%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV824-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 09:04:21 AM UTC 2026
% Result : Unsatisfiable 30.26s 35.52s
% Output : Proof 30.26s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Suc__diff__le_0,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ),
file('theBenchmark.p',cls_Suc__diff__le_0) ).
cnf(cls_sum__squares__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__ge__zero_0) ).
cnf(cls_mod__by__0_0,axiom,
( c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__by__0_0) ).
cnf(cls_mod__self_0,axiom,
( c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__self_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_nat__add__commute_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),
file('theBenchmark.p',cls_nat__add__commute_0) ).
cnf(cls_less__add__eq__less_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_less__add__eq__less_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_mult__eq__1__iff_0,axiom,
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_mult__eq__1__iff_0) ).
cnf(cls_mult__eq__1__iff_1,axiom,
( V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_mult__eq__1__iff_1) ).
cnf(cls_mod__le__divisor_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_mod__le__divisor_0) ).
cnf(cls_diff__less__mono2_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__less__mono2_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
cnf(cls_add__eq__self__zero_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m ),
file('theBenchmark.p',cls_add__eq__self__zero_0) ).
cnf(cls_natgb_Oadd__r0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(tc_nat)
| V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) ),
file('theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
cnf(cls_mult__less__imp__less__right_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__imp__less__right_0) ).
cnf(cls_le__add__iff1_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_le__add__iff1_0) ).
cnf(cls_le__add__iff1_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_le__add__iff1_1) ).
cnf(cls_le__add__iff2_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_le__add__iff2_0) ).
cnf(cls_le__add__iff2_1,axiom,
( ~ c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_le__add__iff2_1) ).
cnf(cls_trans__less__add2_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_trans__less__add2_0) ).
cnf(cls_trans__less__add1_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_trans__less__add1_0) ).
cnf(cls_add__lessD1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat)
| c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ),
file('theBenchmark.p',cls_add__lessD1_0) ).
cnf(cls_termination__basic__simps_I2_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat)
| c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
cnf(cls_termination__basic__simps_I1_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
cnf(cls_less__eq__Suc__le_1,axiom,
( ~ c_lessequals(c_Suc(V_n),V_m,tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ),
file('theBenchmark.p',cls_less__eq__Suc__le_1) ).
cnf(cls_less__eq__Suc__le_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| c_lessequals(c_Suc(V_n),V_m,tc_nat) ),
file('theBenchmark.p',cls_less__eq__Suc__le_0) ).
cnf(cls_Suc__le__eq_0,axiom,
( ~ c_lessequals(c_Suc(V_m),V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__le__eq_0) ).
cnf(cls_Suc__leI_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_lessequals(c_Suc(V_m),V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__leI_0) ).
cnf(cls_add__increasing2_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__increasing2_0) ).
cnf(cls_add__increasing_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,V_c,T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__increasing_0) ).
cnf(cls_min__max_Oinf__sup__distrib1_0,axiom,
( c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
cnf(cls_min__max_Oinf__sup__distrib2_0,axiom,
( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_y,V_x,T_a),c_Orderings_Oord__class_Omin(V_z,V_x,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
cnf(cls_com_Osimps_I3_J_0,axiom,
( V_com1 = V_com1_H
| c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ),
file('theBenchmark.p',cls_com_Osimps_I3_J_0) ).
cnf(cls_com_Osimps_I3_J_1,axiom,
( V_com2 = V_com2_H
| c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ),
file('theBenchmark.p',cls_com_Osimps_I3_J_1) ).
cnf(cls_le__maxI2_0,axiom,
( c_lessequals(V_y,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_le__maxI2_0) ).
cnf(cls_le__maxI1_0,axiom,
( c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_le__maxI1_0) ).
cnf(cls_min__max_Ole__supI_0,axiom,
( ~ c_lessequals(V_a,V_x,T_a)
| ~ c_lessequals(V_b,V_x,T_a)
| c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__supI_0) ).
cnf(cls_min__max_Osup__least_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_z,V_x,T_a)
| c_lessequals(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__least_0) ).
cnf(cls_min__max_Ole__sup__iff_2,axiom,
( ~ c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
cnf(cls_le__diff__conv2_1,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
| c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_le__diff__conv2_1) ).
cnf(cls_le__diff__conv2_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| ~ c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ),
file('theBenchmark.p',cls_le__diff__conv2_0) ).
cnf(cls_less__iff__Suc__add_1,axiom,
c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat),
file('theBenchmark.p',cls_less__iff__Suc__add_1) ).
cnf(cls_less__add__Suc2_0,axiom,
c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat),
file('theBenchmark.p',cls_less__add__Suc2_0) ).
cnf(cls_less__add__Suc1_0,axiom,
c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat),
file('theBenchmark.p',cls_less__add__Suc1_0) ).
cnf(cls_eq__add__iff1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) = V_d
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff1_0) ).
cnf(cls_eq__add__iff2_0,axiom,
( V_c = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff2_0) ).
cnf(cls_nat__less__add__iff2_1,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__less__add__iff2_1) ).
cnf(cls_nat__less__add__iff2_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__less__add__iff2_0) ).
cnf(cls_nat__less__add__iff1_1,axiom,
( ~ c_lessequals(V_j,V_i,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__less__add__iff1_1) ).
cnf(cls_nat__less__add__iff1_0,axiom,
( ~ c_lessequals(V_j,V_i,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__less__add__iff1_0) ).
cnf(cls_eq__add__iff2_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff2_1) ).
cnf(cls_mult__strict__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__mono_0) ).
cnf(cls_zmod__simps_I4_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_zmod__simps_I4_J_0) ).
cnf(cls_min__max_Oinf__le1_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__le1_0) ).
cnf(cls_min__max_Oinf__le2_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__le2_0) ).
cnf(cls_min__max_Ole__infI_0,axiom,
( ~ c_lessequals(V_x,V_a,T_a)
| ~ c_lessequals(V_x,V_b,T_a)
| c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__infI_0) ).
cnf(cls_min__max_Ole__inf__iff_2,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).
cnf(cls_min__max_Oinf__greatest_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__greatest_0) ).
cnf(cls_eq__add__iff1_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff1_1) ).
cnf(cls_diff__is__0__eq_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_diff__is__0__eq_1) ).
cnf(cls_diff__is__0__eq_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_diff__is__0__eq_0) ).
cnf(cls_min__diff__distrib__left_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_min__diff__distrib__left_0) ).
cnf(cls_max__less__iff__conj_2,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_max__less__iff__conj_2) ).
cnf(cls_diff__Suc__diff__eq2_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_m,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(V_j),c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
cnf(cls_add__strict__increasing_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__strict__increasing_0) ).
cnf(cls_add__is__1_4,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('theBenchmark.p',cls_add__is__1_4) ).
cnf(cls_mod__mod__trivial_0,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mod__trivial_0) ).
cnf(cls_mod__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__0_0) ).
cnf(cls_min__less__iff__conj_2,axiom,
( ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__less__iff__conj_2) ).
cnf(cls_natgb_Oadd__mul__solve_1,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat),
file('theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
cnf(cls_natgb_Onoteq__reduce_1,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),tc_nat),
file('theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
cnf(cls_less__Suc0_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_less__Suc0_0) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
cnf(cls_min__max_Oinf__left__idem_0,axiom,
( c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omin(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
cnf(cls_nat__diff__add__eq2_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__diff__add__eq2_0) ).
cnf(cls_nat__diff__add__eq1_0,axiom,
( ~ c_lessequals(V_j,V_i,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__diff__add__eq1_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_mult__le__cancel2_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel2_1) ).
cnf(cls_mult__le__cancel1_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel1_1) ).
cnf(cls_com_Osimps_I49_J_0,axiom,
c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2),
file('theBenchmark.p',cls_com_Osimps_I49_J_0) ).
cnf(cls_add__le__mono_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_lessequals(V_k,V_l,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_add__le__mono_0) ).
cnf(cls_add__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__mono_0) ).
cnf(cls_less__Suc__eq__le_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ),
file('theBenchmark.p',cls_less__Suc__eq__le_1) ).
cnf(cls_less__Suc__eq__le_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_less__Suc__eq__le_0) ).
cnf(cls_le__less__Suc__eq_1,axiom,
( c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat)
| ~ c_lessequals(V_x,V_x,tc_nat) ),
file('theBenchmark.p',cls_le__less__Suc__eq_1) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_nat__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),
file('theBenchmark.p',cls_nat__mult__commute_0) ).
cnf(cls_double__eq__0__iff_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__eq__0__iff_1) ).
cnf(cls_add__is__0_2,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_add__is__0_2) ).
cnf(cls_add__nonneg__eq__0__iff_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_diff__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat),
file('theBenchmark.p',cls_diff__less__Suc_0) ).
cnf(cls_mod__add__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__eq_0) ).
cnf(cls_add__nonneg__nonneg_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonneg__nonneg_0) ).
cnf(cls_order__less__trans_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__trans_0) ).
cnf(cls_xt1_I10_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I10_J_0) ).
cnf(cls_min__max_Ole__iff__sup_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
cnf(cls_min__max_Ole__iff__sup_1,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_Orderings_Oord__class_Omax(V_x,V_y,T_a) != V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
cnf(cls_min__max_Osup__absorb1_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_x
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_add__cancel__21_1,axiom,
( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_nat__add__left__commute_0,axiom,
c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat),
file('theBenchmark.p',cls_nat__add__left__commute_0) ).
cnf(cls_nat__add__assoc_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_nat__add__assoc_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Oab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_add__gr__0_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_add__gr__0_0) ).
cnf(cls_gr__implies__not0_0,axiom,
~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_gr__implies__not0_0) ).
cnf(cls_mult__less__imp__less__left_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__imp__less__left_0) ).
cnf(cls_mult__right__less__imp__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring(T_a) ),
file('theBenchmark.p',cls_mult__right__less__imp__less_0) ).
cnf(cls_mult__left__less__imp__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring(T_a) ),
file('theBenchmark.p',cls_mult__left__less__imp__less_0) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_right__minus__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_right__minus__eq_1) ).
cnf(cls_diff__0__right_0,axiom,
( c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_diff__0__right_0) ).
cnf(cls_diff__self_0,axiom,
( c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_diff__self_0) ).
cnf(cls_diff__self__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_diff__self__eq__0_0) ).
cnf(cls_minus__nat_Odiff__0_0,axiom,
c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m,
file('theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
cnf(cls_mod__mult__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__eq_0) ).
cnf(cls_le__max__iff__disj_0,axiom,
( ~ c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| c_lessequals(V_z,V_x,T_a)
| c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_le__max__iff__disj_0) ).
cnf(cls_nat__eq__add__iff1_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),tc_nat)
| ~ c_lessequals(V_j,V_i,tc_nat) ),
file('theBenchmark.p',cls_nat__eq__add__iff1_1) ).
cnf(cls_nat__mult__eq__cancel__disj_0,axiom,
( V_k = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = V_n
| c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
cnf(cls_mult__cancel1_0,axiom,
( V_m = V_n
| V_k = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_mult__cancel1_0) ).
cnf(cls_mult__cancel2_0,axiom,
( V_m = V_n
| V_k = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat) ),
file('theBenchmark.p',cls_mult__cancel2_0) ).
cnf(cls_min__max_Ole__inf__iff_1,axiom,
( ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
cnf(cls_min__max_Ole__inf__iff_0,axiom,
( ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
cnf(cls_min__le__iff__disj_2,axiom,
( ~ c_lessequals(V_y,V_z,T_a)
| c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__le__iff__disj_2) ).
cnf(cls_min__le__iff__disj_1,axiom,
( ~ c_lessequals(V_x,V_z,T_a)
| c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__le__iff__disj_1) ).
cnf(cls_min__max_Ole__infI2_0,axiom,
( ~ c_lessequals(V_b,V_x,T_a)
| c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__infI2_0) ).
cnf(cls_min__max_Ole__infI1_0,axiom,
( ~ c_lessequals(V_a,V_x,T_a)
| c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__infI1_0) ).
cnf(cls_min__max_Ole__infE_1,axiom,
( ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a)
| c_lessequals(V_x,V_b,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__infE_1) ).
cnf(cls_min__max_Ole__infE_0,axiom,
( ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a)
| c_lessequals(V_x,V_a,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__infE_0) ).
cnf(cls_min__0L_0,axiom,
c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_min__0L_0) ).
cnf(cls_min__0R_0,axiom,
c_Orderings_Oord__class_Omin(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_min__0R_0) ).
cnf(cls_add__nonneg__eq__0__iff_1,axiom,
( V_y = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
cnf(cls_add__nonneg__eq__0__iff_0,axiom,
( V_x = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
cnf(cls_add__is__0_0,axiom,
( V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_add__is__0_0) ).
cnf(cls_add__is__0_1,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_add__is__0_1) ).
cnf(cls_double__eq__0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__eq__0__iff_0) ).
cnf(cls_less__add__iff2_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_less__add__iff2_1) ).
cnf(cls_less__add__iff2_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_less__add__iff2_0) ).
cnf(cls_less__add__iff1_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_less__add__iff1_1) ).
cnf(cls_less__add__iff1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_less__add__iff1_0) ).
cnf(cls_le__mod__geq_0,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_le__mod__geq_0) ).
cnf(cls_nat__eq__add__iff1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat) = V_n
| ~ c_lessequals(V_j,V_i,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__eq__add__iff1_0) ).
cnf(cls_nat__eq__add__iff2_0,axiom,
( V_m = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__eq__add__iff2_0) ).
cnf(cls_min__le__iff__disj_0,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
| c_lessequals(V_x,V_z,T_a)
| c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__le__iff__disj_0) ).
cnf(cls_nat__eq__add__iff2_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ),
file('theBenchmark.p',cls_nat__eq__add__iff2_1) ).
cnf(cls_mult__eq__0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) ),
file('theBenchmark.p',cls_mult__eq__0__iff_0) ).
cnf(cls_no__zero__divisors_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
file('theBenchmark.p',cls_no__zero__divisors_0) ).
cnf(cls_mult__is__0_0,axiom,
( V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_mult__is__0_0) ).
cnf(cls_no__zero__divirors__neq0_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
file('theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
cnf(cls_mod__add__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__cong_0) ).
cnf(cls_less__Suc0_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('theBenchmark.p',cls_less__Suc0_1) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
cnf(cls_even__less__0__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_even__less__0__iff_0) ).
cnf(cls_even__less__0__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_even__less__0__iff_1) ).
cnf(cls_one__is__add_1,axiom,
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_one__is__add_1) ).
cnf(cls_one__is__add_2,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_one__is__add_2) ).
cnf(cls_zero__less__mult__pos2_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_zero__less__mult__pos2_0) ).
cnf(cls_zero__less__mult__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_zero__less__mult__pos_0) ).
cnf(cls_mult__pos__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__pos__pos_0) ).
cnf(cls_mult__neg__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__neg__neg_0) ).
cnf(cls_nat__0__less__mult__iff_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
cnf(cls_min__max_Ole__sup__iff_1,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
cnf(cls_min__max_Ole__sup__iff_0,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
cnf(cls_le__max__iff__disj_2,axiom,
( ~ c_lessequals(V_z,V_y,T_a)
| c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_le__max__iff__disj_2) ).
cnf(cls_le__max__iff__disj_1,axiom,
( ~ c_lessequals(V_z,V_x,T_a)
| c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_le__max__iff__disj_1) ).
cnf(cls_min__max_Ole__supI2_0,axiom,
( ~ c_lessequals(V_x,V_b,T_a)
| c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__supI2_0) ).
cnf(cls_min__max_Ole__supI1_0,axiom,
( ~ c_lessequals(V_x,V_a,T_a)
| c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__supI1_0) ).
cnf(cls_min__max_Ole__supE_1,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a)
| c_lessequals(V_b,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__supE_1) ).
cnf(cls_min__max_Ole__supE_0,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a)
| c_lessequals(V_a,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__supE_0) ).
cnf(cls_le__diff__conv_0,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat)
| c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_le__diff__conv_0) ).
cnf(cls_le__diff__conv_1,axiom,
( ~ c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) ),
file('theBenchmark.p',cls_le__diff__conv_1) ).
cnf(cls_less__max__iff__disj_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_less__max__iff__disj_0) ).
cnf(cls_mult__Suc__right_0,axiom,
c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_mult__Suc__right_0) ).
cnf(cls_mult__Suc_0,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_mult__Suc_0) ).
cnf(cls_not__sum__squares__lt__zero_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
cnf(cls_nat__le__add__iff1_0,axiom,
( ~ c_lessequals(V_j,V_i,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__le__add__iff1_0) ).
cnf(cls_nat__le__add__iff1_1,axiom,
( ~ c_lessequals(V_j,V_i,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__le__add__iff1_1) ).
cnf(cls_nat__le__add__iff2_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_lessequals(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__le__add__iff2_0) ).
cnf(cls_nat__le__add__iff2_1,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_lessequals(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__le__add__iff2_1) ).
cnf(cls_mod__mult__self4_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat)),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat),
file('theBenchmark.p',cls_mod__mult__self4_0) ).
cnf(cls_min__less__iff__disj_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__less__iff__disj_0) ).
cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
( V_w = V_x
| V_y = V_z
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
( V_a = V_b
| V_c = V_d
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
cnf(cls_natgb_Onoteq__reduce_0,axiom,
( V_a = V_b
| V_c = V_d
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_d,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
cnf(cls_natgb_Oadd__mul__solve_0,axiom,
( V_w = V_x
| V_y = V_z
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
cnf(cls_add__nonpos__neg_0,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonpos__neg_0) ).
cnf(cls_add__neg__nonpos_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__neg__nonpos_0) ).
cnf(cls_sum__squares__le__zero__iff_2,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
cnf(cls_mod__mult__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__cong_0) ).
cnf(cls_diff__add__assoc_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__add__assoc_0) ).
cnf(cls_diff__add__assoc2_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) ),
file('theBenchmark.p',cls_diff__add__assoc2_0) ).
cnf(cls_mult__eq__1__iff_2,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('theBenchmark.p',cls_mult__eq__1__iff_2) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
cnf(cls_mult__eq__0__iff_2,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) ),
file('theBenchmark.p',cls_mult__eq__0__iff_2) ).
cnf(cls_mult__eq__0__iff_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) ),
file('theBenchmark.p',cls_mult__eq__0__iff_1) ).
cnf(cls_mult__zero__right_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) ),
file('theBenchmark.p',cls_mult__zero__right_0) ).
cnf(cls_mult__zero__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) ),
file('theBenchmark.p',cls_mult__zero__left_0) ).
cnf(cls_mult__is__0_1,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_mult__is__0_1) ).
cnf(cls_mult__is__0_2,axiom,
c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_mult__is__0_2) ).
cnf(cls_class__semiring_Omul__0_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Omul__0_0) ).
cnf(cls_not__less0_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_not__less0_0) ).
cnf(cls_one__le__mult__iff_1,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ),
file('theBenchmark.p',cls_one__le__mult__iff_1) ).
cnf(cls_one__le__mult__iff_0,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) ),
file('theBenchmark.p',cls_one__le__mult__iff_0) ).
cnf(cls_add__cancel__21_0,axiom,
( c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_y,V_u,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_trans__le__add2_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_trans__le__add2_0) ).
cnf(cls_trans__le__add1_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_trans__le__add1_0) ).
cnf(cls_add__leE_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_add__leE_1) ).
cnf(cls_add__leE_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_add__leE_0) ).
cnf(cls_termination__basic__simps_I4_J_0,axiom,
( ~ c_lessequals(V_x,V_z,tc_nat)
| c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
cnf(cls_termination__basic__simps_I3_J_0,axiom,
( ~ c_lessequals(V_x,V_y,tc_nat)
| c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
cnf(cls_mod__diff__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__left__eq_0) ).
cnf(cls_mod__diff__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__right__eq_0) ).
cnf(cls_min__max_Ole__iff__inf_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_x
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
cnf(cls_min__max_Ole__iff__inf_1,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_Orderings_Oord__class_Omin(V_x,V_y,T_a) != V_x
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
cnf(cls_min__max_Oinf__absorb2_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
cnf(cls_max__diff__distrib__left_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_max__diff__distrib__left_0) ).
cnf(cls_com_Osimps_I48_J_0,axiom,
c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OBODY(V_pname_H),
file('theBenchmark.p',cls_com_Osimps_I48_J_0) ).
cnf(cls_mod__less__divisor_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_mod__less__divisor_0) ).
cnf(cls_not__leE_0,axiom,
( c_lessequals(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_not__leE_0) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__antisym__conv2_1) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( c_lessequals(V_x,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__antisym__conv1_1) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__not__less_1) ).
cnf(cls_linorder__not__less_0,axiom,
( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__not__less_0) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__not__le_1) ).
cnf(cls_linorder__not__le_0,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__not__le_0) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_less__le__not__le_1) ).
cnf(cls_mod__add__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__left__eq_0) ).
cnf(cls_mod__add__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__right__eq_0) ).
cnf(cls_min__max_Oinf__assoc_0,axiom,
( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
cnf(cls_min__max_Oinf__left__commute_0,axiom,
( c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omin(V_y,c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
cnf(cls_one__is__add_5,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('theBenchmark.p',cls_one__is__add_5) ).
cnf(cls_add__strict__increasing2_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__strict__increasing2_0) ).
cnf(cls_diff__le__mono2_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__le__mono2_0) ).
cnf(cls_diff__le__mono_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_l,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_l,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__le__mono_0) ).
cnf(cls_le__diff__iff_1,axiom,
( ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_le__diff__iff_1) ).
cnf(cls_le__diff__iff_0,axiom,
( ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_le__diff__iff_0) ).
cnf(cls_diff__add__0_0,axiom,
c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_diff__add__0_0) ).
cnf(cls_diff__diff__left_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_diff__diff__left_0) ).
cnf(cls_eq__eqI_1,axiom,
( V_xa = V_y
| c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_eq__eqI_0,axiom,
( V_x_H = V_y_H
| c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_eq__diff__iff_0,axiom,
( V_m = V_n
| ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat) != c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat) ),
file('theBenchmark.p',cls_eq__diff__iff_0) ).
cnf(cls_min__max_Oinf__sup__absorb_0,axiom,
( c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = V_x
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
cnf(cls_nat__mult__eq__cancel1_0,axiom,
( V_m = V_n
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
cnf(cls_one__is__add_3,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_one__is__add_3) ).
cnf(cls_one__is__add_0,axiom,
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_one__is__add_0) ).
cnf(cls_mult__less__cancel2_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel2_0) ).
cnf(cls_mult__less__cancel1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel1_0) ).
cnf(cls_mult__le__cancel2_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel2_0) ).
cnf(cls_mult__le__cancel1_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel1_0) ).
cnf(cls_nat__mult__le__cancel1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__mult__le__cancel1_0) ).
cnf(cls_nat__mult__le__cancel1_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__mult__le__cancel1_1) ).
cnf(cls_mult__le__cancel__left__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_lessequals(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
cnf(cls_mult__le__cancel__left__neg_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
cnf(cls_mult__le__cancel__left__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
cnf(cls_mult__le__cancel__left__pos_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
cnf(cls_mult__left__le__imp__le_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__left__le__imp__le_0) ).
cnf(cls_mult__right__le__imp__le_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__right__le__imp__le_0) ).
cnf(cls_one__less__mult_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_one__less__mult_0) ).
cnf(cls_evalc_OSemi_0,axiom,
( ~ c_Natural_Oevalc(V_c0,V_s0,V_s1)
| ~ c_Natural_Oevalc(V_c1,V_s1,V_s2)
| c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_s2) ),
file('theBenchmark.p',cls_evalc_OSemi_0) ).
cnf(cls_diff__0__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_diff__0__eq__0_0) ).
cnf(cls_diff__cancel2_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
file('theBenchmark.p',cls_diff__cancel2_0) ).
cnf(cls_diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
file('theBenchmark.p',cls_diff__cancel_0) ).
cnf(cls_zero__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat),
file('theBenchmark.p',cls_zero__less__Suc_0) ).
cnf(cls_gr0__conv__Suc_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat),
file('theBenchmark.p',cls_gr0__conv__Suc_1) ).
cnf(cls_min__max_Oless__supI1_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a)
| c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oless__supI1_0) ).
cnf(cls_min__max_Oless__supI2_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a)
| c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oless__supI2_0) ).
cnf(cls_less__max__iff__disj_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_less__max__iff__disj_1) ).
cnf(cls_less__max__iff__disj_2,axiom,
( ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_less__max__iff__disj_2) ).
cnf(cls_max__less__iff__conj_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_max__less__iff__conj_0) ).
cnf(cls_max__less__iff__conj_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_max__less__iff__conj_1) ).
cnf(cls_min__max_Oinf__commute_0,axiom,
( c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = c_Orderings_Oord__class_Omin(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__commute_0) ).
cnf(cls_left__add__mult__distrib_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_k,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_u,tc_nat),V_k,tc_nat),
file('theBenchmark.p',cls_left__add__mult__distrib_0) ).
cnf(cls_combine__common__factor_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a)
| ~ class_Ring__and__Field_Osemiring(T_a) ),
file('theBenchmark.p',cls_combine__common__factor_0) ).
cnf(cls_diff__le__self_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat),
file('theBenchmark.p',cls_diff__le__self_0) ).
cnf(cls_nat__0__less__mult__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
cnf(cls_nat__0__less__mult__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ),
file('theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
cnf(cls_add__neg__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__neg__neg_0) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( V_x = V_y
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
cnf(cls_right__minus__eq_0,axiom,
( V_a = V_b
| c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_right__minus__eq_0) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( V_a = V_b
| c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
cnf(cls_sum__squares__le__zero__iff_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
cnf(cls_sum__squares__le__zero__iff_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
cnf(cls_diff__mult__distrib2_0,axiom,
c_HOL_Otimes__class_Otimes(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_diff__mult__distrib2_0) ).
cnf(cls_diff__mult__distrib_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_diff__mult__distrib_0) ).
cnf(cls_min__max_Oless__infI1_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oless__infI1_0) ).
cnf(cls_min__max_Oless__infI2_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oless__infI2_0) ).
cnf(cls_min__less__iff__conj_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__less__iff__conj_0) ).
cnf(cls_min__less__iff__conj_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a)
| c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__less__iff__conj_1) ).
cnf(cls_min__less__iff__disj_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__less__iff__disj_1) ).
cnf(cls_min__less__iff__disj_2,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__less__iff__disj_2) ).
cnf(cls_Nat_Odiff__diff__eq_0,axiom,
( ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
cnf(cls_diff__commute_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat),
file('theBenchmark.p',cls_diff__commute_0) ).
cnf(cls_le0_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),
file('theBenchmark.p',cls_le0_0) ).
cnf(cls_add__nonneg__pos_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonneg__pos_0) ).
cnf(cls_add__pos__nonneg_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__pos__nonneg_0) ).
cnf(cls_diff__less__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat)
| ~ c_lessequals(V_c,V_a,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_c,tc_nat),c_HOL_Ominus__class_Ominus(V_b,V_c,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__less__mono_0) ).
cnf(cls_mult__le__0__iff_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_4) ).
cnf(cls_mult__le__0__iff_5,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_5) ).
cnf(cls_split__mult__neg__le_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_split__mult__neg__le_0) ).
cnf(cls_split__mult__neg__le_1,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_split__mult__neg__le_1) ).
cnf(cls_diff__diff__right_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ),
file('theBenchmark.p',cls_diff__diff__right_0) ).
cnf(cls_mod__1_0,axiom,
c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_mod__1_0) ).
cnf(cls_less__imp__diff__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
file('theBenchmark.p',cls_less__imp__diff__less_0) ).
cnf(cls_mod__if_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = V_m ),
file('theBenchmark.p',cls_mod__if_0) ).
cnf(cls_one__is__add_4,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_one__is__add_4) ).
cnf(cls_less__le__not__le_2,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_less__le__not__le_2) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
file('theBenchmark.p',cls_nat__less__le_1) ).
cnf(cls_less__not__refl_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
file('theBenchmark.p',cls_less__not__refl_0) ).
cnf(cls_order__less__le_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__less__le_1) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__neq__iff_1) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__irrefl_0) ).
cnf(cls_le__imp__diff__is__add_1,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),V_i,tc_nat) = V_k
| ~ c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_le__imp__diff__is__add_1) ).
cnf(cls_min__max_Oinf__idem_0,axiom,
( c_Orderings_Oord__class_Omin(V_x,V_x,T_a) = V_x
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oinf__idem_0) ).
cnf(cls_le__0__eq_0,axiom,
( ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_le__0__eq_0) ).
cnf(cls_add__pos__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__pos__pos_0) ).
cnf(cls_le__add1_0,axiom,
c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat),
file('theBenchmark.p',cls_le__add1_0) ).
cnf(cls_le__add2_0,axiom,
c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_le__add2_0) ).
cnf(cls_le__iff__add_1,axiom,
c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat),
file('theBenchmark.p',cls_le__iff__add_1) ).
cnf(cls_nat__minus__add__max_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),V_m,tc_nat) = c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat),
file('theBenchmark.p',cls_nat__minus__add__max_0) ).
cnf(cls_evalc_OSkip_0,axiom,
c_Natural_Oevalc(c_Com_Ocom_OSKIP,V_s,V_s),
file('theBenchmark.p',cls_evalc_OSkip_0) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
cnf(cls_le__antisym_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(V_n,V_m,tc_nat)
| V_m = V_n ),
file('theBenchmark.p',cls_le__antisym_0) ).
cnf(cls_nat__neq__iff_0,axiom,
( V_m = V_n
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ),
file('theBenchmark.p',cls_nat__neq__iff_0) ).
cnf(cls_com__det_0,axiom,
( ~ c_Natural_Oevalc(V_c,V_s,V_t)
| ~ c_Natural_Oevalc(V_c,V_s,V_u)
| V_u = V_t ),
file('theBenchmark.p',cls_com__det_0) ).
cnf(cls_diffs0__imp__equal_0,axiom,
( V_m = V_n
| c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_diffs0__imp__equal_0) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) ),
file('theBenchmark.p',cls_linorder__neqE__nat_0) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| V_x = V_y
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_linorder__neqE_0,axiom,
( V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__neqE_0) ).
cnf(cls_order__antisym_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| V_x = V_y
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__antisym_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| V_x = V_y
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_linorder__less__linear_0,axiom,
( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__less__linear_0) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__antisym__conv3_0) ).
cnf(cls_mod__diff__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__cong_0) ).
cnf(cls_le__iff__diff__le__0_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__iff__diff__le__0_1) ).
cnf(cls_le__iff__diff__le__0_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__iff__diff__le__0_0) ).
cnf(cls_min__max_Osup__idem_0,axiom,
( c_Orderings_Oord__class_Omax(V_x,V_x,T_a) = V_x
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__idem_0) ).
cnf(cls_add__strict__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__strict__mono_0) ).
cnf(cls_add__less__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_add__less__mono_0) ).
cnf(cls_termination__basic__simps_I5_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| c_lessequals(V_x,V_y,tc_nat) ),
file('theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
cnf(cls_nat__less__le_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__less__le_0) ).
cnf(cls_order__le__less_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__le__less_1) ).
cnf(cls_order__less__imp__le_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__imp__le_0) ).
cnf(cls_diff__Suc__diff__eq1_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(V_m,c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_Suc(V_j),tc_nat) ),
file('theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
cnf(cls_less__iff__diff__less__0_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_less__iff__diff__less__0_1) ).
cnf(cls_less__iff__diff__less__0_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_less__iff__diff__less__0_0) ).
cnf(cls_add__le__cancel__right_1,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__le__cancel__right_1) ).
cnf(cls_add__le__cancel__right_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(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('theBenchmark.p',cls_add__le__cancel__right_0) ).
cnf(cls_add__le__cancel__left_1,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__le__cancel__left_1) ).
cnf(cls_add__le__cancel__left_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(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('theBenchmark.p',cls_add__le__cancel__left_0) ).
cnf(cls_add__right__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__right__mono_0) ).
cnf(cls_add__left__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__left__mono_0) ).
cnf(cls_add__le__mono1_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_add__le__mono1_0) ).
cnf(cls_nat__add__left__cancel__le_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
cnf(cls_nat__add__left__cancel__le_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
cnf(cls_le__imp__diff__is__add_0,axiom,
( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ),
file('theBenchmark.p',cls_le__imp__diff__is__add_0) ).
cnf(cls_le__add__diff__inverse_0,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m ),
file('theBenchmark.p',cls_le__add__diff__inverse_0) ).
cnf(cls_le__add__diff__inverse2_0,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m ),
file('theBenchmark.p',cls_le__add__diff__inverse2_0) ).
cnf(cls_mult__less__cancel1_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel1_1) ).
cnf(cls_mult__less__cancel2_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel2_1) ).
cnf(cls_add__diff__assoc_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) ),
file('theBenchmark.p',cls_add__diff__assoc_0) ).
cnf(cls_add__diff__assoc2_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat) ),
file('theBenchmark.p',cls_add__diff__assoc2_0) ).
cnf(cls_mult__left__idem_0,axiom,
( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) ),
file('theBenchmark.p',cls_mult__left__idem_0) ).
cnf(cls_nat__mod__eq__iff_1,axiom,
( c_Divides_Odiv__class_Omod(V_x,V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_y,V_n,tc_nat)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_n,V_xa,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_y,c_HOL_Otimes__class_Otimes(V_n,V_xb,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__mod__eq__iff_1) ).
cnf(cls_mult__less__le__imp__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__le__imp__less_0) ).
cnf(cls_mult__le__less__imp__less_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__less__imp__less_0) ).
cnf(cls_gr0I_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_gr0I_0) ).
cnf(cls_com_Osimps_I13_J_0,axiom,
c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP,
file('theBenchmark.p',cls_com_Osimps_I13_J_0) ).
cnf(cls_neq0__conv_1,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_neq0__conv_1) ).
cnf(cls_mod__add__self2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__self2_0) ).
cnf(cls_mod__add__self1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__self1_0) ).
cnf(cls_mult__le__0__iff_3,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_3) ).
cnf(cls_mult__le__0__iff_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_2) ).
cnf(cls_mult__le__0__iff_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_1) ).
cnf(cls_mult__le__0__iff_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_0) ).
cnf(cls_mult__pos__neg2_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__pos__neg2_0) ).
cnf(cls_mult__pos__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__pos__neg_0) ).
cnf(cls_mult__neg__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__neg__pos_0) ).
cnf(cls_n__less__m__mult__n_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
| c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_n__less__m__mult__n_0) ).
cnf(cls_n__less__n__mult__m_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
| c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_n__less__n__mult__m_0) ).
cnf(cls_less__diff__iff_0,axiom,
( ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_less__diff__iff_0) ).
cnf(cls_less__diff__iff_1,axiom,
( ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_less__diff__iff_1) ).
cnf(cls_pos__add__strict_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_pos__add__strict_0) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
cnf(cls_mult__cancel1_1,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),
file('theBenchmark.p',cls_mult__cancel1_1) ).
cnf(cls_mult__cancel2_1,axiom,
c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_mult__cancel2_1) ).
cnf(cls_not__add__less1_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat),
file('theBenchmark.p',cls_not__add__less1_0) ).
cnf(cls_not__add__less2_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat),
file('theBenchmark.p',cls_not__add__less2_0) ).
cnf(cls_mod__lemma_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_c,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_r,V_b,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(V_q,V_c,tc_nat),tc_nat),V_r,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mod__lemma_0) ).
cnf(cls_mult__right__mono__neg_0,axiom,
( ~ c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_mult__right__mono__neg_0) ).
cnf(cls_mult__left__mono__neg_0,axiom,
( ~ c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_mult__left__mono__neg_0) ).
cnf(cls_mult__right__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Omult__mono(T_a) ),
file('theBenchmark.p',cls_mult__right__mono_0) ).
cnf(cls_mult__left__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Omult__mono(T_a) ),
file('theBenchmark.p',cls_mult__left__mono_0) ).
cnf(cls_mult__mono1_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Omult__mono1(T_a) ),
file('theBenchmark.p',cls_mult__mono1_0) ).
cnf(cls_mod__if_1,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_mod__if_1) ).
cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
( V_r = c_HOL_Ozero__class_Ozero(T_a)
| V_c = V_d
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom,
( V_r = c_HOL_Ozero__class_Ozero(tc_nat)
| V_c = V_d
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
cnf(cls_sum__squares__eq__zero__iff_1,axiom,
( V_y = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
cnf(cls_sum__squares__eq__zero__iff_0,axiom,
( V_x = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
cnf(cls_mult__nonneg__nonpos_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
cnf(cls_mult__nonpos__nonneg_0,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
cnf(cls_mult__nonneg__nonpos2_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
cnf(cls_not__square__less__zero_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_not__square__less__zero_0) ).
cnf(cls_Suc__mult__less__cancel1_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
cnf(cls_Suc__mult__less__cancel1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
cnf(cls_natgb_Oadd__cancel_0,axiom,
( V_y = V_z
| c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat) != c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat) ),
file('theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
cnf(cls_nat__add__right__cancel_0,axiom,
( V_m = V_n
| c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat) != c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat) ),
file('theBenchmark.p',cls_nat__add__right__cancel_0) ).
cnf(cls_nat__add__left__cancel_0,axiom,
( V_m = V_n
| c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__add__left__cancel_0) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( V_y = V_z
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
cnf(cls_add__imp__eq_0,axiom,
( V_b = V_c
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__imp__eq_0) ).
cnf(cls_add__left__cancel_0,axiom,
( V_b = V_c
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
| ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__left__cancel_0) ).
cnf(cls_add__right__cancel_0,axiom,
( V_b = V_c
| c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
| ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_mod__less__eq__dividend_0,axiom,
c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_m,tc_nat),
file('theBenchmark.p',cls_mod__less__eq__dividend_0) ).
cnf(cls_min__add__distrib__left_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_min__add__distrib__left_0) ).
cnf(cls_le__add__diff_0,axiom,
( ~ c_lessequals(V_k,V_n,tc_nat)
| c_lessequals(V_m,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_le__add__diff_0) ).
cnf(cls_mod__diff__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__eq_0) ).
cnf(cls_mod__Suc_0,axiom,
( c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) != V_n ),
file('theBenchmark.p',cls_mod__Suc_0) ).
cnf(cls_mod__mult__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__left__eq_0) ).
cnf(cls_mod__mult__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__right__eq_0) ).
cnf(cls_add__is__1_3,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_add__is__1_3) ).
cnf(cls_add__is__1_0,axiom,
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_add__is__1_0) ).
cnf(cls_Suc__mult__le__cancel1_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).
cnf(cls_Suc__mult__le__cancel1_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).
cnf(cls_sum__squares__gt__zero__iff_1,axiom,
( V_x = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
cnf(cls_sum__squares__gt__zero__iff_2,axiom,
( V_y = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_com_Osimps_I6_J_0,axiom,
( V_pname = V_pname_H
| c_Com_Ocom_OBODY(V_pname) != c_Com_Ocom_OBODY(V_pname_H) ),
file('theBenchmark.p',cls_com_Osimps_I6_J_0) ).
cnf(cls_min__max_Osup__commute_0,axiom,
( c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = c_Orderings_Oord__class_Omax(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__commute_0) ).
cnf(cls_min__max_Odistrib__inf__le_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a),c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
cnf(cls_max__0R_0,axiom,
c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n,
file('theBenchmark.p',cls_max__0R_0) ).
cnf(cls_max__0L_0,axiom,
c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n,
file('theBenchmark.p',cls_max__0L_0) ).
cnf(cls_min__max_Osup__inf__absorb_0,axiom,
( c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = V_x
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
cnf(cls_le__square_0,axiom,
c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),
file('theBenchmark.p',cls_le__square_0) ).
cnf(cls_mult__less__cancel__left__disj_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
cnf(cls_mult__less__cancel__left__disj_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
cnf(cls_mult__less__cancel__right__disj_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
cnf(cls_mult__less__cancel__right__disj_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
cnf(cls_diff__diff__cancel_0,axiom,
( ~ c_lessequals(V_i,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = V_i ),
file('theBenchmark.p',cls_diff__diff__cancel_0) ).
cnf(cls_mod__mult__distrib2_0,axiom,
c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_mod__mult__distrib2_0) ).
cnf(cls_mod__mult__distrib_0,axiom,
c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_k,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_mod__mult__distrib_0) ).
cnf(cls_mult__less__cancel2_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel2_2) ).
cnf(cls_mult__less__cancel1_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel1_2) ).
cnf(cls_mult__less__mono2_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__less__mono2_0) ).
cnf(cls_mult__less__mono1_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__less__mono1_0) ).
cnf(cls_nat__mult__less__cancel1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
cnf(cls_nat__mult__less__cancel1_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
cnf(cls_mult__less__cancel__left__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
cnf(cls_mult__less__cancel__left__neg_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
cnf(cls_mult__less__cancel__left__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
cnf(cls_mult__less__cancel__left__pos_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
cnf(cls_mult__strict__left__mono__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
cnf(cls_mult__strict__left__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__left__mono_0) ).
cnf(cls_mult__less__cancel__left__disj_4,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
cnf(cls_mult__less__cancel__left__disj_5,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
cnf(cls_mult__strict__right__mono__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
cnf(cls_mult__strict__right__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__right__mono_0) ).
cnf(cls_mult__less__cancel__right__disj_4,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
cnf(cls_mult__less__cancel__right__disj_5,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
cnf(cls_mult__strict__left__mono__comm_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
cnf(cls_com_Osimps_I18_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OBODY(V_pname_H),
file('theBenchmark.p',cls_com_Osimps_I18_J_0) ).
cnf(cls_max__add__distrib__left_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_max__add__distrib__left_0) ).
cnf(cls_mult__le__mono_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_lessequals(V_k,V_l,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_l,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__mono_0) ).
cnf(cls_le__cube_0,axiom,
c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),tc_nat),
file('theBenchmark.p',cls_le__cube_0) ).
cnf(cls_mult__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('theBenchmark.p',cls_mult__mono_0) ).
cnf(cls_mult__mono_H_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('theBenchmark.p',cls_mult__mono_H_0) ).
cnf(cls_min__max_Osup__assoc_0,axiom,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__assoc_0) ).
cnf(cls_min__max_Osup__left__commute_0,axiom,
( c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omax(V_y,c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
cnf(cls_mod__mult__self3_0,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat),V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),
file('theBenchmark.p',cls_mod__mult__self3_0) ).
cnf(cls_mod__mult__self1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self1_0) ).
cnf(cls_mod__mult__self2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self2_0) ).
cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n,
file('theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m,
file('theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
cnf(cls_add__0__left_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_add__0__left_0) ).
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(cls_sum__squares__gt__zero__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
cnf(cls_min__max_Osup__left__idem_0,axiom,
( c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omax(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
cnf(cls_zero__le__mult__iff_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_0) ).
cnf(cls_zero__le__mult__iff_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_1) ).
cnf(cls_zero__le__mult__iff_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_2) ).
cnf(cls_zero__le__mult__iff_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_3) ).
cnf(cls_id__apply_0,axiom,
c_Fun_Oid(V_x,T_a) = V_x,
file('theBenchmark.p',cls_id__apply_0) ).
cnf(cls_diff__add__inverse2_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m,
file('theBenchmark.p',cls_diff__add__inverse2_0) ).
cnf(cls_diff__add__inverse_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat) = V_m,
file('theBenchmark.p',cls_diff__add__inverse_0) ).
cnf(cls_add__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_add__diff__cancel_0) ).
cnf(cls_add__le__less__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__le__less__mono_0) ).
cnf(cls_add__less__le__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__less__le__mono_0) ).
cnf(cls_evalc__elim__cases_I1_J_0,axiom,
( ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,V_s,V_t)
| V_t = V_s ),
file('theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
cnf(cls_add__gr__0_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_add__gr__0_2) ).
cnf(cls_add__gr__0_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_add__gr__0_1) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
cnf(cls_le__0__eq_1,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_le__0__eq_1) ).
cnf(cls_less__diff__conv_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ),
file('theBenchmark.p',cls_less__diff__conv_0) ).
cnf(cls_less__diff__conv_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
| c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_less__diff__conv_1) ).
cnf(cls_add__strict__right__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__strict__right__mono_0) ).
cnf(cls_add__less__cancel__right_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__less__cancel__right_1) ).
cnf(cls_add__less__cancel__right_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__less__cancel__right_0) ).
cnf(cls_add__strict__left__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__strict__left__mono_0) ).
cnf(cls_add__less__cancel__left_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__less__cancel__left_1) ).
cnf(cls_add__less__cancel__left_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__less__cancel__left_0) ).
cnf(cls_add__less__mono1_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_add__less__mono1_0) ).
cnf(cls_nat__add__left__cancel__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
cnf(cls_nat__add__left__cancel__less_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
cnf(cls_one__le__mult__iff_2,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_one__le__mult__iff_2) ).
cnf(cls_xt1_I6_J_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| c_lessequals(V_z,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(cls_xt1_I7_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_xt1_I8_J_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I8_J_0) ).
cnf(cls_add__nonpos__nonpos_0,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonpos__nonpos_0) ).
cnf(cls_order__trans_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__trans_0) ).
cnf(cls_le__refl_0,axiom,
c_lessequals(V_n,V_n,tc_nat),
file('theBenchmark.p',cls_le__refl_0) ).
cnf(cls_le__trans_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_lessequals(V_j,V_k,tc_nat)
| c_lessequals(V_i,V_k,tc_nat) ),
file('theBenchmark.p',cls_le__trans_0) ).
cnf(cls_eq__imp__le_0,axiom,
c_lessequals(V_x,V_x,tc_nat),
file('theBenchmark.p',cls_eq__imp__le_0) ).
cnf(cls_order__eq__iff_0,axiom,
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_order__eq__refl_0,axiom,
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__eq__refl_0) ).
cnf(cls_order__le__less__trans_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__le__less__trans_0) ).
cnf(cls_order__less__le__trans_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__le__trans_0) ).
cnf(cls_le__add__right__mono_0,axiom,
( ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__add__right__mono_0) ).
cnf(cls_min__diff_0,axiom,
c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_m,V_i,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat),V_i,tc_nat),
file('theBenchmark.p',cls_min__diff_0) ).
cnf(cls_add__is__1_5,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('theBenchmark.p',cls_add__is__1_5) ).
cnf(cls_mult__idem_0,axiom,
( c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) ),
file('theBenchmark.p',cls_mult__idem_0) ).
cnf(cls_mod__mult__self2__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
cnf(cls_mod__mult__self1__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
cnf(cls_mod__eq__0__iff_1,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_mod__eq__0__iff_1) ).
cnf(cls_mult__strict__mono_H_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__mono_H_0) ).
cnf(cls_le__less__Suc__eq_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| V_n = V_m ),
file('theBenchmark.p',cls_le__less__Suc__eq_0) ).
cnf(cls_com_Osimps_I19_J_0,axiom,
c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSKIP,
file('theBenchmark.p',cls_com_Osimps_I19_J_0) ).
cnf(cls_mult__le__mono1_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__mono1_0) ).
cnf(cls_mult__le__mono2_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__mono2_0) ).
cnf(cls_mult__le__cancel1_2,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel1_2) ).
cnf(cls_mult__le__cancel2_2,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel2_2) ).
cnf(cls_zero__less__diff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_zero__less__diff_0) ).
cnf(cls_zero__less__diff_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_zero__less__diff_1) ).
cnf(cls_sum__squares__eq__zero__iff_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
cnf(cls_mult__less__cancel__right__disj_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
cnf(cls_mult__less__cancel__right__disj_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
cnf(cls_mult__less__cancel__left__disj_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
cnf(cls_mult__less__cancel__left__disj_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
cnf(cls_Suc__pred_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ),
file('theBenchmark.p',cls_Suc__pred_0) ).
cnf(cls_diff__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ),
file('theBenchmark.p',cls_diff__less_0) ).
cnf(cls_min__max_Odistrib__sup__le_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
cnf(cls_le__eqI_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_y_H,V_x_H,T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__eqI_0) ).
cnf(cls_le__eqI_1,axiom,
( ~ c_lessequals(V_y_H,V_x_H,T_a)
| c_lessequals(V_y,V_x,T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__eqI_1) ).
cnf(cls_less__eqI_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_less__eqI_0) ).
cnf(cls_less__eqI_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_less__eqI_1) ).
cnf(cls_zmod__simps_I1_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_zmod__simps_I1_J_0) ).
cnf(cls_zmod__simps_I2_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_zmod__simps_I2_J_0) ).
cnf(cls_add__diff__inverse_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m ),
file('theBenchmark.p',cls_add__diff__inverse_0) ).
cnf(cls_diff__Suc__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_diff__Suc__less_0) ).
cnf(cls_add__is__1_1,axiom,
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_add__is__1_1) ).
cnf(cls_add__is__1_2,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_add__is__1_2) ).
cnf(cls_min__max_Osup__inf__distrib2_0,axiom,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_y,V_z,T_a),V_x,T_a) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_y,V_x,T_a),c_Orderings_Oord__class_Omax(V_z,V_x,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
cnf(cls_min__max_Osup__inf__distrib1_0,axiom,
( c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
cnf(cls_xt1_I11_J_0,axiom,
( ~ c_lessequals(V_b,V_a,T_a)
| V_a = V_b
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_xt1_I12_J_0,axiom,
( V_a = V_b
| ~ c_lessequals(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I12_J_0) ).
cnf(cls_nat__less__le_2,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| V_m = V_n
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__less__le_2) ).
cnf(cls_le__eq__less__or__eq_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| V_m = V_n ),
file('theBenchmark.p',cls_le__eq__less__or__eq_0) ).
cnf(cls_le__neq__implies__less_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| V_m = V_n
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_le__neq__implies__less_0) ).
cnf(cls_order__le__less_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__le__less_0) ).
cnf(cls_order__less__le_2,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__less__le_2) ).
cnf(cls_order__le__neq__trans_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| V_a = V_b
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__le__neq__trans_0) ).
cnf(cls_order__neq__le__trans_0,axiom,
( V_a = V_b
| ~ c_lessequals(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__neq__le__trans_0) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__antisym__conv1_0) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__antisym__conv2_0) ).
cnf(cls_mult__nonneg__nonneg_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
cnf(cls_zero__le__mult__iff_5,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_5) ).
cnf(cls_zero__le__mult__iff_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_4) ).
cnf(cls_zero__le__square_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__square_0) ).
cnf(cls_mult__nonpos__nonpos_0,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
cnf(cls_split__mult__pos__le_1,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_split__mult__pos__le_1) ).
cnf(cls_split__mult__pos__le_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_split__mult__pos__le_0) ).
cnf(cls_mod__mult__mult2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__mult2_0) ).
cnf(cls_mod__mult__mult1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__mult1_0) ).
cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
file('theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
cnf(cls_nat__mult__assoc_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_nat__mult__assoc_0) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Omul__a_0) ).
cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
cnf(cls_comm__semiring__class_Odistrib_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring(T_a) ),
file('theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
cnf(cls_add__mult__distrib_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_add__mult__distrib_0) ).
cnf(cls_add__mult__distrib2_0,axiom,
c_HOL_Otimes__class_Otimes(V_k,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_add__mult__distrib2_0) ).
cnf(cls_class__semiring_Omul__d_0,axiom,
( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Omul__d_0) ).
cnf(cls_com_Osimps_I12_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H),
file('theBenchmark.p',cls_com_Osimps_I12_J_0) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I9_J_0) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
cnf(cls_nat__le__linear_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(V_n,V_m,tc_nat) ),
file('theBenchmark.p',cls_nat__le__linear_0) ).
cnf(cls_linorder__linear_0,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__linear_0) ).
cnf(cls_order__less__asym_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__asym_0) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__asym_H_0) ).
cnf(cls_Suc__le__mono_1,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ),
file('theBenchmark.p',cls_Suc__le__mono_1) ).
cnf(cls_Suc__le__mono_0,axiom,
( ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat)
| c_lessequals(V_n,V_m,tc_nat) ),
file('theBenchmark.p',cls_Suc__le__mono_0) ).
cnf(cls_Suc__mult__cancel1_0,axiom,
( V_m = V_n
| c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__mult__cancel1_0) ).
cnf(cls_less__SucI_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ),
file('theBenchmark.p',cls_less__SucI_0) ).
cnf(cls_Suc__lessD_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__lessD_0) ).
cnf(cls_evaln__nonstrict_0,axiom,
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_t)
| ~ c_lessequals(V_n,V_m,tc_nat)
| c_Natural_Oevaln(V_c,V_s,V_m,V_t) ),
file('theBenchmark.p',cls_evaln__nonstrict_0) ).
cnf(cls_mod__Suc__eq__Suc__mod_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat),
file('theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
cnf(cls_n__not__Suc__n_0,axiom,
V_n != c_Suc(V_n),
file('theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(V_n) != V_n,
file('theBenchmark.p',cls_Suc__n__not__n_0) ).
cnf(cls_Suc__n__not__le__n_0,axiom,
~ c_lessequals(c_Suc(V_n),V_n,tc_nat),
file('theBenchmark.p',cls_Suc__n__not__le__n_0) ).
cnf(cls_le__SucI_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(V_m,c_Suc(V_n),tc_nat) ),
file('theBenchmark.p',cls_le__SucI_0) ).
cnf(cls_Suc__leD_0,axiom,
( ~ c_lessequals(c_Suc(V_m),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__leD_0) ).
cnf(cls_less__trans__Suc_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat) ),
file('theBenchmark.p',cls_less__trans__Suc_0) ).
cnf(cls_less__Suc__eq_2,axiom,
c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat),
file('theBenchmark.p',cls_less__Suc__eq_2) ).
cnf(cls_lessI_0,axiom,
c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat),
file('theBenchmark.p',cls_lessI_0) ).
cnf(cls_Suc__neq__Zero_0,axiom,
c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_Suc__neq__Zero_0) ).
cnf(cls_nat_Osimps_I3_J_0,axiom,
c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
cnf(cls_evaln_OSkip_0,axiom,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s),
file('theBenchmark.p',cls_evaln_OSkip_0) ).
cnf(cls_evaln__Suc_0,axiom,
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) ),
file('theBenchmark.p',cls_evaln__Suc_0) ).
cnf(cls_not__less__less__Suc__eq_0,axiom,
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| V_n = V_m ),
file('theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
cnf(cls_less__antisym_0,axiom,
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| V_m = V_n ),
file('theBenchmark.p',cls_less__antisym_0) ).
cnf(cls_less__SucE_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| V_m = V_n ),
file('theBenchmark.p',cls_less__SucE_0) ).
cnf(cls_diff__Suc__Suc_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
file('theBenchmark.p',cls_diff__Suc__Suc_0) ).
cnf(cls_id__def_0,axiom,
c_Fun_Oid(v_x,t_a) = v_x,
file('theBenchmark.p',cls_id__def_0) ).
cnf(cls_nat_Oinject_0,axiom,
( V_nat = V_nat_H
| c_Suc(V_nat) != c_Suc(V_nat_H) ),
file('theBenchmark.p',cls_nat_Oinject_0) ).
cnf(cls_Suc__inject_0,axiom,
( V_x = V_y
| c_Suc(V_x) != c_Suc(V_y) ),
file('theBenchmark.p',cls_Suc__inject_0) ).
cnf(cls_evaln__max2_1,axiom,
( ~ c_Natural_Oevaln(V_c1,V_s1,V_n1,V_t1)
| ~ c_Natural_Oevaln(V_c2,V_s2,V_n2,V_t2)
| c_Natural_Oevaln(V_c2,V_s2,c_Natural_Osko__Natural__Xevaln__max2__1__1(V_c1,V_c2,V_s1,V_s2,V_t1,V_t2),V_t2) ),
file('theBenchmark.p',cls_evaln__max2_1) ).
cnf(cls_evaln__max2_0,axiom,
( ~ c_Natural_Oevaln(V_c1,V_s1,V_n1,V_t1)
| ~ c_Natural_Oevaln(V_c2,V_s2,V_n2,V_t2)
| c_Natural_Oevaln(V_c1,V_s1,c_Natural_Osko__Natural__Xevaln__max2__1__1(V_c1,V_c2,V_s1,V_s2,V_t1,V_t2),V_t1) ),
file('theBenchmark.p',cls_evaln__max2_0) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m),
file('theBenchmark.p',cls_Zero__neq__Suc_0) ).
cnf(cls_nat_Osimps_I2_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H),
file('theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
cnf(cls_add__Suc_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)),
file('theBenchmark.p',cls_add__Suc_0) ).
cnf(cls_add__Suc__right_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)),
file('theBenchmark.p',cls_add__Suc__right_0) ).
cnf(cls_max__Suc__Suc_0,axiom,
c_Orderings_Oord__class_Omax(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(V_m,V_n,tc_nat)),
file('theBenchmark.p',cls_max__Suc__Suc_0) ).
cnf(cls_mod__Suc_1,axiom,
( c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) = V_n
| c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) ),
file('theBenchmark.p',cls_mod__Suc_1) ).
cnf(cls_evaln_OSemi_0,axiom,
( ~ c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1)
| ~ c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)
| c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) ),
file('theBenchmark.p',cls_evaln_OSemi_0) ).
cnf(cls_add__Suc__shift_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat),
file('theBenchmark.p',cls_add__Suc__shift_0) ).
cnf(cls_Suc__lessI_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_Suc(V_m) = V_n
| c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__lessI_0) ).
cnf(cls_not__less__eq__eq_1,axiom,
( ~ c_lessequals(c_Suc(V_n),V_m,tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_not__less__eq__eq_1) ).
cnf(cls_not__less__eq__eq_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_Suc(V_n),V_m,tc_nat) ),
file('theBenchmark.p',cls_not__less__eq__eq_0) ).
cnf(cls_Suc__diff__diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat),
file('theBenchmark.p',cls_Suc__diff__diff_0) ).
cnf(cls_le__Suc__eq_2,axiom,
c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat),
file('theBenchmark.p',cls_le__Suc__eq_2) ).
cnf(cls_min__Suc__Suc_0,axiom,
c_Orderings_Oord__class_Omin(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat)),
file('theBenchmark.p',cls_min__Suc__Suc_0) ).
cnf(cls_evaln__elim__cases_I6_J_0,axiom,
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ),
file('theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
cnf(cls_le__SucE_0,axiom,
( ~ c_lessequals(V_m,c_Suc(V_n),tc_nat)
| c_lessequals(V_m,V_n,tc_nat)
| V_m = c_Suc(V_n) ),
file('theBenchmark.p',cls_le__SucE_0) ).
cnf(cls_not__less__less__Suc__eq_1,axiom,
( c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat)
| c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
file('theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
cnf(cls_not__less__eq_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_not__less__eq_1) ).
cnf(cls_not__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ),
file('theBenchmark.p',cls_not__less__eq_0) ).
cnf(cls_evaln__elim__cases_I1_J_0,axiom,
( ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t)
| V_t = V_s ),
file('theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
cnf(cls_less__Suc__eq__0__disj_3,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat) ),
file('theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
cnf(cls_Suc__less__eq_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__less__eq_0) ).
cnf(cls_Suc__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ),
file('theBenchmark.p',cls_Suc__mono_0) ).
cnf(cls_evaln__evalc_0,axiom,
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_t)
| c_Natural_Oevalc(V_c,V_s,V_t) ),
file('theBenchmark.p',cls_evaln__evalc_0) ).
cnf(cls_eval__eq_1,axiom,
( ~ c_Natural_Oevaln(V_c,V_s,V_x,V_t)
| c_Natural_Oevalc(V_c,V_s,V_t) ),
file('theBenchmark.p',cls_eval__eq_1) ).
cnf(cls_conjecture_0,negated_conjecture,
v_fun1(v_x,v_xa),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Natural_Oevaln(v_com,v_xa,v_n,v_xb),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_2,negated_conjecture,
~ v_fun2(v_x,v_xb),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
cnf(clsarity_nat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_nat),
file('theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
cnf(cls_add__nonneg__eq__0__iff_2_simplified,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
inference(simplify_clause,[status(thm)],[cls_add__nonneg__eq__0__iff_2]) ).
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_Suc(Eq_x_0) = c_Suc(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c_HOL_Ominus__class_Ominus(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Ominus__class_Ominus(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_HOL_Ozero__class_Ozero(Eq_x_0) = c_HOL_Ozero__class_Ozero(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( c_HOL_Otimes__class_Otimes(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Otimes__class_Otimes(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_8,axiom,
( c_HOL_Oplus__class_Oplus(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Oplus__class_Oplus(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_9,axiom,
( c_Divides_Odiv__class_Omod(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Odiv__class_Omod(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_10,axiom,
( c_Orderings_Oord__class_Omax(Eq_x_0,Eq_x_1,Eq_x_2) = c_Orderings_Oord__class_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_11,axiom,
( c_Orderings_Oord__class_Omin(Eq_x_0,Eq_x_1,Eq_x_2) = c_Orderings_Oord__class_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_12,axiom,
( c_Com_Ocom_OSemi(Eq_x_0,Eq_x_1) = c_Com_Ocom_OSemi(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( c_Com_Ocom_OBODY(Eq_x_0) = c_Com_Ocom_OBODY(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,axiom,
( c_Natural_Osko__Natural__Xevaln__max2__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_Natural_Osko__Natural__Xevaln__max2__1__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_16,axiom,
( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Natural_Osko__Natural__Xevaln__elim__cases__6__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_17,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_18,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_19,axiom,
( class_Divides_Osemiring__div(Eq_y_0)
| ~ class_Divides_Osemiring__div(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,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_21,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_22,axiom,
( c_HOL_Oord__class_Oless(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_HOL_Oord__class_Oless(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_23,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_24,axiom,
( class_Int_Onumber__ring(Eq_y_0)
| ~ class_Int_Onumber__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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_26,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_27,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_28,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_29,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_30,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_31,axiom,
( class_OrderedGroup_Olordered__ab__group__add(Eq_y_0)
| ~ class_OrderedGroup_Olordered__ab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( class_OrderedGroup_Ogroup__add(Eq_y_0)
| ~ class_OrderedGroup_Ogroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,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_34,axiom,
( class_OrderedGroup_Opordered__comm__monoid__add(Eq_y_0)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( class_Orderings_Opreorder(Eq_y_0)
| ~ class_Orderings_Opreorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,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_37,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_38,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_39,axiom,
( class_Ring__and__Field_Oordered__semiring(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( class_Ring__and__Field_Oring__no__zero__divisors(Eq_y_0)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( class_Ring__and__Field_Ono__zero__divisors(Eq_y_0)
| ~ class_Ring__and__Field_Ono__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,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_43,axiom,
( class_Ring__and__Field_Omult__zero(Eq_y_0)
| ~ class_Ring__and__Field_Omult__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( class_Divides_Oring__div(Eq_y_0)
| ~ class_Divides_Oring__div(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( c_Natural_Oevalc(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Natural_Oevalc(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_46,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_47,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_48,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_49,axiom,
( class_OrderedGroup_Oab__semigroup__idem__mult(Eq_y_0)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,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_51,axiom,
( class_Ring__and__Field_Omult__mono(Eq_y_0)
| ~ class_Ring__and__Field_Omult__mono(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( class_Ring__and__Field_Omult__mono1(Eq_y_0)
| ~ class_Ring__and__Field_Omult__mono1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,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_54,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_55,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_56,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_57,axiom,
( class_OrderedGroup_Omonoid__add(Eq_y_0)
| ~ class_OrderedGroup_Omonoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,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_59,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_60,axiom,
( c_Natural_Oevaln(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ c_Natural_Oevaln(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_61,axiom,
( v_fun1(Eq_y_0,Eq_y_1)
| ~ v_fun1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( v_fun2(Eq_y_0,Eq_y_1)
| ~ v_fun2(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 : SWV824-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n004.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 20 04:47:11 UTC 2026
% 0.09/5.37 % CPUTime :
% 30.26/35.52 % SZS status Unsatisfiable for theBenchmark
% 30.26/35.52 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------