1,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_10,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_11,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_12,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_13,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_14,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_15,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_16,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_17,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_18,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_19,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_2,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_20,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_21,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_22,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_23,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_24,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_25,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_26,axiom,
( class_Ring__and__Field_Oring__1(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_27,axiom,
( class_Ring__and__Field_Osemiring__1__cancel(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_28,axiom,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_3,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_4,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_5,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_6,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_7,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_8,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
cnf(clsrel_Ring__and__Field_Ocomm__ring__1_9,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Ocomm__ring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring_0,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring_0) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring_1,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring_1) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring_2,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Ocomm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring_2) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring_3,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring_3) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring_4,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring_4) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring_5,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Ocomm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring_5) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring_6,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Ocomm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_0,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_1,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_10,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_2,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_3,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_4,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_5,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_6,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_7,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_8,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_9,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_0,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_1,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_10,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_11,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_12,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_13,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_14,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_15,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_16,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_2,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_3,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_4,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_5,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_6,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_7,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_8,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1_9,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20,axiom,
( class_Ring__and__Field_Osemiring__1__cancel(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
cnf(clsrel_Ring__and__Field_Odivision__by__zero_0,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Odivision__by__zero(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Odivision__by__zero_0) ).
cnf(clsrel_Ring__and__Field_Odivision__by__zero_1,axiom,
( class_HOL_Oinverse(T)
| ~ class_Ring__and__Field_Odivision__by__zero(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Odivision__by__zero_1) ).
cnf(clsrel_Ring__and__Field_Ofield_0,axiom,
( class_Ring__and__Field_Ocomm__ring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_0) ).
cnf(clsrel_Ring__and__Field_Ofield_1,axiom,
( class_Ring__and__Field_Ocomm__ring(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_1) ).
cnf(clsrel_Ring__and__Field_Ofield_10,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_10) ).
cnf(clsrel_Ring__and__Field_Ofield_11,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_11) ).
cnf(clsrel_Ring__and__Field_Ofield_12,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_12) ).
cnf(clsrel_Ring__and__Field_Ofield_13,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_13) ).
cnf(clsrel_Ring__and__Field_Ofield_14,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_14) ).
cnf(clsrel_Ring__and__Field_Ofield_15,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_15) ).
cnf(clsrel_Ring__and__Field_Ofield_16,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_16) ).
cnf(clsrel_Ring__and__Field_Ofield_17,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_17) ).
cnf(clsrel_Ring__and__Field_Ofield_18,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_18) ).
cnf(clsrel_Ring__and__Field_Ofield_19,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_19) ).
cnf(clsrel_Ring__and__Field_Ofield_2,axiom,
( class_Ring__and__Field_Oring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_2) ).
cnf(clsrel_Ring__and__Field_Ofield_20,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_20) ).
cnf(clsrel_Ring__and__Field_Ofield_21,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_21) ).
cnf(clsrel_Ring__and__Field_Ofield_22,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_22) ).
cnf(clsrel_Ring__and__Field_Ofield_23,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_23) ).
cnf(clsrel_Ring__and__Field_Ofield_24,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_24) ).
cnf(clsrel_Ring__and__Field_Ofield_25,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_25) ).
cnf(clsrel_Ring__and__Field_Ofield_26,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_26) ).
cnf(clsrel_Ring__and__Field_Ofield_27,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_27) ).
cnf(clsrel_Ring__and__Field_Ofield_28,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_28) ).
cnf(clsrel_Ring__and__Field_Ofield_29,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_29) ).
cnf(clsrel_Ring__and__Field_Ofield_3,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_3) ).
cnf(clsrel_Ring__and__Field_Ofield_30,axiom,
( class_HOL_Oinverse(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_30) ).
cnf(clsrel_Ring__and__Field_Ofield_31,axiom,
( class_Ring__and__Field_Oidom(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_31) ).
cnf(clsrel_Ring__and__Field_Ofield_32,axiom,
( class_Ring__and__Field_Oaxclass__no__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_32) ).
cnf(clsrel_Ring__and__Field_Ofield_4,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_4) ).
cnf(clsrel_Ring__and__Field_Ofield_5,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_5) ).
cnf(clsrel_Ring__and__Field_Ofield_6,axiom,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_6) ).
cnf(clsrel_Ring__and__Field_Ofield_7,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_7) ).
cnf(clsrel_Ring__and__Field_Ofield_8,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_8) ).
cnf(clsrel_Ring__and__Field_Ofield_9,axiom,
( class_Ring__and__Field_Osemiring__1__cancel(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Ofield_9) ).
cnf(clsrel_Ring__and__Field_Oidom_0,axiom,
( class_Ring__and__Field_Ocomm__ring__1(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_0) ).
cnf(clsrel_Ring__and__Field_Oidom_1,axiom,
( class_Ring__and__Field_Ocomm__ring(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_1) ).
cnf(clsrel_Ring__and__Field_Oidom_10,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_10) ).
cnf(clsrel_Ring__and__Field_Oidom_11,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_11) ).
cnf(clsrel_Ring__and__Field_Oidom_12,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_12) ).
cnf(clsrel_Ring__and__Field_Oidom_13,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_13) ).
cnf(clsrel_Ring__and__Field_Oidom_14,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_14) ).
cnf(clsrel_Ring__and__Field_Oidom_15,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_15) ).
cnf(clsrel_Ring__and__Field_Oidom_16,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_16) ).
cnf(clsrel_Ring__and__Field_Oidom_17,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_17) ).
cnf(clsrel_Ring__and__Field_Oidom_18,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_18) ).
cnf(clsrel_Ring__and__Field_Oidom_19,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_19) ).
cnf(clsrel_Ring__and__Field_Oidom_2,axiom,
( class_Ring__and__Field_Oring__1(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_2) ).
cnf(clsrel_Ring__and__Field_Oidom_20,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_20) ).
cnf(clsrel_Ring__and__Field_Oidom_21,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_21) ).
cnf(clsrel_Ring__and__Field_Oidom_22,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_22) ).
cnf(clsrel_Ring__and__Field_Oidom_23,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_23) ).
cnf(clsrel_Ring__and__Field_Oidom_24,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_24) ).
cnf(clsrel_Ring__and__Field_Oidom_25,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_25) ).
cnf(clsrel_Ring__and__Field_Oidom_26,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_26) ).
cnf(clsrel_Ring__and__Field_Oidom_27,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_27) ).
cnf(clsrel_Ring__and__Field_Oidom_28,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_28) ).
cnf(clsrel_Ring__and__Field_Oidom_29,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_29) ).
cnf(clsrel_Ring__and__Field_Oidom_3,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_3) ).
cnf(clsrel_Ring__and__Field_Oidom_30,axiom,
( class_Ring__and__Field_Oaxclass__no__zero__divisors(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_30) ).
cnf(clsrel_Ring__and__Field_Oidom_4,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_4) ).
cnf(clsrel_Ring__and__Field_Oidom_5,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_5) ).
cnf(clsrel_Ring__and__Field_Oidom_6,axiom,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_6) ).
cnf(clsrel_Ring__and__Field_Oidom_7,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_7) ).
cnf(clsrel_Ring__and__Field_Oidom_8,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_8) ).
cnf(clsrel_Ring__and__Field_Oidom_9,axiom,
( class_Ring__and__Field_Osemiring__1__cancel(T)
| ~ class_Ring__and__Field_Oidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oidom_9) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_0,axiom,
( class_Ring__and__Field_Opordered__ring(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_0) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_1,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_1) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_10,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_10) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_11,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_11) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_12,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_12) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_13,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_13) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_14,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_14) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_15,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_15) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_16,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_16) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_17,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_17) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_18,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_18) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_19,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_19) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_2,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_2) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_20,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_20) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_21,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_21) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_22,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_22) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_23,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_23) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_24,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_24) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_25,axiom,
( class_OrderedGroup_Olordered__ab__group(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_25) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_26,axiom,
( class_LOrder_Olorder(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_26) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_27,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_27) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_28,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_28) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_29,axiom,
( class_OrderedGroup_Olordered__ab__group__meet(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_29) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_3,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_3) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_30,axiom,
( class_OrderedGroup_Olordered__ab__group__join(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_30) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_4,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_4) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_5,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_5) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_6,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_6) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_7,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_7) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_8,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_8) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_9,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Olordered__ring_9) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12,axiom,
( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13,axiom,
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14,axiom,
( class_LOrder_Olorder(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28,axiom,
( class_Ring__and__Field_Opordered__cancel__comm__semiring(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29,axiom,
( class_Ring__and__Field_Opordered__comm__semiring(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).
cnf(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).
cnf(clsrel_Ring__and__Field_Oordered__field_0,axiom,
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_1,axiom,
( class_HOL_Oinverse(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_1) ).
cnf(clsrel_Ring__and__Field_Oordered__field_10,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_10) ).
cnf(clsrel_Ring__and__Field_Oordered__field_11,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_11) ).
cnf(clsrel_Ring__and__Field_Oordered__field_12,axiom,
( class_Ring__and__Field_Osemiring__1__cancel(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_12) ).
cnf(clsrel_Ring__and__Field_Oordered__field_13,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_13) ).
cnf(clsrel_Ring__and__Field_Oordered__field_14,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_14) ).
cnf(clsrel_Ring__and__Field_Oordered__field_15,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_15) ).
cnf(clsrel_Ring__and__Field_Oordered__field_16,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_16) ).
cnf(clsrel_Ring__and__Field_Oordered__field_17,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_17) ).
cnf(clsrel_Ring__and__Field_Oordered__field_18,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_18) ).
cnf(clsrel_Ring__and__Field_Oordered__field_19,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_19) ).
cnf(clsrel_Ring__and__Field_Oordered__field_2,axiom,
( class_Ring__and__Field_Oidom(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_2) ).
cnf(clsrel_Ring__and__Field_Oordered__field_20,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_20) ).
cnf(clsrel_Ring__and__Field_Oordered__field_21,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_21) ).
cnf(clsrel_Ring__and__Field_Oordered__field_22,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_22) ).
cnf(clsrel_Ring__and__Field_Oordered__field_23,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_23) ).
cnf(clsrel_Ring__and__Field_Oordered__field_24,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_24) ).
cnf(clsrel_Ring__and__Field_Oordered__field_25,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_25) ).
cnf(clsrel_Ring__and__Field_Oordered__field_26,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_26) ).
cnf(clsrel_Ring__and__Field_Oordered__field_27,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_27) ).
cnf(clsrel_Ring__and__Field_Oordered__field_28,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_28) ).
cnf(clsrel_Ring__and__Field_Oordered__field_29,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_29) ).
cnf(clsrel_Ring__and__Field_Oordered__field_3,axiom,
( class_Ring__and__Field_Ocomm__ring__1(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_3) ).
cnf(clsrel_Ring__and__Field_Oordered__field_30,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_30) ).
cnf(clsrel_Ring__and__Field_Oordered__field_31,axiom,
( class_Ring__and__Field_Oaxclass__no__zero__divisors(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_31) ).
cnf(clsrel_Ring__and__Field_Oordered__field_32,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_32) ).
cnf(clsrel_Ring__and__Field_Oordered__field_33,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_33) ).
cnf(clsrel_Ring__and__Field_Oordered__field_34,axiom,
( class_Ring__and__Field_Oordered__idom(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_34) ).
cnf(clsrel_Ring__and__Field_Oordered__field_35,axiom,
( class_Ring__and__Field_Oordered__comm__semiring__strict(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_35) ).
cnf(clsrel_Ring__and__Field_Oordered__field_36,axiom,
( class_Ring__and__Field_Opordered__cancel__comm__semiring(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_36) ).
cnf(clsrel_Ring__and__Field_Oordered__field_37,axiom,
( class_Ring__and__Field_Opordered__comm__semiring(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_37) ).
cnf(clsrel_Ring__and__Field_Oordered__field_38,axiom,
( class_Ring__and__Field_Oordered__ring__strict(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_38) ).
cnf(clsrel_Ring__and__Field_Oordered__field_39,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_39) ).
cnf(clsrel_Ring__and__Field_Oordered__field_4,axiom,
( class_Ring__and__Field_Ocomm__ring(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_4) ).
cnf(clsrel_Ring__and__Field_Oordered__field_40,axiom,
( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_40) ).
cnf(clsrel_Ring__and__Field_Oordered__field_41,axiom,
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_41) ).
cnf(clsrel_Ring__and__Field_Oordered__field_42,axiom,
( class_Ring__and__Field_Oaxclass__abs__if(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_42) ).
cnf(clsrel_Ring__and__Field_Oordered__field_43,axiom,
( class_Ring__and__Field_Olordered__ring(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_43) ).
cnf(clsrel_Ring__and__Field_Oordered__field_44,axiom,
( class_Ring__and__Field_Opordered__ring(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_44) ).
cnf(clsrel_Ring__and__Field_Oordered__field_45,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_45) ).
cnf(clsrel_Ring__and__Field_Oordered__field_46,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_46) ).
cnf(clsrel_Ring__and__Field_Oordered__field_47,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_47) ).
cnf(clsrel_Ring__and__Field_Oordered__field_48,axiom,
( class_OrderedGroup_Olordered__ab__group__meet(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_48) ).
cnf(clsrel_Ring__and__Field_Oordered__field_49,axiom,
( class_OrderedGroup_Olordered__ab__group__join(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_49) ).
cnf(clsrel_Ring__and__Field_Oordered__field_5,axiom,
( class_Ring__and__Field_Oring__1(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_5) ).
cnf(clsrel_Ring__and__Field_Oordered__field_50,axiom,
( class_OrderedGroup_Olordered__ab__group(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_50) ).
cnf(clsrel_Ring__and__Field_Oordered__field_51,axiom,
( class_LOrder_Olorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_51) ).
cnf(clsrel_Ring__and__Field_Oordered__field_52,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_52) ).
cnf(clsrel_Ring__and__Field_Oordered__field_53,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_53) ).
cnf(clsrel_Ring__and__Field_Oordered__field_54,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_54) ).
cnf(clsrel_Ring__and__Field_Oordered__field_55,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_55) ).
cnf(clsrel_Ring__and__Field_Oordered__field_56,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_56) ).
cnf(clsrel_Ring__and__Field_Oordered__field_57,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_57) ).
cnf(clsrel_Ring__and__Field_Oordered__field_58,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_58) ).
cnf(clsrel_Ring__and__Field_Oordered__field_59,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_59) ).
cnf(clsrel_Ring__and__Field_Oordered__field_6,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_6) ).
cnf(clsrel_Ring__and__Field_Oordered__field_60,axiom,
( class_Ring__and__Field_Oordered__semidom(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_60) ).
cnf(clsrel_Ring__and__Field_Oordered__field_7,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_7) ).
cnf(clsrel_Ring__and__Field_Oordered__field_8,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_8) ).
cnf(clsrel_Ring__and__Field_Oordered__field_9,axiom,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_9) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_0,axiom,
( class_Ring__and__Field_Ocomm__ring__1(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_1,axiom,
( class_Ring__and__Field_Ocomm__ring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_10,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_10) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_11,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_11) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_12,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_12) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_13,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_13) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_14,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_14) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_15,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_15) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_16,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_16) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_17,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_17) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_18,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_18) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_19,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_19) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_2,axiom,
( class_Ring__and__Field_Oring__1(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_2) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_20,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_20) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_21) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_22,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_22) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_24,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_24) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_25,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_25) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_26,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_26) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_27,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_27) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_28,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_28) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_29,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_29) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_3,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_3) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_30,axiom,
( class_Ring__and__Field_Oordered__comm__semiring__strict(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_30) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_31,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_31) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_32,axiom,
( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_32) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_34,axiom,
( class_LOrder_Olorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_34) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_35) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_36,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_36) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_37,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_37) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_38,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_38) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_39,axiom,
( class_Ring__and__Field_Opordered__cancel__comm__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_39) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_40) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_41,axiom,
( class_Ring__and__Field_Opordered__comm__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_41) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_42) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_43,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_43) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_44,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_44) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_45,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_45) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_46,axiom,
( class_Ring__and__Field_Oaxclass__abs__if(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_46) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_47,axiom,
( class_Ring__and__Field_Oordered__ring__strict(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_47) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_48,axiom,
( class_Ring__and__Field_Olordered__ring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_48) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_49,axiom,
( class_Ring__and__Field_Opordered__ring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_49) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_5,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_5) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_51,axiom,
( class_OrderedGroup_Olordered__ab__group__meet(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_51) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_52,axiom,
( class_OrderedGroup_Olordered__ab__group__join(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_52) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_53,axiom,
( class_OrderedGroup_Olordered__ab__group(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_53) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_55,axiom,
( class_Ring__and__Field_Oordered__semidom(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_55) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_56,axiom,
( class_Ring__and__Field_Oaxclass__no__zero__divisors(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_56) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_57,axiom,
( class_Ring__and__Field_Oidom(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_57) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_6,axiom,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_6) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_7,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_7) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_8,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_8) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_9,axiom,
( class_Ring__and__Field_Osemiring__1__cancel(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_9) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_0,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_1,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_10,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_11,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_12,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_13,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_14,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_15,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_16,axiom,
( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_17,axiom,
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_18,axiom,
( class_LOrder_Olorder(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_19,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_2,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_20,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_21,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_22,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_23,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_24,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_25,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_26,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_27,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_28,axiom,
( class_Ring__and__Field_Oaxclass__abs__if(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_29,axiom,
( class_OrderedGroup_Olordered__ab__group(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_3,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_30,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_31,axiom,
( class_Ring__and__Field_Olordered__ring(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_32,axiom,
( class_Ring__and__Field_Opordered__ring(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_33,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_34,axiom,
( class_OrderedGroup_Olordered__ab__group__meet(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_35,axiom,
( class_OrderedGroup_Olordered__ab__group__join(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_36,axiom,
( class_Ring__and__Field_Oaxclass__no__zero__divisors(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_4,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_5,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_6,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_7,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_8,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).
cnf(clsrel_Ring__and__Field_Oordered__ring__strict_9,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Oordered__ring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_0,axiom,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_0) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_1,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_1) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_10,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_10) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_11,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_11) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_12,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_12) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_13,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_13) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_14,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_14) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_15,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_15) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_16,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_16) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_17,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_17) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_18,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_18) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_19,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_19) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_2,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_2) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_20,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_20) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_21,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_21) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_22,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_22) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_23,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_23) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_24,axiom,
( class_Ring__and__Field_Oordered__comm__semiring__strict(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_24) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_25,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_25) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_26,axiom,
( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_26) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_27,axiom,
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_27) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_28,axiom,
( class_LOrder_Olorder(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_28) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_29,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_29) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_3,axiom,
( class_Ring__and__Field_Osemiring__1__cancel(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_3) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_30,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_30) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_31,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_31) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_32,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_32) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_33,axiom,
( class_Ring__and__Field_Opordered__cancel__comm__semiring(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_33) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_34,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_34) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_35,axiom,
( class_Ring__and__Field_Opordered__comm__semiring(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_35) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_36,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_36) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_37,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_37) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_38,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_38) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_39,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_39) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_4,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_4) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_5,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_5) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_6,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_6) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_7,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_7) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_8,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_8) ).
cnf(clsrel_Ring__and__Field_Oordered__semidom_9,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semidom_9) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_0,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_1,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_10,axiom,
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_11,axiom,
( class_LOrder_Olorder(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_12,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_13,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_14,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_15,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_16,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_17,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_18,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_19,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_2,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_20,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_21,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_22,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_23,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_3,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_4,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_5,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_6,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_7,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_8,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).
cnf(clsrel_Ring__and__Field_Oordered__semiring__strict_9,axiom,
( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0,axiom,
( class_Ring__and__Field_Opordered__comm__semiring(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_0,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_1,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_10,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_11,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_12,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_13,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_14,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_15,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_2,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_3,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_4,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_5,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_6,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_7,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_8,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).
cnf(clsrel_Ring__and__Field_Opordered__cancel__semiring_9,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_0,axiom,
( class_Ring__and__Field_Ocomm__ring(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_0) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_1,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_1) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_10,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_10) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_11,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_11) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_12,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_12) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_13,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_13) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_14,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_14) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_15,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_15) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_16,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_16) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_17,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_17) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_18,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_18) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_19,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_19) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_2,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_2) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_20,axiom,
( class_Ring__and__Field_Opordered__comm__semiring(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_20) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_21,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_21) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_22,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_22) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_23,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_23) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_24,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_24) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_3,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_3) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_4,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_4) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_5,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_5) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_6,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_6) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_7,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_7) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_8,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_8) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__ring_9,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Opordered__comm__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__ring_9) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_1,axiom,
( class_Ring__and__Field_Ocomm__semiring(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_10,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_11,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_12,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_13,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_14,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_15,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_2,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_3,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_4,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_5,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_6,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_7,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_8,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).
cnf(clsrel_Ring__and__Field_Opordered__comm__semiring_9,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Opordered__comm__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_0,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_0) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_1,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_1) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_10,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_10) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_11,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_11) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_12,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_12) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_13,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_13) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_14,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_14) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_15,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_15) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_16,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_16) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_17,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_17) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_18,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_18) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_19,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_19) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_2,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_2) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_20,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_20) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_21,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_21) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_22,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_22) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_3,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_3) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_4,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_4) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_5,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_5) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_6,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_6) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_7,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_7) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_8,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_8) ).
cnf(clsrel_Ring__and__Field_Opordered__ring_9,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__ring_9) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_0,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_0) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_1,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_1) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_10,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_10) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_11,axiom,
( class_Orderings_Oord(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_11) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_2,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_2) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_3,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_3) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_4,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_4) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_5,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_5) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_6,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_6) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_7,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_7) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_8,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_8) ).
cnf(clsrel_Ring__and__Field_Opordered__semiring_9,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Opordered__semiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Opordered__semiring_9) ).
cnf(clsrel_Ring__and__Field_Oring_0,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_0) ).
cnf(clsrel_Ring__and__Field_Oring_1,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_1) ).
cnf(clsrel_Ring__and__Field_Oring_10,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_10) ).
cnf(clsrel_Ring__and__Field_Oring_11,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_11) ).
cnf(clsrel_Ring__and__Field_Oring_12,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_12) ).
cnf(clsrel_Ring__and__Field_Oring_13,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_13) ).
cnf(clsrel_Ring__and__Field_Oring_2,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_2) ).
cnf(clsrel_Ring__and__Field_Oring_3,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_3) ).
cnf(clsrel_Ring__and__Field_Oring_4,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_4) ).
cnf(clsrel_Ring__and__Field_Oring_5,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_5) ).
cnf(clsrel_Ring__and__Field_Oring_6,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_6) ).
cnf(clsrel_Ring__and__Field_Oring_7,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_7) ).
cnf(clsrel_Ring__and__Field_Oring_8,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_8) ).
cnf(clsrel_Ring__and__Field_Oring_9,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring_9) ).
cnf(clsrel_Ring__and__Field_Oring__1_0,axiom,
( class_Ring__and__Field_Oring(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_0) ).
cnf(clsrel_Ring__and__Field_Oring__1_1,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_1) ).
cnf(clsrel_Ring__and__Field_Oring__1_10,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_10) ).
cnf(clsrel_Ring__and__Field_Oring__1_11,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_11) ).
cnf(clsrel_Ring__and__Field_Oring__1_12,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_12) ).
cnf(clsrel_Ring__and__Field_Oring__1_13,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_13) ).
cnf(clsrel_Ring__and__Field_Oring__1_14,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_14) ).
cnf(clsrel_Ring__and__Field_Oring__1_15,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_15) ).
cnf(clsrel_Ring__and__Field_Oring__1_16,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_16) ).
cnf(clsrel_Ring__and__Field_Oring__1_17,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_17) ).
cnf(clsrel_Ring__and__Field_Oring__1_18,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_18) ).
cnf(clsrel_Ring__and__Field_Oring__1_19,axiom,
( class_Ring__and__Field_Osemiring__1__cancel(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_19) ).
cnf(clsrel_Ring__and__Field_Oring__1_2,axiom,
( class_HOL_Ominus(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_2) ).
cnf(clsrel_Ring__and__Field_Oring__1_3,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_3) ).
cnf(clsrel_Ring__and__Field_Oring__1_4,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_4) ).
cnf(clsrel_Ring__and__Field_Oring__1_5,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_5) ).
cnf(clsrel_Ring__and__Field_Oring__1_6,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_6) ).
cnf(clsrel_Ring__and__Field_Oring__1_7,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_7) ).
cnf(clsrel_Ring__and__Field_Oring__1_8,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_8) ).
cnf(clsrel_Ring__and__Field_Oring__1_9,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Oring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Oring__1_9) ).
cnf(clsrel_Ring__and__Field_Osemiring_0,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Osemiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring_0) ).
cnf(clsrel_Ring__and__Field_Osemiring_1,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Osemiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring_1) ).
cnf(clsrel_Ring__and__Field_Osemiring_2,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Osemiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring_2) ).
cnf(clsrel_Ring__and__Field_Osemiring_3,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Osemiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring_3) ).
cnf(clsrel_Ring__and__Field_Osemiring_4,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Osemiring(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring_4) ).
cnf(clsrel_Ring__and__Field_Osemiring__0_0,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Osemiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0_0) ).
cnf(clsrel_Ring__and__Field_Osemiring__0_1,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0_1) ).
cnf(clsrel_Ring__and__Field_Osemiring__0_2,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0_2) ).
cnf(clsrel_Ring__and__Field_Osemiring__0_3,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Osemiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0_3) ).
cnf(clsrel_Ring__and__Field_Osemiring__0_4,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Osemiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0_4) ).
cnf(clsrel_Ring__and__Field_Osemiring__0_5,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Osemiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0_5) ).
cnf(clsrel_Ring__and__Field_Osemiring__0_6,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Osemiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0_6) ).
cnf(clsrel_Ring__and__Field_Osemiring__0_7,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Osemiring__0(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0_7) ).
cnf(clsrel_Ring__and__Field_Osemiring__0__cancel_0,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Osemiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
cnf(clsrel_Ring__and__Field_Osemiring__0__cancel_1,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Osemiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
cnf(clsrel_Ring__and__Field_Osemiring__0__cancel_10,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
cnf(clsrel_Ring__and__Field_Osemiring__0__cancel_2,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Osemiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).
cnf(clsrel_Ring__and__Field_Osemiring__0__cancel_3,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Osemiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).
cnf(clsrel_Ring__and__Field_Osemiring__0__cancel_4,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Osemiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
cnf(clsrel_Ring__and__Field_Osemiring__0__cancel_5,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).
cnf(clsrel_Ring__and__Field_Osemiring__0__cancel_6,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).
cnf(clsrel_Ring__and__Field_Osemiring__0__cancel_7,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Osemiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).
cnf(clsrel_Ring__and__Field_Osemiring__0__cancel_8,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Osemiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).
cnf(clsrel_Ring__and__Field_Osemiring__0__cancel_9,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__0__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_0,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_0) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_1,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_1) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_10,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_10) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_11,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_11) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_2,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_2) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_3,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_3) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_4,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_4) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_5,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_5) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_6,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_6) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_7,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_7) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_8,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_8) ).
cnf(clsrel_Ring__and__Field_Osemiring__1_9,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__1(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1_9) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_0,axiom,
( class_Ring__and__Field_Osemiring__1(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_1,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_10,axiom,
( class_HOL_Oone(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_11,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_12,axiom,
( class_HOL_Otimes(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_13,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_14,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_15,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_2,axiom,
( class_Ring__and__Field_Osemiring__0(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_3,axiom,
( class_Ring__and__Field_Osemiring(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_4,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_5,axiom,
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_6,axiom,
( class_OrderedGroup_Oab__semigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_7,axiom,
( class_OrderedGroup_Osemigroup__add(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_8,axiom,
( class_HOL_Oplus(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).
cnf(clsrel_Ring__and__Field_Osemiring__1__cancel_9,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Osemiring__1__cancel(T) ),
file('MSC001-0.ax',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
cnf(clsrel_Wellfounded__Recursion_Owellorder_0,axiom,
( class_Orderings_Oord(T)
| ~ class_Wellfounded__Recursion_Owellorder(T) ),
file('MSC001-0.ax',clsrel_Wellfounded__Recursion_Owellorder_0) ).
cnf(clsrel_Wellfounded__Recursion_Owellorder_1,axiom,
( class_Orderings_Oorder(T)
| ~ class_Wellfounded__Recursion_Owellorder(T) ),
file('MSC001-0.ax',clsrel_Wellfounded__Recursion_Owellorder_1) ).
cnf(clsrel_Wellfounded__Recursion_Owellorder_2,axiom,
( class_LOrder_Omeet__semilorder(T)
| ~ class_Wellfounded__Recursion_Owellorder(T) ),
file('MSC001-0.ax',clsrel_Wellfounded__Recursion_Owellorder_2) ).
cnf(clsrel_Wellfounded__Recursion_Owellorder_3,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Wellfounded__Recursion_Owellorder(T) ),
file('MSC001-0.ax',clsrel_Wellfounded__Recursion_Owellorder_3) ).
cnf(clsrel_Wellfounded__Recursion_Owellorder_4,axiom,
( class_LOrder_Olorder(T)
| ~ class_Wellfounded__Recursion_Owellorder(T) ),
file('MSC001-0.ax',clsrel_Wellfounded__Recursion_Owellorder_4) ).
cnf(clsrel_Wellfounded__Recursion_Owellorder_5,axiom,
( class_Orderings_Olinorder(T)
| ~ class_Wellfounded__Recursion_Owellorder(T) ),
file('MSC001-0.ax',clsrel_Wellfounded__Recursion_Owellorder_5) ).
cnf(cls_Binomial_Obinomial__0__Suc_0,axiom,
c_Binomial_Obinomial(c_0,c_Suc(V_k)) = c_0,
file('MSC001-1.ax',cls_Binomial_Obinomial__0__Suc_0) ).
cnf(cls_Binomial_Obinomial__1_0,axiom,
c_Binomial_Obinomial(V_y,c_Suc(c_0)) = V_y,
file('MSC001-1.ax',cls_Binomial_Obinomial__1_0) ).
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),
file('MSC001-1.ax',cls_Binomial_Obinomial__Suc__Suc_0) ).
cnf(cls_Binomial_Obinomial__Suc__n_0,axiom,
c_Binomial_Obinomial(c_Suc(V_n),V_n) = c_Suc(V_n),
file('MSC001-1.ax',cls_Binomial_Obinomial__Suc__n_0) ).
cnf(cls_Binomial_Obinomial__n__0_0,axiom,
c_Binomial_Obinomial(V_n,c_0) = c_1,
file('MSC001-1.ax',cls_Binomial_Obinomial__n__0_0) ).
cnf(cls_Binomial_Obinomial__n__n_0,axiom,
c_Binomial_Obinomial(V_n,V_n) = c_1,
file('MSC001-1.ax',cls_Binomial_Obinomial__n__n_0) ).
cnf(cls_Datatype_Oelem__o2s_0,axiom,
( V_xo = c_Datatype_Ooption_OSome(V_x,T_a)
| ~ c_in(V_x,c_Datatype_Oo2s(V_xo,T_a),T_a) ),
file('MSC001-1.ax',cls_Datatype_Oelem__o2s_0) ).
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),
file('MSC001-1.ax',cls_Datatype_Oelem__o2s_1) ).
cnf(cls_Datatype_Onot__None__eq_0,axiom,
( V_x = c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(V_x,T_a),T_a)
| V_x = c_Datatype_Ooption_ONone ),
file('MSC001-1.ax',cls_Datatype_Onot__None__eq_0) ).
cnf(cls_Datatype_Onot__Some__eq_0,axiom,
( V_x = c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(V_x,T_a),T_a)
| V_x = c_Datatype_Ooption_ONone ),
file('MSC001-1.ax',cls_Datatype_Onot__Some__eq_0) ).
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),
file('MSC001-1.ax',cls_Datatype_Oo2s_Osimps__2_0) ).
cnf(cls_Datatype_Oo2s__empty__eq_0,axiom,
( V_xo = c_Datatype_Ooption_ONone
| c_Datatype_Oo2s(V_xo,T_a) != c_emptyset ),
file('MSC001-1.ax',cls_Datatype_Oo2s__empty__eq_0) ).
cnf(cls_Datatype_Oo2s__empty__eq_1,axiom,
c_Datatype_Oo2s(c_Datatype_Ooption_ONone,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Datatype_Oo2s__empty__eq_1) ).
cnf(cls_Datatype_Ooption_Odistinct__1_0,axiom,
c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(V_a_H,T_a),
file('MSC001-1.ax',cls_Datatype_Ooption_Odistinct__1_0) ).
cnf(cls_Datatype_Ooption_Odistinct__2_0,axiom,
c_Datatype_Ooption_OSome(V_a_H,T_a) != c_Datatype_Ooption_ONone,
file('MSC001-1.ax',cls_Datatype_Ooption_Odistinct__2_0) ).
cnf(cls_Datatype_Ooption_Oinject_0,axiom,
( V_a = V_a_H
| c_Datatype_Ooption_OSome(V_a,T_a) != c_Datatype_Ooption_OSome(V_a_H,T_a) ),
file('MSC001-1.ax',cls_Datatype_Ooption_Oinject_0) ).
cnf(cls_Datatype_Ooption_Osize__1_0,axiom,
c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(T_a)) = c_0,
file('MSC001-1.ax',cls_Datatype_Ooption_Osize__1_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,
file('MSC001-1.ax',cls_Datatype_Ooption_Osize__2_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,
file('MSC001-1.ax',cls_Datatype_Oprod_Osize_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,
file('MSC001-1.ax',cls_Datatype_Osum_Osize__1_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,
file('MSC001-1.ax',cls_Datatype_Osum_Osize__2_0) ).
cnf(cls_Datatype_Othe_Osimps_0,axiom,
c_Datatype_Othe(c_Datatype_Ooption_OSome(V_y,T_a),T_a) = V_y,
file('MSC001-1.ax',cls_Datatype_Othe_Osimps_0) ).
cnf(cls_Datatype_Ounit_Ocases_0,axiom,
c_Datatype_Ounit_Ounit__case(V_y,c_Product__Type_OUnity,T_a) = V_y,
file('MSC001-1.ax',cls_Datatype_Ounit_Ocases_0) ).
cnf(cls_Datatype_Ounit_Orecs_0,axiom,
c_Datatype_Ounit_Ounit__rec(V_y,c_Product__Type_OUnity,T_a) = V_y,
file('MSC001-1.ax',cls_Datatype_Ounit_Orecs_0) ).
cnf(cls_Datatype_Ounit_Osize_0,axiom,
c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
file('MSC001-1.ax',cls_Datatype_Ounit_Osize_0) ).
cnf(cls_Datatype__Universe_OAtom__Atom__eq_0,axiom,
( V_a = V_b
| c_Datatype__Universe_OAtom(V_a,T_a,T_b) != c_Datatype__Universe_OAtom(V_b,T_a,T_b) ),
file('MSC001-1.ax',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_OAtom__not__Scons_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_ODomain__dprod_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_ODomain__dsum_0) ).
cnf(cls_Datatype__Universe_OIn0__eq_0,axiom,
( V_M = V_N
| c_Datatype__Universe_OIn0(V_M,T_a,T_b) != c_Datatype__Universe_OIn0(V_N,T_a,T_b) ),
file('MSC001-1.ax',cls_Datatype__Universe_OIn0__eq_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_OIn0__not__In1_0) ).
cnf(cls_Datatype__Universe_OIn1__eq_0,axiom,
( V_M = V_N
| c_Datatype__Universe_OIn1(V_M,T_a,T_b) != c_Datatype__Universe_OIn1(V_N,T_a,T_b) ),
file('MSC001-1.ax',cls_Datatype__Universe_OIn1__eq_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_OIn1__not__In0_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_OLeaf__not__Numb_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_OLeaf__not__Scons_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_ONumb__not__Leaf_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_ONumb__not__Scons_0) ).
cnf(cls_Datatype__Universe_OScons__Scons__eq_0,axiom,
( V_M = V_M_H
| 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) ),
file('MSC001-1.ax',cls_Datatype__Universe_OScons__Scons__eq_0) ).
cnf(cls_Datatype__Universe_OScons__Scons__eq_1,axiom,
( V_N = V_N_H
| 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) ),
file('MSC001-1.ax',cls_Datatype__Universe_OScons__Scons__eq_1) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_OScons__not__Atom_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_OScons__not__Leaf_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_OScons__not__Numb_0) ).
cnf(cls_Datatype__Universe_Ontrunc__0_0,axiom,
c_Datatype__Universe_Ontrunc(c_0,V_M,T_a,T_b) = c_emptyset,
file('MSC001-1.ax',cls_Datatype__Universe_Ontrunc__0_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_Ontrunc__Atom_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_Ontrunc__In0_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_Ontrunc__In1_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_Ontrunc__Leaf_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_Ontrunc__Numb_0) ).
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),
file('MSC001-1.ax',cls_Datatype__Universe_Ontrunc__Scons_0) ).
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,
file('MSC001-1.ax',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
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,
file('MSC001-1.ax',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
cnf(cls_Divides_ODIVISION__BY__ZERO__DIV_0,axiom,
c_div(V_a,c_0,tc_nat) = c_0,
file('MSC001-1.ax',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
cnf(cls_Divides_ODIVISION__BY__ZERO__MOD_0,axiom,
c_Divides_Oop_Amod(V_y,c_0,tc_nat) = V_y,
file('MSC001-1.ax',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
cnf(cls_Divides_Odiv__0_0,axiom,
c_div(c_0,V_m,tc_nat) = c_0,
file('MSC001-1.ax',cls_Divides_Odiv__0_0) ).
cnf(cls_Divides_Odiv__1_0,axiom,
c_div(V_y,c_Suc(c_0),tc_nat) = V_y,
file('MSC001-1.ax',cls_Divides_Odiv__1_0) ).
cnf(cls_Divides_Odiv__le__dividend_0,axiom,
c_lessequals(c_div(V_m,V_n,tc_nat),V_m,tc_nat),
file('MSC001-1.ax',cls_Divides_Odiv__le__dividend_0) ).
cnf(cls_Divides_Odiv__less_0,axiom,
( c_div(V_m,V_n,tc_nat) = c_0
| ~ c_less(V_m,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Odiv__less_0) ).
cnf(cls_Divides_Odiv__less__dividend_0,axiom,
( c_less(c_div(V_m,V_n,tc_nat),V_m,tc_nat)
| ~ c_less(c_1,V_n,tc_nat)
| ~ c_less(c_0,V_m,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Odiv__less__dividend_0) ).
cnf(cls_Divides_Odiv__mult__mult1_0,axiom,
( 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)
| ~ c_less(c_0,V_c,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Odiv__mult__mult1_0) ).
cnf(cls_Divides_Odiv__mult__mult2_0,axiom,
( 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)
| ~ c_less(c_0,V_c,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Odiv__mult__mult2_0) ).
cnf(cls_Divides_Odiv__mult__self1_0,axiom,
( 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)
| ~ c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Odiv__mult__self1_0) ).
cnf(cls_Divides_Odiv__mult__self1__is__m_0,axiom,
( c_div(c_times(V_n,V_y,tc_nat),V_n,tc_nat) = V_y
| ~ c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Odiv__mult__self1__is__m_0) ).
cnf(cls_Divides_Odiv__mult__self2_0,axiom,
( 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)
| ~ c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Odiv__mult__self2_0) ).
cnf(cls_Divides_Odiv__mult__self__is__m_0,axiom,
( c_div(c_times(V_y,V_n,tc_nat),V_n,tc_nat) = V_y
| ~ c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Odiv__mult__self__is__m_0) ).
cnf(cls_Divides_Odiv__self_0,axiom,
( c_div(V_n,V_n,tc_nat) = c_1
| ~ c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Odiv__self_0) ).
cnf(cls_Divides_Odvd__0__left__iff_0,axiom,
( V_m = c_0
| ~ c_Divides_Oop_Advd(c_0,V_m,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Odvd__0__left__iff_0) ).
cnf(cls_Divides_Odvd__0__left__iff_1,axiom,
c_Divides_Oop_Advd(c_0,c_0,tc_nat),
file('MSC001-1.ax',cls_Divides_Odvd__0__left__iff_1) ).
cnf(cls_Divides_Odvd__1__iff__1_0,axiom,
( V_m = c_Suc(c_0)
| ~ c_Divides_Oop_Advd(V_m,c_Suc(c_0),tc_nat) ),
file('MSC001-1.ax',cls_Divides_Odvd__1__iff__1_0) ).
cnf(cls_Divides_Odvd__1__iff__1_1,axiom,
c_Divides_Oop_Advd(c_Suc(c_0),c_Suc(c_0),tc_nat),
file('MSC001-1.ax',cls_Divides_Odvd__1__iff__1_1) ).
cnf(cls_Divides_Odvd__refl_0,axiom,
c_Divides_Oop_Advd(V_m,V_m,tc_nat),
file('MSC001-1.ax',cls_Divides_Odvd__refl_0) ).
cnf(cls_Divides_Omod__0_0,axiom,
c_Divides_Oop_Amod(c_0,V_m,tc_nat) = c_0,
file('MSC001-1.ax',cls_Divides_Omod__0_0) ).
cnf(cls_Divides_Omod__1_0,axiom,
c_Divides_Oop_Amod(V_m,c_Suc(c_0),tc_nat) = c_0,
file('MSC001-1.ax',cls_Divides_Omod__1_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),
file('MSC001-1.ax',cls_Divides_Omod__add__self1_0) ).
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),
file('MSC001-1.ax',cls_Divides_Omod__add__self2_0) ).
cnf(cls_Divides_Omod__le__divisor_0,axiom,
( c_lessequals(c_Divides_Oop_Amod(V_m,V_n,tc_nat),V_n,tc_nat)
| ~ c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Omod__le__divisor_0) ).
cnf(cls_Divides_Omod__less_0,axiom,
( c_Divides_Oop_Amod(V_y,V_n,tc_nat) = V_y
| ~ c_less(V_y,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Omod__less_0) ).
cnf(cls_Divides_Omod__less__divisor_0,axiom,
( c_less(c_Divides_Oop_Amod(V_m,V_n,tc_nat),V_n,tc_nat)
| ~ c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Divides_Omod__less__divisor_0) ).
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),
file('MSC001-1.ax',cls_Divides_Omod__mult__self1_0) ).
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,
file('MSC001-1.ax',cls_Divides_Omod__mult__self1__is__0_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),
file('MSC001-1.ax',cls_Divides_Omod__mult__self2_0) ).
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,
file('MSC001-1.ax',cls_Divides_Omod__mult__self__is__0_0) ).
cnf(cls_Divides_Omod__self_0,axiom,
c_Divides_Oop_Amod(V_n,V_n,tc_nat) = c_0,
file('MSC001-1.ax',cls_Divides_Omod__self_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,
file('MSC001-1.ax',cls_Divides_Onat__mod__div__trivial_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),
file('MSC001-1.ax',cls_Divides_Onat__mod__mod__trivial_0) ).
cnf(cls_Equiv__Relations_Oquotient__is__empty2_0,axiom,
( V_A = c_emptyset
| c_emptyset != c_Equiv__Relations_Oquotient(V_A,V_r,T_a) ),
file('MSC001-1.ax',cls_Equiv__Relations_Oquotient__is__empty2_0) ).
cnf(cls_Equiv__Relations_Oquotient__is__empty2_1,axiom,
c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,V_r,T_a),
file('MSC001-1.ax',cls_Equiv__Relations_Oquotient__is__empty2_1) ).
cnf(cls_Equiv__Relations_Oquotient__is__empty_0,axiom,
( V_A = c_emptyset
| c_Equiv__Relations_Oquotient(V_A,V_r,T_a) != c_emptyset ),
file('MSC001-1.ax',cls_Equiv__Relations_Oquotient__is__empty_0) ).
cnf(cls_Equiv__Relations_Oquotient__is__empty_1,axiom,
c_Equiv__Relations_Oquotient(c_emptyset,V_r,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Equiv__Relations_Oquotient__is__empty_1) ).
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,
file('MSC001-1.ax',cls_Extraction_Osumbool_Ocases__1_0) ).
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,
file('MSC001-1.ax',cls_Extraction_Osumbool_Ocases__2_0) ).
cnf(cls_Extraction_Osumbool_Odistinct__1_0,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('MSC001-1.ax',cls_Extraction_Osumbool_Odistinct__1_0) ).
cnf(cls_Extraction_Osumbool_Odistinct__2_0,axiom,
c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
file('MSC001-1.ax',cls_Extraction_Osumbool_Odistinct__2_0) ).
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,
file('MSC001-1.ax',cls_Extraction_Osumbool_Orecs__1_0) ).
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,
file('MSC001-1.ax',cls_Extraction_Osumbool_Orecs__2_0) ).
cnf(cls_Extraction_Osumbool_Osize__1_0,axiom,
c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) = c_0,
file('MSC001-1.ax',cls_Extraction_Osumbool_Osize__1_0) ).
cnf(cls_Extraction_Osumbool_Osize__2_0,axiom,
c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) = c_0,
file('MSC001-1.ax',cls_Extraction_Osumbool_Osize__2_0) ).
cnf(cls_Finite__Set_OMax__ge_0,axiom,
( V_A = c_emptyset
| c_lessequals(V_x,c_Finite__Set_OMax(V_A,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_x,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMax__ge_0) ).
cnf(cls_Finite__Set_OMax__in_0,axiom,
( V_A = c_emptyset
| c_in(c_Finite__Set_OMax(V_A,T_a),V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMax__in_0) ).
cnf(cls_Finite__Set_OMax__insert_0,axiom,
( 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)
| V_A = c_emptyset
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_b))
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Finite__Set_OMax__insert_0) ).
cnf(cls_Finite__Set_OMax__le__iff_0,axiom,
( V_A = c_emptyset
| c_lessequals(V_U,V_x,T_a)
| ~ c_lessequals(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMax__le__iff_0) ).
cnf(cls_Finite__Set_OMax__le__iff_1,axiom,
( V_A = c_emptyset
| c_lessequals(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| c_in(c_Main_OMax__le__iff__1(V_A,V_x,T_a),V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMax__le__iff_1) ).
cnf(cls_Finite__Set_OMax__le__iff_2,axiom,
( V_A = c_emptyset
| c_lessequals(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| ~ c_lessequals(c_Main_OMax__le__iff__1(V_A,V_x,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMax__le__iff_2) ).
cnf(cls_Finite__Set_OMax__less__iff_0,axiom,
( V_A = c_emptyset
| c_less(V_U,V_x,T_a)
| ~ c_less(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMax__less__iff_0) ).
cnf(cls_Finite__Set_OMax__less__iff_1,axiom,
( V_A = c_emptyset
| c_less(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| c_in(c_Main_OMax__less__iff__1(V_A,V_x,T_a),V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMax__less__iff_1) ).
cnf(cls_Finite__Set_OMax__less__iff_2,axiom,
( V_A = c_emptyset
| c_less(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| ~ c_less(c_Main_OMax__less__iff__1(V_A,V_x,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMax__less__iff_2) ).
cnf(cls_Finite__Set_OMax__singleton_0,axiom,
( c_Finite__Set_OMax(c_insert(V_y,c_emptyset,T_a),T_a) = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMax__singleton_0) ).
cnf(cls_Finite__Set_OMin__ge__iff_0,axiom,
( V_A = c_emptyset
| c_lessequals(V_x,V_U,T_a)
| ~ c_lessequals(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMin__ge__iff_0) ).
cnf(cls_Finite__Set_OMin__ge__iff_1,axiom,
( V_A = c_emptyset
| c_lessequals(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| c_in(c_Main_OMin__ge__iff__1(V_A,V_x,T_a),V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMin__ge__iff_1) ).
cnf(cls_Finite__Set_OMin__ge__iff_2,axiom,
( V_A = c_emptyset
| c_lessequals(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_lessequals(V_x,c_Main_OMin__ge__iff__1(V_A,V_x,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMin__ge__iff_2) ).
cnf(cls_Finite__Set_OMin__gr__iff_0,axiom,
( V_A = c_emptyset
| c_less(V_x,V_U,T_a)
| ~ c_less(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMin__gr__iff_0) ).
cnf(cls_Finite__Set_OMin__gr__iff_1,axiom,
( V_A = c_emptyset
| c_less(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| c_in(c_Main_OMin__gr__iff__1(V_A,V_x,T_a),V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMin__gr__iff_1) ).
cnf(cls_Finite__Set_OMin__gr__iff_2,axiom,
( V_A = c_emptyset
| c_less(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_less(V_x,c_Main_OMin__gr__iff__1(V_A,V_x,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMin__gr__iff_2) ).
cnf(cls_Finite__Set_OMin__in_0,axiom,
( V_A = c_emptyset
| c_in(c_Finite__Set_OMin(V_A,T_a),V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMin__in_0) ).
cnf(cls_Finite__Set_OMin__insert_0,axiom,
( 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)
| V_A = c_emptyset
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_b))
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Finite__Set_OMin__insert_0) ).
cnf(cls_Finite__Set_OMin__le_0,axiom,
( V_A = c_emptyset
| c_lessequals(c_Finite__Set_OMin(V_A,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_x,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMin__le_0) ).
cnf(cls_Finite__Set_OMin__singleton_0,axiom,
( c_Finite__Set_OMin(c_insert(V_y,c_emptyset,T_a),T_a) = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Finite__Set_OMin__singleton_0) ).
cnf(cls_Finite__Set_Ocard__0__eq_0,axiom,
( V_A = c_emptyset
| c_Finite__Set_Ocard(V_A,T_a) != c_0
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Finite__Set_Ocard__0__eq_0) ).
cnf(cls_Finite__Set_Ocard__0__eq_1,axiom,
( c_Finite__Set_Ocard(c_emptyset,T_a) = c_0
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Finite__Set_Ocard__0__eq_1) ).
cnf(cls_Finite__Set_Ocard__empty_0,axiom,
c_Finite__Set_Ocard(c_emptyset,T_a) = c_0,
file('MSC001-1.ax',cls_Finite__Set_Ocard__empty_0) ).
cnf(cls_Finite__Set_Ocard__infinite_0,axiom,
( c_Finite__Set_Ocard(V_A,T_a) = c_0
| c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Finite__Set_Ocard__infinite_0) ).
cnf(cls_Finite__Set_Ocard__insert__disjoint_0,axiom,
( c_Finite__Set_Ocard(c_insert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a))
| c_in(V_x,V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Finite__Set_Ocard__insert__disjoint_0) ).
cnf(cls_Finite__Set_Ofinite__Diff_0,axiom,
( c_in(c_minus(V_B,V_Ba,tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_B,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Finite__Set_Ofinite__Diff_0) ).
cnf(cls_Finite__Set_Ofinite__Diff__insert_0,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)) ),
file('MSC001-1.ax',cls_Finite__Set_Ofinite__Diff__insert_0) ).
cnf(cls_Finite__Set_Ofinite__Diff__insert_1,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)) ),
file('MSC001-1.ax',cls_Finite__Set_Ofinite__Diff__insert_1) ).
cnf(cls_Finite__Set_Ofinite__Pow__iff_0,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))) ),
file('MSC001-1.ax',cls_Finite__Set_Ofinite__Pow__iff_0) ).
cnf(cls_Finite__Set_Ofinite__Pow__iff_1,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)) ),
file('MSC001-1.ax',cls_Finite__Set_Ofinite__Pow__iff_1) ).
cnf(cls_Finite__Set_Ofinite__Un_0,axiom,
( 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)) ),
file('MSC001-1.ax',cls_Finite__Set_Ofinite__Un_0) ).
cnf(cls_Finite__Set_Ofinite__Un_1,axiom,
( c_in(V_G,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)) ),
file('MSC001-1.ax',cls_Finite__Set_Ofinite__Un_1) ).
cnf(cls_Finite__Set_Ofinite__Un_2,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))
| ~ c_in(V_G,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Finite__Set_Ofinite__Un_2) ).
cnf(cls_Finite__Set_Ofinite__converse_0,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))) ),
file('MSC001-1.ax',cls_Finite__Set_Ofinite__converse_0) ).
cnf(cls_Finite__Set_Ofinite__converse_1,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))) ),
file('MSC001-1.ax',cls_Finite__Set_Ofinite__converse_1) ).
cnf(cls_Finite__Set_Ofinite__insert_0,axiom,
( c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(c_insert(V_a,V_A,T_a),c_Finite__Set_OFinites,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Finite__Set_Ofinite__insert_0) ).
cnf(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0,axiom,
( V_A = c_emptyset
| c_lessequals(c_Finite__Set_OMin(V_A,T_b),c_Finite__Set_OMax(V_A,T_b),T_b)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_b))
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
cnf(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0,axiom,
( c_Orderings_Omin(V_y,c_Finite__Set_OMax(V_A,T_b),T_b) = V_y
| V_A = c_emptyset
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_b))
| ~ c_in(V_y,V_A,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
cnf(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0,axiom,
( c_Orderings_Omax(V_y,c_Finite__Set_OMin(V_A,T_b),T_b) = V_y
| V_A = c_emptyset
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_b))
| ~ c_in(V_y,V_A,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
cnf(cls_Finite__Set_Oof__nat__id_0,axiom,
c_NatArith_Oof__nat(V_y,tc_nat) = V_y,
file('MSC001-1.ax',cls_Finite__Set_Oof__nat__id_0) ).
cnf(cls_Fun_Oid__apply_0,axiom,
c_Fun_Oid(V_y,T_a) = V_y,
file('MSC001-1.ax',cls_Fun_Oid__apply_0) ).
cnf(cls_GCD_Ogcd__0_0,axiom,
c_GCD_Ogcd(c_Pair(V_y,c_0,tc_nat,tc_nat)) = V_y,
file('MSC001-1.ax',cls_GCD_Ogcd__0_0) ).
cnf(cls_GCD_Ogcd__0__left_0,axiom,
c_GCD_Ogcd(c_Pair(c_0,V_y,tc_nat,tc_nat)) = V_y,
file('MSC001-1.ax',cls_GCD_Ogcd__0__left_0) ).
cnf(cls_GCD_Ogcd__1_0,axiom,
c_GCD_Ogcd(c_Pair(V_m,c_Suc(c_0),tc_nat,tc_nat)) = c_1,
file('MSC001-1.ax',cls_GCD_Ogcd__1_0) ).
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,
file('MSC001-1.ax',cls_GCD_Ogcd__1__left_0) ).
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)),
file('MSC001-1.ax',cls_GCD_Ogcd__add1_0) ).
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)),
file('MSC001-1.ax',cls_GCD_Ogcd__add2_0) ).
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)),
file('MSC001-1.ax',cls_GCD_Ogcd__add2_H_0) ).
cnf(cls_GCD_Ogcd__greatest__iff_0,axiom,
( 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) ),
file('MSC001-1.ax',cls_GCD_Ogcd__greatest__iff_0) ).
cnf(cls_GCD_Ogcd__greatest__iff_1,axiom,
( c_Divides_Oop_Advd(V_k,V_n,tc_nat)
| ~ c_Divides_Oop_Advd(V_k,c_GCD_Ogcd(c_Pair(V_m,V_n,tc_nat,tc_nat)),tc_nat) ),
file('MSC001-1.ax',cls_GCD_Ogcd__greatest__iff_1) ).
cnf(cls_GCD_Ogcd__greatest__iff_2,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)
| ~ c_Divides_Oop_Advd(V_k,V_n,tc_nat) ),
file('MSC001-1.ax',cls_GCD_Ogcd__greatest__iff_2) ).
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,
file('MSC001-1.ax',cls_GCD_Ogcd__mult_0) ).
cnf(cls_GCD_Ogcd__self_0,axiom,
c_GCD_Ogcd(c_Pair(V_y,V_y,tc_nat,tc_nat)) = V_y,
file('MSC001-1.ax',cls_GCD_Ogcd__self_0) ).
cnf(cls_Infinite__Set_Onat__infinite_0,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
file('MSC001-1.ax',cls_Infinite__Set_Onat__infinite_0) ).
cnf(cls_IntArith_Oabs__minus__one_0,axiom,
( c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),T_a) = c_1
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oabs__minus__one_0) ).
cnf(cls_IntArith_Oabs__power__minus__one_0,axiom,
( c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),V_n,T_a),T_a) = c_1
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oabs__power__minus__one_0) ).
cnf(cls_IntArith_Oarith__special__10_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__10_0) ).
cnf(cls_IntArith_Oarith__special__10_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__10_1) ).
cnf(cls_IntArith_Oarith__special__11_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__11_0) ).
cnf(cls_IntArith_Oarith__special__11_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__11_1) ).
cnf(cls_IntArith_Oarith__special__12_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__12_0) ).
cnf(cls_IntArith_Oarith__special__12_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__12_1) ).
cnf(cls_IntArith_Oarith__special__13_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__13_0) ).
cnf(cls_IntArith_Oarith__special__13_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__13_1) ).
cnf(cls_IntArith_Oarith__special__14_0,axiom,
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_y,T_a),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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__14_0) ).
cnf(cls_IntArith_Oarith__special__14_1,axiom,
( c_lessequals(c_0,c_Numeral_Onumber__of(V_y,T_a),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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__14_1) ).
cnf(cls_IntArith_Oarith__special__15_0,axiom,
( ~ c_lessequals(c_1,c_Numeral_Onumber__of(V_y,T_a),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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__15_0) ).
cnf(cls_IntArith_Oarith__special__15_1,axiom,
( c_lessequals(c_1,c_Numeral_Onumber__of(V_y,T_a),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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__15_1) ).
cnf(cls_IntArith_Oarith__special__16_0,axiom,
( ~ c_lessequals(c_Numeral_Onumber__of(V_x,T_a),c_0,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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__16_0) ).
cnf(cls_IntArith_Oarith__special__16_1,axiom,
( c_lessequals(c_Numeral_Onumber__of(V_x,T_a),c_0,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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__16_1) ).
cnf(cls_IntArith_Oarith__special__17_0,axiom,
( ~ c_lessequals(c_Numeral_Onumber__of(V_x,T_a),c_1,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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__17_0) ).
cnf(cls_IntArith_Oarith__special__17_1,axiom,
( c_lessequals(c_Numeral_Onumber__of(V_x,T_a),c_1,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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__17_1) ).
cnf(cls_IntArith_Oarith__special__1_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__1_0) ).
cnf(cls_IntArith_Oarith__special__2_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__2_0) ).
cnf(cls_IntArith_Oarith__special__3_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__3_0) ).
cnf(cls_IntArith_Oarith__special__4_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__4_0) ).
cnf(cls_IntArith_Oarith__special__5_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__5_0) ).
cnf(cls_IntArith_Oarith__special__6_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__6_0) ).
cnf(cls_IntArith_Oarith__special__6_1,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__6_1) ).
cnf(cls_IntArith_Oarith__special__7_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__7_0) ).
cnf(cls_IntArith_Oarith__special__7_1,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__7_1) ).
cnf(cls_IntArith_Oarith__special__8_0,axiom,
( 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
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__8_0) ).
cnf(cls_IntArith_Oarith__special__8_1,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__8_1) ).
cnf(cls_IntArith_Oarith__special__9_0,axiom,
( 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
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__9_0) ).
cnf(cls_IntArith_Oarith__special__9_1,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oarith__special__9_1) ).
cnf(cls_IntArith_Oint__eq__iff__number__of_0,axiom,
( V_m = c_IntDef_Onat(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint))
| c_IntDef_Oint(V_m) != c_Numeral_Onumber__of(V_v,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntArith_Oint__eq__iff__number__of_0) ).
cnf(cls_IntArith_Oint__eq__iff__number__of_1,axiom,
( c_lessequals(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oint(V_m) != c_Numeral_Onumber__of(V_v,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntArith_Oint__eq__iff__number__of_1) ).
cnf(cls_IntArith_Oint__eq__iff__number__of_2,axiom,
( c_IntDef_Oint(c_IntDef_Onat(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint))) = 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) ),
file('MSC001-1.ax',cls_IntArith_Oint__eq__iff__number__of_2) ).
cnf(cls_IntArith_Onat__1_0,axiom,
c_IntDef_Onat(c_1) = c_Suc(c_0),
file('MSC001-1.ax',cls_IntArith_Onat__1_0) ).
cnf(cls_IntArith_Oof__int__m1_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_IntArith_Oof__int__m1_0) ).
cnf(cls_IntArith_Oone__less__nat__eq_0,axiom,
( c_less(c_1,V_z,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(V_z),tc_nat) ),
file('MSC001-1.ax',cls_IntArith_Oone__less__nat__eq_0) ).
cnf(cls_IntArith_Oone__less__nat__eq_1,axiom,
( c_less(c_Suc(c_0),c_IntDef_Onat(V_z),tc_nat)
| ~ c_less(c_1,V_z,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntArith_Oone__less__nat__eq_1) ).
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),
file('MSC001-1.ax',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
cnf(cls_IntArith_Ozabs__less__one__iff_0,axiom,
( V_z = c_0
| ~ c_less(c_HOL_Oabs(V_z,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntArith_Ozabs__less__one__iff_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),
file('MSC001-1.ax',cls_IntArith_Ozabs__less__one__iff_1) ).
cnf(cls_IntArith_Ozle__add1__eq__le_0,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) ),
file('MSC001-1.ax',cls_IntArith_Ozle__add1__eq__le_0) ).
cnf(cls_IntArith_Ozle__add1__eq__le_1,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) ),
file('MSC001-1.ax',cls_IntArith_Ozle__add1__eq__le_1) ).
cnf(cls_IntArith_Ozle__diff1__eq_0,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) ),
file('MSC001-1.ax',cls_IntArith_Ozle__diff1__eq_0) ).
cnf(cls_IntArith_Ozle__diff1__eq_1,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) ),
file('MSC001-1.ax',cls_IntArith_Ozle__diff1__eq_1) ).
cnf(cls_IntDef_OInteg_OAbs__Integ__inject_0,axiom,
( V_x = V_y
| c_IntDef_OAbs__Integ(V_x) != c_IntDef_OAbs__Integ(V_y)
| ~ c_in(V_x,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(V_y,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('MSC001-1.ax',cls_IntDef_OInteg_OAbs__Integ__inject_0) ).
cnf(cls_IntDef_OInteg_OAbs__Integ__inverse_0,axiom,
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(V_y)) = V_y
| ~ c_in(V_y,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('MSC001-1.ax',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).
cnf(cls_IntDef_OInts__0_0,axiom,
( c_in(c_0,c_IntDef_OInts,T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_OInts__0_0) ).
cnf(cls_IntDef_OInts__1_0,axiom,
( c_in(c_1,c_IntDef_OInts,T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_OInts__1_0) ).
cnf(cls_IntDef_OInts__add_0,axiom,
( c_in(c_plus(V_a,V_b,T_a),c_IntDef_OInts,T_a)
| ~ c_in(V_a,c_IntDef_OInts,T_a)
| ~ c_in(V_b,c_IntDef_OInts,T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_OInts__add_0) ).
cnf(cls_IntDef_OInts__diff_0,axiom,
( c_in(c_minus(V_a,V_b,T_a),c_IntDef_OInts,T_a)
| ~ c_in(V_a,c_IntDef_OInts,T_a)
| ~ c_in(V_b,c_IntDef_OInts,T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_OInts__diff_0) ).
cnf(cls_IntDef_OInts__minus_0,axiom,
( c_in(c_uminus(V_a,T_a),c_IntDef_OInts,T_a)
| ~ c_in(V_a,c_IntDef_OInts,T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_OInts__minus_0) ).
cnf(cls_IntDef_OInts__mult_0,axiom,
( c_in(c_times(V_a,V_b,T_a),c_IntDef_OInts,T_a)
| ~ c_in(V_a,c_IntDef_OInts,T_a)
| ~ c_in(V_b,c_IntDef_OInts,T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_OInts__mult_0) ).
cnf(cls_IntDef_ONats__0_0,axiom,
( c_in(c_0,c_IntDef_ONats,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
file('MSC001-1.ax',cls_IntDef_ONats__0_0) ).
cnf(cls_IntDef_ONats__1_0,axiom,
( c_in(c_1,c_IntDef_ONats,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
file('MSC001-1.ax',cls_IntDef_ONats__1_0) ).
cnf(cls_IntDef_ONats__add_0,axiom,
( c_in(c_plus(V_a,V_b,T_a),c_IntDef_ONats,T_a)
| ~ c_in(V_a,c_IntDef_ONats,T_a)
| ~ c_in(V_b,c_IntDef_ONats,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
file('MSC001-1.ax',cls_IntDef_ONats__add_0) ).
cnf(cls_IntDef_ONats__mult_0,axiom,
( c_in(c_times(V_a,V_b,T_a),c_IntDef_ONats,T_a)
| ~ c_in(V_a,c_IntDef_ONats,T_a)
| ~ c_in(V_b,c_IntDef_ONats,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
file('MSC001-1.ax',cls_IntDef_ONats__mult_0) ).
cnf(cls_IntDef_Oabs__int__eq_0,axiom,
c_HOL_Oabs(c_IntDef_Oint(V_m),tc_IntDef_Oint) = c_IntDef_Oint(V_m),
file('MSC001-1.ax',cls_IntDef_Oabs__int__eq_0) ).
cnf(cls_IntDef_Oequiv__intrel__iff_0,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)) ),
file('MSC001-1.ax',cls_IntDef_Oequiv__intrel__iff_0) ).
cnf(cls_IntDef_Oequiv__intrel__iff_1,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))) ),
file('MSC001-1.ax',cls_IntDef_Oequiv__intrel__iff_1) ).
cnf(cls_IntDef_Oint__0__neq__1_0,axiom,
c_0 != c_1,
file('MSC001-1.ax',cls_IntDef_Oint__0__neq__1_0) ).
cnf(cls_IntDef_Oint__1_0,axiom,
c_IntDef_Oint(c_1) = c_1,
file('MSC001-1.ax',cls_IntDef_Oint__1_0) ).
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),
file('MSC001-1.ax',cls_IntDef_Oint__Suc_0) ).
cnf(cls_IntDef_Oint__eq__0__conv_0,axiom,
( V_n = c_0
| c_IntDef_Oint(V_n) != c_0 ),
file('MSC001-1.ax',cls_IntDef_Oint__eq__0__conv_0) ).
cnf(cls_IntDef_Oint__eq__0__conv_1,axiom,
c_IntDef_Oint(c_0) = c_0,
file('MSC001-1.ax',cls_IntDef_Oint__eq__0__conv_1) ).
cnf(cls_IntDef_Oint__int__eq_0,axiom,
( V_m = V_n
| c_IntDef_Oint(V_m) != c_IntDef_Oint(V_n) ),
file('MSC001-1.ax',cls_IntDef_Oint__int__eq_0) ).
cnf(cls_IntDef_Oint__le__0__conv_0,axiom,
( V_n = c_0
| ~ c_lessequals(c_IntDef_Oint(V_n),c_0,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDef_Oint__le__0__conv_0) ).
cnf(cls_IntDef_Oint__le__0__conv_1,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
file('MSC001-1.ax',cls_IntDef_Oint__le__0__conv_1) ).
cnf(cls_IntDef_Oint__less__0__conv_0,axiom,
~ c_less(c_IntDef_Oint(V_k),c_0,tc_IntDef_Oint),
file('MSC001-1.ax',cls_IntDef_Oint__less__0__conv_0) ).
cnf(cls_IntDef_Oint__nat__eq_0,axiom,
( c_IntDef_Oint(c_IntDef_Onat(V_z)) = V_z
| ~ c_lessequals(c_0,V_z,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDef_Oint__nat__eq_0) ).
cnf(cls_IntDef_Oint__nat__eq_1,axiom,
( c_IntDef_Oint(c_IntDef_Onat(V_z)) = c_0
| c_lessequals(c_0,V_z,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDef_Oint__nat__eq_1) ).
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))),
file('MSC001-1.ax',cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0) ).
cnf(cls_IntDef_Ointrel__iff_0,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))) ),
file('MSC001-1.ax',cls_IntDef_Ointrel__iff_0) ).
cnf(cls_IntDef_Ointrel__iff_1,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) ),
file('MSC001-1.ax',cls_IntDef_Ointrel__iff_1) ).
cnf(cls_IntDef_Onat__int_0,axiom,
c_IntDef_Onat(c_IntDef_Oint(V_y)) = V_y,
file('MSC001-1.ax',cls_IntDef_Onat__int_0) ).
cnf(cls_IntDef_Onat__le__0_0,axiom,
( c_IntDef_Onat(V_z) = c_0
| ~ c_lessequals(V_z,c_0,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDef_Onat__le__0_0) ).
cnf(cls_IntDef_Onat__zero_0,axiom,
c_IntDef_Onat(c_0) = c_0,
file('MSC001-1.ax',cls_IntDef_Onat__zero_0) ).
cnf(cls_IntDef_Onat__zminus__int_0,axiom,
c_IntDef_Onat(c_uminus(c_IntDef_Oint(V_n),tc_IntDef_Oint)) = c_0,
file('MSC001-1.ax',cls_IntDef_Onat__zminus__int_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),
file('MSC001-1.ax',cls_IntDef_Oneg__zminus__int_0) ).
cnf(cls_IntDef_Onegative__eq__positive_0,axiom,
( V_n = c_0
| c_uminus(c_IntDef_Oint(V_n),tc_IntDef_Oint) != c_IntDef_Oint(V_m) ),
file('MSC001-1.ax',cls_IntDef_Onegative__eq__positive_0) ).
cnf(cls_IntDef_Onegative__eq__positive_1,axiom,
( V_m = c_0
| c_uminus(c_IntDef_Oint(V_n),tc_IntDef_Oint) != c_IntDef_Oint(V_m) ),
file('MSC001-1.ax',cls_IntDef_Onegative__eq__positive_1) ).
cnf(cls_IntDef_Onegative__eq__positive_2,axiom,
c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint) = c_IntDef_Oint(c_0),
file('MSC001-1.ax',cls_IntDef_Onegative__eq__positive_2) ).
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),
file('MSC001-1.ax',cls_IntDef_Onot__int__zless__negative_0) ).
cnf(cls_IntDef_Onot__neg__int_0,axiom,
~ c_IntDef_Oneg(c_IntDef_Oint(V_n),tc_IntDef_Oint),
file('MSC001-1.ax',cls_IntDef_Onot__neg__int_0) ).
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),
file('MSC001-1.ax',cls_IntDef_Onot__zle__0__negative_0) ).
cnf(cls_IntDef_Oof__int__0__eq__iff_0,axiom,
( c_0 = V_z
| c_0 != c_IntDef_Oof__int(V_z,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__0__eq__iff_0) ).
cnf(cls_IntDef_Oof__int__0__eq__iff_1,axiom,
( c_0 = c_IntDef_Oof__int(c_0,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__0__eq__iff_1) ).
cnf(cls_IntDef_Oof__int__0__le__iff_0,axiom,
( c_lessequals(c_0,V_z,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(V_z,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__0__le__iff_0) ).
cnf(cls_IntDef_Oof__int__0__le__iff_1,axiom,
( c_lessequals(c_0,c_IntDef_Oof__int(V_z,T_a),T_a)
| ~ c_lessequals(c_0,V_z,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__0__le__iff_1) ).
cnf(cls_IntDef_Oof__int__0__less__iff_0,axiom,
( c_less(c_0,V_z,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(V_z,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__0__less__iff_0) ).
cnf(cls_IntDef_Oof__int__0__less__iff_1,axiom,
( c_less(c_0,c_IntDef_Oof__int(V_z,T_a),T_a)
| ~ c_less(c_0,V_z,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__0__less__iff_1) ).
cnf(cls_IntDef_Oof__int__1_0,axiom,
( c_IntDef_Oof__int(c_1,T_a) = c_1
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__1_0) ).
cnf(cls_IntDef_Oof__int__add_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__add_0) ).
cnf(cls_IntDef_Oof__int__diff_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__diff_0) ).
cnf(cls_IntDef_Oof__int__eq__0__iff_0,axiom,
( V_w = c_0
| c_IntDef_Oof__int(V_w,T_a) != c_0
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__eq__0__iff_0) ).
cnf(cls_IntDef_Oof__int__eq__0__iff_1,axiom,
( c_IntDef_Oof__int(c_0,T_a) = c_0
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__eq__0__iff_1) ).
cnf(cls_IntDef_Oof__int__eq__iff_0,axiom,
( V_w = V_z
| c_IntDef_Oof__int(V_w,T_a) != c_IntDef_Oof__int(V_z,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__eq__iff_0) ).
cnf(cls_IntDef_Oof__int__int__eq_0,axiom,
( c_IntDef_Oof__int(c_IntDef_Oint(V_n),T_a) = c_NatArith_Oof__nat(V_n,T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__int__eq_0) ).
cnf(cls_IntDef_Oof__int__le__0__iff_0,axiom,
( c_lessequals(V_w,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(V_w,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__le__0__iff_0) ).
cnf(cls_IntDef_Oof__int__le__0__iff_1,axiom,
( c_lessequals(c_IntDef_Oof__int(V_w,T_a),c_0,T_a)
| ~ c_lessequals(V_w,c_0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__le__0__iff_1) ).
cnf(cls_IntDef_Oof__int__le__iff_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__le__iff_0) ).
cnf(cls_IntDef_Oof__int__le__iff_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__le__iff_1) ).
cnf(cls_IntDef_Oof__int__less__0__iff_0,axiom,
( c_less(V_w,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(V_w,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__less__0__iff_0) ).
cnf(cls_IntDef_Oof__int__less__0__iff_1,axiom,
( c_less(c_IntDef_Oof__int(V_w,T_a),c_0,T_a)
| ~ c_less(V_w,c_0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__less__0__iff_1) ).
cnf(cls_IntDef_Oof__int__less__iff_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__less__iff_0) ).
cnf(cls_IntDef_Oof__int__less__iff_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__less__iff_1) ).
cnf(cls_IntDef_Oof__int__minus_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__minus_0) ).
cnf(cls_IntDef_Oof__int__mult_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__mult_0) ).
cnf(cls_IntDef_Oof__int__of__nat__eq_0,axiom,
( c_IntDef_Oof__int(c_NatArith_Oof__nat(V_n,tc_IntDef_Oint),T_a) = c_NatArith_Oof__nat(V_n,T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__int__of__nat__eq_0) ).
cnf(cls_IntDef_Oof__nat__in__Nats_0,axiom,
( c_in(c_NatArith_Oof__nat(V_n,T_a),c_IntDef_ONats,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
file('MSC001-1.ax',cls_IntDef_Oof__nat__in__Nats_0) ).
cnf(cls_IntDef_Ozero__less__int__conv_0,axiom,
( c_less(c_0,V_n,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(V_n),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDef_Ozero__less__int__conv_0) ).
cnf(cls_IntDef_Ozero__less__int__conv_1,axiom,
( c_less(c_0,c_IntDef_Oint(V_n),tc_IntDef_Oint)
| ~ c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_IntDef_Ozero__less__int__conv_1) ).
cnf(cls_IntDef_Ozero__less__nat__eq_0,axiom,
( c_less(c_0,V_z,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(V_z),tc_nat) ),
file('MSC001-1.ax',cls_IntDef_Ozero__less__nat__eq_0) ).
cnf(cls_IntDef_Ozero__less__nat__eq_1,axiom,
( c_less(c_0,c_IntDef_Onat(V_z),tc_nat)
| ~ c_less(c_0,V_z,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDef_Ozero__less__nat__eq_1) ).
cnf(cls_IntDef_Ozero__zle__int_0,axiom,
c_lessequals(c_0,c_IntDef_Oint(V_n),tc_IntDef_Oint),
file('MSC001-1.ax',cls_IntDef_Ozero__zle__int_0) ).
cnf(cls_IntDef_Ozle__int_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(V_m),c_IntDef_Oint(V_n),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDef_Ozle__int_0) ).
cnf(cls_IntDef_Ozle__int_1,axiom,
( c_lessequals(c_IntDef_Oint(V_m),c_IntDef_Oint(V_n),tc_IntDef_Oint)
| ~ c_lessequals(V_m,V_n,tc_nat) ),
file('MSC001-1.ax',cls_IntDef_Ozle__int_1) ).
cnf(cls_IntDef_Ozless__int_0,axiom,
( c_less(V_m,V_n,tc_nat)
| ~ c_less(c_IntDef_Oint(V_m),c_IntDef_Oint(V_n),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDef_Ozless__int_0) ).
cnf(cls_IntDef_Ozless__int_1,axiom,
( c_less(c_IntDef_Oint(V_m),c_IntDef_Oint(V_n),tc_IntDef_Oint)
| ~ c_less(V_m,V_n,tc_nat) ),
file('MSC001-1.ax',cls_IntDef_Ozless__int_1) ).
cnf(cls_IntDef_Ozless__nat__conj_0,axiom,
( c_less(c_0,V_z,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(V_w),c_IntDef_Onat(V_z),tc_nat) ),
file('MSC001-1.ax',cls_IntDef_Ozless__nat__conj_0) ).
cnf(cls_IntDef_Ozless__nat__conj_1,axiom,
( c_less(V_w,V_z,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(V_w),c_IntDef_Onat(V_z),tc_nat) ),
file('MSC001-1.ax',cls_IntDef_Ozless__nat__conj_1) ).
cnf(cls_IntDef_Ozless__nat__conj_2,axiom,
( c_less(c_IntDef_Onat(V_w),c_IntDef_Onat(V_z),tc_nat)
| ~ c_less(c_0,V_z,tc_IntDef_Oint)
| ~ c_less(V_w,V_z,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDef_Ozless__nat__conj_2) ).
cnf(cls_IntDiv_ODIVISION__BY__ZERO_0,axiom,
c_Divides_Oop_Amod(V_y,c_0,tc_IntDef_Oint) = V_y,
file('MSC001-1.ax',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
cnf(cls_IntDiv_Odiv__neg__neg__number__of_0,axiom,
( 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)
| ~ c_lessequals(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Odiv__neg__neg__number__of_0) ).
cnf(cls_IntDiv_Odiv__neg__pos__number__of_0,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Odiv__neg__pos__number__of_0) ).
cnf(cls_IntDiv_Odiv__pos__neg__1__number__of_0,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Odiv__pos__neg__1__number__of_0) ).
cnf(cls_IntDiv_Odiv__pos__neg__number__of_0,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Odiv__pos__neg__number__of_0) ).
cnf(cls_IntDiv_Odiv__pos__pos__1__number__of_0,axiom,
( 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)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Odiv__pos__pos__1__number__of_0) ).
cnf(cls_IntDiv_Odiv__pos__pos__number__of_0,axiom,
( 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)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Odiv__pos__pos__number__of_0) ).
cnf(cls_IntDiv_Odvd__zminus__iff_0,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) ),
file('MSC001-1.ax',cls_IntDiv_Odvd__zminus__iff_0) ).
cnf(cls_IntDiv_Odvd__zminus__iff_1,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) ),
file('MSC001-1.ax',cls_IntDiv_Odvd__zminus__iff_1) ).
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,
file('MSC001-1.ax',cls_IntDiv_Omod__div__trivial_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),
file('MSC001-1.ax',cls_IntDiv_Omod__mod__trivial_0) ).
cnf(cls_IntDiv_Omod__neg__neg__number__of_0,axiom,
( 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)
| ~ c_lessequals(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Omod__neg__neg__number__of_0) ).
cnf(cls_IntDiv_Omod__neg__pos__number__of_0,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Omod__neg__pos__number__of_0) ).
cnf(cls_IntDiv_Omod__pos__neg__1__number__of_0,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Omod__pos__neg__1__number__of_0) ).
cnf(cls_IntDiv_Omod__pos__neg__number__of_0,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Omod__pos__neg__number__of_0) ).
cnf(cls_IntDiv_Omod__pos__pos__1__number__of_0,axiom,
( 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)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Omod__pos__pos__1__number__of_0) ).
cnf(cls_IntDiv_Omod__pos__pos__number__of_0,axiom,
( 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)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Omod__pos__pos__number__of_0) ).
cnf(cls_IntDiv_OnegDivAlg__eqn__1__number__of_0,axiom,
( 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)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_OnegDivAlg__eqn__1__number__of_0) ).
cnf(cls_IntDiv_OnegDivAlg__eqn__1__number__of_1,axiom,
( 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)))
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_OnegDivAlg__eqn__1__number__of_1) ).
cnf(cls_IntDiv_OnegDivAlg__eqn__number__of_0,axiom,
( 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)
| ~ 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_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_OnegDivAlg__eqn__number__of_0) ).
cnf(cls_IntDiv_OnegDivAlg__eqn__number__of_1,axiom,
( 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)))
| 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_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_OnegDivAlg__eqn__number__of_1) ).
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),
file('MSC001-1.ax',cls_IntDiv_OnegDivAlg__minus1_0) ).
cnf(cls_IntDiv_Oneg__mod__bound_0,axiom,
( c_less(V_b,c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(V_b,c_0,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Oneg__mod__bound_0) ).
cnf(cls_IntDiv_Oneg__mod__sign_0,axiom,
( c_lessequals(c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(V_b,c_0,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Oneg__mod__sign_0) ).
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),
file('MSC001-1.ax',cls_IntDiv_OnegateSnd__eq_0) ).
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),
file('MSC001-1.ax',cls_IntDiv_OposDivAlg__0_0) ).
cnf(cls_IntDiv_OposDivAlg__eqn__1__number__of_0,axiom,
( 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)
| ~ c_less(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_OposDivAlg__eqn__1__number__of_0) ).
cnf(cls_IntDiv_OposDivAlg__eqn__1__number__of_1,axiom,
( 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)))
| c_less(c_1,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_OposDivAlg__eqn__1__number__of_1) ).
cnf(cls_IntDiv_OposDivAlg__eqn__number__of_0,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_OposDivAlg__eqn__number__of_0) ).
cnf(cls_IntDiv_OposDivAlg__eqn__number__of_1,axiom,
( 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)))
| c_less(c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_OposDivAlg__eqn__number__of_1) ).
cnf(cls_IntDiv_Opos__mod__bound_0,axiom,
( c_less(c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),V_b,tc_IntDef_Oint)
| ~ c_less(c_0,V_b,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Opos__mod__bound_0) ).
cnf(cls_IntDiv_Opos__mod__sign_0,axiom,
( c_lessequals(c_0,c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,V_b,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Opos__mod__sign_0) ).
cnf(cls_IntDiv_Opower_Osimps__1_0,axiom,
c_Nat_Opower(V_p,c_0,tc_IntDef_Oint) = c_1,
file('MSC001-1.ax',cls_IntDiv_Opower_Osimps__1_0) ).
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),
file('MSC001-1.ax',cls_IntDiv_Opower_Osimps__2_0) ).
cnf(cls_IntDiv_Ozdiv__1_0,axiom,
c_div(V_y,c_1,tc_IntDef_Oint) = V_y,
file('MSC001-1.ax',cls_IntDiv_Ozdiv__1_0) ).
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),
file('MSC001-1.ax',cls_IntDiv_Ozdiv__minus1__right_0) ).
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),
file('MSC001-1.ax',cls_IntDiv_Ozdiv__number__of__BIT_0) ).
cnf(cls_IntDiv_Ozdiv__number__of__BIT_1,axiom,
( 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)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Ozdiv__number__of__BIT_1) ).
cnf(cls_IntDiv_Ozdiv__number__of__BIT_2,axiom,
( 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)
| V_b = c_Numeral_Obit_OB0
| c_lessequals(c_0,c_Numeral_Onumber__of(V_w,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Ozdiv__number__of__BIT_2) ).
cnf(cls_IntDiv_Ozdiv__self_0,axiom,
( c_div(V_a,V_a,tc_IntDef_Oint) = c_1
| V_a = c_0 ),
file('MSC001-1.ax',cls_IntDiv_Ozdiv__self_0) ).
cnf(cls_IntDiv_Ozdiv__zadd__self1_0,axiom,
( 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)
| V_a = c_0 ),
file('MSC001-1.ax',cls_IntDiv_Ozdiv__zadd__self1_0) ).
cnf(cls_IntDiv_Ozdiv__zadd__self2_0,axiom,
( 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)
| V_a = c_0 ),
file('MSC001-1.ax',cls_IntDiv_Ozdiv__zadd__self2_0) ).
cnf(cls_IntDiv_Ozdiv__zero_0,axiom,
c_div(c_0,V_b,tc_IntDef_Oint) = c_0,
file('MSC001-1.ax',cls_IntDiv_Ozdiv__zero_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),
file('MSC001-1.ax',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
cnf(cls_IntDiv_Ozdiv__zmult__self1_0,axiom,
( c_div(c_times(V_y,V_b,tc_IntDef_Oint),V_b,tc_IntDef_Oint) = V_y
| V_b = c_0 ),
file('MSC001-1.ax',cls_IntDiv_Ozdiv__zmult__self1_0) ).
cnf(cls_IntDiv_Ozdiv__zmult__self2_0,axiom,
( c_div(c_times(V_b,V_y,tc_IntDef_Oint),V_b,tc_IntDef_Oint) = V_y
| V_b = c_0 ),
file('MSC001-1.ax',cls_IntDiv_Ozdiv__zmult__self2_0) ).
cnf(cls_IntDiv_Ozdvd__0__left_0,axiom,
( V_m = c_0
| ~ c_Divides_Oop_Advd(c_0,V_m,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Ozdvd__0__left_0) ).
cnf(cls_IntDiv_Ozdvd__0__left_1,axiom,
c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
file('MSC001-1.ax',cls_IntDiv_Ozdvd__0__left_1) ).
cnf(cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0,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) ),
file('MSC001-1.ax',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).
cnf(cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1,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 ),
file('MSC001-1.ax',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).
cnf(cls_IntDiv_Ozdvd__refl_0,axiom,
c_Divides_Oop_Advd(V_m,V_m,tc_IntDef_Oint),
file('MSC001-1.ax',cls_IntDiv_Ozdvd__refl_0) ).
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),
file('MSC001-1.ax',cls_IntDiv_Ozero__le__zpower__abs_0) ).
cnf(cls_IntDiv_Ozero__less__zpower__abs__iff_0,axiom,
( V_n = c_0
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),V_n,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
cnf(cls_IntDiv_Ozero__less__zpower__abs__iff_1,axiom,
( V_x = c_0
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(V_x,tc_IntDef_Oint),V_n,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
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),
file('MSC001-1.ax',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
cnf(cls_IntDiv_Ozminus__dvd__iff_0,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) ),
file('MSC001-1.ax',cls_IntDiv_Ozminus__dvd__iff_0) ).
cnf(cls_IntDiv_Ozminus__dvd__iff_1,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) ),
file('MSC001-1.ax',cls_IntDiv_Ozminus__dvd__iff_1) ).
cnf(cls_IntDiv_Ozmod__1_0,axiom,
c_Divides_Oop_Amod(V_a,c_1,tc_IntDef_Oint) = c_0,
file('MSC001-1.ax',cls_IntDiv_Ozmod__1_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,
file('MSC001-1.ax',cls_IntDiv_Ozmod__minus1__right_0) ).
cnf(cls_IntDiv_Ozmod__self_0,axiom,
c_Divides_Oop_Amod(V_a,V_a,tc_IntDef_Oint) = c_0,
file('MSC001-1.ax',cls_IntDiv_Ozmod__self_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),
file('MSC001-1.ax',cls_IntDiv_Ozmod__zadd__self1_0) ).
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),
file('MSC001-1.ax',cls_IntDiv_Ozmod__zadd__self2_0) ).
cnf(cls_IntDiv_Ozmod__zero_0,axiom,
c_Divides_Oop_Amod(c_0,V_b,tc_IntDef_Oint) = c_0,
file('MSC001-1.ax',cls_IntDiv_Ozmod__zero_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),
file('MSC001-1.ax',cls_IntDiv_Ozmod__zminus__zminus_0) ).
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,
file('MSC001-1.ax',cls_IntDiv_Ozmod__zmult__self1_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,
file('MSC001-1.ax',cls_IntDiv_Ozmod__zmult__self2_0) ).
cnf(cls_LOrder_Ojoin__idempotent_0,axiom,
( c_LOrder_Ojoin(V_y,V_y,T_a) = V_y
| ~ class_LOrder_Ojoin__semilorder(T_a) ),
file('MSC001-1.ax',cls_LOrder_Ojoin__idempotent_0) ).
cnf(cls_LOrder_Omeet__idempotent_0,axiom,
( c_LOrder_Omeet(V_y,V_y,T_a) = V_y
| ~ class_LOrder_Omeet__semilorder(T_a) ),
file('MSC001-1.ax',cls_LOrder_Omeet__idempotent_0) ).
cnf(cls_List_OCons__in__lex_0,axiom,
( V_x = V_y
| c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,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))) ),
file('MSC001-1.ax',cls_List_OCons__in__lex_0) ).
cnf(cls_List_OCons__in__lex_1,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(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,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))) ),
file('MSC001-1.ax',cls_List_OCons__in__lex_1) ).
cnf(cls_List_OCons__in__lex_2,axiom,
( c_Nat_Osize(V_xs,tc_List_Olist(T_a)) = c_Nat_Osize(V_ys,tc_List_Olist(T_a))
| V_x = V_y
| ~ 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))) ),
file('MSC001-1.ax',cls_List_OCons__in__lex_2) ).
cnf(cls_List_OCons__in__lex_3,axiom,
( c_Nat_Osize(V_xs,tc_List_Olist(T_a)) = c_Nat_Osize(V_ys,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_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))) ),
file('MSC001-1.ax',cls_List_OCons__in__lex_3) ).
cnf(cls_List_OCons__in__lex_4,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_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_ys,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)) ),
file('MSC001-1.ax',cls_List_OCons__in__lex_4) ).
cnf(cls_List_OCons__in__lex_5,axiom,
( 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)))
| ~ 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))) ),
file('MSC001-1.ax',cls_List_OCons__in__lex_5) ).
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))),
file('MSC001-1.ax',cls_List_ONil2__notin__lex_0) ).
cnf(cls_List_ONil__eq__concat__conv_0,axiom,
( V_U = c_List_Olist_ONil
| c_List_Olist_ONil != c_List_Oconcat(V_xss,T_a)
| ~ c_in(V_U,c_List_Oset(V_xss,tc_List_Olist(T_a)),tc_List_Olist(T_a)) ),
file('MSC001-1.ax',cls_List_ONil__eq__concat__conv_0) ).
cnf(cls_List_ONil__eq__concat__conv_1,axiom,
( c_List_Olist_ONil = c_List_Oconcat(V_xss,T_a)
| 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)) ),
file('MSC001-1.ax',cls_List_ONil__eq__concat__conv_1) ).
cnf(cls_List_ONil__eq__concat__conv_2,axiom,
( c_List_Olist_ONil = c_List_Oconcat(V_xss,T_a)
| c_Main_ONil__eq__concat__conv__1(V_xss,T_a) != c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_ONil__eq__concat__conv_2) ).
cnf(cls_List_ONil__is__append__conv_0,axiom,
( V_xs = c_List_Olist_ONil
| c_List_Olist_ONil != c_append(V_xs,V_ys,T_a) ),
file('MSC001-1.ax',cls_List_ONil__is__append__conv_0) ).
cnf(cls_List_ONil__is__append__conv_1,axiom,
( V_ys = c_List_Olist_ONil
| c_List_Olist_ONil != c_append(V_xs,V_ys,T_a) ),
file('MSC001-1.ax',cls_List_ONil__is__append__conv_1) ).
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),
file('MSC001-1.ax',cls_List_ONil__is__append__conv_2) ).
cnf(cls_List_ONil__is__rev__conv_0,axiom,
( V_xs = c_List_Olist_ONil
| c_List_Olist_ONil != c_List_Orev(V_xs,T_a) ),
file('MSC001-1.ax',cls_List_ONil__is__rev__conv_0) ).
cnf(cls_List_ONil__is__rev__conv_1,axiom,
c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,T_a),
file('MSC001-1.ax',cls_List_ONil__is__rev__conv_1) ).
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))),
file('MSC001-1.ax',cls_List_ONil__notin__lex_0) ).
cnf(cls_List_Oappend1__eq__conv_0,axiom,
( V_xs = V_ys
| 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) ),
file('MSC001-1.ax',cls_List_Oappend1__eq__conv_0) ).
cnf(cls_List_Oappend1__eq__conv_1,axiom,
( V_x = V_y
| 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) ),
file('MSC001-1.ax',cls_List_Oappend1__eq__conv_1) ).
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),
file('MSC001-1.ax',cls_List_Oappend__assoc_0) ).
cnf(cls_List_Oappend__butlast__last__id_0,axiom,
( 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
| V_y = c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Oappend__butlast__last__id_0) ).
cnf(cls_List_Oappend__eq__append__conv_0,axiom,
( V_xs = V_ys
| c_append(V_xs,V_us,T_a) != c_append(V_ys,V_vs,T_a)
| c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_ys,tc_List_Olist(T_a)) ),
file('MSC001-1.ax',cls_List_Oappend__eq__append__conv_0) ).
cnf(cls_List_Oappend__eq__append__conv_1,axiom,
( V_us = V_vs
| c_append(V_xs,V_us,T_a) != c_append(V_ys,V_vs,T_a)
| c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_ys,tc_List_Olist(T_a)) ),
file('MSC001-1.ax',cls_List_Oappend__eq__append__conv_1) ).
cnf(cls_List_Oappend__eq__append__conv_2,axiom,
( V_xs = V_ys
| c_append(V_xs,V_us,T_a) != c_append(V_ys,V_vs,T_a)
| c_Nat_Osize(V_us,tc_List_Olist(T_a)) != c_Nat_Osize(V_vs,tc_List_Olist(T_a)) ),
file('MSC001-1.ax',cls_List_Oappend__eq__append__conv_2) ).
cnf(cls_List_Oappend__eq__append__conv_3,axiom,
( V_us = V_vs
| c_append(V_xs,V_us,T_a) != c_append(V_ys,V_vs,T_a)
| c_Nat_Osize(V_us,tc_List_Olist(T_a)) != c_Nat_Osize(V_vs,tc_List_Olist(T_a)) ),
file('MSC001-1.ax',cls_List_Oappend__eq__append__conv_3) ).
cnf(cls_List_Oappend__in__lists__conv_0,axiom,
( 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)) ),
file('MSC001-1.ax',cls_List_Oappend__in__lists__conv_0) ).
cnf(cls_List_Oappend__in__lists__conv_1,axiom,
( c_in(V_ys,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)) ),
file('MSC001-1.ax',cls_List_Oappend__in__lists__conv_1) ).
cnf(cls_List_Oappend__in__lists__conv_2,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))
| ~ c_in(V_ys,c_List_Olists(V_A,T_a),tc_List_Olist(T_a)) ),
file('MSC001-1.ax',cls_List_Oappend__in__lists__conv_2) ).
cnf(cls_List_Oappend__is__Nil__conv_0,axiom,
( V_xs = c_List_Olist_ONil
| c_append(V_xs,V_ys,T_a) != c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Oappend__is__Nil__conv_0) ).
cnf(cls_List_Oappend__is__Nil__conv_1,axiom,
( V_ys = c_List_Olist_ONil
| c_append(V_xs,V_ys,T_a) != c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Oappend__is__Nil__conv_1) ).
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,
file('MSC001-1.ax',cls_List_Oappend__is__Nil__conv_2) ).
cnf(cls_List_Oappend__same__eq_0,axiom,
( V_ys = V_zs
| c_append(V_ys,V_xs,T_a) != c_append(V_zs,V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Oappend__same__eq_0) ).
cnf(cls_List_Oappend__self__conv2_0,axiom,
( V_xs = c_List_Olist_ONil
| c_append(V_xs,V_ys,T_a) != V_ys ),
file('MSC001-1.ax',cls_List_Oappend__self__conv2_0) ).
cnf(cls_List_Oappend__self__conv2_1,axiom,
c_append(c_List_Olist_ONil,V_ys,T_a) = V_ys,
file('MSC001-1.ax',cls_List_Oappend__self__conv2_1) ).
cnf(cls_List_Oappend__self__conv_0,axiom,
( V_ys = c_List_Olist_ONil
| c_append(V_xs,V_ys,T_a) != V_xs ),
file('MSC001-1.ax',cls_List_Oappend__self__conv_0) ).
cnf(cls_List_Oappend__self__conv_1,axiom,
c_append(V_xs,c_List_Olist_ONil,T_a) = V_xs,
file('MSC001-1.ax',cls_List_Oappend__self__conv_1) ).
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,
file('MSC001-1.ax',cls_List_Oappend__take__drop__id_0) ).
cnf(cls_List_Obutlast_Osimps__1_0,axiom,
c_List_Obutlast(c_List_Olist_ONil,T_a__1) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Obutlast_Osimps__1_0) ).
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,
file('MSC001-1.ax',cls_List_Obutlast_Osimps__2_0) ).
cnf(cls_List_Obutlast_Osimps__2_1,axiom,
( 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)
| V_xs = c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Obutlast_Osimps__2_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,
file('MSC001-1.ax',cls_List_Obutlast__snoc_0) ).
cnf(cls_List_Ochar_Oinject_0,axiom,
( V_nibble1 = V_nibble1_H
| c_List_Ochar_OChar(V_nibble1,V_nibble2) != c_List_Ochar_OChar(V_nibble1_H,V_nibble2_H) ),
file('MSC001-1.ax',cls_List_Ochar_Oinject_0) ).
cnf(cls_List_Ochar_Oinject_1,axiom,
( V_nibble2 = V_nibble2_H
| c_List_Ochar_OChar(V_nibble1,V_nibble2) != c_List_Ochar_OChar(V_nibble1_H,V_nibble2_H) ),
file('MSC001-1.ax',cls_List_Ochar_Oinject_1) ).
cnf(cls_List_Ochar_Osize_0,axiom,
c_Nat_Osize(c_List_Ochar_OChar(V_nibble1,V_nibble2),tc_List_Ochar) = c_0,
file('MSC001-1.ax',cls_List_Ochar_Osize_0) ).
cnf(cls_List_Oconcat_Osimps__1_0,axiom,
c_List_Oconcat(c_List_Olist_ONil,T_a__1) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Oconcat_Osimps__1_0) ).
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),
file('MSC001-1.ax',cls_List_Oconcat_Osimps__2_0) ).
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),
file('MSC001-1.ax',cls_List_Oconcat__append_0) ).
cnf(cls_List_Oconcat__eq__Nil__conv_0,axiom,
( V_U = c_List_Olist_ONil
| c_List_Oconcat(V_xss,T_a) != c_List_Olist_ONil
| ~ c_in(V_U,c_List_Oset(V_xss,tc_List_Olist(T_a)),tc_List_Olist(T_a)) ),
file('MSC001-1.ax',cls_List_Oconcat__eq__Nil__conv_0) ).
cnf(cls_List_Oconcat__eq__Nil__conv_1,axiom,
( c_List_Oconcat(V_xss,T_a) = c_List_Olist_ONil
| 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)) ),
file('MSC001-1.ax',cls_List_Oconcat__eq__Nil__conv_1) ).
cnf(cls_List_Oconcat__eq__Nil__conv_2,axiom,
( c_List_Oconcat(V_xss,T_a) = c_List_Olist_ONil
| c_Main_Oconcat__eq__Nil__conv__1(V_xss,T_a) != c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Oconcat__eq__Nil__conv_2) ).
cnf(cls_List_Odistinct1__rotate_0,axiom,
( c_List_Odistinct(V_xs,T_a)
| ~ c_List_Odistinct(c_List_Orotate1(V_xs,T_a),T_a) ),
file('MSC001-1.ax',cls_List_Odistinct1__rotate_0) ).
cnf(cls_List_Odistinct1__rotate_1,axiom,
( c_List_Odistinct(c_List_Orotate1(V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Odistinct1__rotate_1) ).
cnf(cls_List_Odistinct_Osimps__1_0,axiom,
c_List_Odistinct(c_List_Olist_ONil,T_a__1),
file('MSC001-1.ax',cls_List_Odistinct_Osimps__1_0) ).
cnf(cls_List_Odistinct_Osimps__2_0,axiom,
( ~ c_in(V_x,c_List_Oset(V_xs,T_a__1),T_a__1)
| ~ c_List_Odistinct(c_List_Olist_OCons(V_x,V_xs,T_a__1),T_a__1) ),
file('MSC001-1.ax',cls_List_Odistinct_Osimps__2_0) ).
cnf(cls_List_Odistinct_Osimps__2_1,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) ),
file('MSC001-1.ax',cls_List_Odistinct_Osimps__2_1) ).
cnf(cls_List_Odistinct_Osimps__2_2,axiom,
( c_in(V_x,c_List_Oset(V_xs,T_a__1),T_a__1)
| 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) ),
file('MSC001-1.ax',cls_List_Odistinct_Osimps__2_2) ).
cnf(cls_List_Odistinct__append_0,axiom,
( c_List_Odistinct(V_xs,T_a)
| ~ c_List_Odistinct(c_append(V_xs,V_ys,T_a),T_a) ),
file('MSC001-1.ax',cls_List_Odistinct__append_0) ).
cnf(cls_List_Odistinct__append_1,axiom,
( c_List_Odistinct(V_ys,T_a)
| ~ c_List_Odistinct(c_append(V_xs,V_ys,T_a),T_a) ),
file('MSC001-1.ax',cls_List_Odistinct__append_1) ).
cnf(cls_List_Odistinct__append_2,axiom,
( 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) ),
file('MSC001-1.ax',cls_List_Odistinct__append_2) ).
cnf(cls_List_Odistinct__append_3,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
| ~ c_List_Odistinct(V_xs,T_a)
| ~ c_List_Odistinct(V_ys,T_a) ),
file('MSC001-1.ax',cls_List_Odistinct__append_3) ).
cnf(cls_List_Odistinct__drop_0,axiom,
( c_List_Odistinct(c_List_Odrop(V_i,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Odistinct__drop_0) ).
cnf(cls_List_Odistinct__remove1_0,axiom,
( c_List_Odistinct(c_List_Oremove1(V_x,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Odistinct__remove1_0) ).
cnf(cls_List_Odistinct__rev_0,axiom,
( c_List_Odistinct(V_xs,T_a)
| ~ c_List_Odistinct(c_List_Orev(V_xs,T_a),T_a) ),
file('MSC001-1.ax',cls_List_Odistinct__rev_0) ).
cnf(cls_List_Odistinct__rev_1,axiom,
( c_List_Odistinct(c_List_Orev(V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Odistinct__rev_1) ).
cnf(cls_List_Odistinct__rotate_0,axiom,
( c_List_Odistinct(V_xs,T_a)
| ~ c_List_Odistinct(c_List_Orotate(V_n,V_xs,T_a),T_a) ),
file('MSC001-1.ax',cls_List_Odistinct__rotate_0) ).
cnf(cls_List_Odistinct__rotate_1,axiom,
( c_List_Odistinct(c_List_Orotate(V_n,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Odistinct__rotate_1) ).
cnf(cls_List_Odistinct__sublistI_0,axiom,
( c_List_Odistinct(c_List_Osublist(V_xs,V_I,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Odistinct__sublistI_0) ).
cnf(cls_List_Odistinct__take_0,axiom,
( c_List_Odistinct(c_List_Otake(V_i,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Odistinct__take_0) ).
cnf(cls_List_Odistinct__upt_0,axiom,
c_List_Odistinct(c_List_Oupt(V_i,V_j),tc_nat),
file('MSC001-1.ax',cls_List_Odistinct__upt_0) ).
cnf(cls_List_Odrop_Odrop__Nil_0,axiom,
c_List_Odrop(V_n,c_List_Olist_ONil,T_a__1) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Odrop_Odrop__Nil_0) ).
cnf(cls_List_Odrop__0_0,axiom,
c_List_Odrop(c_0,V_y,T_a) = V_y,
file('MSC001-1.ax',cls_List_Odrop__0_0) ).
cnf(cls_List_Odrop__Cons__number__of_0,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_Olist_OCons(V_x,V_xs,T_a)
| c_Numeral_Onumber__of(V_v,tc_nat) != c_0 ),
file('MSC001-1.ax',cls_List_Odrop__Cons__number__of_0) ).
cnf(cls_List_Odrop__Cons__number__of_1,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_Odrop(c_minus(c_Numeral_Onumber__of(V_v,tc_nat),c_1,tc_nat),V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Odrop__Cons__number__of_1) ).
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),
file('MSC001-1.ax',cls_List_Odrop__Suc__Cons_0) ).
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),
file('MSC001-1.ax',cls_List_Odrop__append_0) ).
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),
file('MSC001-1.ax',cls_List_Odrop__drop_0) ).
cnf(cls_List_Odrop__eq__Nil_0,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 ),
file('MSC001-1.ax',cls_List_Odrop__eq__Nil_0) ).
cnf(cls_List_Odrop__eq__Nil_1,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) ),
file('MSC001-1.ax',cls_List_Odrop__eq__Nil_1) ).
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),
file('MSC001-1.ax',cls_List_Odrop__replicate_0) ).
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),
file('MSC001-1.ax',cls_List_Odrop__upt_0) ).
cnf(cls_List_Ohd_Osimps_0,axiom,
c_List_Ohd(c_List_Olist_OCons(V_y,V_xs,T_a),T_a) = V_y,
file('MSC001-1.ax',cls_List_Ohd_Osimps_0) ).
cnf(cls_List_Ohd__Cons__tl_0,axiom,
( c_List_Olist_OCons(c_List_Ohd(V_y,T_a),c_List_Otl(V_y,T_a),T_a) = V_y
| V_y = c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Ohd__Cons__tl_0) ).
cnf(cls_List_Ohd__append2_0,axiom,
( c_List_Ohd(c_append(V_xs,V_ys,T_a),T_a) = c_List_Ohd(V_xs,T_a)
| V_xs = c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Ohd__append2_0) ).
cnf(cls_List_Ohd__in__set_0,axiom,
( V_xs = c_List_Olist_ONil
| c_in(c_List_Ohd(V_xs,T_a),c_List_Oset(V_xs,T_a),T_a) ),
file('MSC001-1.ax',cls_List_Ohd__in__set_0) ).
cnf(cls_List_Ohd__replicate_0,axiom,
( c_List_Ohd(c_List_Oreplicate(V_n,V_y,T_a),T_a) = V_y
| V_n = c_0 ),
file('MSC001-1.ax',cls_List_Ohd__replicate_0) ).
cnf(cls_List_Ohd__upt_0,axiom,
( c_List_Ohd(c_List_Oupt(V_y,V_j),tc_nat) = V_y
| ~ c_less(V_y,V_j,tc_nat) ),
file('MSC001-1.ax',cls_List_Ohd__upt_0) ).
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),
file('MSC001-1.ax',cls_List_Oitrev_0) ).
cnf(cls_List_Oitrev_Osimps__1_0,axiom,
c_List_Oitrev(c_List_Olist_ONil,V_y,T_a__1) = V_y,
file('MSC001-1.ax',cls_List_Oitrev_Osimps__1_0) ).
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),
file('MSC001-1.ax',cls_List_Oitrev_Osimps__2_0) ).
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,
file('MSC001-1.ax',cls_List_Olast_Osimps_0) ).
cnf(cls_List_Olast_Osimps_1,axiom,
( c_List_Olast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olast(V_xs,T_a)
| V_xs = c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Olast_Osimps_1) ).
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),
file('MSC001-1.ax',cls_List_Olast__appendL_0) ).
cnf(cls_List_Olast__appendR_0,axiom,
( c_List_Olast(c_append(V_xs,V_ys,T_a),T_a) = c_List_Olast(V_ys,T_a)
| V_ys = c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Olast__appendR_0) ).
cnf(cls_List_Olast__drop_0,axiom,
( c_List_Olast(c_List_Odrop(V_n,V_xs,T_a),T_a) = c_List_Olast(V_xs,T_a)
| ~ c_less(V_n,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ),
file('MSC001-1.ax',cls_List_Olast__drop_0) ).
cnf(cls_List_Olast__in__set_0,axiom,
( V_as = c_List_Olist_ONil
| c_in(c_List_Olast(V_as,T_a),c_List_Oset(V_as,T_a),T_a) ),
file('MSC001-1.ax',cls_List_Olast__in__set_0) ).
cnf(cls_List_Olast__replicate_0,axiom,
( c_List_Olast(c_List_Oreplicate(V_n,V_y,T_a),T_a) = V_y
| V_n = c_0 ),
file('MSC001-1.ax',cls_List_Olast__replicate_0) ).
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,
file('MSC001-1.ax',cls_List_Olast__snoc_0) ).
cnf(cls_List_Olast__upt_0,axiom,
( c_List_Olast(c_List_Oupt(V_i,V_j),tc_nat) = c_minus(V_j,c_1,tc_nat)
| ~ c_less(V_i,V_j,tc_nat) ),
file('MSC001-1.ax',cls_List_Olast__upt_0) ).
cnf(cls_List_Olength__0__conv_0,axiom,
( V_xs = c_List_Olist_ONil
| c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_0 ),
file('MSC001-1.ax',cls_List_Olength__0__conv_0) ).
cnf(cls_List_Olength__0__conv_1,axiom,
c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(T_a)) = c_0,
file('MSC001-1.ax',cls_List_Olength__0__conv_1) ).
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),
file('MSC001-1.ax',cls_List_Olength__append_0) ).
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),
file('MSC001-1.ax',cls_List_Olength__butlast_0) ).
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),
file('MSC001-1.ax',cls_List_Olength__drop_0) ).
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),
file('MSC001-1.ax',cls_List_Olength__greater__0__conv_0) ).
cnf(cls_List_Olength__greater__0__conv_1,axiom,
( V_xs = c_List_Olist_ONil
| c_less(c_0,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ),
file('MSC001-1.ax',cls_List_Olength__greater__0__conv_1) ).
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)),
file('MSC001-1.ax',cls_List_Olength__list__update_0) ).
cnf(cls_List_Olength__remdups__eq_0,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)) ),
file('MSC001-1.ax',cls_List_Olength__remdups__eq_0) ).
cnf(cls_List_Olength__remdups__eq_1,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 ),
file('MSC001-1.ax',cls_List_Olength__remdups__eq_1) ).
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,
file('MSC001-1.ax',cls_List_Olength__replicate_0) ).
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)),
file('MSC001-1.ax',cls_List_Olength__rev_0) ).
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)),
file('MSC001-1.ax',cls_List_Olength__rotate1_0) ).
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)),
file('MSC001-1.ax',cls_List_Olength__rotate_0) ).
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),
file('MSC001-1.ax',cls_List_Olength__take_0) ).
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),
file('MSC001-1.ax',cls_List_Olength__tl_0) ).
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),
file('MSC001-1.ax',cls_List_Olength__upt_0) ).
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),
file('MSC001-1.ax',cls_List_Olength__zip_0) ).
cnf(cls_List_Olexn_Osimps__1_0,axiom,
c_List_Olexn(V_r,c_0,T_a__1) = c_emptyset,
file('MSC001-1.ax',cls_List_Olexn_Osimps__1_0) ).
cnf(cls_List_Olexord__Nil__left_0,axiom,
( 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)
| ~ 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))) ),
file('MSC001-1.ax',cls_List_Olexord__Nil__left_0) ).
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))),
file('MSC001-1.ax',cls_List_Olexord__Nil__left_1) ).
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))),
file('MSC001-1.ax',cls_List_Olexord__Nil__right_0) ).
cnf(cls_List_Olexord__cons__cons_0,axiom,
( V_a = V_b
| 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))) ),
file('MSC001-1.ax',cls_List_Olexord__cons__cons_0) ).
cnf(cls_List_Olexord__cons__cons_1,axiom,
( 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)))
| 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))) ),
file('MSC001-1.ax',cls_List_Olexord__cons__cons_1) ).
cnf(cls_List_Olexord__cons__cons_2,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)) ),
file('MSC001-1.ax',cls_List_Olexord__cons__cons_2) ).
cnf(cls_List_Olexord__cons__cons_3,axiom,
( 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)))
| ~ 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))) ),
file('MSC001-1.ax',cls_List_Olexord__cons__cons_3) ).
cnf(cls_List_Olist_Odistinct__1_0,axiom,
c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
file('MSC001-1.ax',cls_List_Olist_Odistinct__1_0) ).
cnf(cls_List_Olist_Odistinct__2_0,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Olist_Odistinct__2_0) ).
cnf(cls_List_Olist_Oinject_0,axiom,
( V_a = V_a_H
| c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
file('MSC001-1.ax',cls_List_Olist_Oinject_0) ).
cnf(cls_List_Olist_Oinject_1,axiom,
( V_list = V_list_H
| c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
file('MSC001-1.ax',cls_List_Olist_Oinject_1) ).
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),
file('MSC001-1.ax',cls_List_Olist_Osize__2_0) ).
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,
file('MSC001-1.ax',cls_List_Olist__inter_Osimps__1_0) ).
cnf(cls_List_Olist__inter_Osimps__2_0,axiom,
( 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)
| ~ c_in(V_a,c_List_Oset(V_bs,T_a__1),T_a__1) ),
file('MSC001-1.ax',cls_List_Olist__inter_Osimps__2_0) ).
cnf(cls_List_Olist__inter_Osimps__2_1,axiom,
( 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)
| c_in(V_a,c_List_Oset(V_bs,T_a__1),T_a__1) ),
file('MSC001-1.ax',cls_List_Olist__inter_Osimps__2_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,
file('MSC001-1.ax',cls_List_Olist__update_Osimps__1_0) ).
cnf(cls_List_Olist__update__beyond_0,axiom,
( c_List_Olist__update(V_y,V_i,V_x,T_a) = V_y
| ~ c_lessequals(c_Nat_Osize(V_y,tc_List_Olist(T_a)),V_i,tc_nat) ),
file('MSC001-1.ax',cls_List_Olist__update__beyond_0) ).
cnf(cls_List_Olist__update__id_0,axiom,
( c_List_Olist__update(V_y,V_i,c_List_Onth(V_y,V_i,T_a),T_a) = V_y
| ~ c_less(V_i,c_Nat_Osize(V_y,tc_List_Olist(T_a)),tc_nat) ),
file('MSC001-1.ax',cls_List_Olist__update__id_0) ).
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),
file('MSC001-1.ax',cls_List_Olist__update__length_0) ).
cnf(cls_List_Olist__update__overwrite_0,axiom,
( 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)
| ~ c_less(V_i,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ),
file('MSC001-1.ax',cls_List_Olist__update__overwrite_0) ).
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)),
file('MSC001-1.ax',cls_List_Olistrel__Nil_0) ).
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)),
file('MSC001-1.ax',cls_List_Olists__Int__eq_0) ).
cnf(cls_List_Olists__UNIV_0,axiom,
c_List_Olists(c_UNIV,T_a) = c_UNIV,
file('MSC001-1.ax',cls_List_Olists__UNIV_0) ).
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)),
file('MSC001-1.ax',cls_List_Olistset_Osimps__1_0) ).
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),
file('MSC001-1.ax',cls_List_Olistset_Osimps__2_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__10_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__11_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__12_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__13_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__14_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__15_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__16_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__1_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__2_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__3_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__4_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__5_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__6_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__7_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__8_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Ocases__9_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__10_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__11_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__12_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__13_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__14_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__15_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__16_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__1_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__2_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__3_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__4_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__5_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__6_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__7_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__8_0) ).
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,
file('MSC001-1.ax',cls_List_Onibble_Orecs__9_0) ).
cnf(cls_List_Onibble_Osize__10_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__10_0) ).
cnf(cls_List_Onibble_Osize__11_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__11_0) ).
cnf(cls_List_Onibble_Osize__12_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__12_0) ).
cnf(cls_List_Onibble_Osize__13_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__13_0) ).
cnf(cls_List_Onibble_Osize__14_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__14_0) ).
cnf(cls_List_Onibble_Osize__15_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__15_0) ).
cnf(cls_List_Onibble_Osize__16_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__16_0) ).
cnf(cls_List_Onibble_Osize__1_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__1_0) ).
cnf(cls_List_Onibble_Osize__2_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__2_0) ).
cnf(cls_List_Onibble_Osize__3_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__3_0) ).
cnf(cls_List_Onibble_Osize__4_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__4_0) ).
cnf(cls_List_Onibble_Osize__5_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__5_0) ).
cnf(cls_List_Onibble_Osize__6_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__6_0) ).
cnf(cls_List_Onibble_Osize__7_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__7_0) ).
cnf(cls_List_Onibble_Osize__8_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__8_0) ).
cnf(cls_List_Onibble_Osize__9_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) = c_0,
file('MSC001-1.ax',cls_List_Onibble_Osize__9_0) ).
cnf(cls_List_Onot__Cons__self_0,axiom,
V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
file('MSC001-1.ax',cls_List_Onot__Cons__self_0) ).
cnf(cls_List_Onotin__set__remove1_0,axiom,
( c_in(V_x,c_List_Oset(V_xs,T_a),T_a)
| ~ c_in(V_x,c_List_Oset(c_List_Oremove1(V_y,V_xs,T_a),T_a),T_a) ),
file('MSC001-1.ax',cls_List_Onotin__set__remove1_0) ).
cnf(cls_List_Onotin__set__sublistI_0,axiom,
( c_in(V_x,c_List_Oset(V_xs,T_a),T_a)
| ~ c_in(V_x,c_List_Oset(c_List_Osublist(V_xs,V_I,T_a),T_a),T_a) ),
file('MSC001-1.ax',cls_List_Onotin__set__sublistI_0) ).
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,
file('MSC001-1.ax',cls_List_Onth__Cons__0_0) ).
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),
file('MSC001-1.ax',cls_List_Onth__Cons__Suc_0) ).
cnf(cls_List_Onth__Cons__number__of_0,axiom,
( 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
| c_Numeral_Onumber__of(V_v,tc_nat) != c_0 ),
file('MSC001-1.ax',cls_List_Onth__Cons__number__of_0) ).
cnf(cls_List_Onth__Cons__number__of_1,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) = c_List_Onth(V_xs,c_minus(c_Numeral_Onumber__of(V_v,tc_nat),c_1,tc_nat),T_a) ),
file('MSC001-1.ax',cls_List_Onth__Cons__number__of_1) ).
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,
file('MSC001-1.ax',cls_List_Onth__append__length_0) ).
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),
file('MSC001-1.ax',cls_List_Onth__append__length__plus_0) ).
cnf(cls_List_Onth__drop_0,axiom,
( 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)
| ~ c_lessequals(c_plus(V_n,V_i,tc_nat),c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ),
file('MSC001-1.ax',cls_List_Onth__drop_0) ).
cnf(cls_List_Onth__list__update__eq_0,axiom,
( c_List_Onth(c_List_Olist__update(V_xs,V_i,V_y,T_a),V_i,T_a) = V_y
| ~ c_less(V_i,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ),
file('MSC001-1.ax',cls_List_Onth__list__update__eq_0) ).
cnf(cls_List_Onth__list__update__neq_0,axiom,
( 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)
| V_i = V_j ),
file('MSC001-1.ax',cls_List_Onth__list__update__neq_0) ).
cnf(cls_List_Onth__mem_0,axiom,
( c_in(c_List_Onth(V_xs,V_n,T_a),c_List_Oset(V_xs,T_a),T_a)
| ~ c_less(V_n,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ),
file('MSC001-1.ax',cls_List_Onth__mem_0) ).
cnf(cls_List_Onth__replicate_0,axiom,
( c_List_Onth(c_List_Oreplicate(V_n,V_y,T_a),V_i,T_a) = V_y
| ~ c_less(V_i,V_n,tc_nat) ),
file('MSC001-1.ax',cls_List_Onth__replicate_0) ).
cnf(cls_List_Onth__take_0,axiom,
( 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)
| ~ c_less(V_i,V_n,tc_nat) ),
file('MSC001-1.ax',cls_List_Onth__take_0) ).
cnf(cls_List_Onth__upt_0,axiom,
( c_List_Onth(c_List_Oupt(V_i,V_j),V_k,tc_nat) = c_plus(V_i,V_k,tc_nat)
| ~ c_less(c_plus(V_i,V_k,tc_nat),V_j,tc_nat) ),
file('MSC001-1.ax',cls_List_Onth__upt_0) ).
cnf(cls_List_Onth__zip_0,axiom,
( 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)
| ~ c_less(V_i,c_Nat_Osize(V_xs,tc_List_Olist(T_a)),tc_nat)
| ~ c_less(V_i,c_Nat_Osize(V_ys,tc_List_Olist(T_b)),tc_nat) ),
file('MSC001-1.ax',cls_List_Onth__zip_0) ).
cnf(cls_List_Onull_Osimps__1_0,axiom,
c_List_Onull(c_List_Olist_ONil,T_a__1),
file('MSC001-1.ax',cls_List_Onull_Osimps__1_0) ).
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),
file('MSC001-1.ax',cls_List_Onull_Osimps__2_0) ).
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),
file('MSC001-1.ax',cls_List_Oop_A_64_Oappend__Cons_0) ).
cnf(cls_List_Oop_Amem_Osimps__1_0,axiom,
~ c_List_Oop_Amem(V_x,c_List_Olist_ONil,T_a__1),
file('MSC001-1.ax',cls_List_Oop_Amem_Osimps__1_0) ).
cnf(cls_List_Oop_Amem_Osimps__2_0,axiom,
( V_y = V_x
| 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) ),
file('MSC001-1.ax',cls_List_Oop_Amem_Osimps__2_0) ).
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),
file('MSC001-1.ax',cls_List_Oop_Amem_Osimps__2_1) ).
cnf(cls_List_Oop_Amem_Osimps__2_2,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) ),
file('MSC001-1.ax',cls_List_Oop_Amem_Osimps__2_2) ).
cnf(cls_List_Oremdups_Osimps__2_0,axiom,
( 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)
| ~ c_in(V_x,c_List_Oset(V_xs,T_a__1),T_a__1) ),
file('MSC001-1.ax',cls_List_Oremdups_Osimps__2_0) ).
cnf(cls_List_Oremdups_Osimps__2_1,axiom,
( 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)
| c_in(V_x,c_List_Oset(V_xs,T_a__1),T_a__1) ),
file('MSC001-1.ax',cls_List_Oremdups_Osimps__2_1) ).
cnf(cls_List_Oremdups__eq__nil__iff_0,axiom,
( V_x = c_List_Olist_ONil
| c_List_Oremdups(V_x,T_a) != c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Oremdups__eq__nil__iff_0) ).
cnf(cls_List_Oremdups__eq__nil__iff_1,axiom,
c_List_Oremdups(c_List_Olist_ONil,T_a) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Oremdups__eq__nil__iff_1) ).
cnf(cls_List_Oremdups__eq__nil__right__iff_0,axiom,
( V_x = c_List_Olist_ONil
| c_List_Olist_ONil != c_List_Oremdups(V_x,T_a) ),
file('MSC001-1.ax',cls_List_Oremdups__eq__nil__right__iff_0) ).
cnf(cls_List_Oremdups__eq__nil__right__iff_1,axiom,
c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,T_a),
file('MSC001-1.ax',cls_List_Oremdups__eq__nil__right__iff_1) ).
cnf(cls_List_Oremove1_Osimps__1_0,axiom,
c_List_Oremove1(V_x,c_List_Olist_ONil,T_a__1) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Oremove1_Osimps__1_0) ).
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,
file('MSC001-1.ax',cls_List_Oremove1_Osimps__2_0) ).
cnf(cls_List_Oremove1_Osimps__2_1,axiom,
( 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)
| V_x = V_y ),
file('MSC001-1.ax',cls_List_Oremove1_Osimps__2_1) ).
cnf(cls_List_Oreplicate_Oreplicate__0_0,axiom,
c_List_Oreplicate(c_0,V_x,T_a__1) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Oreplicate_Oreplicate__0_0) ).
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),
file('MSC001-1.ax',cls_List_Oreplicate_Oreplicate__Suc_0) ).
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),
file('MSC001-1.ax',cls_List_Orev_Osimps__2_0) ).
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),
file('MSC001-1.ax',cls_List_Orev__append_0) ).
cnf(cls_List_Orev__eq__Cons__iff_0,axiom,
( 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)
| c_List_Orev(V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a) ),
file('MSC001-1.ax',cls_List_Orev__eq__Cons__iff_0) ).
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),
file('MSC001-1.ax',cls_List_Orev__eq__Cons__iff_1) ).
cnf(cls_List_Orev__is__Nil__conv_0,axiom,
( V_xs = c_List_Olist_ONil
| c_List_Orev(V_xs,T_a) != c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Orev__is__Nil__conv_0) ).
cnf(cls_List_Orev__is__Nil__conv_1,axiom,
c_List_Orev(c_List_Olist_ONil,T_a) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Orev__is__Nil__conv_1) ).
cnf(cls_List_Orev__is__rev__conv_0,axiom,
( V_xs = V_ys
| c_List_Orev(V_xs,T_a) != c_List_Orev(V_ys,T_a) ),
file('MSC001-1.ax',cls_List_Orev__is__rev__conv_0) ).
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),
file('MSC001-1.ax',cls_List_Orev__replicate_0) ).
cnf(cls_List_Orev__rev__ident_0,axiom,
c_List_Orev(c_List_Orev(V_y,T_a),T_a) = V_y,
file('MSC001-1.ax',cls_List_Orev__rev__ident_0) ).
cnf(cls_List_Orev__singleton__conv_0,axiom,
( V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a)
| c_List_Orev(V_xs,T_a) != c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a) ),
file('MSC001-1.ax',cls_List_Orev__singleton__conv_0) ).
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),
file('MSC001-1.ax',cls_List_Orev__singleton__conv_1) ).
cnf(cls_List_Orotate1__is__Nil__conv_0,axiom,
( V_xs = c_List_Olist_ONil
| c_List_Orotate1(V_xs,T_a) != c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Orotate1__is__Nil__conv_0) ).
cnf(cls_List_Orotate1__is__Nil__conv_1,axiom,
c_List_Orotate1(c_List_Olist_ONil,T_a) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Orotate1__is__Nil__conv_1) ).
cnf(cls_List_Orotate1__length01_0,axiom,
( c_List_Orotate1(V_y,T_a) = V_y
| ~ c_lessequals(c_Nat_Osize(V_y,tc_List_Olist(T_a)),c_1,tc_nat) ),
file('MSC001-1.ax',cls_List_Orotate1__length01_0) ).
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),
file('MSC001-1.ax',cls_List_Orotate__Suc_0) ).
cnf(cls_List_Orotate__id_0,axiom,
( c_List_Orotate(V_n,V_y,T_a) = V_y
| c_Divides_Oop_Amod(V_n,c_Nat_Osize(V_y,tc_List_Olist(T_a)),tc_nat) != c_0 ),
file('MSC001-1.ax',cls_List_Orotate__id_0) ).
cnf(cls_List_Orotate__is__Nil__conv_0,axiom,
( V_xs = c_List_Olist_ONil
| c_List_Orotate(V_n,V_xs,T_a) != c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Orotate__is__Nil__conv_0) ).
cnf(cls_List_Orotate__is__Nil__conv_1,axiom,
c_List_Orotate(V_n,c_List_Olist_ONil,T_a) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Orotate__is__Nil__conv_1) ).
cnf(cls_List_Orotate__length01_0,axiom,
( c_List_Orotate(V_n,V_y,T_a) = V_y
| ~ c_lessequals(c_Nat_Osize(V_y,tc_List_Olist(T_a)),c_1,tc_nat) ),
file('MSC001-1.ax',cls_List_Orotate__length01_0) ).
cnf(cls_List_Osame__append__eq_0,axiom,
( V_ys = V_zs
| c_append(V_xs,V_ys,T_a) != c_append(V_xs,V_zs,T_a) ),
file('MSC001-1.ax',cls_List_Osame__append__eq_0) ).
cnf(cls_List_Oself__append__conv2_0,axiom,
( V_xs = c_List_Olist_ONil
| V_ys != c_append(V_xs,V_ys,T_a) ),
file('MSC001-1.ax',cls_List_Oself__append__conv2_0) ).
cnf(cls_List_Oself__append__conv2_1,axiom,
V_ys = c_append(c_List_Olist_ONil,V_ys,T_a),
file('MSC001-1.ax',cls_List_Oself__append__conv2_1) ).
cnf(cls_List_Oself__append__conv_0,axiom,
( V_ys = c_List_Olist_ONil
| V_xs != c_append(V_xs,V_ys,T_a) ),
file('MSC001-1.ax',cls_List_Oself__append__conv_0) ).
cnf(cls_List_Oself__append__conv_1,axiom,
V_xs = c_append(V_xs,c_List_Olist_ONil,T_a),
file('MSC001-1.ax',cls_List_Oself__append__conv_1) ).
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),
file('MSC001-1.ax',cls_List_Oset_Osimps__2_0) ).
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),
file('MSC001-1.ax',cls_List_Oset__append_0) ).
cnf(cls_List_Oset__empty2_0,axiom,
( V_xs = c_List_Olist_ONil
| c_emptyset != c_List_Oset(V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Oset__empty2_0) ).
cnf(cls_List_Oset__empty2_1,axiom,
c_emptyset = c_List_Oset(c_List_Olist_ONil,T_a),
file('MSC001-1.ax',cls_List_Oset__empty2_1) ).
cnf(cls_List_Oset__empty_0,axiom,
( V_xs = c_List_Olist_ONil
| c_List_Oset(V_xs,T_a) != c_emptyset ),
file('MSC001-1.ax',cls_List_Oset__empty_0) ).
cnf(cls_List_Oset__empty_1,axiom,
c_List_Oset(c_List_Olist_ONil,T_a) = c_emptyset,
file('MSC001-1.ax',cls_List_Oset__empty_1) ).
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),
file('MSC001-1.ax',cls_List_Oset__remdups_0) ).
cnf(cls_List_Oset__remove1__eq_0,axiom,
( 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))
| ~ c_List_Odistinct(V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Oset__remove1__eq_0) ).
cnf(cls_List_Oset__replicate_0,axiom,
( c_List_Oset(c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_insert(V_x,c_emptyset,T_a)
| V_n = c_0 ),
file('MSC001-1.ax',cls_List_Oset__replicate_0) ).
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),
file('MSC001-1.ax',cls_List_Oset__rev_0) ).
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),
file('MSC001-1.ax',cls_List_Oset__rotate1_0) ).
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),
file('MSC001-1.ax',cls_List_Oset__rotate_0) ).
cnf(cls_List_Osingleton__rev__conv_0,axiom,
( V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a)
| c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a) != c_List_Orev(V_xs,T_a) ),
file('MSC001-1.ax',cls_List_Osingleton__rev__conv_0) ).
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),
file('MSC001-1.ax',cls_List_Osingleton__rev__conv_1) ).
cnf(cls_List_Osublist__empty_0,axiom,
c_List_Osublist(V_xs,c_emptyset,T_a) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Osublist__empty_0) ).
cnf(cls_List_Osublist__nil_0,axiom,
c_List_Osublist(c_List_Olist_ONil,V_A,T_a) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Osublist__nil_0) ).
cnf(cls_List_Osublist__singleton_0,axiom,
( 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)
| ~ c_in(c_0,V_A,tc_nat) ),
file('MSC001-1.ax',cls_List_Osublist__singleton_0) ).
cnf(cls_List_Osublist__singleton_1,axiom,
( c_List_Osublist(c_List_Olist_OCons(V_x,c_List_Olist_ONil,T_a),V_A,T_a) = c_List_Olist_ONil
| c_in(c_0,V_A,tc_nat) ),
file('MSC001-1.ax',cls_List_Osublist__singleton_1) ).
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),
file('MSC001-1.ax',cls_List_Osublist__upt__eq__take_0) ).
cnf(cls_List_Otake__Cons__number__of_0,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_ONil
| c_Numeral_Onumber__of(V_v,tc_nat) != c_0 ),
file('MSC001-1.ax',cls_List_Otake__Cons__number__of_0) ).
cnf(cls_List_Otake__Cons__number__of_1,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_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) ),
file('MSC001-1.ax',cls_List_Otake__Cons__number__of_1) ).
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),
file('MSC001-1.ax',cls_List_Otake__Suc__Cons_0) ).
cnf(cls_List_Otake__all_0,axiom,
( c_List_Otake(V_n,V_y,T_a) = V_y
| ~ c_lessequals(c_Nat_Osize(V_y,tc_List_Olist(T_a)),V_n,tc_nat) ),
file('MSC001-1.ax',cls_List_Otake__all_0) ).
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),
file('MSC001-1.ax',cls_List_Otake__append_0) ).
cnf(cls_List_Otake__eq__Nil_0,axiom,
( V_xs = c_List_Olist_ONil
| V_n = c_0
| c_List_Otake(V_n,V_xs,T_a) != c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Otake__eq__Nil_0) ).
cnf(cls_List_Otake__eq__Nil_1,axiom,
c_List_Otake(c_0,V_xs,T_a) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Otake__eq__Nil_1) ).
cnf(cls_List_Otake__eq__Nil_2,axiom,
c_List_Otake(V_n,c_List_Olist_ONil,T_a) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Otake__eq__Nil_2) ).
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),
file('MSC001-1.ax',cls_List_Otake__replicate_0) ).
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),
file('MSC001-1.ax',cls_List_Otake__take_0) ).
cnf(cls_List_Otake__upt_0,axiom,
( 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))
| ~ c_lessequals(c_plus(V_i,V_m,tc_nat),V_n,tc_nat) ),
file('MSC001-1.ax',cls_List_Otake__upt_0) ).
cnf(cls_List_Otl_Osimps__1_0,axiom,
c_List_Otl(c_List_Olist_ONil,T_a__1) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Otl_Osimps__1_0) ).
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,
file('MSC001-1.ax',cls_List_Otl_Osimps__2_0) ).
cnf(cls_List_Otl__append2_0,axiom,
( 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)
| V_xs = c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Otl__append2_0) ).
cnf(cls_List_Otl__replicate_0,axiom,
( 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)
| V_n = c_0 ),
file('MSC001-1.ax',cls_List_Otl__replicate_0) ).
cnf(cls_List_Oupt_Oupt__Suc_0,axiom,
( 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)
| ~ c_lessequals(V_i,V_j,tc_nat) ),
file('MSC001-1.ax',cls_List_Oupt_Oupt__Suc_0) ).
cnf(cls_List_Oupt_Oupt__Suc_1,axiom,
( c_List_Oupt(V_i,c_Suc(V_j)) = c_List_Olist_ONil
| c_lessequals(V_i,V_j,tc_nat) ),
file('MSC001-1.ax',cls_List_Oupt_Oupt__Suc_1) ).
cnf(cls_List_Oupt__eq__Nil__conv_0,axiom,
( V_j = c_0
| c_lessequals(V_j,V_i,tc_nat)
| c_List_Oupt(V_i,V_j) != c_List_Olist_ONil ),
file('MSC001-1.ax',cls_List_Oupt__eq__Nil__conv_0) ).
cnf(cls_List_Oupt__eq__Nil__conv_1,axiom,
c_List_Oupt(V_i,c_0) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Oupt__eq__Nil__conv_1) ).
cnf(cls_List_Oupt__eq__Nil__conv_2,axiom,
( c_List_Oupt(V_i,V_j) = c_List_Olist_ONil
| ~ c_lessequals(V_j,V_i,tc_nat) ),
file('MSC001-1.ax',cls_List_Oupt__eq__Nil__conv_2) ).
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,
file('MSC001-1.ax',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
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,
file('MSC001-1.ax',cls_List_Ozip_Osimps__1_0) ).
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)),
file('MSC001-1.ax',cls_List_Ozip__Cons__Cons_0) ).
cnf(cls_List_Ozip__Nil_0,axiom,
c_List_Ozip(c_List_Olist_ONil,V_ys,T_a,T_b) = c_List_Olist_ONil,
file('MSC001-1.ax',cls_List_Ozip__Nil_0) ).
cnf(cls_List_Ozip__append_0,axiom,
( 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))
| c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_us,tc_List_Olist(T_b))
| c_Nat_Osize(V_ys,tc_List_Olist(T_a)) != c_Nat_Osize(V_vs,tc_List_Olist(T_b)) ),
file('MSC001-1.ax',cls_List_Ozip__append_0) ).
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)),
file('MSC001-1.ax',cls_List_Ozip__replicate_0) ).
cnf(cls_Map_Omap__of__zip__is__None_0,axiom,
( c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_ys,tc_List_Olist(T_b))
| 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_in(V_x,c_List_Oset(V_xs,T_a),T_a) ),
file('MSC001-1.ax',cls_Map_Omap__of__zip__is__None_0) ).
cnf(cls_Map_Omap__of__zip__is__None_1,axiom,
( 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_in(V_x,c_List_Oset(V_xs,T_a),T_a)
| c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize(V_ys,tc_List_Olist(T_b)) ),
file('MSC001-1.ax',cls_Map_Omap__of__zip__is__None_1) ).
cnf(cls_NatArith_Oadd__diff__assoc2_0,axiom,
( 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)
| ~ c_lessequals(V_k,V_j,tc_nat) ),
file('MSC001-1.ax',cls_NatArith_Oadd__diff__assoc2_0) ).
cnf(cls_NatArith_Oadd__diff__assoc_0,axiom,
( 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)
| ~ c_lessequals(V_k,V_j,tc_nat) ),
file('MSC001-1.ax',cls_NatArith_Oadd__diff__assoc_0) ).
cnf(cls_NatArith_Odiff__Suc__diff__eq1_0,axiom,
( 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)
| ~ c_lessequals(V_k,V_j,tc_nat) ),
file('MSC001-1.ax',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
cnf(cls_NatArith_Odiff__Suc__diff__eq2_0,axiom,
( 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)
| ~ c_lessequals(V_k,V_j,tc_nat) ),
file('MSC001-1.ax',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
cnf(cls_NatArith_Odiff__diff__cancel_0,axiom,
( c_minus(V_n,c_minus(V_n,V_y,tc_nat),tc_nat) = V_y
| ~ c_lessequals(V_y,V_n,tc_nat) ),
file('MSC001-1.ax',cls_NatArith_Odiff__diff__cancel_0) ).
cnf(cls_NatArith_Odiff__diff__right_0,axiom,
( 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)
| ~ c_lessequals(V_k,V_j,tc_nat) ),
file('MSC001-1.ax',cls_NatArith_Odiff__diff__right_0) ).
cnf(cls_NatArith_Odiff__less_0,axiom,
( c_less(c_minus(V_m,V_n,tc_nat),V_m,tc_nat)
| ~ c_less(c_0,V_n,tc_nat)
| ~ c_less(c_0,V_m,tc_nat) ),
file('MSC001-1.ax',cls_NatArith_Odiff__less_0) ).
cnf(cls_NatArith_Oof__nat_Oof__nat__Suc_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a__1) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
cnf(cls_NatArith_Oof__nat__0__eq__iff_0,axiom,
( c_0 = V_n
| c_0 != c_NatArith_Oof__nat(V_n,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__0__eq__iff_0) ).
cnf(cls_NatArith_Oof__nat__0__eq__iff_1,axiom,
( c_0 = c_NatArith_Oof__nat(c_0,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__0__eq__iff_1) ).
cnf(cls_NatArith_Oof__nat__0__le__iff_0,axiom,
( c_lessequals(c_0,c_NatArith_Oof__nat(V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__0__le__iff_0) ).
cnf(cls_NatArith_Oof__nat__0__less__iff_0,axiom,
( c_less(c_0,V_n,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__0__less__iff_0) ).
cnf(cls_NatArith_Oof__nat__0__less__iff_1,axiom,
( c_less(c_0,c_NatArith_Oof__nat(V_n,T_a),T_a)
| ~ c_less(c_0,V_n,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__0__less__iff_1) ).
cnf(cls_NatArith_Oof__nat__1_0,axiom,
( c_NatArith_Oof__nat(c_1,T_a) = c_1
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__1_0) ).
cnf(cls_NatArith_Oof__nat__add_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__add_0) ).
cnf(cls_NatArith_Oof__nat__diff_0,axiom,
( 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)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__diff_0) ).
cnf(cls_NatArith_Oof__nat__eq__0__iff_0,axiom,
( V_m = c_0
| c_NatArith_Oof__nat(V_m,T_a) != c_0
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__eq__0__iff_0) ).
cnf(cls_NatArith_Oof__nat__eq__0__iff_1,axiom,
( c_NatArith_Oof__nat(c_0,T_a) = c_0
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__eq__0__iff_1) ).
cnf(cls_NatArith_Oof__nat__eq__iff_0,axiom,
( V_m = V_n
| c_NatArith_Oof__nat(V_m,T_a) != c_NatArith_Oof__nat(V_n,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__eq__iff_0) ).
cnf(cls_NatArith_Oof__nat__le__0__iff_0,axiom,
( V_m = c_0
| ~ c_lessequals(c_NatArith_Oof__nat(V_m,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__le__0__iff_0) ).
cnf(cls_NatArith_Oof__nat__le__0__iff_1,axiom,
( c_lessequals(c_NatArith_Oof__nat(c_0,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__le__0__iff_1) ).
cnf(cls_NatArith_Oof__nat__le__iff_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__le__iff_0) ).
cnf(cls_NatArith_Oof__nat__le__iff_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__le__iff_1) ).
cnf(cls_NatArith_Oof__nat__less__0__iff_0,axiom,
( ~ c_less(c_NatArith_Oof__nat(V_m,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__less__0__iff_0) ).
cnf(cls_NatArith_Oof__nat__less__iff_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__less__iff_0) ).
cnf(cls_NatArith_Oof__nat__less__iff_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__less__iff_1) ).
cnf(cls_NatArith_Oof__nat__mult_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
file('MSC001-1.ax',cls_NatArith_Oof__nat__mult_0) ).
cnf(cls_NatBin_OSuc__nat__number__of_0,axiom,
( c_Suc(c_Numeral_Onumber__of(V_v,tc_nat)) = c_1
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_OSuc__nat__number__of_0) ).
cnf(cls_NatBin_OSuc__nat__number__of_1,axiom,
( c_Suc(c_Numeral_Onumber__of(V_v,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(V_v),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_OSuc__nat__number__of_1) ).
cnf(cls_NatBin_Oadd__nat__number__of_0,axiom,
( 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)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oadd__nat__number__of_0) ).
cnf(cls_NatBin_Oadd__nat__number__of_1,axiom,
( 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)
| 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) ),
file('MSC001-1.ax',cls_NatBin_Oadd__nat__number__of_1) ).
cnf(cls_NatBin_Oadd__nat__number__of_2,axiom,
( 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)
| 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) ),
file('MSC001-1.ax',cls_NatBin_Oadd__nat__number__of_2) ).
cnf(cls_NatBin_Odiv__nat__number__of_0,axiom,
( c_div(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_0
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Odiv__nat__number__of_0) ).
cnf(cls_NatBin_Odiv__nat__number__of_1,axiom,
( 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))
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Odiv__nat__number__of_1) ).
cnf(cls_NatBin_Odvd__eq__mod__eq__0__number__of_0,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) ),
file('MSC001-1.ax',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).
cnf(cls_NatBin_Odvd__eq__mod__eq__0__number__of_1,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 ),
file('MSC001-1.ax',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).
cnf(cls_NatBin_Oeq__0__number__of_0,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| 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) ),
file('MSC001-1.ax',cls_NatBin_Oeq__0__number__of_0) ).
cnf(cls_NatBin_Oeq__0__number__of_1,axiom,
( c_0 = c_Numeral_Onumber__of(V_v,tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oeq__0__number__of_1) ).
cnf(cls_NatBin_Oeq__0__number__of_2,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) ),
file('MSC001-1.ax',cls_NatBin_Oeq__0__number__of_2) ).
cnf(cls_NatBin_Oeq__nat__number__of_0,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(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_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_0) ).
cnf(cls_NatBin_Oeq__nat__number__of_1,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(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_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_1) ).
cnf(cls_NatBin_Oeq__nat__number__of_10,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat)
| ~ 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) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_10) ).
cnf(cls_NatBin_Oeq__nat__number__of_11,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat)
| ~ 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_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_11) ).
cnf(cls_NatBin_Oeq__nat__number__of_12,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat)
| ~ c_IntDef_Oneg(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_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_12) ).
cnf(cls_NatBin_Oeq__nat__number__of_2,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_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) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_2) ).
cnf(cls_NatBin_Oeq__nat__number__of_3,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat)
| 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_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) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_3) ).
cnf(cls_NatBin_Oeq__nat__number__of_4,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat)
| 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_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_4) ).
cnf(cls_NatBin_Oeq__nat__number__of_5,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat)
| c_IntDef_Oneg(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_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_5) ).
cnf(cls_NatBin_Oeq__nat__number__of_6,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat)
| ~ c_IntDef_Oneg(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) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_6) ).
cnf(cls_NatBin_Oeq__nat__number__of_7,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat)
| c_IntDef_Oneg(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_Oiszero(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_7) ).
cnf(cls_NatBin_Oeq__nat__number__of_8,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,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(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_8) ).
cnf(cls_NatBin_Oeq__nat__number__of_9,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_Oiszero(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oeq__nat__number__of_9) ).
cnf(cls_NatBin_Oeq__number__of__0_0,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| 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 ),
file('MSC001-1.ax',cls_NatBin_Oeq__number__of__0_0) ).
cnf(cls_NatBin_Oeq__number__of__0_1,axiom,
( c_Numeral_Onumber__of(V_v,tc_nat) = c_0
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oeq__number__of__0_1) ).
cnf(cls_NatBin_Oeq__number__of__0_2,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) ),
file('MSC001-1.ax',cls_NatBin_Oeq__number__of__0_2) ).
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),
file('MSC001-1.ax',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
cnf(cls_NatBin_Oint__nat__number__of_0,axiom,
( c_IntDef_Oint(c_Numeral_Onumber__of(V_v,tc_nat)) = c_0
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oint__nat__number__of_0) ).
cnf(cls_NatBin_Oint__nat__number__of_1,axiom,
( c_IntDef_Oint(c_Numeral_Onumber__of(V_v,tc_nat)) = c_Numeral_Onumber__of(V_v,tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oint__nat__number__of_1) ).
cnf(cls_NatBin_Oless__0__number__of_0,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) ),
file('MSC001-1.ax',cls_NatBin_Oless__0__number__of_0) ).
cnf(cls_NatBin_Oless__0__number__of_1,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) ),
file('MSC001-1.ax',cls_NatBin_Oless__0__number__of_1) ).
cnf(cls_NatBin_Oless__nat__number__of_0,axiom,
( 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)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oless__nat__number__of_0) ).
cnf(cls_NatBin_Oless__nat__number__of_1,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) ),
file('MSC001-1.ax',cls_NatBin_Oless__nat__number__of_1) ).
cnf(cls_NatBin_Oless__nat__number__of_2,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) ),
file('MSC001-1.ax',cls_NatBin_Oless__nat__number__of_2) ).
cnf(cls_NatBin_Oless__nat__number__of_3,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(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) ),
file('MSC001-1.ax',cls_NatBin_Oless__nat__number__of_3) ).
cnf(cls_NatBin_Oless__nat__number__of_4,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(c_Numeral_Obin__minus(V_v_H),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) ),
file('MSC001-1.ax',cls_NatBin_Oless__nat__number__of_4) ).
cnf(cls_NatBin_Omod__nat__number__of_0,axiom,
( 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
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Omod__nat__number__of_0) ).
cnf(cls_NatBin_Omod__nat__number__of_1,axiom,
( 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)
| 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) ),
file('MSC001-1.ax',cls_NatBin_Omod__nat__number__of_1) ).
cnf(cls_NatBin_Omod__nat__number__of_2,axiom,
( 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))
| 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) ),
file('MSC001-1.ax',cls_NatBin_Omod__nat__number__of_2) ).
cnf(cls_NatBin_Omult__nat__number__of_0,axiom,
( c_times(c_Numeral_Onumber__of(V_v,tc_nat),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_0
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Omult__nat__number__of_0) ).
cnf(cls_NatBin_Omult__nat__number__of_1,axiom,
( 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)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Omult__nat__number__of_1) ).
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),
file('MSC001-1.ax',cls_NatBin_Onat__number__of_0) ).
cnf(cls_NatBin_Onat__numeral__0__eq__0_0,axiom,
c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
file('MSC001-1.ax',cls_NatBin_Onat__numeral__0__eq__0_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,
file('MSC001-1.ax',cls_NatBin_Onat__numeral__1__eq__1_0) ).
cnf(cls_NatBin_Oof__nat__number__of__eq_0,axiom,
( c_NatArith_Oof__nat(c_Numeral_Onumber__of(V_v,tc_nat),T_a) = c_0
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_NatBin_Oof__nat__number__of__eq_0) ).
cnf(cls_NatBin_Oof__nat__number__of__eq_1,axiom,
( c_NatArith_Oof__nat(c_Numeral_Onumber__of(V_v,tc_nat),T_a) = c_Numeral_Onumber__of(V_v,T_a)
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_NatBin_Oof__nat__number__of__eq_1) ).
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)),
file('MSC001-1.ax',cls_NatBin_Oone__div__nat__number__of_0) ).
cnf(cls_NatBin_Oone__mod__nat__number__of_0,axiom,
( c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(V_v_H,tc_nat),tc_nat) = c_Suc(c_0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oone__mod__nat__number__of_0) ).
cnf(cls_NatBin_Oone__mod__nat__number__of_1,axiom,
( 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))
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Oone__mod__nat__number__of_1) ).
cnf(cls_NatBin_Oone__power2_0,axiom,
( 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
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_NatBin_Oone__power2_0) ).
cnf(cls_NatBin_Opower2__eq__square__number__of_0,axiom,
( 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)
| ~ class_Power_Orecpower(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatBin_Opower2__eq__square__number__of_0) ).
cnf(cls_NatBin_Opower__minus__even_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_NatBin_Opower__minus__even_0) ).
cnf(cls_NatBin_Opower__nat__number__of__number__of_0,axiom,
( 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)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Opower__nat__number__of__number__of_0) ).
cnf(cls_NatBin_Opower__nat__number__of__number__of_1,axiom,
( 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))
| c_IntDef_Oneg(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_NatBin_Opower__nat__number__of__number__of_1) ).
cnf(cls_NatBin_Ozero__power2_0,axiom,
( 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
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_NatBin_Ozero__power2_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),
file('MSC001-1.ax',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).
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),
file('MSC001-1.ax',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).
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)),
file('MSC001-1.ax',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).
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)),
file('MSC001-1.ax',cls_NatSimprocs_Oadd__2__eq__Suc_H_0) ).
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,
file('MSC001-1.ax',cls_NatSimprocs_Oadd__self__div__2_0) ).
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)),
file('MSC001-1.ax',cls_NatSimprocs_Odiv2__Suc__Suc_0) ).
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),
file('MSC001-1.ax',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).
cnf(cls_NatSimprocs_Odivide__eq__eq__number__of_0,axiom,
( c_Numeral_Onumber__of(V_w,T_b) = c_0
| 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)
| ~ class_Ring__and__Field_Ofield(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__eq__eq__number__of_0) ).
cnf(cls_NatSimprocs_Odivide__eq__eq__number__of_1,axiom,
( c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b) = c_0
| c_Numeral_Onumber__of(V_w,T_b) != c_0
| ~ class_Ring__and__Field_Ofield(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__eq__eq__number__of_1) ).
cnf(cls_NatSimprocs_Odivide__eq__eq__number__of_3,axiom,
( 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
| c_Numeral_Onumber__of(V_w,T_b) = c_0
| ~ class_Ring__and__Field_Ofield(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__eq__eq__number__of_3) ).
cnf(cls_NatSimprocs_Odivide__eq__eq__number__of_4,axiom,
( 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
| ~ class_Ring__and__Field_Ofield(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__eq__eq__number__of_4) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_0,axiom,
( c_lessequals(c_Numeral_Onumber__of(V_w,T_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__0__iff__number__of_0) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_1,axiom,
( c_lessequals(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(c_0,V_b,T_b)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__0__iff__number__of_1) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_2,axiom,
( c_lessequals(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_lessequals(V_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__0__iff__number__of_2) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_3,axiom,
( c_lessequals(c_0,V_b,T_b)
| c_lessequals(V_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__0__iff__number__of_3) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_4,axiom,
( 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(V_b,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__0__iff__number__of_4) ).
cnf(cls_NatSimprocs_Odivide__le__0__iff__number__of_5,axiom,
( c_lessequals(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| ~ c_lessequals(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_lessequals(c_0,V_b,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__0__iff__number__of_5) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_0,axiom,
( 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)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__eq__number__of_0) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_1,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__eq__number__of_1) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_2,axiom,
( c_lessequals(c_0,V_a,T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__eq__number__of_2) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_3,axiom,
( c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ c_lessequals(c_0,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__eq__number__of_3) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_4,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__eq__number__of_4) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_5,axiom,
( 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)
| ~ c_lessequals(c_0,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__eq__number__of_5) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_6,axiom,
( 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)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__eq__number__of_6) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_7,axiom,
( c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_lessequals(c_0,V_a,T_b)
| ~ c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__eq__number__of_7) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_8,axiom,
( c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),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(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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__eq__number__of_8) ).
cnf(cls_NatSimprocs_Odivide__le__eq__number__of_9,axiom,
( c_lessequals(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),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_0,V_a,T_b)
| ~ c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__le__eq__number__of_9) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_0,axiom,
( c_less(c_Numeral_Onumber__of(V_w,T_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__0__iff__number__of_0) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_1,axiom,
( c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_0,V_b,T_b)
| ~ c_less(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__0__iff__number__of_1) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_2,axiom,
( c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(V_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__0__iff__number__of_2) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_3,axiom,
( c_less(c_0,V_b,T_b)
| c_less(V_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__0__iff__number__of_3) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_4,axiom,
( 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(V_b,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__0__iff__number__of_4) ).
cnf(cls_NatSimprocs_Odivide__less__0__iff__number__of_5,axiom,
( c_less(c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),c_0,T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_less(c_0,V_b,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__0__iff__number__of_5) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_0,axiom,
( c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),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(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__eq__number__of_0) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_1,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__eq__number__of_1) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_2,axiom,
( c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(c_0,V_a,T_b)
| ~ c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__eq__number__of_2) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_3,axiom,
( c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ c_less(c_0,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__eq__number__of_3) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_4,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__eq__number__of_4) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_5,axiom,
( 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)
| ~ c_less(c_0,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__eq__number__of_5) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_6,axiom,
( 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(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__eq__number__of_6) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_7,axiom,
( c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),V_a,T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_less(c_0,V_a,T_b)
| ~ c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__eq__number__of_7) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_8,axiom,
( c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),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_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__eq__number__of_8) ).
cnf(cls_NatSimprocs_Odivide__less__eq__number__of_9,axiom,
( c_less(c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),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,V_a,T_b)
| ~ c_less(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__less__eq__number__of_9) ).
cnf(cls_NatSimprocs_Odivide__minus1_0,axiom,
( c_divide(V_x,c_Numeral_Onumber__of(c_Numeral_OMin,T_a),T_a) = c_uminus(V_x,T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_NatSimprocs_Odivide__minus1_0) ).
cnf(cls_NatSimprocs_Oeq__divide__eq__number__of_0,axiom,
( 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
| c_Numeral_Onumber__of(V_w,T_b) = c_0
| ~ class_Ring__and__Field_Ofield(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oeq__divide__eq__number__of_0) ).
cnf(cls_NatSimprocs_Oeq__divide__eq__number__of_2,axiom,
( c_0 = c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_Numeral_Onumber__of(V_w,T_b) != c_0
| ~ class_Ring__and__Field_Ofield(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oeq__divide__eq__number__of_2) ).
cnf(cls_NatSimprocs_Oeq__divide__eq__number__of_3,axiom,
( c_Numeral_Onumber__of(V_w,T_b) = c_0
| 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)
| ~ class_Ring__and__Field_Ofield(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oeq__divide__eq__number__of_3) ).
cnf(cls_NatSimprocs_Oeq__divide__eq__number__of_4,axiom,
( 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)
| ~ class_Ring__and__Field_Ofield(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oeq__divide__eq__number__of_4) ).
cnf(cls_NatSimprocs_Oequation__minus__iff__1_0,axiom,
( V_b = c_uminus(c_1,T_b)
| c_uminus(V_b,T_b) != c_1
| ~ class_OrderedGroup_Oab__group__add(T_b)
| ~ class_HOL_Oone(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oequation__minus__iff__1_0) ).
cnf(cls_NatSimprocs_Oequation__minus__iff__1_1,axiom,
( c_uminus(c_uminus(c_1,T_b),T_b) = c_1
| ~ class_OrderedGroup_Oab__group__add(T_b)
| ~ class_HOL_Oone(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oequation__minus__iff__1_1) ).
cnf(cls_NatSimprocs_Oequation__minus__iff__number__of_0,axiom,
( V_b = c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b)
| c_Numeral_Onumber__of(V_v,T_b) != c_uminus(V_b,T_b)
| ~ class_OrderedGroup_Oab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).
cnf(cls_NatSimprocs_Oequation__minus__iff__number__of_1,axiom,
( c_Numeral_Onumber__of(V_v,T_b) = c_uminus(c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),T_b)
| ~ class_OrderedGroup_Oab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oequation__minus__iff__number__of_1) ).
cnf(cls_NatSimprocs_Ohalf__gt__zero_0,axiom,
( 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)
| ~ c_less(c_0,V_r,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_NatSimprocs_Ohalf__gt__zero_0) ).
cnf(cls_NatSimprocs_Oinverse__eq__divide__number__of_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ofield(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oinverse__eq__divide__number__of_0) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_0,axiom,
( 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)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__divide__eq__number__of_0) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_1,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__divide__eq__number__of_1) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_2,axiom,
( c_lessequals(V_a,c_0,T_b)
| c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__divide__eq__number__of_2) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_3,axiom,
( c_lessequals(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(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ c_lessequals(V_a,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__divide__eq__number__of_3) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_4,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__divide__eq__number__of_4) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_5,axiom,
( 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)
| ~ c_lessequals(V_a,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__divide__eq__number__of_5) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_6,axiom,
( 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)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__divide__eq__number__of_6) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_7,axiom,
( c_lessequals(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_lessequals(c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| ~ c_lessequals(V_a,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__divide__eq__number__of_7) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_8,axiom,
( 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)
| ~ c_lessequals(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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__divide__eq__number__of_8) ).
cnf(cls_NatSimprocs_Ole__divide__eq__number__of_9,axiom,
( 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)
| ~ c_lessequals(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_lessequals(V_a,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__divide__eq__number__of_9) ).
cnf(cls_NatSimprocs_Ole__minus__iff__1_0,axiom,
( c_lessequals(V_b,c_uminus(c_1,T_b),T_b)
| ~ c_lessequals(c_1,c_uminus(V_b,T_b),T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_HOL_Oone(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__minus__iff__1_0) ).
cnf(cls_NatSimprocs_Ole__minus__iff__1_1,axiom,
( c_lessequals(c_1,c_uminus(V_b,T_b),T_b)
| ~ c_lessequals(V_b,c_uminus(c_1,T_b),T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_HOL_Oone(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__minus__iff__1_1) ).
cnf(cls_NatSimprocs_Ole__minus__iff__number__of_0,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).
cnf(cls_NatSimprocs_Ole__minus__iff__number__of_1,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).
cnf(cls_NatSimprocs_Oleft__diff__distrib__number__of_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oring(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).
cnf(cls_NatSimprocs_Oleft__distrib__number__of_0,axiom,
( 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)
| ~ class_Ring__and__Field_Osemiring(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oleft__distrib__number__of_0) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_0,axiom,
( 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(V_a,c_divide(V_b,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__divide__eq__number__of_0) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_1,axiom,
( c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__divide__eq__number__of_1) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_2,axiom,
( c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__divide__eq__number__of_2) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_3,axiom,
( c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_w,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(V_a,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__divide__eq__number__of_3) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_4,axiom,
( c_less(c_0,c_Numeral_Onumber__of(V_w,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_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__divide__eq__number__of_4) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_5,axiom,
( c_less(c_0,c_Numeral_Onumber__of(V_w,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(V_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_less(V_a,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__divide__eq__number__of_5) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_6,axiom,
( c_less(V_a,c_divide(V_b,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(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__divide__eq__number__of_6) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_7,axiom,
( 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_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),V_b,T_b)
| ~ c_less(V_a,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__divide__eq__number__of_7) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_8,axiom,
( c_less(V_a,c_divide(V_b,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(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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__divide__eq__number__of_8) ).
cnf(cls_NatSimprocs_Oless__divide__eq__number__of_9,axiom,
( c_less(V_a,c_divide(V_b,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_b,c_times(V_a,c_Numeral_Onumber__of(V_w,T_b),T_b),T_b)
| ~ c_less(V_a,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__divide__eq__number__of_9) ).
cnf(cls_NatSimprocs_Oless__minus__iff__1_0,axiom,
( c_less(V_b,c_uminus(c_1,T_b),T_b)
| ~ c_less(c_1,c_uminus(V_b,T_b),T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_HOL_Oone(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__minus__iff__1_0) ).
cnf(cls_NatSimprocs_Oless__minus__iff__1_1,axiom,
( c_less(c_1,c_uminus(V_b,T_b),T_b)
| ~ c_less(V_b,c_uminus(c_1,T_b),T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_HOL_Oone(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__minus__iff__1_1) ).
cnf(cls_NatSimprocs_Oless__minus__iff__number__of_0,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).
cnf(cls_NatSimprocs_Oless__minus__iff__number__of_1,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).
cnf(cls_NatSimprocs_Ominus1__divide_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_NatSimprocs_Ominus1__divide_0) ).
cnf(cls_NatSimprocs_Ominus__equation__iff__number__of_0,axiom,
( c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b) = V_a
| c_uminus(V_a,T_b) != c_Numeral_Onumber__of(V_v,T_b)
| ~ class_OrderedGroup_Oab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ominus__equation__iff__number__of_0) ).
cnf(cls_NatSimprocs_Ominus__equation__iff__number__of_1,axiom,
( c_uminus(c_uminus(c_Numeral_Onumber__of(V_v,T_b),T_b),T_b) = c_Numeral_Onumber__of(V_v,T_b)
| ~ class_OrderedGroup_Oab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ominus__equation__iff__number__of_1) ).
cnf(cls_NatSimprocs_Ominus__le__iff__1_0,axiom,
( c_lessequals(c_uminus(c_1,T_b),V_a,T_b)
| ~ c_lessequals(c_uminus(V_a,T_b),c_1,T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_HOL_Oone(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ominus__le__iff__1_0) ).
cnf(cls_NatSimprocs_Ominus__le__iff__1_1,axiom,
( c_lessequals(c_uminus(V_a,T_b),c_1,T_b)
| ~ c_lessequals(c_uminus(c_1,T_b),V_a,T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_HOL_Oone(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ominus__le__iff__1_1) ).
cnf(cls_NatSimprocs_Ominus__le__iff__number__of_0,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).
cnf(cls_NatSimprocs_Ominus__le__iff__number__of_1,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).
cnf(cls_NatSimprocs_Ominus__less__iff__1_0,axiom,
( c_less(c_uminus(c_1,T_b),V_a,T_b)
| ~ c_less(c_uminus(V_a,T_b),c_1,T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_HOL_Oone(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ominus__less__iff__1_0) ).
cnf(cls_NatSimprocs_Ominus__less__iff__1_1,axiom,
( c_less(c_uminus(V_a,T_b),c_1,T_b)
| ~ c_less(c_uminus(c_1,T_b),V_a,T_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_HOL_Oone(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ominus__less__iff__1_1) ).
cnf(cls_NatSimprocs_Ominus__less__iff__number__of_0,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).
cnf(cls_NatSimprocs_Ominus__less__iff__number__of_1,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).
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),
file('MSC001-1.ax',cls_NatSimprocs_Omod2__Suc__Suc_0) ).
cnf(cls_NatSimprocs_Omod2__gr__0_0,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) ),
file('MSC001-1.ax',cls_NatSimprocs_Omod2__gr__0_0) ).
cnf(cls_NatSimprocs_Omod2__gr__0_1,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 ),
file('MSC001-1.ax',cls_NatSimprocs_Omod2__gr__0_1) ).
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),
file('MSC001-1.ax',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_0,axiom,
( 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)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_1,axiom,
( c_lessequals(V_b,V_a,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_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_2,axiom,
( 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_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_3,axiom,
( 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_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| ~ c_lessequals(V_b,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_4,axiom,
( 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_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| ~ c_lessequals(V_a,V_b,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).
cnf(cls_NatSimprocs_Omult__le__cancel__left__number__of_5,axiom,
( 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)
| ~ c_lessequals(V_b,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_0,axiom,
( 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)
| ~ c_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_1,axiom,
( c_lessequals(V_b,V_a,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_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_2,axiom,
( 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_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| c_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_3,axiom,
( 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_less(c_0,c_Numeral_Onumber__of(V_v,T_b),T_b)
| ~ c_lessequals(V_b,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_4,axiom,
( 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_less(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| ~ c_lessequals(V_a,V_b,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).
cnf(cls_NatSimprocs_Omult__le__cancel__right__number__of_5,axiom,
( 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)
| ~ c_lessequals(V_b,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_0,axiom,
( c_less(V_a,V_b,T_b)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_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)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_1,axiom,
( c_less(V_b,V_a,T_b)
| ~ c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,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)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_2,axiom,
( c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_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)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_3,axiom,
( c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_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_less(V_b,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_4,axiom,
( c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,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_less(V_a,V_b,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).
cnf(cls_NatSimprocs_Omult__less__cancel__left__number__of_5,axiom,
( 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_less(V_a,V_b,T_b)
| ~ c_less(V_b,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_0,axiom,
( c_less(V_a,V_b,T_b)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_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)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_1,axiom,
( c_less(V_b,V_a,T_b)
| ~ c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,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)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_2,axiom,
( c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,T_b)
| c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_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)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_3,axiom,
( c_lessequals(c_0,c_Numeral_Onumber__of(V_v,T_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_less(V_b,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_4,axiom,
( c_lessequals(c_Numeral_Onumber__of(V_v,T_b),c_0,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_less(V_a,V_b,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).
cnf(cls_NatSimprocs_Omult__less__cancel__right__number__of_5,axiom,
( 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_less(V_a,V_b,T_b)
| ~ c_less(V_b,V_a,T_b)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).
cnf(cls_NatSimprocs_Oright__diff__distrib__number__of_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oring(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).
cnf(cls_NatSimprocs_Oright__distrib__number__of_0,axiom,
( 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)
| ~ class_Ring__and__Field_Osemiring(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Oright__distrib__number__of_0) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_0,axiom,
( c_lessequals(c_Numeral_Onumber__of(V_w,T_b),c_0,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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__le__divide__iff__number__of_0) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_1,axiom,
( c_lessequals(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_lessequals(V_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__le__divide__iff__number__of_1) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_2,axiom,
( c_lessequals(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_lessequals(c_0,V_b,T_b)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__le__divide__iff__number__of_2) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_3,axiom,
( c_lessequals(c_0,V_b,T_b)
| c_lessequals(V_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__le__divide__iff__number__of_3) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_4,axiom,
( 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_0,V_b,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__le__divide__iff__number__of_4) ).
cnf(cls_NatSimprocs_Ozero__le__divide__iff__number__of_5,axiom,
( c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| ~ c_lessequals(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_lessequals(V_b,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__le__divide__iff__number__of_5) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_0,axiom,
( c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__less__divide__iff__number__of_0) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_1,axiom,
( c_less(c_0,c_Numeral_Onumber__of(V_w,T_b),T_b)
| c_less(V_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__less__divide__iff__number__of_1) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_2,axiom,
( c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| c_less(c_0,V_b,T_b)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__less__divide__iff__number__of_2) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_3,axiom,
( c_less(c_0,V_b,T_b)
| c_less(V_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)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__less__divide__iff__number__of_3) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_4,axiom,
( 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_0,V_b,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__less__divide__iff__number__of_4) ).
cnf(cls_NatSimprocs_Ozero__less__divide__iff__number__of_5,axiom,
( c_less(c_0,c_divide(c_Numeral_Onumber__of(V_w,T_b),V_b,T_b),T_b)
| ~ c_less(c_Numeral_Onumber__of(V_w,T_b),c_0,T_b)
| ~ c_less(V_b,c_0,T_b)
| ~ class_Ring__and__Field_Oordered__field(T_b)
| ~ class_Ring__and__Field_Odivision__by__zero(T_b)
| ~ class_Numeral_Onumber(T_b) ),
file('MSC001-1.ax',cls_NatSimprocs_Ozero__less__divide__iff__number__of_5) ).
cnf(cls_Nat_OOne__nat__def_0,axiom,
c_1 = c_Suc(c_0),
file('MSC001-1.ax',cls_Nat_OOne__nat__def_0) ).
cnf(cls_Nat_OSuc__Suc__eq_0,axiom,
( V_m = V_n
| c_Suc(V_m) != c_Suc(V_n) ),
file('MSC001-1.ax',cls_Nat_OSuc__Suc__eq_0) ).
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),
file('MSC001-1.ax',cls_Nat_OSuc__diff__diff_0) ).
cnf(cls_Nat_OSuc__le__mono_0,axiom,
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ),
file('MSC001-1.ax',cls_Nat_OSuc__le__mono_0) ).
cnf(cls_Nat_OSuc__le__mono_1,axiom,
( c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat)
| ~ c_lessequals(V_n,V_m,tc_nat) ),
file('MSC001-1.ax',cls_Nat_OSuc__le__mono_1) ).
cnf(cls_Nat_OSuc__less__eq_0,axiom,
( c_less(V_m,V_n,tc_nat)
| ~ c_less(c_Suc(V_m),c_Suc(V_n),tc_nat) ),
file('MSC001-1.ax',cls_Nat_OSuc__less__eq_0) ).
cnf(cls_Nat_OSuc__less__eq_1,axiom,
( c_less(c_Suc(V_m),c_Suc(V_n),tc_nat)
| ~ c_less(V_m,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_OSuc__less__eq_1) ).
cnf(cls_Nat_OSuc__not__Zero_0,axiom,
c_Suc(V_m) != c_0,
file('MSC001-1.ax',cls_Nat_OSuc__not__Zero_0) ).
cnf(cls_Nat_OSuc__pred_0,axiom,
( c_Suc(c_minus(V_y,c_Suc(c_0),tc_nat)) = V_y
| ~ c_less(c_0,V_y,tc_nat) ),
file('MSC001-1.ax',cls_Nat_OSuc__pred_0) ).
cnf(cls_Nat_OZero__not__Suc_0,axiom,
c_0 != c_Suc(V_m),
file('MSC001-1.ax',cls_Nat_OZero__not__Suc_0) ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
c_plus(V_y,c_0,tc_nat) = V_y,
file('MSC001-1.ax',cls_Nat_Oadd__0__right_0) ).
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)),
file('MSC001-1.ax',cls_Nat_Oadd__Suc__right_0) ).
cnf(cls_Nat_Oadd__gr__0_0,axiom,
( c_less(c_0,V_m,tc_nat)
| c_less(c_0,V_n,tc_nat)
| ~ c_less(c_0,c_plus(V_m,V_n,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Nat_Oadd__gr__0_0) ).
cnf(cls_Nat_Oadd__gr__0_1,axiom,
( c_less(c_0,c_plus(V_m,V_n,tc_nat),tc_nat)
| ~ c_less(c_0,V_m,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Oadd__gr__0_1) ).
cnf(cls_Nat_Oadd__gr__0_2,axiom,
( c_less(c_0,c_plus(V_m,V_n,tc_nat),tc_nat)
| ~ c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Oadd__gr__0_2) ).
cnf(cls_Nat_Oadd__is__0_0,axiom,
( V_m = c_0
| c_plus(V_m,V_n,tc_nat) != c_0 ),
file('MSC001-1.ax',cls_Nat_Oadd__is__0_0) ).
cnf(cls_Nat_Oadd__is__0_1,axiom,
( V_n = c_0
| c_plus(V_m,V_n,tc_nat) != c_0 ),
file('MSC001-1.ax',cls_Nat_Oadd__is__0_1) ).
cnf(cls_Nat_Oadd__is__0_2,axiom,
c_plus(c_0,c_0,tc_nat) = c_0,
file('MSC001-1.ax',cls_Nat_Oadd__is__0_2) ).
cnf(cls_Nat_Odiff__0__eq__0_0,axiom,
c_minus(c_0,V_n,tc_nat) = c_0,
file('MSC001-1.ax',cls_Nat_Odiff__0__eq__0_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),
file('MSC001-1.ax',cls_Nat_Odiff__Suc__Suc_0) ).
cnf(cls_Nat_Odiff__Suc__less_0,axiom,
( c_less(c_minus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat)
| ~ c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Odiff__Suc__less_0) ).
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),
file('MSC001-1.ax',cls_Nat_Odiff__diff__left_0) ).
cnf(cls_Nat_Odiff__is__0__eq_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| c_minus(V_m,V_n,tc_nat) != c_0 ),
file('MSC001-1.ax',cls_Nat_Odiff__is__0__eq_0) ).
cnf(cls_Nat_Odiff__is__0__eq_H_0,axiom,
( c_minus(V_m,V_n,tc_nat) = c_0
| ~ c_lessequals(V_m,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Odiff__is__0__eq_H_0) ).
cnf(cls_Nat_Odiff__le__self_0,axiom,
c_lessequals(c_minus(V_m,V_n,tc_nat),V_m,tc_nat),
file('MSC001-1.ax',cls_Nat_Odiff__le__self_0) ).
cnf(cls_Nat_Odiff__self__eq__0_0,axiom,
c_minus(V_m,V_m,tc_nat) = c_0,
file('MSC001-1.ax',cls_Nat_Odiff__self__eq__0_0) ).
cnf(cls_Nat_Ole__0__eq_0,axiom,
( V_i = c_0
| ~ c_lessequals(V_i,c_0,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Ole__0__eq_0) ).
cnf(cls_Nat_Ole__0__eq_1,axiom,
c_lessequals(c_0,c_0,tc_nat),
file('MSC001-1.ax',cls_Nat_Ole__0__eq_1) ).
cnf(cls_Nat_Ole__add__diff__inverse2_0,axiom,
( c_plus(c_minus(V_y,V_n,tc_nat),V_n,tc_nat) = V_y
| ~ c_lessequals(V_n,V_y,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Ole__add__diff__inverse2_0) ).
cnf(cls_Nat_Ole__add__diff__inverse_0,axiom,
( c_plus(V_n,c_minus(V_y,V_n,tc_nat),tc_nat) = V_y
| ~ c_lessequals(V_n,V_y,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Ole__add__diff__inverse_0) ).
cnf(cls_Nat_Oless__Suc0_0,axiom,
( V_n = c_0
| ~ c_less(V_n,c_Suc(c_0),tc_nat) ),
file('MSC001-1.ax',cls_Nat_Oless__Suc0_0) ).
cnf(cls_Nat_Oless__Suc0_1,axiom,
c_less(c_0,c_Suc(c_0),tc_nat),
file('MSC001-1.ax',cls_Nat_Oless__Suc0_1) ).
cnf(cls_Nat_Oless__one_0,axiom,
( V_n = c_0
| ~ c_less(V_n,c_1,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Oless__one_0) ).
cnf(cls_Nat_Oless__one_1,axiom,
c_less(c_0,c_1,tc_nat),
file('MSC001-1.ax',cls_Nat_Oless__one_1) ).
cnf(cls_Nat_Omax__0L_0,axiom,
c_Orderings_Omax(c_0,V_y,tc_nat) = V_y,
file('MSC001-1.ax',cls_Nat_Omax__0L_0) ).
cnf(cls_Nat_Omax__0R_0,axiom,
c_Orderings_Omax(V_y,c_0,tc_nat) = V_y,
file('MSC001-1.ax',cls_Nat_Omax__0R_0) ).
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)),
file('MSC001-1.ax',cls_Nat_Omax__Suc__Suc_0) ).
cnf(cls_Nat_Omin__0L_0,axiom,
c_Orderings_Omin(c_0,V_n,tc_nat) = c_0,
file('MSC001-1.ax',cls_Nat_Omin__0L_0) ).
cnf(cls_Nat_Omin__0R_0,axiom,
c_Orderings_Omin(V_n,c_0,tc_nat) = c_0,
file('MSC001-1.ax',cls_Nat_Omin__0R_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)),
file('MSC001-1.ax',cls_Nat_Omin__Suc__Suc_0) ).
cnf(cls_Nat_Omult__0__right_0,axiom,
c_times(V_m,c_0,tc_nat) = c_0,
file('MSC001-1.ax',cls_Nat_Omult__0__right_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),
file('MSC001-1.ax',cls_Nat_Omult__Suc__right_0) ).
cnf(cls_Nat_Omult__cancel1_0,axiom,
( V_k = c_0
| V_m = V_n
| c_times(V_k,V_m,tc_nat) != c_times(V_k,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Omult__cancel1_0) ).
cnf(cls_Nat_Omult__cancel1_1,axiom,
c_times(c_0,V_m,tc_nat) = c_times(c_0,V_n,tc_nat),
file('MSC001-1.ax',cls_Nat_Omult__cancel1_1) ).
cnf(cls_Nat_Omult__cancel2_0,axiom,
( V_k = c_0
| V_m = V_n
| c_times(V_m,V_k,tc_nat) != c_times(V_n,V_k,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Omult__cancel2_0) ).
cnf(cls_Nat_Omult__cancel2_1,axiom,
c_times(V_m,c_0,tc_nat) = c_times(V_n,c_0,tc_nat),
file('MSC001-1.ax',cls_Nat_Omult__cancel2_1) ).
cnf(cls_Nat_Omult__eq__1__iff_0,axiom,
( V_m = c_1
| c_times(V_m,V_n,tc_nat) != c_Suc(c_0) ),
file('MSC001-1.ax',cls_Nat_Omult__eq__1__iff_0) ).
cnf(cls_Nat_Omult__eq__1__iff_1,axiom,
( V_n = c_1
| c_times(V_m,V_n,tc_nat) != c_Suc(c_0) ),
file('MSC001-1.ax',cls_Nat_Omult__eq__1__iff_1) ).
cnf(cls_Nat_Omult__eq__1__iff_2,axiom,
c_times(c_1,c_1,tc_nat) = c_Suc(c_0),
file('MSC001-1.ax',cls_Nat_Omult__eq__1__iff_2) ).
cnf(cls_Nat_Omult__is__0_0,axiom,
( V_m = c_0
| V_n = c_0
| c_times(V_m,V_n,tc_nat) != c_0 ),
file('MSC001-1.ax',cls_Nat_Omult__is__0_0) ).
cnf(cls_Nat_Omult__le__cancel1_0,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)
| ~ c_less(c_0,V_k,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Omult__le__cancel1_0) ).
cnf(cls_Nat_Omult__le__cancel1_1,axiom,
( c_lessequals(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) ),
file('MSC001-1.ax',cls_Nat_Omult__le__cancel1_1) ).
cnf(cls_Nat_Omult__le__cancel1_2,axiom,
( 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) ),
file('MSC001-1.ax',cls_Nat_Omult__le__cancel1_2) ).
cnf(cls_Nat_Omult__le__cancel2_0,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)
| ~ c_less(c_0,V_k,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Omult__le__cancel2_0) ).
cnf(cls_Nat_Omult__le__cancel2_1,axiom,
( c_lessequals(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) ),
file('MSC001-1.ax',cls_Nat_Omult__le__cancel2_1) ).
cnf(cls_Nat_Omult__le__cancel2_2,axiom,
( 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) ),
file('MSC001-1.ax',cls_Nat_Omult__le__cancel2_2) ).
cnf(cls_Nat_Omult__less__cancel1_0,axiom,
( 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) ),
file('MSC001-1.ax',cls_Nat_Omult__less__cancel1_0) ).
cnf(cls_Nat_Omult__less__cancel1_1,axiom,
( c_less(V_m,V_n,tc_nat)
| ~ c_less(c_times(V_k,V_m,tc_nat),c_times(V_k,V_n,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Nat_Omult__less__cancel1_1) ).
cnf(cls_Nat_Omult__less__cancel1_2,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)
| ~ c_less(V_m,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Omult__less__cancel1_2) ).
cnf(cls_Nat_Omult__less__cancel2_0,axiom,
( 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) ),
file('MSC001-1.ax',cls_Nat_Omult__less__cancel2_0) ).
cnf(cls_Nat_Omult__less__cancel2_1,axiom,
( c_less(V_m,V_n,tc_nat)
| ~ c_less(c_times(V_m,V_k,tc_nat),c_times(V_n,V_k,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Nat_Omult__less__cancel2_1) ).
cnf(cls_Nat_Omult__less__cancel2_2,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)
| ~ c_less(V_m,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Omult__less__cancel2_2) ).
cnf(cls_Nat_Onat__0__less__mult__iff_0,axiom,
( c_less(c_0,V_m,tc_nat)
| ~ c_less(c_0,c_times(V_m,V_n,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Nat_Onat__0__less__mult__iff_0) ).
cnf(cls_Nat_Onat__0__less__mult__iff_1,axiom,
( c_less(c_0,V_n,tc_nat)
| ~ c_less(c_0,c_times(V_m,V_n,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Nat_Onat__0__less__mult__iff_1) ).
cnf(cls_Nat_Onat__0__less__mult__iff_2,axiom,
( c_less(c_0,c_times(V_m,V_n,tc_nat),tc_nat)
| ~ c_less(c_0,V_m,tc_nat)
| ~ c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Onat__0__less__mult__iff_2) ).
cnf(cls_Nat_Onat__add__left__cancel_0,axiom,
( V_m = V_n
| c_plus(V_k,V_m,tc_nat) != c_plus(V_k,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Onat__add__left__cancel_0) ).
cnf(cls_Nat_Onat__add__left__cancel__le_0,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) ),
file('MSC001-1.ax',cls_Nat_Onat__add__left__cancel__le_0) ).
cnf(cls_Nat_Onat__add__left__cancel__le_1,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) ),
file('MSC001-1.ax',cls_Nat_Onat__add__left__cancel__le_1) ).
cnf(cls_Nat_Onat__add__left__cancel__less_0,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) ),
file('MSC001-1.ax',cls_Nat_Onat__add__left__cancel__less_0) ).
cnf(cls_Nat_Onat__add__left__cancel__less_1,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) ),
file('MSC001-1.ax',cls_Nat_Onat__add__left__cancel__less_1) ).
cnf(cls_Nat_Onat__add__right__cancel_0,axiom,
( V_m = V_n
| c_plus(V_m,V_k,tc_nat) != c_plus(V_n,V_k,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Onat__add__right__cancel_0) ).
cnf(cls_Nat_Onot__add__less1_0,axiom,
~ c_less(c_plus(V_i,V_j,tc_nat),V_i,tc_nat),
file('MSC001-1.ax',cls_Nat_Onot__add__less1_0) ).
cnf(cls_Nat_Onot__add__less2_0,axiom,
~ c_less(c_plus(V_j,V_i,tc_nat),V_i,tc_nat),
file('MSC001-1.ax',cls_Nat_Onot__add__less2_0) ).
cnf(cls_Nat_Onot__gr0_0,axiom,
( V_n = c_0
| c_less(c_0,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Onot__gr0_0) ).
cnf(cls_Nat_Onot__gr0_1,axiom,
~ c_less(c_0,c_0,tc_nat),
file('MSC001-1.ax',cls_Nat_Onot__gr0_1) ).
cnf(cls_Nat_Onot__less0_0,axiom,
~ c_less(V_n,c_0,tc_nat),
file('MSC001-1.ax',cls_Nat_Onot__less0_0) ).
cnf(cls_Nat_Oone__eq__mult__iff_0,axiom,
( V_m = c_1
| c_Suc(c_0) != c_times(V_m,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Oone__eq__mult__iff_0) ).
cnf(cls_Nat_Oone__eq__mult__iff_1,axiom,
( V_n = c_1
| c_Suc(c_0) != c_times(V_m,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Oone__eq__mult__iff_1) ).
cnf(cls_Nat_Oone__eq__mult__iff_2,axiom,
c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
file('MSC001-1.ax',cls_Nat_Oone__eq__mult__iff_2) ).
cnf(cls_Nat_Oone__le__mult__iff_0,axiom,
( c_lessequals(c_1,V_m,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(V_m,V_n,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Nat_Oone__le__mult__iff_0) ).
cnf(cls_Nat_Oone__le__mult__iff_1,axiom,
( c_lessequals(c_1,V_n,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(V_m,V_n,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Nat_Oone__le__mult__iff_1) ).
cnf(cls_Nat_Oone__le__mult__iff_2,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)
| ~ c_lessequals(c_1,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Oone__le__mult__iff_2) ).
cnf(cls_Nat_Oop_A_K_Omult__0_0,axiom,
c_times(c_0,V_n,tc_nat) = c_0,
file('MSC001-1.ax',cls_Nat_Oop_A_K_Omult__0_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),
file('MSC001-1.ax',cls_Nat_Oop_A_K_Omult__Suc_0) ).
cnf(cls_Nat_Oop_A_L_Oadd__0_0,axiom,
c_plus(c_0,V_y,tc_nat) = V_y,
file('MSC001-1.ax',cls_Nat_Oop_A_L_Oadd__0_0) ).
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)),
file('MSC001-1.ax',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
cnf(cls_Nat_Oop_A_N_Odiff__0_0,axiom,
c_minus(V_y,c_0,tc_nat) = V_y,
file('MSC001-1.ax',cls_Nat_Oop_A_N_Odiff__0_0) ).
cnf(cls_Nat_Ozero__less__diff_0,axiom,
( c_less(V_m,V_n,tc_nat)
| ~ c_less(c_0,c_minus(V_n,V_m,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Nat_Ozero__less__diff_0) ).
cnf(cls_Nat_Ozero__less__diff_1,axiom,
( c_less(c_0,c_minus(V_n,V_m,tc_nat),tc_nat)
| ~ c_less(V_m,V_n,tc_nat) ),
file('MSC001-1.ax',cls_Nat_Ozero__less__diff_1) ).
cnf(cls_Numeral_OMin__1__eq_0,axiom,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_OMin,
file('MSC001-1.ax',cls_Numeral_OMin__1__eq_0) ).
cnf(cls_Numeral_OPls__0__eq_0,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_OPls,
file('MSC001-1.ax',cls_Numeral_OPls__0__eq_0) ).
cnf(cls_Numeral_Oadd__number__of__diff2_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Oadd__number__of__diff2_0) ).
cnf(cls_Numeral_Oadd__number__of__left_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Oadd__number__of__left_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__add__BIT__0_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__add__BIT__10_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__add__BIT__11_0) ).
cnf(cls_Numeral_Obin__add__Min_0,axiom,
c_Numeral_Obin__add(c_Numeral_OMin,V_w) = c_Numeral_Obin__pred(V_w),
file('MSC001-1.ax',cls_Numeral_Obin__add__Min_0) ).
cnf(cls_Numeral_Obin__add__Min__right_0,axiom,
c_Numeral_Obin__add(V_w,c_Numeral_OMin) = c_Numeral_Obin__pred(V_w),
file('MSC001-1.ax',cls_Numeral_Obin__add__Min__right_0) ).
cnf(cls_Numeral_Obin__add__Pls_0,axiom,
c_Numeral_Obin__add(c_Numeral_OPls,V_y) = V_y,
file('MSC001-1.ax',cls_Numeral_Obin__add__Pls_0) ).
cnf(cls_Numeral_Obin__add__Pls__right_0,axiom,
c_Numeral_Obin__add(V_y,c_Numeral_OPls) = V_y,
file('MSC001-1.ax',cls_Numeral_Obin__add__Pls__right_0) ).
cnf(cls_Numeral_Obin__arith__extra__simps__1_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__arith__extra__simps__1_0) ).
cnf(cls_Numeral_Obin__arith__extra__simps__2_0,axiom,
( c_uminus(c_Numeral_Onumber__of(V_w,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(V_w),T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__arith__extra__simps__2_0) ).
cnf(cls_Numeral_Obin__arith__extra__simps__3_0,axiom,
( c_uminus(c_1,T_a) = c_Numeral_Onumber__of(c_Numeral_OMin,T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__arith__extra__simps__3_0) ).
cnf(cls_Numeral_Obin__arith__extra__simps__4_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__arith__extra__simps__4_0) ).
cnf(cls_Numeral_Obin__arith__extra__simps__5_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__arith__extra__simps__5_0) ).
cnf(cls_Numeral_Obin__arith__extra__simps__6_0,axiom,
( 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)
| ~ c_less(c_Numeral_Onumber__of(V_x,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__arith__extra__simps__6_0) ).
cnf(cls_Numeral_Obin__arith__extra__simps__6_1,axiom,
( c_HOL_Oabs(c_Numeral_Onumber__of(V_x,T_a),T_a) = c_Numeral_Onumber__of(V_x,T_a)
| c_less(c_Numeral_Onumber__of(V_x,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__arith__extra__simps__6_1) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__minus__0_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__minus__1_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__minus__Min_0) ).
cnf(cls_Numeral_Obin__minus__Pls_0,axiom,
c_Numeral_Obin__minus(c_Numeral_OPls) = c_Numeral_OPls,
file('MSC001-1.ax',cls_Numeral_Obin__minus__Pls_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__mult__0_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__mult__1_0) ).
cnf(cls_Numeral_Obin__mult__Min_0,axiom,
c_Numeral_Obin__mult(c_Numeral_OMin,V_w) = c_Numeral_Obin__minus(V_w),
file('MSC001-1.ax',cls_Numeral_Obin__mult__Min_0) ).
cnf(cls_Numeral_Obin__mult__Pls_0,axiom,
c_Numeral_Obin__mult(c_Numeral_OPls,V_w) = c_Numeral_OPls,
file('MSC001-1.ax',cls_Numeral_Obin__mult__Pls_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__pred__0_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__pred__1_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__pred__Min_0) ).
cnf(cls_Numeral_Obin__pred__Pls_0,axiom,
c_Numeral_Obin__pred(c_Numeral_OPls) = c_Numeral_OMin,
file('MSC001-1.ax',cls_Numeral_Obin__pred__Pls_0) ).
cnf(cls_Numeral_Obin__rel__simps__10_0,axiom,
( ~ c_IntDef_Oiszero(c_1,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__10_0) ).
cnf(cls_Numeral_Obin__rel__simps__11_0,axiom,
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__11_0) ).
cnf(cls_Numeral_Obin__rel__simps__12_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__12_0) ).
cnf(cls_Numeral_Obin__rel__simps__12_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__12_1) ).
cnf(cls_Numeral_Obin__rel__simps__13_0,axiom,
( ~ c_lessequals(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_y,c_Numeral_Obin__minus(V_x)),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__13_0) ).
cnf(cls_Numeral_Obin__rel__simps__13_1,axiom,
( c_lessequals(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_y,c_Numeral_Obin__minus(V_x)),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__13_1) ).
cnf(cls_Numeral_Obin__rel__simps__1_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__1_0) ).
cnf(cls_Numeral_Obin__rel__simps__1_1,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__1_1) ).
cnf(cls_Numeral_Obin__rel__simps__2_0,axiom,
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,T_a),T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__2_0) ).
cnf(cls_Numeral_Obin__rel__simps__3_0,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__3_0) ).
cnf(cls_Numeral_Obin__rel__simps__4_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__4_0) ).
cnf(cls_Numeral_Obin__rel__simps__4_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__4_1) ).
cnf(cls_Numeral_Obin__rel__simps__5_0,axiom,
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(V_w,c_Numeral_Obit_OB1),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__5_0) ).
cnf(cls_Numeral_Obin__rel__simps__6_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__6_0) ).
cnf(cls_Numeral_Obin__rel__simps__6_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__6_1) ).
cnf(cls_Numeral_Obin__rel__simps__7_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__7_0) ).
cnf(cls_Numeral_Obin__rel__simps__8_0,axiom,
( ~ c_IntDef_Oneg(c_0,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__8_0) ).
cnf(cls_Numeral_Obin__rel__simps__9_0,axiom,
( ~ c_IntDef_Oneg(c_1,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_Numeral_Obin__rel__simps__9_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__succ__0_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__succ__1_0) ).
cnf(cls_Numeral_Obin__succ__Min_0,axiom,
c_Numeral_Obin__succ(c_Numeral_OMin) = c_Numeral_OPls,
file('MSC001-1.ax',cls_Numeral_Obin__succ__Min_0) ).
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),
file('MSC001-1.ax',cls_Numeral_Obin__succ__Pls_0) ).
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,
file('MSC001-1.ax',cls_Numeral_Obit_Ocases__1_0) ).
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,
file('MSC001-1.ax',cls_Numeral_Obit_Ocases__2_0) ).
cnf(cls_Numeral_Obit_Odistinct__1_0,axiom,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
file('MSC001-1.ax',cls_Numeral_Obit_Odistinct__1_0) ).
cnf(cls_Numeral_Obit_Odistinct__2_0,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('MSC001-1.ax',cls_Numeral_Obit_Odistinct__2_0) ).
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,
file('MSC001-1.ax',cls_Numeral_Obit_Orecs__1_0) ).
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,
file('MSC001-1.ax',cls_Numeral_Obit_Orecs__2_0) ).
cnf(cls_Numeral_Obit_Osize__1_0,axiom,
c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) = c_0,
file('MSC001-1.ax',cls_Numeral_Obit_Osize__1_0) ).
cnf(cls_Numeral_Obit_Osize__2_0,axiom,
c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) = c_0,
file('MSC001-1.ax',cls_Numeral_Obit_Osize__2_0) ).
cnf(cls_Numeral_Ominus__number__of__mult_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Ominus__number__of__mult_0) ).
cnf(cls_Numeral_Omult__minus1_0,axiom,
( c_times(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),V_z,T_a) = c_uminus(V_z,T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Omult__minus1_0) ).
cnf(cls_Numeral_Omult__minus1__right_0,axiom,
( c_times(V_z,c_Numeral_Onumber__of(c_Numeral_OMin,T_a),T_a) = c_uminus(V_z,T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Omult__minus1__right_0) ).
cnf(cls_Numeral_Omult__number__of__left_0,axiom,
( 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)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Omult__number__of__left_0) ).
cnf(cls_Numeral_Onumeral__0__eq__0_0,axiom,
( c_Numeral_Onumber__of(c_Numeral_OPls,T_a) = c_0
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Onumeral__0__eq__0_0) ).
cnf(cls_Numeral_Onumeral__1__eq__1_0,axiom,
( c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),T_a) = c_1
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Numeral_Onumeral__1__eq__1_0) ).
cnf(cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0,axiom,
( c_plus(c_uminus(V_a,T_a),V_a,T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
cnf(cls_OrderedGroup_Oabs__0__eq_0,axiom,
( V_a = c_0
| c_0 != c_HOL_Oabs(V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__0__eq_0) ).
cnf(cls_OrderedGroup_Oabs__0__eq_1,axiom,
( c_0 = c_HOL_Oabs(c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__0__eq_1) ).
cnf(cls_OrderedGroup_Oabs__add__abs_0,axiom,
( 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)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__add__abs_0) ).
cnf(cls_OrderedGroup_Oabs__eq__0_0,axiom,
( V_a = c_0
| c_HOL_Oabs(V_a,T_a) != c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__eq__0_0) ).
cnf(cls_OrderedGroup_Oabs__eq__0_1,axiom,
( c_HOL_Oabs(c_0,T_a) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__eq__0_1) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(cls_OrderedGroup_Oabs__idempotent_0,axiom,
( c_HOL_Oabs(c_HOL_Oabs(V_a,T_a),T_a) = c_HOL_Oabs(V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__idempotent_0) ).
cnf(cls_OrderedGroup_Oabs__le__zero__iff_0,axiom,
( V_a = c_0
| ~ c_lessequals(c_HOL_Oabs(V_a,T_a),c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
cnf(cls_OrderedGroup_Oabs__le__zero__iff_1,axiom,
( c_lessequals(c_HOL_Oabs(c_0,T_a),c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
cnf(cls_OrderedGroup_Oabs__minus__cancel_0,axiom,
( c_HOL_Oabs(c_uminus(V_a,T_a),T_a) = c_HOL_Oabs(V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__minus__cancel_0) ).
cnf(cls_OrderedGroup_Oabs__not__less__zero_0,axiom,
( ~ c_less(c_HOL_Oabs(V_a,T_a),c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__not__less__zero_0) ).
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( c_HOL_Oabs(V_y,T_a) = V_y
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonneg_0) ).
cnf(cls_OrderedGroup_Oabs__of__nonpos_0,axiom,
( c_HOL_Oabs(V_a,T_a) = c_uminus(V_a,T_a)
| ~ c_lessequals(V_a,c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonpos_0) ).
cnf(cls_OrderedGroup_Oadd__0__right_0,axiom,
( c_plus(V_y,c_0,T_a) = V_y
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oadd__0__right_0) ).
cnf(cls_OrderedGroup_Oadd__le__cancel__left_0,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
cnf(cls_OrderedGroup_Oadd__le__cancel__left_1,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
cnf(cls_OrderedGroup_Oadd__le__cancel__right_0,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
cnf(cls_OrderedGroup_Oadd__le__cancel__right_1,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
cnf(cls_OrderedGroup_Oadd__left__cancel_0,axiom,
( V_b = V_c
| c_plus(V_a,V_b,T_a) != c_plus(V_a,V_c,T_a)
| ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oadd__left__cancel_0) ).
cnf(cls_OrderedGroup_Oadd__less__cancel__left_0,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
cnf(cls_OrderedGroup_Oadd__less__cancel__left_1,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
cnf(cls_OrderedGroup_Oadd__less__cancel__right_0,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
cnf(cls_OrderedGroup_Oadd__less__cancel__right_1,axiom,
( 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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
cnf(cls_OrderedGroup_Oadd__right__cancel_0,axiom,
( V_b = V_c
| c_plus(V_b,V_a,T_a) != c_plus(V_c,V_a,T_a)
| ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oadd__right__cancel_0) ).
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
( c_plus(c_0,V_y,T_a) = V_y
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(cls_OrderedGroup_Odiff__0_0,axiom,
( c_minus(c_0,V_a,T_a) = c_uminus(V_a,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odiff__0_0) ).
cnf(cls_OrderedGroup_Odiff__0__right_0,axiom,
( c_minus(V_y,c_0,T_a) = V_y
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odiff__0__right_0) ).
cnf(cls_OrderedGroup_Odiff__eq__0__iff__eq_0,axiom,
( V_a = V_b
| c_minus(V_a,V_b,T_a) != c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
cnf(cls_OrderedGroup_Odiff__le__0__iff__le_0,axiom,
( c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
cnf(cls_OrderedGroup_Odiff__le__0__iff__le_1,axiom,
( c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
cnf(cls_OrderedGroup_Odiff__less__0__iff__less_0,axiom,
( c_less(V_a,V_b,T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
cnf(cls_OrderedGroup_Odiff__less__0__iff__less_1,axiom,
( c_less(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
cnf(cls_OrderedGroup_Odiff__minus__eq__add_0,axiom,
( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
cnf(cls_OrderedGroup_Odiff__self_0,axiom,
( c_minus(V_a,V_a,T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odiff__self_0) ).
cnf(cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0,axiom,
( c_lessequals(V_a,c_0,T_a)
| ~ c_lessequals(c_plus(V_a,V_a,T_a),c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
cnf(cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1,axiom,
( c_lessequals(c_plus(V_a,V_a,T_a),c_0,T_a)
| ~ c_lessequals(V_a,c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
cnf(cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0,axiom,
( c_less(V_a,c_0,T_a)
| ~ c_less(c_plus(V_a,V_a,T_a),c_0,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).
cnf(cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1,axiom,
( c_less(c_plus(V_a,V_a,T_a),c_0,T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).
cnf(cls_OrderedGroup_Ojoin__0__eq__0_0,axiom,
( V_a = c_0
| c_LOrder_Ojoin(V_a,c_uminus(V_a,T_a),T_a) != c_0
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
cnf(cls_OrderedGroup_Ojoin__0__eq__0_1,axiom,
( c_LOrder_Ojoin(c_0,c_uminus(c_0,T_a),T_a) = c_0
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
cnf(cls_OrderedGroup_Omeet__0__eq__0_0,axiom,
( V_a = c_0
| c_LOrder_Omeet(V_a,c_uminus(V_a,T_a),T_a) != c_0
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Omeet__0__eq__0_0) ).
cnf(cls_OrderedGroup_Omeet__0__eq__0_1,axiom,
( c_LOrder_Omeet(c_0,c_uminus(c_0,T_a),T_a) = c_0
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Omeet__0__eq__0_1) ).
cnf(cls_OrderedGroup_Ominus__add__distrib_0,axiom,
( 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)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Ominus__add__distrib_0) ).
cnf(cls_OrderedGroup_Ominus__diff__eq_0,axiom,
( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Ominus__diff__eq_0) ).
cnf(cls_OrderedGroup_Ominus__minus_0,axiom,
( c_uminus(c_uminus(V_y,T_a),T_a) = V_y
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Ominus__minus_0) ).
cnf(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0,axiom,
( c_times(c_1,V_y,T_a) = V_y
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
cnf(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0,axiom,
( c_times(V_y,c_1,T_a) = V_y
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
cnf(cls_OrderedGroup_Oneg__0__equal__iff__equal_0,axiom,
( c_0 = V_a
| c_0 != c_uminus(V_a,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__0__equal__iff__equal_0) ).
cnf(cls_OrderedGroup_Oneg__0__equal__iff__equal_1,axiom,
( c_0 = c_uminus(c_0,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
cnf(cls_OrderedGroup_Oneg__0__le__iff__le_0,axiom,
( c_lessequals(V_a,c_0,T_a)
| ~ c_lessequals(c_0,c_uminus(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
cnf(cls_OrderedGroup_Oneg__0__le__iff__le_1,axiom,
( c_lessequals(c_0,c_uminus(V_a,T_a),T_a)
| ~ c_lessequals(V_a,c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
cnf(cls_OrderedGroup_Oneg__0__less__iff__less_0,axiom,
( c_less(V_a,c_0,T_a)
| ~ c_less(c_0,c_uminus(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
cnf(cls_OrderedGroup_Oneg__0__less__iff__less_1,axiom,
( c_less(c_0,c_uminus(V_a,T_a),T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
cnf(cls_OrderedGroup_Oneg__equal__0__iff__equal_0,axiom,
( V_a = c_0
| c_uminus(V_a,T_a) != c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
cnf(cls_OrderedGroup_Oneg__equal__0__iff__equal_1,axiom,
( c_uminus(c_0,T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__equal__0__iff__equal_1) ).
cnf(cls_OrderedGroup_Oneg__equal__iff__equal_0,axiom,
( V_a = V_b
| c_uminus(V_a,T_a) != c_uminus(V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
cnf(cls_OrderedGroup_Oneg__join__eq__meet_0,axiom,
( 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)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
cnf(cls_OrderedGroup_Oneg__le__0__iff__le_0,axiom,
( c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_uminus(V_a,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
cnf(cls_OrderedGroup_Oneg__le__0__iff__le_1,axiom,
( c_lessequals(c_uminus(V_a,T_a),c_0,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
cnf(cls_OrderedGroup_Oneg__le__iff__le_0,axiom,
( c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__le__iff__le_0) ).
cnf(cls_OrderedGroup_Oneg__le__iff__le_1,axiom,
( c_lessequals(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__le__iff__le_1) ).
cnf(cls_OrderedGroup_Oneg__less__0__iff__less_0,axiom,
( c_less(c_0,V_a,T_a)
| ~ c_less(c_uminus(V_a,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
cnf(cls_OrderedGroup_Oneg__less__0__iff__less_1,axiom,
( c_less(c_uminus(V_a,T_a),c_0,T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
cnf(cls_OrderedGroup_Oneg__less__iff__less_0,axiom,
( c_less(V_a,V_b,T_a)
| ~ c_less(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__less__iff__less_0) ).
cnf(cls_OrderedGroup_Oneg__less__iff__less_1,axiom,
( c_less(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a)
| ~ c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__less__iff__less_1) ).
cnf(cls_OrderedGroup_Oneg__meet__eq__join_0,axiom,
( 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)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
cnf(cls_OrderedGroup_Onprt__0_0,axiom,
( c_OrderedGroup_Onprt(c_0,T_a) = c_0
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Onprt__0_0) ).
cnf(cls_OrderedGroup_Onprt__eq__0_0,axiom,
( c_OrderedGroup_Onprt(V_x,T_a) = c_0
| ~ c_lessequals(c_0,V_x,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Onprt__eq__0_0) ).
cnf(cls_OrderedGroup_Onprt__eq__id_0,axiom,
( c_OrderedGroup_Onprt(V_y,T_a) = V_y
| ~ c_lessequals(V_y,c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Onprt__eq__id_0) ).
cnf(cls_OrderedGroup_Onprt__le__zero_0,axiom,
( c_lessequals(c_OrderedGroup_Onprt(V_a,T_a),c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Onprt__le__zero_0) ).
cnf(cls_OrderedGroup_Onprt__mono_0,axiom,
( c_lessequals(c_OrderedGroup_Onprt(V_a,T_a),c_OrderedGroup_Onprt(V_b,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Onprt__mono_0) ).
cnf(cls_OrderedGroup_Opprt__0_0,axiom,
( c_OrderedGroup_Opprt(c_0,T_a) = c_0
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Opprt__0_0) ).
cnf(cls_OrderedGroup_Opprt__eq__0_0,axiom,
( c_OrderedGroup_Opprt(V_x,T_a) = c_0
| ~ c_lessequals(V_x,c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Opprt__eq__0_0) ).
cnf(cls_OrderedGroup_Opprt__eq__id_0,axiom,
( c_OrderedGroup_Opprt(V_y,T_a) = V_y
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Opprt__eq__id_0) ).
cnf(cls_OrderedGroup_Opprt__mono_0,axiom,
( c_lessequals(c_OrderedGroup_Opprt(V_a,T_a),c_OrderedGroup_Opprt(V_b,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Opprt__mono_0) ).
cnf(cls_OrderedGroup_Oright__minus_0,axiom,
( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Oright__minus_0) ).
cnf(cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0,axiom,
( c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,c_plus(V_a,V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
cnf(cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1,axiom,
( c_lessequals(c_0,c_plus(V_a,V_a,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
cnf(cls_OrderedGroup_Ozero__le__pprt_0,axiom,
( c_lessequals(c_0,c_OrderedGroup_Opprt(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Ozero__le__pprt_0) ).
cnf(cls_OrderedGroup_Ozero__less__abs__iff_0,axiom,
( ~ c_less(c_0,c_HOL_Oabs(c_0,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
cnf(cls_OrderedGroup_Ozero__less__abs__iff_1,axiom,
( V_a = c_0
| c_less(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('MSC001-1.ax',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
cnf(cls_Orderings_Omax__less__iff__conj_0,axiom,
( c_less(V_x,V_z,T_a)
| ~ c_less(c_Orderings_Omax(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Orderings_Omax__less__iff__conj_0) ).
cnf(cls_Orderings_Omax__less__iff__conj_1,axiom,
( c_less(V_y,V_z,T_a)
| ~ c_less(c_Orderings_Omax(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Orderings_Omax__less__iff__conj_1) ).
cnf(cls_Orderings_Omax__less__iff__conj_2,axiom,
( c_less(c_Orderings_Omax(V_x,V_y,T_a),V_z,T_a)
| ~ c_less(V_x,V_z,T_a)
| ~ c_less(V_y,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Orderings_Omax__less__iff__conj_2) ).
cnf(cls_Orderings_Omin__less__iff__conj_0,axiom,
( c_less(V_z,V_x,T_a)
| ~ c_less(V_z,c_Orderings_Omin(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Orderings_Omin__less__iff__conj_0) ).
cnf(cls_Orderings_Omin__less__iff__conj_1,axiom,
( c_less(V_z,V_y,T_a)
| ~ c_less(V_z,c_Orderings_Omin(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Orderings_Omin__less__iff__conj_1) ).
cnf(cls_Orderings_Omin__less__iff__conj_2,axiom,
( c_less(V_z,c_Orderings_Omin(V_x,V_y,T_a),T_a)
| ~ c_less(V_z,V_x,T_a)
| ~ c_less(V_z,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_Orderings_Omin__less__iff__conj_2) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0,axiom,
( c_lessequals(V_x,V_y,T_b)
| ~ c_lessequals(V_x,c_Orderings_Omin(V_y,V_z,T_b),T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1,axiom,
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_x,c_Orderings_Omin(V_y,V_z,T_b),T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2,axiom,
( c_lessequals(V_x,c_Orderings_Omin(V_y,V_z,T_b),T_b)
| ~ c_lessequals(V_x,V_y,T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0,axiom,
( c_Orderings_Omin(V_y,V_y,T_b) = V_y
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0,axiom,
( 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)
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0,axiom,
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1,axiom,
( c_lessequals(V_y,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
( c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0,axiom,
( c_Orderings_Omax(V_y,V_y,T_b) = V_y
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0,axiom,
( 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)
| ~ class_Orderings_Olinorder(T_b) ),
file('MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
cnf(cls_Orderings_Oorder__less__irrefl_0,axiom,
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('MSC001-1.ax',cls_Orderings_Oorder__less__irrefl_0) ).
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_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) ),
file('MSC001-1.ax',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0) ).
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_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) ),
file('MSC001-1.ax',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1) ).
cnf(cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0,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) ),
file('MSC001-1.ax',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0) ).
cnf(cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1,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 ),
file('MSC001-1.ax',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1) ).
cnf(cls_Parity_Oeven__difference_0,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) ),
file('MSC001-1.ax',cls_Parity_Oeven__difference_0) ).
cnf(cls_Parity_Oeven__difference_1,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) ),
file('MSC001-1.ax',cls_Parity_Oeven__difference_1) ).
cnf(cls_Parity_Oeven__difference_2,axiom,
( c_Parity_Oeven(c_minus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(V_x,tc_IntDef_Oint)
| ~ c_Parity_Oeven(V_y,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__difference_2) ).
cnf(cls_Parity_Oeven__difference_3,axiom,
( c_Parity_Oeven(c_minus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(V_x,tc_IntDef_Oint)
| c_Parity_Oeven(V_y,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__difference_3) ).
cnf(cls_Parity_Oeven__nat__Suc_0,axiom,
( ~ c_Parity_Oeven(c_Suc(V_x),tc_nat)
| ~ c_Parity_Oeven(V_x,tc_nat) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__Suc_0) ).
cnf(cls_Parity_Oeven__nat__Suc_1,axiom,
( c_Parity_Oeven(c_Suc(V_x),tc_nat)
| c_Parity_Oeven(V_x,tc_nat) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__Suc_1) ).
cnf(cls_Parity_Oeven__nat__power_0,axiom,
( c_Parity_Oeven(V_x,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(V_x,V_y,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__power_0) ).
cnf(cls_Parity_Oeven__nat__power_1,axiom,
( c_less(c_0,V_y,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(V_x,V_y,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__power_1) ).
cnf(cls_Parity_Oeven__nat__power_2,axiom,
( c_Parity_Oeven(c_Nat_Opower(V_x,V_y,tc_nat),tc_nat)
| ~ c_less(c_0,V_y,tc_nat)
| ~ c_Parity_Oeven(V_x,tc_nat) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__power_2) ).
cnf(cls_Parity_Oeven__nat__product_0,axiom,
( c_Parity_Oeven(V_x,tc_nat)
| c_Parity_Oeven(V_y,tc_nat)
| ~ c_Parity_Oeven(c_times(V_x,V_y,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__product_0) ).
cnf(cls_Parity_Oeven__nat__product_1,axiom,
( c_Parity_Oeven(c_times(V_x,V_y,tc_nat),tc_nat)
| ~ c_Parity_Oeven(V_x,tc_nat) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__product_1) ).
cnf(cls_Parity_Oeven__nat__product_2,axiom,
( c_Parity_Oeven(c_times(V_x,V_y,tc_nat),tc_nat)
| ~ c_Parity_Oeven(V_y,tc_nat) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__product_2) ).
cnf(cls_Parity_Oeven__nat__sum_0,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) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__sum_0) ).
cnf(cls_Parity_Oeven__nat__sum_1,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) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__sum_1) ).
cnf(cls_Parity_Oeven__nat__sum_2,axiom,
( c_Parity_Oeven(c_plus(V_x,V_y,tc_nat),tc_nat)
| ~ c_Parity_Oeven(V_x,tc_nat)
| ~ c_Parity_Oeven(V_y,tc_nat) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__sum_2) ).
cnf(cls_Parity_Oeven__nat__sum_3,axiom,
( c_Parity_Oeven(c_plus(V_x,V_y,tc_nat),tc_nat)
| c_Parity_Oeven(V_x,tc_nat)
| c_Parity_Oeven(V_y,tc_nat) ),
file('MSC001-1.ax',cls_Parity_Oeven__nat__sum_3) ).
cnf(cls_Parity_Oeven__nat__zero_0,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('MSC001-1.ax',cls_Parity_Oeven__nat__zero_0) ).
cnf(cls_Parity_Oeven__neg_0,axiom,
( c_Parity_Oeven(V_x,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(V_x,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__neg_0) ).
cnf(cls_Parity_Oeven__neg_1,axiom,
( c_Parity_Oeven(c_uminus(V_x,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(V_x,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__neg_1) ).
cnf(cls_Parity_Oeven__power_0,axiom,
( c_Parity_Oeven(V_x,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(V_x,V_n,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__power_0) ).
cnf(cls_Parity_Oeven__power_1,axiom,
( c_less(c_0,V_n,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(V_x,V_n,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__power_1) ).
cnf(cls_Parity_Oeven__power_2,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)
| ~ c_Parity_Oeven(V_x,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__power_2) ).
cnf(cls_Parity_Oeven__product_0,axiom,
( c_Parity_Oeven(V_x,tc_IntDef_Oint)
| c_Parity_Oeven(V_y,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__product_0) ).
cnf(cls_Parity_Oeven__product_1,axiom,
( c_Parity_Oeven(c_times(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(V_x,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__product_1) ).
cnf(cls_Parity_Oeven__product_2,axiom,
( c_Parity_Oeven(c_times(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(V_y,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__product_2) ).
cnf(cls_Parity_Oeven__sum_0,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) ),
file('MSC001-1.ax',cls_Parity_Oeven__sum_0) ).
cnf(cls_Parity_Oeven__sum_1,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) ),
file('MSC001-1.ax',cls_Parity_Oeven__sum_1) ).
cnf(cls_Parity_Oeven__sum_2,axiom,
( c_Parity_Oeven(c_plus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(V_x,tc_IntDef_Oint)
| ~ c_Parity_Oeven(V_y,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__sum_2) ).
cnf(cls_Parity_Oeven__sum_3,axiom,
( c_Parity_Oeven(c_plus(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(V_x,tc_IntDef_Oint)
| c_Parity_Oeven(V_y,tc_IntDef_Oint) ),
file('MSC001-1.ax',cls_Parity_Oeven__sum_3) ).
cnf(cls_Parity_Oeven__zero_0,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('MSC001-1.ax',cls_Parity_Oeven__zero_0) ).
cnf(cls_Parity_Ominus__one__even__power_0,axiom,
( c_Nat_Opower(c_uminus(c_1,T_a),V_x,T_a) = c_1
| ~ c_Parity_Oeven(V_x,tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Ominus__one__even__power_0) ).
cnf(cls_Parity_Ominus__one__odd__power_0,axiom,
( c_Nat_Opower(c_uminus(c_1,T_a),V_x,T_a) = c_uminus(c_1,T_a)
| c_Parity_Oeven(V_x,tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Ominus__one__odd__power_0) ).
cnf(cls_Parity_Oneg__one__even__power_0,axiom,
( c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,T_a),V_x,T_a) = c_1
| ~ c_Parity_Oeven(V_x,tc_nat)
| ~ class_Power_Orecpower(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Parity_Oneg__one__even__power_0) ).
cnf(cls_Parity_Oneg__one__odd__power_0,axiom,
( 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)
| c_Parity_Oeven(V_x,tc_nat)
| ~ class_Power_Orecpower(T_a)
| ~ class_Numeral_Onumber__ring(T_a) ),
file('MSC001-1.ax',cls_Parity_Oneg__one__odd__power_0) ).
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_1
| 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 ),
file('MSC001-1.ax',cls_Parity_Oneq__one__mod__two_0) ).
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_1
| 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 ),
file('MSC001-1.ax',cls_Parity_Oneq__one__mod__two_1) ).
cnf(cls_Parity_Oodd__one_0,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('MSC001-1.ax',cls_Parity_Oodd__one_0) ).
cnf(cls_Parity_Opower__0__left__number__of_0,axiom,
( c_Nat_Opower(c_0,c_Numeral_Onumber__of(V_w,tc_nat),T_a) = c_1
| c_Numeral_Onumber__of(V_w,tc_nat) != c_0
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__0__left__number__of_0) ).
cnf(cls_Parity_Opower__0__left__number__of_1,axiom,
( 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_0
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__0__left__number__of_1) ).
cnf(cls_Parity_Opower__eq__0__iff__number__of_0,axiom,
( V_a = c_0
| c_Nat_Opower(V_a,c_Numeral_Onumber__of(V_w,tc_nat),T_a) != c_0
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__eq__0__iff__number__of_0) ).
cnf(cls_Parity_Opower__eq__0__iff__number__of_1,axiom,
( c_less(c_0,c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| c_Nat_Opower(V_a,c_Numeral_Onumber__of(V_w,tc_nat),T_a) != c_0
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__eq__0__iff__number__of_1) ).
cnf(cls_Parity_Opower__eq__0__iff__number__of_2,axiom,
( c_Nat_Opower(c_0,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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__eq__0__iff__number__of_2) ).
cnf(cls_Parity_Opower__even__abs__number__of_0,axiom,
( 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)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(V_w,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__even__abs__number__of_0) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_0,axiom,
( c_Numeral_Onumber__of(V_w,tc_nat) != c_0
| ~ c_lessequals(c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__le__zero__eq__number__of_0) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_1,axiom,
( V_x = c_0
| ~ 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__le__zero__eq__number__of_1) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_2,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__le__zero__eq__number__of_2) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_3,axiom,
( V_x = c_0
| c_lessequals(V_x,c_0,T_a)
| ~ c_lessequals(c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__le__zero__eq__number__of_3) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_4,axiom,
( c_Numeral_Onumber__of(V_w,tc_nat) = c_0
| 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__le__zero__eq__number__of_4) ).
cnf(cls_Parity_Opower__le__zero__eq__number__of_5,axiom,
( c_Numeral_Onumber__of(V_w,tc_nat) = c_0
| c_lessequals(c_Nat_Opower(c_0,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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__le__zero__eq__number__of_5) ).
cnf(cls_Parity_Opower__less__zero__eq__number__of_0,axiom,
( ~ c_less(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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__less__zero__eq__number__of_0) ).
cnf(cls_Parity_Opower__less__zero__eq__number__of_1,axiom,
( c_less(V_x,c_0,T_a)
| ~ c_less(c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__less__zero__eq__number__of_1) ).
cnf(cls_Parity_Opower__less__zero__eq__number__of_2,axiom,
( c_less(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_less(V_x,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__less__zero__eq__number__of_2) ).
cnf(cls_Parity_Opower__minus__even_0,axiom,
( c_Nat_Opower(c_uminus(V_x,T_a),V_n,T_a) = c_Nat_Opower(V_x,V_n,T_a)
| ~ c_Parity_Oeven(V_n,tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__minus__even_0) ).
cnf(cls_Parity_Opower__minus__odd_0,axiom,
( 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)
| c_Parity_Oeven(V_n,tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Opower__minus__odd_0) ).
cnf(cls_Parity_Ozero__le__power__eq__number__of_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Ozero__le__power__eq__number__of_0) ).
cnf(cls_Parity_Ozero__le__power__eq__number__of_1,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Ozero__le__power__eq__number__of_1) ).
cnf(cls_Parity_Ozero__le__power__eq__number__of_2,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Ozero__le__power__eq__number__of_2) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_0,axiom,
( c_Numeral_Onumber__of(V_w,tc_nat) = c_0
| 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Ozero__less__power__eq__number__of_0) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_1,axiom,
( c_Numeral_Onumber__of(V_w,tc_nat) = c_0
| ~ c_less(c_0,c_Nat_Opower(c_0,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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Ozero__less__power__eq__number__of_1) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_2,axiom,
( c_Numeral_Onumber__of(V_w,tc_nat) = c_0
| c_less(c_0,c_0,T_a)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(V_w,tc_nat),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Ozero__less__power__eq__number__of_2) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_3,axiom,
( c_less(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),T_a),T_a)
| c_Numeral_Onumber__of(V_w,tc_nat) != c_0
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Ozero__less__power__eq__number__of_3) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_4,axiom,
( V_x = c_0
| 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Ozero__less__power__eq__number__of_4) ).
cnf(cls_Parity_Ozero__less__power__eq__number__of_5,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Parity_Ozero__less__power__eq__number__of_5) ).
cnf(cls_Parity_Ozero__less__power__nat__eq__number__of_0,axiom,
( c_Numeral_Onumber__of(V_w,tc_nat) = c_0
| 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) ),
file('MSC001-1.ax',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
cnf(cls_Parity_Ozero__less__power__nat__eq__number__of_1,axiom,
( c_less(c_0,c_Nat_Opower(V_x,c_Numeral_Onumber__of(V_w,tc_nat),tc_nat),tc_nat)
| c_Numeral_Onumber__of(V_w,tc_nat) != c_0 ),
file('MSC001-1.ax',cls_Parity_Ozero__less__power__nat__eq__number__of_1) ).
cnf(cls_Parity_Ozero__less__power__nat__eq__number__of_2,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) ),
file('MSC001-1.ax',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
cnf(cls_Power_Onat__one__le__power_0,axiom,
( c_lessequals(c_Suc(c_0),c_Nat_Opower(V_i,V_n,tc_nat),tc_nat)
| ~ c_lessequals(c_1,V_i,tc_nat) ),
file('MSC001-1.ax',cls_Power_Onat__one__le__power_0) ).
cnf(cls_Power_Onat__zero__less__power__iff_0,axiom,
( V_n = c_0
| ~ c_less(c_0,c_Nat_Opower(c_0,V_n,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Power_Onat__zero__less__power__iff_0) ).
cnf(cls_Power_Onat__zero__less__power__iff_1,axiom,
( V_x = c_0
| c_less(c_0,c_Nat_Opower(V_x,V_n,tc_nat),tc_nat) ),
file('MSC001-1.ax',cls_Power_Onat__zero__less__power__iff_1) ).
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),
file('MSC001-1.ax',cls_Power_Onat__zero__less__power__iff_2) ).
cnf(cls_Power_Opower_Osimps__1_0,axiom,
c_Nat_Opower(V_p,c_0,tc_nat) = c_1,
file('MSC001-1.ax',cls_Power_Opower_Osimps__1_0) ).
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),
file('MSC001-1.ax',cls_Power_Opower_Osimps__2_0) ).
cnf(cls_Power_Opower__0__Suc_0,axiom,
( c_Nat_Opower(c_0,c_Suc(V_n),T_a) = c_0
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Opower__0__Suc_0) ).
cnf(cls_Power_Opower__eq__0__iff_0,axiom,
( V_a = c_0
| c_Nat_Opower(V_a,V_n,T_a) != c_0
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Opower__eq__0__iff_0) ).
cnf(cls_Power_Opower__eq__0__iff_1,axiom,
( c_less(c_0,V_n,tc_nat)
| c_Nat_Opower(V_a,V_n,T_a) != c_0
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Opower__eq__0__iff_1) ).
cnf(cls_Power_Opower__eq__0__iff_2,axiom,
( c_Nat_Opower(c_0,V_n,T_a) = c_0
| ~ c_less(c_0,V_n,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Opower__eq__0__iff_2) ).
cnf(cls_Power_Opower__increasing__iff_0,axiom,
( 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)
| ~ c_less(c_1,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Opower__increasing__iff_0) ).
cnf(cls_Power_Opower__increasing__iff_1,axiom,
( 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)
| ~ c_less(c_1,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Opower__increasing__iff_1) ).
cnf(cls_Power_Opower__inject__exp_0,axiom,
( V_m = V_n
| c_Nat_Opower(V_a,V_m,T_a) != c_Nat_Opower(V_a,V_n,T_a)
| ~ c_less(c_1,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Opower__inject__exp_0) ).
cnf(cls_Power_Opower__one_0,axiom,
( c_Nat_Opower(c_1,V_n,T_a) = c_1
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Opower__one_0) ).
cnf(cls_Power_Opower__one__right_0,axiom,
( c_Nat_Opower(V_y,c_1,T_a) = V_y
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Opower__one__right_0) ).
cnf(cls_Power_Opower__strict__increasing__iff_0,axiom,
( c_less(V_x,V_y,tc_nat)
| ~ c_less(c_Nat_Opower(V_b,V_x,T_a),c_Nat_Opower(V_b,V_y,T_a),T_a)
| ~ c_less(c_1,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Opower__strict__increasing__iff_0) ).
cnf(cls_Power_Opower__strict__increasing__iff_1,axiom,
( c_less(c_Nat_Opower(V_b,V_x,T_a),c_Nat_Opower(V_b,V_y,T_a),T_a)
| ~ c_less(c_1,V_b,T_a)
| ~ c_less(V_x,V_y,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Opower__strict__increasing__iff_1) ).
cnf(cls_Power_Orecpower__class_Oaxioms__1_0,axiom,
( c_Nat_Opower(V_a,c_0,T_a) = c_1
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Orecpower__class_Oaxioms__1_0) ).
cnf(cls_Power_Ozero__le__power__abs_0,axiom,
( c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(V_a,T_a),V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Ozero__le__power__abs_0) ).
cnf(cls_Power_Ozero__less__power__abs__iff_0,axiom,
( V_n = c_0
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,T_a),V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Ozero__less__power__abs__iff_0) ).
cnf(cls_Power_Ozero__less__power__abs__iff_1,axiom,
( V_a = c_0
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(V_a,T_a),V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Ozero__less__power__abs__iff_1) ).
cnf(cls_Power_Ozero__less__power__abs__iff_2,axiom,
( c_less(c_0,c_Nat_Opower(c_HOL_Oabs(V_a,T_a),c_0,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ class_Power_Orecpower(T_a) ),
file('MSC001-1.ax',cls_Power_Ozero__less__power__abs__iff_2) ).
cnf(cls_Product__Type_OPair__eq_0,axiom,
( V_a = V_a_H
| c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b) ),
file('MSC001-1.ax',cls_Product__Type_OPair__eq_0) ).
cnf(cls_Product__Type_OPair__eq_1,axiom,
( V_b = V_b_H
| c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b) ),
file('MSC001-1.ax',cls_Product__Type_OPair__eq_1) ).
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,
file('MSC001-1.ax',cls_Product__Type_Ofst__conv_0) ).
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,
file('MSC001-1.ax',cls_Product__Type_Opair__collapse_0) ).
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,
file('MSC001-1.ax',cls_Product__Type_Osnd__conv_0) ).
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),
file('MSC001-1.ax',cls_Product__Type_Osurj__pair_0) ).
cnf(cls_Relation_ODomain__Id_0,axiom,
c_Relation_ODomain(c_Relation_OId,T_a,T_a) = c_UNIV,
file('MSC001-1.ax',cls_Relation_ODomain__Id_0) ).
cnf(cls_Relation_ODomain__diag_0,axiom,
c_Relation_ODomain(c_Relation_Odiag(V_y,T_a),T_a,T_a) = V_y,
file('MSC001-1.ax',cls_Relation_ODomain__diag_0) ).
cnf(cls_Relation_ODomain__empty_0,axiom,
c_Relation_ODomain(c_emptyset,T_a,T_b) = c_emptyset,
file('MSC001-1.ax',cls_Relation_ODomain__empty_0) ).
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,
file('MSC001-1.ax',cls_Relation_OId__O__R_0) ).
cnf(cls_Relation_OImage__Id_0,axiom,
c_Relation_OImage(c_Relation_OId,V_y,T_a,T_a) = V_y,
file('MSC001-1.ax',cls_Relation_OImage__Id_0) ).
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),
file('MSC001-1.ax',cls_Relation_OImage__diag_0) ).
cnf(cls_Relation_OImage__empty_0,axiom,
c_Relation_OImage(V_R,c_emptyset,T_b,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Relation_OImage__empty_0) ).
cnf(cls_Relation_OImage__singleton__iff_0,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) ),
file('MSC001-1.ax',cls_Relation_OImage__singleton__iff_0) ).
cnf(cls_Relation_OImage__singleton__iff_1,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)) ),
file('MSC001-1.ax',cls_Relation_OImage__singleton__iff_1) ).
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,
file('MSC001-1.ax',cls_Relation_OR__O__Id_0) ).
cnf(cls_Relation_ORange__Id_0,axiom,
c_Relation_ORange(c_Relation_OId,T_a,T_a) = c_UNIV,
file('MSC001-1.ax',cls_Relation_ORange__Id_0) ).
cnf(cls_Relation_ORange__diag_0,axiom,
c_Relation_ORange(c_Relation_Odiag(V_y,T_a),T_a,T_a) = V_y,
file('MSC001-1.ax',cls_Relation_ORange__diag_0) ).
cnf(cls_Relation_ORange__empty_0,axiom,
c_Relation_ORange(c_emptyset,T_b,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Relation_ORange__empty_0) ).
cnf(cls_Relation_Oconverse__Id_0,axiom,
c_Relation_Oconverse(c_Relation_OId,T_a,T_a) = c_Relation_OId,
file('MSC001-1.ax',cls_Relation_Oconverse__Id_0) ).
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,
file('MSC001-1.ax',cls_Relation_Oconverse__converse_0) ).
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),
file('MSC001-1.ax',cls_Relation_Oconverse__diag_0) ).
cnf(cls_Relation_Oconverse__iff_0,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)) ),
file('MSC001-1.ax',cls_Relation_Oconverse__iff_0) ).
cnf(cls_Relation_Oconverse__iff_1,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)) ),
file('MSC001-1.ax',cls_Relation_Oconverse__iff_1) ).
cnf(cls_Relation_Odiag__empty_0,axiom,
c_Relation_Odiag(c_emptyset,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Relation_Odiag__empty_0) ).
cnf(cls_Relation_Opair__in__Id__conv_0,axiom,
( V_a = V_b
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)) ),
file('MSC001-1.ax',cls_Relation_Opair__in__Id__conv_0) ).
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)),
file('MSC001-1.ax',cls_Relation_Opair__in__Id__conv_1) ).
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,
file('MSC001-1.ax',cls_Relation__Power_Orel__pow__1_0) ).
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,
file('MSC001-1.ax',cls_Relation__Power_Orelpow_Osimps__1_0) ).
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),
file('MSC001-1.ax',cls_Relation__Power_Orelpow_Osimps__2_0) ).
cnf(cls_Ring__and__Field_Oabs__divide_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oabs__divide_0) ).
cnf(cls_Ring__and__Field_Oabs__inverse_0,axiom,
( c_HOL_Oabs(c_HOL_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse(c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oabs__inverse_0) ).
cnf(cls_Ring__and__Field_Oabs__one_0,axiom,
( c_HOL_Oabs(c_1,T_a) = c_1
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oabs__one_0) ).
cnf(cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0,axiom,
( c_0 != c_1
| ~ class_Ring__and__Field_Oaxclass__0__neq__1(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0) ).
cnf(cls_Ring__and__Field_Odivide__1_0,axiom,
( c_divide(V_y,c_1,T_a) = V_y
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__1_0) ).
cnf(cls_Ring__and__Field_Odivide__cancel__left_0,axiom,
( V_c = c_0
| V_a = V_b
| c_divide(V_c,V_a,T_a) != c_divide(V_c,V_b,T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__cancel__left_0) ).
cnf(cls_Ring__and__Field_Odivide__cancel__left_1,axiom,
( c_divide(c_0,V_a,T_a) = c_divide(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__cancel__left_1) ).
cnf(cls_Ring__and__Field_Odivide__cancel__right_0,axiom,
( V_c = c_0
| V_a = V_b
| c_divide(V_a,V_c,T_a) != c_divide(V_b,V_c,T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__cancel__right_0) ).
cnf(cls_Ring__and__Field_Odivide__cancel__right_1,axiom,
( c_divide(V_a,c_0,T_a) = c_divide(V_b,c_0,T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__cancel__right_1) ).
cnf(cls_Ring__and__Field_Odivide__divide__eq__left_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__divide__eq__left_0) ).
cnf(cls_Ring__and__Field_Odivide__divide__eq__right_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__divide__eq__right_0) ).
cnf(cls_Ring__and__Field_Odivide__eq__0__iff_0,axiom,
( V_a = c_0
| V_b = c_0
| c_divide(V_a,V_b,T_a) != c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__eq__0__iff_0) ).
cnf(cls_Ring__and__Field_Odivide__eq__0__iff_1,axiom,
( c_divide(c_0,V_b,T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__eq__0__iff_1) ).
cnf(cls_Ring__and__Field_Odivide__eq__0__iff_2,axiom,
( c_divide(V_a,c_0,T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__eq__0__iff_2) ).
cnf(cls_Ring__and__Field_Odivide__eq__1__iff_1,axiom,
( V_a = V_b
| c_divide(V_a,V_b,T_a) != c_1
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__eq__1__iff_1) ).
cnf(cls_Ring__and__Field_Odivide__eq__eq__1_0,axiom,
( c_divide(V_b,c_0,T_a) != c_1
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__eq__eq__1_0) ).
cnf(cls_Ring__and__Field_Odivide__eq__eq__1_1,axiom,
( V_a = V_b
| c_divide(V_b,V_a,T_a) != c_1
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__eq__eq__1_1) ).
cnf(cls_Ring__and__Field_Odivide__eq__eq__1_2,axiom,
( c_divide(V_x,V_x,T_a) = c_1
| V_x = c_0
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__eq__eq__1_2) ).
cnf(cls_Ring__and__Field_Odivide__le__0__1__iff_0,axiom,
( c_lessequals(V_b,c_0,T_a)
| ~ c_lessequals(c_divide(c_1,V_b,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__le__0__1__iff_0) ).
cnf(cls_Ring__and__Field_Odivide__le__0__1__iff_1,axiom,
( c_lessequals(c_divide(c_1,V_b,T_a),c_0,T_a)
| ~ c_lessequals(V_b,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__le__0__1__iff_1) ).
cnf(cls_Ring__and__Field_Odivide__le__eq__1__neg_0,axiom,
( c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_divide(V_b,V_a,T_a),c_1,T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__le__eq__1__neg_0) ).
cnf(cls_Ring__and__Field_Odivide__le__eq__1__neg_1,axiom,
( c_lessequals(c_divide(V_b,V_a,T_a),c_1,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__le__eq__1__neg_1) ).
cnf(cls_Ring__and__Field_Odivide__le__eq__1__pos_0,axiom,
( c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(c_divide(V_b,V_a,T_a),c_1,T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__le__eq__1__pos_0) ).
cnf(cls_Ring__and__Field_Odivide__le__eq__1__pos_1,axiom,
( c_lessequals(c_divide(V_b,V_a,T_a),c_1,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__le__eq__1__pos_1) ).
cnf(cls_Ring__and__Field_Odivide__less__0__1__iff_0,axiom,
( c_less(V_b,c_0,T_a)
| ~ c_less(c_divide(c_1,V_b,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__less__0__1__iff_0) ).
cnf(cls_Ring__and__Field_Odivide__less__0__1__iff_1,axiom,
( c_less(c_divide(c_1,V_b,T_a),c_0,T_a)
| ~ c_less(V_b,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__less__0__1__iff_1) ).
cnf(cls_Ring__and__Field_Odivide__less__eq__1__neg_0,axiom,
( c_less(V_a,V_b,T_a)
| ~ c_less(c_divide(V_b,V_a,T_a),c_1,T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__less__eq__1__neg_0) ).
cnf(cls_Ring__and__Field_Odivide__less__eq__1__neg_1,axiom,
( c_less(c_divide(V_b,V_a,T_a),c_1,T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_less(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__less__eq__1__neg_1) ).
cnf(cls_Ring__and__Field_Odivide__less__eq__1__pos_0,axiom,
( c_less(V_b,V_a,T_a)
| ~ c_less(c_divide(V_b,V_a,T_a),c_1,T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__less__eq__1__pos_0) ).
cnf(cls_Ring__and__Field_Odivide__less__eq__1__pos_1,axiom,
( c_less(c_divide(V_b,V_a,T_a),c_1,T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_less(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__less__eq__1__pos_1) ).
cnf(cls_Ring__and__Field_Odivide__minus__left_0,axiom,
( c_divide(c_uminus(V_a,T_a),V_b,T_a) = c_uminus(c_divide(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__minus__left_0) ).
cnf(cls_Ring__and__Field_Odivide__minus__right_0,axiom,
( c_divide(V_a,c_uminus(V_b,T_a),T_a) = c_uminus(c_divide(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__minus__right_0) ).
cnf(cls_Ring__and__Field_Odivide__self__if_0,axiom,
( c_divide(c_0,c_0,T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Odivide__self__if_0) ).
cnf(cls_Ring__and__Field_Oeq__divide__eq__1_0,axiom,
( c_1 != c_divide(V_b,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oeq__divide__eq__1_0) ).
cnf(cls_Ring__and__Field_Oeq__divide__eq__1_1,axiom,
( V_a = V_b
| c_1 != c_divide(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oeq__divide__eq__1_1) ).
cnf(cls_Ring__and__Field_Oeq__divide__eq__1_2,axiom,
( c_1 = c_divide(V_x,V_x,T_a)
| V_x = c_0
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oeq__divide__eq__1_2) ).
cnf(cls_Ring__and__Field_Ofield__class_Oaxioms__1_0,axiom,
( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
cnf(cls_Ring__and__Field_Ofield__mult__cancel__left_0,axiom,
( V_c = c_0
| V_a = V_b
| c_times(V_c,V_a,T_a) != c_times(V_c,V_b,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ofield__mult__cancel__left_0) ).
cnf(cls_Ring__and__Field_Ofield__mult__cancel__left_1,axiom,
( c_times(c_0,V_a,T_a) = c_times(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ofield__mult__cancel__left_1) ).
cnf(cls_Ring__and__Field_Ofield__mult__cancel__right_0,axiom,
( V_c = c_0
| V_a = V_b
| c_times(V_a,V_c,T_a) != c_times(V_b,V_c,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ofield__mult__cancel__right_0) ).
cnf(cls_Ring__and__Field_Ofield__mult__cancel__right_1,axiom,
( c_times(V_a,c_0,T_a) = c_times(V_b,c_0,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ofield__mult__cancel__right_1) ).
cnf(cls_Ring__and__Field_Oinverse__divide_0,axiom,
( c_HOL_Oinverse(c_divide(V_a,V_b,T_a),T_a) = c_divide(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__divide_0) ).
cnf(cls_Ring__and__Field_Oinverse__eq__1__iff_0,axiom,
( V_x = c_1
| c_HOL_Oinverse(V_x,T_a) != c_1
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__eq__1__iff_0) ).
cnf(cls_Ring__and__Field_Oinverse__eq__1__iff_1,axiom,
( c_HOL_Oinverse(c_1,T_a) = c_1
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__eq__1__iff_1) ).
cnf(cls_Ring__and__Field_Oinverse__eq__iff__eq_0,axiom,
( V_a = V_b
| c_HOL_Oinverse(V_a,T_a) != c_HOL_Oinverse(V_b,T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__eq__iff__eq_0) ).
cnf(cls_Ring__and__Field_Oinverse__inverse__eq_0,axiom,
( c_HOL_Oinverse(c_HOL_Oinverse(V_y,T_a),T_a) = V_y
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__inverse__eq_0) ).
cnf(cls_Ring__and__Field_Oinverse__le__iff__le_0,axiom,
( 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)
| ~ c_less(c_0,V_a,T_a)
| ~ c_less(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__le__iff__le_0) ).
cnf(cls_Ring__and__Field_Oinverse__le__iff__le_1,axiom,
( 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)
| ~ c_less(c_0,V_a,T_a)
| ~ c_less(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__le__iff__le_1) ).
cnf(cls_Ring__and__Field_Oinverse__le__iff__le__neg_0,axiom,
( 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)
| ~ c_less(V_a,c_0,T_a)
| ~ c_less(V_b,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__le__iff__le__neg_0) ).
cnf(cls_Ring__and__Field_Oinverse__le__iff__le__neg_1,axiom,
( 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)
| ~ c_less(V_a,c_0,T_a)
| ~ c_less(V_b,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__le__iff__le__neg_1) ).
cnf(cls_Ring__and__Field_Oinverse__less__iff__less_0,axiom,
( c_less(V_b,V_a,T_a)
| ~ c_less(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_less(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__less__iff__less_0) ).
cnf(cls_Ring__and__Field_Oinverse__less__iff__less_1,axiom,
( c_less(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_less(c_0,V_b,T_a)
| ~ c_less(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__less__iff__less_1) ).
cnf(cls_Ring__and__Field_Oinverse__less__iff__less__neg_0,axiom,
( c_less(V_b,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_a,c_0,T_a)
| ~ c_less(V_b,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__less__iff__less__neg_0) ).
cnf(cls_Ring__and__Field_Oinverse__less__iff__less__neg_1,axiom,
( c_less(c_HOL_Oinverse(V_a,T_a),c_HOL_Oinverse(V_b,T_a),T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_less(V_b,c_0,T_a)
| ~ c_less(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__less__iff__less__neg_1) ).
cnf(cls_Ring__and__Field_Oinverse__minus__eq_0,axiom,
( c_HOL_Oinverse(c_uminus(V_a,T_a),T_a) = c_uminus(c_HOL_Oinverse(V_a,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__minus__eq_0) ).
cnf(cls_Ring__and__Field_Oinverse__mult__distrib_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__mult__distrib_0) ).
cnf(cls_Ring__and__Field_Oinverse__negative__iff__negative_0,axiom,
( c_less(V_a,c_0,T_a)
| ~ c_less(c_HOL_Oinverse(V_a,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__negative__iff__negative_0) ).
cnf(cls_Ring__and__Field_Oinverse__negative__iff__negative_1,axiom,
( c_less(c_HOL_Oinverse(V_a,T_a),c_0,T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__negative__iff__negative_1) ).
cnf(cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_0,axiom,
( c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,c_HOL_Oinverse(V_a,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_0) ).
cnf(cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_1,axiom,
( c_lessequals(c_0,c_HOL_Oinverse(V_a,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_1) ).
cnf(cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_0,axiom,
( c_lessequals(V_a,c_0,T_a)
| ~ c_lessequals(c_HOL_Oinverse(V_a,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_0) ).
cnf(cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_1,axiom,
( c_lessequals(c_HOL_Oinverse(V_a,T_a),c_0,T_a)
| ~ c_lessequals(V_a,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_1) ).
cnf(cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_0,axiom,
( V_a = c_0
| c_HOL_Oinverse(V_a,T_a) != c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_0) ).
cnf(cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_1,axiom,
( c_HOL_Oinverse(c_0,T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_1) ).
cnf(cls_Ring__and__Field_Oinverse__positive__iff__positive_0,axiom,
( c_less(c_0,V_a,T_a)
| ~ c_less(c_0,c_HOL_Oinverse(V_a,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__positive__iff__positive_0) ).
cnf(cls_Ring__and__Field_Oinverse__positive__iff__positive_1,axiom,
( c_less(c_0,c_HOL_Oinverse(V_a,T_a),T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oinverse__positive__iff__positive_1) ).
cnf(cls_Ring__and__Field_Ole__divide__eq__1__neg_0,axiom,
( c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(c_1,c_divide(V_b,V_a,T_a),T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ole__divide__eq__1__neg_0) ).
cnf(cls_Ring__and__Field_Ole__divide__eq__1__neg_1,axiom,
( c_lessequals(c_1,c_divide(V_b,V_a,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ole__divide__eq__1__neg_1) ).
cnf(cls_Ring__and__Field_Ole__divide__eq__1__pos_0,axiom,
( c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_1,c_divide(V_b,V_a,T_a),T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ole__divide__eq__1__pos_0) ).
cnf(cls_Ring__and__Field_Ole__divide__eq__1__pos_1,axiom,
( c_lessequals(c_1,c_divide(V_b,V_a,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ole__divide__eq__1__pos_1) ).
cnf(cls_Ring__and__Field_Oless__divide__eq__1__neg_0,axiom,
( c_less(V_b,V_a,T_a)
| ~ c_less(c_1,c_divide(V_b,V_a,T_a),T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oless__divide__eq__1__neg_0) ).
cnf(cls_Ring__and__Field_Oless__divide__eq__1__neg_1,axiom,
( c_less(c_1,c_divide(V_b,V_a,T_a),T_a)
| ~ c_less(V_a,c_0,T_a)
| ~ c_less(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oless__divide__eq__1__neg_1) ).
cnf(cls_Ring__and__Field_Oless__divide__eq__1__pos_0,axiom,
( c_less(V_a,V_b,T_a)
| ~ c_less(c_1,c_divide(V_b,V_a,T_a),T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oless__divide__eq__1__pos_0) ).
cnf(cls_Ring__and__Field_Oless__divide__eq__1__pos_1,axiom,
( c_less(c_1,c_divide(V_b,V_a,T_a),T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ c_less(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oless__divide__eq__1__pos_1) ).
cnf(cls_Ring__and__Field_Ominus__divide__divide_0,axiom,
( c_divide(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) = c_divide(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ominus__divide__divide_0) ).
cnf(cls_Ring__and__Field_Ominus__mult__minus_0,axiom,
( c_times(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) = c_times(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ominus__mult__minus_0) ).
cnf(cls_Ring__and__Field_Omult__cancel__left1_0,axiom,
( V_b = c_1
| V_c = c_0
| V_c != c_times(V_c,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__cancel__left1_0) ).
cnf(cls_Ring__and__Field_Omult__cancel__left1_1,axiom,
( c_0 = c_times(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__cancel__left1_1) ).
cnf(cls_Ring__and__Field_Omult__cancel__left1_2,axiom,
( V_c = c_times(V_c,c_1,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__cancel__left1_2) ).
cnf(cls_Ring__and__Field_Omult__cancel__left2_0,axiom,
( V_a = c_1
| V_c = c_0
| c_times(V_c,V_a,T_a) != V_c
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__cancel__left2_0) ).
cnf(cls_Ring__and__Field_Omult__cancel__right1_0,axiom,
( V_b = c_1
| V_c = c_0
| V_c != c_times(V_b,V_c,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__cancel__right1_0) ).
cnf(cls_Ring__and__Field_Omult__cancel__right1_1,axiom,
( c_0 = c_times(V_b,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__cancel__right1_1) ).
cnf(cls_Ring__and__Field_Omult__cancel__right1_2,axiom,
( V_c = c_times(c_1,V_c,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__cancel__right1_2) ).
cnf(cls_Ring__and__Field_Omult__cancel__right2_0,axiom,
( V_a = c_1
| V_c = c_0
| c_times(V_a,V_c,T_a) != V_c
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__cancel__right2_0) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if1_0,axiom,
( c_divide(c_0,c_times(c_0,V_b,T_a),T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__left__if1_0) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if1_1,axiom,
( c_divide(V_c,c_times(V_c,V_b,T_a),T_a) = c_divide(c_1,V_b,T_a)
| V_c = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__left__if1_1) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if2_0,axiom,
( c_divide(c_times(c_0,V_a,T_a),c_0,T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__left__if2_0) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if2_1,axiom,
( c_divide(c_times(V_c,V_a,T_a),V_c,T_a) = V_a
| V_c = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__left__if2_1) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if_0,axiom,
( c_divide(c_times(c_0,V_a,T_a),c_times(c_0,V_b,T_a),T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__left__if_0) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__left__if_1,axiom,
( 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)
| V_c = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__left__if_1) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if1_0,axiom,
( c_divide(c_0,c_times(V_b,c_0,T_a),T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__right__if1_0) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if1_1,axiom,
( c_divide(V_c,c_times(V_b,V_c,T_a),T_a) = c_divide(c_1,V_b,T_a)
| V_c = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__right__if1_1) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if2_0,axiom,
( c_divide(c_times(V_a,c_0,T_a),c_0,T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__right__if2_0) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if2_1,axiom,
( c_divide(c_times(V_a,V_c,T_a),V_c,T_a) = V_a
| V_c = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__right__if2_1) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if_0,axiom,
( c_divide(c_times(V_a,c_0,T_a),c_times(V_b,c_0,T_a),T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__right__if_0) ).
cnf(cls_Ring__and__Field_Omult__divide__cancel__right__if_1,axiom,
( 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)
| V_c = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__divide__cancel__right__if_1) ).
cnf(cls_Ring__and__Field_Omult__eq__0__iff_0,axiom,
( V_a = c_0
| V_b = c_0
| c_times(V_a,V_b,T_a) != c_0
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
cnf(cls_Ring__and__Field_Omult__minus__left_0,axiom,
( c_times(c_uminus(V_a,T_a),V_b,T_a) = c_uminus(c_times(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__minus__left_0) ).
cnf(cls_Ring__and__Field_Omult__minus__right_0,axiom,
( c_times(V_a,c_uminus(V_b,T_a),T_a) = c_uminus(c_times(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__minus__right_0) ).
cnf(cls_Ring__and__Field_Omult__zero__left_0,axiom,
( c_times(c_0,V_a,T_a) = c_0
| ~ class_Ring__and__Field_Osemiring__0__cancel(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__zero__left_0) ).
cnf(cls_Ring__and__Field_Omult__zero__right_0,axiom,
( c_times(V_a,c_0,T_a) = c_0
| ~ class_Ring__and__Field_Osemiring__0__cancel(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Omult__zero__right_0) ).
cnf(cls_Ring__and__Field_Onot__one__le__zero_0,axiom,
( ~ c_lessequals(c_1,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Onot__one__le__zero_0) ).
cnf(cls_Ring__and__Field_Onot__one__less__zero_0,axiom,
( ~ c_less(c_1,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Onot__one__less__zero_0) ).
cnf(cls_Ring__and__Field_Oone__divide__eq__0__iff_0,axiom,
( V_a = c_0
| c_divide(c_1,V_a,T_a) != c_0
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oone__divide__eq__0__iff_0) ).
cnf(cls_Ring__and__Field_Oone__divide__eq__0__iff_1,axiom,
( c_divide(c_1,c_0,T_a) = c_0
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oone__divide__eq__0__iff_1) ).
cnf(cls_Ring__and__Field_Oone__eq__divide__iff_1,axiom,
( V_a = V_b
| c_1 != c_divide(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oone__eq__divide__iff_1) ).
cnf(cls_Ring__and__Field_Oone__neq__zero_0,axiom,
( c_1 != c_0
| ~ class_Ring__and__Field_Oaxclass__0__neq__1(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oone__neq__zero_0) ).
cnf(cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0,axiom,
( c_less(c_0,c_1,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
cnf(cls_Ring__and__Field_Oright__inverse_0,axiom,
( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Oright__inverse_0) ).
cnf(cls_Ring__and__Field_Otimes__divide__eq__1_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Otimes__divide__eq__1_0) ).
cnf(cls_Ring__and__Field_Otimes__divide__eq__2_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Otimes__divide__eq__2_0) ).
cnf(cls_Ring__and__Field_Otimes__divide__self__left_0,axiom,
( c_times(c_divide(V_b,c_0,T_a),c_0,T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Otimes__divide__self__left_0) ).
cnf(cls_Ring__and__Field_Otimes__divide__self__left_1,axiom,
( c_times(c_divide(V_b,V_a,T_a),V_a,T_a) = V_b
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Otimes__divide__self__left_1) ).
cnf(cls_Ring__and__Field_Otimes__divide__self__right_0,axiom,
( c_times(c_0,c_divide(V_b,c_0,T_a),T_a) = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Otimes__divide__self__right_0) ).
cnf(cls_Ring__and__Field_Otimes__divide__self__right_1,axiom,
( c_times(V_a,c_divide(V_b,V_a,T_a),T_a) = V_b
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Otimes__divide__self__right_1) ).
cnf(cls_Ring__and__Field_Ozero__eq__1__divide__iff_0,axiom,
( V_a = c_0
| c_0 != c_divide(c_1,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ozero__eq__1__divide__iff_0) ).
cnf(cls_Ring__and__Field_Ozero__eq__1__divide__iff_1,axiom,
( c_0 = c_divide(c_1,c_0,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ozero__eq__1__divide__iff_1) ).
cnf(cls_Ring__and__Field_Ozero__le__divide__1__iff_0,axiom,
( c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,c_divide(c_1,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ozero__le__divide__1__iff_0) ).
cnf(cls_Ring__and__Field_Ozero__le__divide__1__iff_1,axiom,
( c_lessequals(c_0,c_divide(c_1,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ozero__le__divide__1__iff_1) ).
cnf(cls_Ring__and__Field_Ozero__le__one_0,axiom,
( c_lessequals(c_0,c_1,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ozero__le__one_0) ).
cnf(cls_Ring__and__Field_Ozero__less__divide__1__iff_0,axiom,
( c_less(c_0,V_b,T_a)
| ~ c_less(c_0,c_divide(c_1,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ozero__less__divide__1__iff_0) ).
cnf(cls_Ring__and__Field_Ozero__less__divide__1__iff_1,axiom,
( c_less(c_0,c_divide(c_1,V_b,T_a),T_a)
| ~ c_less(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('MSC001-1.ax',cls_Ring__and__Field_Ozero__less__divide__1__iff_1) ).
cnf(cls_SetInterval_OCompl__atLeast_0,axiom,
( c_uminus(c_SetInterval_OatLeast(V_k,T_a),tc_set(T_a)) = c_SetInterval_OlessThan(V_k,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OCompl__atLeast_0) ).
cnf(cls_SetInterval_OCompl__atMost_0,axiom,
( c_uminus(c_SetInterval_OatMost(V_k,T_a),tc_set(T_a)) = c_SetInterval_OgreaterThan(V_k,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OCompl__atMost_0) ).
cnf(cls_SetInterval_OCompl__greaterThan_0,axiom,
( c_uminus(c_SetInterval_OgreaterThan(V_k,T_a),tc_set(T_a)) = c_SetInterval_OatMost(V_k,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OCompl__greaterThan_0) ).
cnf(cls_SetInterval_OCompl__lessThan_0,axiom,
( c_uminus(c_SetInterval_OlessThan(V_k,T_a),tc_set(T_a)) = c_SetInterval_OatLeast(V_k,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OCompl__lessThan_0) ).
cnf(cls_SetInterval_OatLeastAtMost__empty_0,axiom,
( c_SetInterval_OatLeastAtMost(V_m,V_n,T_a) = c_emptyset
| ~ c_less(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeastAtMost__empty_0) ).
cnf(cls_SetInterval_OatLeastAtMost__iff_0,axiom,
( c_lessequals(V_l,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeastAtMost(V_l,V_u,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeastAtMost__iff_0) ).
cnf(cls_SetInterval_OatLeastAtMost__iff_1,axiom,
( c_lessequals(V_i,V_u,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeastAtMost(V_l,V_u,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeastAtMost__iff_1) ).
cnf(cls_SetInterval_OatLeastAtMost__iff_2,axiom,
( c_in(V_i,c_SetInterval_OatLeastAtMost(V_l,V_u,T_a),T_a)
| ~ c_lessequals(V_l,V_i,T_a)
| ~ c_lessequals(V_i,V_u,T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeastAtMost__iff_2) ).
cnf(cls_SetInterval_OatLeastAtMost__singleton_0,axiom,
( c_SetInterval_OatLeastAtMost(V_a,V_a,T_a) = c_insert(V_a,c_emptyset,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeastAtMost__singleton_0) ).
cnf(cls_SetInterval_OatLeastLessThan__empty_0,axiom,
( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeastLessThan__empty_0) ).
cnf(cls_SetInterval_OatLeastLessThan__iff_0,axiom,
( c_lessequals(V_l,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeastLessThan(V_l,V_u,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeastLessThan__iff_0) ).
cnf(cls_SetInterval_OatLeastLessThan__iff_1,axiom,
( c_less(V_i,V_u,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeastLessThan(V_l,V_u,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeastLessThan__iff_1) ).
cnf(cls_SetInterval_OatLeastLessThan__iff_2,axiom,
( c_in(V_i,c_SetInterval_OatLeastLessThan(V_l,V_u,T_a),T_a)
| ~ c_lessequals(V_l,V_i,T_a)
| ~ c_less(V_i,V_u,T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeastLessThan__iff_2) ).
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),
file('MSC001-1.ax',cls_SetInterval_OatLeastLessThan__singleton_0) ).
cnf(cls_SetInterval_OatLeast__0_0,axiom,
c_SetInterval_OatLeast(c_0,tc_nat) = c_UNIV,
file('MSC001-1.ax',cls_SetInterval_OatLeast__0_0) ).
cnf(cls_SetInterval_OatLeast__eq__iff_0,axiom,
( V_x = V_y
| c_SetInterval_OatLeast(V_x,T_a) != c_SetInterval_OatLeast(V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeast__eq__iff_0) ).
cnf(cls_SetInterval_OatLeast__iff_0,axiom,
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeast__iff_0) ).
cnf(cls_SetInterval_OatLeast__iff_1,axiom,
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ c_lessequals(V_k,V_i,T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeast__iff_1) ).
cnf(cls_SetInterval_OatLeast__subset__iff_0,axiom,
( 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))
| ~ class_Orderings_Oorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeast__subset__iff_0) ).
cnf(cls_SetInterval_OatLeast__subset__iff_1,axiom,
( 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)
| ~ class_Orderings_Oorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatLeast__subset__iff_1) ).
cnf(cls_SetInterval_OatMost__0_0,axiom,
c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
file('MSC001-1.ax',cls_SetInterval_OatMost__0_0) ).
cnf(cls_SetInterval_OatMost__eq__iff_0,axiom,
( V_x = V_y
| c_SetInterval_OatMost(V_x,T_a) != c_SetInterval_OatMost(V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatMost__eq__iff_0) ).
cnf(cls_SetInterval_OatMost__iff_0,axiom,
( c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatMost__iff_0) ).
cnf(cls_SetInterval_OatMost__iff_1,axiom,
( c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatMost__iff_1) ).
cnf(cls_SetInterval_OatMost__subset__iff_0,axiom,
( 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))
| ~ class_Orderings_Oorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatMost__subset__iff_0) ).
cnf(cls_SetInterval_OatMost__subset__iff_1,axiom,
( 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)
| ~ class_Orderings_Oorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OatMost__subset__iff_1) ).
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),
file('MSC001-1.ax',cls_SetInterval_Ocard__atLeastAtMost_0) ).
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)),
file('MSC001-1.ax',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).
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),
file('MSC001-1.ax',cls_SetInterval_Ocard__atLeastLessThan_0) ).
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)),
file('MSC001-1.ax',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
cnf(cls_SetInterval_Ocard__atMost_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OatMost(V_u,tc_nat),tc_nat) = c_Suc(V_u),
file('MSC001-1.ax',cls_SetInterval_Ocard__atMost_0) ).
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),
file('MSC001-1.ax',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
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)),
file('MSC001-1.ax',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
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),
file('MSC001-1.ax',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
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)),
file('MSC001-1.ax',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).
cnf(cls_SetInterval_Ocard__lessThan_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OlessThan(V_y,tc_nat),tc_nat) = V_y,
file('MSC001-1.ax',cls_SetInterval_Ocard__lessThan_0) ).
cnf(cls_SetInterval_OgreaterThanAtMost__empty_0,axiom,
( c_SetInterval_OgreaterThanAtMost(V_k,V_l,T_a) = c_emptyset
| ~ c_lessequals(V_l,V_k,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
cnf(cls_SetInterval_OgreaterThanAtMost__iff_0,axiom,
( c_less(V_l,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OgreaterThanAtMost(V_l,V_u,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
cnf(cls_SetInterval_OgreaterThanAtMost__iff_1,axiom,
( c_lessequals(V_i,V_u,T_a)
| ~ c_in(V_i,c_SetInterval_OgreaterThanAtMost(V_l,V_u,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
cnf(cls_SetInterval_OgreaterThanAtMost__iff_2,axiom,
( c_in(V_i,c_SetInterval_OgreaterThanAtMost(V_l,V_u,T_a),T_a)
| ~ c_lessequals(V_i,V_u,T_a)
| ~ c_less(V_l,V_i,T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
cnf(cls_SetInterval_OgreaterThanLessThan__iff_0,axiom,
( c_less(V_l,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OgreaterThanLessThan(V_l,V_u,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
cnf(cls_SetInterval_OgreaterThanLessThan__iff_1,axiom,
( c_less(V_i,V_u,T_a)
| ~ c_in(V_i,c_SetInterval_OgreaterThanLessThan(V_l,V_u,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
cnf(cls_SetInterval_OgreaterThanLessThan__iff_2,axiom,
( c_in(V_i,c_SetInterval_OgreaterThanLessThan(V_l,V_u,T_a),T_a)
| ~ c_less(V_l,V_i,T_a)
| ~ c_less(V_i,V_u,T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
cnf(cls_SetInterval_OgreaterThan__eq__iff_0,axiom,
( V_x = V_y
| c_SetInterval_OgreaterThan(V_x,T_a) != c_SetInterval_OgreaterThan(V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThan__eq__iff_0) ).
cnf(cls_SetInterval_OgreaterThan__iff_0,axiom,
( c_less(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OgreaterThan(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThan__iff_0) ).
cnf(cls_SetInterval_OgreaterThan__iff_1,axiom,
( c_in(V_i,c_SetInterval_OgreaterThan(V_k,T_a),T_a)
| ~ c_less(V_k,V_i,T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThan__iff_1) ).
cnf(cls_SetInterval_OgreaterThan__subset__iff_0,axiom,
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThan__subset__iff_0) ).
cnf(cls_SetInterval_OgreaterThan__subset__iff_1,axiom,
( 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)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OgreaterThan__subset__iff_1) ).
cnf(cls_SetInterval_Oivl__diff_0,axiom,
( 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)
| ~ c_lessequals(V_i,V_n,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_Oivl__diff_0) ).
cnf(cls_SetInterval_Oivl__subset_0,axiom,
( c_lessequals(V_j,V_i,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))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_Oivl__subset_0) ).
cnf(cls_SetInterval_Oivl__subset_1,axiom,
( c_lessequals(V_j,V_i,T_a)
| c_lessequals(V_j,V_n,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))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_Oivl__subset_1) ).
cnf(cls_SetInterval_Oivl__subset_2,axiom,
( 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_i,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_Oivl__subset_2) ).
cnf(cls_SetInterval_Oivl__subset_3,axiom,
( 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_n,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_Oivl__subset_3) ).
cnf(cls_SetInterval_OlessThan__0_0,axiom,
c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
file('MSC001-1.ax',cls_SetInterval_OlessThan__0_0) ).
cnf(cls_SetInterval_OlessThan__eq__iff_0,axiom,
( V_x = V_y
| c_SetInterval_OlessThan(V_x,T_a) != c_SetInterval_OlessThan(V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OlessThan__eq__iff_0) ).
cnf(cls_SetInterval_OlessThan__iff_0,axiom,
( c_less(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OlessThan(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OlessThan__iff_0) ).
cnf(cls_SetInterval_OlessThan__iff_1,axiom,
( c_in(V_i,c_SetInterval_OlessThan(V_k,T_a),T_a)
| ~ c_less(V_i,V_k,T_a)
| ~ class_Orderings_Oord(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OlessThan__iff_1) ).
cnf(cls_SetInterval_OlessThan__subset__iff_0,axiom,
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OlessThan__subset__iff_0) ).
cnf(cls_SetInterval_OlessThan__subset__iff_1,axiom,
( 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)
| ~ class_Orderings_Olinorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_OlessThan__subset__iff_1) ).
cnf(cls_SetInterval_Osingle__Diff__lessThan_0,axiom,
( 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)
| ~ class_Orderings_Oorder(T_a) ),
file('MSC001-1.ax',cls_SetInterval_Osingle__Diff__lessThan_0) ).
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),
file('MSC001-1.ax',cls_Set_OCompl__Diff__eq_0) ).
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),
file('MSC001-1.ax',cls_Set_OCompl__Int_0) ).
cnf(cls_Set_OCompl__UNIV__eq_0,axiom,
c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset,
file('MSC001-1.ax',cls_Set_OCompl__UNIV__eq_0) ).
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),
file('MSC001-1.ax',cls_Set_OCompl__Un_0) ).
cnf(cls_Set_OCompl__disjoint2_0,axiom,
c_inter(c_uminus(V_A,tc_set(T_a)),V_A,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Set_OCompl__disjoint2_0) ).
cnf(cls_Set_OCompl__disjoint_0,axiom,
c_inter(V_A,c_uminus(V_A,tc_set(T_a)),T_a) = c_emptyset,
file('MSC001-1.ax',cls_Set_OCompl__disjoint_0) ).
cnf(cls_Set_OCompl__empty__eq_0,axiom,
c_uminus(c_emptyset,tc_set(T_a)) = c_UNIV,
file('MSC001-1.ax',cls_Set_OCompl__empty__eq_0) ).
cnf(cls_Set_OCompl__eq__Compl__iff_0,axiom,
( V_A = V_B
| c_uminus(V_A,tc_set(T_a)) != c_uminus(V_B,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OCompl__eq__Compl__iff_0) ).
cnf(cls_Set_OCompl__iff_0,axiom,
( ~ c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('MSC001-1.ax',cls_Set_OCompl__iff_0) ).
cnf(cls_Set_OCompl__iff_1,axiom,
( c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a)
| c_in(V_c,V_A,T_a) ),
file('MSC001-1.ax',cls_Set_OCompl__iff_1) ).
cnf(cls_Set_OCompl__subset__Compl__iff_0,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)) ),
file('MSC001-1.ax',cls_Set_OCompl__subset__Compl__iff_0) ).
cnf(cls_Set_OCompl__subset__Compl__iff_1,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)) ),
file('MSC001-1.ax',cls_Set_OCompl__subset__Compl__iff_1) ).
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),
file('MSC001-1.ax',cls_Set_ODiff__Compl_0) ).
cnf(cls_Set_ODiff__UNIV_0,axiom,
c_minus(V_A,c_UNIV,tc_set(T_a)) = c_emptyset,
file('MSC001-1.ax',cls_Set_ODiff__UNIV_0) ).
cnf(cls_Set_ODiff__cancel_0,axiom,
c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset,
file('MSC001-1.ax',cls_Set_ODiff__cancel_0) ).
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,
file('MSC001-1.ax',cls_Set_ODiff__disjoint_0) ).
cnf(cls_Set_ODiff__empty_0,axiom,
c_minus(V_y,c_emptyset,tc_set(T_a)) = V_y,
file('MSC001-1.ax',cls_Set_ODiff__empty_0) ).
cnf(cls_Set_ODiff__eq__empty__iff_0,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_minus(V_A,V_B,tc_set(T_a)) != c_emptyset ),
file('MSC001-1.ax',cls_Set_ODiff__eq__empty__iff_0) ).
cnf(cls_Set_ODiff__eq__empty__iff_1,axiom,
( c_minus(V_A,V_B,tc_set(T_a)) = c_emptyset
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_ODiff__eq__empty__iff_1) ).
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)),
file('MSC001-1.ax',cls_Set_ODiff__idemp_0) ).
cnf(cls_Set_ODiff__iff_0,axiom,
( c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ),
file('MSC001-1.ax',cls_Set_ODiff__iff_0) ).
cnf(cls_Set_ODiff__iff_1,axiom,
( ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('MSC001-1.ax',cls_Set_ODiff__iff_1) ).
cnf(cls_Set_ODiff__iff_2,axiom,
( c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('MSC001-1.ax',cls_Set_ODiff__iff_2) ).
cnf(cls_Set_ODiff__insert0_0,axiom,
( 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))
| c_in(V_x,V_A,T_a) ),
file('MSC001-1.ax',cls_Set_ODiff__insert0_0) ).
cnf(cls_Set_OInt__UNIV_0,axiom,
( V_A = c_UNIV
| c_inter(V_A,V_B,T_a) != c_UNIV ),
file('MSC001-1.ax',cls_Set_OInt__UNIV_0) ).
cnf(cls_Set_OInt__UNIV_1,axiom,
( V_B = c_UNIV
| c_inter(V_A,V_B,T_a) != c_UNIV ),
file('MSC001-1.ax',cls_Set_OInt__UNIV_1) ).
cnf(cls_Set_OInt__UNIV_2,axiom,
c_inter(c_UNIV,c_UNIV,T_a) = c_UNIV,
file('MSC001-1.ax',cls_Set_OInt__UNIV_2) ).
cnf(cls_Set_OInt__UNIV__left_0,axiom,
c_inter(c_UNIV,V_y,T_a) = V_y,
file('MSC001-1.ax',cls_Set_OInt__UNIV__left_0) ).
cnf(cls_Set_OInt__UNIV__right_0,axiom,
c_inter(V_y,c_UNIV,T_a) = V_y,
file('MSC001-1.ax',cls_Set_OInt__UNIV__right_0) ).
cnf(cls_Set_OInt__absorb_0,axiom,
c_inter(V_y,V_y,T_a) = V_y,
file('MSC001-1.ax',cls_Set_OInt__absorb_0) ).
cnf(cls_Set_OInt__empty__left_0,axiom,
c_inter(c_emptyset,V_B,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Set_OInt__empty__left_0) ).
cnf(cls_Set_OInt__empty__right_0,axiom,
c_inter(V_A,c_emptyset,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Set_OInt__empty__right_0) ).
cnf(cls_Set_OInt__iff_0,axiom,
( c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
file('MSC001-1.ax',cls_Set_OInt__iff_0) ).
cnf(cls_Set_OInt__iff_1,axiom,
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
file('MSC001-1.ax',cls_Set_OInt__iff_1) ).
cnf(cls_Set_OInt__iff_2,axiom,
( c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('MSC001-1.ax',cls_Set_OInt__iff_2) ).
cnf(cls_Set_OInt__subset__iff_0,axiom,
( 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)) ),
file('MSC001-1.ax',cls_Set_OInt__subset__iff_0) ).
cnf(cls_Set_OInt__subset__iff_1,axiom,
( c_lessequals(V_C,V_B,tc_set(T_a))
| ~ c_lessequals(V_C,c_inter(V_A,V_B,T_a),tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OInt__subset__iff_1) ).
cnf(cls_Set_OInt__subset__iff_2,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))
| ~ c_lessequals(V_C,V_B,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OInt__subset__iff_2) ).
cnf(cls_Set_OInter__UNIV_0,axiom,
c_Inter(c_UNIV,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Set_OInter__UNIV_0) ).
cnf(cls_Set_OInter__UNIV__conv__1_0,axiom,
( V_U = c_UNIV
| c_Inter(V_A,T_a) != c_UNIV
| ~ c_in(V_U,V_A,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OInter__UNIV__conv__1_0) ).
cnf(cls_Set_OInter__UNIV__conv__1_1,axiom,
( c_Inter(V_A,T_a) = c_UNIV
| c_in(c_Main_OInter__UNIV__conv__1__1(V_A,T_a),V_A,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OInter__UNIV__conv__1_1) ).
cnf(cls_Set_OInter__UNIV__conv__1_2,axiom,
( c_Inter(V_A,T_a) = c_UNIV
| c_Main_OInter__UNIV__conv__1__1(V_A,T_a) != c_UNIV ),
file('MSC001-1.ax',cls_Set_OInter__UNIV__conv__1_2) ).
cnf(cls_Set_OInter__UNIV__conv__2_0,axiom,
( V_U = c_UNIV
| c_UNIV != c_Inter(V_A,T_a)
| ~ c_in(V_U,V_A,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OInter__UNIV__conv__2_0) ).
cnf(cls_Set_OInter__UNIV__conv__2_1,axiom,
( c_UNIV = c_Inter(V_A,T_a)
| c_in(c_Main_OInter__UNIV__conv__2__1(V_A,T_a),V_A,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OInter__UNIV__conv__2_1) ).
cnf(cls_Set_OInter__UNIV__conv__2_2,axiom,
( c_UNIV = c_Inter(V_A,T_a)
| c_Main_OInter__UNIV__conv__2__1(V_A,T_a) != c_UNIV ),
file('MSC001-1.ax',cls_Set_OInter__UNIV__conv__2_2) ).
cnf(cls_Set_OInter__empty_0,axiom,
c_Inter(c_emptyset,T_a) = c_UNIV,
file('MSC001-1.ax',cls_Set_OInter__empty_0) ).
cnf(cls_Set_OInter__iff_0,axiom,
( c_in(V_A,V_U,T_a)
| ~ c_in(V_A,c_Inter(V_C,T_a),T_a)
| ~ c_in(V_U,V_C,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OInter__iff_0) ).
cnf(cls_Set_OInter__iff_1,axiom,
( c_in(c_Main_OInter__iff__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_in(V_A,c_Inter(V_C,T_a),T_a) ),
file('MSC001-1.ax',cls_Set_OInter__iff_1) ).
cnf(cls_Set_OInter__iff_2,axiom,
( c_in(V_A,c_Inter(V_C,T_a),T_a)
| ~ c_in(V_A,c_Main_OInter__iff__1(V_A,V_C,T_a),T_a) ),
file('MSC001-1.ax',cls_Set_OInter__iff_2) ).
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),
file('MSC001-1.ax',cls_Set_OInter__insert_0) ).
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)),
file('MSC001-1.ax',cls_Set_OPow__Int__eq_0) ).
cnf(cls_Set_OPow__UNIV_0,axiom,
c_Pow(c_UNIV,T_a) = c_UNIV,
file('MSC001-1.ax',cls_Set_OPow__UNIV_0) ).
cnf(cls_Set_OPow__empty_0,axiom,
c_Pow(c_emptyset,T_a) = c_insert(c_emptyset,c_emptyset,tc_set(T_a)),
file('MSC001-1.ax',cls_Set_OPow__empty_0) ).
cnf(cls_Set_OPow__iff_0,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)) ),
file('MSC001-1.ax',cls_Set_OPow__iff_0) ).
cnf(cls_Set_OPow__iff_1,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)) ),
file('MSC001-1.ax',cls_Set_OPow__iff_1) ).
cnf(cls_Set_OUNIV__not__empty_0,axiom,
c_UNIV != c_emptyset,
file('MSC001-1.ax',cls_Set_OUNIV__not__empty_0) ).
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),
file('MSC001-1.ax',cls_Set_OUn__Diff__cancel2_0) ).
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),
file('MSC001-1.ax',cls_Set_OUn__Diff__cancel_0) ).
cnf(cls_Set_OUn__UNIV__left_0,axiom,
c_union(c_UNIV,V_B,T_a) = c_UNIV,
file('MSC001-1.ax',cls_Set_OUn__UNIV__left_0) ).
cnf(cls_Set_OUn__UNIV__right_0,axiom,
c_union(V_A,c_UNIV,T_a) = c_UNIV,
file('MSC001-1.ax',cls_Set_OUn__UNIV__right_0) ).
cnf(cls_Set_OUn__absorb_0,axiom,
c_union(V_y,V_y,T_a) = V_y,
file('MSC001-1.ax',cls_Set_OUn__absorb_0) ).
cnf(cls_Set_OUn__empty_0,axiom,
( V_A = c_emptyset
| c_union(V_A,V_B,T_a) != c_emptyset ),
file('MSC001-1.ax',cls_Set_OUn__empty_0) ).
cnf(cls_Set_OUn__empty_1,axiom,
( V_B = c_emptyset
| c_union(V_A,V_B,T_a) != c_emptyset ),
file('MSC001-1.ax',cls_Set_OUn__empty_1) ).
cnf(cls_Set_OUn__empty_2,axiom,
c_union(c_emptyset,c_emptyset,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Set_OUn__empty_2) ).
cnf(cls_Set_OUn__empty__left_0,axiom,
c_union(c_emptyset,V_y,T_a) = V_y,
file('MSC001-1.ax',cls_Set_OUn__empty__left_0) ).
cnf(cls_Set_OUn__empty__right_0,axiom,
c_union(V_y,c_emptyset,T_a) = V_y,
file('MSC001-1.ax',cls_Set_OUn__empty__right_0) ).
cnf(cls_Set_OUn__iff_0,axiom,
( c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
file('MSC001-1.ax',cls_Set_OUn__iff_0) ).
cnf(cls_Set_OUn__iff_1,axiom,
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('MSC001-1.ax',cls_Set_OUn__iff_1) ).
cnf(cls_Set_OUn__iff_2,axiom,
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('MSC001-1.ax',cls_Set_OUn__iff_2) ).
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),
file('MSC001-1.ax',cls_Set_OUn__insert__left_0) ).
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),
file('MSC001-1.ax',cls_Set_OUn__insert__right_0) ).
cnf(cls_Set_OUn__subset__iff_0,axiom,
( 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)) ),
file('MSC001-1.ax',cls_Set_OUn__subset__iff_0) ).
cnf(cls_Set_OUn__subset__iff_1,axiom,
( c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OUn__subset__iff_1) ).
cnf(cls_Set_OUn__subset__iff_2,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))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OUn__subset__iff_2) ).
cnf(cls_Set_OUnion__Pow__eq_0,axiom,
c_Union(c_Pow(V_y,T_a),T_a) = V_y,
file('MSC001-1.ax',cls_Set_OUnion__Pow__eq_0) ).
cnf(cls_Set_OUnion__UNIV_0,axiom,
c_Union(c_UNIV,T_a) = c_UNIV,
file('MSC001-1.ax',cls_Set_OUnion__UNIV_0) ).
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),
file('MSC001-1.ax',cls_Set_OUnion__Un__distrib_0) ).
cnf(cls_Set_OUnion__empty_0,axiom,
c_Union(c_emptyset,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Set_OUnion__empty_0) ).
cnf(cls_Set_OUnion__empty__conv_0,axiom,
( V_U = c_emptyset
| c_Union(V_A,T_a) != c_emptyset
| ~ c_in(V_U,V_A,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OUnion__empty__conv_0) ).
cnf(cls_Set_OUnion__empty__conv_1,axiom,
( c_Union(V_A,T_a) = c_emptyset
| c_in(c_Main_OUnion__empty__conv__1(V_A,T_a),V_A,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_OUnion__empty__conv_1) ).
cnf(cls_Set_OUnion__empty__conv_2,axiom,
( c_Union(V_A,T_a) = c_emptyset
| c_Main_OUnion__empty__conv__1(V_A,T_a) != c_emptyset ),
file('MSC001-1.ax',cls_Set_OUnion__empty__conv_2) ).
cnf(cls_Set_OUnion__iff_0,axiom,
( c_in(c_Main_OUnion__iff__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('MSC001-1.ax',cls_Set_OUnion__iff_0) ).
cnf(cls_Set_OUnion__iff_1,axiom,
( c_in(V_A,c_Main_OUnion__iff__1(V_A,V_C,T_a),T_a)
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('MSC001-1.ax',cls_Set_OUnion__iff_1) ).
cnf(cls_Set_OUnion__iff_2,axiom,
( c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_U,V_C,tc_set(T_a))
| ~ c_in(V_A,V_U,T_a) ),
file('MSC001-1.ax',cls_Set_OUnion__iff_2) ).
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),
file('MSC001-1.ax',cls_Set_OUnion__insert_0) ).
cnf(cls_Set_Oall__not__in__conv_0,axiom,
( V_A = c_emptyset
| c_in(c_Main_Oall__not__in__conv__1(V_A,T_a),V_A,T_a) ),
file('MSC001-1.ax',cls_Set_Oall__not__in__conv_0) ).
cnf(cls_Set_Ocontents__eq_0,axiom,
c_Set_Ocontents(c_insert(V_y,c_emptyset,T_a),T_a) = V_y,
file('MSC001-1.ax',cls_Set_Ocontents__eq_0) ).
cnf(cls_Set_Odisjoint__insert__1_0,axiom,
( c_inter(V_B,c_insert(V_a,V_A,T_a),T_a) != c_emptyset
| ~ c_in(V_a,V_B,T_a) ),
file('MSC001-1.ax',cls_Set_Odisjoint__insert__1_0) ).
cnf(cls_Set_Odisjoint__insert__1_1,axiom,
( c_inter(V_B,V_A,T_a) = c_emptyset
| c_inter(V_B,c_insert(V_a,V_A,T_a),T_a) != c_emptyset ),
file('MSC001-1.ax',cls_Set_Odisjoint__insert__1_1) ).
cnf(cls_Set_Odisjoint__insert__1_2,axiom,
( c_inter(V_B,c_insert(V_a,V_A,T_a),T_a) = c_emptyset
| c_in(V_a,V_B,T_a)
| c_inter(V_B,V_A,T_a) != c_emptyset ),
file('MSC001-1.ax',cls_Set_Odisjoint__insert__1_2) ).
cnf(cls_Set_Odisjoint__insert__2_0,axiom,
( c_emptyset != c_inter(V_A,c_insert(V_b,V_B,T_a),T_a)
| ~ c_in(V_b,V_A,T_a) ),
file('MSC001-1.ax',cls_Set_Odisjoint__insert__2_0) ).
cnf(cls_Set_Odisjoint__insert__2_1,axiom,
( c_emptyset = c_inter(V_A,V_B,T_a)
| c_emptyset != c_inter(V_A,c_insert(V_b,V_B,T_a),T_a) ),
file('MSC001-1.ax',cls_Set_Odisjoint__insert__2_1) ).
cnf(cls_Set_Odisjoint__insert__2_2,axiom,
( c_emptyset = c_inter(V_A,c_insert(V_b,V_B,T_a),T_a)
| c_in(V_b,V_A,T_a)
| c_emptyset != c_inter(V_A,V_B,T_a) ),
file('MSC001-1.ax',cls_Set_Odisjoint__insert__2_2) ).
cnf(cls_Set_Odouble__complement_0,axiom,
c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y,
file('MSC001-1.ax',cls_Set_Odouble__complement_0) ).
cnf(cls_Set_Oempty__Diff_0,axiom,
c_minus(c_emptyset,V_A,tc_set(T_a)) = c_emptyset,
file('MSC001-1.ax',cls_Set_Oempty__Diff_0) ).
cnf(cls_Set_Oempty__Union__conv_0,axiom,
( V_U = c_emptyset
| c_emptyset != c_Union(V_A,T_a)
| ~ c_in(V_U,V_A,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_Oempty__Union__conv_0) ).
cnf(cls_Set_Oempty__Union__conv_1,axiom,
( c_emptyset = c_Union(V_A,T_a)
| c_in(c_Main_Oempty__Union__conv__1(V_A,T_a),V_A,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_Oempty__Union__conv_1) ).
cnf(cls_Set_Oempty__Union__conv_2,axiom,
( c_emptyset = c_Union(V_A,T_a)
| c_Main_Oempty__Union__conv__1(V_A,T_a) != c_emptyset ),
file('MSC001-1.ax',cls_Set_Oempty__Union__conv_2) ).
cnf(cls_Set_Oempty__iff_0,axiom,
~ c_in(V_c,c_emptyset,T_a),
file('MSC001-1.ax',cls_Set_Oempty__iff_0) ).
cnf(cls_Set_Oempty__not__insert_0,axiom,
c_emptyset != c_insert(V_a,V_A,T_a),
file('MSC001-1.ax',cls_Set_Oempty__not__insert_0) ).
cnf(cls_Set_Oinsert__Diff1_0,axiom,
( 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))
| ~ c_in(V_x,V_B,T_a) ),
file('MSC001-1.ax',cls_Set_Oinsert__Diff1_0) ).
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),
file('MSC001-1.ax',cls_Set_Oinsert__Diff__single_0) ).
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),
file('MSC001-1.ax',cls_Set_Oinsert__absorb2_0) ).
cnf(cls_Set_Oinsert__disjoint__1_0,axiom,
( c_inter(c_insert(V_a,V_A,T_a),V_B,T_a) != c_emptyset
| ~ c_in(V_a,V_B,T_a) ),
file('MSC001-1.ax',cls_Set_Oinsert__disjoint__1_0) ).
cnf(cls_Set_Oinsert__disjoint__1_1,axiom,
( c_inter(V_A,V_B,T_a) = c_emptyset
| c_inter(c_insert(V_a,V_A,T_a),V_B,T_a) != c_emptyset ),
file('MSC001-1.ax',cls_Set_Oinsert__disjoint__1_1) ).
cnf(cls_Set_Oinsert__disjoint__1_2,axiom,
( c_inter(c_insert(V_a,V_A,T_a),V_B,T_a) = c_emptyset
| c_in(V_a,V_B,T_a)
| c_inter(V_A,V_B,T_a) != c_emptyset ),
file('MSC001-1.ax',cls_Set_Oinsert__disjoint__1_2) ).
cnf(cls_Set_Oinsert__disjoint__2_0,axiom,
( c_emptyset != c_inter(c_insert(V_a,V_A,T_a),V_B,T_a)
| ~ c_in(V_a,V_B,T_a) ),
file('MSC001-1.ax',cls_Set_Oinsert__disjoint__2_0) ).
cnf(cls_Set_Oinsert__disjoint__2_1,axiom,
( c_emptyset = c_inter(V_A,V_B,T_a)
| c_emptyset != c_inter(c_insert(V_a,V_A,T_a),V_B,T_a) ),
file('MSC001-1.ax',cls_Set_Oinsert__disjoint__2_1) ).
cnf(cls_Set_Oinsert__disjoint__2_2,axiom,
( c_emptyset = c_inter(c_insert(V_a,V_A,T_a),V_B,T_a)
| c_in(V_a,V_B,T_a)
| c_emptyset != c_inter(V_A,V_B,T_a) ),
file('MSC001-1.ax',cls_Set_Oinsert__disjoint__2_2) ).
cnf(cls_Set_Oinsert__iff_0,axiom,
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
file('MSC001-1.ax',cls_Set_Oinsert__iff_0) ).
cnf(cls_Set_Oinsert__iff_1,axiom,
c_in(V_x,c_insert(V_x,V_A,T_a),T_a),
file('MSC001-1.ax',cls_Set_Oinsert__iff_1) ).
cnf(cls_Set_Oinsert__iff_2,axiom,
( c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| ~ c_in(V_a,V_A,T_a) ),
file('MSC001-1.ax',cls_Set_Oinsert__iff_2) ).
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),
file('MSC001-1.ax',cls_Set_Oinsert__inter__insert_0) ).
cnf(cls_Set_Oinsert__not__empty_0,axiom,
c_insert(V_a,V_A,T_a) != c_emptyset,
file('MSC001-1.ax',cls_Set_Oinsert__not__empty_0) ).
cnf(cls_Set_Oinsert__subset_0,axiom,
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_Oinsert__subset_0) ).
cnf(cls_Set_Oinsert__subset_1,axiom,
( 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)) ),
file('MSC001-1.ax',cls_Set_Oinsert__subset_1) ).
cnf(cls_Set_Oinsert__subset_2,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))
| ~ c_in(V_x,V_B,T_a) ),
file('MSC001-1.ax',cls_Set_Oinsert__subset_2) ).
cnf(cls_Set_Onot__psubset__empty_0,axiom,
~ c_less(V_A,c_emptyset,tc_set(T_a)),
file('MSC001-1.ax',cls_Set_Onot__psubset__empty_0) ).
cnf(cls_Set_Osingleton__insert__inj__eq_0,axiom,
( V_a = V_b
| c_insert(V_b,c_emptyset,T_a) != c_insert(V_a,V_A,T_a) ),
file('MSC001-1.ax',cls_Set_Osingleton__insert__inj__eq_0) ).
cnf(cls_Set_Osingleton__insert__inj__eq_1,axiom,
( c_lessequals(V_A,c_insert(V_b,c_emptyset,T_a),tc_set(T_a))
| c_insert(V_b,c_emptyset,T_a) != c_insert(V_a,V_A,T_a) ),
file('MSC001-1.ax',cls_Set_Osingleton__insert__inj__eq_1) ).
cnf(cls_Set_Osingleton__insert__inj__eq_2,axiom,
( c_insert(V_x,c_emptyset,T_a) = c_insert(V_x,V_A,T_a)
| ~ c_lessequals(V_A,c_insert(V_x,c_emptyset,T_a),tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_Osingleton__insert__inj__eq_2) ).
cnf(cls_Set_Osingleton__insert__inj__eq_H_0,axiom,
( V_a = V_b
| c_insert(V_a,V_A,T_a) != c_insert(V_b,c_emptyset,T_a) ),
file('MSC001-1.ax',cls_Set_Osingleton__insert__inj__eq_H_0) ).
cnf(cls_Set_Osingleton__insert__inj__eq_H_1,axiom,
( c_lessequals(V_A,c_insert(V_b,c_emptyset,T_a),tc_set(T_a))
| c_insert(V_a,V_A,T_a) != c_insert(V_b,c_emptyset,T_a) ),
file('MSC001-1.ax',cls_Set_Osingleton__insert__inj__eq_H_1) ).
cnf(cls_Set_Osingleton__insert__inj__eq_H_2,axiom,
( c_insert(V_x,V_A,T_a) = c_insert(V_x,c_emptyset,T_a)
| ~ c_lessequals(V_A,c_insert(V_x,c_emptyset,T_a),tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_Osingleton__insert__inj__eq_H_2) ).
cnf(cls_Set_Osubset__UNIV_0,axiom,
c_lessequals(V_A,c_UNIV,tc_set(T_a)),
file('MSC001-1.ax',cls_Set_Osubset__UNIV_0) ).
cnf(cls_Set_Osubset__empty_0,axiom,
( V_A = c_emptyset
| ~ c_lessequals(V_A,c_emptyset,tc_set(T_a)) ),
file('MSC001-1.ax',cls_Set_Osubset__empty_0) ).
cnf(cls_Set_Osubset__empty_1,axiom,
c_lessequals(c_emptyset,c_emptyset,tc_set(T_a)),
file('MSC001-1.ax',cls_Set_Osubset__empty_1) ).
cnf(cls_Sum__Type_OInl__eq_0,axiom,
( V_x = V_y
| c_Sum__Type_OInl(V_x,T_a,T_b) != c_Sum__Type_OInl(V_y,T_a,T_b) ),
file('MSC001-1.ax',cls_Sum__Type_OInl__eq_0) ).
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),
file('MSC001-1.ax',cls_Sum__Type_OInl__not__Inr_0) ).
cnf(cls_Sum__Type_OInr__eq_0,axiom,
( V_x = V_y
| c_Sum__Type_OInr(V_x,T_b,T_a) != c_Sum__Type_OInr(V_y,T_b,T_a) ),
file('MSC001-1.ax',cls_Sum__Type_OInr__eq_0) ).
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),
file('MSC001-1.ax',cls_Sum__Type_OInr__not__Inl_0) ).
cnf(cls_Sum__Type_OUNIV__Plus__UNIV_0,axiom,
c_Sum__Type_OPlus(c_UNIV,c_UNIV,T_a,T_b) = c_UNIV,
file('MSC001-1.ax',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
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,
file('MSC001-1.ax',cls_Transitive__Closure_ODomain__rtrancl_0) ).
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,
file('MSC001-1.ax',cls_Transitive__Closure_ORange__rtrancl_0) ).
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),
file('MSC001-1.ax',cls_Transitive__Closure_Oreflcl__trancl_0) ).
cnf(cls_Transitive__Closure_Ortrancl__empty_0,axiom,
c_Transitive__Closure_Ortrancl(c_emptyset,T_a) = c_Relation_OId,
file('MSC001-1.ax',cls_Transitive__Closure_Ortrancl__empty_0) ).
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),
file('MSC001-1.ax',cls_Transitive__Closure_Ortrancl__idemp_0) ).
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),
file('MSC001-1.ax',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
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),
file('MSC001-1.ax',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
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),
file('MSC001-1.ax',cls_Transitive__Closure_Otrancl__domain_0) ).
cnf(cls_Transitive__Closure_Otrancl__empty_0,axiom,
c_Transitive__Closure_Otrancl(c_emptyset,T_a) = c_emptyset,
file('MSC001-1.ax',cls_Transitive__Closure_Otrancl__empty_0) ).
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),
file('MSC001-1.ax',cls_Transitive__Closure_Otrancl__range_0) ).
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),
file('MSC001-1.ax',cls_Transitive__Closure_Otrancl__reflcl_0) ).
cnf(cls_Wellfounded__Recursion_Oacyclic__converse_0,axiom,
( c_Wellfounded__Recursion_Oacyclic(V_r,T_a)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ),
file('MSC001-1.ax',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
cnf(cls_Wellfounded__Recursion_Oacyclic__converse_1,axiom,
( c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(V_r,T_a,T_a),T_a)
| ~ c_Wellfounded__Recursion_Oacyclic(V_r,T_a) ),
file('MSC001-1.ax',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
cnf(cls_Wellfounded__Recursion_Oacyclic__insert_0,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) ),
file('MSC001-1.ax',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
cnf(cls_Wellfounded__Recursion_Oacyclic__insert_1,axiom,
( ~ 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))
| ~ 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) ),
file('MSC001-1.ax',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
cnf(cls_Wellfounded__Recursion_Oacyclic__insert_2,axiom,
( 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))
| 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) ),
file('MSC001-1.ax',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
cnf(cls_Wellfounded__Recursion_Owf__insert_0,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) ),
file('MSC001-1.ax',cls_Wellfounded__Recursion_Owf__insert_0) ).
cnf(cls_Wellfounded__Recursion_Owf__insert_1,axiom,
( ~ 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))
| ~ 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) ),
file('MSC001-1.ax',cls_Wellfounded__Recursion_Owf__insert_1) ).
cnf(cls_Wellfounded__Recursion_Owf__insert_2,axiom,
( 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))
| 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) ),
file('MSC001-1.ax',cls_Wellfounded__Recursion_Owf__insert_2) ).
cnf(cls_Wellfounded__Recursion_Owf__not__refl_0,axiom,
( ~ c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Wellfounded__Recursion_Owf(V_r,T_a) ),
file('MSC001-1.ax',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
cnf(cls_Wellfounded__Relations_Oless__than__iff_0,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)) ),
file('MSC001-1.ax',cls_Wellfounded__Relations_Oless__than__iff_0) ).
cnf(cls_Wellfounded__Relations_Oless__than__iff_1,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) ),
file('MSC001-1.ax',cls_Wellfounded__Relations_Oless__than__iff_1) ).
cnf(cls_Message_OMPair__parts_0,axiom,
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('SWV005-0.ax',cls_Message_OMPair__parts_0) ).
cnf(cls_Message_OMPair__parts_1,axiom,
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('SWV005-0.ax',cls_Message_OMPair__parts_1) ).
cnf(cls_Message_Oagent_Odistinct__1_0,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OFriend(V_nat_H),
file('SWV005-0.ax',cls_Message_Oagent_Odistinct__1_0) ).
cnf(cls_Message_Oagent_Odistinct__2_0,axiom,
c_Message_Oagent_OFriend(V_nat_H) != c_Message_Oagent_OServer,
file('SWV005-0.ax',cls_Message_Oagent_Odistinct__2_0) ).
cnf(cls_Message_Oagent_Odistinct__3_0,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('SWV005-0.ax',cls_Message_Oagent_Odistinct__3_0) ).
cnf(cls_Message_Oagent_Odistinct__4_0,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('SWV005-0.ax',cls_Message_Oagent_Odistinct__4_0) ).
cnf(cls_Message_Oagent_Odistinct__5_0,axiom,
c_Message_Oagent_OFriend(V_nat) != c_Message_Oagent_OSpy,
file('SWV005-0.ax',cls_Message_Oagent_Odistinct__5_0) ).
cnf(cls_Message_Oagent_Odistinct__6_0,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(V_nat),
file('SWV005-0.ax',cls_Message_Oagent_Odistinct__6_0) ).
cnf(cls_Message_Oagent_Oinject_0,axiom,
( V_nat = V_nat_H
| c_Message_Oagent_OFriend(V_nat) != c_Message_Oagent_OFriend(V_nat_H) ),
file('SWV005-0.ax',cls_Message_Oagent_Oinject_0) ).
cnf(cls_Message_Oagent_Osize__1_0,axiom,
c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) = c_0,
file('SWV005-0.ax',cls_Message_Oagent_Osize__1_0) ).
cnf(cls_Message_Oagent_Osize__2_0,axiom,
c_Nat_Osize(c_Message_Oagent_OFriend(V_nat),tc_Message_Oagent) = c_0,
file('SWV005-0.ax',cls_Message_Oagent_Osize__2_0) ).
cnf(cls_Message_Oagent_Osize__3_0,axiom,
c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) = c_0,
file('SWV005-0.ax',cls_Message_Oagent_Osize__3_0) ).
cnf(cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0,axiom,
c_Message_OinvKey(c_Message_OinvKey(V_y)) = V_y,
file('SWV005-0.ax',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
cnf(cls_Message_OinvKey__eq_0,axiom,
( V_K = V_K_H
| c_Message_OinvKey(V_K) != c_Message_OinvKey(V_K_H) ),
file('SWV005-0.ax',cls_Message_OinvKey__eq_0) ).
cnf(cls_Message_OkeysFor__Un_0,axiom,
c_Message_OkeysFor(c_union(V_H,V_H_H,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(V_H),c_Message_OkeysFor(V_H_H),tc_nat),
file('SWV005-0.ax',cls_Message_OkeysFor__Un_0) ).
cnf(cls_Message_OkeysFor__empty_0,axiom,
c_Message_OkeysFor(c_emptyset) = c_emptyset,
file('SWV005-0.ax',cls_Message_OkeysFor__empty_0) ).
cnf(cls_Message_OkeysFor__insert__Agent_0,axiom,
c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(V_A),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H),
file('SWV005-0.ax',cls_Message_OkeysFor__insert__Agent_0) ).
cnf(cls_Message_OkeysFor__insert__Crypt_0,axiom,
c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(V_K),c_Message_OkeysFor(V_H),tc_nat),
file('SWV005-0.ax',cls_Message_OkeysFor__insert__Crypt_0) ).
cnf(cls_Message_OkeysFor__insert__Hash_0,axiom,
c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(V_X),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H),
file('SWV005-0.ax',cls_Message_OkeysFor__insert__Hash_0) ).
cnf(cls_Message_OkeysFor__insert__Key_0,axiom,
c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H),
file('SWV005-0.ax',cls_Message_OkeysFor__insert__Key_0) ).
cnf(cls_Message_OkeysFor__insert__MPair_0,axiom,
c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H),
file('SWV005-0.ax',cls_Message_OkeysFor__insert__MPair_0) ).
cnf(cls_Message_OkeysFor__insert__Nonce_0,axiom,
c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(V_N),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H),
file('SWV005-0.ax',cls_Message_OkeysFor__insert__Nonce_0) ).
cnf(cls_Message_OkeysFor__insert__Number_0,axiom,
c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(V_N),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H),
file('SWV005-0.ax',cls_Message_OkeysFor__insert__Number_0) ).
cnf(cls_Message_Omsg_Oinject__1_0,axiom,
( V_agent = V_agent_H
| c_Message_Omsg_OAgent(V_agent) != c_Message_Omsg_OAgent(V_agent_H) ),
file('SWV005-0.ax',cls_Message_Omsg_Oinject__1_0) ).
cnf(cls_Message_Omsg_Oinject__2_0,axiom,
( V_nat = V_nat_H
| c_Message_Omsg_ONumber(V_nat) != c_Message_Omsg_ONumber(V_nat_H) ),
file('SWV005-0.ax',cls_Message_Omsg_Oinject__2_0) ).
cnf(cls_Message_Omsg_Oinject__3_0,axiom,
( V_nat = V_nat_H
| c_Message_Omsg_ONonce(V_nat) != c_Message_Omsg_ONonce(V_nat_H) ),
file('SWV005-0.ax',cls_Message_Omsg_Oinject__3_0) ).
cnf(cls_Message_Omsg_Oinject__4_0,axiom,
( V_nat = V_nat_H
| c_Message_Omsg_OKey(V_nat) != c_Message_Omsg_OKey(V_nat_H) ),
file('SWV005-0.ax',cls_Message_Omsg_Oinject__4_0) ).
cnf(cls_Message_Omsg_Oinject__5_0,axiom,
( V_msg = V_msg_H
| c_Message_Omsg_OHash(V_msg) != c_Message_Omsg_OHash(V_msg_H) ),
file('SWV005-0.ax',cls_Message_Omsg_Oinject__5_0) ).
cnf(cls_Message_Omsg_Oinject__6_0,axiom,
( V_msg1 = V_msg1_H
| c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) ),
file('SWV005-0.ax',cls_Message_Omsg_Oinject__6_0) ).
cnf(cls_Message_Omsg_Oinject__6_1,axiom,
( V_msg2 = V_msg2_H
| c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) ),
file('SWV005-0.ax',cls_Message_Omsg_Oinject__6_1) ).
cnf(cls_Message_Omsg_Oinject__7_0,axiom,
( V_nat = V_nat_H
| c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) ),
file('SWV005-0.ax',cls_Message_Omsg_Oinject__7_0) ).
cnf(cls_Message_Omsg_Oinject__7_1,axiom,
( V_msg = V_msg_H
| c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) ),
file('SWV005-0.ax',cls_Message_Omsg_Oinject__7_1) ).
cnf(cls_Message_Omsg_Osize__1_0,axiom,
c_Nat_Osize(c_Message_Omsg_OAgent(V_agent),tc_Message_Omsg) = c_0,
file('SWV005-0.ax',cls_Message_Omsg_Osize__1_0) ).
cnf(cls_Message_Omsg_Osize__2_0,axiom,
c_Nat_Osize(c_Message_Omsg_ONumber(V_nat),tc_Message_Omsg) = c_0,
file('SWV005-0.ax',cls_Message_Omsg_Osize__2_0) ).
cnf(cls_Message_Omsg_Osize__3_0,axiom,
c_Nat_Osize(c_Message_Omsg_ONonce(V_nat),tc_Message_Omsg) = c_0,
file('SWV005-0.ax',cls_Message_Omsg_Osize__3_0) ).
cnf(cls_Message_Omsg_Osize__4_0,axiom,
c_Nat_Osize(c_Message_Omsg_OKey(V_nat),tc_Message_Omsg) = c_0,
file('SWV005-0.ax',cls_Message_Omsg_Osize__4_0) ).
cnf(cls_Message_Omsg_Osize__5_0,axiom,
c_Nat_Osize(c_Message_Omsg_OHash(V_msg),tc_Message_Omsg) = c_plus(c_Nat_Osize(V_msg,tc_Message_Omsg),c_Suc(c_0),tc_nat),
file('SWV005-0.ax',cls_Message_Omsg_Osize__5_0) ).
cnf(cls_Message_Omsg_Osize__6_0,axiom,
c_Nat_Osize(c_Message_Omsg_OMPair(V_msg1,V_msg2),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(V_msg1,tc_Message_Omsg),c_Nat_Osize(V_msg2,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat),
file('SWV005-0.ax',cls_Message_Omsg_Osize__6_0) ).
cnf(cls_Message_Omsg_Osize__7_0,axiom,
c_Nat_Osize(c_Message_Omsg_OCrypt(V_nat,V_msg),tc_Message_Omsg) = c_plus(c_Nat_Osize(V_msg,tc_Message_Omsg),c_Suc(c_0),tc_nat),
file('SWV005-0.ax',cls_Message_Omsg_Osize__7_0) ).
cnf(cls_Message_Oparts_OInj_0,axiom,
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,V_H,tc_Message_Omsg) ),
file('SWV005-0.ax',cls_Message_Oparts_OInj_0) ).
cnf(cls_Message_Oparts__Un_0,axiom,
c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),
file('SWV005-0.ax',cls_Message_Oparts__Un_0) ).
cnf(cls_Message_Oparts__emptyE_0,axiom,
~ c_in(V_X,c_Message_Oparts(c_emptyset),tc_Message_Omsg),
file('SWV005-0.ax',cls_Message_Oparts__emptyE_0) ).
cnf(cls_Message_Oparts__empty_0,axiom,
c_Message_Oparts(c_emptyset) = c_emptyset,
file('SWV005-0.ax',cls_Message_Oparts__empty_0) ).
cnf(cls_Message_Ostrange__Un__eq_0,axiom,
c_union(V_A,c_union(V_B,V_A,T_a),T_a) = c_union(V_B,V_A,T_a),
file('SWV005-0.ax',cls_Message_Ostrange__Un__eq_0) ).
cnf(cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0,axiom,
~ c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent),
file('SWV005-2.ax',cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0) ).
cnf(cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0,axiom,
c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent),
file('SWV005-2.ax',cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0) ).
cnf(cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0,axiom,
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).
cnf(cls_Event_Oevent_Odistinct__1_0,axiom,
c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OGets(V_agent_H,V_msg_H),
file('SWV005-2.ax',cls_Event_Oevent_Odistinct__1_0) ).
cnf(cls_Event_Oevent_Odistinct__2_0,axiom,
c_Event_Oevent_OGets(V_agent_H,V_msg_H) != c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg),
file('SWV005-2.ax',cls_Event_Oevent_Odistinct__2_0) ).
cnf(cls_Event_Oevent_Odistinct__3_0,axiom,
c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H),
file('SWV005-2.ax',cls_Event_Oevent_Odistinct__3_0) ).
cnf(cls_Event_Oevent_Odistinct__4_0,axiom,
c_Event_Oevent_ONotes(V_agent_H,V_msg_H) != c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg),
file('SWV005-2.ax',cls_Event_Oevent_Odistinct__4_0) ).
cnf(cls_Event_Oevent_Odistinct__5_0,axiom,
c_Event_Oevent_OGets(V_agent,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H),
file('SWV005-2.ax',cls_Event_Oevent_Odistinct__5_0) ).
cnf(cls_Event_Oevent_Odistinct__6_0,axiom,
c_Event_Oevent_ONotes(V_agent_H,V_msg_H) != c_Event_Oevent_OGets(V_agent,V_msg),
file('SWV005-2.ax',cls_Event_Oevent_Odistinct__6_0) ).
cnf(cls_Event_Oevent_Oinject__1_0,axiom,
( V_agent1 = V_agent1_H
| c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) ),
file('SWV005-2.ax',cls_Event_Oevent_Oinject__1_0) ).
cnf(cls_Event_Oevent_Oinject__1_1,axiom,
( V_agent2 = V_agent2_H
| c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) ),
file('SWV005-2.ax',cls_Event_Oevent_Oinject__1_1) ).
cnf(cls_Event_Oevent_Oinject__1_2,axiom,
( V_msg = V_msg_H
| c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) ),
file('SWV005-2.ax',cls_Event_Oevent_Oinject__1_2) ).
cnf(cls_Event_Oevent_Oinject__2_0,axiom,
( V_agent = V_agent_H
| c_Event_Oevent_OGets(V_agent,V_msg) != c_Event_Oevent_OGets(V_agent_H,V_msg_H) ),
file('SWV005-2.ax',cls_Event_Oevent_Oinject__2_0) ).
cnf(cls_Event_Oevent_Oinject__2_1,axiom,
( V_msg = V_msg_H
| c_Event_Oevent_OGets(V_agent,V_msg) != c_Event_Oevent_OGets(V_agent_H,V_msg_H) ),
file('SWV005-2.ax',cls_Event_Oevent_Oinject__2_1) ).
cnf(cls_Event_Oevent_Oinject__3_0,axiom,
( V_agent = V_agent_H
| c_Event_Oevent_ONotes(V_agent,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H) ),
file('SWV005-2.ax',cls_Event_Oevent_Oinject__3_0) ).
cnf(cls_Event_Oevent_Oinject__3_1,axiom,
( V_msg = V_msg_H
| c_Event_Oevent_ONotes(V_agent,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H) ),
file('SWV005-2.ax',cls_Event_Oevent_Oinject__3_1) ).
cnf(cls_Event_Oevent_Osize__1_0,axiom,
c_Nat_Osize(c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg),tc_Event_Oevent) = c_0,
file('SWV005-2.ax',cls_Event_Oevent_Osize__1_0) ).
cnf(cls_Event_Oevent_Osize__2_0,axiom,
c_Nat_Osize(c_Event_Oevent_OGets(V_agent,V_msg),tc_Event_Oevent) = c_0,
file('SWV005-2.ax',cls_Event_Oevent_Osize__2_0) ).
cnf(cls_Event_Oevent_Osize__3_0,axiom,
c_Nat_Osize(c_Event_Oevent_ONotes(V_agent,V_msg),tc_Event_Oevent) = c_0,
file('SWV005-2.ax',cls_Event_Oevent_Osize__3_0) ).
cnf(cls_Event_OkeysFor__synth_H_0,axiom,
( c_in(c_Message_Omsg_OKey(v_sko__uhi(V_H,V_K)),V_H,tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Osynth(V_H)),tc_nat) ),
file('SWV005-2.ax',cls_Event_OkeysFor__synth_H_0) ).
cnf(cls_Event_OkeysFor__synth_H_1,axiom,
( V_K = c_Message_OinvKey(v_sko__uhi(V_H,V_K))
| c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Osynth(V_H)),tc_nat) ),
file('SWV005-2.ax',cls_Event_OkeysFor__synth_H_1) ).
cnf(cls_Event_OkeysFor__synth_H_2,axiom,
( c_in(V_K,c_Message_OkeysFor(c_Message_Osynth(V_H)),tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(V_H),tc_nat) ),
file('SWV005-2.ax',cls_Event_OkeysFor__synth_H_2) ).
cnf(cls_Event_OkeysFor__synth_H_3,axiom,
( c_in(c_Message_OinvKey(V_U),c_Message_OkeysFor(c_Message_Osynth(V_H)),tc_nat)
| ~ c_in(c_Message_Omsg_OKey(V_U),V_H,tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Event_OkeysFor__synth_H_3) ).
cnf(cls_Event_Oknows_Oknows__Nil_0,axiom,
c_Event_Oknows(V_A,c_List_Olist_ONil) = c_Event_OinitState(V_A),
file('SWV005-2.ax',cls_Event_Oknows_Oknows__Nil_0) ).
cnf(cls_Event_Oknows__Spy__Gets_0,axiom,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(V_A,V_X),V_evs,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),
file('SWV005-2.ax',cls_Event_Oknows__Spy__Gets_0) ).
cnf(cls_Event_Oknows__Spy__Notes_0,axiom,
( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A,V_X),V_evs,tc_Event_Oevent)) = c_insert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)
| ~ c_in(V_A,c_Event_Obad,tc_Message_Oagent) ),
file('SWV005-2.ax',cls_Event_Oknows__Spy__Notes_0) ).
cnf(cls_Event_Oknows__Spy__Notes_1,axiom,
( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A,V_X),V_evs,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent) ),
file('SWV005-2.ax',cls_Event_Oknows__Spy__Notes_1) ).
cnf(cls_Event_Oknows__Spy__Says_0,axiom,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_insert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg),
file('SWV005-2.ax',cls_Event_Oknows__Spy__Says_0) ).
cnf(cls_Event_Oused__Gets_0,axiom,
c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(V_A,V_X),V_evs,tc_Event_Oevent)) = c_Event_Oused(V_evs),
file('SWV005-2.ax',cls_Event_Oused__Gets_0) ).
cnf(cls_Event_Oused__Notes_0,axiom,
c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A,V_X),V_evs,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(V_X,c_emptyset,tc_Message_Omsg)),c_Event_Oused(V_evs),tc_Message_Omsg),
file('SWV005-2.ax',cls_Event_Oused__Notes_0) ).
cnf(cls_Event_Oused__Says_0,axiom,
c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(V_X,c_emptyset,tc_Message_Omsg)),c_Event_Oused(V_evs),tc_Message_Omsg),
file('SWV005-2.ax',cls_Event_Oused__Says_0) ).
cnf(cls_Message_OAgent__synth_0,axiom,
c_in(c_Message_Omsg_OAgent(V_A),c_Message_Osynth(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_OAgent__synth_0) ).
cnf(cls_Message_OCrypt__synth_1,axiom,
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OCrypt__synth_1) ).
cnf(cls_Message_OCrypt__synth__eq_0,axiom,
( c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OCrypt__synth__eq_0) ).
cnf(cls_Message_OCrypt__synth__eq_1,axiom,
( c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OCrypt__synth__eq_1) ).
cnf(cls_Message_OFake__analz__eq_0,axiom,
( c_Message_Osynth(c_Message_Oanalz(c_insert(V_X,V_H,tc_Message_Omsg))) = c_Message_Osynth(c_Message_Oanalz(V_H))
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OFake__analz__eq_0) ).
cnf(cls_Message_OHPair__eq_0,axiom,
( V_X_H = V_X
| c_Message_OHPair(V_X_H,V_Y_H) != c_Message_OHPair(V_X,V_Y) ),
file('SWV005-2.ax',cls_Message_OHPair__eq_0) ).
cnf(cls_Message_OHPair__eq_1,axiom,
( V_Y_H = V_Y
| c_Message_OHPair(V_X_H,V_Y_H) != c_Message_OHPair(V_X,V_Y) ),
file('SWV005-2.ax',cls_Message_OHPair__eq_1) ).
cnf(cls_Message_OHPair__eq__MPair_0,axiom,
( V_X_H = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y))
| c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OMPair(V_X_H,V_Y_H) ),
file('SWV005-2.ax',cls_Message_OHPair__eq__MPair_0) ).
cnf(cls_Message_OHPair__eq__MPair_1,axiom,
( V_Y_H = V_Y
| c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OMPair(V_X_H,V_Y_H) ),
file('SWV005-2.ax',cls_Message_OHPair__eq__MPair_1) ).
cnf(cls_Message_OHPair__eq__MPair_2,axiom,
c_Message_OHPair(V_X,V_x) = c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_x)),V_x),
file('SWV005-2.ax',cls_Message_OHPair__eq__MPair_2) ).
cnf(cls_Message_OHPair__neqs__1_0,axiom,
c_Message_Omsg_OAgent(V_A) != c_Message_OHPair(V_X,V_Y),
file('SWV005-2.ax',cls_Message_OHPair__neqs__1_0) ).
cnf(cls_Message_OHPair__neqs__2_0,axiom,
c_Message_Omsg_ONonce(V_N) != c_Message_OHPair(V_X,V_Y),
file('SWV005-2.ax',cls_Message_OHPair__neqs__2_0) ).
cnf(cls_Message_OHPair__neqs__3_0,axiom,
c_Message_Omsg_ONumber(V_N) != c_Message_OHPair(V_X,V_Y),
file('SWV005-2.ax',cls_Message_OHPair__neqs__3_0) ).
cnf(cls_Message_OHPair__neqs__4_0,axiom,
c_Message_Omsg_OKey(V_K) != c_Message_OHPair(V_X,V_Y),
file('SWV005-2.ax',cls_Message_OHPair__neqs__4_0) ).
cnf(cls_Message_OHPair__neqs__5_0,axiom,
c_Message_Omsg_OHash(V_Z) != c_Message_OHPair(V_X,V_Y),
file('SWV005-2.ax',cls_Message_OHPair__neqs__5_0) ).
cnf(cls_Message_OHPair__neqs__6_0,axiom,
c_Message_Omsg_OCrypt(V_K,V_X_H) != c_Message_OHPair(V_X,V_Y),
file('SWV005-2.ax',cls_Message_OHPair__neqs__6_0) ).
cnf(cls_Message_OHPair__synth__analz_0,axiom,
( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y)),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(c_Message_OHPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OHPair__synth__analz_0) ).
cnf(cls_Message_OHPair__synth__analz_1,axiom,
( c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_Y,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(c_Message_OHPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OHPair__synth__analz_1) ).
cnf(cls_Message_OHPair__synth__analz_2,axiom,
( c_in(c_Message_OHPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y)),c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(V_Y,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OHPair__synth__analz_2) ).
cnf(cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0,axiom,
c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OAgent(V_A),
file('SWV005-2.ax',cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0) ).
cnf(cls_Message_OHash_91X2_93_AY2_A_61_ACrypt_AK2_AX_H2_A_61_61_AFalse_0,axiom,
c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OCrypt(V_K,V_X_H),
file('SWV005-2.ax',cls_Message_OHash_91X2_93_AY2_A_61_ACrypt_AK2_AX_H2_A_61_61_AFalse_0) ).
cnf(cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0,axiom,
c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OHash(V_Z),
file('SWV005-2.ax',cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0) ).
cnf(cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0,axiom,
c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OKey(V_K),
file('SWV005-2.ax',cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0) ).
cnf(cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0,axiom,
c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_ONonce(V_N),
file('SWV005-2.ax',cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0) ).
cnf(cls_Message_OHash_91X2_93_AY2_A_61_ANumber_AN2_A_61_61_AFalse_0,axiom,
c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_ONumber(V_N),
file('SWV005-2.ax',cls_Message_OHash_91X2_93_AY2_A_61_ANumber_AN2_A_61_61_AFalse_0) ).
cnf(cls_Message_OHash__synth_0,axiom,
( c_in(c_Message_Omsg_OHash(V_X),V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(V_X),c_Message_Osynth(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OHash__synth_0) ).
cnf(cls_Message_OHash__synth__analz_0,axiom,
( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y)),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y)),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OHash__synth__analz_0) ).
cnf(cls_Message_OHash__synth__analz_1,axiom,
( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y)),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y)),c_Message_Oanalz(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OHash__synth__analz_1) ).
cnf(cls_Message_OKey__synth__eq_0,axiom,
( c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Osynth(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OKey__synth__eq_0) ).
cnf(cls_Message_OKey__synth__eq_1,axiom,
( c_in(c_Message_Omsg_OKey(V_K),c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OKey__synth__eq_1) ).
cnf(cls_Message_OMPair__analz_0,axiom,
( c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OMPair__analz_0) ).
cnf(cls_Message_OMPair__analz_1,axiom,
( c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OMPair__analz_1) ).
cnf(cls_Message_OMPair__eq__HPair_0,axiom,
( V_X_H = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y))
| c_Message_Omsg_OMPair(V_X_H,V_Y_H) != c_Message_OHPair(V_X,V_Y) ),
file('SWV005-2.ax',cls_Message_OMPair__eq__HPair_0) ).
cnf(cls_Message_OMPair__eq__HPair_1,axiom,
( V_Y_H = V_Y
| c_Message_Omsg_OMPair(V_X_H,V_Y_H) != c_Message_OHPair(V_X,V_Y) ),
file('SWV005-2.ax',cls_Message_OMPair__eq__HPair_1) ).
cnf(cls_Message_OMPair__eq__HPair_2,axiom,
c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_x)),V_x) = c_Message_OHPair(V_X,V_x),
file('SWV005-2.ax',cls_Message_OMPair__eq__HPair_2) ).
cnf(cls_Message_OMPair__synth_0,axiom,
( c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| c_in(V_Y,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OMPair__synth_0) ).
cnf(cls_Message_OMPair__synth_1,axiom,
( c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OMPair__synth_1) ).
cnf(cls_Message_OMPair__synth__analz_0,axiom,
( c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OMPair__synth__analz_0) ).
cnf(cls_Message_OMPair__synth__analz_1,axiom,
( c_in(V_Y,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OMPair__synth__analz_1) ).
cnf(cls_Message_OMPair__synth__analz_2,axiom,
( c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(V_Y,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_OMPair__synth__analz_2) ).
cnf(cls_Message_ONonce__synth__eq_0,axiom,
( c_in(c_Message_Omsg_ONonce(V_N),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(V_N),c_Message_Osynth(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_ONonce__synth__eq_0) ).
cnf(cls_Message_ONonce__synth__eq_1,axiom,
( c_in(c_Message_Omsg_ONonce(V_N),c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(V_N),V_H,tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_ONonce__synth__eq_1) ).
cnf(cls_Message_ONumber__synth_0,axiom,
c_in(c_Message_Omsg_ONumber(V_n),c_Message_Osynth(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_ONumber__synth_0) ).
cnf(cls_Message_Oanalz_ODecrypt__dest_0,axiom,
( c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oanalz(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Oanalz_ODecrypt__dest_0) ).
cnf(cls_Message_Oanalz_OInj_0,axiom,
( c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(V_X,V_H,tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Oanalz_OInj_0) ).
cnf(cls_Message_Oanalz__Crypt__if_0,axiom,
( c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oanalz(c_insert(V_X,V_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oanalz(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Oanalz__Crypt__if_0) ).
cnf(cls_Message_Oanalz__Crypt__if_1,axiom,
( c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oanalz(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Oanalz__Crypt__if_1) ).
cnf(cls_Message_Oanalz__analzD__dest_0,axiom,
( c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(c_Message_Oanalz(V_H)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Oanalz__analzD__dest_0) ).
cnf(cls_Message_Oanalz__analz__Un_0,axiom,
c_Message_Oanalz(c_union(c_Message_Oanalz(V_G),V_H,tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),
file('SWV005-2.ax',cls_Message_Oanalz__analz__Un_0) ).
cnf(cls_Message_Oanalz__conj__parts_0,axiom,
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Oanalz__conj__parts_0) ).
cnf(cls_Message_Oanalz__empty_0,axiom,
c_Message_Oanalz(c_emptyset) = c_emptyset,
file('SWV005-2.ax',cls_Message_Oanalz__empty_0) ).
cnf(cls_Message_Oanalz__idem_0,axiom,
c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H),
file('SWV005-2.ax',cls_Message_Oanalz__idem_0) ).
cnf(cls_Message_Oanalz__insert__Agent_0,axiom,
c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(V_agt),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(V_agt),c_Message_Oanalz(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oanalz__insert__Agent_0) ).
cnf(cls_Message_Oanalz__insert__HPair_0,axiom,
c_Message_Oanalz(c_insert(c_Message_OHPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_insert(c_Message_OHPair(V_X,V_Y),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y)),c_Message_Oanalz(c_insert(V_Y,V_H,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oanalz__insert__HPair_0) ).
cnf(cls_Message_Oanalz__insert__Hash_0,axiom,
c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(V_X),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(V_X),c_Message_Oanalz(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oanalz__insert__Hash_0) ).
cnf(cls_Message_Oanalz__insert__Key_0,axiom,
( c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oanalz(V_H)),tc_nat) ),
file('SWV005-2.ax',cls_Message_Oanalz__insert__Key_0) ).
cnf(cls_Message_Oanalz__insert__MPair_0,axiom,
c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(c_insert(V_X,c_insert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oanalz__insert__MPair_0) ).
cnf(cls_Message_Oanalz__insert__Nonce_0,axiom,
c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(V_N),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(V_N),c_Message_Oanalz(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oanalz__insert__Nonce_0) ).
cnf(cls_Message_Oanalz__insert__Number_0,axiom,
c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(V_N),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(V_N),c_Message_Oanalz(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oanalz__insert__Number_0) ).
cnf(cls_Message_Oanalz__parts_0,axiom,
c_Message_Oanalz(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H),
file('SWV005-2.ax',cls_Message_Oanalz__parts_0) ).
cnf(cls_Message_Oanalz__subset__iff_0,axiom,
( c_lessequals(V_G,c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ),
file('SWV005-2.ax',cls_Message_Oanalz__subset__iff_0) ).
cnf(cls_Message_Oanalz__subset__iff_1,axiom,
( c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(V_G,c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ),
file('SWV005-2.ax',cls_Message_Oanalz__subset__iff_1) ).
cnf(cls_Message_Oanalz__synth_0,axiom,
c_Message_Oanalz(c_Message_Osynth(V_H)) = c_union(c_Message_Oanalz(V_H),c_Message_Osynth(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oanalz__synth_0) ).
cnf(cls_Message_Oanalz__synth__Un_0,axiom,
c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oanalz__synth__Un_0) ).
cnf(cls_Message_Oin__parts__UnE_0,axiom,
( c_in(V_c,c_Message_Oparts(V_G),tc_Message_Omsg)
| c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Oin__parts__UnE_0) ).
cnf(cls_Message_OkeysFor__insert__HPair_0,axiom,
c_Message_OkeysFor(c_insert(c_Message_OHPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H),
file('SWV005-2.ax',cls_Message_OkeysFor__insert__HPair_0) ).
cnf(cls_Message_Oparts__analz_0,axiom,
c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H),
file('SWV005-2.ax',cls_Message_Oparts__analz_0) ).
cnf(cls_Message_Oparts__cut__eq_0,axiom,
( c_Message_Oparts(c_insert(V_X,V_H,tc_Message_Omsg)) = c_Message_Oparts(V_H)
| ~ c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Oparts__cut__eq_0) ).
cnf(cls_Message_Oparts__idem_0,axiom,
c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H),
file('SWV005-2.ax',cls_Message_Oparts__idem_0) ).
cnf(cls_Message_Oparts__insert__Agent_0,axiom,
c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(V_agt),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(V_agt),c_Message_Oparts(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oparts__insert__Agent_0) ).
cnf(cls_Message_Oparts__insert__Crypt_0,axiom,
c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(c_insert(V_X,V_H,tc_Message_Omsg)),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oparts__insert__Crypt_0) ).
cnf(cls_Message_Oparts__insert__HPair_0,axiom,
c_Message_Oparts(c_insert(c_Message_OHPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_insert(c_Message_OHPair(V_X,V_Y),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y)),c_Message_Oparts(c_insert(V_Y,V_H,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oparts__insert__HPair_0) ).
cnf(cls_Message_Oparts__insert__Hash_0,axiom,
c_Message_Oparts(c_insert(c_Message_Omsg_OHash(V_X),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(V_X),c_Message_Oparts(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oparts__insert__Hash_0) ).
cnf(cls_Message_Oparts__insert__Key_0,axiom,
c_Message_Oparts(c_insert(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(V_K),c_Message_Oparts(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oparts__insert__Key_0) ).
cnf(cls_Message_Oparts__insert__MPair_0,axiom,
c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_insert(V_X,c_insert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oparts__insert__MPair_0) ).
cnf(cls_Message_Oparts__insert__Nonce_0,axiom,
c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(V_N),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(V_N),c_Message_Oparts(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oparts__insert__Nonce_0) ).
cnf(cls_Message_Oparts__insert__Number_0,axiom,
c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(V_N),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(V_N),c_Message_Oparts(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oparts__insert__Number_0) ).
cnf(cls_Message_Oparts__partsD__dest_0,axiom,
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oparts(c_Message_Oparts(V_H)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Oparts__partsD__dest_0) ).
cnf(cls_Message_Oparts__subset__iff_0,axiom,
( c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
file('SWV005-2.ax',cls_Message_Oparts__subset__iff_0) ).
cnf(cls_Message_Oparts__subset__iff_1,axiom,
( c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
file('SWV005-2.ax',cls_Message_Oparts__subset__iff_1) ).
cnf(cls_Message_Oparts__synth_0,axiom,
c_Message_Oparts(c_Message_Osynth(V_H)) = c_union(c_Message_Oparts(V_H),c_Message_Osynth(V_H),tc_Message_Omsg),
file('SWV005-2.ax',cls_Message_Oparts__synth_0) ).
cnf(cls_Message_Osynth_OCrypt_0,axiom,
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Osynth_OCrypt_0) ).
cnf(cls_Message_Osynth_OHash_0,axiom,
( c_in(c_Message_Omsg_OHash(V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Osynth_OHash_0) ).
cnf(cls_Message_Osynth_OInj_0,axiom,
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(V_X,V_H,tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Osynth_OInj_0) ).
cnf(cls_Message_Osynth_OMPair_0,axiom,
( c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(V_Y,c_Message_Osynth(V_H),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Osynth_OMPair_0) ).
cnf(cls_Message_Osynth__subset__iff_0,axiom,
( c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) ),
file('SWV005-2.ax',cls_Message_Osynth__subset__iff_0) ).
cnf(cls_Message_Osynth__subset__iff_1,axiom,
( c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) ),
file('SWV005-2.ax',cls_Message_Osynth__subset__iff_1) ).
cnf(cls_Message_Osynth__synthD__dest_0,axiom,
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Osynth(V_H)),tc_Message_Omsg) ),
file('SWV005-2.ax',cls_Message_Osynth__synthD__dest_0) ).
cnf(cls_Public_OCrypt__notin__used__empty_0,axiom,
~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_OCrypt__notin__used__empty_0) ).
cnf(cls_Public_OMPair__used_0,axiom,
( c_in(V_Y,c_Event_Oused(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Event_Oused(V_H),tc_Message_Omsg) ),
file('SWV005-3.ax',cls_Public_OMPair__used_0) ).
cnf(cls_Public_OMPair__used_1,axiom,
( c_in(V_X,c_Event_Oused(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Event_Oused(V_H),tc_Message_Omsg) ),
file('SWV005-3.ax',cls_Public_OMPair__used_1) ).
cnf(cls_Public_ONonce__notin__initState_0,axiom,
~ c_in(c_Message_Omsg_ONonce(V_N),c_Message_Oparts(c_Event_OinitState(V_B)),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_ONonce__notin__initState_0) ).
cnf(cls_Public_ONonce__notin__used__empty_0,axiom,
~ c_in(c_Message_Omsg_ONonce(V_N),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_ONonce__notin__used__empty_0) ).
cnf(cls_Public_OSpy__spies__bad__privateKey_0,axiom,
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A))),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)
| ~ c_in(V_A,c_Event_Obad,tc_Message_Oagent) ),
file('SWV005-3.ax',cls_Public_OSpy__spies__bad__privateKey_0) ).
cnf(cls_Public_OSpy__spies__bad__shrK_0,axiom,
( c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)
| ~ c_in(V_A,c_Event_Obad,tc_Message_Oagent) ),
file('SWV005-3.ax',cls_Public_OSpy__spies__bad__shrK_0) ).
cnf(cls_Public_Oanalz__spies__pubK_0,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(V_b,V_A)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_Oanalz__spies__pubK_0) ).
cnf(cls_Public_OinvKey__K_0,axiom,
( c_Message_OinvKey(V_y) = V_y
| ~ c_in(V_y,c_Message_OsymKeys,tc_nat) ),
file('SWV005-3.ax',cls_Public_OinvKey__K_0) ).
cnf(cls_Public_OinvKey__shrK_0,axiom,
c_Message_OinvKey(c_Public_OshrK(V_A)) = c_Public_OshrK(V_A),
file('SWV005-3.ax',cls_Public_OinvKey__shrK_0) ).
cnf(cls_Public_Okeymode_Ocases__1_0,axiom,
c_Public_Okeymode_Okeymode__case(V_y,V_f2,c_Public_Okeymode_OSignature,T_a) = V_y,
file('SWV005-3.ax',cls_Public_Okeymode_Ocases__1_0) ).
cnf(cls_Public_Okeymode_Ocases__2_0,axiom,
c_Public_Okeymode_Okeymode__case(V_f1,V_y,c_Public_Okeymode_OEncryption,T_a) = V_y,
file('SWV005-3.ax',cls_Public_Okeymode_Ocases__2_0) ).
cnf(cls_Public_Okeymode_Odistinct__1_0,axiom,
c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
file('SWV005-3.ax',cls_Public_Okeymode_Odistinct__1_0) ).
cnf(cls_Public_Okeymode_Odistinct__2_0,axiom,
c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
file('SWV005-3.ax',cls_Public_Okeymode_Odistinct__2_0) ).
cnf(cls_Public_Okeymode_Orecs__1_0,axiom,
c_Public_Okeymode_Okeymode__rec(V_y,V_f2,c_Public_Okeymode_OSignature,T_a) = V_y,
file('SWV005-3.ax',cls_Public_Okeymode_Orecs__1_0) ).
cnf(cls_Public_Okeymode_Orecs__2_0,axiom,
c_Public_Okeymode_Okeymode__rec(V_f1,V_y,c_Public_Okeymode_OEncryption,T_a) = V_y,
file('SWV005-3.ax',cls_Public_Okeymode_Orecs__2_0) ).
cnf(cls_Public_Okeymode_Osize__1_0,axiom,
c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) = c_0,
file('SWV005-3.ax',cls_Public_Okeymode_Osize__1_0) ).
cnf(cls_Public_Okeymode_Osize__2_0,axiom,
c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) = c_0,
file('SWV005-3.ax',cls_Public_Okeymode_Osize__2_0) ).
cnf(cls_Public_OkeysFor__parts__initState_0,axiom,
c_Message_OkeysFor(c_Message_Oparts(c_Event_OinitState(V_C))) = c_emptyset,
file('SWV005-3.ax',cls_Public_OkeysFor__parts__initState_0) ).
cnf(cls_Public_Onot__symKeys__priK_0,axiom,
~ c_in(c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A)),c_Message_OsymKeys,tc_nat),
file('SWV005-3.ax',cls_Public_Onot__symKeys__priK_0) ).
cnf(cls_Public_Onot__symKeys__pubK_0,axiom,
~ c_in(c_Public_OpublicKey(V_b,V_A),c_Message_OsymKeys,tc_nat),
file('SWV005-3.ax',cls_Public_Onot__symKeys__pubK_0) ).
cnf(cls_Public_OpriEK__noteq__shrK_0,axiom,
c_Message_OinvKey(c_Public_OpublicKey(c_Public_Okeymode_OEncryption,V_A)) != c_Public_OshrK(V_B),
file('SWV005-3.ax',cls_Public_OpriEK__noteq__shrK_0) ).
cnf(cls_Public_OpriK__in__initState_0,axiom,
c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A))),c_Event_OinitState(V_A),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_OpriK__in__initState_0) ).
cnf(cls_Public_OpriK__neq__shrK_0,axiom,
c_Public_OshrK(V_A) != c_Message_OinvKey(c_Public_OpublicKey(V_b,V_C)),
file('SWV005-3.ax',cls_Public_OpriK__neq__shrK_0) ).
cnf(cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0,axiom,
c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A)) != c_Public_OpublicKey(V_c,V_A_H),
file('SWV005-3.ax',cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0) ).
cnf(cls_Public_OprivateKey__into__used_0,axiom,
c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A))),c_Event_Oused(V_evs),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_OprivateKey__into__used_0) ).
cnf(cls_Public_OpubK__neq__shrK_0,axiom,
c_Public_OshrK(V_A) != c_Public_OpublicKey(V_b,V_C),
file('SWV005-3.ax',cls_Public_OpubK__neq__shrK_0) ).
cnf(cls_Public_OpublicKey__in__initState_0,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(V_b,V_A)),c_Event_OinitState(V_B),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_OpublicKey__in__initState_0) ).
cnf(cls_Public_OpublicKey__inject_0,axiom,
( V_b = V_c
| c_Public_OpublicKey(V_b,V_A) != c_Public_OpublicKey(V_c,V_A_H) ),
file('SWV005-3.ax',cls_Public_OpublicKey__inject_0) ).
cnf(cls_Public_OpublicKey__inject_1,axiom,
( V_A = V_A_H
| c_Public_OpublicKey(V_b,V_A) != c_Public_OpublicKey(V_c,V_A_H) ),
file('SWV005-3.ax',cls_Public_OpublicKey__inject_1) ).
cnf(cls_Public_OpublicKey__into__used_0,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(V_b,V_A)),c_Event_Oused(V_evs),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_OpublicKey__into__used_0) ).
cnf(cls_Public_OpublicKey__neq__privateKey_0,axiom,
c_Public_OpublicKey(V_c,V_A_H) != c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A)),
file('SWV005-3.ax',cls_Public_OpublicKey__neq__privateKey_0) ).
cnf(cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0,axiom,
c_in(c_Public_OshrK(V_X),c_Message_OsymKeys,tc_nat),
file('SWV005-3.ax',cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0) ).
cnf(cls_Public_OshrK__in__initState_0,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_OinitState(V_A),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_OshrK__in__initState_0) ).
cnf(cls_Public_OshrK__in__knows_0,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_Oknows(V_A,V_evs),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_OshrK__in__knows_0) ).
cnf(cls_Public_OshrK__in__used_0,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_Oused(V_evs),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_OshrK__in__used_0) ).
cnf(cls_Public_OshrK__injective_0,axiom,
( V_x = V_y
| c_Public_OshrK(V_x) != c_Public_OshrK(V_y) ),
file('SWV005-3.ax',cls_Public_OshrK__injective_0) ).
cnf(cls_Public_OshrK__neq__priK_0,axiom,
c_Message_OinvKey(c_Public_OpublicKey(V_b,V_C)) != c_Public_OshrK(V_A),
file('SWV005-3.ax',cls_Public_OshrK__neq__priK_0) ).
cnf(cls_Public_OshrK__neq__pubK_0,axiom,
c_Public_OpublicKey(V_b,V_C) != c_Public_OshrK(V_A),
file('SWV005-3.ax',cls_Public_OshrK__neq__pubK_0) ).
cnf(cls_Public_Ospies__pubK_0,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(V_b,V_A)),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg),
file('SWV005-3.ax',cls_Public_Ospies__pubK_0) ).
cnf(cls_Public_OsymKeys__invKey__iff_0,axiom,
( c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(c_Message_OinvKey(V_K),c_Message_OsymKeys,tc_nat) ),
file('SWV005-3.ax',cls_Public_OsymKeys__invKey__iff_0) ).
cnf(cls_Public_OsymKeys__invKey__iff_1,axiom,
( c_in(c_Message_OinvKey(V_K),c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ),
file('SWV005-3.ax',cls_Public_OsymKeys__invKey__iff_1) ).
cnf(cls_Event_OSays__imp__analz__Spy__dest_0,axiom,
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
file('SWV005-4.ax',cls_Event_OSays__imp__analz__Spy__dest_0) ).
cnf(cls_Message_OFake__parts__insert__in__Un__dest_0,axiom,
( c_in(V_Z,c_union(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_Message_Omsg),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(V_Z,c_Message_Oparts(c_insert(V_X,V_H,tc_Message_Omsg)),tc_Message_Omsg) ),
file('SWV005-4.ax',cls_Message_OFake__parts__insert__in__Un__dest_0) ).
cnf(cls_Message_Oparts_OBody__dest_0,axiom,
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('SWV005-4.ax',cls_Message_Oparts_OBody__dest_0) ).
cnf(cls_Yahalom_OGets__imp__analz__Spy__dest_0,axiom,
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('SWV005-4.ax',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).
cnf(cls_Yahalom_OSpy__analz__shrK_0,axiom,
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('SWV005-4.ax',cls_Yahalom_OSpy__analz__shrK_0) ).
cnf(cls_Yahalom_OSpy__analz__shrK_1,axiom,
( c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_A,c_Event_Obad,tc_Message_Oagent) ),
file('SWV005-4.ax',cls_Yahalom_OSpy__analz__shrK_1) ).
cnf(cls_Yahalom_OSpy__see__shrK_0,axiom,
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('SWV005-4.ax',cls_Yahalom_OSpy__see__shrK_0) ).
cnf(cls_Yahalom_OSpy__see__shrK_1,axiom,
( c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_A,c_Event_Obad,tc_Message_Oagent) ),
file('SWV005-4.ax',cls_Yahalom_OSpy__see__shrK_1) ).
cnf(cls_Yahalom_Onew__keys__not__used_0,axiom,
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ),
file('theBenchmark.p',cls_Yahalom_Onew__keys__not__used_0) ).
cnf(cls_Yahalom_Ounique__session__keys__dest_0,axiom,
( V_A = V_A_H
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na_H,V_nb_H)))),V_X_H)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_0) ).
cnf(cls_Yahalom_Ounique__session__keys__dest_1,axiom,
( V_B = V_B_H
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na_H,V_nb_H)))),V_X_H)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_1) ).
cnf(cls_Yahalom_Ounique__session__keys__dest_2,axiom,
( V_na = V_na_H
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na_H,V_nb_H)))),V_X_H)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_2) ).
cnf(cls_Yahalom_Ounique__session__keys__dest_3,axiom,
( V_nb = V_nb_H
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na_H,V_nb_H)))),V_X_H)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_3) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_2,negated_conjecture,
c_in(v_K,c_Message_OsymKeys,tc_nat),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OKey(v_K))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_6,negated_conjecture,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(cls_conjecture_7,negated_conjecture,
~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_7) ).
cnf(cls_conjecture_8,negated_conjecture,
c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_8) ).
cnf(cls_NatBin_Oeq__nat__number__of_11_simplified,plain,
( c_Numeral_Onumber__of(V_v,tc_nat) = c_Numeral_Onumber__of(V_v_H,tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(V_v_H,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(V_v,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(simplify_clause,[status(thm)],[cls_NatBin_Oeq__nat__number__of_11]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( c_Datatype__Universe_OLeaf(Eq_x_0,Eq_x_1,Eq_x_2) = c_Datatype__Universe_OLeaf(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c_Datatype__Universe_ONumb(Eq_x_0,Eq_x_1,Eq_x_2) = c_Datatype__Universe_ONumb(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( c_Datatype__Universe_Odprod(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Datatype__Universe_Odprod(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( tc_Datatype__Universe_Onode(Eq_x_0,Eq_x_1) = tc_Datatype__Universe_Onode(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( tc_set(Eq_x_0) = tc_set(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( tc_prod(Eq_x_0,Eq_x_1) = tc_prod(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( c_Main_OdprodE__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Main_OdprodE__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( c_Main_OdprodE__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Main_OdprodE__2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( c_Datatype__Universe_OScons(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Datatype__Universe_OScons(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( c_Main_OdprodE__3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Main_OdprodE__3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( c_Main_OdprodE__4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Main_OdprodE__4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( c_Pair(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Pair(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( c_Datatype__Universe_Odsum(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Datatype__Universe_Odsum(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( c_Main_OdsumE__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_OdsumE__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( c_Datatype__Universe_OIn0(Eq_x_0,Eq_x_1,Eq_x_2) = c_Datatype__Universe_OIn0(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( c_Main_OdsumE__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_OdsumE__2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( c_Main_OdsumE__3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_OdsumE__3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( c_Datatype__Universe_OIn1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Datatype__Universe_OIn1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( c_Main_OdsumE__4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_OdsumE__4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( c_Datatype__Universe_Ouprod(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Datatype__Universe_Ouprod(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( c_Main_OuprodE__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Main_OuprodE__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( c_Main_OuprodE__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Main_OuprodE__2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( c_Datatype__Universe_Ousum(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Datatype__Universe_Ousum(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( c_Main_OusumE__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_OusumE__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( c_Main_OusumE__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_OusumE__2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( c_Suc(Eq_x_0) = c_Suc(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( c_times(Eq_x_0,Eq_x_1,Eq_x_2) = c_times(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( c_Divides_Oop_Amod(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Oop_Amod(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( c_Main_Omod__eq__0D__dest__1(Eq_x_0,Eq_x_1) = c_Main_Omod__eq__0D__dest__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( c_insert(Eq_x_0,Eq_x_1,Eq_x_2) = c_insert(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( c_inter(Eq_x_0,Eq_x_1,Eq_x_2) = c_inter(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( c_Main_Ofinite__Union__1(Eq_x_0,Eq_x_1) = c_Main_Ofinite__Union__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( c_Union(Eq_x_0,Eq_x_1) = c_Union(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( c_GCD_Ogcd(Eq_x_0) = c_GCD_Ogcd(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( c_IntDef_Oint(Eq_x_0) = c_IntDef_Oint(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( c_uminus(Eq_x_0,Eq_x_1) = c_uminus(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( c_Main_Ozmod__eq__0D__dest__1(Eq_x_0,Eq_x_1) = c_Main_Ozmod__eq__0D__dest__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( c_List_Oremdups(Eq_x_0,Eq_x_1) = c_List_Oremdups(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( c_List_Oset(Eq_x_0,Eq_x_1) = c_List_Oset(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( c_List_Olists(Eq_x_0,Eq_x_1) = c_List_Olists(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( tc_List_Olist(Eq_x_0) = tc_List_Olist(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( c_Main_Oin__listsI__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_Oin__listsI__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( c_Nat_Osize(Eq_x_0,Eq_x_1) = c_Nat_Osize(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( c_List_Olist_OCons(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Olist_OCons(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( c_List_Olistrel(Eq_x_0,Eq_x_1) = c_List_Olistrel(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( c_Main_Olistrel__Cons1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Main_Olistrel__Cons1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( c_Main_Olistrel__Cons1__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Main_Olistrel__Cons1__2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( c_Main_Olistrel__Cons2__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Main_Olistrel__Cons2__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( c_Main_Olistrel__Cons2__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Main_Olistrel__Cons2__2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( c_List_Olenlex(Eq_x_0,Eq_x_1) = c_List_Olenlex(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( c_List_Olex(Eq_x_0,Eq_x_1) = c_List_Olex(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( c_Relation_ODomain(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_ODomain(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( c_Main_ODomainE__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_ODomainE__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( c_Main_OIdE__1(Eq_x_0,Eq_x_1) = c_Main_OIdE__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( c_Relation_OImage(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Relation_OImage(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( c_Main_OImageE__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Main_OImageE__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( c_Relation_ORange(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_ORange(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( c_Main_ORangeE__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_ORangeE__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( c_Relation_Oconverse(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_Oconverse(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( c_Main_OconverseE__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_OconverseE__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( c_Main_OconverseE__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_OconverseE__2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( c_Relation_Odiag(Eq_x_0,Eq_x_1) = c_Relation_Odiag(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,axiom,
( c_Main_OdiagE__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_OdiagE__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( c_Relation_Orel__comp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Relation_Orel__comp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( c_Main_Orel__compE__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_Main_Orel__compE__2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( c_Main_Orel__compE__3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_Main_Orel__compE__3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( c_Main_Orel__compE__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_Main_Orel__compE__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( c_SetInterval_OatLeastAtMost(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_OatLeastAtMost(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( c_SetInterval_OatLeastLessThan(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_OatLeastLessThan(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( c_SetInterval_OatMost(Eq_x_0,Eq_x_1) = c_SetInterval_OatMost(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( c_SetInterval_OgreaterThanAtMost(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_OgreaterThanAtMost(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( c_SetInterval_OgreaterThanLessThan(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_OgreaterThanLessThan(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( c_SetInterval_OlessThan(Eq_x_0,Eq_x_1) = c_SetInterval_OlessThan(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,axiom,
( c_Inter(Eq_x_0,Eq_x_1) = c_Inter(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( c_Main_OInterI__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_OInterI__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( c_Main_OUnionE__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_OUnionE__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( c_Main_OsubsetI__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_OsubsetI__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( c_Sum__Type_OInl(Eq_x_0,Eq_x_1,Eq_x_2) = c_Sum__Type_OInl(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( c_Sum__Type_OPlus(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Sum__Type_OPlus(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,axiom,
( tc_sum(Eq_x_0,Eq_x_1) = tc_sum(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( c_Sum__Type_OInr(Eq_x_0,Eq_x_1,Eq_x_2) = c_Sum__Type_OInr(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( c_Main_OPlusE__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_OPlusE__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( c_Main_OPlusE__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Main_OPlusE__2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( c_Transitive__Closure_Ortrancl(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Ortrancl(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,axiom,
( c_Transitive__Closure_Otrancl(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Otrancl(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_89,axiom,
( c_Wellfounded__Relations_Olex__prod(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Wellfounded__Relations_Olex__prod(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( tc_Datatype_Ooption(Eq_x_0) = tc_Datatype_Ooption(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,axiom,
( tc_fun(Eq_x_0,Eq_x_1) = tc_fun(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( c_Binomial_Obinomial(Eq_x_0,Eq_x_1) = c_Binomial_Obinomial(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,axiom,
( c_plus(Eq_x_0,Eq_x_1,Eq_x_2) = c_plus(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( c_Datatype_Oo2s(Eq_x_0,Eq_x_1) = c_Datatype_Oo2s(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( c_Datatype_Ooption_OSome(Eq_x_0,Eq_x_1) = c_Datatype_Ooption_OSome(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,axiom,
( c_Main_Onot__None__eq__1(Eq_x_0,Eq_x_1) = c_Main_Onot__None__eq__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,axiom,
( c_Main_Onot__Some__eq__1(Eq_x_0,Eq_x_1) = c_Main_Onot__Some__eq__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( c_Datatype_Othe(Eq_x_0,Eq_x_1) = c_Datatype_Othe(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( c_Datatype_Ounit_Ounit__case(Eq_x_0,Eq_x_1,Eq_x_2) = c_Datatype_Ounit_Ounit__case(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_100,axiom,
( c_Datatype_Ounit_Ounit__rec(Eq_x_0,Eq_x_1,Eq_x_2) = c_Datatype_Ounit_Ounit__rec(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_101,axiom,
( c_Datatype__Universe_OAtom(Eq_x_0,Eq_x_1,Eq_x_2) = c_Datatype__Universe_OAtom(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( c_Datatype__Universe_Ontrunc(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Datatype__Universe_Ontrunc(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( c_div(Eq_x_0,Eq_x_1,Eq_x_2) = c_div(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_104,axiom,
( c_Equiv__Relations_Oquotient(Eq_x_0,Eq_x_1,Eq_x_2) = c_Equiv__Relations_Oquotient(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_105,axiom,
( c_Extraction_Osumbool_Osumbool__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Extraction_Osumbool_Osumbool__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_106,axiom,
( c_Extraction_Osumbool_Osumbool__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Extraction_Osumbool_Osumbool__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_107,axiom,
( c_Finite__Set_OMax(Eq_x_0,Eq_x_1) = c_Finite__Set_OMax(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_108,axiom,
( c_Orderings_Omax(Eq_x_0,Eq_x_1,Eq_x_2) = c_Orderings_Omax(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,axiom,
( c_Main_OMax__le__iff__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_OMax__le__iff__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_110,axiom,
( c_Main_OMax__less__iff__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_OMax__less__iff__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_111,axiom,
( c_Finite__Set_OMin(Eq_x_0,Eq_x_1) = c_Finite__Set_OMin(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_112,axiom,
( c_Main_OMin__ge__iff__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_OMin__ge__iff__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_113,axiom,
( c_Main_OMin__gr__iff__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_OMin__gr__iff__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_114,axiom,
( c_Orderings_Omin(Eq_x_0,Eq_x_1,Eq_x_2) = c_Orderings_Omin(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_115,axiom,
( c_Finite__Set_Ocard(Eq_x_0,Eq_x_1) = c_Finite__Set_Ocard(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,axiom,
( c_minus(Eq_x_0,Eq_x_1,Eq_x_2) = c_minus(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_117,axiom,
( c_Pow(Eq_x_0,Eq_x_1) = c_Pow(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_118,axiom,
( c_union(Eq_x_0,Eq_x_1,Eq_x_2) = c_union(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_119,axiom,
( c_NatArith_Oof__nat(Eq_x_0,Eq_x_1) = c_NatArith_Oof__nat(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( c_Fun_Oid(Eq_x_0,Eq_x_1) = c_Fun_Oid(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_121,axiom,
( c_Numeral_Onumber__of(Eq_x_0,Eq_x_1) = c_Numeral_Onumber__of(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,axiom,
( c_HOL_Oabs(Eq_x_0,Eq_x_1) = c_HOL_Oabs(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_123,axiom,
( c_Nat_Opower(Eq_x_0,Eq_x_1,Eq_x_2) = c_Nat_Opower(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_124,axiom,
( c_Numeral_Obin__minus(Eq_x_0) = c_Numeral_Obin__minus(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_125,axiom,
( c_Numeral_Obin__add(Eq_x_0,Eq_x_1) = c_Numeral_Obin__add(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_126,axiom,
( c_Numeral_OBit(Eq_x_0,Eq_x_1) = c_Numeral_OBit(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_127,axiom,
( c_IntDef_Onat(Eq_x_0) = c_IntDef_Onat(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_128,axiom,
( c_IntDef_Oof__int(Eq_x_0,Eq_x_1) = c_IntDef_Oof__int(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_129,axiom,
( c_IntDef_OAbs__Integ(Eq_x_0) = c_IntDef_OAbs__Integ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_130,axiom,
( c_IntDef_ORep__Integ(Eq_x_0) = c_IntDef_ORep__Integ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_131,axiom,
( c_IntDiv_OposDivAlg(Eq_x_0) = c_IntDiv_OposDivAlg(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,axiom,
( c_IntDiv_OnegateSnd(Eq_x_0) = c_IntDiv_OnegateSnd(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_133,axiom,
( c_fst(Eq_x_0,Eq_x_1,Eq_x_2) = c_fst(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_134,axiom,
( c_IntDiv_OnegDivAlg(Eq_x_0) = c_IntDiv_OnegDivAlg(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_135,axiom,
( c_snd(Eq_x_0,Eq_x_1,Eq_x_2) = c_snd(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_136,axiom,
( c_IntDiv_Oadjust(Eq_x_0,Eq_x_1) = c_IntDiv_Oadjust(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_137,axiom,
( c_LOrder_Ojoin(Eq_x_0,Eq_x_1,Eq_x_2) = c_LOrder_Ojoin(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,axiom,
( c_LOrder_Omeet(Eq_x_0,Eq_x_1,Eq_x_2) = c_LOrder_Omeet(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_139,axiom,
( c_List_Oconcat(Eq_x_0,Eq_x_1) = c_List_Oconcat(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_140,axiom,
( c_Main_ONil__eq__concat__conv__1(Eq_x_0,Eq_x_1) = c_Main_ONil__eq__concat__conv__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_141,axiom,
( c_append(Eq_x_0,Eq_x_1,Eq_x_2) = c_append(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_142,axiom,
( c_List_Orev(Eq_x_0,Eq_x_1) = c_List_Orev(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_143,axiom,
( c_List_Obutlast(Eq_x_0,Eq_x_1) = c_List_Obutlast(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_144,axiom,
( c_List_Olast(Eq_x_0,Eq_x_1) = c_List_Olast(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_145,axiom,
( c_List_Otake(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Otake(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_146,axiom,
( c_List_Odrop(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Odrop(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_147,axiom,
( c_List_Ochar_OChar(Eq_x_0,Eq_x_1) = c_List_Ochar_OChar(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,axiom,
( c_Main_Oconcat__eq__Nil__conv__1(Eq_x_0,Eq_x_1) = c_Main_Oconcat__eq__Nil__conv__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_149,axiom,
( c_List_Orotate1(Eq_x_0,Eq_x_1) = c_List_Orotate1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_150,axiom,
( c_List_Oremove1(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oremove1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_151,axiom,
( c_List_Orotate(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Orotate(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_152,axiom,
( c_List_Osublist(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Osublist(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_153,axiom,
( c_List_Oupt(Eq_x_0,Eq_x_1) = c_List_Oupt(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_154,axiom,
( c_List_Oreplicate(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oreplicate(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_155,axiom,
( c_List_Ohd(Eq_x_0,Eq_x_1) = c_List_Ohd(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_156,axiom,
( c_List_Otl(Eq_x_0,Eq_x_1) = c_List_Otl(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_157,axiom,
( c_List_Oitrev(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oitrev(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_158,axiom,
( c_List_Olist__update(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Olist__update(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_159,axiom,
( c_List_Ozip(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Ozip(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_160,axiom,
( c_List_Olexn(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Olexn(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_161,axiom,
( c_List_Olexord(Eq_x_0,Eq_x_1) = c_List_Olexord(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_162,axiom,
( c_Main_Olexord__Nil__left__1(Eq_x_0,Eq_x_1) = c_Main_Olexord__Nil__left__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_163,axiom,
( c_Main_Olexord__Nil__left__2(Eq_x_0,Eq_x_1) = c_Main_Olexord__Nil__left__2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_164,axiom,
( c_List_Olist__inter(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Olist__inter(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_165,axiom,
( c_List_Onth(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Onth(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_166,axiom,
( c_List_Olistset(Eq_x_0,Eq_x_1) = c_List_Olistset(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_167,axiom,
( c_List_Oset__Cons(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oset__Cons(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_168,axiom,
( c_List_Onibble_Onibble__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10,Eq_x_11,Eq_x_12,Eq_x_13,Eq_x_14,Eq_x_15,Eq_x_16,Eq_x_17) = c_List_Onibble_Onibble__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10,Eq_y_11,Eq_y_12,Eq_y_13,Eq_y_14,Eq_y_15,Eq_y_16,Eq_y_17)
| Eq_x_17 != Eq_y_17
| Eq_x_16 != Eq_y_16
| Eq_x_15 != Eq_y_15
| Eq_x_14 != Eq_y_14
| Eq_x_13 != Eq_y_13
| Eq_x_12 != Eq_y_12
| Eq_x_11 != Eq_y_11
| Eq_x_10 != Eq_y_10
| Eq_x_9 != Eq_y_9
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_169,axiom,
( c_List_Onibble_Onibble__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10,Eq_x_11,Eq_x_12,Eq_x_13,Eq_x_14,Eq_x_15,Eq_x_16,Eq_x_17) = c_List_Onibble_Onibble__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10,Eq_y_11,Eq_y_12,Eq_y_13,Eq_y_14,Eq_y_15,Eq_y_16,Eq_y_17)
| Eq_x_17 != Eq_y_17
| Eq_x_16 != Eq_y_16
| Eq_x_15 != Eq_y_15
| Eq_x_14 != Eq_y_14
| Eq_x_13 != Eq_y_13
| Eq_x_12 != Eq_y_12
| Eq_x_11 != Eq_y_11
| Eq_x_10 != Eq_y_10
| Eq_x_9 != Eq_y_9
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_170,axiom,
( c_Map_Omap__of(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Map_Omap__of(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_171,axiom,
( c_Numeral_Obin__succ(Eq_x_0) = c_Numeral_Obin__succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_172,axiom,
( c_Numeral_Obin__mult(Eq_x_0,Eq_x_1) = c_Numeral_Obin__mult(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_173,axiom,
( c_divide(Eq_x_0,Eq_x_1,Eq_x_2) = c_divide(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_174,axiom,
( c_HOL_Oinverse(Eq_x_0,Eq_x_1) = c_HOL_Oinverse(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_175,axiom,
( c_Numeral_Obin__pred(Eq_x_0) = c_Numeral_Obin__pred(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_176,axiom,
( c_Numeral_Obit_Obit__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Numeral_Obit_Obit__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_177,axiom,
( c_Numeral_Obit_Obit__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Numeral_Obit_Obit__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_178,axiom,
( c_OrderedGroup_Onprt(Eq_x_0,Eq_x_1) = c_OrderedGroup_Onprt(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_179,axiom,
( c_OrderedGroup_Opprt(Eq_x_0,Eq_x_1) = c_OrderedGroup_Opprt(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_180,axiom,
( c_Main_Osurj__pair__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_Osurj__pair__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_181,axiom,
( c_Main_Osurj__pair__2(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_Osurj__pair__2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_182,axiom,
( c_SetInterval_OatLeast(Eq_x_0,Eq_x_1) = c_SetInterval_OatLeast(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_183,axiom,
( c_SetInterval_OgreaterThan(Eq_x_0,Eq_x_1) = c_SetInterval_OgreaterThan(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_184,axiom,
( c_Main_OInter__UNIV__conv__1__1(Eq_x_0,Eq_x_1) = c_Main_OInter__UNIV__conv__1__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_185,axiom,
( c_Main_OInter__UNIV__conv__2__1(Eq_x_0,Eq_x_1) = c_Main_OInter__UNIV__conv__2__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_186,axiom,
( c_Main_OInter__iff__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_OInter__iff__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_187,axiom,
( c_Main_OUnion__empty__conv__1(Eq_x_0,Eq_x_1) = c_Main_OUnion__empty__conv__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_188,axiom,
( c_Main_OUnion__iff__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Main_OUnion__iff__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_189,axiom,
( c_Main_Oall__not__in__conv__1(Eq_x_0,Eq_x_1) = c_Main_Oall__not__in__conv__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_190,axiom,
( c_Set_Ocontents(Eq_x_0,Eq_x_1) = c_Set_Ocontents(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_191,axiom,
( c_Main_Oempty__Union__conv__1(Eq_x_0,Eq_x_1) = c_Main_Oempty__Union__conv__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_192,axiom,
( c_Message_Omsg_OMPair(Eq_x_0,Eq_x_1) = c_Message_Omsg_OMPair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_193,axiom,
( c_Message_Oparts(Eq_x_0) = c_Message_Oparts(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_194,axiom,
( c_Message_Oagent_OFriend(Eq_x_0) = c_Message_Oagent_OFriend(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_195,axiom,
( c_Message_OinvKey(Eq_x_0) = c_Message_OinvKey(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_196,axiom,
( c_Message_OkeysFor(Eq_x_0) = c_Message_OkeysFor(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_197,axiom,
( c_Message_Omsg_OAgent(Eq_x_0) = c_Message_Omsg_OAgent(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_198,axiom,
( c_Message_Omsg_OCrypt(Eq_x_0,Eq_x_1) = c_Message_Omsg_OCrypt(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_199,axiom,
( c_Message_Omsg_OHash(Eq_x_0) = c_Message_Omsg_OHash(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_200,axiom,
( c_Message_Omsg_OKey(Eq_x_0) = c_Message_Omsg_OKey(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_201,axiom,
( c_Message_Omsg_ONonce(Eq_x_0) = c_Message_Omsg_ONonce(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_202,axiom,
( c_Message_Omsg_ONumber(Eq_x_0) = c_Message_Omsg_ONumber(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_203,axiom,
( c_Event_Oknows(Eq_x_0,Eq_x_1) = c_Event_Oknows(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_204,axiom,
( c_Event_Oused(Eq_x_0) = c_Event_Oused(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_205,axiom,
( c_Event_Oevent_OSays(Eq_x_0,Eq_x_1,Eq_x_2) = c_Event_Oevent_OSays(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_206,axiom,
( c_Event_Oevent_OGets(Eq_x_0,Eq_x_1) = c_Event_Oevent_OGets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_207,axiom,
( c_Event_Oevent_ONotes(Eq_x_0,Eq_x_1) = c_Event_Oevent_ONotes(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_208,axiom,
( c_Message_Osynth(Eq_x_0) = c_Message_Osynth(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_209,axiom,
( v_sko__uhi(Eq_x_0,Eq_x_1) = v_sko__uhi(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_210,axiom,
( c_Event_OinitState(Eq_x_0) = c_Event_OinitState(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_211,axiom,
( c_Message_Oanalz(Eq_x_0) = c_Message_Oanalz(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_212,axiom,
( c_Message_OHPair(Eq_x_0,Eq_x_1) = c_Message_OHPair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_213,axiom,
( c_Public_OpublicKey(Eq_x_0,Eq_x_1) = c_Public_OpublicKey(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_214,axiom,
( c_Public_OshrK(Eq_x_0) = c_Public_OshrK(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_215,axiom,
( c_Public_Okeymode_Okeymode__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Public_Okeymode_Okeymode__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_216,axiom,
( c_Public_Okeymode_Okeymode__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Public_Okeymode_Okeymode__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_217,axiom,
( c_in(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_in(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_218,axiom,
( c_Divides_Oop_Advd(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Divides_Oop_Advd(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_219,axiom,
( c_Infinite__Set_Oatmost__one(Eq_y_0,Eq_y_1)
| ~ c_Infinite__Set_Oatmost__one(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_220,axiom,
( c_lessequals(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_lessequals(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_221,axiom,
( c_less(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_less(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_222,axiom,
( c_List_Odistinct(Eq_y_0,Eq_y_1)
| ~ c_List_Odistinct(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_223,axiom,
( c_Wellfounded__Recursion_Owf(Eq_y_0,Eq_y_1)
| ~ c_Wellfounded__Recursion_Owf(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_224,axiom,
( class_Orderings_Oorder(Eq_y_0)
| ~ class_Orderings_Oorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_225,axiom,
( c_Relation_Otrans(Eq_y_0,Eq_y_1)
| ~ c_Relation_Otrans(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_226,axiom,
( class_Finite__Set_Ofinite(Eq_y_0)
| ~ class_Finite__Set_Ofinite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_227,axiom,
( class_HOL_Ominus(Eq_y_0)
| ~ class_HOL_Ominus(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_228,axiom,
( class_HOL_Oone(Eq_y_0)
| ~ class_HOL_Oone(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_229,axiom,
( class_Ring__and__Field_Osemiring(Eq_y_0)
| ~ class_Ring__and__Field_Osemiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_230,axiom,
( class_Ring__and__Field_Ocomm__semiring(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_231,axiom,
( class_OrderedGroup_Ocomm__monoid__add(Eq_y_0)
| ~ class_OrderedGroup_Ocomm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_232,axiom,
( class_Ring__and__Field_Osemiring__0(Eq_y_0)
| ~ class_Ring__and__Field_Osemiring__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_233,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_234,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Ocancel__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_235,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_236,axiom,
( class_OrderedGroup_Oab__group__add(Eq_y_0)
| ~ class_OrderedGroup_Oab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_237,axiom,
( class_Ring__and__Field_Osemiring__0__cancel(Eq_y_0)
| ~ class_Ring__and__Field_Osemiring__0__cancel(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_238,axiom,
( class_Ring__and__Field_Oring(Eq_y_0)
| ~ class_Ring__and__Field_Oring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_239,axiom,
( class_HOL_Oplus(Eq_y_0)
| ~ class_HOL_Oplus(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_240,axiom,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_241,axiom,
( class_Ring__and__Field_Ocomm__ring(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_242,axiom,
( class_Ring__and__Field_Oaxclass__0__neq__1(Eq_y_0)
| ~ class_Ring__and__Field_Oaxclass__0__neq__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_243,axiom,
( class_OrderedGroup_Omonoid__mult(Eq_y_0)
| ~ class_OrderedGroup_Omonoid__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_244,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(Eq_y_0)
| ~ class_OrderedGroup_Ocomm__monoid__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_245,axiom,
( class_Ring__and__Field_Osemiring__1(Eq_y_0)
| ~ class_Ring__and__Field_Osemiring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_246,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_247,axiom,
( class_Ring__and__Field_Osemiring__1__cancel(Eq_y_0)
| ~ class_Ring__and__Field_Osemiring__1__cancel(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_248,axiom,
( class_Ring__and__Field_Oring__1(Eq_y_0)
| ~ class_Ring__and__Field_Oring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_249,axiom,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_250,axiom,
( class_HOL_Otimes(Eq_y_0)
| ~ class_HOL_Otimes(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_251,axiom,
( class_Ring__and__Field_Ocomm__ring__1(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__ring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_252,axiom,
( class_LOrder_Omeet__semilorder(Eq_y_0)
| ~ class_LOrder_Omeet__semilorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_253,axiom,
( class_LOrder_Ojoin__semilorder(Eq_y_0)
| ~ class_LOrder_Ojoin__semilorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_254,axiom,
( class_LOrder_Olorder(Eq_y_0)
| ~ class_LOrder_Olorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_255,axiom,
( class_Orderings_Olinorder(Eq_y_0)
| ~ class_Orderings_Olinorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_256,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_257,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_258,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(Eq_y_0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_259,axiom,
( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_260,axiom,
( class_HOL_Ozero(Eq_y_0)
| ~ class_HOL_Ozero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_261,axiom,
( class_Ring__and__Field_Opordered__semiring(Eq_y_0)
| ~ class_Ring__and__Field_Opordered__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_262,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(Eq_y_0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_263,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_264,axiom,
( class_Ring__and__Field_Opordered__comm__semiring(Eq_y_0)
| ~ class_Ring__and__Field_Opordered__comm__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_265,axiom,
( class_Ring__and__Field_Opordered__cancel__comm__semiring(Eq_y_0)
| ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_266,axiom,
( class_Ring__and__Field_Oordered__comm__semiring__strict(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_267,axiom,
( class_Ring__and__Field_Oaxclass__abs__if(Eq_y_0)
| ~ class_Ring__and__Field_Oaxclass__abs__if(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_268,axiom,
( class_OrderedGroup_Opordered__ab__group__add(Eq_y_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_269,axiom,
( class_OrderedGroup_Olordered__ab__group(Eq_y_0)
| ~ class_OrderedGroup_Olordered__ab__group(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_270,axiom,
( class_Ring__and__Field_Opordered__ring(Eq_y_0)
| ~ class_Ring__and__Field_Opordered__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_271,axiom,
( class_Orderings_Oord(Eq_y_0)
| ~ class_Orderings_Oord(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_272,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(Eq_y_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_273,axiom,
( class_OrderedGroup_Olordered__ab__group__meet(Eq_y_0)
| ~ class_OrderedGroup_Olordered__ab__group__meet(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_274,axiom,
( class_OrderedGroup_Olordered__ab__group__join(Eq_y_0)
| ~ class_OrderedGroup_Olordered__ab__group__join(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_275,axiom,
( class_Ring__and__Field_Olordered__ring(Eq_y_0)
| ~ class_Ring__and__Field_Olordered__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_276,axiom,
( class_Ring__and__Field_Oaxclass__no__zero__divisors(Eq_y_0)
| ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_277,axiom,
( class_Ring__and__Field_Oordered__ring__strict(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__ring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_278,axiom,
( class_Ring__and__Field_Oordered__semidom(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__semidom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_279,axiom,
( class_Ring__and__Field_Oidom(Eq_y_0)
| ~ class_Ring__and__Field_Oidom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_280,axiom,
( class_Ring__and__Field_Oordered__idom(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__idom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_281,axiom,
( class_Numeral_Onumber(Eq_y_0)
| ~ class_Numeral_Onumber(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_282,axiom,
( class_OrderedGroup_Osemigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Osemigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_283,axiom,
( class_Numeral_Onumber__ring(Eq_y_0)
| ~ class_Numeral_Onumber__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_284,axiom,
( class_Divides_Odiv(Eq_y_0)
| ~ class_Divides_Odiv(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_285,axiom,
( class_Nat_Opower(Eq_y_0)
| ~ class_Nat_Opower(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_286,axiom,
( class_Power_Orecpower(Eq_y_0)
| ~ class_Power_Orecpower(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_287,axiom,
( class_Parity_Oeven__odd(Eq_y_0)
| ~ class_Parity_Oeven__odd(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_288,axiom,
( class_OrderedGroup_Oab__semigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Oab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_289,axiom,
( class_OrderedGroup_Osemigroup__mult(Eq_y_0)
| ~ class_OrderedGroup_Osemigroup__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_290,axiom,
( class_OrderedGroup_Oab__semigroup__mult(Eq_y_0)
| ~ class_OrderedGroup_Oab__semigroup__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_291,axiom,
( class_Wellfounded__Recursion_Owellorder(Eq_y_0)
| ~ class_Wellfounded__Recursion_Owellorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_292,axiom,
( class_Ring__and__Field_Odivision__by__zero(Eq_y_0)
| ~ class_Ring__and__Field_Odivision__by__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_293,axiom,
( class_HOL_Oinverse(Eq_y_0)
| ~ class_HOL_Oinverse(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_294,axiom,
( class_Ring__and__Field_Ofield(Eq_y_0)
| ~ class_Ring__and__Field_Ofield(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_295,axiom,
( class_Ring__and__Field_Oordered__field(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__field(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_296,axiom,
( class_Ring__and__Field_Opordered__comm__ring(Eq_y_0)
| ~ class_Ring__and__Field_Opordered__comm__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_297,axiom,
( c_IntDef_Oneg(Eq_y_0,Eq_y_1)
| ~ c_IntDef_Oneg(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_298,axiom,
( c_IntDef_Oiszero(Eq_y_0,Eq_y_1)
| ~ c_IntDef_Oiszero(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_299,axiom,
( c_List_Onull(Eq_y_0,Eq_y_1)
| ~ c_List_Onull(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_300,axiom,
( c_List_Oop_Amem(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_List_Oop_Amem(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_301,axiom,
( c_Parity_Oeven(Eq_y_0,Eq_y_1)
| ~ c_Parity_Oeven(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_302,axiom,
( c_Wellfounded__Recursion_Oacyclic(Eq_y_0,Eq_y_1)
| ~ c_Wellfounded__Recursion_Oacyclic(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV341-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 03:23:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 150.25/150.55 % SZS status Unsatisfiable for theBenchmark
% 150.25/150.55 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------