TSTP Solution File: SWV595-1 by Mace4---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Mace4---1109a
% Problem : SWV595-1 : TPTP v6.4.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : mace4 -t %d -f %s
% Computer : n031.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.75MB
% OS : Linux 3.10.0-327.36.3.el7.x86_64
% CPULimit : 300s
% DateTime : Wed Feb 8 10:07:54 EST 2017
% Result : Satisfiable 0.41s
% Output : FiniteModel 0.41s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV595-1 : TPTP v6.4.0. Released v4.1.0.
% 0.00/0.04 % Command : mace4 -t %d -f %s
% 0.03/0.23 % Computer : n031.star.cs.uiowa.edu
% 0.03/0.23 % Model : x86_64 x86_64
% 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23 % Memory : 32218.75MB
% 0.03/0.23 % OS : Linux 3.10.0-327.36.3.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Tue Feb 7 23:16:16 CST 2017
% 0.03/0.23 % CPUTime :
% 0.41/0.68 % SZS status Satisfiable
% 0.41/0.68 ============================== Mace4 =================================
% 0.41/0.68 Mace4 (32) version 2009-11A, November 2009.
% 0.41/0.68 Process 54545 was started by sandbox2 on n031.star.cs.uiowa.edu,
% 0.41/0.68 Tue Feb 7 23:16:16 2017
% 0.41/0.68 The command was "/export/starexec/sandbox2/solver/bin/mace4 -t 300 -f /tmp/Mace4_input_54512_n031.star.cs.uiowa.edu".
% 0.41/0.68 ============================== end of head ===========================
% 0.41/0.68
% 0.41/0.68 ============================== INPUT =================================
% 0.41/0.68
% 0.41/0.68 % Reading from file /tmp/Mace4_input_54512_n031.star.cs.uiowa.edu
% 0.41/0.68
% 0.41/0.68 set(prolog_style_variables).
% 0.41/0.68 set(print_models_tabular).
% 0.41/0.68 % set(print_models_tabular) -> clear(print_models).
% 0.41/0.68
% 0.41/0.68 formulas(sos).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oab__semigroup__mult(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom).
% 0.41/0.68 -class_Divides_Oring__div(T_a) | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) # label(cls_dvd__neg__div_0) # label(axiom).
% 0.41/0.68 -class_Divides_Oring__div(T_a) | c_Divides_Odiv__class_Odiv(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) # label(cls_dvd__div__neg_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(T_a) | c_RealVector_Oof__real(V_r,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Oone__class_Oone(T_a),T_a) # label(cls_of__real__def_0) # label(axiom).
% 0.41/0.68 -class_Int_Onumber__ring(T_a) | c_HOL_Ouminus__class_Ouminus(V_x,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_x,T_a) # label(cls_class__ring_Oneg__mul_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) | V_b = c_HOL_Ozero__class_Ozero(T_a) | V_a = V_b # label(cls_right__inverse__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_mult__nonneg__nonneg_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_zero__le__mult__iff_5) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_zero__le__mult__iff_4) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) # label(cls_zero__le__square_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_mult__nonpos__nonpos_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_split__mult__pos__le_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_split__mult__pos__le_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) # label(cls_inverse__minus__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) # label(cls_power__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),T_a) | -c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_a,V_b,T_a) # label(cls_divide__right__mono__neg_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) | -c_lessequals(V_a,V_b,T_a) # label(cls_divide__right__mono_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ocomm__monoid__mult(T_a) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) # label(cls_power__mult__distrib_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_q,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),c_Power_Opower__class_Opower(V_y,V_q,T_a),T_a) # label(cls_class__semiring_Opwr__mul_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(T_a) | c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(V_x,T_a),c_RealVector_Oof__real(V_y,T_a),T_a) # label(cls_of__real__mult_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_inverse__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_inverse__nonzero__iff__nonzero_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) | V_a = V_b | V_b = c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_nonzero__inverse__eq__imp__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) | V_a = V_b # label(cls_inverse__eq__iff__eq_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(T_a) | c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_of__real__eq__0__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oab__semigroup__idem__mult(T_a) | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x # label(cls_mult__idem_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b # label(cls_inverse__unique_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Log_Opowr(V_x,V_a),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) # label(cls_ge__one__powr__ge__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) | -c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_b,V_a,T_a) # label(cls_mult__right__mono__neg_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) | -c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_b,V_a,T_a) # label(cls_mult__left__mono__neg_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Omult__mono(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) | -c_lessequals(V_a,V_b,T_a) # label(cls_mult__right__mono_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Omult__mono(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) | -c_lessequals(V_a,V_b,T_a) # label(cls_mult__left__mono_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Omult__mono1(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) | -c_lessequals(V_a,V_b,T_a) # label(cls_mult__mono1_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_b,V_a,T_a) # label(cls_inverse__divide_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(V_x,T_a),T_a) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | V_x = c_HOL_Ozero__class_Ozero(T_a) # label(cls_norm__sgn_1) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(V_x) != c_NthRoot_Osqrt(V_y) | V_x = V_y # label(cls_real__sqrt__eq__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) # label(cls_dvd__mult__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) # label(cls_dvd__mult__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) # label(cls_dvd__mult2_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) # label(cls_dvd__mult_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) # label(cls_real__sqrt__ge__zero_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) # label(cls_real__sqrt__ge__0__iff_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) # label(cls_real__sqrt__ge__0__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) | -c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) # label(cls_abs__le__D2_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ouminus__class_Ouminus(V_r,tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) # label(cls_abs__le__interval__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_mult__le__0__iff_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_mult__le__0__iff_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_mult__le__0__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_mult__le__0__iff_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_div__mult__mult1__if_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | V_x = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | V_x = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__mult__is__one_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_neg__le__0__iff__le_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_neg__le__0__iff__le_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),c_Divides_Odiv__class_Odiv(V_w,V_z,T_a),T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_x,V_w,T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) # label(cls_div__mult__div__if__dvd_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_field__power__not__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ozero__neq__one(T_a) | -class_Ring__and__Field_Ono__zero__divisors(T_a) | -class_Ring__and__Field_Omult__zero(T_a) | -class_Power_Opower(T_a) | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_power__eq__0__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oab__semigroup__idem__mult(T_a) | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) # label(cls_mult__left__idem_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring(T_a) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) # label(cls_minus__mult__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring(T_a) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) # label(cls_minus__mult__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(V_x,T_a),T_a) # label(cls_sgn__minus_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_z,V_w,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_y,V_w,T_a),T_a) # label(cls_mult__frac__frac_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring__abs(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_abs__eq__mult_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring__abs(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_abs__eq__mult_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring__abs(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_abs__eq__mult_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring__abs(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_abs__eq__mult_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) # label(cls_abs__mult_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(T_a) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) # label(cls_dvd__mult__cancel__right_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(T_a) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) # label(cls_dvd__mult__cancel__left_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) # label(cls_dvd__trans_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a) # label(cls_dvd__refl_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_abs__of__nonneg_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Oorder(T_a) | V_x = V_y | -c_lessequals(V_x,V_y,T_a) | -c_lessequals(V_y,V_x,T_a) # label(cls_order__antisym__conv_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Oorder(T_a) | V_x = V_y | -c_lessequals(V_y,V_x,T_a) | -c_lessequals(V_x,V_y,T_a) # label(cls_order__eq__iff_2) # label(axiom).
% 0.41/0.68 -class_Orderings_Oorder(T_a) | V_x = V_y | -c_lessequals(V_y,V_x,T_a) | -c_lessequals(V_x,V_y,T_a) # label(cls_order__antisym_0) # label(axiom).
% 0.41/0.68 V_z = V_w | -c_lessequals(V_w,V_z,tc_RealDef_Oreal) | -c_lessequals(V_z,V_w,tc_RealDef_Oreal) # label(cls_real__le__antisym_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) # label(cls_power__divide_0) # label(axiom).
% 0.41/0.68 -class_Lattices_Oboolean__algebra(T_a) | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a) | V_x = V_y # label(cls_compl__eq__compl__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(T_a) | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) | V_a = V_b # label(cls_neg__equal__iff__equal_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | V_c = c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) # label(cls_eq__divide__imp_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | V_c = c_HOL_Ozero__class_Ozero(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a # label(cls_divide__eq__imp_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) | V_c = c_HOL_Ozero__class_Ozero(T_a) # label(cls_eq__divide__eq_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a | V_c = c_HOL_Ozero__class_Ozero(T_a) # label(cls_divide__eq__eq_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_divide__le__0__1__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_divide__le__0__1__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) | -c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_abs__le__zero__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(T_a) | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_neg__equal__0__iff__equal_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(T_a) | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_of__real__0_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | -class_RealVector_Oreal__algebra__1(T_a) | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_of__real_Ozero_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = V_a | V_b = c_HOL_Ozero__class_Ozero(T_a) # label(cls_div__mult__self2__is__id_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_z1,V_z2,tc_RealDef_Oreal),V_z3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_z1,c_HOL_Otimes__class_Otimes(V_z2,V_z3,tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__mult__assoc_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) # label(cls_class__semiring_Omul__a_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) # label(cls_minus__divide__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) # label(cls_minus__divide__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) # label(cls_zero__le__mult__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) # label(cls_zero__le__mult__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) # label(cls_zero__le__mult__iff_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) # label(cls_zero__le__mult__iff_3) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(T_a) | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_neg__equal__zero_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_Transcendental_Osin(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_sin__le__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_nonzero__inverse__eq__divide_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) # label(cls_mult_Ominus__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) # label(cls_mult__left_Ominus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) # label(cls_mult_Ominus__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) # label(cls_mult__right_Ominus_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) # label(cls_square__eq__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) # label(cls_minus__mult__minus_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_field__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_left__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_right__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(V_c,V_d,T_a) | -c_lessequals(V_a,V_b,T_a) # label(cls_mult__mono_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(V_c,V_d,T_a) | -c_lessequals(V_a,V_b,T_a) # label(cls_mult__mono_H_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a) | V_c = c_HOL_Ozero__class_Ozero(T_a) # label(cls_div__mult__mult1_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a) | V_c = c_HOL_Ozero__class_Ozero(T_a) # label(cls_div__mult__mult2_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) = c_HOL_Osgn__class_Osgn(V_a,T_a) # label(cls_sgn__sgn_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) # label(cls_norm__ge__zero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(T_a) | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(V_x,T_a),T_a) # label(cls_of__real__minus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | -class_RealVector_Oreal__algebra__1(T_a) | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(V_x,T_a),T_a) # label(cls_of__real_Ominus_0) # label(axiom).
% 0.41/0.68 c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_sin__zero_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_real__sqrt__zero_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__sqrt__le__1__iff_1) # label(axiom).
% 0.41/0.68 c_lessequals(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__sqrt__le__1__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Oabs__class_Oabs(V_k,T_a) = c_HOL_Otimes__class_Otimes(V_k,c_HOL_Osgn__class_Osgn(V_k,T_a),T_a) # label(cls_abs__sgn_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_real__sum__squares__cancel__a_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) | V_y = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_real__sum__squares__cancel__a_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) | V_b = c_HOL_Ozero__class_Ozero(T_a) # label(cls_nonzero__minus__divide__divide_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) # label(cls_div__dvd__div_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) # label(cls_div__dvd__div_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__ring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) # label(cls_dvd__minus__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__ring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) # label(cls_dvd__minus__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__ring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) # label(cls_minus__dvd__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__ring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) # label(cls_minus__dvd__iff_1) # label(axiom).
% 0.41/0.68 c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) # label(cls_sin__minus_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),V_x,T_a) | -c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) # label(cls_mult__left__le__one__le_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_x,T_a) | -c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) # label(cls_mult__right__le__one__le_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) | -c_lessequals(V_a,V_b,tc_RealDef_Oreal) # label(cls_powr__mono_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_divide__self__if_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) | -c_lessequals(V_x,V_r,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(V_r,tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) # label(cls_abs__le__interval__iff_2) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) | -c_lessequals(V_a,V_b,T_a) # label(cls_abs__leI_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) | -c_lessequals(V_a,V_b,T_a) # label(cls_abs__le__iff_2) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) # label(cls_abs__minus__cancel_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_mult__le__0__iff_4) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_mult__le__0__iff_5) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_split__mult__neg__le_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_split__mult__neg__le_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_mult__nonneg__nonpos_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_mult__nonpos__nonneg_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_mult__nonneg__nonpos2_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) # label(cls_inverse__mult__distrib_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) | V_b = c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_nonzero__inverse__mult__distrib_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_abs__le__zero__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_dvd__0__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_nonzero__inverse__inverse__eq_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_abs__sin__le__one_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) # label(cls_neg__0__le__iff__le_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_neg__0__le__iff__le_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_x = c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_scaleR__eq__0__iff_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_a,T_a),V_b,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) # label(cls_mult_OscaleR__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) # label(cls_mult__left_OscaleR_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) # label(cls_mult_OscaleR__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(V_xa,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) # label(cls_mult__right_OscaleR_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra(T_a) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) # label(cls_mult__scaleR__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra(T_a) | c_HOL_Otimes__class_Otimes(V_x,c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) # label(cls_mult__scaleR__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) # label(cls_norm__scaleR_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_nonzero__abs__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) | V_b = c_HOL_Ozero__class_Ozero(T_a) # label(cls_nonzero__abs__divide_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_real__sqrt__eq__zero__cancel_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a),T_a) # label(cls_zero__le__power__abs_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) | -c_lessequals(V_x,V_y,tc_RealDef_Oreal) # label(cls_real__sqrt__le__iff_1) # label(axiom).
% 0.41/0.68 c_lessequals(V_x,V_y,tc_RealDef_Oreal) | -c_lessequals(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) # label(cls_real__sqrt__le__iff_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__field(T_a) | c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) # label(cls_divide_OscaleR_0) # label(axiom).
% 0.41/0.68 V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_c,c_HOL_Oabs__class_Oabs(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_rabs__ratiotest__lemma_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) # label(cls_inverse__nonnegative__iff__nonnegative_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_inverse__nonnegative__iff__nonnegative_1) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Divides_Odiv__class_Odiv(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_div__self_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_real__sqrt__eq__0__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_zero__le__power__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__semidom(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_zero__le__power_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Olordered__ab__group__add(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) # label(cls_le__minus__self__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Olordered__ab__group__add(T_a) | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_le__minus__self__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Olordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) # label(cls_minus__le__self__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Olordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_minus__le__self__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) # label(cls_less__eq__neg__nonpos_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(T_a) | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_less__eq__neg__nonpos_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) # label(cls_neg__less__eq__nonneg_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_neg__less__eq__nonneg_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra__1(T_a) | c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(V_r,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) # label(cls_norm__of__real_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = V_a | V_b = c_HOL_Ozero__class_Ozero(T_a) # label(cls_div__mult__self1__is__id_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring__no__zero__divisors(T_a) | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_b = c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_mult__eq__0__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ono__zero__divisors(T_a) | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_b = c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_no__zero__divisors_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ono__zero__divisors(T_a) | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) | V_b = c_HOL_Ozero__class_Ozero(T_a) # label(cls_no__zero__divirors__neq0_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_div__by__0_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_div__0_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(T_a) | c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) | V_a = V_b # label(cls_square__eq__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a),T_a) # label(cls_dvd__power_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Oabs__class_Oabs(V_x,T_a),T_a) = V_x # label(cls_mult__sgn__abs_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) | -c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_inverse__le__1__iff_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__mult__ineq_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_a,T_a) # label(cls_abs__norm__cancel_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) # label(cls_zero__le__divide__1__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) # label(cls_zero__le__divide__1__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_divide__le__0__iff_5) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_divide__le__0__iff_4) # label(axiom).
% 0.41/0.68 c_Log_Opowr(c_Log_Opowr(V_x,V_a),V_b) = c_Log_Opowr(c_Log_Opowr(V_x,V_b),V_a) # label(cls_powr__powr__swap_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) # label(cls_scaleR__minus__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) # label(cls_scaleR_Ominus__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) # label(cls_scaleR__minus__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_xa,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_x,V_xa,T_a),T_a) # label(cls_scaleR__left_Ominus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) # label(cls_scaleR_Ominus__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | V_x = c_HOL_Ozero__class_Ozero(T_a) # label(cls_norm__eq__zero_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_abs__minus__le__zero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(T_a) | c_RealVector_Oof__real(V_x,T_a) != c_RealVector_Oof__real(V_y,T_a) | V_x = V_y # label(cls_of__real__eq__iff_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__le__zero__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(V_a,V_b,T_a) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) # label(cls_neg__le__iff__le_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) | -c_lessequals(V_a,V_b,T_a) # label(cls_le__imp__neg__le_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Olordered__ring(T_a) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) # label(cls_abs__le__mult_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_lessequals(V_a,V_b,T_a) | -c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) # label(cls_abs__le__D1_0) # label(axiom).
% 0.41/0.68 c_lessequals(V_x,V_r,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) # label(cls_abs__le__interval__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) # label(cls_inverse__eq__divide_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Int_Onumber__ring(T_a) | c_HOL_Oinverse__class_Oinverse(V_x,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a) # label(cls_class__fieldgb_Oinverse__divide_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | V_x = c_HOL_Ozero__class_Ozero(T_a) | -c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__le__zero__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) # label(cls_dvd__triv__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) # label(cls_dvd__triv__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odvd(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a) # label(cls_dvdI_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) # label(cls_power__one__over_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) | V_b = c_HOL_Ozero__class_Ozero(T_a) # label(cls_nonzero__minus__divide__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a # label(cls_inverse__inverse__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) # label(cls_class__semiring_Omul__c_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(V_z,V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,V_z,tc_RealDef_Oreal) # label(cls_real__mult__commute_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_abs__eq__0_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(T_a) | c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(V_r,T_a),V_x,T_a) # label(cls_scaleR__conv__of__real_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(T_a) | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a) | c_HOL_Ozero__class_Ozero(T_a) = V_a # label(cls_neg__0__equal__iff__equal_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | V_x = c_HOL_Ozero__class_Ozero(T_a) | c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a) # label(cls_right__inverse__eq_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_divide__self_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_divide__self__if_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) # label(cls_zero__le__divide__iff_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) # label(cls_zero__le__divide__iff_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) # label(cls_zero__le__divide__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) # label(cls_zero__le__divide__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__semidom(T_a) | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(V_a,V_b,T_a) # label(cls_power__mono_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) # label(cls_inverse__le__1__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | V_x = c_HOL_Ozero__class_Ozero(T_a) | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_power__le__zero__eq_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) # label(cls_minus__divide__divide_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__field(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) # label(cls_divide_Ominus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_RealDef_Oreal),V_x,T_a) # label(cls_real__vector_Oscale__scale_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_scaleR_Ozero__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_scaleR_Ozero__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_scaleR__eq__0__iff_2) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_scaleR__eq__0__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_divide__zero__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_divide__eq__eq_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_divide__zero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__field(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_divide_Ozero_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) # label(cls_real__sqrt__mult_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_inverse__nonpositive__iff__nonpositive_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_inverse__nonpositive__iff__nonpositive_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_c,T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),V_a,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) # label(cls_dvd__div__mult_0) # label(axiom).
% 0.41/0.68 c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__sqrt__le__0__iff_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__sqrt__le__0__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a) # label(cls_power__abs_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) # label(cls_dvd__power__same_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) # label(cls_abs__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) # label(cls_abs__divide_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_sgn__0__0_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_HOL_Osgn__class_Osgn(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_x = c_HOL_Ozero__class_Ozero(T_a) # label(cls_sgn__zero__iff_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_u,V_u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__minus__mult__self__le_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) | V_c = c_HOL_Ozero__class_Ozero(T_a) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) | V_c = c_HOL_Ozero__class_Ozero(T_a) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),V_y,T_a) # label(cls_mult__frac__num_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a) = V_b | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) # label(cls_dvd__mult__div__cancel_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a) = V_b | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) # label(cls_dvd__div__mult__self_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_abs__of__nonpos_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) | V_c = c_HOL_Ozero__class_Ozero(T_a) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) # label(cls_dvd__mult__cancel__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) | V_c = c_HOL_Ozero__class_Ozero(T_a) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) # label(cls_dvd__mult__cancel__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) | -c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) # label(cls_le__divide__eq_9) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) | -c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) # label(cls_divide__le__eq_9) # label(axiom).
% 0.41/0.68 c_Fun_Oid(V_x,T_a) = V_x # label(cls_id__apply_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(T_a) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b # label(cls_minus__equation__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(T_a) | V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) # label(cls_equation__minus__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(T_a) | V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) # label(cls_equation__minus__iff_0) # label(axiom).
% 0.41/0.68 -class_Lattices_Oboolean__algebra(T_a) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x # label(cls_double__compl_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(T_a) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a # label(cls_minus__minus_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) # label(cls_minus__le__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) # label(cls_minus__le__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) | -c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) # label(cls_le__minus__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) | -c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) # label(cls_le__minus__iff_0) # label(axiom).
% 0.41/0.68 c_Transcendental_Osin(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(V_x),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_sin__zero__abs__cos__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(T_a) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) # label(cls_dvd__mult__cancel__left_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(T_a) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) # label(cls_dvd__mult__cancel__right_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__semidom(T_a) | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) | -c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) # label(cls_one__le__power_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) # label(cls_abs__idempotent_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) # label(cls_norm__minus__cancel_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) # label(cls_real__sqrt__minus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) # label(cls_scaleR_OscaleR__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) # label(cls_scaleR__left__commute_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_ra,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_ra,V_x,T_a),T_a) # label(cls_scaleR__right_OscaleR_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_divide__le__0__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) | -c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_divide__le__0__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_divide__le__0__iff_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_divide__le__0__iff_3) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_norm__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring__1(T_a) | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_n,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) # label(cls_power__minus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__div__algebra(T_a) | c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal) # label(cls_norm__mult_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Omonoid__mult(T_a) | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) # label(cls_power__commutes_0) # label(axiom).
% 0.41/0.68 c_Log_Opowr(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_powr__zero__eq__one_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(V_c,V_a,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_c,V_b,tc_RealDef_Oreal) | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | V_a = V_b # label(cls_real__mult__left__cancel_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(V_a,V_c,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_b,V_c,tc_RealDef_Oreal) | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | V_a = V_b # label(cls_real__mult__right__cancel_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) | -c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) # label(cls_inverse__le__1__iff_2) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) # label(cls_abs__ge__minus__self_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) # label(cls_abs__ge__self_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) # label(cls_eq__divide__eq_4) # label(axiom).
% 0.41/0.68 c_Log_Opowr(V_x,V_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_powr__not__zero_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),V_n,T_a) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) # label(cls_div__power_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) # label(cls_abs__mult__self_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_nonzero__power__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_nonzero__inverse__minus__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_dvd__0__right_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) # label(cls_real__sqrt__ge__1__iff_1) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) # label(cls_real__sqrt__ge__1__iff_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) # label(cls_real__sqrt__ge__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) | V_c = c_HOL_Ozero__class_Ozero(T_a) # label(cls_divide__eq__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b | V_c = c_HOL_Ozero__class_Ozero(T_a) # label(cls_eq__divide__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__semidom(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) # label(cls_zero__le__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_mult__left_Ozero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_mult_Ozero__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_mult_Ozero__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(T_a) | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_mult__right_Ozero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_class__semiring_Omul__0_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Omult__zero(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_mult__zero__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Omult__zero(T_a) | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_mult__zero__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring__no__zero__divisors(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_mult__eq__0__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring__no__zero__divisors(T_a) | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_mult__eq__0__iff_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) # label(cls_abs__power__minus_0) # label(axiom).
% 0.41/0.68 c_Log_Opowr(c_Log_Opowr(V_x,V_a),V_b) = c_Log_Opowr(V_x,c_HOL_Otimes__class_Otimes(V_a,V_b,tc_RealDef_Oreal)) # label(cls_powr__powr_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Osemiring__1(T_a) | V_z = c_HOL_Ozero__class_Ozero(T_a) | -c_Int_Oiszero(V_z,T_a) # label(cls_iszero__def_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_y,T_a),V_x,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) # label(cls_abs__mult__pos_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) | -c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) # label(cls_one__le__inverse__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) # label(cls_abs__dvd__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) # label(cls_abs__dvd__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) # label(cls_dvd__abs__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) # label(cls_dvd__abs__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__semidom(T_a) | -c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_not__one__le__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) | -c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) # label(cls_zero__le__divide__iff_4) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) | -c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) | -c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_zero__le__divide__iff_5) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Log_Opowr(V_x,V_y),tc_RealDef_Oreal) # label(cls_powr__ge__pzero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_sgn__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Osgn__if(T_a) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_sgn0_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_sgn__0__0_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(T_a) | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_neg__0__equal__iff__equal_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_inverse__nonzero__iff__nonzero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_inverse__zero__imp__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) # label(cls_minus__mult__commute_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(T_a) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_minus__zero_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(T_a) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_neg__equal__zero_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) # label(cls_divide__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Int_Onumber__ring(T_a) | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) # label(cls_class__fieldgb_Odivide__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Osemiring__1(T_a) | c_Int_Oiszero(c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_iszero__0_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal) # label(cls_real__sqrt__abs2_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) | V_b = c_HOL_Ozero__class_Ozero(T_a) # label(cls_nonzero__power__divide_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a) | -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) # label(cls_mult__dvd__mono_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) | V_a = c_HOL_Ozero__class_Ozero(T_a) # label(cls_abs__eq__0_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Opreorder(T_a) | c_lessequals(V_x,V_x,T_a) # label(cls_order__eq__refl_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Oorder(T_a) | c_lessequals(V_x,V_x,T_a) # label(cls_order__eq__iff_0) # label(axiom).
% 0.41/0.68 c_lessequals(V_i,V_k,tc_RealDef_Oreal) | -c_lessequals(V_j,V_k,tc_RealDef_Oreal) | -c_lessequals(V_i,V_j,tc_RealDef_Oreal) # label(cls_real__le__trans_0) # label(axiom).
% 0.41/0.68 c_lessequals(V_w,V_w,tc_RealDef_Oreal) # label(cls_real__le__refl_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Opreorder(T_a) | c_lessequals(V_x,V_z,T_a) | -c_lessequals(V_y,V_z,T_a) | -c_lessequals(V_x,V_y,T_a) # label(cls_order__trans_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Oorder(T_a) | c_lessequals(V_z,V_x,T_a) | -c_lessequals(V_z,V_y,T_a) | -c_lessequals(V_y,V_x,T_a) # label(cls_xt1_I6_J_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,T_a) # label(cls_scaleR__cancel__left_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_scaleR__cancel__right_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | V_x = c_HOL_Ozero__class_Ozero(T_a) | -c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Otimes__class_Otimes(V_c,c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__ratiotest__lemma_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a) | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | V_x = V_y # label(cls_scaleR__cancel__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a) | V_x = c_HOL_Ozero__class_Ozero(T_a) | V_a = V_b # label(cls_scaleR__cancel__right_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__mult__is__one_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) # label(cls_eq__divide__eq_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) | V_z = c_HOL_Ozero__class_Ozero(T_a) | V_y = c_HOL_Ozero__class_Ozero(T_a) | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) # label(cls_frac__eq__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) | V_z = c_HOL_Ozero__class_Ozero(T_a) | V_y = c_HOL_Ozero__class_Ozero(T_a) | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) # label(cls_frac__eq__eq_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(T_a) | c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_norm__sgn_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__div__algebra(T_a) | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Osgn__class_Osgn(V_y,T_a),T_a) # label(cls_sgn__mult_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Osgn__class_Osgn(V_b,T_a),T_a) # label(cls_sgn__times_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) # label(cls_abs__ge__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) = c_HOL_Ozero__class_Ozero(T_a) # label(cls_divide__eq__eq_4) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Oabs__class_Oabs(V_l,T_a) != c_HOL_Oabs__class_Oabs(V_k,T_a) | c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a) # label(cls_dvd__if__abs__eq_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Olinorder(T_a) | c_lessequals(V_y,V_x,T_a) | c_lessequals(V_x,V_y,T_a) # label(cls_linorder__linear_0) # label(axiom).
% 0.41/0.68 c_lessequals(V_w,V_z,tc_RealDef_Oreal) | c_lessequals(V_z,V_w,tc_RealDef_Oreal) # label(cls_real__le__linear_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Osemiring__1(T_a) | -c_Int_Oiszero(c_HOL_Oone__class_Oone(T_a),T_a) # label(cls_not__iszero__1_0) # label(axiom).
% 0.41/0.68 c_Log_Opowr(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_a) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_powr__one__eq__one_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__sqrt__one_0) # label(axiom).
% 0.41/0.68 c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_Transcendental_Ocos(V_x) # label(cls_cos__minus_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(T_a) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) # label(cls_inverse__1_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) # label(cls_inverse__eq__1__iff_1) # label(axiom).
% 0.41/0.68 c_Transcendental_Ocos(V_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | c_Transcendental_Osin(V_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_cos__one__sin__zero_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Omonoid__mult(T_a) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) # label(cls_power__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ozero__neq__one(T_a) | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) # label(cls_zero__neq__one_0) # label(axiom).
% 0.41/0.68 c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__zero__not__eq__one_0) # label(axiom).
% 0.41/0.68 c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_cos__zero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra__1(T_a) | c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_norm__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a # label(cls_divide__1_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(T_a) | c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),T_a) = c_HOL_Oone__class_Oone(T_a) # label(cls_of__real__1_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) # label(cls_abs__one_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_abs__cos__le__one_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(T_a) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,T_a) = V_x # label(cls_real__vector_Oscale__one_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_Transcendental_Ocos(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_cos__le__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a) # label(cls_one__dvd_0) # label(axiom).
% 0.41/0.68 c_Fun_Oid(v_x,t_a) = v_x # label(cls_id__def_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ozero__neq__one(T_a) | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) # label(cls_one__neq__zero_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(V_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | V_x = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__sqrt__eq__1__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Omonoid__mult(T_a) | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a # label(cls_mult__1__right_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Omonoid__mult(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a # label(cls_mult__1__left_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ocomm__monoid__mult(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a # label(cls_mult__1_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x # label(cls_class__semiring_Omul__1_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) = V_z # label(cls_real__mult__1_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra__1(T_a) | c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) # label(cls_sgn__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(T_a) | -class_Ring__and__Field_Odivision__by__zero(T_a) | c_HOL_Oinverse__class_Oinverse(V_x,T_a) != c_HOL_Oone__class_Oone(T_a) | V_x = c_HOL_Oone__class_Oone(T_a) # label(cls_inverse__eq__1__iff_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__mult__is__one_1) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(T_a) | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a # label(cls_div__by__1_0) # label(axiom).
% 0.41/0.68 v_x = c_Transcendental_Opi # label(cls_CHAINED_0) # label(axiom).
% 0.41/0.68 c_Transcendental_Ocos(v_x) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_conjecture_0) # label(negated_conjecture).
% 0.41/0.68 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__vector) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Ofield(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ofield) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oidom) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Odvd(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odvd) # label(axiom).
% 0.41/0.68 class_Orderings_Opreorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Opreorder) # label(axiom).
% 0.41/0.68 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Olinorder) # label(axiom).
% 0.41/0.68 class_Orderings_Oorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Oorder) # label(axiom).
% 0.41/0.68 class_Int_Onumber__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Int_Onumber__ring) # label(axiom).
% 0.41/0.68 class_Power_Opower(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Power_Opower) # label(axiom).
% 0.41/0.68 end_of_list.
% 0.41/0.68
% 0.41/0.68 % From the command line: assign(max_seconds, 300).
% 0.41/0.68
% 0.41/0.68 ============================== end of input ==========================
% 0.41/0.68
% 0.41/0.68 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.68
% 0.41/0.68 % Formulas that are not ordinary clauses:
% 0.41/0.68
% 0.41/0.68 ============================== end of process non-clausal formulas ===
% 0.41/0.68
% 0.41/0.68 ============================== CLAUSES FOR SEARCH ====================
% 0.41/0.68
% 0.41/0.68 formulas(mace4_clauses).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oab__semigroup__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom).
% 0.41/0.68 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(B,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__neg__div_0) # label(axiom).
% 0.41/0.68 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(B,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__neg_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(B,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Oone__class_Oone(A),A) # label(cls_of__real__def_0) # label(axiom).
% 0.41/0.68 -class_Int_Onumber__ring(A) | c_HOL_Ouminus__class_Ouminus(B,A) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A),B,A) # label(cls_class__ring_Oneg__mul_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oone__class_Oone(A) | C = c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__inverse__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonneg_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__mult__iff_5) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__mult__iff_4) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,B,A),A) # label(cls_zero__le__square_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonpos_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__pos__le_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__pos__le_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(B,A),A) # label(cls_inverse__minus__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(B,A),C,A) # label(cls_power__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_divide__right__mono__neg_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_divide__right__mono_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__mult__distrib_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_class__semiring_Opwr__mul_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),A) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(B,A),c_RealVector_Oof__real(C,A),A) # label(cls_of__real__mult_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oinverse__class_Oinverse(C,A) | B = C | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__imp__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oinverse__class_Oinverse(C,A) | B = C # label(cls_inverse__eq__iff__eq_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_of__real__eq__0__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oab__semigroup__idem__mult(A) | c_HOL_Otimes__class_Otimes(B,B,A) = B # label(cls_mult__idem_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Oone__class_Oone(A) | c_HOL_Oinverse__class_Oinverse(B,A) = C # label(cls_inverse__unique_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Log_Opowr(A,B),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) # label(cls_ge__one__powr__ge__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_mult__right__mono__neg_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,C,A) # label(cls_mult__left__mono__neg_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_mult__right__mono_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__left__mono_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Omult__mono1(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__mono1_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(C,B,A) # label(cls_inverse__divide_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(B,A),A) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_norm__sgn_1) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(A) != c_NthRoot_Osqrt(B) | A = B # label(cls_real__sqrt__eq__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(D,B,A),C,A) # label(cls_dvd__mult__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_dvd__mult__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mult2_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mult_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(A),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) # label(cls_real__sqrt__ge__zero_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(A),tc_RealDef_Oreal) # label(cls_real__sqrt__ge__0__iff_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(A),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) # label(cls_real__sqrt__ge__0__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__le__D2_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),A,tc_RealDef_Oreal) # label(cls_abs__le__interval__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1__if_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | A = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | A = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__mult__is__one_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__le__0__iff__le_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__le__0__iff__le_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,E,A),A) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(E,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__mult__div__if__dvd_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oab__semigroup__idem__mult(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(B,C,A) # label(cls_mult__left__idem_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__mult__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__mult__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(B,A),A) # label(cls_sgn__minus_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A) # label(cls_mult__frac__frac_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_abs__mult_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(C,c_HOL_Ozero__class_Ozero(A),A),A) # label(cls_dvd__mult__cancel__right_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A) # label(cls_dvd__mult__cancel__left_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__trans_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,B,A) # label(cls_dvd__refl_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__nonneg_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Oorder(A) | B = C | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) # label(cls_order__antisym__conv_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__eq__iff_2) # label(axiom).
% 0.41/0.68 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__antisym_0) # label(axiom).
% 0.41/0.68 A = B | -c_lessequals(B,A,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal) # label(cls_real__le__antisym_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__divide_0) # label(axiom).
% 0.41/0.68 -class_Lattices_Oboolean__algebra(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_compl__eq__compl__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(C,B,A),B,A) # label(cls_eq__divide__imp_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(C,B,A),B,A) = C # label(cls_divide__eq__imp_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__1__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__1__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Otimes__class_Otimes(D,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),E,A),A) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(D,E,A),A),A) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__real__0_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__real_Ozero_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2__is__id_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) = c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__mult__assoc_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) # label(cls_class__semiring_Omul__a_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__divide__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__divide__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_3) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_Transcendental_Osin(A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_sin__le__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Oinverse(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__divide_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult_Ominus__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult__left_Ominus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult_Ominus__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult__right_Ominus_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Otimes__class_Otimes(B,B,A) # label(cls_square__eq__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Otimes__class_Otimes(B,C,A) # label(cls_minus__mult__minus_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_left__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(B,A),A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_right__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_H_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_Divides_Odiv__class_Odiv(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) = c_Divides_Odiv__class_Odiv(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult2_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(B,A),A) = c_HOL_Osgn__class_Osgn(B,A) # label(cls_sgn__sgn_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(B,A),tc_RealDef_Oreal) # label(cls_norm__ge__zero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(B,A),A) # label(cls_of__real__minus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(B,A),A) # label(cls_of__real_Ominus_0) # label(axiom).
% 0.41/0.68 c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_sin__zero_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_real__sqrt__zero_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_NthRoot_Osqrt(A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__sqrt__le__1__iff_1) # label(axiom).
% 0.41/0.68 c_lessequals(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_NthRoot_Osqrt(A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__sqrt__le__1__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Osgn__class_Osgn(B,A),A) # label(cls_abs__sgn_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_real__sum__squares__cancel__a_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_real__sum__squares__cancel__a_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Oinverse__class_Odivide(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__divide_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,D,A),c_Divides_Odiv__class_Odiv(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,A) # label(cls_div__dvd__div_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__dvd__div_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_dvd__minus__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__minus__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__dvd__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_minus__dvd__iff_1) # label(axiom).
% 0.41/0.68 c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(A),tc_RealDef_Oreal) # label(cls_sin__minus_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),C,A) | -c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__left__le__one__le_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),B,A) | -c_lessequals(C,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__right__le__one__le_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_Log_Opowr(A,B),c_Log_Opowr(A,C),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal) # label(cls_powr__mono_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A,tc_RealDef_Oreal) # label(cls_abs__le__interval__iff_2) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(B,C,A) # label(cls_abs__leI_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(B,C,A) # label(cls_abs__le__iff_2) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__minus__cancel_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__0__iff_4) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_5) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__neg__le_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__neg__le_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonpos_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonneg_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__nonneg__nonpos2_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A) # label(cls_inverse__mult__distrib_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(C,A),c_HOL_Oinverse__class_Oinverse(B,A),A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__mult__distrib_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_dvd__0__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A) = B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__inverse__eq_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(A),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_abs__sin__le__one_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__0__le__iff__le_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__le__iff__le_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,C,A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_scaleR__eq__0__iff_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult_OscaleR__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__left_OscaleR_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult_OscaleR__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__right_OscaleR_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__scaleR__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__scaleR__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(C,A),tc_RealDef_Oreal) # label(cls_norm__scaleR_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(B,A),A) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(B,A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__abs__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__abs__divide_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_real__sqrt__eq__zero__cancel_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),C,A),A) # label(cls_zero__le__power__abs_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_NthRoot_Osqrt(A),c_NthRoot_Osqrt(B),tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal) # label(cls_real__sqrt__le__iff_1) # label(axiom).
% 0.41/0.68 c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_NthRoot_Osqrt(A),c_NthRoot_Osqrt(B),tc_RealDef_Oreal) # label(cls_real__sqrt__le__iff_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_divide_OscaleR_0) # label(axiom).
% 0.41/0.68 A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,c_HOL_Oabs__class_Oabs(C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_rabs__ratiotest__lemma_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Oinverse(B,A),A) # label(cls_inverse__nonnegative__iff__nonnegative_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Oinverse(B,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_inverse__nonnegative__iff__nonnegative_1) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__self_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_real__sqrt__eq__0__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__self__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__minus__self__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) # label(cls_minus__le__self__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_minus__le__self__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__eq__neg__nonpos_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__eq__neg__nonpos_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) # label(cls_neg__less__eq__nonneg_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__eq__nonneg_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra__1(A) | c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(B,A),A) = c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal) # label(cls_norm__of__real_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),B,A) = C | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1__is__id_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ono__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divisors_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ono__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divirors__neq0_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__by__0_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__0_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,B,A) != c_HOL_Otimes__class_Otimes(C,C,A) | B = c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_square__eq__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A),A) # label(cls_dvd__power_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Oabs__class_Oabs(B,A),A) = B # label(cls_mult__sgn__abs_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oone__class_Oone(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_inverse__le__1__iff_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(B,C,A),A),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(B,A),c_RealVector_Onorm__class_Onorm(C,A),tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__mult__ineq_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(B,A),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(B,A) # label(cls_abs__norm__cancel_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__divide__1__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),A) # label(cls_zero__le__divide__1__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_5) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide__le__0__iff_4) # label(axiom).
% 0.41/0.68 c_Log_Opowr(c_Log_Opowr(A,B),C) = c_Log_Opowr(c_Log_Opowr(A,C),B) # label(cls_powr__powr__swap_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR__minus__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR_Ominus__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),C,A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR__minus__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),C,A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR__left_Ominus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),C,A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR_Ominus__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(B,A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_norm__eq__zero_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(B,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__minus__le__zero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(B,A) != c_RealVector_Oof__real(C,A) | B = C # label(cls_of__real__eq__iff_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__le__zero__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__le__iff__le_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,B,A) # label(cls_le__imp__neg__le_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__le__mult_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__le__D1_0) # label(axiom).
% 0.41/0.68 c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) # label(cls_abs__le__interval__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Oinverse(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) # label(cls_inverse__eq__divide_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) # label(cls_class__fieldgb_Oinverse__divide_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_RealVector_Onorm__class_Onorm(B,A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__le__zero__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_dvd__triv__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_dvd__triv__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odvd(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_dvdI_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),C,A) # label(cls_power__one__over_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A) = B # label(cls_inverse__inverse__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,C,A) = c_HOL_Otimes__class_Otimes(C,B,A) # label(cls_class__semiring_Omul__c_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal) # label(cls_real__mult__commute_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,C,A) = c_HOL_Otimes__class_Otimes(C,B,A) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_OscaleR__class_OscaleR(B,C,A) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(B,A),C,A) # label(cls_scaleR__conv__of__real_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Ouminus__class_Ouminus(B,A) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) # label(cls_right__inverse__eq_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(C,B,A),A) # label(cls_zero__le__divide__iff_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_zero__le__divide__iff_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(C,B,A),A) # label(cls_zero__le__divide__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_zero__le__divide__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(B,D,A) # label(cls_power__mono_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oone__class_Oone(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oone__class_Oone(A),A) # label(cls_inverse__le__1__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_3) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Oinverse__class_Odivide(B,C,A) # label(cls_minus__divide__divide_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_divide_Ominus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),D,A) # label(cls_real__vector_Oscale__scale_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR_Ozero__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR_Ozero__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR__eq__0__iff_2) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR__eq__0__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(A),c_NthRoot_Osqrt(B),tc_RealDef_Oreal) # label(cls_real__sqrt__mult_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_inverse__nonpositive__iff__nonpositive_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_inverse__nonpositive__iff__nonpositive_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),D,A) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__mult_0) # label(axiom).
% 0.41/0.68 c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_NthRoot_Osqrt(A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__sqrt__le__0__iff_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_NthRoot_Osqrt(A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__sqrt__le__0__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_power__abs_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__power__same_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(B,A),A) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_abs__divide_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__0__0_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__zero__iff_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_real__minus__mult__self__le_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) = c_HOL_Oinverse__class_Odivide(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Oinverse__class_Odivide(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_mult__frac__num_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A) = C | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mult__div__cancel_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A) = B | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__mult__self_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__nonpos_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_dvd__mult__cancel__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_dvd__mult__cancel__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_le__divide__eq_9) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,A),B,A) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_divide__le__eq_9) # label(axiom).
% 0.41/0.68 c_Fun_Oid(A,B) = A # label(cls_id__apply_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__equation__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_0) # label(axiom).
% 0.41/0.68 -class_Lattices_Oboolean__algebra(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_double__compl_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__minus_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__le__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__le__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__iff_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__iff_0) # label(axiom).
% 0.41/0.68 c_Transcendental_Osin(A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(A),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_sin__zero__abs__cos__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,A) # label(cls_dvd__mult__cancel__left_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mult__cancel__right_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__le__power_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__idempotent_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_RealVector_Onorm__class_Onorm(B,A) # label(cls_norm__minus__cancel_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(A),tc_RealDef_Oreal) # label(cls_real__sqrt__minus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR_OscaleR__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR__left__commute_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR__right_OscaleR_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_3) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_norm__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring__1(A) | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A),C,A),c_Power_Opower__class_Opower(B,C,A),A) # label(cls_power__minus_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__div__algebra(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(B,A),c_RealVector_Onorm__class_Onorm(C,A),tc_RealDef_Oreal) # label(cls_norm__mult_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Omonoid__mult(A) | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A) # label(cls_power__commutes_0) # label(axiom).
% 0.41/0.68 c_Log_Opowr(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_powr__zero__eq__one_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = C # label(cls_real__mult__left__cancel_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = C # label(cls_real__mult__right__cancel_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_inverse__le__1__iff_2) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__minus__self_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__self_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),B,A) # label(cls_eq__divide__eq_4) # label(axiom).
% 0.41/0.68 c_Log_Opowr(A,B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_powr__not__zero_0) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(B,C,A),D,A) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__power_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(B,A),A) = c_HOL_Otimes__class_Otimes(B,B,A) # label(cls_abs__mult__self_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(B,A),C,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(B,A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__minus__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_dvd__0__right_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(A),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) # label(cls_real__sqrt__ge__1__iff_1) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(A),tc_RealDef_Oreal) # label(cls_real__sqrt__ge__1__iff_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(A),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) # label(cls_real__sqrt__ge__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__le__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Omult__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__left_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Omult__zero(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__right_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(B,A),C,A),A) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(B,C,A),A) # label(cls_abs__power__minus_0) # label(axiom).
% 0.41/0.68 c_Log_Opowr(c_Log_Opowr(A,B),C) = c_Log_Opowr(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal)) # label(cls_powr__powr_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Osemiring__1(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Int_Oiszero(B,A) # label(cls_iszero__def_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),C,A) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_abs__mult__pos_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Oinverse__class_Oinverse(B,A),A) # label(cls_one__le__inverse__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__dvd__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_abs__dvd__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_dvd__abs__iff_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oabs__class_Oabs(C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__abs__iff_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__le__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__divide__iff_4) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__divide__iff_5) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Log_Opowr(A,B),tc_RealDef_Oreal) # label(cls_powr__ge__pzero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Osgn__if(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn0_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__0__0_1) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__equal__iff__equal_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__zero__imp__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__mult__commute_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(C,A),A) # label(cls_divide__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Odivide(B,C,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(C,A),A) # label(cls_class__fieldgb_Odivide__inverse_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Osemiring__1(A) | c_Int_Oiszero(c_HOL_Ozero__class_Ozero(A),A) # label(cls_iszero__0_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) # label(cls_real__sqrt__abs2_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__divide_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,E,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_mult__dvd__mono_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Opreorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__refl_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__iff_0) # label(axiom).
% 0.41/0.68 c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) # label(cls_real__le__trans_0) # label(axiom).
% 0.41/0.68 c_lessequals(A,A,tc_RealDef_Oreal) # label(cls_real__le__refl_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_lessequals(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__trans_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Oorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,D,A) | -c_lessequals(D,C,A) # label(cls_xt1_I6_J_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,A) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,A) # label(cls_scaleR__cancel__left_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_scaleR__cancel__right_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_RealVector_Onorm__class_Onorm(B,A),c_HOL_Otimes__class_Otimes(C,c_RealVector_Onorm__class_Onorm(D,A),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__ratiotest__lemma_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,C,A) != c_RealVector_OscaleR__class_OscaleR(B,D,A) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | C = D # label(cls_scaleR__cancel__left_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,C,A) != c_RealVector_OscaleR__class_OscaleR(D,C,A) | C = c_HOL_Ozero__class_Ozero(A) | B = D # label(cls_scaleR__cancel__right_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__mult__is__one_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_eq__divide__eq_2) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oinverse__class_Odivide(D,E,A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | c_HOL_Otimes__class_Otimes(B,E,A) = c_HOL_Otimes__class_Otimes(D,C,A) # label(cls_frac__eq__eq_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Otimes__class_Otimes(D,E,A) | C = c_HOL_Ozero__class_Ozero(A) | E = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,E,A) = c_HOL_Oinverse__class_Odivide(D,C,A) # label(cls_frac__eq__eq_1) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_norm__sgn_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__div__algebra(A) | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Osgn__class_Osgn(C,A),A) # label(cls_sgn__mult_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Osgn__class_Osgn(C,A),A) # label(cls_sgn__times_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__zero_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_4) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,A) != c_HOL_Oabs__class_Oabs(C,A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__if__abs__eq_0) # label(axiom).
% 0.41/0.68 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom).
% 0.41/0.68 c_lessequals(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal) # label(cls_real__le__linear_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Osemiring__1(A) | -c_Int_Oiszero(c_HOL_Oone__class_Oone(A),A) # label(cls_not__iszero__1_0) # label(axiom).
% 0.41/0.68 c_Log_Opowr(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_powr__one__eq__one_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__sqrt__one_0) # label(axiom).
% 0.41/0.68 c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)) = c_Transcendental_Ocos(A) # label(cls_cos__minus_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__1_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_1) # label(axiom).
% 0.41/0.68 c_Transcendental_Ocos(A) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | c_Transcendental_Osin(A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_cos__one__sin__zero_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom).
% 0.41/0.68 c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__zero__not__eq__one_0) # label(axiom).
% 0.41/0.68 c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_cos__zero_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra__1(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_norm__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_divide__1_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__real__1_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_abs__one_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(A),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_abs__cos__le__one_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),B,A) = B # label(cls_real__vector_Oscale__one_0) # label(axiom).
% 0.41/0.68 c_lessequals(c_Transcendental_Ocos(A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_cos__le__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__dvd_0) # label(axiom).
% 0.41/0.68 c_Fun_Oid(v_x,t_a) = v_x # label(cls_id__def_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom).
% 0.41/0.68 c_NthRoot_Osqrt(A) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | A = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__sqrt__eq__1__iff_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Omonoid__mult(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_mult__1__right_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Omonoid__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_mult__1__left_0) # label(axiom).
% 0.41/0.68 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_mult__1_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_class__semiring_Omul__1_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = A # label(cls_real__mult__1_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom).
% 0.41/0.68 -class_RealVector_Oreal__normed__algebra__1(A) | c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_sgn__one_0) # label(axiom).
% 0.41/0.68 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oone__class_Oone(A) | B = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_0) # label(axiom).
% 0.41/0.68 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_real__mult__is__one_1) # label(axiom).
% 0.41/0.68 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_div__by__1_0) # label(axiom).
% 0.41/0.68 v_x = c_Transcendental_Opi # label(cls_CHAINED_0) # label(axiom).
% 0.41/0.68 c_Transcendental_Ocos(v_x) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_conjecture_0) # label(negated_conjecture).
% 0.41/0.68 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra) # label(axiom).
% 0.41/0.68 class_RealVector_Oreal__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__vector) # label(axiom).
% 0.41/0.68 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Ofield(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ofield) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oidom) # label(axiom).
% 0.41/0.68 class_Ring__and__Field_Odvd(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odvd) # label(axiom).
% 0.41/0.68 class_Orderings_Opreorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Opreorder) # label(axiom).
% 0.41/0.68 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Olinorder) # label(axiom).
% 0.41/0.68 class_Orderings_Oorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Oorder) # label(axiom).
% 0.41/0.68 class_Int_Onumber__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Int_Onumber__ring) # label(axiom).
% 0.41/0.68 class_Power_Opower(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Power_Opower) # label(axiom).
% 0.41/0.68 end_of_list.
% 0.41/0.68
% 0.41/0.68 ============================== end of clauses for search =============
% 0.41/0.68 % SZS output start FiniteModel
% 0.41/0.68
% 0.41/0.68 % There are no natural numbers in the input.
% 0.41/0.68
% 0.41/0.68 c_Transcendental_Opi : 0
% 0.41/0.68
% 0.41/0.68 t_a : 0
% 0.41/0.68
% 0.41/0.68 tc_RealDef_Oreal : 0
% 0.41/0.68
% 0.41/0.68 v_x : 0
% 0.41/0.68
% 0.41/0.68 c_HOL_Oone__class_Oone :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 0 0 0
% 0.41/0.68
% 0.41/0.68 c_HOL_Ozero__class_Ozero :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 c_NthRoot_Osqrt :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 0 1 2
% 0.41/0.68
% 0.41/0.68 c_Transcendental_Ocos :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 0 0 0
% 0.41/0.68
% 0.41/0.68 c_Transcendental_Osin :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 1 1
% 0.41/0.68
% 0.41/0.68 c_Fun_Oid :
% 0.41/0.68 | 0 1 2
% 0.41/0.68 --+------
% 0.41/0.68 0 | 0 0 0
% 0.41/0.68 1 | 1 1 1
% 0.41/0.68 2 | 2 2 2
% 0.41/0.68
% 0.41/0.68 c_HOL_Oabs__class_Oabs :
% 0.41/0.68 | 0 1 2
% 0.41/0.68 --+------
% 0.41/0.68 0 | 0 0 0
% 0.41/0.68 1 | 1 0 0
% 0.41/0.68 2 | 0 0 0
% 0.41/0.68
% 0.41/0.68 c_HOL_Oinverse__class_Oinverse :
% 0.41/0.68 | 0 1 2
% 0.41/0.68 --+------
% 0.41/0.68 0 | 0 0 0
% 0.41/0.68 1 | 1 0 0
% 0.41/0.68 2 | 2 0 0
% 0.41/0.68
% 0.41/0.68 c_HOL_Osgn__class_Osgn :
% 0.41/0.68 | 0 1 2
% 0.41/0.68 --+------
% 0.41/0.68 0 | 0 0 0
% 0.41/0.68 1 | 1 0 0
% 0.41/0.68 2 | 2 0 0
% 0.41/0.68
% 0.41/0.68 c_HOL_Ouminus__class_Ouminus :
% 0.41/0.68 | 0 1 2
% 0.41/0.68 --+------
% 0.41/0.68 0 | 2 0 0
% 0.41/0.68 1 | 1 0 0
% 0.41/0.68 2 | 0 0 0
% 0.41/0.68
% 0.41/0.68 c_Log_Opowr :
% 0.41/0.68 | 0 1 2
% 0.41/0.68 --+------
% 0.41/0.68 0 | 0 0 0
% 0.41/0.68 1 | 0 0 0
% 0.41/0.68 2 | 0 0 0
% 0.41/0.68
% 0.41/0.68 c_RealVector_Onorm__class_Onorm :
% 0.41/0.68 | 0 1 2
% 0.41/0.68 --+------
% 0.41/0.68 0 | 0 0 0
% 0.41/0.68 1 | 1 0 0
% 0.41/0.68 2 | 0 0 0
% 0.41/0.68
% 0.41/0.68 c_RealVector_Oof__real :
% 0.41/0.68 | 0 1 2
% 0.41/0.68 --+------
% 0.41/0.68 0 | 0 0 0
% 0.41/0.68 1 | 1 0 0
% 0.41/0.68 2 | 2 0 0
% 0.41/0.68 c_Divides_Odiv__class_Odiv(0,0,0) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(0,0,1) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(0,0,2) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(0,1,0) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(0,1,1) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(0,1,2) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(0,2,0) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(0,2,1) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(0,2,2) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(1,0,0) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(1,0,1) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(1,0,2) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(1,1,0) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(1,1,1) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(1,1,2) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(1,2,0) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(1,2,1) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(1,2,2) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(2,0,0) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(2,0,1) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(2,0,2) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(2,1,0) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(2,1,1) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(2,1,2) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(2,2,0) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(2,2,1) = 0.
% 0.41/0.68 c_Divides_Odiv__class_Odiv(2,2,2) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(0,0,0) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(0,0,1) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(0,0,2) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(0,1,0) = 1.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(0,1,1) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(0,1,2) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(0,2,0) = 2.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(0,2,1) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(0,2,2) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(1,0,0) = 1.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(1,0,1) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(1,0,2) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(1,1,0) = 1.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(1,1,1) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(1,1,2) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(1,2,0) = 1.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(1,2,1) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(1,2,2) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(2,0,0) = 2.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(2,0,1) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(2,0,2) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(2,1,0) = 1.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(2,1,1) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(2,1,2) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(2,2,0) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(2,2,1) = 0.
% 0.41/0.68 c_HOL_Oinverse__class_Odivide(2,2,2) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(0,0,0) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(0,0,1) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(0,0,2) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(0,1,0) = 1.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(0,1,1) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(0,1,2) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(0,2,0) = 2.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(0,2,1) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(0,2,2) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(1,0,0) = 1.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(1,0,1) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(1,0,2) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(1,1,0) = 1.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(1,1,1) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(1,1,2) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(1,2,0) = 1.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(1,2,1) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(1,2,2) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(2,0,0) = 2.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(2,0,1) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(2,0,2) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(2,1,0) = 1.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(2,1,1) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(2,1,2) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(2,2,0) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(2,2,1) = 0.
% 0.41/0.68 c_HOL_Otimes__class_Otimes(2,2,2) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(0,0,0) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(0,0,1) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(0,0,2) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(0,1,0) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(0,1,1) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(0,1,2) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(0,2,0) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(0,2,1) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(0,2,2) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(1,0,0) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(1,0,1) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(1,0,2) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(1,1,0) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(1,1,1) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(1,1,2) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(1,2,0) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(1,2,1) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(1,2,2) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(2,0,0) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(2,0,1) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(2,0,2) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(2,1,0) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(2,1,1) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(2,1,2) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(2,2,0) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(2,2,1) = 0.
% 0.41/0.68 c_Power_Opower__class_Opower(2,2,2) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(0,0,0) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(0,0,1) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(0,0,2) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(0,1,0) = 1.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(0,1,1) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(0,1,2) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(0,2,0) = 2.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(0,2,1) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(0,2,2) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(1,0,0) = 1.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(1,0,1) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(1,0,2) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(1,1,0) = 1.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(1,1,1) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(1,1,2) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(1,2,0) = 1.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(1,2,1) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(1,2,2) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(2,0,0) = 2.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(2,0,1) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(2,0,2) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(2,1,0) = 1.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(2,1,1) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(2,1,2) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(2,2,0) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(2,2,1) = 0.
% 0.41/0.68 c_RealVector_OscaleR__class_OscaleR(2,2,2) = 0.
% 0.41/0.68
% 0.41/0.68 class_Divides_Oring__div :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 0 0 0
% 0.41/0.68
% 0.41/0.68 class_Divides_Osemiring__div :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 0 0 0
% 0.41/0.68
% 0.41/0.68 class_Int_Onumber__ring :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Lattices_Oboolean__algebra :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 0 0 0
% 0.41/0.68
% 0.41/0.68 class_OrderedGroup_Oab__semigroup__idem__mult :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 0 0 0
% 0.41/0.68
% 0.41/0.68 class_OrderedGroup_Oab__semigroup__mult :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_OrderedGroup_Ocomm__monoid__mult :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_OrderedGroup_Ogroup__add :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_OrderedGroup_Olordered__ab__group__add :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_OrderedGroup_Omonoid__mult :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_OrderedGroup_Oordered__ab__group__add :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_OrderedGroup_Opordered__ab__group__add :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_OrderedGroup_Opordered__ab__group__add__abs :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Orderings_Olinorder :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Orderings_Oorder :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Orderings_Opreorder :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Power_Opower :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_RealVector_Oreal__algebra :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_RealVector_Oreal__algebra__1 :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_RealVector_Oreal__normed__algebra :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_RealVector_Oreal__normed__algebra__1 :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_RealVector_Oreal__normed__div__algebra :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_RealVector_Oreal__normed__field :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_RealVector_Oreal__normed__vector :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_RealVector_Oreal__vector :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Ocomm__ring__1 :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Ocomm__semiring__1 :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Odivision__by__zero :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Odivision__ring :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Odvd :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Ofield :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Oidom :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Olordered__ring :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Omult__mono :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Omult__mono1 :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Omult__zero :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Ono__zero__divisors :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Oordered__field :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Oordered__idom :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Oordered__ring__strict :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Oordered__semidom :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Opordered__cancel__semiring :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Opordered__ring :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Opordered__ring__abs :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Opordered__semiring :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Oring :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Oring__1 :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Oring__1__no__zero__divisors :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Oring__no__zero__divisors :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Osemiring__1 :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Osgn__if :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 class_Ring__and__Field_Ozero__neq__one :
% 0.41/0.68 0 1 2
% 0.41/0.68 ---------
% 0.41/0.68 1 0 0
% 0.41/0.68
% 0.41/0.68 c_Int_Oiszero :
% 0.41/0.68 | 0 1 2
% 0.41/0.68 --+------
% 0.41/0.68 0 | 0 0 0
% 0.41/0.68 1 | 1 0 0
% 0.41/0.68 2 | 0 0 0
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(0,0,0) = 1.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(0,0,1) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(0,0,2) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(0,1,0) = 1.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(0,1,1) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(0,1,2) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(0,2,0) = 1.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(0,2,1) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(0,2,2) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(1,0,0) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(1,0,1) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(1,0,2) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(1,1,0) = 1.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(1,1,1) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(1,1,2) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(1,2,0) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(1,2,1) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(1,2,2) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(2,0,0) = 1.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(2,0,1) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(2,0,2) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(2,1,0) = 1.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(2,1,1) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(2,1,2) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(2,2,0) = 1.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(2,2,1) = 0.
% 0.41/0.68 c_Ring__and__Field_Odvd__class_Odvd(2,2,2) = 0.
% 0.41/0.68 c_lessequals(0,0,0) = 1.
% 0.41/0.68 c_lessequals(0,0,1) = 0.
% 0.41/0.68 c_lessequals(0,0,2) = 0.
% 0.41/0.68 c_lessequals(0,1,0) = 0.
% 0.41/0.68 c_lessequals(0,1,1) = 0.
% 0.41/0.68 c_lessequals(0,1,2) = 0.
% 0.41/0.68 c_lessequals(0,2,0) = 0.
% 0.41/0.68 c_lessequals(0,2,1) = 0.
% 0.41/0.68 c_lessequals(0,2,2) = 0.
% 0.41/0.68 c_lessequals(1,0,0) = 1.
% 0.41/0.68 c_lessequals(1,0,1) = 0.
% 0.41/0.68 c_lessequals(1,0,2) = 0.
% 0.41/0.68 c_lessequals(1,1,0) = 1.
% 0.41/0.68 c_lessequals(1,1,1) = 0.
% 0.41/0.68 c_lessequals(1,1,2) = 0.
% 0.41/0.68 c_lessequals(1,2,0) = 0.
% 0.41/0.68 c_lessequals(1,2,1) = 0.
% 0.41/0.68 c_lessequals(1,2,2) = 0.
% 0.41/0.68 c_lessequals(2,0,0) = 1.
% 0.41/0.68 c_lessequals(2,0,1) = 0.
% 0.41/0.68 c_lessequals(2,0,2) = 0.
% 0.41/0.68 c_lessequals(2,1,0) = 1.
% 0.41/0.68 c_lessequals(2,1,1) = 0.
% 0.41/0.68 c_lessequals(2,1,2) = 0.
% 0.41/0.68 c_lessequals(2,2,0) = 1.
% 0.41/0.68 c_lessequals(2,2,1) = 0.
% 0.41/0.68 c_lessequals(2,2,2) = 0.
% 0.41/0.68
% 0.41/0.68 % SZS output end FiniteModel
% 0.41/0.68 ------ process 54545 exit (max_models) ------
% 0.41/0.68
% 0.41/0.68 User_CPU=0.10, System_CPU=0.00, Wall_clock=0.
% 0.41/0.68
% 0.41/0.68 Exiting with 1 model.
% 0.41/0.68
% 0.41/0.68 Process 54545 exit (max_models) Tue Feb 7 23:16:16 2017
% 0.41/0.68 The process finished Tue Feb 7 23:16:16 2017
% 0.41/0.68 Mace4 ended
%------------------------------------------------------------------------------