%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV634-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:27:08 PM UTC 2026
% Result : Unsatisfiable 1.30s 1.74s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1428)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_odd__nat__equiv__def2_1,axiom,
~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def2_1) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(cls_odd__0__le__power__imp__0__le_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__0__le__power__imp__0__le_0) ).
cnf(cls_odd__power__less__zero_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat)),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__power__less__zero_0) ).
cnf(cls_power__le__imp__le__base_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_Suc(X4),X1),c_Power_Opower__class_Opower(X3,c_Suc(X4),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
cnf(cls_class__semiring_Osemiring__rules_I37_J_0,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat)),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I37_J_0) ).
cnf(cls_Suc__mult__less__cancel1_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
cnf(cls_Suc__mod__eq__add3__mod__number__of_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(X1))),c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mod__eq__add3__mod__number__of_0) ).
cnf(cls_Suc__mod__eq__add3__mod_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(X1))),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mod__eq__add3__mod_0) ).
cnf(cls_mod__Suc__eq__mod__add3_0,axiom,
c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_Suc(X2))),tc_nat) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__mod__add3_0) ).
cnf(cls_power__odd__eq_0,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat)),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__odd__eq_0) ).
cnf(cls_mod__mult__self4_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).
cnf(cls_odd__Suc__mult__two__ex_1,axiom,
~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__Suc__mult__two__ex_1) ).
cnf(cls_one__less__mult_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
cnf(cls_even__nat__equiv__def2_1,axiom,
c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def2_1) ).
cnf(cls_Suc__mult__less__cancel1_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
cnf(cls_odd__nat__equiv__def_1,axiom,
( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_1) ).
cnf(cls_power__inject__base_0,axiom,
( X2 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) != c_Power_Opower__class_Opower(X4,c_Suc(X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
cnf(cls_n__less__n__mult__m_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
cnf(cls_n__less__m__mult__n_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
cnf(cls_nat__lt__two__imp__zero__or__one_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).
cnf(cls_even__nat__equiv__def_1,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def_1) ).
cnf(cls_power__minus1__odd_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat)),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus1__odd_0) ).
cnf(cls_power__m1__odd_0,axiom,
( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat)),X1) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__m1__odd_0) ).
cnf(cls_power__Suc__less__one_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
cnf(cls_mod__Suc__eq__Suc__mod_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
cnf(cls_mod2__Suc__Suc_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_Suc(X1)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod2__Suc__Suc_0) ).
cnf(cls_Suc__mult__cancel1_0,axiom,
( X2 = X3
| c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
cnf(cls_power__gt1_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
cnf(cls_Suc3__eq__add__3_0,axiom,
c_Suc(c_Suc(c_Suc(X1))) = c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc3__eq__add__3_0) ).
cnf(cls_mod__Suc_1,axiom,
( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat))
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
cnf(cls_Suc__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
cnf(cls_odd__nat__equiv__def_0,axiom,
( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_0) ).
cnf(cls_Suc__times__mod__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__times__mod__eq_0) ).
cnf(cls_numeral__3__eq__3_0,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__3__eq__3_0) ).
cnf(cls_mod__Suc_0,axiom,
( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
cnf(cls_even__nat__equiv__def_0,axiom,
( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def_0) ).
cnf(cls_less__iff__Suc__add_1,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
cnf(cls_less__add__Suc1_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
cnf(cls_less__add__Suc2_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
cnf(cls_less__Suc__eq__0__disj_3,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
cnf(cls_Suc__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
cnf(cls_not__less__eq_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
cnf(cls_power__Suc2_0,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
cnf(cls_power__Suc_0,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc_0) ).
cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
cnf(cls_class__semiring_Opwr__Suc_0,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_Power_Opower__class_Opower(X2,c_Suc(X3),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(X2,c_Suc(X3),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
cnf(cls_less__trans__Suc_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
cnf(cls_dvd__1__iff__1_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__iff__1_0) ).
cnf(cls_add__Suc__shift_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
cnf(cls_add__Suc_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
cnf(cls_add__Suc__right_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
cnf(cls_mult__Suc_0,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
cnf(cls_mult__Suc__right_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
cnf(cls_less__SucE_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
cnf(cls_not__less__less__Suc__eq_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
cnf(cls_less__antisym_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
cnf(cls_Suc__lessD_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
cnf(cls_Suc__lessI_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
cnf(cls_one__is__add_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
cnf(cls_add__is__1_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
cnf(cls_dvd__1__iff__1_1,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__iff__1_1) ).
cnf(cls_less__Suc0_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
cnf(cls_add__2__eq__Suc_0,axiom,
c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat) = c_Suc(c_Suc(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__2__eq__Suc_0) ).
cnf(cls_add__2__eq__Suc_H_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Suc(c_Suc(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__2__eq__Suc_H_0) ).
cnf(cls_less__SucI_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
cnf(cls_one__is__add_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
cnf(cls_one__is__add_3,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
cnf(cls_add__is__1_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
cnf(cls_add__is__1_3,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
cnf(cls_mult__eq__1__iff_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
cnf(cls_mult__eq__1__iff_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
cnf(cls_less__2__cases_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__2__cases_0) ).
cnf(cls_of__nat__Suc_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X2),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
cnf(cls_not__less__less__Suc__eq_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
cnf(cls_not__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
cnf(cls_even__Suc_0,axiom,
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_0) ).
cnf(cls_comp__arith_I115_J_0,axiom,
c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I115_J_0) ).
cnf(cls_numeral__2__eq__2_0,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__2__eq__2_0) ).
cnf(cls_power__0__Suc_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
cnf(cls_one__is__add_2,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
cnf(cls_add__is__1_2,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
cnf(cls_add__nonneg__eq__0__iff_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
cnf(cls_Suc__inject_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
cnf(cls_nat_Oinject_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
cnf(cls_mod__1_0,axiom,
c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_0) ).
cnf(cls_dvd__1__left_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__left_0) ).
cnf(cls_zero__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/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(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
cnf(cls_less__Suc__eq_2,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
cnf(cls_lessI_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
cnf(cls_even__Suc_1,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_1) ).
cnf(cls_Suc__eq__plus1__left_0,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
cnf(cls_nat_Osimps_I3_J_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
cnf(cls_Suc__neq__Zero_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
cnf(cls_nat_Osimps_I2_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(X1) != X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
cnf(cls_n__not__Suc__n_0,axiom,
X1 != c_Suc(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(cls_numeral__1__eq__Suc__0_0,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__1__eq__Suc__0_0) ).
cnf(cls_One__nat__def_0,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
cnf(cls_mult_Oprod__diff__prod_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),X5,X1),X1),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
cnf(cls_abs__diff__triangle__ineq_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X4,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
cnf(cls_DERIV__mult__lemma_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X6,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X5,X1),X6,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X4,X1),X6,X1),X5,X1),X1)
| ~ class_RealVector_Oreal__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
cnf(cls_DERIV__inverse__lemma_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1),X4,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__inverse__lemma_0) ).
cnf(cls_less__add__iff1_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
cnf(cls_le__add__iff1_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
cnf(cls_less__add__iff2_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
cnf(cls_le__add__iff2_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
cnf(cls_less__add__iff1_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
cnf(cls_le__add__iff1_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
cnf(cls_less__add__iff2_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
cnf(cls_le__add__iff2_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
cnf(cls_calculation_0,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_calculation_0) ).
cnf(cls_power2__diff_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X2,X1),X3,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__diff_0) ).
cnf(cls_power2__sum_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X2,X1),X3,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__sum_0) ).
cnf(cls_sum__power2__gt__zero__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_sum__power2__le__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_0) ).
cnf(cls_sum__power2__le__zero__iff_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_1) ).
cnf(cls_not__sum__power2__lt__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__power2__lt__zero_0) ).
cnf(cls_inf__period_I4_J_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X5,X6,X1),X1),X4,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
cnf(cls_inf__period_I4_J_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X6,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X6,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
cnf(cls_sum__squares__gt__zero__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
cnf(cls_eq__add__iff2_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X1),X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
cnf(cls_eq__add__iff1_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
cnf(cls_mod__lemma_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__lemma_0) ).
cnf(cls_divide__less__eq__number__of1_8,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_8) ).
cnf(cls_divide__le__eq__number__of1_8,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_8) ).
cnf(cls_less__divide__eq__number__of1_8,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_8) ).
cnf(cls_le__divide__eq__number__of1_8,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_8) ).
cnf(cls_Deriv_Oinverse__diff__inverse_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).
cnf(cls_sum__power2__le__zero__iff_2,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_2) ).
cnf(cls_divide__less__eq__number__of_9,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_9) ).
cnf(cls_divide__le__eq__number__of_9,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_9) ).
cnf(cls_less__divide__eq__number__of_9,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_9) ).
cnf(cls_le__divide__eq__number__of_9,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_9) ).
cnf(cls_divide__less__eq__number__of1_9,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_9) ).
cnf(cls_divide__le__eq__number__of1_9,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_9) ).
cnf(cls_less__divide__eq__number__of1_9,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_9) ).
cnf(cls_le__divide__eq__number__of1_9,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_9) ).
cnf(cls_sum__power2__gt__zero__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_1) ).
cnf(cls_sum__power2__gt__zero__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_2) ).
cnf(cls_diff__frac__eq_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
cnf(cls_add__frac__eq_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
cnf(cls_sum__power2__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__ge__zero_0) ).
cnf(cls_divide__less__eq__number__of_8,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_8) ).
cnf(cls_divide__le__eq__number__of_8,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_8) ).
cnf(cls_less__divide__eq__number__of_8,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_8) ).
cnf(cls_le__divide__eq__number__of_8,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_8) ).
cnf(cls_sum__squares__le__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
cnf(cls_sum__squares__le__zero__iff_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
cnf(cls_not__sum__squares__lt__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
cnf(cls_even__power__le__0__imp__0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__power__le__0__imp__0_0) ).
cnf(cls_eq__add__iff1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1) = X6
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
cnf(cls_eq__add__iff2_0,axiom,
( X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1)
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
cnf(cls_power2__less__imp__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__less__imp__less_0) ).
cnf(cls_power2__le__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__le__imp__le_0) ).
cnf(cls_combine__common__factor_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1),X5,X1)
| ~ class_Ring__and__Field_Osemiring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
cnf(cls_left__add__mult__distrib_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
cnf(cls_natgb_Onoteq__reduce_0,axiom,
( X2 = X4
| X1 = X3
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
cnf(cls_natgb_Oadd__mul__solve_0,axiom,
( X2 = X4
| X1 = X3
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
cnf(cls_abs__diff__less__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
cnf(cls_divide__less__eq__number__of1_4,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_4) ).
cnf(cls_divide__less__eq__number__of1_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_1) ).
cnf(cls_divide__le__eq__number__of1_4,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_4) ).
cnf(cls_divide__le__eq__number__of1_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_1) ).
cnf(cls_less__divide__eq__number__of1_4,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_4) ).
cnf(cls_less__divide__eq__number__of1_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_1) ).
cnf(cls_le__divide__eq__number__of1_4,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_4) ).
cnf(cls_le__divide__eq__number__of1_1,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_1) ).
cnf(cls_divide__less__eq_9,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
cnf(cls_divide__le__eq_9,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
cnf(cls_divide__less__eq_8,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
cnf(cls_divide__le__eq_8,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
cnf(cls_less__divide__eq_9,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
cnf(cls_less__divide__eq_8,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
cnf(cls_le__divide__eq_8,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
cnf(cls_le__divide__eq_9,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
cnf(cls_mod__diff__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
cnf(cls_mod__add__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
cnf(cls_mod__mult__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
cnf(cls_divide__less__eq__number__of1_7,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_7) ).
cnf(cls_divide__le__eq__number__of1_7,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_7) ).
cnf(cls_less__divide__eq__number__of1_7,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_7) ).
cnf(cls_le__divide__eq__number__of1_7,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_7) ).
cnf(cls_divide__less__eq__number__of1_5,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_5) ).
cnf(cls_divide__le__eq__number__of1_5,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_5) ).
cnf(cls_less__divide__eq__number__of1_5,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_5) ).
cnf(cls_le__divide__eq__number__of1_5,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_5) ).
cnf(cls_abs__triangle__ineq3_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
cnf(cls_divide__less__eq__number__of_5,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_5) ).
cnf(cls_divide__le__eq__number__of_5,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_5) ).
cnf(cls_less__divide__eq__number__of_5,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_5) ).
cnf(cls_le__divide__eq__number__of_5,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_5) ).
cnf(cls_divide__less__eq__number__of_7,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_7) ).
cnf(cls_divide__le__eq__number__of_7,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_7) ).
cnf(cls_less__divide__eq__number__of_7,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_7) ).
cnf(cls_le__divide__eq__number__of_7,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_7) ).
cnf(cls_sum__power2__eq__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_0) ).
cnf(cls_sum__power2__eq__zero__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_1) ).
cnf(cls_gt__half__sum_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
cnf(cls_less__half__sum_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
cnf(cls_divide__left__mono__neg_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
cnf(cls_divide__strict__left__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
cnf(cls_divide__left__mono_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
cnf(cls_divide__strict__left__mono__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
cnf(cls_divide__less__eq__number__of1_6,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_6) ).
cnf(cls_less__divide__eq__number__of1_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_0) ).
cnf(cls_divide__le__eq__number__of1_6,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_6) ).
cnf(cls_le__divide__eq__number__of1_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_0) ).
cnf(cls_less__divide__eq__number__of1_6,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_6) ).
cnf(cls_divide__less__eq__number__of1_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_0) ).
cnf(cls_le__divide__eq__number__of1_6,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_6) ).
cnf(cls_divide__le__eq__number__of1_0,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_0) ).
cnf(cls_divide__less__eq__number__of_4,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_4) ).
cnf(cls_divide__le__eq__number__of_4,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_4) ).
cnf(cls_less__divide__eq__number__of_4,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_4) ).
cnf(cls_le__divide__eq__number__of_4,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_4) ).
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(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
cnf(cls_divide__less__eq__number__of_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_1) ).
cnf(cls_divide__le__eq__number__of_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_1) ).
cnf(cls_less__divide__eq__number__of_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_1) ).
cnf(cls_le__divide__eq__number__of_1,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_1) ).
cnf(cls_power__Suc__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
cnf(cls_mod__diff__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X4,X1),X3,X1)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
cnf(cls_mod__add__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X6,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
cnf(cls_mod__mult__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
cnf(cls_divide__less__eq__number__of_6,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_6) ).
cnf(cls_divide__le__eq__number__of_6,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_6) ).
cnf(cls_less__divide__eq__number__of_6,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_6) ).
cnf(cls_le__divide__eq__number__of_6,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_6) ).
cnf(cls_frac__less2_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X5,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X5,X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).
cnf(cls_frac__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X5,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).
cnf(cls_mult__strict__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
cnf(cls_mult__strict__mono_H_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
cnf(cls_mult__le__less__imp__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
cnf(cls_mult__less__le__imp__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
cnf(cls_frac__le_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X5,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X5,X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).
cnf(cls_mult__mono_H_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
cnf(cls_mult__mono_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
cnf(cls_abs__mult__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X3,X1),X5,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
cnf(cls_abs__diff__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X2,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
cnf(cls_abs__diff__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
cnf(cls_less__divide__eq__number__of_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_0) ).
cnf(cls_le__divide__eq__number__of_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_0) ).
cnf(cls_divide__less__eq__number__of_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_0) ).
cnf(cls_divide__le__eq__number__of_0,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_0) ).
cnf(cls_sum__squares__gt__zero__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
cnf(cls_sum__squares__gt__zero__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
cnf(cls_mod__exhaust__less__4_0,axiom,
( c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)
| c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)
| c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__exhaust__less__4_0) ).
cnf(cls_sum__squares__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
cnf(cls_nat__mod__eq__iff_1,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X4,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).
cnf(cls_divide__less__eq__number__of1_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_2) ).
cnf(cls_divide__le__eq__number__of1_2,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_2) ).
cnf(cls_less__divide__eq__number__of1_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_2) ).
cnf(cls_le__divide__eq__number__of1_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_2) ).
cnf(cls_divide__less__eq_5,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
cnf(cls_divide__le__eq_5,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
cnf(cls_divide__less__eq_4,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
cnf(cls_divide__less__eq_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
cnf(cls_divide__le__eq_4,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
cnf(cls_divide__le__eq_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
cnf(cls_less__divide__eq_5,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
cnf(cls_less__divide__eq_4,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
cnf(cls_less__divide__eq_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
cnf(cls_le__divide__eq_4,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
cnf(cls_le__divide__eq_5,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
cnf(cls_le__divide__eq_1,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
cnf(cls_divide__less__eq_7,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
cnf(cls_divide__le__eq_7,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
cnf(cls_less__divide__eq_7,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
cnf(cls_le__divide__eq_7,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
cnf(cls_power__less__power__Suc_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
cnf(cls_mult__right__less__imp__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
cnf(cls_mult__left__less__imp__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
cnf(cls_mult__less__imp__less__right_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
cnf(cls_mult__less__imp__less__left_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
cnf(cls_power__less__imp__less__base_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
cnf(cls_mult__less__cancel__left__pos_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
cnf(cls_mult__right__le__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
cnf(cls_mult__left__le__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
cnf(cls_mult__le__cancel__left__pos_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
cnf(cls_mult__less__cancel__left__neg_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
cnf(cls_mult__le__cancel__left__neg_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
cnf(cls_power__strict__increasing__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
cnf(cls_power__less__imp__less__exp_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
cnf(cls_inverse__add_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__add_0) ).
cnf(cls_division__ring__inverse__diff_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ominus__class_Ominus(X3,X2,X1),X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).
cnf(cls_division__ring__inverse__add_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).
cnf(cls_left__diff__distrib__number__of_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oring(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).
cnf(cls_left__distrib__number__of_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Osemiring(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).
cnf(cls_right__diff__distrib__number__of_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oring(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).
cnf(cls_right__distrib__number__of_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Osemiring(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).
cnf(cls_zero__le__even__power_H_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__even__power_H_0) ).
cnf(cls_add__frac__num_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
cnf(cls_add__num__frac_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1),X4,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
cnf(cls_nat__mult__dvd__cancel1_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_0) ).
cnf(cls_dvd__mult__cancel_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel_0) ).
cnf(cls_nat__mult__less__cancel1_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
cnf(cls_power__strict__decreasing_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
cnf(cls_mult__less__cancel__left__disj_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
cnf(cls_mult__less__cancel__right__disj_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
cnf(cls_mult__frac__frac_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/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(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
cnf(cls_power__strict__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
cnf(cls_mult__less__cancel__right__disj_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
cnf(cls_mult__less__cancel__left__disj_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
cnf(cls_mult__less__cancel__left__disj_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
cnf(cls_mult__less__cancel__right__disj_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
cnf(cls_Deriv_Oadd__diff__add_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
cnf(cls_zmod__simps_I1_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
cnf(cls_zmod__simps_I4_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
cnf(cls_zmod__simps_I2_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
cnf(cls_mod__diff__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
cnf(cls_mod__add__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
cnf(cls_mod__mult__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
cnf(cls_mod__diff__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
cnf(cls_mod__add__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
cnf(cls_mod__mult__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
cnf(cls_mult__less__cancel__right__disj_3,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
cnf(cls_mult__less__cancel__left__disj_3,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
cnf(cls_comm__ring__1__class_Opower__minus__even_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__ring__1__class_Opower__minus__even_0) ).
cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
( X4 = X5
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X5,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
cnf(cls_class__semiring_Osemiring__rules_I36_J_0,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I36_J_0) ).
cnf(cls_divide__less__eq_6,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).
cnf(cls_less__divide__eq_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
cnf(cls_divide__le__eq_6,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).
cnf(cls_le__divide__eq_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
cnf(cls_less__divide__eq_6,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).
cnf(cls_divide__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
cnf(cls_le__divide__eq_6,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).
cnf(cls_divide__le__eq_0,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
cnf(cls_less__divide__eq__number__of_2,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_2) ).
cnf(cls_le__divide__eq__number__of_2,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_2) ).
cnf(cls_divide__less__eq__number__of_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_2) ).
cnf(cls_divide__le__eq__number__of_2,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_2) ).
cnf(cls_power2__eq__imp__eq_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) != c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__imp__eq_0) ).
cnf(cls_natgb_Onoteq__reduce_1,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
cnf(cls_natgb_Oadd__mul__solve_1,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
cnf(cls_mult__imp__div__pos__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
cnf(cls_mult__imp__div__pos__le_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
cnf(cls_mult__imp__less__div__pos_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
cnf(cls_mult__imp__le__div__pos_0,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
cnf(cls_root__cancel_0,axiom,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X2),X3,tc_Complex_Ocomplex)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__cancel_0) ).
cnf(cls_abs__triangle__ineq2_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
cnf(cls_abs__triangle__ineq4_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
cnf(cls_abs__triangle__ineq_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
cnf(cls_abs__le__mult_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_Ring__and__Field_Olordered__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
cnf(cls_le__add__right__mono_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X5,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
cnf(cls_divide__less__eq__number__of1_3,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_3) ).
cnf(cls_divide__le__eq__number__of1_3,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_3) ).
cnf(cls_less__divide__eq__number__of1_3,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_3) ).
cnf(cls_le__divide__eq__number__of1_3,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_3) ).
cnf(cls_half__gt__zero__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_half__gt__zero__iff_0) ).
cnf(cls_mod2__gr__0_0,axiom,
( c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod2__gr__0_0) ).
cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom,
( X3 = X4
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
cnf(cls_sum__power2__eq__zero__iff_2,axiom,
( c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_2) ).
cnf(cls_dvd__mult__cancel__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
cnf(cls_dvd__mult__cancel__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
cnf(cls_power__gt1__lemma_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
cnf(cls_add__less__cancel__right_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
cnf(cls_add__less__cancel__left_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
cnf(cls_add__le__cancel__right_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
cnf(cls_add__le__cancel__left_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
cnf(cls_estimate__by__abs_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oabs__class_Oabs(X4,X1),X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
cnf(cls_power__even__eq_0,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__eq_0) ).
cnf(cls_divide__less__eq__number__of_3,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_3) ).
cnf(cls_divide__le__eq__number__of_3,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_3) ).
cnf(cls_less__divide__eq__number__of_3,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_3) ).
cnf(cls_le__divide__eq__number__of_3,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_3) ).
cnf(cls_nat__mult__dvd__cancel__disj_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).
cnf(cls_mult__less__cancel1_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
cnf(cls_mult__less__cancel2_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
cnf(cls_divide__right__mono_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
cnf(cls_divide__right__mono__neg_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
cnf(cls_power__mono__even_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X4,X1),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono__even_0) ).
cnf(cls_nat__add__left__cancel__less_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
cnf(cls_mult__less__cancel2_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
cnf(cls_mult__less__cancel1_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
cnf(cls_power__eq__imp__eq__base_0,axiom,
( X2 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
cnf(cls_even__even__mod__4__iff_1,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_1) ).
cnf(cls_divide__strict__right__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
cnf(cls_mult__strict__left__mono__comm_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
cnf(cls_mult__strict__left__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
cnf(cls_mult__less__cancel__left__pos_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
cnf(cls_mult__less__cancel__left__disj_4,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
cnf(cls_mult__strict__right__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
cnf(cls_mult__less__cancel__right__disj_4,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
cnf(cls_power__mono_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
cnf(cls_mult__left__mono_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
cnf(cls_mult__mono1_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Omult__mono1(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
cnf(cls_mult__le__cancel__left__pos_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
cnf(cls_mult__right__mono_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
cnf(cls_divide__strict__right__mono__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
cnf(cls_mult__less__cancel__left__neg_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
cnf(cls_mult__strict__left__mono__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
cnf(cls_mult__less__cancel__left__disj_5,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
cnf(cls_mult__strict__right__mono__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
cnf(cls_mult__less__cancel__right__disj_5,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
cnf(cls_mult__left__mono__neg_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
cnf(cls_mult__le__cancel__left__neg_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
cnf(cls_mult__right__mono__neg_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
cnf(cls_mult__right__le__one__le_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
cnf(cls_mult__left__le__one__le_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
cnf(cls_power__strict__increasing__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
cnf(cls_power__strict__increasing_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
cnf(cls_zero__less__power__eq__number__of_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| c_Int_Onumber__class_Onumber__of(X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_0) ).
cnf(cls_divide__less__eq_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
cnf(cls_divide__le__eq_2,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
cnf(cls_less__divide__eq_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
cnf(cls_le__divide__eq_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
cnf(cls_mult__dvd__mono_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
cnf(cls_add__strict__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
cnf(cls_add__le__less__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
cnf(cls_add__less__le__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
cnf(cls_add__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
cnf(cls_zero__less__power__eq__number__of_2,axiom,
( c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_2) ).
cnf(cls_power__divide_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).
cnf(cls_nonzero__power__divide_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
cnf(cls_sum__squares__eq__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
cnf(cls_sum__squares__eq__zero__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
cnf(cls_zero__le__power__eq__number__of_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_0) ).
cnf(cls_power__le__zero__eq__number__of_2,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_2) ).
cnf(cls_zero__less__power2_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power2_0) ).
cnf(cls_mod__mult__mult2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
cnf(cls_mod__mult__mult1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
cnf(cls_divide_Odiff_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
cnf(cls_diff__divide__distrib_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
cnf(cls_divide_Oadd_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
cnf(cls_add__divide__distrib_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
cnf(cls_power__mult__distrib_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
cnf(cls_class__semiring_Opwr__mul_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
cnf(cls_mult__left_Odiff_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
cnf(cls_mult_Odiff__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
cnf(cls_comm__semiring__class_Odistrib_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
cnf(cls_mult__left_Oadd_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
cnf(cls_mult_Oadd__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
cnf(cls_mult_Odiff__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
cnf(cls_mult__right_Odiff_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
cnf(cls_mult__right_Oadd_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
cnf(cls_mult_Oadd__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
cnf(cls_class__semiring_Omul__d_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
cnf(cls_mod__mult__self2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
cnf(cls_mod__mult__self1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
cnf(cls_zero__less__power__eq__number__of_1,axiom,
( c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_1) ).
cnf(cls_class__semiring_Omul__pwr_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1) = c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
cnf(cls_power__add_0,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__add_0) ).
cnf(cls_nat__mult__dvd__cancel1_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_1) ).
cnf(cls_mult__less__cancel1_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
cnf(cls_mult__less__mono2_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).
cnf(cls_nat__mult__less__cancel1_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
cnf(cls_mult__less__cancel2_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
cnf(cls_mult__less__mono1_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).
cnf(cls_power__minus_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X3,X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus_0) ).
cnf(cls_add__less__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
cnf(cls_zero__less__mult__pos2_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/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(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
cnf(cls_abs__eq__mult_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
cnf(cls_abs__eq__mult_2,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
cnf(cls_abs__eq__mult_1,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
cnf(cls_abs__eq__mult_3,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
cnf(cls_power2__less__0_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__less__0_0) ).
cnf(cls_mod__mult__distrib_0,axiom,
c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).
cnf(cls_add__mult__distrib_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
cnf(cls_mod__mult__distrib2_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).
cnf(cls_add__mult__distrib2_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
cnf(cls_mod__mult__self3_0,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).
cnf(cls_mod2__gr__0_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)
| c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod2__gr__0_1) ).
cnf(cls_power__le__zero__eq__number__of_3,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_3) ).
cnf(cls_power__le__zero__eq__number__of_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_1) ).
cnf(cls_power__less__zero__eq__number__of_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_1) ).
cnf(cls_dvd__mod__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
cnf(cls_dvd__mod__imp__dvd_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
cnf(cls_add__cancel__21_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_divide__less__0__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
cnf(cls_divide__le__0__iff_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
cnf(cls_divide__less__0__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
cnf(cls_divide__less__0__iff_3,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
cnf(cls_divide__le__0__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
cnf(cls_divide__le__0__iff_3,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
cnf(cls_zero__less__divide__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
cnf(cls_zero__less__divide__iff_3,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
cnf(cls_zero__less__divide__iff_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
cnf(cls_zero__less__divide__iff_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
cnf(cls_zero__le__divide__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
cnf(cls_zero__le__divide__iff_3,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
cnf(cls_zero__le__divide__iff_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
cnf(cls_zero__le__divide__iff_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
cnf(cls_divide__less__0__iff_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
cnf(cls_divide__le__0__iff_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
cnf(cls_power__less__zero__eq__number__of_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_0) ).
cnf(cls_divide__less__eq_3,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
cnf(cls_divide__le__eq_3,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
cnf(cls_less__divide__eq_3,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
cnf(cls_le__divide__eq_3,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
cnf(cls_mult__le__0__iff_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
cnf(cls_mult__le__0__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
cnf(cls_mult__le__0__iff_3,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
cnf(cls_zero__le__mult__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
cnf(cls_zero__le__mult__iff_3,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
cnf(cls_zero__le__mult__iff_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
cnf(cls_zero__le__mult__iff_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
cnf(cls_mult__le__0__iff_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
cnf(cls_half__gt__zero_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_half__gt__zero_0) ).
cnf(cls_mod__minus__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X2,X3,X1),X1),X3,X1)
| ~ class_Divides_Oring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
cnf(cls_power__mono__odd_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono__odd_0) ).
cnf(cls_divide__less__0__iff_5,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).
cnf(cls_divide__less__0__iff_4,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).
cnf(cls_divide__le__0__iff_5,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
cnf(cls_divide__le__0__iff_4,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
cnf(cls_zero__less__divide__iff_4,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).
cnf(cls_zero__le__divide__iff_4,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
cnf(cls_zero__less__divide__iff_5,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).
cnf(cls_zero__le__divide__iff_5,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
cnf(cls_power__le__zero__eq__number__of_4,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| c_Int_Onumber__class_Onumber__of(X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_4) ).
cnf(cls_power__le__zero__eq__number__of_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_0) ).
cnf(cls_divide__neg__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
cnf(cls_divide__pos__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
cnf(cls_mult__pos__neg2_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
cnf(cls_mult__neg__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
cnf(cls_mult__pos__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
cnf(cls_divide__nonneg__neg_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
cnf(cls_divide__nonpos__pos_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
cnf(cls_mult__nonneg__nonpos2_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
cnf(cls_mult__nonpos__nonneg_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
cnf(cls_split__mult__neg__le_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
cnf(cls_mult__nonneg__nonpos_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
cnf(cls_split__mult__neg__le_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
cnf(cls_mult__le__0__iff_5,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
cnf(cls_mult__le__0__iff_4,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
cnf(cls_add__neg__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
cnf(cls_add__nonpos__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
cnf(cls_add__neg__nonpos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
cnf(cls_add__nonpos__nonpos_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
cnf(cls_less__1__mult_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
cnf(cls_divide__pos__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
cnf(cls_add__pos__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
cnf(cls_add__nonneg__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
cnf(cls_add__pos__nonneg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
cnf(cls_mult__pos__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
cnf(cls_divide__nonneg__pos_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
cnf(cls_add__nonneg__nonneg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
cnf(cls_mult__nonneg__nonneg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
cnf(cls_split__mult__pos__le_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
cnf(cls_zero__le__mult__iff_4,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
cnf(cls_divide__neg__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
cnf(cls_mult__neg__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
cnf(cls_divide__nonpos__neg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
cnf(cls_mult__nonpos__nonpos_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
cnf(cls_split__mult__pos__le_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
cnf(cls_zero__le__mult__iff_5,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
cnf(cls_add__gr__0_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
cnf(cls_dvd__power__same_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
cnf(cls_dvd__mult__cancel__left_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
cnf(cls_dvd__mult__cancel__right_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
cnf(cls_add__strict__left__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
cnf(cls_add__less__cancel__left_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
cnf(cls_add__strict__right__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
cnf(cls_add__less__cancel__right_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
cnf(cls_add__left__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
cnf(cls_add__le__cancel__left_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
cnf(cls_add__right__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
cnf(cls_add__le__cancel__right_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
cnf(cls_zero__less__power__eq_2,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
cnf(cls_one__less__power_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
cnf(cls_dvd_Oless__trans_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_1) ).
cnf(cls_add__strict__increasing2_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
cnf(cls_add__strict__increasing_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
cnf(cls_add__increasing2_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
cnf(cls_add__increasing_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
cnf(cls_zero__less__divide__1__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
cnf(cls_zero__le__divide__1__iff_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
cnf(cls_divide__less__0__1__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
cnf(cls_divide__le__0__1__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
cnf(cls_power__one__over_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
cnf(cls_power__less__zero__eq__number__of_2,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_2) ).
cnf(cls_zero__less__power__eq__number__of_5,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_5) ).
cnf(cls_zero__le__power__eq__number__of_2,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_2) ).
cnf(cls_le__eq__neg_1,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
cnf(cls_pos__add__strict_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
cnf(cls_le__number__of__eq__not__less_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).
cnf(cls_zero__less__power__eq_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_0) ).
cnf(cls_zero__le__power__iff_0,axiom,
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_0) ).
cnf(cls_zero__le__power__eq_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_0) ).
cnf(cls_zero__le__odd__power_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__odd__power_0) ).
cnf(cls_power__le__zero__eq_2,axiom,
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_2) ).
cnf(cls_nat__mult__dvd__cancel__disj_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).
cnf(cls_nat__add__left__cancel__less_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
cnf(cls_add__less__mono1_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
cnf(cls_mult__divide__mult__cancel__left_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oinverse__class_Odivide(X3,X4,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
cnf(cls_mult__divide__mult__cancel__right_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,X4,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
cnf(cls_dvd__diff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
cnf(cls_dvd__mod_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
cnf(cls_dvd__mod__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
cnf(cls_dvd__add_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__add_0) ).
cnf(cls_mod__minus__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X1),X3,X1)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
cnf(cls_dvd__mult__cancel2_0,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_0) ).
cnf(cls_dvd__mult__cancel1_0,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_0) ).
cnf(cls_abs__add__abs_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
cnf(cls_nat__0__less__mult__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
cnf(cls_power__le__zero__eq_3,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
cnf(cls_mult__frac__num_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
cnf(cls_power__less__zero__eq_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
cnf(cls_even__less__0__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_power__commutes_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_add__cancel__21_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
cnf(cls_sum__squares__eq__zero__iff_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
cnf(cls_dvd_Oless__trans_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_0) ).
cnf(cls_power__mult_0,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult_0) ).
cnf(cls_class__semiring_Opwr__pwr_0,axiom,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
cnf(cls_inverse__less__imp__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).
cnf(cls_inverse__le__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).
cnf(cls_inverse__less__imp__less__neg_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).
cnf(cls_inverse__le__imp__le__neg_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).
cnf(cls_less__iff__diff__less__0_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
cnf(cls_le__iff__diff__le__0_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
cnf(cls_abs__power2_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power2_0) ).
cnf(cls_less__eqI_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
cnf(cls_less__eqI_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
cnf(cls_le__eqI_1,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
cnf(cls_le__eqI_0,axiom,
( c_lessequals(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
cnf(cls_dvd__mult__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
cnf(cls_dvd__mult__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
cnf(cls_zero__less__power__eq_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_1) ).
cnf(cls_nat__add__assoc_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
cnf(cls_nat__mult__assoc_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
cnf(cls_nat__add__left__commute_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
cnf(cls_abs__div__pos_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__div__pos_0) ).
cnf(cls_mod__mod__cancel_0,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
cnf(cls_nat__0__less__mult__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
cnf(cls_nat__0__less__mult__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
cnf(cls_dvd_Ole__less__trans_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_1) ).
cnf(cls_dvd_Oless__le__trans_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_1) ).
cnf(cls_even__even__mod__4__iff_0,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_0) ).
cnf(cls_power__le__zero__eq__number__of_5,axiom,
( c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_5) ).
cnf(cls_abs__mult__pos_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
cnf(cls_less__add__eq__less_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
cnf(cls_power__minus1__even_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus1__even_0) ).
cnf(cls_half_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_half_0) ).
cnf(cls_le__eq__neg_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
cnf(cls_abs__less__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
cnf(cls_abs__le__iff_2,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
cnf(cls_abs__leI_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__leI_0) ).
cnf(cls_abs__power__minus_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
cnf(cls_add__lessD1_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
cnf(cls_dvd__reduce_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__reduce_0) ).
cnf(cls_dvd__mult__cancel__left_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
cnf(cls_dvd__mult__cancel__right_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X1),X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
cnf(cls_frac__eq__eq_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X5 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,X5,X1) = c_HOL_Oinverse__class_Odivide(X4,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Otimes__class_Otimes(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
cnf(cls_frac__eq__eq_0,axiom,
( X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Otimes__class_Otimes(X2,X5,X1) = c_HOL_Otimes__class_Otimes(X4,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) != c_HOL_Oinverse__class_Odivide(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
cnf(cls_add__nonneg__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
cnf(cls_add__nonneg__eq__0__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
cnf(cls_power__le__zero__eq_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_1) ).
cnf(cls_less__imp__inverse__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).
cnf(cls_le__imp__inverse__le_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).
cnf(cls_less__imp__inverse__less__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).
cnf(cls_le__imp__inverse__le__neg_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).
cnf(cls_dvd__eq__mod__eq__0__number__of_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0__number__of_1) ).
cnf(cls_one__less__inverse__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).
cnf(cls_one__le__inverse__iff_2,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).
cnf(cls_dvd__eq__mod__eq__0__number__of_0,axiom,
( c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0__number__of_0) ).
cnf(cls_power__less__zero__eq_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_0) ).
cnf(cls_divide__less__0__1__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
cnf(cls_divide__le__0__1__iff_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
cnf(cls_zero__less__divide__1__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
cnf(cls_zero__le__divide__1__iff_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
cnf(cls_power__le__zero__eq_4,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_4) ).
cnf(cls_power__m1__even_0,axiom,
( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__m1__even_0) ).
cnf(cls_power__less__zero__eq_2,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_2) ).
cnf(cls_zero__less__power__eq_5,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_5) ).
cnf(cls_zero__le__power__eq_2,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_2) ).
cnf(cls_zero__le__odd__power_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__odd__power_1) ).
cnf(cls_zero__less__power__eq__number__of_4,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_4) ).
cnf(cls_power__le__zero__eq_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
cnf(cls_divide__eq__eq__number__of1_3,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) = X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_3) ).
cnf(cls_eq__divide__eq__number__of1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) = X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_0) ).
cnf(cls_eq__divide__eq__number__of1_3,axiom,
( X2 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_3) ).
cnf(cls_divide__eq__eq__number__of1_0,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_0) ).
cnf(cls_number__of__Bit0_0,axiom,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X2),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Bit0_0) ).
cnf(cls_number__of__Bit1_0,axiom,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X2),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Bit1_0) ).
cnf(cls_add__cancel__end_0,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X4,X1)
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
cnf(cls_divide__eq__eq__number__of_4,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X3,X1) = c_Int_Onumber__class_Onumber__of(X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_4) ).
cnf(cls_eq__divide__eq__number__of_4,axiom,
( c_Int_Onumber__class_Onumber__of(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_4) ).
cnf(cls_divide__eq__eq__number__of1_4,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_4) ).
cnf(cls_eq__divide__eq__number__of1_4,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_4) ).
cnf(cls_zero__le__power__eq__number__of_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_1) ).
cnf(cls_power__inject__exp_0,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
cnf(cls_zero__less__power2_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power2_1) ).
cnf(cls_dvd_Ole__less__trans_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_0) ).
cnf(cls_dvd_Oless__le__trans_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_0) ).
cnf(cls_inverse__less__1__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).
cnf(cls_inverse__le__1__iff_0,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).
cnf(cls_nat__mult__dvd__cancel__disj_1,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_1) ).
cnf(cls_not__square__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
cnf(cls_even__less__0__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
cnf(cls_zero__less__power_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
cnf(cls_one__le__power_0,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
cnf(cls_zero__le__power_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
cnf(cls_zero__le__power__iff_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
cnf(cls_power3__eq__cube_0,axiom,
( c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X2,X1),X2,X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power3__eq__cube_0) ).
cnf(cls_zero__le__power2_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power2_0) ).
cnf(cls_less__iff__diff__less__0_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
cnf(cls_le__iff__diff__le__0_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
cnf(cls_dvd__power_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_0) ).
cnf(cls_nat__mult__eq__cancel1_0,axiom,
( X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
cnf(cls_nat__dvd__not__less_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__not__less_0) ).
cnf(cls_dvd__mult2_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
cnf(cls_dvd__mult_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
cnf(cls_divide__eq__eq__number__of_3,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X3,X1) = c_Int_Onumber__class_Onumber__of(X2,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_3) ).
cnf(cls_eq__divide__eq__number__of_3,axiom,
( c_Int_Onumber__class_Onumber__of(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_3) ).
cnf(cls_dvd__mult__cancel2_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_1) ).
cnf(cls_dvd__mult__cancel1_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_1) ).
cnf(cls_abs__minus__commute_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
cnf(cls_add__gr__0_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
cnf(cls_add__gr__0_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
cnf(cls_power2__eq__square__number__of_0,axiom,
( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__square__number__of_0) ).
cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
cnf(cls_not__add__less1_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
cnf(cls_not__add__less2_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
cnf(cls_mod__less__divisor_0,axiom,
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
cnf(cls_nonzero__inverse__mult__distrib_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
cnf(cls_zero__less__power__eq__number__of_3,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_3) ).
cnf(cls_power__even__abs__number__of_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__abs__number__of_0) ).
cnf(cls_inverse__mult__distrib_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
cnf(cls_abs__divide_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__divide_0) ).
cnf(cls_dvd__reduce_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__reduce_1) ).
cnf(cls_trans__less__add1_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
cnf(cls_termination__basic__simps_I1_J_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
cnf(cls_trans__less__add2_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
cnf(cls_termination__basic__simps_I2_J_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
cnf(cls_nonzero__abs__divide_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
cnf(cls_double__number__of__Bit0_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X2),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__number__of__Bit0_0) ).
cnf(cls_power2__minus_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__minus_0) ).
cnf(cls_power2__abs_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__abs_0) ).
cnf(cls_dvd__trans_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
cnf(cls_order__less__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
cnf(cls_order__le__less__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
cnf(cls_order__less__le__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
cnf(cls_xt1_I10_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
cnf(cls_xt1_I7_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_xt1_I8_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
cnf(cls_order__trans_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
cnf(cls_xt1_I6_J_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(cls_Lim_Ominus__diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
cnf(cls_minus__add__distrib_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
cnf(cls_minus__add_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
cnf(cls_abs__mult_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
cnf(cls_minus1__divide_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus1__divide_0) ).
cnf(cls_of__nat__add_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
cnf(cls_of__nat__mult_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).
cnf(cls_abs__number__of_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__number__of_0) ).
cnf(cls_neg__less__iff__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
cnf(cls_neg__le__iff__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
cnf(cls_dvd__pos__nat_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__pos__nat_0) ).
cnf(cls_of__nat__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
cnf(cls_le__number__of__eq__not__less_1,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).
cnf(cls_zero__le__power__abs_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).
cnf(cls_mod__mod__trivial_0,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
cnf(cls_mod__add__self1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
cnf(cls_mod__add__self2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
cnf(cls_mult__left__idem_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
cnf(cls_neg__power__if_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Power_Opower__class_Opower(X2,X3,X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__power__if_1) ).
cnf(cls_add__minus__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
cnf(cls_dvd_Oorder__trans_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).
cnf(cls_odd__add_2,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_2) ).
cnf(cls_even__add_1,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_1) ).
cnf(cls_even__add_0,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_0) ).
cnf(cls_odd__add_3,axiom,
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_3) ).
cnf(cls_even__sum__nat_1,axiom,
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_1) ).
cnf(cls_even__sum__nat_0,axiom,
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_0) ).
cnf(cls_eq__divide__eq__number__of_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1) = X3
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Oinverse__class_Odivide(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_0) ).
cnf(cls_divide__eq__eq__number__of_0,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) != c_Int_Onumber__class_Onumber__of(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).
cnf(cls_power__inverse_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).
cnf(cls_minus__divide__right_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
cnf(cls_minus__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
cnf(cls_minus__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
cnf(cls_abs__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
cnf(cls_minus__le__iff_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
cnf(cls_minus__le__iff_1,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
cnf(cls_abs__le__D2_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
cnf(cls_less__minus__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
cnf(cls_less__minus__iff_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
cnf(cls_le__minus__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
cnf(cls_le__minus__iff_1,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
cnf(cls_nonzero__power__inverse_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X1),X3,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
cnf(cls_nonzero__minus__divide__right_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
cnf(cls_one__less__inverse__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
cnf(cls_inverse__positive__iff__positive_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
cnf(cls_one__le__inverse__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).
cnf(cls_inverse__nonnegative__iff__nonnegative_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).
cnf(cls_inverse__negative__iff__negative_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
cnf(cls_inverse__nonpositive__iff__nonpositive_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).
cnf(cls_one__less__inverse__iff_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
cnf(cls_one__le__inverse__iff_1,axiom,
( c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).
cnf(cls_power__le__zero__eq_5,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_5) ).
cnf(cls_even__mult__two__ex_1,axiom,
c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__mult__two__ex_1) ).
cnf(cls_inverse__positive__imp__positive_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).
cnf(cls_inverse__negative__imp__negative_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).
cnf(cls_even__product__nat_0,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_0) ).
cnf(cls_divide_Ominus_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
cnf(cls_mult_Ominus__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
cnf(cls_mult__left_Ominus_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
cnf(cls_mult_Ominus__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
cnf(cls_mult__right_Ominus_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
cnf(cls_minus__divide__left_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
cnf(cls_minus__mult__left_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
cnf(cls_power__abs_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__abs_0) ).
cnf(cls_minus__mult__right_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
cnf(cls_neg__less__0__iff__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
cnf(cls_neg__le__0__iff__le_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
cnf(cls_neg__0__less__iff__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
cnf(cls_neg__0__le__iff__le_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
cnf(cls_less__le__not__le_2,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
cnf(cls_zero__le__even__power_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__even__power_0) ).
cnf(cls_zero__less__power__eq_4,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_4) ).
cnf(cls_of__nat__0__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
cnf(cls_neg__less__iff__less_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
cnf(cls_le__imp__neg__le_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
cnf(cls_zero__less__two_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
cnf(cls_of__nat__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
cnf(cls_inverse__less__1__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
cnf(cls_inverse__le__1__iff_2,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).
cnf(cls_inverse__less__1__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).
cnf(cls_inverse__negative__iff__negative_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_1) ).
cnf(cls_inverse__le__1__iff_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).
cnf(cls_inverse__nonpositive__iff__nonpositive_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).
cnf(cls_inverse__positive__iff__positive_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_1) ).
cnf(cls_inverse__nonnegative__iff__nonnegative_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).
cnf(cls_square__eq__iff_0,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| c_HOL_Otimes__class_Otimes(X2,X2,X1) != c_HOL_Otimes__class_Otimes(X3,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
cnf(cls_minus__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
cnf(cls_add__cancel__end_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X3,X2,X1),X1) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
cnf(cls_zero__le__power__iff_2,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_2) ).
cnf(cls_zero__le__power__eq_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_1) ).
cnf(cls_neg__less__eq__nonneg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
cnf(cls_minus__le__self__iff_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
cnf(cls_less__minus__self__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
cnf(cls_less__eq__neg__nonpos_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
cnf(cls_le__minus__self__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
cnf(cls_divide__eq__eq_4,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
cnf(cls_eq__divide__eq_4,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
cnf(cls_neg__less__0__iff__less_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
cnf(cls_neg__le__0__iff__le_1,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
cnf(cls_negative__imp__inverse__negative_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).
cnf(cls_positive__imp__inverse__positive_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).
cnf(cls_neg__0__less__iff__less_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
cnf(cls_neg__0__le__iff__le_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
cnf(cls_inverse__divide_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X3,X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
cnf(cls_minus__dvd__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
cnf(cls_abs__dvd__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
cnf(cls_abs__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
cnf(cls_abs__le__D1_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
cnf(cls_dvd__minus__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
cnf(cls_dvd__abs__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oabs__class_Oabs(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
cnf(cls_dvd__power_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_1) ).
cnf(cls_abs__power__minus__one_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X2,X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus__one_0) ).
cnf(cls_neg__less__eq__nonneg_1,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
cnf(cls_minus__le__self__iff_1,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
cnf(cls_less__minus__self__iff_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
cnf(cls_less__eq__neg__nonpos_1,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
cnf(cls_le__minus__self__iff_1,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
cnf(cls_of__nat__0__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
cnf(cls_minus__diff__eq_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
cnf(cls_divide__eq__eq_3,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = X2
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
cnf(cls_eq__divide__eq_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,X1) = X2
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
cnf(cls_eq__divide__eq_3,axiom,
( X2 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
cnf(cls_divide__eq__eq_0,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
cnf(cls_order__antisym_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_zero__less__power__eq_3,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
cnf(cls_less__add__one_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
cnf(cls_power__eq__0__iff__number__of_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_1) ).
cnf(cls_eq__eqI_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_add__right__cancel_0,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_eq__eqI_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_add__left__cancel_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
cnf(cls_add__imp__eq_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
cnf(cls_zero__eq__power2_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__eq__power2_0) ).
cnf(cls_minus__divide__divide_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
cnf(cls_divide__eq__imp_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1) = X3
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
cnf(cls_eq__divide__imp_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
cnf(cls_zero__le__square_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
cnf(cls_minus__dvd__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
cnf(cls_abs__dvd__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
cnf(cls_dvd__minus__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
cnf(cls_dvd__abs__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
cnf(cls_nonzero__minus__divide__divide_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
cnf(cls_mult__cancel2_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
cnf(cls_mult__cancel1_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
cnf(cls_nat__mult__eq__cancel__disj_0,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
cnf(cls_mod__mult__self1__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
cnf(cls_mod__mult__self2__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
cnf(cls_nat__even__iff__2__dvd_1,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__even__iff__2__dvd_1) ).
cnf(cls_dvd_Oneq__le__trans_0,axiom,
( X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oneq__le__trans_0) ).
cnf(cls_dvd_Ole__neq__trans_0,axiom,
( X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__neq__trans_0) ).
cnf(cls_dvd_Oantisym__conv_0,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oantisym__conv_0) ).
cnf(cls_dvd__antisym_0,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__antisym_0) ).
cnf(cls_dvd_Oless__le_0,axiom,
( X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le_0) ).
cnf(cls_dvd_Oantisym_0,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oantisym_0) ).
cnf(cls_dvd_Oeq__iff_2,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_2) ).
cnf(cls_add__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_dvdI_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
cnf(cls_dvd__triv__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
cnf(cls_dvd__triv__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
cnf(cls_nat__add__right__cancel_0,axiom,
( X1 = X3
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
cnf(cls_natgb_Oadd__cancel_0,axiom,
( X2 = X3
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
cnf(cls_nat__add__left__cancel_0,axiom,
( X2 = X3
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
cnf(cls_square__eq__iff_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
cnf(cls_minus__mult__minus_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
cnf(cls_abs__mult__self_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
cnf(cls_minus__mult__commute_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
cnf(cls_mult__2_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X2,X1) = c_HOL_Oplus__class_Oplus(X2,X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__2_0) ).
cnf(cls_mult__2__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X1) = c_HOL_Oplus__class_Oplus(X2,X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__2__right_0) ).
cnf(cls_power2__eq__square_0,axiom,
( c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__square_0) ).
cnf(cls_class__semiring_Osemiring__rules_I29_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X2,X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I29_J_0) ).
cnf(cls_zero__less__abs__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
cnf(cls_neg__power__if_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Power_Opower__class_Opower(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__power__if_0) ).
cnf(cls_power__even__abs_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) = c_Power_Opower__class_Opower(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__abs_0) ).
cnf(cls_power__eq__0__iff__number__of_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_0) ).
cnf(cls_mod__eq__0__iff_1,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
cnf(cls_even__add_3,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_3) ).
cnf(cls_even__sum__nat_2,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_2) ).
cnf(cls_odd__add_0,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_0) ).
cnf(cls_divide__eq__eq__number__of_1,axiom,
( c_Int_Onumber__class_Onumber__of(X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) != c_Int_Onumber__class_Onumber__of(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_1) ).
cnf(cls_eq__divide__eq__number__of_1,axiom,
( c_Int_Onumber__class_Onumber__of(X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).
cnf(cls_abs__number__of_1,axiom,
( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_Int_Onumber__class_Onumber__of(X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__number__of_1) ).
cnf(cls_dvd__eq__mod__eq__0_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
cnf(cls_nat__mult__2_0,axiom,
c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__2_0) ).
cnf(cls_nat__mult__2__right_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__2__right_0) ).
cnf(cls_dvd__imp__mod__0_0,axiom,
( c_Divides_Odiv__class_Omod(X2,X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
cnf(cls_xt1_I11_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_xt1_I12_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
cnf(cls_order__neq__le__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
cnf(cls_order__le__neq__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
cnf(cls_order__le__less_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
cnf(cls_order__less__le_2,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
cnf(cls_class__fieldgb_Odivide__inverse_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).
cnf(cls_abs__le__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
cnf(cls_order__less__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
cnf(cls_order__le__less_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
cnf(cls_abs__minus__le__zero_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
cnf(cls_of__nat__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
cnf(cls_abs__not__less__zero_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
cnf(cls_odd__add_1,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_1) ).
cnf(cls_even__add_2,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_2) ).
cnf(cls_even__sum__nat_3,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_3) ).
cnf(cls_diff__minus__eq__add_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
cnf(cls_class__ring_Osub__add_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
cnf(cls_ab__diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
cnf(cls_diff__def_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
cnf(cls_diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
cnf(cls_divide__inverse_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
cnf(cls_inverse__eq__divide__number__of_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide__number__of_0) ).
cnf(cls_abs__if__lattice_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
cnf(cls_mod__if_0,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
cnf(cls_iszero__number__of__Bit0_0,axiom,
( c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X2),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Bit0_0) ).
cnf(cls_even__product__nat_1,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_1) ).
cnf(cls_even__product__nat_2,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_2) ).
cnf(cls_divide__eq__eq__number__of1_1,axiom,
( c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_1) ).
cnf(cls_eq__divide__eq__number__of1_2,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).
cnf(cls_minus__one__odd__power_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__one__odd__power_0) ).
cnf(cls_power__eq__0__iff__number__of_2,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_2) ).
cnf(cls_abs__if_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_0) ).
cnf(cls_abs__of__neg_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
cnf(cls_abs__of__nonpos_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
cnf(cls_iszero__number__of__Bit0_1,axiom,
( c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X2),X1),X1)
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Bit0_1) ).
cnf(cls_even__mult__two__ex_0,axiom,
( X1 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1(X1),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__mult__two__ex_0) ).
cnf(cls_power__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
cnf(cls_power__0__left__number__of_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_0) ).
cnf(cls_power__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
cnf(cls_divide__eq__eq__number__of_2,axiom,
( c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X1),X1) = c_Int_Onumber__class_Onumber__of(X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_2) ).
cnf(cls_eq__divide__eq__number__of_2,axiom,
( c_Int_Onumber__class_Onumber__of(X2,X1) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_2) ).
cnf(cls_minus__one__even__power_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__one__even__power_0) ).
cnf(cls_nat__even__iff__2__dvd_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__even__iff__2__dvd_0) ).
cnf(cls_linorder__neqE_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
cnf(cls_linorder__less__linear_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
cnf(cls_one__power2_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__power2_0) ).
cnf(cls_zero__power2_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__power2_0) ).
cnf(cls_zero__eq__power2_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__eq__power2_1) ).
cnf(cls_abs__of__pos_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
cnf(cls_abs__of__nonneg_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
cnf(cls_power__0__left__number__of_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_1) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( c_HOL_Oord__class_Oless(X2,X2,X1)
| c_lessequals(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
cnf(cls_linorder__not__less_0,axiom,
( c_lessequals(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
cnf(cls_linorder__not__le_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
cnf(cls_not__leE_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
cnf(cls_linorder__linear_0,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_inverse__unique_0,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = X3
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
cnf(cls_minus__unique_0,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
cnf(cls_eq__neg__iff__add__eq__0_1,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
cnf(cls_class__ring_Oneg__mul_0,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
cnf(cls_abs__ge__minus__self_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
cnf(cls_divide__minus1_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__minus1_0) ).
cnf(cls_not__one__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
cnf(cls_not__one__le__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
cnf(cls_mult__cancel1_1,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).
cnf(cls_mult__cancel2_1,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).
cnf(cls_mult__eq__0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
cnf(cls_no__zero__divirors__neq0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
cnf(cls_no__zero__divisors_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
cnf(cls_neg__one__odd__power_0,axiom,
( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X2,X1) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__one__odd__power_0) ).
cnf(cls_neg__one__even__power_0,axiom,
( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__one__even__power_0) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
cnf(cls_nat__neq__iff_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
cnf(cls_dvd__0__left_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
cnf(cls_right__inverse__eq_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
cnf(cls_dvd__if__abs__eq_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) != c_HOL_Oabs__class_Oabs(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
cnf(cls_abs__le__zero__iff_1,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
cnf(cls_nat__add__commute_0,axiom,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
cnf(cls_nat__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
cnf(cls_field__power__not__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
cnf(cls_double__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
cnf(cls_pos2_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos2_0) ).
cnf(cls_divide__Numeral0_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__Numeral0_0) ).
cnf(cls_divide__numeral__1_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__numeral__1_0) ).
cnf(cls_divide__Numeral1_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__Numeral1_0) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
cnf(cls_right__minus__eq_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
cnf(cls_one__add__one__is__two_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__add__one__is__two_0) ).
cnf(cls_zero__less__abs__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
cnf(cls_mult__minus1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__minus1_0) ).
cnf(cls_mult__minus1__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__minus1__right_0) ).
cnf(cls_power__eq__0__iff_2,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
cnf(cls_left__inverse_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__inverse_0) ).
cnf(cls_field__inverse_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__inverse_0) ).
cnf(cls_right__inverse_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse_0) ).
cnf(cls_iszero__number__of__Bit1_0,axiom,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X2),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Bit1_0) ).
cnf(cls_mult__is__0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
cnf(cls_mult__numeral__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X2,X1) = X2
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).
cnf(cls_mult__numeral__1__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) = X2
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__numeral__1__right_0) ).
cnf(cls_inverse__minus__eq_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
cnf(cls_abs__inverse_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
cnf(cls_of__nat__0__le__iff_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
cnf(cls_zero__le__imp__of__nat_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
cnf(cls_abs__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
cnf(cls_mult__eq__self__implies__10_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat)
| X1 != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).
cnf(cls_nonzero__inverse__minus__eq_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
cnf(cls_nonzero__abs__inverse_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X2,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
cnf(cls_nat__dvd__1__iff__1_0,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).
cnf(cls_ab__left__minus_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
cnf(cls_left__minus_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
cnf(cls_eq__neg__iff__add__eq__0_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
cnf(cls_right__minus_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
cnf(cls_nat__mult__eq__1__iff_0,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).
cnf(cls_add__is__0_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
cnf(cls_nat__mult__eq__1__iff_1,axiom,
( X2 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).
cnf(cls_add__is__0_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
cnf(cls_nat__1__eq__mult__iff_0,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).
cnf(cls_nat__1__eq__mult__iff_1,axiom,
( X2 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).
cnf(cls_abs__if__lattice_1,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
cnf(cls_class__fieldgb_Oinverse__divide_0,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).
cnf(cls_add__eq__self__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
cnf(cls_natgb_Oadd__r0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
cnf(cls_not__less0_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
cnf(cls_gr__implies__not0_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
cnf(cls_root4_0,axiom,
c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)) = c_Complex_Oii,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root4_0) ).
cnf(cls_abs__ge__self_0,axiom,
( c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
cnf(cls_nonzero__inverse__eq__divide_0,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
cnf(cls_add__numeral__0_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1),X2,X1) = X2
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).
cnf(cls_add__numeral__0__right_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1),X1) = X2
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__numeral__0__right_0) ).
cnf(cls_divide__self__if_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
cnf(cls_transfer__int__nat__numerals_I3_J_0,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transfer__int__nat__numerals_I3_J_0) ).
cnf(cls_transfer__int__nat__numerals_I4_J_0,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transfer__int__nat__numerals_I4_J_0) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
cnf(cls_less__not__refl_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
cnf(cls_nat__1__add__1_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__add__1_0) ).
cnf(cls_abs__if_1,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oabs__if(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
cnf(cls_power__0__left_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
cnf(cls_power__0__left_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
cnf(cls_group__add__class_Odiff__0_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
cnf(cls_inverse__eq__divide_0,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
cnf(cls_not__iszero__Numeral1_0,axiom,
( ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__iszero__Numeral1_0) ).
cnf(cls_divide__zero_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
cnf(cls_divide__eq__eq_1,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
cnf(cls_eq__divide__eq_2,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
cnf(cls_divide__self__if_1,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
cnf(cls_double__eq__0__iff_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
cnf(cls_inverse__numeral__1_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__numeral__1_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( X2 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
cnf(cls_zero__less__one_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
cnf(cls_zero__le__one_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
cnf(cls_mod__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
cnf(cls_divide_Ozero_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
cnf(cls_divide__zero__left_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
cnf(cls_power__one_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
cnf(cls_mult__eq__0__iff_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
cnf(cls_mult__left_Ozero_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
cnf(cls_mult_Ozero__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
cnf(cls_mult__zero__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
cnf(cls_class__semiring_Omul__0_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
cnf(cls_mod__by__1_0,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
cnf(cls_mult__eq__0__iff_2,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
cnf(cls_mult_Ozero__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
cnf(cls_mult__right_Ozero_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
cnf(cls_mult__zero__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
cnf(cls_divide__self_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).
cnf(cls_right__inverse__eq_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
cnf(cls_odd__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__pos_0) ).
cnf(cls_power__0_0,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
cnf(cls_class__semiring_Opwr__0_0,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
cnf(cls_add__0__left_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
cnf(cls_mult__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
cnf(cls_mult__1__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
cnf(cls_class__semiring_Omul__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
cnf(cls_diff__0__right_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
cnf(cls_mod__by__0_0,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
cnf(cls_divide__1_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_mult__1__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_one__dvd_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).
cnf(cls_dvd__0__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
cnf(cls_nonzero__number__of__Min_0,axiom,
( ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__number__of__Min_0) ).
cnf(cls_power__one__right_0,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_diff__self_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
cnf(cls_right__minus__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
cnf(cls_mod__self_0,axiom,
( c_Divides_Odiv__class_Omod(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom,
( X2 = X3
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oinverse__class_Oinverse(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
cnf(cls_mult__idem_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X2,X1) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
cnf(cls_dvd__refl_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
cnf(cls_order__eq__refl_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
cnf(cls_order__eq__iff_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
cnf(cls_nat__mult__eq__1__iff_2,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).
cnf(cls_nat__1__eq__mult__iff_2,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).
cnf(cls_root__unity_0,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).
cnf(cls_abs__of__nat_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) = c_Nat_Osemiring__1__class_Oof__nat(X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nat_0) ).
cnf(cls_abs__minus__cancel_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
cnf(cls_abs__idempotent_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
cnf(cls_inverse__eq__iff__eq_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oinverse__class_Oinverse(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
cnf(cls_eq__number__of_0,axiom,
( X2 = X3
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
cnf(cls_gr0I_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
cnf(cls_nat__dvd__1__iff__1_1,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_1) ).
cnf(cls_mult__is__0_1,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
cnf(cls_mult__is__0_2,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
cnf(cls_nat__mult__1_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
cnf(cls_nat__mult__1__right_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(cls_gcd__lcm__complete__lattice__nat_Obot__least_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Obot__least_0) ).
cnf(cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0) ).
cnf(cls_abs__minus__one_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__one_0) ).
cnf(cls_inverse__inverse__eq_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
cnf(cls_of__nat__eq__iff_0,axiom,
( X2 = X3
| ~ class_Nat_Osemiring__char__0(X1)
| c_Nat_Osemiring__1__class_Oof__nat(X2,X1) != c_Nat_Osemiring__1__class_Oof__nat(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
cnf(cls_neg__equal__iff__equal_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
cnf(cls_nonzero__inverse__inverse__eq_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
cnf(cls_dvd_Oeq__iff_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).
cnf(cls_inverse__eq__1__iff_0,axiom,
( X2 = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
cnf(cls_inverse__nonzero__iff__nonzero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
cnf(cls_minus__minus_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
cnf(cls_minus__equation__iff_1,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
cnf(cls_double__compl_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_equation__minus__iff_0,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
cnf(cls_equation__minus__iff_1,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_iszero__number__of__Pls_0,axiom,
( c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Pls_0) ).
cnf(cls_Nat__Transfer_Otransfer__int__nat__relations_I1_J_0,axiom,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(X2,tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat__Transfer_Otransfer__int__nat__relations_I1_J_0) ).
cnf(cls_int__int__eq_0,axiom,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(X2,tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_int__int__eq_0) ).
cnf(cls_neg__0__equal__iff__equal_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Ouminus__class_Ouminus(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
cnf(cls_inverse__zero__imp__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
cnf(cls_neg__equal__0__iff__equal_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
cnf(cls_abs__eq__0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
cnf(cls_arith__simps_I31_J_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arith__simps_I31_J_0) ).
cnf(cls_number__of__Min_0,axiom,
( c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Min_0) ).
cnf(cls_not__iszero__1_0,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X1)
| ~ c_Int_Oiszero(c_HOL_Oone__class_Oone(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__iszero__1_0) ).
cnf(cls_inverse__eq__1__iff_1,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
cnf(cls_inverse__nonzero__iff__nonzero_1,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
cnf(cls_neg__equal__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
cnf(cls_iszero__def_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1)
| ~ c_Int_Oiszero(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__def_0) ).
cnf(cls_eq__number__of__Pls__Min_0,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of__Pls__Min_0) ).
cnf(cls_inverse__1_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
cnf(cls_inverse__zero_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
cnf(cls_neg__equal__zero_1,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
cnf(cls_minus__zero_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
cnf(cls_abs__one_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__one_0) ).
cnf(cls_abs__eq__0_1,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
cnf(cls_neg__0__equal__iff__equal_1,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
cnf(cls_of__nat__1_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
cnf(cls_of__nat__0_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
cnf(cls_numeral__1__eq__1_0,axiom,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__1__eq__1_0) ).
cnf(cls_comp__arith_I110_J_0,axiom,
( c_HOL_Oone__class_Oone(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I110_J_0) ).
cnf(cls_iszero__0_0,axiom,
( c_Int_Oiszero(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__0_0) ).
cnf(cls_odd__1__nat_0,axiom,
~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__1__nat_0) ).
cnf(cls_number__of__Pls_0,axiom,
( c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Pls_0) ).
cnf(cls_comp__arith_I112_J_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I112_J_0) ).
cnf(cls_zero__neq__one_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
cnf(cls_one__neq__zero_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
cnf(cls_nat__numeral__1__eq__1_0,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__numeral__1__eq__1_0) ).
cnf(cls_Numeral1__eq1__nat_0,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral1__eq1__nat_0) ).
cnf(cls_even__zero__nat_0,axiom,
c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).
cnf(cls_rel__simps_I48_J_0,axiom,
( X1 = X2
| c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I48_J_0) ).
cnf(cls_rel__simps_I51_J_0,axiom,
( X1 = X2
| c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I51_J_0) ).
cnf(cls_nat__number__of__Pls_0,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__number__of__Pls_0) ).
cnf(cls_nat__number__of__Min_0,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__number__of__Min_0) ).
cnf(cls_comp__arith_I113_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I113_J_0) ).
cnf(cls_number__of__is__id_0,axiom,
c_Int_Onumber__class_Onumber__of(X1,tc_Int_Oint) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__is__id_0) ).
cnf(cls_rel__simps_I49_J_0,axiom,
c_Int_OBit0(X1) != c_Int_OBit1(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I49_J_0) ).
cnf(cls_rel__simps_I50_J_0,axiom,
c_Int_OBit1(X1) != c_Int_OBit0(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I50_J_0) ).
cnf(cls_root1_0,axiom,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root1_0) ).
cnf(cls_root0_0,axiom,
c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root0_0) ).
cnf(cls_rel__simps_I38_J_0,axiom,
( c_Int_OPls = X1
| c_Int_OPls != c_Int_OBit0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I38_J_0) ).
cnf(cls_rel__simps_I43_J_0,axiom,
( c_Int_OMin = X1
| c_Int_OMin != c_Int_OBit1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I43_J_0) ).
cnf(cls_rel__simps_I44_J_0,axiom,
( X1 = c_Int_OPls
| c_Int_OBit0(X1) != c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I44_J_0) ).
cnf(cls_rel__simps_I47_J_0,axiom,
( X1 = c_Int_OMin
| c_Int_OBit1(X1) != c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I47_J_0) ).
cnf(cls_rel__simps_I45_J_0,axiom,
c_Int_OBit0(X1) != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I45_J_0) ).
cnf(cls_rel__simps_I46_J_0,axiom,
c_Int_OBit1(X1) != c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I46_J_0) ).
cnf(cls_rel__simps_I39_J_0,axiom,
c_Int_OPls != c_Int_OBit1(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I39_J_0) ).
cnf(cls_rel__simps_I42_J_0,axiom,
c_Int_OMin != c_Int_OBit0(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I42_J_0) ).
cnf(cls_complex__i__not__one_0,axiom,
c_Complex_Oii != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__i__not__one_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
cnf(clsarity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oring__1,axiom,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_Int__Oint__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
cnf(clsarity_Int__Oint__Divides_Oring__div,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Oring__div) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
cnf(clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Olordered__ring,axiom,
class_Ring__and__Field_Olordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Olordered__ring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
cnf(clsarity_Int__Oint__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).
cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oabs__if,axiom,
class_Ring__and__Field_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oabs__if) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Odvd,axiom,
class_Ring__and__Field_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Odvd) ).
cnf(clsarity_nat__Ring__and__Field_Odvd,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
cnf(clsarity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
cnf(clsarity_Int__Oint__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Osemiring__div) ).
cnf(clsarity_nat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
cnf(clsarity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
cnf(clsarity_nat__Power_Opower,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
cnf(clsarity_Int__Oint__Int_Onumber,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
cnf(clsarity_nat__Int_Onumber,axiom,
class_Int_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
cnf(clsarity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) ).
cnf(cls_Bit0__Pls_0,axiom,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bit0__Pls_0) ).
cnf(cls_Bit1__Min_0,axiom,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bit1__Min_0) ).
cnf(cls_rel__simps_I38_J_1,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I38_J_1) ).
cnf(cls_rel__simps_I43_J_1,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I43_J_1) ).
cnf(cls_rel__simps_I40_J_0,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I40_J_0) ).
cnf(cls_rel__simps_I37_J_0,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I37_J_0) ).
cnf(i_0_1427,axiom,
~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat)),tc_nat),
cls_odd__nat__equiv__def2_1 ).
cnf(i_0_1428,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
cls_Suc__eq__plus1_0 ).
cnf(i_0_1429,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat)),X1),X1) ),
cls_odd__0__le__power__imp__0__le_0 ).
cnf(i_0_1430,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat)),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_odd__power__less__zero_0 ).
cnf(i_0_1431,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_Suc(X4),X1),c_Power_Opower__class_Opower(X3,c_Suc(X4),X1),X1) ),
cls_power__le__imp__le__base_0 ).
cnf(i_0_1432,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat)),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I37_J_0 ).
cnf(i_0_1433,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
cls_Suc__mult__less__cancel1_0 ).
cnf(i_0_1434,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(X1))),c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat),
cls_Suc__mod__eq__add3__mod__number__of_0 ).
cnf(i_0_1435,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(X1))),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),X2,tc_nat),
cls_Suc__mod__eq__add3__mod_0 ).
cnf(i_0_1436,axiom,
c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_Suc(X2))),tc_nat) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat),tc_nat),
cls_mod__Suc__eq__mod__add3_0 ).
cnf(i_0_1437,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat)),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__odd__eq_0 ).
cnf(i_0_1438,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
cls_mod__mult__self4_0 ).
cnf(i_0_1439,axiom,
~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat)),tc_nat),
cls_odd__Suc__mult__two__ex_1 ).
cnf(i_0_1440,axiom,
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
cls_one__less__mult_0 ).
cnf(i_0_1441,axiom,
c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat),tc_nat),
cls_even__nat__equiv__def2_1 ).
cnf(i_0_1442,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_Suc__mult__less__cancel1_1 ).
cnf(i_0_1443,axiom,
( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_odd__nat__equiv__def_1 ).
cnf(i_0_1444,axiom,
( X2 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) != c_Power_Opower__class_Opower(X4,c_Suc(X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_power__inject__base_0 ).
cnf(i_0_1445,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
cls_n__less__n__mult__m_0 ).
cnf(i_0_1446,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
cls_n__less__m__mult__n_0 ).
cnf(i_0_1447,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
cls_nat__lt__two__imp__zero__or__one_0 ).
cnf(i_0_1448,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_even__nat__equiv__def_1 ).
cnf(i_0_1449,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat)),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
cls_power__minus1__odd_0 ).
cnf(i_0_1450,axiom,
( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat)),X1) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_power__m1__odd_0 ).
cnf(i_0_1451,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_power__Suc__less__one_0 ).
cnf(i_0_1452,axiom,
c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat),
cls_mod__Suc__eq__Suc__mod_0 ).
cnf(i_0_1453,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_Suc(X1)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
cls_mod2__Suc__Suc_0 ).
cnf(i_0_1454,axiom,
( X2 = X3
| c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat) ),
cls_Suc__mult__cancel1_0 ).
cnf(i_0_1455,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_power__gt1_0 ).
cnf(i_0_1456,axiom,
c_Suc(c_Suc(c_Suc(X1))) = c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),
cls_Suc3__eq__add__3_0 ).
cnf(i_0_1457,axiom,
( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat))
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2 ),
cls_mod__Suc_1 ).
cnf(i_0_1458,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
cls_Suc__less__eq_0 ).
cnf(i_0_1459,axiom,
( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_odd__nat__equiv__def_0 ).
cnf(i_0_1460,axiom,
( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
cls_Suc__times__mod__eq_0 ).
cnf(i_0_1461,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
cls_numeral__3__eq__3_0 ).
cnf(i_0_1462,axiom,
( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
cls_mod__Suc_0 ).
cnf(i_0_1463,axiom,
( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_even__nat__equiv__def_0 ).
cnf(i_0_1464,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
cls_less__iff__Suc__add_1 ).
cnf(i_0_1465,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
cls_less__add__Suc1_0 ).
cnf(i_0_1466,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
cls_less__add__Suc2_0 ).
cnf(i_0_1467,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_less__Suc__eq__0__disj_3 ).
cnf(i_0_1468,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_Suc__mono_0 ).
cnf(i_0_1469,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)),
cls_mult__eq__1__iff_2 ).
cnf(i_0_1470,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
cls_not__less__eq_1 ).
cnf(i_0_1471,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__Suc2_0 ).
cnf(i_0_1472,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Power_Opower(X1) ),
cls_power__Suc_0 ).
cnf(i_0_1473,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I35_J_0 ).
cnf(i_0_1474,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Opwr__Suc_0 ).
cnf(i_0_1475,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_Power_Opower__class_Opower(X2,c_Suc(X3),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I28_J_0 ).
cnf(i_0_1476,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(X2,c_Suc(X3),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I27_J_0 ).
cnf(i_0_1477,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_less__trans__Suc_0 ).
cnf(i_0_1478,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
cls_dvd__1__iff__1_0 ).
cnf(i_0_1479,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
cls_add__Suc__shift_0 ).
cnf(i_0_1480,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
cls_add__Suc_0 ).
cnf(i_0_1481,axiom,
c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
cls_add__Suc__right_0 ).
cnf(i_0_1482,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
cls_mult__Suc_0 ).
cnf(i_0_1483,axiom,
c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
cls_mult__Suc__right_0 ).
cnf(i_0_1484,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
cls_less__SucE_0 ).
cnf(i_0_1485,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
cls_not__less__less__Suc__eq_0 ).
cnf(i_0_1486,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
cls_less__antisym_0 ).
cnf(i_0_1487,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
cls_Suc__lessD_0 ).
cnf(i_0_1488,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_Suc__lessI_0 ).
cnf(i_0_1489,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
cls_one__is__add_1 ).
cnf(i_0_1490,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_1 ).
cnf(i_0_1491,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
cls_dvd__1__iff__1_1 ).
cnf(i_0_1492,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
cls_less__Suc0_0 ).
cnf(i_0_1493,axiom,
c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat) = c_Suc(c_Suc(X1)),
cls_add__2__eq__Suc_0 ).
cnf(i_0_1494,axiom,
c_HOL_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Suc(c_Suc(X1)),
cls_add__2__eq__Suc_H_0 ).
cnf(i_0_1495,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_less__SucI_0 ).
cnf(i_0_1496,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
cls_one__is__add_0 ).
cnf(i_0_1497,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
cls_one__is__add_3 ).
cnf(i_0_1498,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_0 ).
cnf(i_0_1499,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_3 ).
cnf(i_0_1500,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_mult__eq__1__iff_0 ).
cnf(i_0_1501,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_mult__eq__1__iff_1 ).
cnf(i_0_1502,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)),
cls_add__is__1_4 ).
cnf(i_0_1503,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)),
cls_add__is__1_5 ).
cnf(i_0_1504,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),
cls_one__is__add_4 ).
cnf(i_0_1505,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),
cls_one__is__add_5 ).
cnf(i_0_1506,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
cls_less__2__cases_0 ).
cnf(i_0_1507,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X2),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__Suc_0 ).
cnf(i_0_1508,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
cls_not__less__less__Suc__eq_1 ).
cnf(i_0_1509,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
cls_not__less__eq_0 ).
cnf(i_0_1510,axiom,
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat) ),
cls_even__Suc_0 ).
cnf(i_0_1511,axiom,
c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
cls_comp__arith_I115_J_0 ).
cnf(i_0_1512,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
cls_numeral__2__eq__2_0 ).
cnf(i_0_1513,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
cls_power__0__Suc_0 ).
cnf(i_0_1514,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
cls_one__is__add_2 ).
cnf(i_0_1515,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_2 ).
cnf(i_0_1516,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonneg__eq__0__iff_2 ).
cnf(i_0_1517,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
cls_Suc__inject_0 ).
cnf(i_0_1518,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
cls_nat_Oinject_0 ).
cnf(i_0_1519,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
cls_less__Suc0_1 ).
cnf(i_0_1520,axiom,
c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_mod__1_0 ).
cnf(i_0_1521,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
cls_dvd__1__left_0 ).
cnf(i_0_1522,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
cls_zero__less__Suc_0 ).
cnf(i_0_1523,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
cls_gr0__conv__Suc_1 ).
cnf(i_0_1524,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
cls_less__Suc__eq_2 ).
cnf(i_0_1525,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
cls_lessI_0 ).
cnf(i_0_1526,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_even__Suc_1 ).
cnf(i_0_1527,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
cls_Suc__eq__plus1__left_0 ).
cnf(i_0_1528,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
cls_nat_Osimps_I3_J_0 ).
cnf(i_0_1529,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
cls_Suc__neq__Zero_0 ).
cnf(i_0_1530,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
cls_Zero__neq__Suc_0 ).
cnf(i_0_1531,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
cls_nat_Osimps_I2_J_0 ).
cnf(i_0_1532,axiom,
c_Suc(X1) != X1,
cls_Suc__n__not__n_0 ).
cnf(i_0_1533,axiom,
X1 != c_Suc(X1),
cls_n__not__Suc__n_0 ).
cnf(i_0_1534,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
cls_numeral__1__eq__Suc__0_0 ).
cnf(i_0_1535,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
cls_One__nat__def_0 ).
cnf(i_0_1536,plain,
~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1427,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1537,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),X5,X1),X1),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Oprod__diff__prod_0,
[final] ).
cnf(i_0_1538,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X4,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__diff__triangle__ineq_0,
[final] ).
cnf(i_0_1539,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X6,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X5,X1),X6,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X4,X1),X6,X1),X5,X1),X1)
| ~ class_RealVector_Oreal__field(X1) ),
cls_DERIV__mult__lemma_0,
[final] ).
cnf(i_0_1540,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1),X4,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
cls_DERIV__inverse__lemma_0,
[final] ).
cnf(i_0_1541,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
cls_less__add__iff1_1,
[final] ).
cnf(i_0_1542,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
cls_le__add__iff1_1,
[final] ).
cnf(i_0_1543,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
cls_less__add__iff2_1,
[final] ).
cnf(i_0_1544,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
cls_le__add__iff2_1,
[final] ).
cnf(i_0_1545,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1),X1) ),
inference(rw,[status(thm)],[i_0_1429,c_0_1428]),
[final] ).
cnf(i_0_1546,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
cls_less__add__iff1_0,
[final] ).
cnf(i_0_1547,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
cls_le__add__iff1_0,
[final] ).
cnf(i_0_1548,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
cls_less__add__iff2_0,
[final] ).
cnf(i_0_1549,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
cls_le__add__iff2_0,
[final] ).
cnf(i_0_1550,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
cls_calculation_0,
[final] ).
cnf(i_0_1551,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X2,X1),X3,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_power2__diff_0,
[final] ).
cnf(i_0_1552,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X2,X1),X3,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_power2__sum_0,
[final] ).
cnf(i_0_1553,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),X1) ),
cls_sum__power2__gt__zero__iff_0,
[final] ).
cnf(i_0_1554,negated_conjecture,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
cls_conjecture_0,
[final] ).
cnf(i_0_1555,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_sum__power2__le__zero__iff_0,
[final] ).
cnf(i_0_1556,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_sum__power2__le__zero__iff_1,
[final] ).
cnf(i_0_1557,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__sum__power2__lt__zero_0,
[final] ).
cnf(i_0_1558,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X5,X6,X1),X1),X4,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,X1) ),
cls_inf__period_I4_J_1,
[final] ).
cnf(i_0_1559,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(rw,[status(thm)],[i_0_1430,c_0_1428]),
[final] ).
cnf(i_0_1560,plain,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1431,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1561,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X6,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X6,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X1) ),
cls_inf__period_I4_J_0,
[final] ).
cnf(i_0_1562,plain,
( c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[i_0_1432,c_0_1428]),
[final] ).
cnf(i_0_1563,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1433,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1564,plain,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1434,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1565,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),X1) ),
cls_sum__squares__gt__zero__iff_0,
[final] ).
cnf(i_0_1566,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X1),X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_eq__add__iff2_1,
[final] ).
cnf(i_0_1567,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_eq__add__iff1_1,
[final] ).
cnf(i_0_1568,plain,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),X2,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1435,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1569,plain,
c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1436,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1570,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
cls_mod__lemma_0,
[final] ).
cnf(i_0_1571,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_divide__less__eq__number__of1_8,
[final] ).
cnf(i_0_1572,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_divide__le__eq__number__of1_8,
[final] ).
cnf(i_0_1573,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
cls_less__divide__eq__number__of1_8,
[final] ).
cnf(i_0_1574,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
cls_le__divide__eq__number__of1_8,
[final] ).
cnf(i_0_1575,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_Deriv_Oinverse__diff__inverse_0,
[final] ).
cnf(i_0_1576,plain,
( c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[i_0_1437,c_0_1428]),
[final] ).
cnf(i_0_1577,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_sum__power2__le__zero__iff_2,
[final] ).
cnf(i_0_1578,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
cls_divide__less__eq__number__of_9,
[final] ).
cnf(i_0_1579,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
cls_divide__le__eq__number__of_9,
[final] ).
cnf(i_0_1580,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
cls_less__divide__eq__number__of_9,
[final] ).
cnf(i_0_1581,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
cls_le__divide__eq__number__of_9,
[final] ).
cnf(i_0_1582,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_divide__less__eq__number__of1_9,
[final] ).
cnf(i_0_1583,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_divide__le__eq__number__of1_9,
[final] ).
cnf(i_0_1584,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
cls_less__divide__eq__number__of1_9,
[final] ).
cnf(i_0_1585,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
cls_le__divide__eq__number__of1_9,
[final] ).
cnf(i_0_1586,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_sum__power2__gt__zero__iff_1,
[final] ).
cnf(i_0_1587,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_sum__power2__gt__zero__iff_2,
[final] ).
cnf(i_0_1588,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_diff__frac__eq_0,
[final] ).
cnf(i_0_1589,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_add__frac__eq_0,
[final] ).
cnf(i_0_1590,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_sum__power2__ge__zero_0,
[final] ).
cnf(i_0_1591,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
cls_divide__less__eq__number__of_8,
[final] ).
cnf(i_0_1592,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
cls_divide__le__eq__number__of_8,
[final] ).
cnf(i_0_1593,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
cls_less__divide__eq__number__of_8,
[final] ).
cnf(i_0_1594,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
cls_le__divide__eq__number__of_8,
[final] ).
cnf(i_0_1595,plain,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1438,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1596,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_sum__squares__le__zero__iff_0,
[final] ).
cnf(i_0_1597,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_sum__squares__le__zero__iff_1,
[final] ).
cnf(i_0_1598,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__sum__squares__lt__zero_0,
[final] ).
cnf(i_0_1599,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_even__power__le__0__imp__0_0,
[final] ).
cnf(i_0_1600,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1) = X6
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
cls_eq__add__iff1_0,
[final] ).
cnf(i_0_1601,axiom,
( X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1)
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
cls_eq__add__iff2_0,
[final] ).
cnf(i_0_1602,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) ),
cls_power2__less__imp__less_0,
[final] ).
cnf(i_0_1603,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) ),
cls_power2__le__imp__le_0,
[final] ).
cnf(i_0_1604,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1),X5,X1)
| ~ class_Ring__and__Field_Osemiring(X1) ),
cls_combine__common__factor_0,
[final] ).
cnf(i_0_1605,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_class__ringb_Onoteq__reduce_0,
[final] ).
cnf(i_0_1606,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_class__ringb_Oadd__mul__solve_0,
[final] ).
cnf(i_0_1607,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
cls_left__add__mult__distrib_0,
[final] ).
cnf(i_0_1608,axiom,
( X2 = X4
| X1 = X3
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
cls_natgb_Onoteq__reduce_0,
[final] ).
cnf(i_0_1609,axiom,
( X2 = X4
| X1 = X3
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
cls_natgb_Oadd__mul__solve_0,
[final] ).
cnf(i_0_1610,plain,
~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1439,c_0_1428]),
[final] ).
cnf(i_0_1611,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X1),X2,X1) ),
cls_abs__diff__less__iff_2,
[final] ).
cnf(i_0_1612,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1440,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1613,plain,
c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1441,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1614,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
cls_divide__less__eq__number__of1_4,
[final] ).
cnf(i_0_1615,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
cls_divide__less__eq__number__of1_1,
[final] ).
cnf(i_0_1616,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
cls_divide__le__eq__number__of1_4,
[final] ).
cnf(i_0_1617,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
cls_divide__le__eq__number__of1_1,
[final] ).
cnf(i_0_1618,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
cls_less__divide__eq__number__of1_4,
[final] ).
cnf(i_0_1619,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
cls_less__divide__eq__number__of1_1,
[final] ).
cnf(i_0_1620,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
cls_le__divide__eq__number__of1_4,
[final] ).
cnf(i_0_1621,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
cls_le__divide__eq__number__of1_1,
[final] ).
cnf(i_0_1622,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1442,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1623,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_divide__less__eq_9,
[final] ).
cnf(i_0_1624,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_divide__le__eq_9,
[final] ).
cnf(i_0_1625,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_divide__less__eq_8,
[final] ).
cnf(i_0_1626,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_divide__le__eq_8,
[final] ).
cnf(i_0_1627,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
cls_less__divide__eq_9,
[final] ).
cnf(i_0_1628,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
cls_less__divide__eq_8,
[final] ).
cnf(i_0_1629,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
cls_le__divide__eq_8,
[final] ).
cnf(i_0_1630,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
cls_le__divide__eq_9,
[final] ).
cnf(i_0_1631,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
cls_mod__diff__eq_0,
[final] ).
cnf(i_0_1632,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__add__eq_0,
[final] ).
cnf(i_0_1633,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__eq_0,
[final] ).
cnf(i_0_1634,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_divide__less__eq__number__of1_7,
[final] ).
cnf(i_0_1635,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_divide__le__eq__number__of1_7,
[final] ).
cnf(i_0_1636,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
cls_less__divide__eq__number__of1_7,
[final] ).
cnf(i_0_1637,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
cls_le__divide__eq__number__of1_7,
[final] ).
cnf(i_0_1638,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
cls_divide__less__eq__number__of1_5,
[final] ).
cnf(i_0_1639,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
cls_divide__le__eq__number__of1_5,
[final] ).
cnf(i_0_1640,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
cls_less__divide__eq__number__of1_5,
[final] ).
cnf(i_0_1641,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1) ),
cls_le__divide__eq__number__of1_5,
[final] ).
cnf(i_0_1642,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq3_0,
[final] ).
cnf(i_0_1643,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1) ),
cls_divide__less__eq__number__of_5,
[final] ).
cnf(i_0_1644,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1) ),
cls_divide__le__eq__number__of_5,
[final] ).
cnf(i_0_1645,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1) ),
cls_less__divide__eq__number__of_5,
[final] ).
cnf(i_0_1646,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1) ),
cls_le__divide__eq__number__of_5,
[final] ).
cnf(i_0_1647,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
cls_divide__less__eq__number__of_7,
[final] ).
cnf(i_0_1648,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
cls_divide__le__eq__number__of_7,
[final] ).
cnf(i_0_1649,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
cls_less__divide__eq__number__of_7,
[final] ).
cnf(i_0_1650,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
cls_le__divide__eq__number__of_7,
[final] ).
cnf(i_0_1651,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__power2__eq__zero__iff_0,
[final] ).
cnf(i_0_1652,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__power2__eq__zero__iff_1,
[final] ).
cnf(i_0_1653,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1443,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1654,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_gt__half__sum_0,
[final] ).
cnf(i_0_1655,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__half__sum_0,
[final] ).
cnf(i_0_1656,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_divide__left__mono__neg_0,
[final] ).
cnf(i_0_1657,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_divide__strict__left__mono_0,
[final] ).
cnf(i_0_1658,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_divide__left__mono_0,
[final] ).
cnf(i_0_1659,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_divide__strict__left__mono__neg_0,
[final] ).
cnf(i_0_1660,plain,
( X2 = X4
| c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) != c_Power_Opower__class_Opower(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1444,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1661,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_divide__less__eq__number__of1_6,
[final] ).
cnf(i_0_1662,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_less__divide__eq__number__of1_0,
[final] ).
cnf(i_0_1663,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_divide__le__eq__number__of1_6,
[final] ).
cnf(i_0_1664,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_le__divide__eq__number__of1_0,
[final] ).
cnf(i_0_1665,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
cls_less__divide__eq__number__of1_6,
[final] ).
cnf(i_0_1666,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
cls_divide__less__eq__number__of1_0,
[final] ).
cnf(i_0_1667,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
cls_le__divide__eq__number__of1_6,
[final] ).
cnf(i_0_1668,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X3,X1) ),
cls_divide__le__eq__number__of1_0,
[final] ).
cnf(i_0_1669,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1) ),
cls_divide__less__eq__number__of_4,
[final] ).
cnf(i_0_1670,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X2,X1) ),
cls_divide__le__eq__number__of_4,
[final] ).
cnf(i_0_1671,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1) ),
cls_less__divide__eq__number__of_4,
[final] ).
cnf(i_0_1672,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1) ),
cls_le__divide__eq__number__of_4,
[final] ).
cnf(i_0_1673,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__le__zero__iff_2,
[final] ).
cnf(i_0_1674,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1445,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1675,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1446,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1676,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
cls_divide__less__eq__number__of_1,
[final] ).
cnf(i_0_1677,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
cls_divide__le__eq__number__of_1,
[final] ).
cnf(i_0_1678,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1) ),
cls_less__divide__eq__number__of_1,
[final] ).
cnf(i_0_1679,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1) ),
cls_le__divide__eq__number__of_1,
[final] ).
cnf(i_0_1680,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1447,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1681,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_power__Suc__less_0,
[final] ).
cnf(i_0_1682,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X4,X1),X3,X1)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
cls_mod__diff__cong_0,
[final] ).
cnf(i_0_1683,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X6,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
cls_mod__add__cong_0,
[final] ).
cnf(i_0_1684,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
cls_mod__mult__cong_0,
[final] ).
cnf(i_0_1685,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I15_J_0,
[final] ).
cnf(i_0_1686,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I14_J_0,
[final] ).
cnf(i_0_1687,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
cls_divide__less__eq__number__of_6,
[final] ).
cnf(i_0_1688,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1),X1) ),
cls_divide__le__eq__number__of_6,
[final] ).
cnf(i_0_1689,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
cls_less__divide__eq__number__of_6,
[final] ).
cnf(i_0_1690,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X3,X1) ),
cls_le__divide__eq__number__of_6,
[final] ).
cnf(i_0_1691,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X5,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X5,X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_frac__less2_0,
[final] ).
cnf(i_0_1692,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X5,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_frac__less_0,
[final] ).
cnf(i_0_1693,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_mult__strict__mono_0,
[final] ).
cnf(i_0_1694,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_mult__strict__mono_H_0,
[final] ).
cnf(i_0_1695,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__le__less__imp__less_0,
[final] ).
cnf(i_0_1696,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_mult__less__le__imp__less_0,
[final] ).
cnf(i_0_1697,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X5,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X5,X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_frac__le_0,
[final] ).
cnf(i_0_1698,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__mono_H_0,
[final] ).
cnf(i_0_1699,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__mono_0,
[final] ).
cnf(i_0_1700,plain,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1448,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1701,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X3,X1),X5,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X4,X1) ),
cls_abs__mult__less_0,
[final] ).
cnf(i_0_1702,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X2,X1),X1),X3,X1) ),
cls_abs__diff__less__iff_0,
[final] ).
cnf(i_0_1703,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1) ),
cls_abs__diff__less__iff_1,
[final] ).
cnf(i_0_1704,plain,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(rw,[status(thm)],[i_0_1449,c_0_1428]),
[final] ).
cnf(i_0_1705,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
cls_less__divide__eq__number__of_0,
[final] ).
cnf(i_0_1706,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
cls_le__divide__eq__number__of_0,
[final] ).
cnf(i_0_1707,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) ),
cls_divide__less__eq__number__of_0,
[final] ).
cnf(i_0_1708,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) ),
cls_divide__le__eq__number__of_0,
[final] ).
cnf(i_0_1709,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__gt__zero__iff_1,
[final] ).
cnf(i_0_1710,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__gt__zero__iff_2,
[final] ).
cnf(i_0_1711,plain,
( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_1450,c_0_1428]),
[final] ).
cnf(i_0_1712,axiom,
( c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)
| c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)
| c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_mod__exhaust__less__4_0,
[final] ).
cnf(i_0_1713,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__ge__zero_0,
[final] ).
cnf(i_0_1714,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X4,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
cls_nat__mod__eq__iff_1,
[final] ).
cnf(i_0_1715,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
cls_divide__less__eq__number__of1_2,
[final] ).
cnf(i_0_1716,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X2,X1) ),
cls_divide__le__eq__number__of1_2,
[final] ).
cnf(i_0_1717,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_less__divide__eq__number__of1_2,
[final] ).
cnf(i_0_1718,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X1) ),
cls_le__divide__eq__number__of1_2,
[final] ).
cnf(i_0_1719,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1) ),
cls_divide__less__eq_5,
[final] ).
cnf(i_0_1720,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1) ),
cls_divide__le__eq_5,
[final] ).
cnf(i_0_1721,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1) ),
cls_divide__less__eq_4,
[final] ).
cnf(i_0_1722,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X3,X1),X2,X1) ),
cls_divide__less__eq_1,
[final] ).
cnf(i_0_1723,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),X2,X1) ),
cls_divide__le__eq_4,
[final] ).
cnf(i_0_1724,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X3,X1),X2,X1) ),
cls_divide__le__eq_1,
[final] ).
cnf(i_0_1725,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_less__divide__eq_5,
[final] ).
cnf(i_0_1726,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_less__divide__eq_4,
[final] ).
cnf(i_0_1727,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1) ),
cls_less__divide__eq_1,
[final] ).
cnf(i_0_1728,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_le__divide__eq_4,
[final] ).
cnf(i_0_1729,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_le__divide__eq_5,
[final] ).
cnf(i_0_1730,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X2,X4,X1),X1) ),
cls_le__divide__eq_1,
[final] ).
cnf(i_0_1731,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_divide__less__eq_7,
[final] ).
cnf(i_0_1732,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_divide__le__eq_7,
[final] ).
cnf(i_0_1733,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
cls_less__divide__eq_7,
[final] ).
cnf(i_0_1734,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
cls_le__divide__eq_7,
[final] ).
cnf(i_0_1735,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(rw,[status(thm)],[i_0_1451,c_0_1428]),
[final] ).
cnf(i_0_1736,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_power__less__power__Suc_0,
[final] ).
cnf(i_0_1737,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
cls_mult__right__less__imp__less_0,
[final] ).
cnf(i_0_1738,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_mult__left__less__imp__less_0,
[final] ).
cnf(i_0_1739,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
cls_mult__less__imp__less__right_0,
[final] ).
cnf(i_0_1740,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_mult__less__imp__less__left_0,
[final] ).
cnf(i_0_1741,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
cls_power__less__imp__less__base_0,
[final] ).
cnf(i_0_1742,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_mult__less__cancel__left__pos_0,
[final] ).
cnf(i_0_1743,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
cls_mult__right__le__imp__le_0,
[final] ).
cnf(i_0_1744,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_mult__left__le__imp__le_0,
[final] ).
cnf(i_0_1745,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_mult__le__cancel__left__pos_0,
[final] ).
cnf(i_0_1746,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__less__cancel__left__neg_0,
[final] ).
cnf(i_0_1747,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__cancel__left__neg_0,
[final] ).
cnf(i_0_1748,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X4,X1) ),
cls_power__strict__increasing__iff_0,
[final] ).
cnf(i_0_1749,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X4,X1) ),
cls_power__less__imp__less__exp_0,
[final] ).
cnf(i_0_1750,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_inverse__add_0,
[final] ).
cnf(i_0_1751,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ominus__class_Ominus(X3,X2,X1),X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_division__ring__inverse__diff_0,
[final] ).
cnf(i_0_1752,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_division__ring__inverse__add_0,
[final] ).
cnf(i_0_1753,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oring(X1)
| ~ class_Int_Onumber(X1) ),
cls_left__diff__distrib__number__of_0,
[final] ).
cnf(i_0_1754,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Osemiring(X1)
| ~ class_Int_Onumber(X1) ),
cls_left__distrib__number__of_0,
[final] ).
cnf(i_0_1755,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oring(X1)
| ~ class_Int_Onumber(X1) ),
cls_right__diff__distrib__number__of_0,
[final] ).
cnf(i_0_1756,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Osemiring(X1)
| ~ class_Int_Onumber(X1) ),
cls_right__distrib__number__of_0,
[final] ).
cnf(i_0_1757,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_zero__le__even__power_H_0,
[final] ).
cnf(i_0_1758,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_add__frac__num_0,
[final] ).
cnf(i_0_1759,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1),X4,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_add__num__frac_0,
[final] ).
cnf(i_0_1760,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
cls_nat__mult__dvd__cancel1_0,
[final] ).
cnf(i_0_1761,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
cls_dvd__mult__cancel_0,
[final] ).
cnf(i_0_1762,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
cls_nat__mult__less__cancel1_0,
[final] ).
cnf(i_0_1763,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
cls_power__strict__decreasing_0,
[final] ).
cnf(i_0_1764,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_mult__less__cancel__left__disj_0,
[final] ).
cnf(i_0_1765,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
cls_mult__less__cancel__right__disj_0,
[final] ).
cnf(i_0_1766,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_mult__frac__frac_0,
[final] ).
cnf(i_0_1767,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Onoteq__reduce_1,
[final] ).
cnf(i_0_1768,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__mul__solve_1,
[final] ).
cnf(i_0_1769,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_power__strict__mono_0,
[final] ).
cnf(i_0_1770,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_mult__less__cancel__right__disj_1,
[final] ).
cnf(i_0_1771,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
cls_mult__less__cancel__left__disj_1,
[final] ).
cnf(i_0_1772,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_mult__less__cancel__left__disj_2,
[final] ).
cnf(i_0_1773,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
cls_mult__less__cancel__right__disj_2,
[final] ).
cnf(i_0_1774,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_Deriv_Oadd__diff__add_0,
[final] ).
cnf(i_0_1775,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I20_J_0,
[final] ).
cnf(i_0_1776,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I13_J_0,
[final] ).
cnf(i_0_1777,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_zmod__simps_I1_J_0,
[final] ).
cnf(i_0_1778,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_zmod__simps_I4_J_0,
[final] ).
cnf(i_0_1779,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_zmod__simps_I2_J_0,
[final] ).
cnf(i_0_1780,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
cls_mod__diff__left__eq_0,
[final] ).
cnf(i_0_1781,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__add__left__eq_0,
[final] ).
cnf(i_0_1782,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__left__eq_0,
[final] ).
cnf(i_0_1783,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
cls_mod__diff__right__eq_0,
[final] ).
cnf(i_0_1784,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__add__right__eq_0,
[final] ).
cnf(i_0_1785,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__right__eq_0,
[final] ).
cnf(i_0_1786,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_mult__less__cancel__right__disj_3,
[final] ).
cnf(i_0_1787,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
cls_mult__less__cancel__left__disj_3,
[final] ).
cnf(i_0_1788,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
cls_comm__ring__1__class_Opower__minus__even_0,
[final] ).
cnf(i_0_1789,plain,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1452,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1790,plain,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1453,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1791,axiom,
( X4 = X5
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X5,X1),X1) ),
cls_class__ringb_Oadd__scale__eq__noteq_0,
[final] ).
cnf(i_0_1792,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I36_J_0,
[final] ).
cnf(i_0_1793,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_divide__less__eq_6,
[final] ).
cnf(i_0_1794,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
cls_less__divide__eq_0,
[final] ).
cnf(i_0_1795,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_divide__le__eq_6,
[final] ).
cnf(i_0_1796,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
cls_le__divide__eq_0,
[final] ).
cnf(i_0_1797,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
cls_less__divide__eq_6,
[final] ).
cnf(i_0_1798,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X4,X1),X3,X1) ),
cls_divide__less__eq_0,
[final] ).
cnf(i_0_1799,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
cls_le__divide__eq_6,
[final] ).
cnf(i_0_1800,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X1),X3,X1) ),
cls_divide__le__eq_0,
[final] ).
cnf(i_0_1801,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
cls_less__divide__eq__number__of_2,
[final] ).
cnf(i_0_1802,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
cls_le__divide__eq__number__of_2,
[final] ).
cnf(i_0_1803,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
cls_divide__less__eq__number__of_2,
[final] ).
cnf(i_0_1804,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
cls_divide__le__eq__number__of_2,
[final] ).
cnf(i_0_1805,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) != c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_power2__eq__imp__eq_0,
[final] ).
cnf(i_0_1806,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
cls_natgb_Onoteq__reduce_1,
[final] ).
cnf(i_0_1807,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
cls_natgb_Oadd__mul__solve_1,
[final] ).
cnf(i_0_1808,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__imp__div__pos__less_0,
[final] ).
cnf(i_0_1809,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__imp__div__pos__le_0,
[final] ).
cnf(i_0_1810,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_mult__imp__less__div__pos_0,
[final] ).
cnf(i_0_1811,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_mult__imp__le__div__pos_0,
[final] ).
cnf(i_0_1812,axiom,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X2),X3,tc_Complex_Ocomplex)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_root__cancel_0,
[final] ).
cnf(i_0_1813,plain,
( X2 = X3
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) != c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1454,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1814,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq2_0,
[final] ).
cnf(i_0_1815,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq4_0,
[final] ).
cnf(i_0_1816,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq_0,
[final] ).
cnf(i_0_1817,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_Ring__and__Field_Olordered__ring(X1) ),
cls_abs__le__mult_0,
[final] ).
cnf(i_0_1818,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X5,X1),X1) ),
cls_le__add__right__mono_0,
[final] ).
cnf(i_0_1819,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_divide__less__eq__number__of1_3,
[final] ).
cnf(i_0_1820,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_divide__le__eq__number__of1_3,
[final] ).
cnf(i_0_1821,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__divide__eq__number__of1_3,
[final] ).
cnf(i_0_1822,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__divide__eq__number__of1_3,
[final] ).
cnf(i_0_1823,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X1),X1) ),
cls_half__gt__zero__iff_0,
[final] ).
cnf(i_0_1824,axiom,
( c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ),
cls_mod2__gr__0_0,
[final] ).
cnf(i_0_1825,axiom,
( X3 = X4
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) ),
cls_natgb_Oadd__scale__eq__noteq_0,
[final] ).
cnf(i_0_1826,axiom,
( c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_sum__power2__eq__zero__iff_2,
[final] ).
cnf(i_0_1827,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
inference(rw,[status(thm)],[i_0_1455,c_0_1428]),
[final] ).
cnf(i_0_1828,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
cls_dvd__mult__cancel__right_0,
[final] ).
cnf(i_0_1829,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_dvd__mult__cancel__left_0,
[final] ).
cnf(i_0_1830,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1456,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1831,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_power__gt1__lemma_0,
[final] ).
cnf(i_0_1832,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
cls_add__less__cancel__right_0,
[final] ).
cnf(i_0_1833,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
cls_add__less__cancel__left_0,
[final] ).
cnf(i_0_1834,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
cls_add__le__cancel__right_0,
[final] ).
cnf(i_0_1835,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
cls_add__le__cancel__left_0,
[final] ).
cnf(i_0_1836,plain,
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1457,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1837,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1458,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1838,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oabs__class_Oabs(X4,X1),X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1) ),
cls_estimate__by__abs_0,
[final] ).
cnf(i_0_1839,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X3,tc_nat),X1) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__even__eq_0,
[final] ).
cnf(i_0_1840,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) ),
cls_divide__less__eq__number__of_3,
[final] ).
cnf(i_0_1841,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) ),
cls_divide__le__eq__number__of_3,
[final] ).
cnf(i_0_1842,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__divide__eq__number__of_3,
[final] ).
cnf(i_0_1843,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__divide__eq__number__of_3,
[final] ).
cnf(i_0_1844,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
cls_nat__mult__dvd__cancel__disj_0,
[final] ).
cnf(i_0_1845,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1459,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1846,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
cls_mult__less__cancel1_0,
[final] ).
cnf(i_0_1847,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
cls_mult__less__cancel2_0,
[final] ).
cnf(i_0_1848,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_divide__right__mono_0,
[final] ).
cnf(i_0_1849,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X2,X1) ),
cls_divide__right__mono__neg_0,
[final] ).
cnf(i_0_1850,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X4,X1),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
cls_power__mono__even_0,
[final] ).
cnf(i_0_1851,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
cls_nat__add__left__cancel__less_0,
[final] ).
cnf(i_0_1852,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
cls_mult__less__cancel2_1,
[final] ).
cnf(i_0_1853,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
cls_mult__less__cancel1_1,
[final] ).
cnf(i_0_1854,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
inference(rw,[status(thm)],[i_0_1460,c_0_1428]),
[final] ).
cnf(i_0_1855,axiom,
( X2 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_power__eq__imp__eq__base_0,
[final] ).
cnf(i_0_1856,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ),
cls_even__even__mod__4__iff_1,
[final] ).
cnf(i_0_1857,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_divide__strict__right__mono_0,
[final] ).
cnf(i_0_1858,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_mult__strict__left__mono__comm_0,
[final] ).
cnf(i_0_1859,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_mult__strict__left__mono_0,
[final] ).
cnf(i_0_1860,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__less__cancel__left__pos_1,
[final] ).
cnf(i_0_1861,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__less__cancel__left__disj_4,
[final] ).
cnf(i_0_1862,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_mult__strict__right__mono_0,
[final] ).
cnf(i_0_1863,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__less__cancel__right__disj_4,
[final] ).
cnf(i_0_1864,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_power__mono_0,
[final] ).
cnf(i_0_1865,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_mult__left__mono_0,
[final] ).
cnf(i_0_1866,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Omult__mono1(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_mult__mono1_0,
[final] ).
cnf(i_0_1867,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__le__cancel__left__pos_1,
[final] ).
cnf(i_0_1868,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__right__mono_0,
[final] ).
cnf(i_0_1869,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1) ),
cls_divide__strict__right__mono__neg_0,
[final] ).
cnf(i_0_1870,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__less__cancel__left__neg_1,
[final] ).
cnf(i_0_1871,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_mult__strict__left__mono__neg_0,
[final] ).
cnf(i_0_1872,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__less__cancel__left__disj_5,
[final] ).
cnf(i_0_1873,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1) ),
cls_mult__strict__right__mono__neg_0,
[final] ).
cnf(i_0_1874,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__less__cancel__right__disj_5,
[final] ).
cnf(i_0_1875,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_mult__left__mono__neg_0,
[final] ).
cnf(i_0_1876,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__cancel__left__neg_1,
[final] ).
cnf(i_0_1877,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X2,X1) ),
cls_mult__right__mono__neg_0,
[final] ).
cnf(i_0_1878,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__right__le__one__le_0,
[final] ).
cnf(i_0_1879,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__left__le__one__le_0,
[final] ).
cnf(i_0_1880,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_power__strict__increasing__iff_1,
[final] ).
cnf(i_0_1881,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
cls_power__strict__increasing_0,
[final] ).
cnf(i_0_1882,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| c_Int_Onumber__class_Onumber__of(X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1) ),
cls_zero__less__power__eq__number__of_0,
[final] ).
cnf(i_0_1883,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X3,X1),X2,X1) ),
cls_divide__less__eq_2,
[final] ).
cnf(i_0_1884,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X3,X1),X2,X1) ),
cls_divide__le__eq_2,
[final] ).
cnf(i_0_1885,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
cls_less__divide__eq_2,
[final] ).
cnf(i_0_1886,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X4,X3,X1),X1) ),
cls_le__divide__eq_2,
[final] ).
cnf(i_0_1887,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_mult__dvd__mono_0,
[final] ).
cnf(i_0_1888,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__strict__mono_0,
[final] ).
cnf(i_0_1889,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__le__less__mono_0,
[final] ).
cnf(i_0_1890,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__less__le__mono_0,
[final] ).
cnf(i_0_1891,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__mono_0,
[final] ).
cnf(i_0_1892,axiom,
( c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1) ),
cls_zero__less__power__eq__number__of_2,
[final] ).
cnf(i_0_1893,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_power__divide_0,
[final] ).
cnf(i_0_1894,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_nonzero__power__divide_0,
[final] ).
cnf(i_0_1895,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__squares__eq__zero__iff_0,
[final] ).
cnf(i_0_1896,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__squares__eq__zero__iff_1,
[final] ).
cnf(i_0_1897,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1) ),
cls_zero__le__power__eq__number__of_0,
[final] ).
cnf(i_0_1898,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__le__zero__eq__number__of_2,
[final] ).
cnf(i_0_1899,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) ),
cls_zero__less__power2_0,
[final] ).
cnf(i_0_1900,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__mult2_0,
[final] ).
cnf(i_0_1901,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I1_J_0,
[final] ).
cnf(i_0_1902,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__mult1_0,
[final] ).
cnf(i_0_1903,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
cls_divide_Odiff_0,
[final] ).
cnf(i_0_1904,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_diff__divide__distrib_0,
[final] ).
cnf(i_0_1905,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
cls_divide_Oadd_0,
[final] ).
cnf(i_0_1906,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_add__divide__distrib_0,
[final] ).
cnf(i_0_1907,axiom,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_power__mult__distrib_0,
[final] ).
cnf(i_0_1908,axiom,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Opwr__mul_0,
[final] ).
cnf(i_0_1909,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Odiff_0,
[final] ).
cnf(i_0_1910,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Odiff__left_0,
[final] ).
cnf(i_0_1911,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
cls_comm__semiring__class_Odistrib_0,
[final] ).
cnf(i_0_1912,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Oadd_0,
[final] ).
cnf(i_0_1913,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Oadd__left_0,
[final] ).
cnf(i_0_1914,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I8_J_0,
[final] ).
cnf(i_0_1915,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Odiff__right_0,
[final] ).
cnf(i_0_1916,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Odiff_0,
[final] ).
cnf(i_0_1917,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Oadd_0,
[final] ).
cnf(i_0_1918,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Oadd__right_0,
[final] ).
cnf(i_0_1919,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__d_0,
[final] ).
cnf(i_0_1920,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__self2_0,
[final] ).
cnf(i_0_1921,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__self1_0,
[final] ).
cnf(i_0_1922,axiom,
( c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat) ),
cls_zero__less__power__eq__number__of_1,
[final] ).
cnf(i_0_1923,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1) = c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__pwr_0,
[final] ).
cnf(i_0_1924,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__add_0,
[final] ).
cnf(i_0_1925,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_nat__mult__dvd__cancel1_1,
[final] ).
cnf(i_0_1926,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_mult__less__cancel1_2,
[final] ).
cnf(i_0_1927,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_mult__less__mono2_0,
[final] ).
cnf(i_0_1928,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_nat__mult__less__cancel1_1,
[final] ).
cnf(i_0_1929,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_mult__less__cancel2_2,
[final] ).
cnf(i_0_1930,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_mult__less__mono1_0,
[final] ).
cnf(i_0_1931,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X3,X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oring__1(X1) ),
cls_power__minus_0,
[final] ).
cnf(i_0_1932,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_add__less__mono_0,
[final] ).
cnf(i_0_1933,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
cls_zero__less__mult__pos2_0,
[final] ).
cnf(i_0_1934,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
cls_zero__less__mult__pos_0,
[final] ).
cnf(i_0_1935,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_abs__eq__mult_0,
[final] ).
cnf(i_0_1936,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__eq__mult_2,
[final] ).
cnf(i_0_1937,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_abs__eq__mult_1,
[final] ).
cnf(i_0_1938,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__eq__mult_3,
[final] ).
cnf(i_0_1939,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1461,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1940,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power2__less__0_0,
[final] ).
cnf(i_0_1941,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1462,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1942,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1463,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_1943,axiom,
c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
cls_mod__mult__distrib_0,
[final] ).
cnf(i_0_1944,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
cls_add__mult__distrib_0,
[final] ).
cnf(i_0_1945,axiom,
c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
cls_mod__mult__distrib2_0,
[final] ).
cnf(i_0_1946,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
cls_add__mult__distrib2_0,
[final] ).
cnf(i_0_1947,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
cls_mod__mult__self3_0,
[final] ).
cnf(i_0_1948,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)
| c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
cls_mod2__gr__0_1,
[final] ).
cnf(i_0_1949,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__le__zero__eq__number__of_3,
[final] ).
cnf(i_0_1950,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__le__zero__eq__number__of_1,
[final] ).
cnf(i_0_1951,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__less__zero__eq__number__of_1,
[final] ).
cnf(i_0_1952,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__mod__iff_0,
[final] ).
cnf(i_0_1953,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1) ),
cls_dvd__mod__imp__dvd_0,
[final] ).
cnf(i_0_1954,axiom,
( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
cls_add__cancel__21_0,
[final] ).
cnf(i_0_1955,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__less__0__iff_1,
[final] ).
cnf(i_0_1956,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__iff_1,
[final] ).
cnf(i_0_1957,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__less__0__iff_0,
[final] ).
cnf(i_0_1958,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__less__0__iff_3,
[final] ).
cnf(i_0_1959,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__iff_0,
[final] ).
cnf(i_0_1960,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__iff_3,
[final] ).
cnf(i_0_1961,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
cls_zero__less__divide__iff_0,
[final] ).
cnf(i_0_1962,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1) ),
cls_zero__less__divide__iff_3,
[final] ).
cnf(i_0_1963,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
cls_zero__less__divide__iff_2,
[final] ).
cnf(i_0_1964,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1) ),
cls_zero__less__divide__iff_1,
[final] ).
cnf(i_0_1965,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
cls_zero__le__divide__iff_0,
[final] ).
cnf(i_0_1966,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1) ),
cls_zero__le__divide__iff_3,
[final] ).
cnf(i_0_1967,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
cls_zero__le__divide__iff_2,
[final] ).
cnf(i_0_1968,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1) ),
cls_zero__le__divide__iff_1,
[final] ).
cnf(i_0_1969,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__less__0__iff_2,
[final] ).
cnf(i_0_1970,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__iff_2,
[final] ).
cnf(i_0_1971,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__less__zero__eq__number__of_0,
[final] ).
cnf(i_0_1972,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_divide__less__eq_3,
[final] ).
cnf(i_0_1973,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_divide__le__eq_3,
[final] ).
cnf(i_0_1974,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__divide__eq_3,
[final] ).
cnf(i_0_1975,axiom,
( c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__divide__eq_3,
[final] ).
cnf(i_0_1976,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_1,
[final] ).
cnf(i_0_1977,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_0,
[final] ).
cnf(i_0_1978,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_3,
[final] ).
cnf(i_0_1979,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
cls_zero__le__mult__iff_0,
[final] ).
cnf(i_0_1980,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
cls_zero__le__mult__iff_3,
[final] ).
cnf(i_0_1981,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
cls_zero__le__mult__iff_2,
[final] ).
cnf(i_0_1982,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
cls_zero__le__mult__iff_1,
[final] ).
cnf(i_0_1983,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_2,
[final] ).
cnf(i_0_1984,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_half__gt__zero_0,
[final] ).
cnf(i_0_1985,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X2,X3,X1),X1),X3,X1)
| ~ class_Divides_Oring__div(X1) ),
cls_mod__minus__eq_0,
[final] ).
cnf(i_0_1986,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_power__mono__odd_0,
[final] ).
cnf(i_0_1987,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__less__0__iff_5,
[final] ).
cnf(i_0_1988,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_divide__less__0__iff_4,
[final] ).
cnf(i_0_1989,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__iff_5,
[final] ).
cnf(i_0_1990,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_divide__le__0__iff_4,
[final] ).
cnf(i_0_1991,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__less__divide__iff_4,
[final] ).
cnf(i_0_1992,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__divide__iff_4,
[final] ).
cnf(i_0_1993,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_zero__less__divide__iff_5,
[final] ).
cnf(i_0_1994,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_zero__le__divide__iff_5,
[final] ).
cnf(i_0_1995,plain,
c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1464,c_0_1428]),
[final] ).
cnf(i_0_1996,plain,
c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1465,c_0_1428]),
[final] ).
cnf(i_0_1997,plain,
c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1466,c_0_1428]),
[final] ).
cnf(i_0_1998,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| c_Int_Onumber__class_Onumber__of(X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__le__zero__eq__number__of_4,
[final] ).
cnf(i_0_1999,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__le__zero__eq__number__of_0,
[final] ).
cnf(i_0_2000,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__neg__pos_0,
[final] ).
cnf(i_0_2001,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_divide__pos__neg_0,
[final] ).
cnf(i_0_2002,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__pos__neg2_0,
[final] ).
cnf(i_0_2003,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__neg__pos_0,
[final] ).
cnf(i_0_2004,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__pos__neg_0,
[final] ).
cnf(i_0_2005,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_divide__nonneg__neg_0,
[final] ).
cnf(i_0_2006,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__nonpos__pos_0,
[final] ).
cnf(i_0_2007,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__nonneg__nonpos2_0,
[final] ).
cnf(i_0_2008,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__nonpos__nonneg_0,
[final] ).
cnf(i_0_2009,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_split__mult__neg__le_1,
[final] ).
cnf(i_0_2010,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__nonneg__nonpos_0,
[final] ).
cnf(i_0_2011,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_split__mult__neg__le_0,
[final] ).
cnf(i_0_2012,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_5,
[final] ).
cnf(i_0_2013,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__le__0__iff_4,
[final] ).
cnf(i_0_2014,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__neg__neg_0,
[final] ).
cnf(i_0_2015,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonpos__neg_0,
[final] ).
cnf(i_0_2016,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__neg__nonpos_0,
[final] ).
cnf(i_0_2017,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonpos__nonpos_0,
[final] ).
cnf(i_0_2018,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_less__1__mult_0,
[final] ).
cnf(i_0_2019,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_divide__pos__pos_0,
[final] ).
cnf(i_0_2020,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__pos__pos_0,
[final] ).
cnf(i_0_2021,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__pos_0,
[final] ).
cnf(i_0_2022,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__pos__nonneg_0,
[final] ).
cnf(i_0_2023,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__pos__pos_0,
[final] ).
cnf(i_0_2024,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_divide__nonneg__pos_0,
[final] ).
cnf(i_0_2025,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__nonneg_0,
[final] ).
cnf(i_0_2026,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__nonneg__nonneg_0,
[final] ).
cnf(i_0_2027,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_split__mult__pos__le_0,
[final] ).
cnf(i_0_2028,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__mult__iff_4,
[final] ).
cnf(i_0_2029,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__neg__neg_0,
[final] ).
cnf(i_0_2030,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__neg__neg_0,
[final] ).
cnf(i_0_2031,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__nonpos__neg_0,
[final] ).
cnf(i_0_2032,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__nonpos__nonpos_0,
[final] ).
cnf(i_0_2033,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_split__mult__pos__le_1,
[final] ).
cnf(i_0_2034,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_zero__le__mult__iff_5,
[final] ).
cnf(i_0_2035,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
cls_add__gr__0_0,
[final] ).
cnf(i_0_2036,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__power__same_0,
[final] ).
cnf(i_0_2037,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1) ),
cls_dvd__mult__cancel__left_2,
[final] ).
cnf(i_0_2038,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__mult__cancel__right_2,
[final] ).
cnf(i_0_2039,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_add__strict__left__mono_0,
[final] ).
cnf(i_0_2040,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_add__less__cancel__left_1,
[final] ).
cnf(i_0_2041,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__strict__right__mono_0,
[final] ).
cnf(i_0_2042,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__less__cancel__right_1,
[final] ).
cnf(i_0_2043,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_add__left__mono_0,
[final] ).
cnf(i_0_2044,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_add__le__cancel__left_1,
[final] ).
cnf(i_0_2045,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__right__mono_0,
[final] ).
cnf(i_0_2046,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__le__cancel__right_1,
[final] ).
cnf(i_0_2047,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1) ),
cls_zero__less__power__eq_2,
[final] ).
cnf(i_0_2048,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_one__less__power_0,
[final] ).
cnf(i_0_2049,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
cls_dvd_Oless__trans_1,
[final] ).
cnf(i_0_2050,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_add__strict__increasing2_0,
[final] ).
cnf(i_0_2051,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_add__strict__increasing_0,
[final] ).
cnf(i_0_2052,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_add__increasing2_0,
[final] ).
cnf(i_0_2053,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_add__increasing_0,
[final] ).
cnf(i_0_2054,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1) ),
cls_zero__less__divide__1__iff_0,
[final] ).
cnf(i_0_2055,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1) ),
cls_zero__le__divide__1__iff_0,
[final] ).
cnf(i_0_2056,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__less__0__1__iff_0,
[final] ).
cnf(i_0_2057,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__1__iff_0,
[final] ).
cnf(i_0_2058,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1467,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2059,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1468,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2060,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_power__one__over_0,
[final] ).
cnf(i_0_2061,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__less__zero__eq__number__of_2,
[final] ).
cnf(i_0_2062,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__less__power__eq__number__of_5,
[final] ).
cnf(i_0_2063,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__power__eq__number__of_2,
[final] ).
cnf(i_0_2064,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__eq__neg_1,
[final] ).
cnf(i_0_2065,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_pos__add__strict_0,
[final] ).
cnf(i_0_2066,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
cls_le__number__of__eq__not__less_0,
[final] ).
cnf(i_0_2067,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
cls_zero__less__power__eq_0,
[final] ).
cnf(i_0_2068,axiom,
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X3,X2,X1),X1) ),
cls_zero__le__power__iff_0,
[final] ).
cnf(i_0_2069,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
cls_zero__le__power__eq_0,
[final] ).
cnf(i_0_2070,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
cls_zero__le__odd__power_0,
[final] ).
cnf(i_0_2071,axiom,
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__le__zero__eq_2,
[final] ).
cnf(i_0_2072,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
cls_nat__mult__dvd__cancel__disj_2,
[final] ).
cnf(i_0_2073,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_nat__add__left__cancel__less_1,
[final] ).
cnf(i_0_2074,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_add__less__mono1_0,
[final] ).
cnf(i_0_2075,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1469,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2076,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oinverse__class_Odivide(X3,X4,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_mult__divide__mult__cancel__left_0,
[final] ).
cnf(i_0_2077,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,X4,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_mult__divide__mult__cancel__right_0,
[final] ).
cnf(i_0_2078,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I2_J_0,
[final] ).
cnf(i_0_2079,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I3_J_0,
[final] ).
cnf(i_0_2080,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__diff_0,
[final] ).
cnf(i_0_2081,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__mod_0,
[final] ).
cnf(i_0_2082,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__mod__iff_1,
[final] ).
cnf(i_0_2083,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__add_0,
[final] ).
cnf(i_0_2084,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[i_0_1470,c_0_1428]),
[final] ).
cnf(i_0_2085,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X1),X3,X1)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1) ),
cls_mod__minus__cong_0,
[final] ).
cnf(i_0_2086,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_dvd__mult__cancel2_0,
[final] ).
cnf(i_0_2087,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_dvd__mult__cancel1_0,
[final] ).
cnf(i_0_2088,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__add__abs_0,
[final] ).
cnf(i_0_2089,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_nat__0__less__mult__iff_2,
[final] ).
cnf(i_0_2090,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__le__zero__eq_3,
[final] ).
cnf(i_0_2091,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_mult__frac__num_0,
[final] ).
cnf(i_0_2092,plain,
( c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[i_0_1471,c_0_1428]),
[final] ).
cnf(i_0_2093,plain,
( c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Power_Opower(X1) ),
inference(rw,[status(thm)],[i_0_1472,c_0_1428]),
[final] ).
cnf(i_0_2094,plain,
( c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[i_0_1473,c_0_1428]),
[final] ).
cnf(i_0_2095,plain,
( c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[i_0_1474,c_0_1428]),
[final] ).
cnf(i_0_2096,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[i_0_1475,c_0_1428]),
[final] ).
cnf(i_0_2097,plain,
( c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[i_0_1476,c_0_1428]),
[final] ).
cnf(i_0_2098,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
cls_zero__less__double__add__iff__zero__less__single__add_0,
[final] ).
cnf(i_0_2099,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
cls_zero__le__double__add__iff__zero__le__single__add_0,
[final] ).
cnf(i_0_2100,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__less__zero__iff__single__less__zero_0,
[final] ).
cnf(i_0_2101,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__less__zero__eq_1,
[final] ).
cnf(i_0_2102,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_even__less__0__iff_0,
[final] ).
cnf(i_0_2103,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__le__zero__iff__single__add__le__zero_0,
[final] ).
cnf(i_0_2104,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(rw,[status(thm)],[i_0_1477,c_0_1428]),
[final] ).
cnf(i_0_2105,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I23_J_0,
[final] ).
cnf(i_0_2106,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I16_J_0,
[final] ).
cnf(i_0_2107,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
[final] ).
cnf(i_0_2108,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__assoc_0,
[final] ).
cnf(i_0_2109,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I21_J_0,
[final] ).
cnf(i_0_2110,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__commutes_0,
[final] ).
cnf(i_0_2111,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,
[final] ).
cnf(i_0_2112,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I17_J_0,
[final] ).
cnf(i_0_2113,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I25_J_0,
[final] ).
cnf(i_0_2114,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__a_0,
[final] ).
cnf(i_0_2115,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I18_J_0,
[final] ).
cnf(i_0_2116,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__a_0,
[final] ).
cnf(i_0_2117,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__left__commute_0,
[final] ).
cnf(i_0_2118,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__21_1,
[final] ).
cnf(i_0_2119,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I22_J_0,
[final] ).
cnf(i_0_2120,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I19_J_0,
[final] ).
cnf(i_0_2121,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__eq__zero__iff_2,
[final] ).
cnf(i_0_2122,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
cls_dvd_Oless__trans_0,
[final] ).
cnf(i_0_2123,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__mult_0,
[final] ).
cnf(i_0_2124,axiom,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Opwr__pwr_0,
[final] ).
cnf(i_0_2125,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1478,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2126,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
cls_inverse__less__imp__less_0,
[final] ).
cnf(i_0_2127,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
cls_inverse__le__imp__le_0,
[final] ).
cnf(i_0_2128,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
cls_inverse__less__imp__less__neg_0,
[final] ).
cnf(i_0_2129,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
cls_inverse__le__imp__le__neg_0,
[final] ).
cnf(i_0_2130,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__iff__diff__less__0_1,
[final] ).
cnf(i_0_2131,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__iff__diff__le__0_1,
[final] ).
cnf(i_0_2132,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1479,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2133,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__power2_0,
[final] ).
cnf(i_0_2134,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1480,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2135,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1481,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2136,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
cls_less__eqI_1,
[final] ).
cnf(i_0_2137,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__eqI_0,
[final] ).
cnf(i_0_2138,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ),
cls_le__eqI_1,
[final] ).
cnf(i_0_2139,axiom,
( c_lessequals(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__eqI_0,
[final] ).
cnf(i_0_2140,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1482,c_0_1428]),
[final] ).
cnf(i_0_2141,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1483,c_0_1428]),
[final] ).
cnf(i_0_2142,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
cls_dvd__mult__left_0,
[final] ).
cnf(i_0_2143,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),X3,X1) ),
cls_dvd__mult__right_0,
[final] ).
cnf(i_0_2144,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
cls_zero__less__power__eq_1,
[final] ).
cnf(i_0_2145,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
cls_nat__add__assoc_0,
[final] ).
cnf(i_0_2146,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
cls_nat__mult__assoc_0,
[final] ).
cnf(i_0_2147,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
cls_nat__add__left__commute_0,
[final] ).
cnf(i_0_2148,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[i_0_1484,c_0_1428]),
[final] ).
cnf(i_0_2149,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[i_0_1485,c_0_1428]),
[final] ).
cnf(i_0_2150,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[i_0_1486,c_0_1428]),
[final] ).
cnf(i_0_2151,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_abs__div__pos_0,
[final] ).
cnf(i_0_2152,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) ),
inference(rw,[status(thm)],[i_0_1487,c_0_1428]),
[final] ).
cnf(i_0_2153,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1) ),
cls_mod__mod__cancel_0,
[final] ).
cnf(i_0_2154,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
cls_nat__0__less__mult__iff_0,
[final] ).
cnf(i_0_2155,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
cls_nat__0__less__mult__iff_1,
[final] ).
cnf(i_0_2156,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
cls_dvd_Ole__less__trans_1,
[final] ).
cnf(i_0_2157,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
cls_dvd_Oless__le__trans_1,
[final] ).
cnf(i_0_2158,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_even__even__mod__4__iff_0,
[final] ).
cnf(i_0_2159,axiom,
( c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X2,tc_nat),tc_nat) ),
cls_power__le__zero__eq__number__of_5,
[final] ).
cnf(i_0_2160,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_abs__mult__pos_0,
[final] ).
cnf(i_0_2161,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1488,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2162,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
cls_less__add__eq__less_0,
[final] ).
cnf(i_0_2163,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
cls_power__minus1__even_0,
[final] ).
cnf(i_0_2164,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_half_0,
[final] ).
cnf(i_0_2165,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) ),
cls_le__eq__neg_0,
[final] ).
cnf(i_0_2166,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_abs__less__iff_2,
[final] ).
cnf(i_0_2167,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_abs__le__iff_2,
[final] ).
cnf(i_0_2168,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_abs__leI_0,
[final] ).
cnf(i_0_2169,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__power__minus_0,
[final] ).
cnf(i_0_2170,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat) ),
cls_add__lessD1_0,
[final] ).
cnf(i_0_2171,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
cls_dvd__reduce_0,
[final] ).
cnf(i_0_2172,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_dvd__mult__cancel__left_1,
[final] ).
cnf(i_0_2173,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X1),X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_dvd__mult__cancel__right_1,
[final] ).
cnf(i_0_2174,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X5 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,X5,X1) = c_HOL_Oinverse__class_Odivide(X4,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Otimes__class_Otimes(X4,X5,X1) ),
cls_frac__eq__eq_1,
[final] ).
cnf(i_0_2175,axiom,
( X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Otimes__class_Otimes(X2,X5,X1) = c_HOL_Otimes__class_Otimes(X4,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) != c_HOL_Oinverse__class_Odivide(X4,X5,X1) ),
cls_frac__eq__eq_0,
[final] ).
cnf(i_0_2176,plain,
( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1489,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2177,plain,
( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1490,c_0_1428]),c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2178,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__eq__0__iff_0,
[final] ).
cnf(i_0_2179,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__eq__0__iff_1,
[final] ).
cnf(i_0_2180,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__le__zero__eq_1,
[final] ).
cnf(i_0_2181,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_less__imp__inverse__less_0,
[final] ).
cnf(i_0_2182,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__imp__inverse__le_0,
[final] ).
cnf(i_0_2183,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_less__imp__inverse__less__neg_0,
[final] ).
cnf(i_0_2184,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__imp__inverse__le__neg_0,
[final] ).
cnf(i_0_2185,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_dvd__eq__mod__eq__0__number__of_1,
[final] ).
cnf(i_0_2186,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_one__less__inverse__iff_2,
[final] ).
cnf(i_0_2187,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_one__le__inverse__iff_2,
[final] ).
cnf(i_0_2188,axiom,
( c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
cls_dvd__eq__mod__eq__0__number__of_0,
[final] ).
cnf(i_0_2189,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__less__zero__eq_0,
[final] ).
cnf(i_0_2190,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__less__0__1__iff_1,
[final] ).
cnf(i_0_2191,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__1__iff_1,
[final] ).
cnf(i_0_2192,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__less__divide__1__iff_1,
[final] ).
cnf(i_0_2193,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__divide__1__iff_1,
[final] ).
cnf(i_0_2194,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__le__zero__eq_4,
[final] ).
cnf(i_0_2195,axiom,
( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_power__m1__even_0,
[final] ).
cnf(i_0_2196,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1491,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2197,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__less__zero__eq_2,
[final] ).
cnf(i_0_2198,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__less__power__eq_5,
[final] ).
cnf(i_0_2199,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__power__eq_2,
[final] ).
cnf(i_0_2200,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__odd__power_1,
[final] ).
cnf(i_0_2201,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat) ),
cls_zero__less__power__eq__number__of_4,
[final] ).
cnf(i_0_2202,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_power__le__zero__eq_0,
[final] ).
cnf(i_0_2203,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) = X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
cls_divide__eq__eq__number__of1_3,
[final] ).
cnf(i_0_2204,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1) = X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
cls_eq__divide__eq__number__of1_0,
[final] ).
cnf(i_0_2205,axiom,
( X2 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
cls_eq__divide__eq__number__of1_3,
[final] ).
cnf(i_0_2206,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
cls_divide__eq__eq__number__of1_0,
[final] ).
cnf(i_0_2207,axiom,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X2),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_number__of__Bit0_0,
[final] ).
cnf(i_0_2208,axiom,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X2),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_number__of__Bit1_0,
[final] ).
cnf(i_0_2209,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X4,X1)
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != X3 ),
cls_add__cancel__end_0,
[final] ).
cnf(i_0_2210,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X3,X1) = c_Int_Onumber__class_Onumber__of(X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_divide__eq__eq__number__of_4,
[final] ).
cnf(i_0_2211,axiom,
( c_Int_Onumber__class_Onumber__of(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__divide__eq__number__of_4,
[final] ).
cnf(i_0_2212,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
cls_divide__eq__eq__number__of1_4,
[final] ).
cnf(i_0_2213,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
cls_eq__divide__eq__number__of1_4,
[final] ).
cnf(i_0_2214,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat) ),
cls_zero__le__power__eq__number__of_1,
[final] ).
cnf(i_0_2215,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_power__inject__exp_0,
[final] ).
cnf(i_0_2216,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_zero__less__power2_1,
[final] ).
cnf(i_0_2217,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
cls_dvd_Ole__less__trans_0,
[final] ).
cnf(i_0_2218,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
cls_dvd_Oless__le__trans_0,
[final] ).
cnf(i_0_2219,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1) ),
cls_inverse__less__1__iff_0,
[final] ).
cnf(i_0_2220,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1) ),
cls_inverse__le__1__iff_0,
[final] ).
cnf(i_0_2221,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat),
cls_nat__mult__dvd__cancel__disj_1,
[final] ).
cnf(i_0_2222,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__square__less__zero_0,
[final] ).
cnf(i_0_2223,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__less__zero__iff__single__less__zero_1,
[final] ).
cnf(i_0_2224,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_even__less__0__iff_1,
[final] ).
cnf(i_0_2225,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__le__zero__iff__single__add__le__zero_1,
[final] ).
cnf(i_0_2226,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__less__power_0,
[final] ).
cnf(i_0_2227,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__less__double__add__iff__zero__less__single__add_1,
[final] ).
cnf(i_0_2228,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_one__le__power_0,
[final] ).
cnf(i_0_2229,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__power_0,
[final] ).
cnf(i_0_2230,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__power__iff_1,
[final] ).
cnf(i_0_2231,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__double__add__iff__zero__le__single__add_1,
[final] ).
cnf(i_0_2232,axiom,
( c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X2,X1),X2,X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power3__eq__cube_0,
[final] ).
cnf(i_0_2233,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[i_0_1492,c_0_1428]),
[final] ).
cnf(i_0_2234,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_zero__le__power2_0,
[final] ).
cnf(i_0_2235,plain,
c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1493,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2236,plain,
c_HOL_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1494,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2237,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__iff__diff__less__0_0,
[final] ).
cnf(i_0_2238,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__diff__le__0_0,
[final] ).
cnf(i_0_2239,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
cls_dvd__power_0,
[final] ).
cnf(i_0_2240,axiom,
( X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_nat__mult__eq__cancel1_0,
[final] ).
cnf(i_0_2241,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_nat__dvd__not__less_0,
[final] ).
cnf(i_0_2242,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__mult2_0,
[final] ).
cnf(i_0_2243,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__mult_0,
[final] ).
cnf(i_0_2244,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X3,X1) = c_Int_Onumber__class_Onumber__of(X2,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
cls_divide__eq__eq__number__of_3,
[final] ).
cnf(i_0_2245,axiom,
( c_Int_Onumber__class_Onumber__of(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1) ),
cls_eq__divide__eq__number__of_3,
[final] ).
cnf(i_0_2246,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_dvd__mult__cancel2_1,
[final] ).
cnf(i_0_2247,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_dvd__mult__cancel1_1,
[final] ).
cnf(i_0_2248,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__commute_0,
[final] ).
cnf(i_0_2249,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_add__gr__0_1,
[final] ).
cnf(i_0_2250,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_add__gr__0_2,
[final] ).
cnf(i_0_2251,axiom,
( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1)
| ~ class_Int_Onumber(X1) ),
cls_power2__eq__square__number__of_0,
[final] ).
cnf(i_0_2252,axiom,
( c_HOL_Oplus__class_Oplus(X2,X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I4_J_0,
[final] ).
cnf(i_0_2253,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[i_0_1495,c_0_1428]),
[final] ).
cnf(i_0_2254,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
cls_not__add__less1_0,
[final] ).
cnf(i_0_2255,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
cls_not__add__less2_0,
[final] ).
cnf(i_0_2256,axiom,
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_mod__less__divisor_0,
[final] ).
cnf(i_0_2257,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_nonzero__inverse__mult__distrib_0,
[final] ).
cnf(i_0_2258,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_zero__less__power__eq__number__of_3,
[final] ).
cnf(i_0_2259,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(X3,tc_nat),tc_nat) ),
cls_power__even__abs__number__of_0,
[final] ).
cnf(i_0_2260,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__mult__distrib_0,
[final] ).
cnf(i_0_2261,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_abs__divide_0,
[final] ).
cnf(i_0_2262,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
cls_dvd__reduce_1,
[final] ).
cnf(i_0_2263,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_trans__less__add1_0,
[final] ).
cnf(i_0_2264,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_termination__basic__simps_I1_J_0,
[final] ).
cnf(i_0_2265,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_trans__less__add2_0,
[final] ).
cnf(i_0_2266,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_termination__basic__simps_I2_J_0,
[final] ).
cnf(i_0_2267,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1496,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2268,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1497,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2269,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1498,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2270,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1499,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2271,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
cls_nonzero__abs__divide_0,
[final] ).
cnf(i_0_2272,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X2),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_double__number__of__Bit0_0,
[final] ).
cnf(i_0_2273,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
cls_power2__minus_0,
[final] ).
cnf(i_0_2274,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_power2__abs_0,
[final] ).
cnf(i_0_2275,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1500,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2276,plain,
( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1501,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2277,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__trans_0,
[final] ).
cnf(i_0_2278,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_order__less__trans_0,
[final] ).
cnf(i_0_2279,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_order__le__less__trans_0,
[final] ).
cnf(i_0_2280,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_order__less__le__trans_0,
[final] ).
cnf(i_0_2281,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I10_J_0,
[final] ).
cnf(i_0_2282,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I7_J_0,
[final] ).
cnf(i_0_2283,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I8_J_0,
[final] ).
cnf(i_0_2284,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_order__trans_0,
[final] ).
cnf(i_0_2285,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I6_J_0,
[final] ).
cnf(i_0_2286,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_Lim_Ominus__diff__minus_0,
[final] ).
cnf(i_0_2287,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__add__distrib_0,
[final] ).
cnf(i_0_2288,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add_0,
[final] ).
cnf(i_0_2289,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__mult_0,
[final] ).
cnf(i_0_2290,axiom,
( c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_minus1__divide_0,
[final] ).
cnf(i_0_2291,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__add_0,
[final] ).
cnf(i_0_2292,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__mult_0,
[final] ).
cnf(i_0_2293,axiom,
( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__number__of_0,
[final] ).
cnf(i_0_2294,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1502,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2295,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1503,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2296,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1504,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2297,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1505,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2298,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_neg__less__iff__less_0,
[final] ).
cnf(i_0_2299,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_neg__le__iff__le_0,
[final] ).
cnf(i_0_2300,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_dvd__pos__nat_0,
[final] ).
cnf(i_0_2301,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
cls_of__nat__less__iff_0,
[final] ).
cnf(i_0_2302,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Int_Onumber(X1) ),
cls_le__number__of__eq__not__less_1,
[final] ).
cnf(i_0_2303,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_zero__le__power__abs_0,
[final] ).
cnf(i_0_2304,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mod__trivial_0,
[final] ).
cnf(i_0_2305,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__add__self1_0,
[final] ).
cnf(i_0_2306,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__add__self2_0,
[final] ).
cnf(i_0_2307,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__left__idem_0,
[final] ).
cnf(i_0_2308,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[i_0_1506,c_0_1428]),
[final] ).
cnf(i_0_2309,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Power_Opower__class_Opower(X2,X3,X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
cls_neg__power__if_1,
[final] ).
cnf(i_0_2310,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__minus__cancel_0,
[final] ).
cnf(i_0_2311,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
cls_dvd_Oorder__trans_0,
[final] ).
cnf(i_0_2312,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(rw,[status(thm)],[i_0_1507,c_0_1428]),
[final] ).
cnf(i_0_2313,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
cls_odd__add_2,
[final] ).
cnf(i_0_2314,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
cls_even__add_1,
[final] ).
cnf(i_0_2315,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
cls_even__add_0,
[final] ).
cnf(i_0_2316,axiom,
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_odd__add_3,
[final] ).
cnf(i_0_2317,axiom,
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
cls_even__sum__nat_1,
[final] ).
cnf(i_0_2318,axiom,
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
cls_even__sum__nat_0,
[final] ).
cnf(i_0_2319,plain,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[i_0_1508,c_0_1428]),
[final] ).
cnf(i_0_2320,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[i_0_1509,c_0_1428]),
[final] ).
cnf(i_0_2321,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1) = X3
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Oinverse__class_Odivide(X3,X4,X1) ),
cls_eq__divide__eq__number__of_0,
[final] ).
cnf(i_0_2322,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) != c_Int_Onumber__class_Onumber__of(X4,X1) ),
cls_divide__eq__eq__number__of_0,
[final] ).
cnf(i_0_2323,axiom,
( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_power__inverse_0,
[final] ).
cnf(i_0_2324,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_minus__divide__right_0,
[final] ).
cnf(i_0_2325,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__less__iff_0,
[final] ).
cnf(i_0_2326,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__less__iff_1,
[final] ).
cnf(i_0_2327,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__less__iff_1,
[final] ).
cnf(i_0_2328,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__le__iff_0,
[final] ).
cnf(i_0_2329,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__le__iff_1,
[final] ).
cnf(i_0_2330,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__le__D2_0,
[final] ).
cnf(i_0_2331,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_less__minus__iff_0,
[final] ).
cnf(i_0_2332,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_less__minus__iff_1,
[final] ).
cnf(i_0_2333,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_le__minus__iff_0,
[final] ).
cnf(i_0_2334,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_le__minus__iff_1,
[final] ).
cnf(i_0_2335,axiom,
( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X1),X3,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_nonzero__power__inverse_0,
[final] ).
cnf(i_0_2336,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_nonzero__minus__divide__right_0,
[final] ).
cnf(i_0_2337,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[i_0_1510,c_0_1428]),
[final] ).
cnf(i_0_2338,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
cls_one__less__inverse__iff_0,
[final] ).
cnf(i_0_2339,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
cls_inverse__positive__iff__positive_0,
[final] ).
cnf(i_0_2340,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
cls_one__le__inverse__iff_0,
[final] ).
cnf(i_0_2341,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
cls_inverse__nonnegative__iff__nonnegative_0,
[final] ).
cnf(i_0_2342,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_inverse__negative__iff__negative_0,
[final] ).
cnf(i_0_2343,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_inverse__nonpositive__iff__nonpositive_0,
[final] ).
cnf(i_0_2344,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
cls_one__less__inverse__iff_1,
[final] ).
cnf(i_0_2345,axiom,
( c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
cls_one__le__inverse__iff_1,
[final] ).
cnf(i_0_2346,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
cls_power__le__zero__eq_5,
[final] ).
cnf(i_0_2347,axiom,
c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat),tc_nat),
cls_even__mult__two__ex_1,
[final] ).
cnf(i_0_2348,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
cls_inverse__positive__imp__positive_0,
[final] ).
cnf(i_0_2349,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_inverse__negative__imp__negative_0,
[final] ).
cnf(i_0_2350,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
cls_even__product__nat_0,
[final] ).
cnf(i_0_2351,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
cls_divide_Ominus_0,
[final] ).
cnf(i_0_2352,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ominus__left_0,
[final] ).
cnf(i_0_2353,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ominus_0,
[final] ).
cnf(i_0_2354,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ominus__right_0,
[final] ).
cnf(i_0_2355,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ominus_0,
[final] ).
cnf(i_0_2356,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_minus__divide__left_0,
[final] ).
cnf(i_0_2357,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__left_0,
[final] ).
cnf(i_0_2358,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_power__abs_0,
[final] ).
cnf(i_0_2359,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__right_0,
[final] ).
cnf(i_0_2360,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__less__0__iff__less_0,
[final] ).
cnf(i_0_2361,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__le__0__iff__le_0,
[final] ).
cnf(i_0_2362,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_neg__0__less__iff__less_0,
[final] ).
cnf(i_0_2363,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_neg__0__le__iff__le_0,
[final] ).
cnf(i_0_2364,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_less__le__not__le_2,
[final] ).
cnf(i_0_2365,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
cls_zero__le__even__power_0,
[final] ).
cnf(i_0_2366,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
cls_zero__less__power__eq_4,
[final] ).
cnf(i_0_2367,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
cls_of__nat__0__less__iff_0,
[final] ).
cnf(i_0_2368,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_neg__less__iff__less_1,
[final] ).
cnf(i_0_2369,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__imp__neg__le_0,
[final] ).
cnf(i_0_2370,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__less__two_0,
[final] ).
cnf(i_0_2371,axiom,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_of__nat__less__iff_1,
[final] ).
cnf(i_0_2372,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_inverse__less__1__iff_2,
[final] ).
cnf(i_0_2373,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_inverse__le__1__iff_2,
[final] ).
cnf(i_0_2374,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_inverse__less__1__iff_1,
[final] ).
cnf(i_0_2375,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_inverse__negative__iff__negative_1,
[final] ).
cnf(i_0_2376,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_inverse__le__1__iff_1,
[final] ).
cnf(i_0_2377,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_inverse__nonpositive__iff__nonpositive_1,
[final] ).
cnf(i_0_2378,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_inverse__positive__iff__positive_1,
[final] ).
cnf(i_0_2379,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_inverse__nonnegative__iff__nonnegative_1,
[final] ).
cnf(i_0_2380,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1511,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2381,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1512,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2382,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| c_HOL_Otimes__class_Otimes(X2,X2,X1) != c_HOL_Otimes__class_Otimes(X3,X3,X1) ),
cls_square__eq__iff_0,
[final] ).
cnf(i_0_2383,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add__cancel_0,
[final] ).
cnf(i_0_2384,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X3,X2,X1),X1) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__end_1,
[final] ).
cnf(i_0_2385,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
cls_zero__le__power__iff_2,
[final] ).
cnf(i_0_2386,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
cls_zero__le__power__eq_1,
[final] ).
cnf(i_0_2387,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
cls_neg__less__eq__nonneg_0,
[final] ).
cnf(i_0_2388,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
cls_minus__le__self__iff_0,
[final] ).
cnf(i_0_2389,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_less__minus__self__iff_0,
[final] ).
cnf(i_0_2390,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_less__eq__neg__nonpos_0,
[final] ).
cnf(i_0_2391,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_le__minus__self__iff_0,
[final] ).
cnf(i_0_2392,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__eq__eq_4,
[final] ).
cnf(i_0_2393,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_eq__divide__eq_4,
[final] ).
cnf(i_0_2394,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_neg__less__0__iff__less_1,
[final] ).
cnf(i_0_2395,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_neg__le__0__iff__le_1,
[final] ).
cnf(i_0_2396,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_negative__imp__inverse__negative_0,
[final] ).
cnf(i_0_2397,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_positive__imp__inverse__positive_0,
[final] ).
cnf(i_0_2398,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__0__less__iff__less_1,
[final] ).
cnf(i_0_2399,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__0__le__iff__le_1,
[final] ).
cnf(i_0_2400,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X3,X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__divide_0,
[final] ).
cnf(i_0_2401,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) ),
cls_minus__dvd__iff_0,
[final] ).
cnf(i_0_2402,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__dvd__iff_0,
[final] ).
cnf(i_0_2403,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__less__iff_0,
[final] ).
cnf(i_0_2404,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__le__D1_0,
[final] ).
cnf(i_0_2405,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) ),
cls_dvd__minus__iff_0,
[final] ).
cnf(i_0_2406,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oabs__class_Oabs(X3,X1),X1) ),
cls_dvd__abs__iff_0,
[final] ).
cnf(i_0_2407,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(rw,[status(thm)],[i_0_1513,c_0_1428]),
[final] ).
cnf(i_0_2408,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_class__ringb_Oadd__cancel_0,
[final] ).
cnf(i_0_2409,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__power_1,
[final] ).
cnf(i_0_2410,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X2,X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_abs__power__minus__one_0,
[final] ).
cnf(i_0_2411,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_neg__less__eq__nonneg_1,
[final] ).
cnf(i_0_2412,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_minus__le__self__iff_1,
[final] ).
cnf(i_0_2413,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__minus__self__iff_1,
[final] ).
cnf(i_0_2414,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__eq__neg__nonpos_1,
[final] ).
cnf(i_0_2415,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__minus__self__iff_1,
[final] ).
cnf(i_0_2416,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[i_0_1514,c_0_1428]),
[final] ).
cnf(i_0_2417,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(rw,[status(thm)],[i_0_1515,c_0_1428]),
[final] ).
cnf(i_0_2418,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(cn,[status(thm)],[i_0_1516]),
[final] ).
cnf(i_0_2419,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_of__nat__0__less__iff_1,
[final] ).
cnf(i_0_2420,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__diff__eq_0,
[final] ).
cnf(i_0_2421,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = X2
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__eq__eq_3,
[final] ).
cnf(i_0_2422,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,X1) = X2
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_eq__divide__eq_0,
[final] ).
cnf(i_0_2423,axiom,
( X2 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_eq__divide__eq_3,
[final] ).
cnf(i_0_2424,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__eq__eq_0,
[final] ).
cnf(i_0_2425,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__antisym_0,
[final] ).
cnf(i_0_2426,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__eq__iff_2,
[final] ).
cnf(i_0_2427,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_order__antisym__conv_0,
[final] ).
cnf(i_0_2428,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_zero__less__power__eq_3,
[final] ).
cnf(i_0_2429,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_less__add__one_0,
[final] ).
cnf(i_0_2430,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_power__eq__0__iff__number__of_1,
[final] ).
cnf(i_0_2431,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
cls_eq__eqI_1,
[final] ).
cnf(i_0_2432,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
cls_add__right__cancel_0,
[final] ).
cnf(i_0_2433,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
cls_eq__eqI_0,
[final] ).
cnf(i_0_2434,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_add__left__cancel_0,
[final] ).
cnf(i_0_2435,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_add__imp__eq_0,
[final] ).
cnf(i_0_2436,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_order__less__asym_H_0,
[final] ).
cnf(i_0_2437,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_order__less__asym_0,
[final] ).
cnf(i_0_2438,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_less__le__not__le_1,
[final] ).
cnf(i_0_2439,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_xt1_I9_J_0,
[final] ).
cnf(i_0_2440,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_not__less__iff__gr__or__eq_1,
[final] ).
cnf(i_0_2441,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__antisym__conv2_1,
[final] ).
cnf(i_0_2442,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_linorder__not__le_1,
[final] ).
cnf(i_0_2443,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_linorder__not__less_1,
[final] ).
cnf(i_0_2444,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_zero__eq__power2_0,
[final] ).
cnf(i_0_2445,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1517,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2446,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1518,c_0_1428]),c_0_1428]),
[final] ).
cnf(i_0_2447,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_minus__divide__divide_0,
[final] ).
cnf(i_0_2448,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1) = X3
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__eq__imp_0,
[final] ).
cnf(i_0_2449,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_eq__divide__imp_0,
[final] ).
cnf(i_0_2450,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_zero__le__square_0,
[final] ).
cnf(i_0_2451,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_minus__dvd__iff_1,
[final] ).
cnf(i_0_2452,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_abs__dvd__iff_1,
[final] ).
cnf(i_0_2453,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__minus__iff_1,
[final] ).
cnf(i_0_2454,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__abs__iff_1,
[final] ).
cnf(i_0_2455,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_nonzero__minus__divide__divide_0,
[final] ).
cnf(i_0_2456,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
cls_mult__cancel2_0,
[final] ).
cnf(i_0_2457,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
cls_mult__cancel1_0,
[final] ).
cnf(i_0_2458,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
cls_nat__mult__eq__cancel__disj_0,
[final] ).
cnf(i_0_2459,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__self1__is__0_0,
[final] ).
cnf(i_0_2460,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__self2__is__0_0,
[final] ).
cnf(i_0_2461,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1519,c_0_1428]),
[final] ).
cnf(i_0_2462,plain,
c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[i_0_1520,c_0_1428]),
[final] ).
cnf(i_0_2463,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat) ),
cls_nat__even__iff__2__dvd_1,
[final] ).
cnf(i_0_2464,axiom,
( X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
cls_dvd_Oneq__le__trans_0,
[final] ).
cnf(i_0_2465,axiom,
( X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
cls_dvd_Ole__neq__trans_0,
[final] ).
cnf(i_0_2466,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
cls_dvd_Oantisym__conv_0,
[final] ).
cnf(i_0_2467,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
cls_dvd__antisym_0,
[final] ).
cnf(i_0_2468,axiom,
( X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
cls_dvd_Oless__le_0,
[final] ).
cnf(i_0_2469,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
cls_dvd_Oantisym_0,
[final] ).
cnf(i_0_2470,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
cls_dvd_Oeq__iff_2,
[final] ).
cnf(i_0_2471,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__diff__cancel_0,
[final] ).
cnf(i_0_2472,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__add__cancel_0,
[final] ).
cnf(i_0_2473,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
inference(rw,[status(thm)],[i_0_1521,c_0_1428]),
[final] ).
cnf(i_0_2474,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1) ),
cls_dvdI_0,
[final] ).
cnf(i_0_2475,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__triv__left_0,
[final] ).
cnf(i_0_2476,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__triv__right_0,
[final] ).
cnf(i_0_2477,axiom,
( X1 = X3
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
cls_nat__add__right__cancel_0,
[final] ).
cnf(i_0_2478,axiom,
( X2 = X3
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) ),
cls_natgb_Oadd__cancel_0,
[final] ).
cnf(i_0_2479,axiom,
( X2 = X3
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) ),
cls_nat__add__left__cancel_0,
[final] ).
cnf(i_0_2480,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_square__eq__iff_1,
[final] ).
cnf(i_0_2481,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__minus_0,
[final] ).
cnf(i_0_2482,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__mult__self_0,
[final] ).
cnf(i_0_2483,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__commute_0,
[final] ).
cnf(i_0_2484,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X2,X1) = c_HOL_Oplus__class_Oplus(X2,X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_mult__2_0,
[final] ).
cnf(i_0_2485,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1),X1) = c_HOL_Oplus__class_Oplus(X2,X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_mult__2__right_0,
[final] ).
cnf(i_0_2486,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1522,c_0_1428]),
[final] ).
cnf(i_0_2487,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1523,c_0_1428]),
[final] ).
cnf(i_0_2488,axiom,
( c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power2__eq__square_0,
[final] ).
cnf(i_0_2489,axiom,
( c_HOL_Otimes__class_Otimes(X2,X2,X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I29_J_0,
[final] ).
cnf(i_0_2490,plain,
c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1524,c_0_1428]),
[final] ).
cnf(i_0_2491,plain,
c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1525,c_0_1428]),
[final] ).
cnf(i_0_2492,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1) ),
cls_zero__less__abs__iff_0,
[final] ).
cnf(i_0_2493,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Power_Opower__class_Opower(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
cls_neg__power__if_0,
[final] ).
cnf(i_0_2494,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) = c_Power_Opower__class_Opower(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat) ),
cls_power__even__abs_0,
[final] ).
cnf(i_0_2495,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_power__eq__0__iff__number__of_0,
[final] ).
cnf(i_0_2496,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_mod__eq__0__iff_1,
[final] ).
cnf(i_0_2497,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_even__add_3,
[final] ).
cnf(i_0_2498,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_even__sum__nat_2,
[final] ).
cnf(i_0_2499,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
cls_odd__add_0,
[final] ).
cnf(i_0_2500,axiom,
( c_Int_Onumber__class_Onumber__of(X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) != c_Int_Onumber__class_Onumber__of(X3,X1) ),
cls_divide__eq__eq__number__of_1,
[final] ).
cnf(i_0_2501,axiom,
( c_Int_Onumber__class_Onumber__of(X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_eq__divide__eq__number__of_1,
[final] ).
cnf(i_0_2502,axiom,
( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_Int_Onumber__class_Onumber__of(X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_abs__number__of_1,
[final] ).
cnf(i_0_2503,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_dvd__eq__mod__eq__0_1,
[final] ).
cnf(i_0_2504,axiom,
c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X1,tc_nat),
cls_nat__mult__2_0,
[final] ).
cnf(i_0_2505,axiom,
c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,X1,tc_nat),
cls_nat__mult__2__right_0,
[final] ).
cnf(i_0_2506,axiom,
( c_Divides_Odiv__class_Omod(X2,X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
cls_dvd__imp__mod__0_0,
[final] ).
cnf(i_0_2507,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I11_J_0,
[final] ).
cnf(i_0_2508,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I12_J_0,
[final] ).
cnf(i_0_2509,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__neq__le__trans_0,
[final] ).
cnf(i_0_2510,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__le__neq__trans_0,
[final] ).
cnf(i_0_2511,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__le__less_0,
[final] ).
cnf(i_0_2512,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__less__le_2,
[final] ).
cnf(i_0_2513,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_linorder__antisym__conv2_0,
[final] ).
cnf(i_0_2514,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_linorder__antisym__conv1_0,
[final] ).
cnf(i_0_2515,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__fieldgb_Odivide__inverse_0,
[final] ).
cnf(i_0_2516,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__le__zero__iff_0,
[final] ).
cnf(i_0_2517,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_order__less__imp__le_0,
[final] ).
cnf(i_0_2518,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_order__le__less_1,
[final] ).
cnf(i_0_2519,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__le__zero_0,
[final] ).
cnf(i_0_2520,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_of__nat__less__0__iff_0,
[final] ).
cnf(i_0_2521,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__not__less__zero_0,
[final] ).
cnf(i_0_2522,axiom,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
cls_odd__add_1,
[final] ).
cnf(i_0_2523,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_even__add_2,
[final] ).
cnf(i_0_2524,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_even__sum__nat_3,
[final] ).
cnf(i_0_2525,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__minus__eq__add_0,
[final] ).
cnf(i_0_2526,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ring_Osub__add_0,
[final] ).
cnf(i_0_2527,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_ab__diff__minus_0,
[final] ).
cnf(i_0_2528,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_diff__def_0,
[final] ).
cnf(i_0_2529,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__minus_0,
[final] ).
cnf(i_0_2530,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__inverse_0,
[final] ).
cnf(i_0_2531,axiom,
( c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber(X1) ),
cls_inverse__eq__divide__number__of_0,
[final] ).
cnf(i_0_2532,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__if__lattice_0,
[final] ).
cnf(i_0_2533,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_mod__if_0,
[final] ).
cnf(i_0_2534,axiom,
( c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X2),X1),X1) ),
cls_iszero__number__of__Bit0_0,
[final] ).
cnf(i_0_2535,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_even__product__nat_1,
[final] ).
cnf(i_0_2536,axiom,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
cls_even__product__nat_2,
[final] ).
cnf(i_0_2537,plain,
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[i_0_1526,c_0_1428]),
[final] ).
cnf(i_0_2538,axiom,
( c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_divide__eq__eq__number__of1_1,
[final] ).
cnf(i_0_2539,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__divide__eq__number__of1_2,
[final] ).
cnf(i_0_2540,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
cls_minus__one__odd__power_0,
[final] ).
cnf(i_0_2541,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1) ),
cls_power__eq__0__iff__number__of_2,
[final] ).
cnf(i_0_2542,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__if_0,
[final] ).
cnf(i_0_2543,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__of__neg_0,
[final] ).
cnf(i_0_2544,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__of__nonpos_0,
[final] ).
cnf(i_0_2545,axiom,
( c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X2),X1),X1)
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
cls_iszero__number__of__Bit0_1,
[final] ).
cnf(i_0_2546,axiom,
( X1 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1(X1),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_even__mult__two__ex_0,
[final] ).
cnf(i_0_2547,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_power__eq__0__iff_0,
[final] ).
cnf(i_0_2548,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_power__0__left__number__of_0,
[final] ).
cnf(i_0_2549,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_power__eq__0__iff_1,
[final] ).
cnf(i_0_2550,axiom,
( c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X1),X1) = c_Int_Onumber__class_Onumber__of(X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_divide__eq__eq__number__of_2,
[final] ).
cnf(i_0_2551,axiom,
( c_Int_Onumber__class_Onumber__of(X2,X1) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__divide__eq__number__of_2,
[final] ).
cnf(i_0_2552,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
cls_minus__one__even__power_0,
[final] ).
cnf(i_0_2553,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_nat__even__iff__2__dvd_0,
[final] ).
cnf(i_0_2554,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__neqE_0,
[final] ).
cnf(i_0_2555,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__less__linear_0,
[final] ).
cnf(i_0_2556,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv3_0,
[final] ).
cnf(i_0_2557,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_not__less__iff__gr__or__eq_0,
[final] ).
cnf(i_0_2558,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_linorder__neqE__ordered__idom_0,
[final] ).
cnf(i_0_2559,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_one__power2_0,
[final] ).
cnf(i_0_2560,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_zero__power2_0,
[final] ).
cnf(i_0_2561,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_zero__eq__power2_1,
[final] ).
cnf(i_0_2562,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_abs__of__pos_0,
[final] ).
cnf(i_0_2563,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_abs__of__nonneg_0,
[final] ).
cnf(i_0_2564,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
cls_power__0__left__number__of_1,
[final] ).
cnf(i_0_2565,axiom,
( c_HOL_Oord__class_Oless(X2,X2,X1)
| c_lessequals(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv1_1,
[final] ).
cnf(i_0_2566,axiom,
( c_lessequals(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__less_0,
[final] ).
cnf(i_0_2567,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__le_0,
[final] ).
cnf(i_0_2568,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_not__leE_0,
[final] ).
cnf(i_0_2569,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__linear_0,
[final] ).
cnf(i_0_2570,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__commute_0,
[final] ).
cnf(i_0_2571,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__c_0,
[final] ).
cnf(i_0_2572,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I24_J_0,
[final] ).
cnf(i_0_2573,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I7_J_0,
[final] ).
cnf(i_0_2574,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__c_0,
[final] ).
cnf(i_0_2575,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = X3
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Oone__class_Oone(X1) ),
cls_inverse__unique_0,
[final] ).
cnf(i_0_2576,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_minus__unique_0,
[final] ).
cnf(i_0_2577,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__neg__iff__add__eq__0_1,
[final] ).
cnf(i_0_2578,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ring_Oneg__mul_0,
[final] ).
cnf(i_0_2579,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__minus__self_0,
[final] ).
cnf(i_0_2580,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_divide__minus1_0,
[final] ).
cnf(i_0_2581,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__one__less__zero_0,
[final] ).
cnf(i_0_2582,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__one__le__zero_0,
[final] ).
cnf(i_0_2583,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
cls_mult__cancel1_1,
[final] ).
cnf(i_0_2584,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
inference(rw,[status(thm)],[i_0_1527,c_0_1428]),
[final] ).
cnf(i_0_2585,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_mult__cancel2_1,
[final] ).
cnf(i_0_2586,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_mult__eq__0__iff_0,
[final] ).
cnf(i_0_2587,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divirors__neq0_0,
[final] ).
cnf(i_0_2588,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divisors_0,
[final] ).
cnf(i_0_2589,axiom,
( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X2,X1) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Int_Onumber__ring(X1) ),
cls_neg__one__odd__power_0,
[final] ).
cnf(i_0_2590,axiom,
( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
cls_neg__one__even__power_0,
[final] ).
cnf(i_0_2591,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
cls_linorder__neqE__nat_0,
[final] ).
cnf(i_0_2592,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
cls_nat__neq__iff_0,
[final] ).
cnf(i_0_2593,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_class__ringb_Osubr0__iff_0,
[final] ).
cnf(i_0_2594,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_dvd__0__left_0,
[final] ).
cnf(i_0_2595,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
cls_class__ringb_Oadd__r0__iff_0,
[final] ).
cnf(i_0_2596,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) != c_HOL_Oone__class_Oone(X1) ),
cls_right__inverse__eq_0,
[final] ).
cnf(i_0_2597,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) != c_HOL_Oabs__class_Oabs(X3,X1) ),
cls_dvd__if__abs__eq_0,
[final] ).
cnf(i_0_2598,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__le__zero__iff_1,
[final] ).
cnf(i_0_2599,axiom,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
cls_nat__add__commute_0,
[final] ).
cnf(i_0_2600,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
cls_nat__mult__commute_0,
[final] ).
cnf(i_0_2601,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_field__power__not__zero_0,
[final] ).
cnf(i_0_2602,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_double__eq__0__iff_0,
[final] ).
cnf(i_0_2603,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
cls_pos2_0,
[final] ).
cnf(i_0_2604,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_divide__Numeral0_0,
[final] ).
cnf(i_0_2605,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_divide__numeral__1_0,
[final] ).
cnf(i_0_2606,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_divide__Numeral1_0,
[final] ).
cnf(i_0_2607,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__iff__diff__eq__0_1,
[final] ).
cnf(i_0_2608,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_right__minus__eq_0,
[final] ).
cnf(i_0_2609,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_one__add__one__is__two_0,
[final] ).
cnf(i_0_2610,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_zero__less__abs__iff_1,
[final] ).
cnf(i_0_2611,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_mult__minus1_0,
[final] ).
cnf(i_0_2612,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_mult__minus1__right_0,
[final] ).
cnf(i_0_2613,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1) ),
cls_power__eq__0__iff_2,
[final] ).
cnf(i_0_2614,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_left__inverse_0,
[final] ).
cnf(i_0_2615,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_field__inverse_0,
[final] ).
cnf(i_0_2616,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_right__inverse_0,
[final] ).
cnf(i_0_2617,axiom,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X2),X1),X1) ),
cls_iszero__number__of__Bit1_0,
[final] ).
cnf(i_0_2618,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_mult__is__0_0,
[final] ).
cnf(i_0_2619,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X2,X1) = X2
| ~ class_Int_Onumber__ring(X1) ),
cls_mult__numeral__1_0,
[final] ).
cnf(i_0_2620,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) = X2
| ~ class_Int_Onumber__ring(X1) ),
cls_mult__numeral__1__right_0,
[final] ).
cnf(i_0_2621,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__minus__eq_0,
[final] ).
cnf(i_0_2622,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_abs__inverse_0,
[final] ).
cnf(i_0_2623,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_of__nat__0__le__iff_0,
[final] ).
cnf(i_0_2624,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__le__imp__of__nat_0,
[final] ).
cnf(i_0_2625,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__zero_0,
[final] ).
cnf(i_0_2626,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__irrefl_0,
[final] ).
cnf(i_0_2627,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__le_1,
[final] ).
cnf(i_0_2628,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__neq__iff_1,
[final] ).
cnf(i_0_2629,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_neq0__conv_1,
[final] ).
cnf(i_0_2630,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat)
| X1 != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
cls_mult__eq__self__implies__10_0,
[final] ).
cnf(i_0_2631,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_nonzero__inverse__minus__eq_0,
[final] ).
cnf(i_0_2632,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X2,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
cls_nonzero__abs__inverse_0,
[final] ).
cnf(i_0_2633,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
cls_nat__dvd__1__iff__1_0,
[final] ).
cnf(i_0_2634,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[i_0_1528,c_0_1428]),
[final] ).
cnf(i_0_2635,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[i_0_1529,c_0_1428]),
[final] ).
cnf(i_0_2636,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1530,c_0_1428]),
[final] ).
cnf(i_0_2637,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1531,c_0_1428]),
[final] ).
cnf(i_0_2638,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_ab__left__minus_0,
[final] ).
cnf(i_0_2639,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_left__minus_0,
[final] ).
cnf(i_0_2640,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_eq__neg__iff__add__eq__0_0,
[final] ).
cnf(i_0_2641,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus_0,
[final] ).
cnf(i_0_2642,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
cls_nat__mult__eq__1__iff_0,
[final] ).
cnf(i_0_2643,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_add__is__0_0,
[final] ).
cnf(i_0_2644,axiom,
( X2 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
cls_nat__mult__eq__1__iff_1,
[final] ).
cnf(i_0_2645,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_add__is__0_1,
[final] ).
cnf(i_0_2646,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
cls_nat__1__eq__mult__iff_0,
[final] ).
cnf(i_0_2647,axiom,
( X2 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
cls_nat__1__eq__mult__iff_1,
[final] ).
cnf(i_0_2648,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1) ),
cls_abs__if__lattice_1,
[final] ).
cnf(i_0_2649,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
inference(rw,[status(thm)],[i_0_1532,c_0_1428]),
[final] ).
cnf(i_0_2650,plain,
X1 != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1533,c_0_1428]),
[final] ).
cnf(i_0_2651,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__fieldgb_Oinverse__divide_0,
[final] ).
cnf(i_0_2652,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != X1 ),
cls_add__eq__self__zero_0,
[final] ).
cnf(i_0_2653,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
cls_natgb_Oadd__r0__iff_0,
[final] ).
cnf(i_0_2654,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_not__less0_0,
[final] ).
cnf(i_0_2655,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_gr__implies__not0_0,
[final] ).
cnf(i_0_2656,axiom,
c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)) = c_Complex_Oii,
cls_root4_0,
[final] ).
cnf(i_0_2657,axiom,
( c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__self_0,
[final] ).
cnf(i_0_2658,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_nonzero__inverse__eq__divide_0,
[final] ).
cnf(i_0_2659,axiom,
( c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1),X2,X1) = X2
| ~ class_Int_Onumber__ring(X1) ),
cls_add__numeral__0_0,
[final] ).
cnf(i_0_2660,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1),X1) = X2
| ~ class_Int_Onumber__ring(X1) ),
cls_add__numeral__0__right_0,
[final] ).
cnf(i_0_2661,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__self__if_0,
[final] ).
cnf(i_0_2662,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_Int_Oint),
cls_transfer__int__nat__numerals_I3_J_0,
[final] ).
cnf(i_0_2663,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_Int_Oint),
cls_transfer__int__nat__numerals_I4_J_0,
[final] ).
cnf(i_0_2664,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_nat__less__le_1,
[final] ).
cnf(i_0_2665,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_less__not__refl_0,
[final] ).
cnf(i_0_2666,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
cls_nat__1__add__1_0,
[final] ).
cnf(i_0_2667,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oabs__if(X1) ),
cls_abs__if_1,
[final] ).
cnf(i_0_2668,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
cls_power__0__left_1,
[final] ).
cnf(i_0_2669,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
cls_power__0__left_0,
[final] ).
cnf(i_0_2670,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_group__add__class_Odiff__0_0,
[final] ).
cnf(i_0_2671,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_inverse__eq__divide_0,
[final] ).
cnf(i_0_2672,axiom,
( ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) ),
cls_not__iszero__Numeral1_0,
[final] ).
cnf(i_0_2673,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__zero_0,
[final] ).
cnf(i_0_2674,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__eq__eq_1,
[final] ).
cnf(i_0_2675,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_eq__divide__eq_2,
[final] ).
cnf(i_0_2676,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__self__if_1,
[final] ).
cnf(i_0_2677,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_double__eq__0__iff_1,
[final] ).
cnf(i_0_2678,axiom,
( c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_inverse__numeral__1_0,
[final] ).
cnf(i_0_2679,axiom,
( X2 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__r0__iff_1,
[final] ).
cnf(i_0_2680,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1534,c_0_1428]),
[final] ).
cnf(i_0_2681,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__less__one_0,
[final] ).
cnf(i_0_2682,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__le__one_0,
[final] ).
cnf(i_0_2683,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Osubr0__iff_1,
[final] ).
cnf(i_0_2684,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__0_0,
[final] ).
cnf(i_0_2685,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
cls_divide_Ozero_0,
[final] ).
cnf(i_0_2686,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__zero__left_0,
[final] ).
cnf(i_0_2687,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__one_0,
[final] ).
cnf(i_0_2688,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
cls_mult__eq__0__iff_1,
[final] ).
cnf(i_0_2689,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ozero_0,
[final] ).
cnf(i_0_2690,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ozero__left_0,
[final] ).
cnf(i_0_2691,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
cls_mult__zero__left_0,
[final] ).
cnf(i_0_2692,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I9_J_0,
[final] ).
cnf(i_0_2693,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__0_0,
[final] ).
cnf(i_0_2694,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__by__1_0,
[final] ).
cnf(i_0_2695,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
cls_mult__eq__0__iff_2,
[final] ).
cnf(i_0_2696,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ozero__right_0,
[final] ).
cnf(i_0_2697,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ozero_0,
[final] ).
cnf(i_0_2698,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
cls_mult__zero__right_0,
[final] ).
cnf(i_0_2699,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I10_J_0,
[final] ).
cnf(i_0_2700,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__self_0,
[final] ).
cnf(i_0_2701,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_right__inverse__eq_1,
[final] ).
cnf(i_0_2702,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
cls_odd__pos_0,
[final] ).
cnf(i_0_2703,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
cls_power__0_0,
[final] ).
cnf(i_0_2704,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Opwr__0_0,
[final] ).
cnf(i_0_2705,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_add__0__left_0,
[final] ).
cnf(i_0_2706,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1_0,
[final] ).
cnf(i_0_2707,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I5_J_0,
[final] ).
cnf(i_0_2708,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__0_0,
[final] ).
cnf(i_0_2709,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_mult__1_0,
[final] ).
cnf(i_0_2710,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_mult__1__left_0,
[final] ).
cnf(i_0_2711,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I11_J_0,
[final] ).
cnf(i_0_2712,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__1_0,
[final] ).
cnf(i_0_2713,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__0__right_0,
[final] ).
cnf(i_0_2714,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__by__0_0,
[final] ).
cnf(i_0_2715,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__1_0,
[final] ).
cnf(i_0_2716,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_monoid__add__class_Oadd__0__right_0,
[final] ).
cnf(i_0_2717,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1__right_0,
[final] ).
cnf(i_0_2718,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I6_J_0,
[final] ).
cnf(i_0_2719,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_mult__1__right_0,
[final] ).
cnf(i_0_2720,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I12_J_0,
[final] ).
cnf(i_0_2721,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_one__dvd_0,
[final] ).
cnf(i_0_2722,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__0__right_0,
[final] ).
cnf(i_0_2723,axiom,
( ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X1) ),
cls_nonzero__number__of__Min_0,
[final] ).
cnf(i_0_2724,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__one__right_0,
[final] ).
cnf(i_0_2725,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I33_J_0,
[final] ).
cnf(i_0_2726,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_eq__iff__diff__eq__0_0,
[final] ).
cnf(i_0_2727,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__self_0,
[final] ).
cnf(i_0_2728,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus__eq_1,
[final] ).
cnf(i_0_2729,axiom,
( c_Divides_Odiv__class_Omod(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__self_0,
[final] ).
cnf(i_0_2730,axiom,
( X2 = X3
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oinverse__class_Oinverse(X3,X1) ),
cls_nonzero__inverse__eq__imp__eq_0,
[final] ).
cnf(i_0_2731,axiom,
( c_HOL_Otimes__class_Otimes(X2,X2,X1) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__idem_0,
[final] ).
cnf(i_0_2732,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__refl_0,
[final] ).
cnf(i_0_2733,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
cls_order__eq__refl_0,
[final] ).
cnf(i_0_2734,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0,
[final] ).
cnf(i_0_2735,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),
cls_add__is__0_2,
[final] ).
cnf(i_0_2736,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
cls_nat__mult__eq__1__iff_2,
[final] ).
cnf(i_0_2737,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[i_0_1535,c_0_1428]),
[final] ).
cnf(i_0_2738,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
cls_nat__1__eq__mult__iff_2,
[final] ).
cnf(i_0_2739,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
cls_root__unity_0,
[final] ).
cnf(i_0_2740,axiom,
( c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) = c_Nat_Osemiring__1__class_Oof__nat(X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__of__nat_0,
[final] ).
cnf(i_0_2741,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__cancel_0,
[final] ).
cnf(i_0_2742,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__idempotent_0,
[final] ).
cnf(i_0_2743,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oinverse__class_Oinverse(X3,X1) ),
cls_inverse__eq__iff__eq_0,
[final] ).
cnf(i_0_2744,axiom,
( X2 = X3
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X3,X1) ),
cls_eq__number__of_0,
[final] ).
cnf(i_0_2745,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_gr0I_0,
[final] ).
cnf(i_0_2746,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
cls_nat__dvd__1__iff__1_1,
[final] ).
cnf(i_0_2747,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_mult__is__0_1,
[final] ).
cnf(i_0_2748,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_mult__is__0_2,
[final] ).
cnf(i_0_2749,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
cls_plus__nat_Oadd__0_0,
[final] ).
cnf(i_0_2750,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
cls_nat__mult__1_0,
[final] ).
cnf(i_0_2751,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
cls_Nat_Oadd__0__right_0,
[final] ).
cnf(i_0_2752,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
cls_nat__mult__1__right_0,
[final] ).
cnf(i_0_2753,axiom,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_natgb_Oadd__r0__iff_1,
[final] ).
cnf(i_0_2754,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
cls_gcd__lcm__complete__lattice__nat_Obot__least_0,
[final] ).
cnf(i_0_2755,axiom,
c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0,
[final] ).
cnf(i_0_2756,axiom,
( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_abs__minus__one_0,
[final] ).
cnf(i_0_2757,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__inverse__eq_0,
[final] ).
cnf(i_0_2758,axiom,
( X2 = X3
| ~ class_Nat_Osemiring__char__0(X1)
| c_Nat_Osemiring__1__class_Oof__nat(X2,X1) != c_Nat_Osemiring__1__class_Oof__nat(X3,X1) ),
cls_of__nat__eq__iff_0,
[final] ).
cnf(i_0_2759,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
cls_neg__equal__iff__equal_0,
[final] ).
cnf(i_0_2760,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
cls_compl__eq__compl__iff_0,
[final] ).
cnf(i_0_2761,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_nonzero__inverse__inverse__eq_0,
[final] ).
cnf(i_0_2762,axiom,
c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
cls_dvd_Oeq__iff_0,
[final] ).
cnf(i_0_2763,axiom,
( X2 = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oone__class_Oone(X1) ),
cls_inverse__eq__1__iff_0,
[final] ).
cnf(i_0_2764,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_inverse__nonzero__iff__nonzero_0,
[final] ).
cnf(i_0_2765,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__minus_0,
[final] ).
cnf(i_0_2766,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__equation__iff_1,
[final] ).
cnf(i_0_2767,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0,
[final] ).
cnf(i_0_2768,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_0,
[final] ).
cnf(i_0_2769,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_1,
[final] ).
cnf(i_0_2770,axiom,
( c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_iszero__number__of__Pls_0,
[final] ).
cnf(i_0_2771,axiom,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(X2,tc_Int_Oint) ),
cls_Nat__Transfer_Otransfer__int__nat__relations_I1_J_0,
[final] ).
cnf(i_0_2772,axiom,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(X2,tc_Int_Oint) ),
cls_int__int__eq_0,
[final] ).
cnf(i_0_2773,axiom,
( c_HOL_Ozero__class_Ozero(X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Ouminus__class_Ouminus(X2,X1) ),
cls_neg__0__equal__iff__equal_0,
[final] ).
cnf(i_0_2774,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_inverse__zero__imp__zero_0,
[final] ).
cnf(i_0_2775,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_neg__equal__0__iff__equal_0,
[final] ).
cnf(i_0_2776,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_abs__eq__0_0,
[final] ).
cnf(i_0_2777,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_arith__simps_I31_J_0,
[final] ).
cnf(i_0_2778,axiom,
( c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_number__of__Min_0,
[final] ).
cnf(i_0_2779,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X1)
| ~ c_Int_Oiszero(c_HOL_Oone__class_Oone(X1),X1) ),
cls_not__iszero__1_0,
[final] ).
cnf(i_0_2780,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__eq__1__iff_1,
[final] ).
cnf(i_0_2781,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__nonzero__iff__nonzero_1,
[final] ).
cnf(i_0_2782,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != X2 ),
cls_neg__equal__zero_0,
[final] ).
cnf(i_0_2783,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1)
| ~ c_Int_Oiszero(X2,X1) ),
cls_iszero__def_0,
[final] ).
cnf(i_0_2784,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint),
cls_eq__number__of__Pls__Min_0,
[final] ).
cnf(i_0_2785,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_inverse__1_0,
[final] ).
cnf(i_0_2786,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__zero_0,
[final] ).
cnf(i_0_2787,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
cls_neg__equal__zero_1,
[final] ).
cnf(i_0_2788,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__zero_0,
[final] ).
cnf(i_0_2789,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__one_0,
[final] ).
cnf(i_0_2790,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__eq__0_1,
[final] ).
cnf(i_0_2791,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_neg__0__equal__iff__equal_1,
[final] ).
cnf(i_0_2792,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__1_0,
[final] ).
cnf(i_0_2793,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__0_0,
[final] ).
cnf(i_0_2794,axiom,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_numeral__1__eq__1_0,
[final] ).
cnf(i_0_2795,axiom,
( c_HOL_Oone__class_Oone(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_comp__arith_I110_J_0,
[final] ).
cnf(i_0_2796,axiom,
( c_Int_Oiszero(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_iszero__0_0,
[final] ).
cnf(i_0_2797,axiom,
~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat),
cls_odd__1__nat_0,
[final] ).
cnf(i_0_2798,axiom,
( c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_number__of__Pls_0,
[final] ).
cnf(i_0_2799,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_comp__arith_I112_J_0,
[final] ).
cnf(i_0_2800,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
cls_zero__neq__one_0,
[final] ).
cnf(i_0_2801,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_one__neq__zero_0,
[final] ).
cnf(i_0_2802,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
cls_nat__numeral__1__eq__1_0,
[final] ).
cnf(i_0_2803,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),
cls_Numeral1__eq1__nat_0,
[final] ).
cnf(i_0_2804,axiom,
c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_even__zero__nat_0,
[final] ).
cnf(i_0_2805,axiom,
( X1 = X2
| c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
cls_rel__simps_I48_J_0,
[final] ).
cnf(i_0_2806,axiom,
( X1 = X2
| c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
cls_rel__simps_I51_J_0,
[final] ).
cnf(i_0_2807,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_nat__number__of__Pls_0,
[final] ).
cnf(i_0_2808,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_nat__number__of__Min_0,
[final] ).
cnf(i_0_2809,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),
cls_comp__arith_I113_J_0,
[final] ).
cnf(i_0_2810,axiom,
c_Int_Onumber__class_Onumber__of(X1,tc_Int_Oint) = X1,
cls_number__of__is__id_0,
[final] ).
cnf(i_0_2811,axiom,
c_Int_OBit0(X1) != c_Int_OBit1(X2),
cls_rel__simps_I49_J_0,
[final] ).
cnf(i_0_2812,axiom,
c_Int_OBit1(X1) != c_Int_OBit0(X2),
cls_rel__simps_I50_J_0,
[final] ).
cnf(i_0_2813,axiom,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
cls_root1_0,
[final] ).
cnf(i_0_2814,axiom,
c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
cls_root0_0,
[final] ).
cnf(i_0_2815,axiom,
( c_Int_OPls = X1
| c_Int_OPls != c_Int_OBit0(X1) ),
cls_rel__simps_I38_J_0,
[final] ).
cnf(i_0_2816,axiom,
( c_Int_OMin = X1
| c_Int_OMin != c_Int_OBit1(X1) ),
cls_rel__simps_I43_J_0,
[final] ).
cnf(i_0_2817,axiom,
( X1 = c_Int_OPls
| c_Int_OBit0(X1) != c_Int_OPls ),
cls_rel__simps_I44_J_0,
[final] ).
cnf(i_0_2818,axiom,
( X1 = c_Int_OMin
| c_Int_OBit1(X1) != c_Int_OMin ),
cls_rel__simps_I47_J_0,
[final] ).
cnf(i_0_2819,axiom,
c_Int_OBit0(X1) != c_Int_OMin,
cls_rel__simps_I45_J_0,
[final] ).
cnf(i_0_2820,axiom,
c_Int_OBit1(X1) != c_Int_OPls,
cls_rel__simps_I46_J_0,
[final] ).
cnf(i_0_2821,axiom,
c_Int_OPls != c_Int_OBit1(X1),
cls_rel__simps_I39_J_0,
[final] ).
cnf(i_0_2822,axiom,
c_Int_OMin != c_Int_OBit0(X1),
cls_rel__simps_I42_J_0,
[final] ).
cnf(i_0_2823,axiom,
c_Complex_Oii != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
cls_complex__i__not__one_0,
[final] ).
cnf(i_0_2824,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_2825,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_2826,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_2827,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Oring__char__0,
[final] ).
cnf(i_0_2828,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
clsarity_Int__Oint__Int_Oring__char__0,
[final] ).
cnf(i_0_2829,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,
[final] ).
cnf(i_0_2830,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors,
[final] ).
cnf(i_0_2831,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,
[final] ).
cnf(i_0_2832,axiom,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oring__1,
[final] ).
cnf(i_0_2833,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_2834,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_2835,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_2836,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,
[final] ).
cnf(i_0_2837,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult,
[final] ).
cnf(i_0_2838,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
clsarity_nat__OrderedGroup_Ocomm__monoid__mult,
[final] ).
cnf(i_0_2839,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_2840,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_2841,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_2842,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,
[final] ).
cnf(i_0_2843,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors,
[final] ).
cnf(i_0_2844,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__field,
[final] ).
cnf(i_0_2845,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_2846,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_2847,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_2848,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_2849,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
clsarity_nat__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_2850,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict,
[final] ).
cnf(i_0_2851,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,
[final] ).
cnf(i_0_2852,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_2853,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_2854,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_2855,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_2856,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_2857,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_2858,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,
[final] ).
cnf(i_0_2859,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Omonoid__mult,
[final] ).
cnf(i_0_2860,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
clsarity_nat__OrderedGroup_Omonoid__mult,
[final] ).
cnf(i_0_2861,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
[final] ).
cnf(i_0_2862,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_2863,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_2864,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_2865,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
clsarity_Int__Oint__Orderings_Opreorder,
[final] ).
cnf(i_0_2866,axiom,
class_Orderings_Opreorder(tc_nat),
clsarity_nat__Orderings_Opreorder,
[final] ).
cnf(i_0_2867,axiom,
class_Divides_Oring__div(tc_Int_Oint),
clsarity_Int__Oint__Divides_Oring__div,
[final] ).
cnf(i_0_2868,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__semiring,
[final] ).
cnf(i_0_2869,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Opordered__semiring,
[final] ).
cnf(i_0_2870,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add,
[final] ).
cnf(i_0_2871,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring,
[final] ).
cnf(i_0_2872,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,
[final] ).
cnf(i_0_2873,axiom,
class_Ring__and__Field_Olordered__ring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Olordered__ring,
[final] ).
cnf(i_0_2874,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring,
[final] ).
cnf(i_0_2875,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oring,
[final] ).
cnf(i_0_2876,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_2877,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_2878,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_2879,axiom,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Nat_Osemiring__char__0,
[final] ).
cnf(i_0_2880,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
clsarity_Int__Oint__Nat_Osemiring__char__0,
[final] ).
cnf(i_0_2881,axiom,
class_Nat_Osemiring__char__0(tc_nat),
clsarity_nat__Nat_Osemiring__char__0,
[final] ).
cnf(i_0_2882,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__semiring,
[final] ).
cnf(i_0_2883,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__semiring,
[final] ).
cnf(i_0_2884,axiom,
class_Ring__and__Field_Oabs__if(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oabs__if,
[final] ).
cnf(i_0_2885,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,
[final] ).
cnf(i_0_2886,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__ring,
[final] ).
cnf(i_0_2887,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odvd,
[final] ).
cnf(i_0_2888,axiom,
class_Ring__and__Field_Odvd(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Odvd,
[final] ).
cnf(i_0_2889,axiom,
class_Ring__and__Field_Odvd(tc_nat),
clsarity_nat__Ring__and__Field_Odvd,
[final] ).
cnf(i_0_2890,axiom,
class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1,
[final] ).
cnf(i_0_2891,axiom,
class_Ring__and__Field_Osemiring__1(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Osemiring__1,
[final] ).
cnf(i_0_2892,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring__1,
[final] ).
cnf(i_0_2893,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,
[final] ).
cnf(i_0_2894,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Onumber__ring,
[final] ).
cnf(i_0_2895,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
clsarity_Int__Oint__Int_Onumber__ring,
[final] ).
cnf(i_0_2896,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__ring,
[final] ).
cnf(i_0_2897,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Omult__mono,
[final] ).
cnf(i_0_2898,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
clsarity_nat__Ring__and__Field_Omult__mono,
[final] ).
cnf(i_0_2899,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Omult__mono1,
[final] ).
cnf(i_0_2900,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
clsarity_nat__Ring__and__Field_Omult__mono1,
[final] ).
cnf(i_0_2901,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
clsarity_Int__Oint__Divides_Osemiring__div,
[final] ).
cnf(i_0_2902,axiom,
class_Divides_Osemiring__div(tc_nat),
clsarity_nat__Divides_Osemiring__div,
[final] ).
cnf(i_0_2903,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_2904,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_2905,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_2906,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_2907,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_2908,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
clsarity_nat__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_2909,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_2910,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_2911,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
clsarity_nat__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_2912,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Power_Opower,
[final] ).
cnf(i_0_2913,axiom,
class_Power_Opower(tc_Int_Oint),
clsarity_Int__Oint__Power_Opower,
[final] ).
cnf(i_0_2914,axiom,
class_Power_Opower(tc_nat),
clsarity_nat__Power_Opower,
[final] ).
cnf(i_0_2915,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_2916,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_2917,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,
[final] ).
cnf(i_0_2918,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1,
[final] ).
cnf(i_0_2919,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,
[final] ).
cnf(i_0_2920,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,
[final] ).
cnf(i_0_2921,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict,
[final] ).
cnf(i_0_2922,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__semiring__strict,
[final] ).
cnf(i_0_2923,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__semidom,
[final] ).
cnf(i_0_2924,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__semidom,
[final] ).
cnf(i_0_2925,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_2926,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_2927,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
clsarity_nat__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_2928,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,
[final] ).
cnf(i_0_2929,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add,
[final] ).
cnf(i_0_2930,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
[final] ).
cnf(i_0_2931,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict,
[final] ).
cnf(i_0_2932,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Onumber,
[final] ).
cnf(i_0_2933,axiom,
class_Int_Onumber(tc_Int_Oint),
clsarity_Int__Oint__Int_Onumber,
[final] ).
cnf(i_0_2934,axiom,
class_Int_Onumber(tc_nat),
clsarity_nat__Int_Onumber,
[final] ).
cnf(i_0_2935,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,
[final] ).
cnf(i_0_2936,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs,
[final] ).
cnf(i_0_2937,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,
[final] ).
cnf(i_0_2938,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_2939,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_2940,axiom,
class_Orderings_Oorder(tc_Int_Oint),
clsarity_Int__Oint__Orderings_Oorder,
[final] ).
cnf(i_0_2941,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat__Orderings_Oorder,
[final] ).
cnf(i_0_2942,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
clsarity_Int__Oint__Orderings_Olinorder,
[final] ).
cnf(i_0_2943,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder,
[final] ).
cnf(i_0_2944,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs,
[final] ).
cnf(i_0_2945,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_2946,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_2947,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_2948,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__idom,
[final] ).
cnf(i_0_2949,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_2950,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_2951,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add,
[final] ).
cnf(i_0_2952,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,
[final] ).
cnf(i_0_2953,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_2954,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_2955,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs,
[final] ).
cnf(i_0_2956,axiom,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
cls_Bit0__Pls_0,
[final] ).
cnf(i_0_2957,axiom,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
cls_Bit1__Min_0,
[final] ).
cnf(i_0_2958,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
cls_rel__simps_I38_J_1,
[final] ).
cnf(i_0_2959,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
cls_rel__simps_I43_J_1,
[final] ).
cnf(i_0_2960,axiom,
c_Int_OMin != c_Int_OPls,
cls_rel__simps_I40_J_0,
[final] ).
cnf(i_0_2961,axiom,
c_Int_OPls != c_Int_OMin,
cls_rel__simps_I37_J_0,
[final] ).
cnf(i_0_2962,axiom,
X1 = X1 ).
cnf(i_0_2963,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_2964,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_2965,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_2966,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_2967,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_2968,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_2969,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_2970,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_2971,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_2972,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_2973,axiom,
( X1 != X2
| c_Int_OBit0(X1) = c_Int_OBit0(X2) ) ).
cnf(i_0_2974,axiom,
( X1 != X2
| c_Int_OBit1(X1) = c_Int_OBit1(X2) ) ).
cnf(i_0_2975,axiom,
( X1 != X2
| c_FFT__Mirabelle_Oroot(X1) = c_FFT__Mirabelle_Oroot(X2) ) ).
cnf(i_0_2976,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_2977,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_2978,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_2979,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).
cnf(i_0_2980,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).
cnf(i_0_2981,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_2982,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_2983,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_2984,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_2985,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_2986,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_2987,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_2988,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_2989,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_2990,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_2991,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X1,X3,X4) = c_HOL_Oinverse__class_Odivide(X2,X3,X4) ) ).
cnf(i_0_2992,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X3,X1,X4) = c_HOL_Oinverse__class_Odivide(X3,X2,X4) ) ).
cnf(i_0_2993,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X3,X4,X1) = c_HOL_Oinverse__class_Odivide(X3,X4,X2) ) ).
cnf(i_0_2994,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Oinverse(X1,X3) = c_HOL_Oinverse__class_Oinverse(X2,X3) ) ).
cnf(i_0_2995,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Oinverse(X3,X1) = c_HOL_Oinverse__class_Oinverse(X3,X2) ) ).
cnf(i_0_2996,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_2997,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_2998,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X1,X3)
| c_Parity_Oeven__odd__class_Oeven(X2,X3) ) ).
cnf(i_0_2999,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X3,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,X2) ) ).
cnf(i_0_3000,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_3001,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_3002,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_3003,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_3004,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odvd(X1)
| class_Ring__and__Field_Odvd(X2) ) ).
cnf(i_0_3005,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(X2) ) ).
cnf(i_0_3006,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_3007,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_3008,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_3009,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_3010,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__field(X2) ) ).
cnf(i_0_3011,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| class_Ring__and__Field_Odivision__by__zero(X2) ) ).
cnf(i_0_3012,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_3013,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_3014,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| class_Ring__and__Field_Odivision__ring(X2) ) ).
cnf(i_0_3015,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__mult(X1)
| class_OrderedGroup_Omonoid__mult(X2) ) ).
cnf(i_0_3016,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ofield(X2) ) ).
cnf(i_0_3017,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_3018,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_3019,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_3020,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_3021,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).
cnf(i_0_3022,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| class_Ring__and__Field_Opordered__semiring(X2) ) ).
cnf(i_0_3023,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_3024,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_3025,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_3026,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(X2) ) ).
cnf(i_0_3027,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| class_Ring__and__Field_Oordered__semiring(X2) ) ).
cnf(i_0_3028,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_3029,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Olordered__ring(X1)
| class_Ring__and__Field_Olordered__ring(X2) ) ).
cnf(i_0_3030,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_3031,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_3032,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_3033,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).
cnf(i_0_3034,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono(X1)
| class_Ring__and__Field_Omult__mono(X2) ) ).
cnf(i_0_3035,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono1(X1)
| class_Ring__and__Field_Omult__mono1(X2) ) ).
cnf(i_0_3036,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_3037,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_3038,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_3039,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_3040,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_3041,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1(X1)
| class_Ring__and__Field_Oring__1(X2) ) ).
cnf(i_0_3042,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| class_Ring__and__Field_Opordered__ring__abs(X2) ) ).
cnf(i_0_3043,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).
cnf(i_0_3044,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_3045,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_3046,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_3047,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__field(X1)
| class_RealVector_Oreal__field(X2) ) ).
cnf(i_0_3048,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_3049,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_3050,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_3051,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_3052,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_3053,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_3054,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_3055,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__1(X1)
| class_Ring__and__Field_Osemiring__1(X2) ) ).
cnf(i_0_3056,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_3057,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_3058,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_3059,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_3060,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_3061,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_3062,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_3063,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_3064,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_3065,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X1,X3)
| c_Int_Oiszero(X2,X3) ) ).
cnf(i_0_3066,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X3,X1)
| c_Int_Oiszero(X3,X2) ) ).
cnf(i_0_3067,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_3068,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oabs__if(X1)
| class_Ring__and__Field_Oabs__if(X2) ) ).
cnf(i_0_3069,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_3070,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_3071,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_3072,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_3073,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_3074,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_3075,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_3076,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_3077,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_3078,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_2962_001,axiom,
X1 = X1 ).
cnf(i_0_2963_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_2964_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_2965_004,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_2966_005,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_2967_006,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_2968_007,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_2969_008,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_2970_009,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_2971_010,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_2972_011,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_2973_012,axiom,
( X1 != X2
| c_Int_OBit0(X1) = c_Int_OBit0(X2) ) ).
cnf(i_0_2974_013,axiom,
( X1 != X2
| c_Int_OBit1(X1) = c_Int_OBit1(X2) ) ).
cnf(i_0_2975_014,axiom,
( X1 != X2
| c_FFT__Mirabelle_Oroot(X1) = c_FFT__Mirabelle_Oroot(X2) ) ).
cnf(i_0_2976_015,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_2977_016,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_2978_017,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_2979_018,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).
cnf(i_0_2980_019,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).
cnf(i_0_2981_020,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_2982_021,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_2983_022,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_2984_023,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_2985_024,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_2986_025,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_2987_026,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_2988_027,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_2989_028,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_2990_029,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_2991_030,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X1,X3,X4) = c_HOL_Oinverse__class_Odivide(X2,X3,X4) ) ).
cnf(i_0_2992_031,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X3,X1,X4) = c_HOL_Oinverse__class_Odivide(X3,X2,X4) ) ).
cnf(i_0_2993_032,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X3,X4,X1) = c_HOL_Oinverse__class_Odivide(X3,X4,X2) ) ).
cnf(i_0_2994_033,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Oinverse(X1,X3) = c_HOL_Oinverse__class_Oinverse(X2,X3) ) ).
cnf(i_0_2995_034,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Oinverse(X3,X1) = c_HOL_Oinverse__class_Oinverse(X3,X2) ) ).
cnf(i_0_2996_035,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_2997_036,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_2998_037,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X1,X3)
| c_Parity_Oeven__odd__class_Oeven(X2,X3) ) ).
cnf(i_0_2999_038,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X3,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,X2) ) ).
cnf(i_0_3000_039,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_3001_040,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_3002_041,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_3003_042,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_3004_043,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odvd(X1)
| class_Ring__and__Field_Odvd(X2) ) ).
cnf(i_0_3005_044,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(X2) ) ).
cnf(i_0_3006_045,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_3007_046,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_3008_047,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_3009_048,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_3010_049,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__field(X2) ) ).
cnf(i_0_3011_050,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| class_Ring__and__Field_Odivision__by__zero(X2) ) ).
cnf(i_0_3012_051,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_3013_052,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_3014_053,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| class_Ring__and__Field_Odivision__ring(X2) ) ).
cnf(i_0_3015_054,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__mult(X1)
| class_OrderedGroup_Omonoid__mult(X2) ) ).
cnf(i_0_3016_055,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ofield(X2) ) ).
cnf(i_0_3017_056,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_3018_057,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_3019_058,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_3020_059,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_3021_060,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).
cnf(i_0_3022_061,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| class_Ring__and__Field_Opordered__semiring(X2) ) ).
cnf(i_0_3023_062,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_3024_063,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_3025_064,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_3026_065,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(X2) ) ).
cnf(i_0_3027_066,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| class_Ring__and__Field_Oordered__semiring(X2) ) ).
cnf(i_0_3028_067,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_3029_068,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Olordered__ring(X1)
| class_Ring__and__Field_Olordered__ring(X2) ) ).
cnf(i_0_3030_069,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_3031_070,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_3032_071,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_3033_072,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).
cnf(i_0_3034_073,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono(X1)
| class_Ring__and__Field_Omult__mono(X2) ) ).
cnf(i_0_3035_074,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono1(X1)
| class_Ring__and__Field_Omult__mono1(X2) ) ).
cnf(i_0_3036_075,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_3037_076,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_3038_077,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_3039_078,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_3040_079,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_3041_080,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1(X1)
| class_Ring__and__Field_Oring__1(X2) ) ).
cnf(i_0_3042_081,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| class_Ring__and__Field_Opordered__ring__abs(X2) ) ).
cnf(i_0_3043_082,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).
cnf(i_0_3044_083,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_3045_084,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_3046_085,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_3047_086,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__field(X1)
| class_RealVector_Oreal__field(X2) ) ).
cnf(i_0_3048_087,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_3049_088,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_3050_089,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_3051_090,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_3052_091,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_3053_092,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_3054_093,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_3055_094,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__1(X1)
| class_Ring__and__Field_Osemiring__1(X2) ) ).
cnf(i_0_3056_095,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_3057_096,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_3058_097,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_3059_098,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_3060_099,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_3061_100,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_3062_101,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_3063_102,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_3064_103,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_3065_104,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X1,X3)
| c_Int_Oiszero(X2,X3) ) ).
cnf(i_0_3066_105,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X3,X1)
| c_Int_Oiszero(X3,X2) ) ).
cnf(i_0_3067_106,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_3068_107,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oabs__if(X1)
| class_Ring__and__Field_Oabs__if(X2) ) ).
cnf(i_0_3069_108,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_3070_109,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_3071_110,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_3072_111,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_3073_112,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_3074_113,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_3075_114,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_3076_115,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_3077_116,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_3078_117,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_3079,plain,
( ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X2,X1),X3,X1),X4,X1) = X4 ),
inference(equality_inference,[],[1600]) ).
cnf(i_0_3080,plain,
( ~ class_Ring__and__Field_Oring(X1)
| X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X3,X1),X4,X1),X2,X1) ),
inference(equality_inference,[],[1601]) ).
cnf(i_0_3081,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| X3 = X4
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[1606]) ).
cnf(i_0_3082,plain,
( X1 = X1
| X2 = X3 ),
inference(equality_inference,[],[1609]) ).
cnf(i_0_3083,plain,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| X2 = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(equality_inference,[],[1660]) ).
cnf(i_0_3084,plain,
c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat),
inference(equality_inference,[],[1714]) ).
cnf(i_0_3085,plain,
( ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 = X2
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[1791]) ).
cnf(i_0_3086,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2) ),
inference(equality_inference,[],[1805]) ).
cnf(i_0_3087,plain,
X1 = X1,
inference(equality_inference,[],[1813]) ).
cnf(i_0_3088,plain,
( X1 = X1
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(equality_inference,[],[1825]) ).
cnf(i_0_3089,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(equality_inference,[],[1855]) ).
cnf(i_0_3090,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
inference(equality_inference,[],[1954]) ).
cnf(i_0_3091,plain,
( ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) ),
inference(equality_inference,[],[2085]) ).
cnf(i_0_3092,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Oinverse__class_Odivide(X2,X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[2174]) ).
cnf(i_0_3093,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[2175]) ).
cnf(i_0_3094,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(equality_inference,[],[2176]) ).
cnf(i_0_3095,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(equality_inference,[],[2177]) ).
cnf(i_0_3096,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2) ),
inference(equality_inference,[],[2215]) ).
cnf(i_0_3097,plain,
( X1 = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(equality_inference,[],[2240]) ).
cnf(i_0_3098,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(equality_inference,[],[2267]) ).
cnf(i_0_3099,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(equality_inference,[],[2268]) ).
cnf(i_0_3100,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(equality_inference,[],[2269]) ).
cnf(i_0_3101,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(equality_inference,[],[2270]) ).
cnf(i_0_3102,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oidom(X2)
| X1 = c_HOL_Ouminus__class_Ouminus(X1,X2) ),
inference(equality_inference,[],[2382]) ).
cnf(i_0_3103,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[2408]) ).
cnf(i_0_3104,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(equality_inference,[],[2416]) ).
cnf(i_0_3105,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(equality_inference,[],[2417]) ).
cnf(i_0_3106,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[2431]) ).
cnf(i_0_3107,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[2432]) ).
cnf(i_0_3108,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[2433]) ).
cnf(i_0_3109,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[2434]) ).
cnf(i_0_3110,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[2435]) ).
cnf(i_0_3111,plain,
( X1 = X1
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(equality_inference,[],[2456]) ).
cnf(i_0_3112,plain,
( X1 = X1
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(equality_inference,[],[2458]) ).
cnf(i_0_3113,plain,
X1 = X1,
inference(equality_inference,[],[2477]) ).
cnf(i_0_3114,plain,
X1 = X1,
inference(equality_inference,[],[2479]) ).
cnf(i_0_3115,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1) ),
inference(equality_inference,[],[2597]) ).
cnf(i_0_3116,plain,
( ~ class_Ring__and__Field_Odivision__ring(X1)
| X2 = X2
| X2 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[2730]) ).
cnf(i_0_3117,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| X2 = X2
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
inference(equality_inference,[],[2743]) ).
cnf(i_0_3118,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Int_Oring__char__0(X1) ),
inference(equality_inference,[],[2744]) ).
cnf(i_0_3119,plain,
( X1 = X1
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(equality_inference,[],[2758]) ).
cnf(i_0_3120,plain,
( X1 = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(equality_inference,[],[2759]) ).
cnf(i_0_3121,plain,
( X1 = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(equality_inference,[],[2760]) ).
cnf(i_0_3122,plain,
X1 = X1,
inference(equality_inference,[],[2772]) ).
cnf(i_0_3123,plain,
X1 = X1,
inference(equality_inference,[],[2805]) ).
cnf(i_0_3124,plain,
X1 = X1,
inference(equality_inference,[],[2806]) ).
cnf(i_0_3125,plain,
$false,
inference(scs_inference,[],[i_0_1554,i_0_2603,i_0_1812]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWV634-1 : TPTP v9.2.1. Released v4.1.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 05:42:17 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.30/1.74 % Version : CSE_E---1.7
% 1.30/1.74 % Problem : theBenchmark.p
% 1.30/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.30/1.74 % SZS output start CNFRefutation
% See solution above
% 1.38/1.83 % Total time : 1.384s
%------------------------------------------------------------------------------