%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG377-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.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 04:08:35 PM UTC 2026
% Result : Unsatisfiable 0.70s 1.67s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 608)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_abs__sum__triangle__ineq_0,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__sum__triangle__ineq_0) ).
cnf(cls_CHAINED_0,axiom,
c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_div__Suc_0,axiom,
c_Divides_Odiv__class_Odiv(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),c_Divides_Odiv__class_Odiv(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat),tc_nat),X2,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__Suc_0) ).
cnf(cls_div__add1__eq_0,axiom,
c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X3,tc_nat),c_Divides_Odiv__class_Odiv(X2,X3,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X3,tc_nat),c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X3,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add1__eq_0) ).
cnf(cls_th00_0,axiom,
c_lessequals(c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_th00_0) ).
cnf(cls_real__of__nat__div__aux_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),tc_nat),c_HOL_Oinverse__class_Odivide(c_RealDef_Oreal(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__div__aux_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/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_less__half__sum_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/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
cnf(cls_norm__add__less_0,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(X4,X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X1),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__add__less_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_frac__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/sandbox/benchmark/theBenchmark.p',cls_frac__le_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_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/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
cnf(cls_zmod__simps_I2_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_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/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
cnf(cls_mod__add__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_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/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq_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/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
cnf(cls_norm__triangle__ineq_0,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__triangle__ineq_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
cnf(cls_th000_I3_J_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_th000_I3_J_0) ).
cnf(cls_real__of__nat__div4_0,axiom,
c_lessequals(c_RealDef_Oreal(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),tc_nat),c_HOL_Oinverse__class_Odivide(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__div4_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/sandbox/benchmark/theBenchmark.p',cls_estimate__by__abs_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono__neg_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/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_divide__strict__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/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
cnf(cls_natfloor__eq_0,axiom,
( c_RComplete_Onatfloor(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X2,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealDef_Oreal(X2,tc_nat),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__eq_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__mono_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_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/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
cnf(cls_nat__less__real__le_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__real__le_1) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
cnf(cls_natfloor__div__nat_0,axiom,
( c_RComplete_Onatfloor(c_HOL_Oinverse__class_Odivide(X1,c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)) = c_Divides_Odiv__class_Odiv(c_RComplete_Onatfloor(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__div__nat_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/sandbox/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
cnf(cls_real__sum__gt__zero__less_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__gt__zero__less_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_divide__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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_divide__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/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
cnf(cls_real__0__le__divide__iff_1,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_1) ).
cnf(cls_real__0__le__divide__iff_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_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/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
cnf(cls_real__add__left__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__left__mono_0) ).
cnf(cls_div__add__self1_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X3,X1),X2,X1) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
cnf(cls_div__add__self2_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_HOL_Oone__class_Oone(X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_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/sandbox/benchmark/theBenchmark.p',cls_mod__minus__cong_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/sandbox/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
cnf(cls_real__0__le__divide__iff_4,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_4) ).
cnf(cls_real__0__le__divide__iff_2,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_2) ).
cnf(cls_real__0__le__divide__iff_5,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_5) ).
cnf(cls_real__0__le__divide__iff_3,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_3) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
cnf(cls_even__less__0__iff_0,axiom,
( c_HOL_Oord__class_Oless(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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_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/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_abs__add__one__not__less__self_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__not__less__self_0) ).
cnf(cls_real__0__less__add__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__less__add__iff_0) ).
cnf(cls_real__0__le__add__iff_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__add__iff_0) ).
cnf(cls_real__add__less__0__iff_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__less__0__iff_0) ).
cnf(cls_real__add__le__0__iff_0,axiom,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__le__0__iff_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/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
cnf(cls_abs__minus__add__cancel_0,axiom,
c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__add__cancel_0) ).
cnf(cls_nat__less__real__le_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__real__le_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_nat__add__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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__div__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/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_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/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
cnf(cls_natfloor__add_0,axiom,
( c_RComplete_Onatfloor(c_HOL_Oplus__class_Oplus(X1,c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_RComplete_Onatfloor(X1),X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__add_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/sandbox/benchmark/theBenchmark.p',cls_abs__less__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/sandbox/benchmark/theBenchmark.p',cls_abs__leI_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
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/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
cnf(cls_real__less__sum__gt__zero_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__sum__gt__zero_0) ).
cnf(cls_abs__le__interval__iff_2,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_2) ).
cnf(cls_real__add__less__0__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__less__0__iff_1) ).
cnf(cls_real__add__le__0__iff_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__le__0__iff_1) ).
cnf(cls_real__0__less__add__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__less__add__iff_1) ).
cnf(cls_real__0__le__add__iff_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__add__iff_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_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/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_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/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_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/sandbox/benchmark/theBenchmark.p',cls_abs__divide_0) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
cnf(cls_norm__divide_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__divide_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/sandbox/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
cnf(cls_nonzero__norm__divide_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__norm__divide_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_order__less__le__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/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_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/sandbox/benchmark/theBenchmark.p',cls_order__trans_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
cnf(cls_real__natfloor__add__one__gt_0,axiom,
c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(c_RComplete_Onatfloor(X1),tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__natfloor__add__one__gt_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/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_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/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_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/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
cnf(cls_div__if_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__if_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/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_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/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
cnf(cls_real__le__trans_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_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/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_minus__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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
cnf(cls_real__of__nat__add_0,axiom,
c_RealDef_Oreal(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__add_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/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
cnf(cls_abs__add__one__gt__zero_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__gt__zero_0) ).
cnf(cls_real__of__nat__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__less__iff_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/sandbox/benchmark/theBenchmark.p',cls_divide_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/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
cnf(cls_abs__le__interval__iff_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_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/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_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/sandbox/benchmark/theBenchmark.p',cls_le__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/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__le__D1_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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_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/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_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/sandbox/benchmark/theBenchmark.p',cls_le__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/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
cnf(cls_real__of__nat__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__less__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/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_real__of__nat__gt__zero__cancel__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_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__gt__zero__cancel__iff_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_add__right__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/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_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/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_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/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
cnf(cls_real__natfloor__le_0,axiom,
( c_lessequals(c_RealDef_Oreal(c_RComplete_Onatfloor(X1),tc_nat),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__natfloor__le_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/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
cnf(cls_abs__le__interval__iff_1,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).
cnf(cls_mod__div__trivial_0,axiom,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
cnf(cls_real__le__antisym_0,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_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/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__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/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__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/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
cnf(cls_real__of__nat__gt__zero__cancel__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__gt__zero__cancel__iff_1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_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/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
cnf(cls_zero__less__norm__iff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__norm__iff_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_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/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_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/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_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/sandbox/benchmark/theBenchmark.p',cls_less__SucE_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/sandbox/benchmark/theBenchmark.p',cls_less__antisym_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/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_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/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_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/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_abs__minus__le__zero_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/sandbox/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_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/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
cnf(cls_norm__le__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).
cnf(cls_real__less__def_2,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).
cnf(cls_div__less_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
cnf(cls_real__less__def_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).
cnf(cls_norm__not__less__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
cnf(cls_real__of__nat__le__zero__cancel__iff_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__le__zero__cancel__iff_0) ).
cnf(cls_real__add__minus__iff_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__minus__iff_0) ).
cnf(cls_not__real__of__nat__less__zero_0,axiom,
~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__of__nat__less__zero_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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_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/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonneg_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/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_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/sandbox/benchmark/theBenchmark.p',cls_not__leE_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/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
cnf(cls_linorder__linear_0,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_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/sandbox/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
cnf(cls_real__abs__def_0,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
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/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
cnf(cls_real__le__linear_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_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/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).
cnf(cls_norm__le__zero__iff_1,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
cnf(cls_real__add__eq__0__iff_0,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_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/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
cnf(cls_real__of__nat__Suc_0,axiom,
c_RealDef_Oreal(c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__Suc_0) ).
cnf(cls_natfloor__neg_0,axiom,
( c_RComplete_Onatfloor(X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__neg_0) ).
cnf(cls_zero__less__norm__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__norm__iff_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_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/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_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/sandbox/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
cnf(cls_real__of__nat__Suc__gt__zero_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(X1),tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__Suc__gt__zero_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/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_add__is__0_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/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
cnf(cls_norm__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__ge__zero_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_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/sandbox/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
cnf(cls_real__of__nat__le__zero__cancel__iff_1,axiom,
c_lessequals(c_RealDef_Oreal(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__le__zero__cancel__iff_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
cnf(cls_real__less__def_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_1) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_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/sandbox/benchmark/theBenchmark.p',cls_abs__if_1) ).
cnf(cls_real__of__nat__ge__zero_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__ge__zero_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
cnf(cls_real__add__eq__0__iff_1,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
cnf(cls_div__0_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
cnf(cls_div__by__0_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__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/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
cnf(cls_div__self_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
cnf(cls_real__abs__def_1,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_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/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
cnf(cls_div__by__1_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_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/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
cnf(cls_div__1_0,axiom,
c_Divides_Odiv__class_Odiv(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__1_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_mod__self_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/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
cnf(cls_order__eq__iff_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_order__eq__refl_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_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/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
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/sandbox/benchmark/theBenchmark.p',cls_abs__of__nat_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/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_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/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
cnf(cls_norm__minus__cancel_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__cancel_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/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
cnf(cls_abs__norm__cancel_0,axiom,
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__norm__cancel_0) ).
cnf(cls_th000_I2_J_0,axiom,
c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_th000_I2_J_0) ).
cnf(cls_th000_I1_J_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_th000_I1_J_0) ).
cnf(cls_less__Suc__eq_2,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__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/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_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/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__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/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
cnf(cls_real__le__refl_0,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_double__compl_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_abs__real__of__nat__cancel_0,axiom,
c_HOL_Oabs__class_Oabs(c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal) = c_RealDef_Oreal(X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__real__of__nat__cancel_0) ).
cnf(cls_real__of__nat__inject_0,axiom,
( X1 = X2
| c_RealDef_Oreal(X1,tc_nat) != c_RealDef_Oreal(X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__inject_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/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__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/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_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/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
cnf(cls_norm__eq__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X2,X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_neg__equal__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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_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/sandbox/benchmark/theBenchmark.p',cls_minus__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/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_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/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
cnf(cls_norm__one_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__one_0) ).
cnf(cls_norm__zero_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__zero_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/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
cnf(cls_natfloor__real__of__nat_0,axiom,
c_RComplete_Onatfloor(c_RealDef_Oreal(X1,tc_nat)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__real__of__nat_0) ).
cnf(cls_real__of__nat__zero__iff_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_RealDef_Oreal(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__zero__iff_0) ).
cnf(cls_real__of__nat__one_0,axiom,
c_RealDef_Oreal(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__one_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
cnf(cls_real__of__nat__zero_0,axiom,
c_RealDef_Oreal(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__zero_0) ).
cnf(cls_nat_Oinject_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
cnf(cls_Suc__inject_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
cnf(cls_Suc__neq__Zero_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
cnf(cls_nat_Osimps_I3_J_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
cnf(cls_natfloor__zero_0,axiom,
c_RComplete_Onatfloor(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__zero_0) ).
cnf(cls_real__zero__not__eq__one_0,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(X1) != X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
cnf(cls_n__not__Suc__n_0,axiom,
X1 != c_Suc(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__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/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__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/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
cnf(clsarity_RealDef__Oreal__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Nat_Osemiring__char__0) ).
cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__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/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__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/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__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/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__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/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__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/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__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/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__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/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
cnf(clsarity_nat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
cnf(i_0_559,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_560,negated_conjecture,
~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_conjecture_0,
[final] ).
cnf(i_0_561,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_abs__sum__triangle__ineq_0,
[final] ).
cnf(i_0_562,axiom,
c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_CHAINED_0,
[final] ).
cnf(i_0_563,axiom,
c_Divides_Odiv__class_Odiv(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),c_Divides_Odiv__class_Odiv(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat),tc_nat),X2,tc_nat),tc_nat),
cls_div__Suc_0,
[final] ).
cnf(i_0_564,axiom,
c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X3,tc_nat),c_Divides_Odiv__class_Odiv(X2,X3,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X3,tc_nat),c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X3,tc_nat),tc_nat),
cls_div__add1__eq_0,
[final] ).
cnf(i_0_565,axiom,
c_lessequals(c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),
cls_th00_0,
[final] ).
cnf(i_0_566,axiom,
( c_HOL_Oinverse__class_Odivide(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),tc_nat),c_HOL_Oinverse__class_Odivide(c_RealDef_Oreal(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_real__of__nat__div__aux_0,
[final] ).
cnf(i_0_567,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_568,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_569,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_570,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_571,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(X4,X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X1),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),X4,tc_RealDef_Oreal) ),
cls_norm__add__less_0,
[final] ).
cnf(i_0_572,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_573,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_574,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_575,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_576,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_577,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_578,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_579,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_580,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_581,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_582,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__triangle__ineq_0,
[final] ).
cnf(i_0_583,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_584,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_585,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_586,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_587,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),
cls_th000_I3_J_0,
[final] ).
cnf(i_0_588,axiom,
c_lessequals(c_RealDef_Oreal(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),tc_nat),c_HOL_Oinverse__class_Odivide(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__of__nat__div4_0,
[final] ).
cnf(i_0_589,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_590,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_591,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_592,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_593,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_594,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_595,axiom,
( c_RComplete_Onatfloor(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X2,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealDef_Oreal(X2,tc_nat),X1,tc_RealDef_Oreal) ),
cls_natfloor__eq_0,
[final] ).
cnf(i_0_596,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_597,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_598,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_599,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_600,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_601,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_602,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_603,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_604,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_605,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_606,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_607,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) ),
cls_nat__less__real__le_1,
[final] ).
cnf(i_0_608,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_609,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_610,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_611,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_612,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_613,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_614,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_615,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_616,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_617,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_618,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_619,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_620,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_621,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_622,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_623,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_624,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_625,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_626,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_627,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_628,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_629,axiom,
( c_RComplete_Onatfloor(c_HOL_Oinverse__class_Odivide(X1,c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)) = c_Divides_Odiv__class_Odiv(c_RComplete_Onatfloor(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_natfloor__div__nat_0,
[final] ).
cnf(i_0_630,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_631,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__sum__gt__zero__less_0,
[final] ).
cnf(i_0_632,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_633,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_634,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_635,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_636,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_637,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_638,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_639,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_640,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_641,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_642,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_643,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_644,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_645,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_646,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_647,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_648,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_649,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_650,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_651,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_652,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_653,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_654,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_655,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_656,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_657,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__0__le__divide__iff_1,
[final] ).
cnf(i_0_658,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__0__le__divide__iff_0,
[final] ).
cnf(i_0_659,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_660,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_661,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_662,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_663,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_664,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_665,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_666,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_667,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_668,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_669,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_670,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_671,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_672,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_673,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_674,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_675,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_676,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_677,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_678,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_679,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_RealDef_Oreal) ),
cls_real__add__left__mono_0,
[final] ).
cnf(i_0_680,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X3,X1),X2,X1) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__add__self1_0,
[final] ).
cnf(i_0_681,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_HOL_Oone__class_Oone(X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__add__self2_0,
[final] ).
cnf(i_0_682,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_683,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_684,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_real__0__le__divide__iff_4,
[final] ).
cnf(i_0_685,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__0__le__divide__iff_2,
[final] ).
cnf(i_0_686,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_real__0__le__divide__iff_5,
[final] ).
cnf(i_0_687,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__0__le__divide__iff_3,
[final] ).
cnf(i_0_688,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_689,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_690,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_691,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_692,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_693,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_694,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_695,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_696,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_697,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_698,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_699,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_700,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_701,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_702,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
cls_abs__add__one__not__less__self_0,
[final] ).
cnf(i_0_703,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__0__less__add__iff_0,
[final] ).
cnf(i_0_704,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__0__le__add__iff_0,
[final] ).
cnf(i_0_705,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__add__less__0__iff_0,
[final] ).
cnf(i_0_706,axiom,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__add__le__0__iff_0,
[final] ).
cnf(i_0_707,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,
[final] ).
cnf(i_0_708,axiom,
c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_abs__minus__add__cancel_0,
[final] ).
cnf(i_0_709,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_nat__less__real__le_0,
[final] ).
cnf(i_0_710,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_711,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_712,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_713,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_714,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_715,axiom,
( c_RComplete_Onatfloor(c_HOL_Oplus__class_Oplus(X1,c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_RComplete_Onatfloor(X1),X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_natfloor__add_0,
[final] ).
cnf(i_0_716,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_717,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_718,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_719,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_720,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_721,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_722,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_723,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_724,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_725,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_726,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal) ),
cls_real__less__sum__gt__zero_0,
[final] ).
cnf(i_0_727,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_abs__le__interval__iff_2,
[final] ).
cnf(i_0_728,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__add__less__0__iff_1,
[final] ).
cnf(i_0_729,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__add__le__0__iff_1,
[final] ).
cnf(i_0_730,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_real__0__less__add__iff_1,
[final] ).
cnf(i_0_731,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_real__0__le__add__iff_1,
[final] ).
cnf(i_0_732,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_733,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,
[final] ).
cnf(i_0_734,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_735,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_736,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_737,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_738,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_739,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,
[final] ).
cnf(i_0_740,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,
[final] ).
cnf(i_0_741,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,
[final] ).
cnf(i_0_742,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_743,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_744,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_745,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_746,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_747,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_748,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_749,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_750,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_751,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_752,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
cls_norm__divide_0,
[final] ).
cnf(i_0_753,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_754,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
cls_nonzero__norm__divide_0,
[final] ).
cnf(i_0_755,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_756,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_757,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_758,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_759,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_760,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_761,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_762,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_763,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_764,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_765,axiom,
c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(c_RComplete_Onatfloor(X1),tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__natfloor__add__one__gt_0,
[final] ).
cnf(i_0_766,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,
[final] ).
cnf(i_0_767,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_768,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_769,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_770,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_771,axiom,
( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_div__if_0,
[final] ).
cnf(i_0_772,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,
[final] ).
cnf(i_0_773,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_774,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_775,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_776,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_777,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal) ),
cls_real__le__trans_0,
[final] ).
cnf(i_0_778,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_779,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_780,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_781,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_782,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_783,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_784,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_785,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_786,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_787,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_788,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_789,axiom,
c_RealDef_Oreal(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal),
cls_real__of__nat__add_0,
[final] ).
cnf(i_0_790,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_791,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_abs__add__one__gt__zero_0,
[final] ).
cnf(i_0_792,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) ),
cls_real__of__nat__less__iff_0,
[final] ).
cnf(i_0_793,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_794,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_795,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_796,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_797,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_798,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_799,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_800,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_801,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_802,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_803,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_804,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_805,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_abs__le__interval__iff_0,
[final] ).
cnf(i_0_806,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_807,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_808,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_809,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_810,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_811,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_812,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_813,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_814,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_815,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_816,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_817,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_818,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_819,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_820,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_821,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_822,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_823,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_824,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_825,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_559]),
[final] ).
cnf(i_0_826,axiom,
( c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_real__of__nat__less__iff_1,
[final] ).
cnf(i_0_827,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_828,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_829,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_830,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_831,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_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal) ),
cls_real__of__nat__gt__zero__cancel__iff_0,
[final] ).
cnf(i_0_832,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_833,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_834,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_835,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_836,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_837,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_838,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_839,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_840,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_841,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_842,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_843,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_844,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,
[final] ).
cnf(i_0_845,axiom,
( c_lessequals(c_RealDef_Oreal(c_RComplete_Onatfloor(X1),tc_nat),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_real__natfloor__le_0,
[final] ).
cnf(i_0_846,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_847,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_848,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_abs__le__interval__iff_1,
[final] ).
cnf(i_0_849,axiom,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__div__trivial_0,
[final] ).
cnf(i_0_850,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__le__antisym_0,
[final] ).
cnf(i_0_851,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_852,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_853,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_854,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_real__of__nat__gt__zero__cancel__iff_1,
[final] ).
cnf(i_0_855,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,
[final] ).
cnf(i_0_856,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,
[final] ).
cnf(i_0_857,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_858,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,
[final] ).
cnf(i_0_859,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),tc_RealDef_Oreal) ),
cls_zero__less__norm__iff_0,
[final] ).
cnf(i_0_860,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_861,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_862,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_863,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_864,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_865,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_866,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_867,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_868,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,
[final] ).
cnf(i_0_869,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,
[final] ).
cnf(i_0_870,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_871,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,
[final] ).
cnf(i_0_872,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,
[final] ).
cnf(i_0_873,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,
[final] ).
cnf(i_0_874,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,
[final] ).
cnf(i_0_875,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_876,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_877,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,
[final] ).
cnf(i_0_878,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_879,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,
[final] ).
cnf(i_0_880,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_881,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_882,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,
[final] ).
cnf(i_0_883,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_norm__le__zero__iff_0,
[final] ).
cnf(i_0_884,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__less__def_2,
[final] ).
cnf(i_0_885,axiom,
( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_div__less_0,
[final] ).
cnf(i_0_886,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_887,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_888,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
cls_real__less__def_0,
[final] ).
cnf(i_0_889,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_norm__not__less__zero_0,
[final] ).
cnf(i_0_890,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_891,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_892,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_893,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__of__nat__le__zero__cancel__iff_0,
[final] ).
cnf(i_0_894,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
cls_real__add__minus__iff_0,
[final] ).
cnf(i_0_895,axiom,
~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_not__real__of__nat__less__zero_0,
[final] ).
cnf(i_0_896,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_897,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_898,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_899,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_900,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_901,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_902,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_903,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,
[final] ).
cnf(i_0_904,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_905,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_906,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_907,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_908,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__linear_0,
[final] ).
cnf(i_0_909,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_910,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_911,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_912,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_913,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_914,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,
[final] ).
cnf(i_0_915,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_916,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__abs__def_0,
[final] ).
cnf(i_0_917,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,
[final] ).
cnf(i_0_918,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,
[final] ).
cnf(i_0_919,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_920,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_921,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,
[final] ).
cnf(i_0_922,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,
[final] ).
cnf(i_0_923,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_924,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_925,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_926,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_927,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,
[final] ).
cnf(i_0_928,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,
[final] ).
cnf(i_0_929,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,
[final] ).
cnf(i_0_930,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,
[final] ).
cnf(i_0_931,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,
[final] ).
cnf(i_0_932,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
cls_real__le__linear_0,
[final] ).
cnf(i_0_933,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_934,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_935,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_936,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,
[final] ).
cnf(i_0_937,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,
[final] ).
cnf(i_0_938,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__le__zero__iff_1,
[final] ).
cnf(i_0_939,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
cls_real__add__eq__0__iff_0,
[final] ).
cnf(i_0_940,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_941,axiom,
c_RealDef_Oreal(c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__of__nat__Suc_0,
[final] ).
cnf(i_0_942,axiom,
( c_RComplete_Onatfloor(X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_natfloor__neg_0,
[final] ).
cnf(i_0_943,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_zero__less__norm__iff_1,
[final] ).
cnf(i_0_944,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_945,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_946,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_947,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__le_1,
[final] ).
cnf(i_0_948,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__irrefl_0,
[final] ).
cnf(i_0_949,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__neq__iff_1,
[final] ).
cnf(i_0_950,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_951,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_952,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_953,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_954,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_955,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(X1),tc_nat),tc_RealDef_Oreal),
cls_real__of__nat__Suc__gt__zero_0,
[final] ).
cnf(i_0_956,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_957,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_958,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_959,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__ge__zero_0,
[final] ).
cnf(i_0_960,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_961,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_962,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_not__less0_0,
[final] ).
cnf(i_0_963,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_964,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_965,axiom,
c_lessequals(c_RealDef_Oreal(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__of__nat__le__zero__cancel__iff_1,
[final] ).
cnf(i_0_966,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_967,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
cls_real__less__def_1,
[final] ).
cnf(i_0_968,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_nat__less__le_1,
[final] ).
cnf(i_0_969,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_less__not__refl_0,
[final] ).
cnf(i_0_970,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_971,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal),
cls_real__of__nat__ge__zero_0,
[final] ).
cnf(i_0_972,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_973,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_974,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_975,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
cls_real__add__eq__0__iff_1,
[final] ).
cnf(i_0_976,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_977,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_978,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_979,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,
[final] ).
cnf(i_0_980,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,
[final] ).
cnf(i_0_981,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,
[final] ).
cnf(i_0_982,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,
[final] ).
cnf(i_0_983,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_984,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_985,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_986,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_987,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__0_0,
[final] ).
cnf(i_0_988,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_989,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__by__0_0,
[final] ).
cnf(i_0_990,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_991,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_992,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_993,axiom,
( c_Divides_Odiv__class_Odiv(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__self_0,
[final] ).
cnf(i_0_994,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__abs__def_1,
[final] ).
cnf(i_0_995,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_996,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_997,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_998,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_999,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_1000,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__by__1_0,
[final] ).
cnf(i_0_1001,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_1002,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_1003,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_1004,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_1005,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,
[final] ).
cnf(i_0_1006,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,
[final] ).
cnf(i_0_1007,axiom,
c_Divides_Odiv__class_Odiv(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X1,
cls_div__1_0,
[final] ).
cnf(i_0_1008,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_1009,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
cls_gr0__conv__Suc_1,
[final] ).
cnf(i_0_1010,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
cls_zero__less__Suc_0,
[final] ).
cnf(i_0_1011,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0,
[final] ).
cnf(i_0_1012,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
cls_order__eq__refl_0,
[final] ).
cnf(i_0_1013,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_1014,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_1015,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_1016,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_1017,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__minus__cancel_0,
[final] ).
cnf(i_0_1018,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_1019,axiom,
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_abs__norm__cancel_0,
[final] ).
cnf(i_0_1020,axiom,
c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_th000_I2_J_0,
[final] ).
cnf(i_0_1021,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_th000_I1_J_0,
[final] ).
cnf(i_0_1022,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
cls_less__Suc__eq_2,
[final] ).
cnf(i_0_1023,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
cls_lessI_0,
[final] ).
cnf(i_0_1024,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_1025,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_1026,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_1027,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_1028,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_1029,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_1030,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
cls_real__le__refl_0,
[final] ).
cnf(i_0_1031,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_1032,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_1033,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_1034,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_1035,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_1036,axiom,
c_HOL_Oabs__class_Oabs(c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal) = c_RealDef_Oreal(X1,tc_nat),
cls_abs__real__of__nat__cancel_0,
[final] ).
cnf(i_0_1037,axiom,
( X1 = X2
| c_RealDef_Oreal(X1,tc_nat) != c_RealDef_Oreal(X2,tc_nat) ),
cls_real__of__nat__inject_0,
[final] ).
cnf(i_0_1038,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_1039,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_1040,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_1041,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X2,X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
cls_norm__eq__zero_0,
[final] ).
cnf(i_0_1042,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_1043,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_1044,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_1045,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_1046,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_1047,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_1048,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
cls_norm__one_0,
[final] ).
cnf(i_0_1049,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__zero_0,
[final] ).
cnf(i_0_1050,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_1051,axiom,
c_RComplete_Onatfloor(c_RealDef_Oreal(X1,tc_nat)) = X1,
cls_natfloor__real__of__nat_0,
[final] ).
cnf(i_0_1052,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_RealDef_Oreal(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
cls_real__of__nat__zero__iff_0,
[final] ).
cnf(i_0_1053,axiom,
c_RealDef_Oreal(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
cls_real__of__nat__one_0,
[final] ).
cnf(i_0_1054,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_1055,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_1056,axiom,
c_RealDef_Oreal(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
cls_real__of__nat__zero_0,
[final] ).
cnf(i_0_1057,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
cls_nat_Oinject_0,
[final] ).
cnf(i_0_1058,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
cls_Suc__inject_0,
[final] ).
cnf(i_0_1059,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
cls_Zero__neq__Suc_0,
[final] ).
cnf(i_0_1060,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
cls_nat_Osimps_I2_J_0,
[final] ).
cnf(i_0_1061,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
cls_Suc__neq__Zero_0,
[final] ).
cnf(i_0_1062,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
cls_nat_Osimps_I3_J_0,
[final] ).
cnf(i_0_1063,axiom,
c_RComplete_Onatfloor(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_natfloor__zero_0,
[final] ).
cnf(i_0_1064,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
cls_real__zero__not__eq__one_0,
[final] ).
cnf(i_0_1065,axiom,
c_Suc(X1) != X1,
cls_Suc__n__not__n_0,
[final] ).
cnf(i_0_1066,axiom,
X1 != c_Suc(X1),
cls_n__not__Suc__n_0,
[final] ).
cnf(i_0_1067,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_1068,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_1069,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_1070,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_1071,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_1072,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_1073,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,
[final] ).
cnf(i_0_1074,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,
[final] ).
cnf(i_0_1075,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,
[final] ).
cnf(i_0_1076,axiom,
class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Nat_Osemiring__char__0,
[final] ).
cnf(i_0_1077,axiom,
class_Nat_Osemiring__char__0(tc_nat),
clsarity_nat__Nat_Osemiring__char__0,
[final] ).
cnf(i_0_1078,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,
[final] ).
cnf(i_0_1079,axiom,
class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1,
[final] ).
cnf(i_0_1080,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring__1,
[final] ).
cnf(i_0_1081,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_1082,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,
[final] ).
cnf(i_0_1083,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Oorder,
[final] ).
cnf(i_0_1084,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat__Orderings_Oorder,
[final] ).
cnf(i_0_1085,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Opreorder,
[final] ).
cnf(i_0_1086,axiom,
class_Orderings_Opreorder(tc_nat),
clsarity_nat__Orderings_Opreorder,
[final] ).
cnf(i_0_1087,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Olinorder,
[final] ).
cnf(i_0_1088,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder,
[final] ).
cnf(i_0_1089,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,
[final] ).
cnf(i_0_1090,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
[final] ).
cnf(i_0_1091,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_1092,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_1093,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_1094,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_1095,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,
[final] ).
cnf(i_0_1096,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_1097,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
clsarity_nat__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_1098,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Onumber__ring,
[final] ).
cnf(i_0_1099,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_1100,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_1101,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_1102,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_1103,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_1104,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,
[final] ).
cnf(i_0_1105,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__semidom,
[final] ).
cnf(i_0_1106,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,
[final] ).
cnf(i_0_1107,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_1108,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
clsarity_nat__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_1109,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,
[final] ).
cnf(i_0_1110,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,
[final] ).
cnf(i_0_1111,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,
[final] ).
cnf(i_0_1112,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ofield,
[final] ).
cnf(i_0_1113,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,
[final] ).
cnf(i_0_1114,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,
[final] ).
cnf(i_0_1115,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,
[final] ).
cnf(i_0_1116,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_1117,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,
[final] ).
cnf(i_0_1118,axiom,
class_Divides_Osemiring__div(tc_nat),
clsarity_nat__Divides_Osemiring__div,
[final] ).
cnf(i_0_1119,axiom,
X1 = X1 ).
cnf(i_0_1120,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1121,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1122,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_1123,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_1124,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_1125,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1126,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_1127,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_1128,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_1129,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_1130,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_1131,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_1132,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).
cnf(i_0_1133,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).
cnf(i_0_1134,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_1135,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_1136,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X1,X3,X4) = c_HOL_Oinverse__class_Odivide(X2,X3,X4) ) ).
cnf(i_0_1137,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X3,X1,X4) = c_HOL_Oinverse__class_Odivide(X3,X2,X4) ) ).
cnf(i_0_1138,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X3,X4,X1) = c_HOL_Oinverse__class_Odivide(X3,X4,X2) ) ).
cnf(i_0_1139,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_1140,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_1141,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_1142,axiom,
( X1 != X2
| c_Suc(X1) = c_Suc(X2) ) ).
cnf(i_0_1143,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_1144,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_1145,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_1146,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_1147,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_1148,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_1149,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_1150,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_1151,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1152,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| class_Ring__and__Field_Odivision__by__zero(X2) ) ).
cnf(i_0_1153,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1154,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1155,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_1156,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ofield(X2) ) ).
cnf(i_0_1157,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1158,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_1159,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_1160,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1161,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1162,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1163,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1164,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1165,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_1166,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_1167,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_1168,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1169,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1170,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1171,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__1(X1)
| class_Ring__and__Field_Osemiring__1(X2) ) ).
cnf(i_0_1172,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_1173,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1174,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_1175,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_1176,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1177,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1178,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1179,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oabs__if(X1)
| class_Ring__and__Field_Oabs__if(X2) ) ).
cnf(i_0_1180,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_1181,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_1182,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_1183,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_1184,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_1185,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__field(X2) ) ).
cnf(i_0_1186,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_1187,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1188,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1189,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1190,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1119_001,axiom,
X1 = X1 ).
cnf(i_0_1120_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1121_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1122_004,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_1123_005,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_1124_006,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_1125_007,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1126_008,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_1127_009,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_1128_010,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_1129_011,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_1130_012,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_1131_013,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_1132_014,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).
cnf(i_0_1133_015,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).
cnf(i_0_1134_016,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_1135_017,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_1136_018,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X1,X3,X4) = c_HOL_Oinverse__class_Odivide(X2,X3,X4) ) ).
cnf(i_0_1137_019,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X3,X1,X4) = c_HOL_Oinverse__class_Odivide(X3,X2,X4) ) ).
cnf(i_0_1138_020,axiom,
( X1 != X2
| c_HOL_Oinverse__class_Odivide(X3,X4,X1) = c_HOL_Oinverse__class_Odivide(X3,X4,X2) ) ).
cnf(i_0_1139_021,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_1140_022,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_1141_023,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_1142_024,axiom,
( X1 != X2
| c_Suc(X1) = c_Suc(X2) ) ).
cnf(i_0_1143_025,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_1144_026,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_1145_027,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_1146_028,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_1147_029,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_1148_030,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_1149_031,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_1150_032,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_1151_033,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1152_034,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| class_Ring__and__Field_Odivision__by__zero(X2) ) ).
cnf(i_0_1153_035,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1154_036,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1155_037,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_1156_038,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ofield(X2) ) ).
cnf(i_0_1157_039,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1158_040,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_1159_041,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_1160_042,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1161_043,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1162_044,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1163_045,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1164_046,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1165_047,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_1166_048,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_1167_049,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_1168_050,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1169_051,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1170_052,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1171_053,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__1(X1)
| class_Ring__and__Field_Osemiring__1(X2) ) ).
cnf(i_0_1172_054,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_1173_055,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1174_056,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_1175_057,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_1176_058,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1177_059,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1178_060,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1179_061,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oabs__if(X1)
| class_Ring__and__Field_Oabs__if(X2) ) ).
cnf(i_0_1180_062,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_1181_063,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_1182_064,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_1183_065,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_1184_066,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_1185_067,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__field(X2) ) ).
cnf(i_0_1186_068,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_1187_069,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1188_070,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1189_071,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1190_072,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1191,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,[],[608]) ).
cnf(i_0_1192,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,[],[682]) ).
cnf(i_0_1193,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[819]) ).
cnf(i_0_1194,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[833]) ).
cnf(i_0_1195,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[834]) ).
cnf(i_0_1196,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[835]) ).
cnf(i_0_1197,plain,
X1 = X1,
inference(equality_inference,[],[851]) ).
cnf(i_0_1198,plain,
X1 = X1,
inference(equality_inference,[],[853]) ).
cnf(i_0_1199,plain,
( X1 = X1
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(equality_inference,[],[1027]) ).
cnf(i_0_1200,plain,
( X1 = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(equality_inference,[],[1028]) ).
cnf(i_0_1201,plain,
( X1 = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(equality_inference,[],[1029]) ).
cnf(i_0_1202,plain,
X1 = X1,
inference(equality_inference,[],[1037]) ).
cnf(i_0_1203,plain,
X1 = X1,
inference(equality_inference,[],[1058]) ).
cnf(i_0_1204,plain,
$false,
inference(scs_inference,[],[i_0_560,i_0_1073,i_0_562,i_0_1030,i_0_603]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG377-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:32:41 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.70/1.67 % Version : CSE_E---1.7
% 0.70/1.67 % Problem : theBenchmark.p
% 0.70/1.67 % SZS status Unsatisfiable for theBenchmark.p
% 0.70/1.67 % SZS output start CNFRefutation
% See solution above
% 0.75/1.72 % Total time : 1.325s
%------------------------------------------------------------------------------