TSTP Solution File: SWV689-1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWV689-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 21:34:53 EDT 2023
% Result : Unsatisfiable 0.78s 0.94s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV689-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 10:02:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 0.76/0.89 %-------------------------------------------
% 0.76/0.89 % File :CSE---1.6
% 0.76/0.89 % Problem :theBenchmark
% 0.76/0.89 % Transform :cnf
% 0.76/0.89 % Format :tptp:raw
% 0.76/0.89 % Command :java -jar mcs_scs.jar %d %s
% 0.76/0.89
% 0.76/0.89 % Result :Theorem 0.060000s
% 0.76/0.89 % Output :CNFRefutation 0.060000s
% 0.76/0.89 %-------------------------------------------
% 0.76/0.90 %------------------------------------------------------------------------------
% 0.76/0.90 % File : SWV689-1 : TPTP v8.1.2. Released v4.1.0.
% 0.76/0.90 % Domain : Software Verification
% 0.76/0.90 % Problem : Fast Fourier Transform 435_47
% 0.76/0.90 % Version : Especial.
% 0.76/0.90 % English : Formalization of a functional implementation of the FFT algorithm
% 0.76/0.90 % over the complex numbers, and its inverse. Both are shown
% 0.76/0.90 % equivalent to the usual definitions of these operations through
% 0.76/0.90 % Vandermonde matrices. They are also shown to be inverse to each
% 0.76/0.90 % other, more precisely, that composition of the inverse and the
% 0.76/0.90 % transformation yield the identity up to a scalar.
% 0.76/0.90
% 0.76/0.90 % Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% 0.76/0.90 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.76/0.90 % Source : [Nip10]
% 0.76/0.90 % Names : FFT-435_47 [Nip10]
% 0.76/0.90
% 0.76/0.90 % Status : Unsatisfiable
% 0.76/0.90 % Rating : 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.30 v5.4.0, 0.25 v5.3.0, 0.33 v5.2.0, 0.25 v5.1.0, 0.29 v5.0.0, 0.21 v4.1.0
% 0.76/0.90 % Syntax : Number of clauses : 798 ( 130 unt; 102 nHn; 494 RR)
% 0.76/0.90 % Number of literals : 2057 ( 429 equ;1183 neg)
% 0.76/0.90 % Maximal clause size : 6 ( 2 avg)
% 0.76/0.90 % Maximal term depth : 6 ( 1 avg)
% 0.76/0.90 % Number of predicates : 57 ( 56 usr; 0 prp; 1-3 aty)
% 0.76/0.90 % Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% 0.76/0.90 % Number of variables : 2225 ( 142 sgn)
% 0.76/0.90 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.76/0.90
% 0.76/0.90 % Comments :
% 0.76/0.90 %------------------------------------------------------------------------------
% 0.76/0.90 cnf(cls_zero__less__mult__pos_0,axiom,
% 0.76/0.90 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.76/0.90 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.76/0.90 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.76/0.90 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_zero__less__mult__pos2_0,axiom,
% 0.76/0.90 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.76/0.90 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.76/0.90 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.76/0.90 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_mult__Suc_0,axiom,
% 0.76/0.90 c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_mult__Suc__right_0,axiom,
% 0.76/0.90 c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_not__sum__squares__lt__zero_0,axiom,
% 0.76/0.90 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.76/0.90 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_dvd__1__iff__1_1,axiom,
% 0.76/0.90 c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_add__neg__nonpos_0,axiom,
% 0.76/0.90 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.76/0.90 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.76/0.90 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.76/0.90 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_add__nonpos__neg_0,axiom,
% 0.76/0.90 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.76/0.90 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.76/0.90 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.76/0.90 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_sum__squares__le__zero__iff_2,axiom,
% 0.76/0.90 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.76/0.90 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_diff__add__assoc2_0,axiom,
% 0.76/0.90 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat)
% 0.76/0.90 | ~ c_lessequals(V_k,V_j,tc_nat) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_diff__add__assoc_0,axiom,
% 0.76/0.90 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
% 0.76/0.90 | ~ c_lessequals(V_k,V_j,tc_nat) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
% 0.76/0.90 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.76/0.90 | 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) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
% 0.76/0.90 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.76/0.90 | 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) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
% 0.76/0.90 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.76/0.90 | 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) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_abs__le__zero__iff_0,axiom,
% 0.76/0.90 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.76/0.90 | V_a = c_HOL_Ozero__class_Ozero(T_a)
% 0.76/0.90 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_min__max_Oinf__idem_0,axiom,
% 0.76/0.90 ( ~ class_Orderings_Olinorder(T_a)
% 0.76/0.90 | c_Orderings_Oord__class_Omin(V_x,V_x,T_a) = V_x ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_estimate__by__abs_0,axiom,
% 0.76/0.90 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
% 0.76/0.90 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a)
% 0.76/0.90 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_le__0__eq_0,axiom,
% 0.76/0.90 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.76/0.90 | ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_order__antisym_0,axiom,
% 0.76/0.90 ( ~ class_Orderings_Oorder(T_a)
% 0.76/0.90 | V_x = V_y
% 0.76/0.90 | ~ c_lessequals(V_y,V_x,T_a)
% 0.76/0.90 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_order__eq__iff_2,axiom,
% 0.76/0.90 ( ~ class_Orderings_Oorder(T_a)
% 0.76/0.90 | V_x = V_y
% 0.76/0.90 | ~ c_lessequals(V_y,V_x,T_a)
% 0.76/0.90 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_dvd_Oneq__le__trans_0,axiom,
% 0.76/0.90 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat)
% 0.76/0.90 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat)
% 0.76/0.90 | V_a = V_b ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_dvd_Ole__neq__trans_0,axiom,
% 0.76/0.90 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat)
% 0.76/0.90 | V_a = V_b
% 0.76/0.90 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_dvd_Oantisym__conv_0,axiom,
% 0.76/0.90 ( V_x = V_y
% 0.76/0.90 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
% 0.76/0.90 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_dvd__antisym_0,axiom,
% 0.76/0.90 ( V_m = V_n
% 0.76/0.90 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat)
% 0.76/0.90 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_dvd_Oless__le_0,axiom,
% 0.76/0.90 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
% 0.76/0.90 | V_x = V_y
% 0.76/0.90 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_dvd_Oantisym_0,axiom,
% 0.76/0.90 ( V_x = V_y
% 0.76/0.90 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
% 0.76/0.90 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_le__antisym_0,axiom,
% 0.76/0.90 ( V_m = V_n
% 0.76/0.90 | ~ c_lessequals(V_n,V_m,tc_nat)
% 0.76/0.90 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.76/0.90
% 0.76/0.90 cnf(cls_dvd_Oeq__iff_2,axiom,
% 0.76/0.90 ( V_x = V_y
% 0.76/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
% 0.76/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_order__antisym__conv_0,axiom,
% 0.76/0.91 ( ~ class_Orderings_Oorder(T_a)
% 0.76/0.91 | V_x = V_y
% 0.76/0.91 | ~ c_lessequals(V_x,V_y,T_a)
% 0.76/0.91 | ~ c_lessequals(V_y,V_x,T_a) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_abs__of__nonneg_0,axiom,
% 0.76/0.91 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.76/0.91 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
% 0.76/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_dvd_Oorder__trans_0,axiom,
% 0.76/0.91 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)
% 0.76/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
% 0.76/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_dvd_Oless__trans_0,axiom,
% 0.76/0.91 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)
% 0.76/0.91 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
% 0.76/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
% 0.76/0.91 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
% 0.76/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_dvd__pos__nat_0,axiom,
% 0.76/0.91 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
% 0.76/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)
% 0.76/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_dvd_Oeq__iff_0,axiom,
% 0.76/0.91 c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_dvd__refl_0,axiom,
% 0.76/0.91 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.76/0.91 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_dvd__trans_0,axiom,
% 0.76/0.91 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.76/0.91 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
% 0.76/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
% 0.76/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_diff__Suc__diff__eq1_0,axiom,
% 0.76/0.91 ( c_HOL_Ominus__class_Ominus(V_m,c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_Suc(V_j),tc_nat)
% 0.76/0.91 | ~ c_lessequals(V_k,V_j,tc_nat) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_nat__mult__dvd__cancel__disj_1,axiom,
% 0.76/0.91 c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_dvd__mult__cancel__left_1,axiom,
% 0.76/0.91 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.76/0.91 | 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) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_dvd__mult__cancel__right_1,axiom,
% 0.76/0.91 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.76/0.91 | 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) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_nat__add__left__cancel__le_1,axiom,
% 0.76/0.91 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)
% 0.76/0.91 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_nat__add__left__cancel__le_0,axiom,
% 0.76/0.91 ( c_lessequals(V_m,V_n,tc_nat)
% 0.76/0.91 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_add__le__mono1_0,axiom,
% 0.76/0.91 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat)
% 0.76/0.91 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_add__left__mono_0,axiom,
% 0.76/0.91 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
% 0.76/0.91 | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
% 0.76/0.91 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_add__right__mono_0,axiom,
% 0.76/0.91 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
% 0.76/0.91 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
% 0.76/0.91 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_add__le__cancel__left_0,axiom,
% 0.76/0.91 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.76/0.91 | c_lessequals(V_a,V_b,T_a)
% 0.76/0.91 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_add__le__cancel__left_1,axiom,
% 0.76/0.91 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.76/0.91 | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
% 0.76/0.91 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_add__le__cancel__right_0,axiom,
% 0.76/0.91 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.76/0.91 | c_lessequals(V_a,V_b,T_a)
% 0.76/0.91 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_add__le__cancel__right_1,axiom,
% 0.76/0.91 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.76/0.91 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
% 0.76/0.91 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_abs__mult_0,axiom,
% 0.76/0.91 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.76/0.91 | 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) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_abs__eq__mult_0,axiom,
% 0.76/0.91 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
% 0.76/0.91 | 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)
% 0.76/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.76/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.76/0.91
% 0.76/0.91 cnf(cls_abs__eq__mult_1,axiom,
% 0.76/0.91 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
% 0.78/0.91 | 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)
% 0.78/0.91 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_abs__eq__mult_2,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
% 0.78/0.91 | 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)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.91 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_abs__eq__mult_3,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
% 0.78/0.91 | 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)
% 0.78/0.91 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__left__idem_0,axiom,
% 0.78/0.91 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
% 0.78/0.91 | 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) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_even__nat__equiv__def_1,axiom,
% 0.78/0.91 ( c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.91 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_even__nat__equiv__def_0,axiom,
% 0.78/0.91 ( c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.91 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mod__add__self1_0,axiom,
% 0.78/0.91 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.91 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mod__add__self2_0,axiom,
% 0.78/0.91 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.91 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__le__0__iff_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.91 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__le__0__iff_1,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.91 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.91 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__le__0__iff_2,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.91 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__le__0__iff_3,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.91 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.91 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__neg__pos_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__pos__neg_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__pos__neg2_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__pos__pos_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__neg__neg_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_nat__0__less__mult__iff_2,axiom,
% 0.78/0.91 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
% 0.78/0.91 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
% 0.78/0.91 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_even__less__0__iff_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_even__less__0__iff_1,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__eq__0__iff_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
% 0.78/0.91 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.91 | V_b = c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.91 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_no__zero__divisors_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
% 0.78/0.91 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.91 | V_b = c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.91 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_no__zero__divirors__neq0_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
% 0.78/0.91 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.91 | V_a = c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.91 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__is__0_0,axiom,
% 0.78/0.91 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.91 | V_n = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.91 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_nat__eq__add__iff2_0,axiom,
% 0.78/0.91 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat)
% 0.78/0.91 | ~ c_lessequals(V_i,V_j,tc_nat)
% 0.78/0.91 | V_m = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_nat__eq__add__iff1_0,axiom,
% 0.78/0.91 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat)
% 0.78/0.91 | ~ c_lessequals(V_j,V_i,tc_nat)
% 0.78/0.91 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat) = V_n ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_even__nat__equiv__def2_1,axiom,
% 0.78/0.91 c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_xa,tc_nat),tc_nat) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_le__mod__geq_0,axiom,
% 0.78/0.91 ( c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat)
% 0.78/0.91 | ~ c_lessequals(V_n,V_m,tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_add__nonneg__eq__0__iff_1,axiom,
% 0.78/0.91 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.78/0.91 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
% 0.78/0.91 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_add__nonneg__eq__0__iff_0,axiom,
% 0.78/0.91 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.78/0.91 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
% 0.78/0.91 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_add__is__0_0,axiom,
% 0.78/0.91 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.91 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_add__is__0_1,axiom,
% 0.78/0.91 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.91 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_double__eq__0__iff_0,axiom,
% 0.78/0.91 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.78/0.91 | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.91 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_min__0L_0,axiom,
% 0.78/0.91 c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_min__0R_0,axiom,
% 0.78/0.91 c_Orderings_Oord__class_Omin(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_nat__eq__add__iff1_1,axiom,
% 0.78/0.91 ( ~ c_lessequals(V_j,V_i,tc_nat)
% 0.78/0.91 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__less__imp__less__right_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__less__imp__less__left_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__right__less__imp__less_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__semiring(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__left__less__imp__less_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__semiring(T_a)
% 0.78/0.91 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.91 | ~ class_Int_Onumber__ring(T_a)
% 0.78/0.91 | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a)
% 0.78/0.91 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_natgb_Oadd__r0__iff_0,axiom,
% 0.78/0.91 ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat)
% 0.78/0.91 | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_add__eq__self__zero_0,axiom,
% 0.78/0.91 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m
% 0.78/0.91 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_of__nat__eq__iff_0,axiom,
% 0.78/0.91 ( ~ class_Nat_Osemiring__char__0(T_a)
% 0.78/0.91 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
% 0.78/0.91 | V_m = V_n ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mod__le__divisor_0,axiom,
% 0.78/0.91 ( c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat)
% 0.78/0.91 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__eq__1__iff_0,axiom,
% 0.78/0.91 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.91 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_mult__eq__1__iff_1,axiom,
% 0.78/0.91 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.91 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_sum__squares__ge__zero_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.91 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_Suc__diff__le_0,axiom,
% 0.78/0.91 ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat))
% 0.78/0.91 | ~ c_lessequals(V_n,V_m,tc_nat) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_dvd__mod__imp__dvd_0,axiom,
% 0.78/0.91 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.91 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
% 0.78/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
% 0.78/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_dvd__mod__iff_1,axiom,
% 0.78/0.91 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.91 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
% 0.78/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
% 0.78/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_dvd__mod__iff_0,axiom,
% 0.78/0.91 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.91 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
% 0.78/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
% 0.78/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_dvd__mod_0,axiom,
% 0.78/0.91 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.91 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
% 0.78/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
% 0.78/0.91 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_le__add__iff2_1,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.91 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
% 0.78/0.91 | ~ c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.91 cnf(cls_le__add__iff2_0,axiom,
% 0.78/0.91 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.91 | c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
% 0.78/0.91 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).
% 0.78/0.91
% 0.78/0.92 cnf(cls_le__add__iff1_1,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_le__add__iff1_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_Suc__leI_0,axiom,
% 0.78/0.92 ( c_lessequals(c_Suc(V_m),V_n,tc_nat)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_Suc__le__eq_0,axiom,
% 0.78/0.92 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.92 | ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_less__eq__Suc__le_0,axiom,
% 0.78/0.92 ( c_lessequals(c_Suc(V_n),V_m,tc_nat)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_less__eq__Suc__le_1,axiom,
% 0.78/0.92 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
% 0.78/0.92 | ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_add__increasing2_0,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.78/0.92 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.78/0.92 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_b,V_a,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_add__increasing_0,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.78/0.92 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.78/0.92 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_b,V_c,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_le__diff__conv2_0,axiom,
% 0.78/0.92 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_k,V_j,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_le__diff__conv2_1,axiom,
% 0.78/0.92 ( c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_k,V_j,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_less__add__Suc1_0,axiom,
% 0.78/0.92 c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_less__add__Suc2_0,axiom,
% 0.78/0.92 c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_less__iff__Suc__add_1,axiom,
% 0.78/0.92 c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_nat__less__add__iff2_1,axiom,
% 0.78/0.92 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_nat__less__add__iff2_0,axiom,
% 0.78/0.92 ( c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_nat__less__add__iff1_1,axiom,
% 0.78/0.92 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_j,V_i,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_nat__less__add__iff1_0,axiom,
% 0.78/0.92 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_j,V_i,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_eq__add__iff2_1,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oring(T_a)
% 0.78/0.92 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_nat_Osimps_I2_J_0,axiom,
% 0.78/0.92 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_Zero__neq__Suc_0,axiom,
% 0.78/0.92 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_abs__le__mult_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Olordered__ring(T_a)
% 0.78/0.92 | 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) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_abs__le__D1_0,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.92 | c_lessequals(V_a,V_b,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__strict__mono_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.92 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zmod__simps_I4_J_0,axiom,
% 0.78/0.92 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.92 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_min__max_Oinf__greatest_0,axiom,
% 0.78/0.92 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.92 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_x,V_z,T_a)
% 0.78/0.92 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_min__max_Ole__inf__iff_2,axiom,
% 0.78/0.92 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.92 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_x,V_z,T_a)
% 0.78/0.92 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_min__max_Ole__infI_0,axiom,
% 0.78/0.92 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.92 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_x,V_b,T_a)
% 0.78/0.92 | ~ c_lessequals(V_x,V_a,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_min__max_Oinf__le2_0,axiom,
% 0.78/0.92 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.92 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_y,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_min__max_Oinf__le1_0,axiom,
% 0.78/0.92 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.92 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_x,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_diff__Suc__diff__eq2_0,axiom,
% 0.78/0.92 ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_m,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(V_j),c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_k,V_j,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_dvd__triv__right_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_dvd__triv__left_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_dvdI_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Odvd(T_a)
% 0.78/0.92 | c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_add__is__1_4,axiom,
% 0.78/0.92 c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_of__nat__le__iff_1,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.78/0.92 | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_of__nat__le__iff_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.78/0.92 | c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.92 | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mod__0_0,axiom,
% 0.78/0.92 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.92 | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.92 | ~ class_Int_Onumber__ring(T_a)
% 0.78/0.92 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.92 | ~ class_Int_Onumber__ring(T_a)
% 0.78/0.92 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_natgb_Oadd__mul__solve_1,axiom,
% 0.78/0.92 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_natgb_Onoteq__reduce_1,axiom,
% 0.78/0.92 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_less__Suc0_0,axiom,
% 0.78/0.92 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_abs__triangle__ineq3_0,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_min__max_Oinf__left__idem_0,axiom,
% 0.78/0.92 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.92 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omin(V_x,V_y,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_abs__mult__less_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.92 | c_HOL_Oord__class_Oless(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_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mod__Suc_1,axiom,
% 0.78/0.92 ( c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))
% 0.78/0.92 | c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) = V_n ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__le__cancel1_1,axiom,
% 0.78/0.92 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
% 0.78/0.92 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__le__cancel2_1,axiom,
% 0.78/0.92 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)
% 0.78/0.92 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_add__nonneg__eq__0__iff_2,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.92 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__semiring_Omul__c_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_add__is__0_2,axiom,
% 0.78/0.92 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_double__eq__0__iff_1,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.78/0.92 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_nat__mult__commute_0,axiom,
% 0.78/0.92 c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mod__add__eq_0,axiom,
% 0.78/0.92 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.92 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_abs__eq__0_1,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.92 | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.78/0.92 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.78/0.92 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_dvd__mult_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
% 0.78/0.92 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_dvd__mult2_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
% 0.78/0.92 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_dvd__mult__left_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
% 0.78/0.92 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_dvd__mult__right_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
% 0.78/0.92 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_pos__add__strict_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.78/0.92 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__cancel2_1,axiom,
% 0.78/0.92 c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__cancel1_1,axiom,
% 0.78/0.92 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mod__lemma_0,axiom,
% 0.78/0.92 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(V_q,V_c,tc_nat),tc_nat),V_r,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(V_r,V_b,tc_nat)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_c,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__mono1_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Omult__mono1(T_a)
% 0.78/0.92 | 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)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.92 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__left__mono_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Omult__mono(T_a)
% 0.78/0.92 | 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)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.92 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__right__mono_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Omult__mono(T_a)
% 0.78/0.92 | 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)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.92 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__left__mono__neg_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.92 | 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)
% 0.78/0.92 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_b,V_a,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__right__mono__neg_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.92 | 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)
% 0.78/0.92 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_b,V_a,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom,
% 0.78/0.92 ( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat),tc_nat)
% 0.78/0.92 | V_c = V_d
% 0.78/0.92 | V_r = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.92 | ~ class_Int_Onumber__ring(T_a)
% 0.78/0.92 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,T_a),T_a)
% 0.78/0.92 | V_c = V_d
% 0.78/0.92 | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_sum__squares__eq__zero__iff_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.92 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.92 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_sum__squares__eq__zero__iff_1,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.92 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.92 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_n__not__Suc__n_0,axiom,
% 0.78/0.92 V_n != c_Suc(V_n) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_Suc__n__not__n_0,axiom,
% 0.78/0.92 c_Suc(V_n) != V_n ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__idem_0,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
% 0.78/0.92 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__strict__mono_H_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.92 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__le__cancel2_2,axiom,
% 0.78/0.92 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__le__cancel1_2,axiom,
% 0.78/0.92 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__le__mono2_0,axiom,
% 0.78/0.92 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__le__mono1_0,axiom,
% 0.78/0.92 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_Suc__mult__cancel1_0,axiom,
% 0.78/0.92 ( c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat)
% 0.78/0.92 | V_m = V_n ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_of__nat__add_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Osemiring__1(T_a)
% 0.78/0.92 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zmod__simps_I2_J_0,axiom,
% 0.78/0.92 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.92 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zmod__simps_I1_J_0,axiom,
% 0.78/0.92 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.92 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_inf__period_I4_J_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Odvd(T_a)
% 0.78/0.92 | ~ class_Ring__and__Field_Ocomm__ring(T_a)
% 0.78/0.92 | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
% 0.78/0.92 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
% 0.78/0.92 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_inf__period_I4_J_1,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Odvd(T_a)
% 0.78/0.92 | ~ class_Ring__and__Field_Ocomm__ring(T_a)
% 0.78/0.92 | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
% 0.78/0.92 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
% 0.78/0.92 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_add__is__1_2,axiom,
% 0.78/0.92 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.92 | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.92 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_add__is__1_1,axiom,
% 0.78/0.92 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.92 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.92 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_split__mult__pos__le_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_split__mult__pos__le_1,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__nonpos__nonpos_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zero__le__square_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zero__le__mult__iff_4,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zero__le__mult__iff_5,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__nonneg__nonneg_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_abs__triangle__ineq2_0,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
% 0.78/0.92 | 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) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | 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) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | 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) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | 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) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | 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) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_nat__mult__assoc_0,axiom,
% 0.78/0.92 c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__semiring_Omul__a_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | 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) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__right_Oadd_0,axiom,
% 0.78/0.92 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.92 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult_Oadd__right_0,axiom,
% 0.78/0.92 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.92 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__left_Oadd_0,axiom,
% 0.78/0.92 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.92 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult_Oadd__left_0,axiom,
% 0.78/0.92 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.92 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_add__mult__distrib2_0,axiom,
% 0.78/0.92 c_HOL_Otimes__class_Otimes(V_k,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_add__mult__distrib_0,axiom,
% 0.78/0.92 c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__semiring_Omul__d_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_comm__semiring__class_Odistrib_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring(T_a)
% 0.78/0.92 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_add__gr__0_2,axiom,
% 0.78/0.92 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_add__gr__0_1,axiom,
% 0.78/0.92 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.78/0.92 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
% 0.78/0.92 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.78/0.92 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zero__le__mult__iff_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.92 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zero__le__mult__iff_1,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.92 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zero__le__mult__iff_2,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.92 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_zero__le__mult__iff_3,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.92 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_sum__squares__gt__zero__iff_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.92 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__le__mono_0,axiom,
% 0.78/0.92 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_l,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_k,V_l,tc_nat)
% 0.78/0.92 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_le__cube_0,axiom,
% 0.78/0.92 c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),tc_nat) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__mono_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
% 0.78/0.92 | 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)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.92 | ~ c_lessequals(V_c,V_d,T_a)
% 0.78/0.92 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_mult__mono_H_0,axiom,
% 0.78/0.92 ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
% 0.78/0.92 | 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)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.78/0.92 | ~ c_lessequals(V_c,V_d,T_a)
% 0.78/0.92 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_even__sum__nat_3,axiom,
% 0.78/0.92 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat)
% 0.78/0.92 | c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
% 0.78/0.92 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_even__sum__nat_2,axiom,
% 0.78/0.92 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
% 0.78/0.92 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_even__sum__nat_1,axiom,
% 0.78/0.92 ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
% 0.78/0.92 | c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
% 0.78/0.92 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_even__sum__nat_0,axiom,
% 0.78/0.92 ( ~ c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
% 0.78/0.92 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
% 0.78/0.92 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_even__add_3,axiom,
% 0.78/0.92 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
% 0.78/0.92 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
% 0.78/0.92 | ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_even__add_2,axiom,
% 0.78/0.92 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
% 0.78/0.92 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
% 0.78/0.92 | c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) ) ).
% 0.78/0.92
% 0.78/0.92 cnf(cls_even__add_1,axiom,
% 0.78/0.93 ( c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)
% 0.78/0.93 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
% 0.78/0.93 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_even__add_0,axiom,
% 0.78/0.93 ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
% 0.78/0.93 | ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)
% 0.78/0.93 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_odd__add_3,axiom,
% 0.78/0.93 ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
% 0.78/0.93 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
% 0.78/0.93 | ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_odd__add_2,axiom,
% 0.78/0.93 ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
% 0.78/0.93 | c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_odd__add_1,axiom,
% 0.78/0.93 ( c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)
% 0.78/0.93 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
% 0.78/0.93 | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_odd__add_0,axiom,
% 0.78/0.93 ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
% 0.78/0.93 | ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)
% 0.78/0.93 | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_le__SucE_0,axiom,
% 0.78/0.93 ( V_m = c_Suc(V_n)
% 0.78/0.93 | c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_m,c_Suc(V_n),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__left__disj_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__right__disj_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__add_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_odd__nat__equiv__def_1,axiom,
% 0.78/0.93 ( c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.93 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_odd__nat__equiv__def_0,axiom,
% 0.78/0.93 ( c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.93 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__of__nat_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.93 | c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__add__distrib__left_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__add__right__cancel_0,axiom,
% 0.78/0.93 ( c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat) != c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat)
% 0.78/0.93 | V_m = V_n ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__add__left__cancel_0,axiom,
% 0.78/0.93 ( c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)
% 0.78/0.93 | V_m = V_n ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_natgb_Oadd__cancel_0,axiom,
% 0.78/0.93 ( c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat) != c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat)
% 0.78/0.93 | V_y = V_z ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__ringb_Oadd__cancel_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.93 | ~ class_Int_Onumber__ring(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)
% 0.78/0.93 | V_y = V_z ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__imp__eq_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
% 0.78/0.93 | V_b = V_c ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__left__cancel_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
% 0.78/0.93 | V_b = V_c ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__right__cancel_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
% 0.78/0.93 | V_b = V_c ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_not__square__less__zero_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__semiring_Oadd__a_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__cancel__21_1,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Oab__group__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__add__assoc_0,axiom,
% 0.78/0.93 c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__add__left__commute_0,axiom,
% 0.78/0.93 c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__gr__0_0,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__1__left_0,axiom,
% 0.78/0.93 c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__triangle__ineq_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_termination__basic__simps_I3_J_0,axiom,
% 0.78/0.93 ( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_x,V_y,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_termination__basic__simps_I4_J_0,axiom,
% 0.78/0.93 ( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_x,V_z,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__leE_0,axiom,
% 0.78/0.93 ( c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__leE_1,axiom,
% 0.78/0.93 ( c_lessequals(V_k,V_n,tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_trans__le__add1_0,axiom,
% 0.78/0.93 ( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_trans__le__add2_0,axiom,
% 0.78/0.93 ( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_odd__nat__equiv__def2_1,axiom,
% 0.78/0.93 ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_xa,tc_nat)),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__add__right__eq_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__add__left__eq_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__strict__increasing2_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.78/0.93 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_diff__add__0_0,axiom,
% 0.78/0.93 c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__mult__eq__cancel1_0,axiom,
% 0.78/0.93 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
% 0.78/0.93 | V_m = V_n ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel1_0,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel2_0,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__right__le__imp__le_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.93 | c_lessequals(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.93 | ~ 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) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__left__le__imp__le_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.93 | c_lessequals(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.93 | ~ 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) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__le__cancel__left__pos_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | 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)
% 0.78/0.93 | ~ c_lessequals(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__le__cancel__left__pos_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_lessequals(V_a,V_b,T_a)
% 0.78/0.93 | ~ 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)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__le__cancel__left__neg_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | 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)
% 0.78/0.93 | ~ c_lessequals(V_b,V_a,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__le__cancel__left__neg_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_lessequals(V_b,V_a,T_a)
% 0.78/0.93 | ~ 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)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__mult__le__cancel1_1,axiom,
% 0.78/0.93 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__mult__le__cancel1_0,axiom,
% 0.78/0.93 ( c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__le__cancel1_0,axiom,
% 0.78/0.93 ( c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__le__cancel2_0,axiom,
% 0.78/0.93 ( c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__lt__two__imp__zero__or__one_0,axiom,
% 0.78/0.93 ( V_x = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.93 | V_x = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult_Oprod__diff__prod_0,axiom,
% 0.78/0.93 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.93 | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_gr0__conv__Suc_1,axiom,
% 0.78/0.93 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_zero__less__Suc_0,axiom,
% 0.78/0.93 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Oinf__commute_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = c_Orderings_Oord__class_Omin(V_y,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_combine__common__factor_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Osemiring(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_left__add__mult__distrib_0,axiom,
% 0.78/0.93 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_k,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_u,tc_nat),V_k,tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__0__less__mult__iff_0,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__0__less__mult__iff_1,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__neg__neg_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_sum__squares__le__zero__iff_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | V_y = c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_sum__squares__le__zero__iff_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | V_x = c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_le0_0,axiom,
% 0.78/0.93 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_Suc__mult__less__cancel1_0,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_Suc__mult__less__cancel1_1,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_not__less__eq__eq_0,axiom,
% 0.78/0.93 ( c_lessequals(c_Suc(V_n),V_m,tc_nat)
% 0.78/0.93 | c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_not__less__eq__eq_1,axiom,
% 0.78/0.93 ( ~ c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_odd__pos_0,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.78/0.93 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__less__eq__dividend_0,axiom,
% 0.78/0.93 c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_m,tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_le__add__diff_0,axiom,
% 0.78/0.93 ( c_lessequals(V_m,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_k,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_k,V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__Suc_0,axiom,
% 0.78/0.93 ( c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) != V_n
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__of__pos_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.93 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__mult__right__eq_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__mult__left__eq_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__is__1_0,axiom,
% 0.78/0.93 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.93 | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.93 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__is__1_3,axiom,
% 0.78/0.93 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.93 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.93 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_Suc__mult__le__cancel1_0,axiom,
% 0.78/0.93 ( c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_Suc__mult__le__cancel1_1,axiom,
% 0.78/0.93 ( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_sum__squares__gt__zero__iff_2,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)
% 0.78/0.93 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_sum__squares__gt__zero__iff_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)
% 0.78/0.93 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_of__nat__less__0__iff_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_le__Suc__eq_2,axiom,
% 0.78/0.93 c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_even__Suc_0,axiom,
% 0.78/0.93 ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
% 0.78/0.93 | ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(V_x),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_even__Suc_1,axiom,
% 0.78/0.93 ( c_Parity_Oeven__odd__class_Oeven(c_Suc(V_x),tc_nat)
% 0.78/0.93 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__1__iff__1_0,axiom,
% 0.78/0.93 ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_le__square_0,axiom,
% 0.78/0.93 c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__Suc__Suc_0,axiom,
% 0.78/0.93 c_Orderings_Oord__class_Omin(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat)) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__mult__distrib_0,axiom,
% 0.78/0.93 c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_k,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__mult__distrib2_0,axiom,
% 0.78/0.93 c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__strict__left__mono__comm_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__right__disj_5,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__right__disj_4,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__strict__right__mono_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__strict__right__mono__neg_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__left__disj_5,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__left__disj_4,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__strict__left__mono_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__strict__left__mono__neg_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__left__pos_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__left__pos_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__left__neg_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__left__neg_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__mult__less__cancel1_1,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__mult__less__cancel1_0,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__mono1_0,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__mono2_0,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel1_2,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel2_2,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__mult__self2_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__mult__self1_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__mult__self3_0,axiom,
% 0.78/0.93 c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat),V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__mult__cancel__right_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.93 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
% 0.78/0.93 | V_c = c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.93 | ~ 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) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__mult__cancel__left_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.93 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
% 0.78/0.93 | V_c = c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.93 | ~ 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) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__mult__dvd__cancel__disj_0,axiom,
% 0.78/0.93 ( c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)
% 0.78/0.93 | V_k = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__le__0__iff_4,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__le__0__iff_5,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.93 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_split__mult__neg__le_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_split__mult__neg__le_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.93 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__nonneg__nonpos_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__nonpos__nonneg_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.93 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__nonneg__nonpos2_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__le__zero__iff_1,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.93 | 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) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__nonneg__pos_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__pos__nonneg_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__imp__mod__0_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__eq__mod__eq__0_1,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.93 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__0__left_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | V_a = c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_of__nat__0_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Osemiring__1(T_a)
% 0.78/0.93 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_one__less__mult_0,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__Suc__shift_0,axiom,
% 0.78/0.93 c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_one__is__add_3,axiom,
% 0.78/0.93 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
% 0.78/0.93 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.93 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_one__is__add_0,axiom,
% 0.78/0.93 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
% 0.78/0.93 | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.93 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_one__is__add_5,axiom,
% 0.78/0.93 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Oinf__assoc_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Oinf__left__commute_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omin(V_y,c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd_Oless__trans_1,axiom,
% 0.78/0.93 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat)
% 0.78/0.93 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
% 0.78/0.93 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__less__divisor_0,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Ole__iff__inf_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_x
% 0.78/0.93 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Ole__iff__inf_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) != V_x
% 0.78/0.93 | c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Oinf__absorb2_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_y
% 0.78/0.93 | ~ c_lessequals(V_y,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__cancel__21_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Oab__group__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_y,V_u,T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_one__le__mult__iff_1,axiom,
% 0.78/0.93 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_one__le__mult__iff_0,axiom,
% 0.78/0.93 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__nonneg__nonneg_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_less__Suc__eq__le_1,axiom,
% 0.78/0.93 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_less__Suc__eq__le_0,axiom,
% 0.78/0.93 ( c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_le__less__Suc__eq_1,axiom,
% 0.78/0.93 ( ~ c_lessequals(V_x,V_x,tc_nat)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__le__mono_0,axiom,
% 0.78/0.93 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_k,V_l,tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__mono_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(V_c,V_d,T_a)
% 0.78/0.93 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__diff__add__eq1_0,axiom,
% 0.78/0.93 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_j,V_i,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__diff__add__eq2_0,axiom,
% 0.78/0.93 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__mod__trivial_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__diff__triangle__ineq_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),T_a),T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__strict__increasing_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.78/0.93 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(V_b,V_c,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_diff__is__0__eq_1,axiom,
% 0.78/0.93 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_diff__is__0__eq_0,axiom,
% 0.78/0.93 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.93 | c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__diffD1_0,axiom,
% 0.78/0.93 ( c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_n,V_m,tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__diffD_0,axiom,
% 0.78/0.93 ( c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_n,V_m,tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_eq__add__iff1_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oring(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__mult__dvd__cancel__disj_2,axiom,
% 0.78/0.93 ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__mult__cancel__left_2,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.93 | 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)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__mult__cancel__right_2,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.93 | 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)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__idempotent_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.93 | 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) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__Suc_0,axiom,
% 0.78/0.93 c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__Suc__right_0,axiom,
% 0.78/0.93 c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_eq__add__iff1_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oring(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) = V_d ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_eq__add__iff2_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oring(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
% 0.78/0.93 | V_c = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_zero__less__abs__iff_1,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
% 0.78/0.93 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_even__product__nat_2,axiom,
% 0.78/0.93 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_even__product__nat_1,axiom,
% 0.78/0.93 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__by__0_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__self_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__add__commute_0,axiom,
% 0.78/0.93 c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__semiring_Oadd__c_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__mult__eq_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__cancel2_0,axiom,
% 0.78/0.93 ( c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)
% 0.78/0.93 | V_k = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.93 | V_m = V_n ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__cancel1_0,axiom,
% 0.78/0.93 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)
% 0.78/0.93 | V_k = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.93 | V_m = V_n ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__mult__eq__cancel__disj_0,axiom,
% 0.78/0.93 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)
% 0.78/0.93 | V_m = V_n
% 0.78/0.93 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Ole__infE_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_lessequals(V_x,V_a,T_a)
% 0.78/0.93 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Ole__infE_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_lessequals(V_x,V_b,T_a)
% 0.78/0.93 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Ole__infI1_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
% 0.78/0.93 | ~ c_lessequals(V_a,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Ole__infI2_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
% 0.78/0.93 | ~ c_lessequals(V_b,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__le__iff__disj_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
% 0.78/0.93 | ~ c_lessequals(V_x,V_z,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__le__iff__disj_2,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
% 0.78/0.93 | ~ c_lessequals(V_y,V_z,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Ole__inf__iff_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_lessequals(V_x,V_y,T_a)
% 0.78/0.93 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Ole__inf__iff_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_lessequals(V_x,V_z,T_a)
% 0.78/0.93 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat_Oinject_0,axiom,
% 0.78/0.93 ( c_Suc(V_nat) != c_Suc(V_nat_H)
% 0.78/0.93 | V_nat = V_nat_H ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_Suc__inject_0,axiom,
% 0.78/0.93 ( c_Suc(V_x) != c_Suc(V_y)
% 0.78/0.93 | V_x = V_y ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__ge__self_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.93 | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__le__iff__disj_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_lessequals(V_y,V_z,T_a)
% 0.78/0.93 | c_lessequals(V_x,V_z,T_a)
% 0.78/0.93 | ~ c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__eq__add__iff2_1,axiom,
% 0.78/0.93 ( ~ c_lessequals(V_i,V_j,tc_nat)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__add__cong_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_less__Suc0_1,axiom,
% 0.78/0.93 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_one__is__add_2,axiom,
% 0.78/0.93 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
% 0.78/0.93 | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.93 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_one__is__add_1,axiom,
% 0.78/0.93 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
% 0.78/0.93 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.78/0.93 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_le__diff__conv_1,axiom,
% 0.78/0.93 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_le__diff__conv_0,axiom,
% 0.78/0.93 ( c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_even__zero__nat_0,axiom,
% 0.78/0.93 c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__le__add__iff1_0,axiom,
% 0.78/0.93 ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_j,V_i,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__le__add__iff1_1,axiom,
% 0.78/0.93 ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_j,V_i,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__le__add__iff2_0,axiom,
% 0.78/0.93 ( c_lessequals(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_nat__le__add__iff2_1,axiom,
% 0.78/0.93 ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat)
% 0.78/0.93 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_of__nat__mult_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Osemiring__1(T_a)
% 0.78/0.93 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__mult__self4_0,axiom,
% 0.78/0.93 c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat)),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_natgb_Onoteq__reduce_0,axiom,
% 0.78/0.93 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_d,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)
% 0.78/0.93 | V_c = V_d
% 0.78/0.93 | V_a = V_b ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_natgb_Oadd__mul__solve_0,axiom,
% 0.78/0.93 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat)
% 0.78/0.93 | V_y = V_z
% 0.78/0.93 | V_w = V_x ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.93 | ~ class_Int_Onumber__ring(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
% 0.78/0.93 | V_c = V_d
% 0.78/0.93 | V_a = V_b ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.93 | ~ class_Int_Onumber__ring(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
% 0.78/0.93 | V_y = V_z
% 0.78/0.93 | V_w = V_x ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__mult__self_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.93 | 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) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__mult__cong_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_zero__le__imp__of__nat_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_of__nat__0__le__iff_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.78/0.93 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__0__left_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.93 | ~ class_Int_Onumber__ring(T_a)
% 0.78/0.93 | V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__semiring_Oadd__0_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_comm__monoid__add_Omult__1_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_natgb_Oadd__r0__iff_1,axiom,
% 0.78/0.93 V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_Nat_Oadd__0__right_0,axiom,
% 0.78/0.93 c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_plus__nat_Oadd__0_0,axiom,
% 0.78/0.93 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__less__le__mono_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
% 0.78/0.93 | ~ c_lessequals(V_c,V_d,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__le__less__mono_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
% 0.78/0.93 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd_Ole__less__trans_1,axiom,
% 0.78/0.93 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat)
% 0.78/0.93 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd_Oless__le__trans_1,axiom,
% 0.78/0.93 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
% 0.78/0.93 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_xt1_I7_J_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
% 0.78/0.93 | ~ c_lessequals(V_z,V_y,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_xt1_I8_J_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
% 0.78/0.93 | ~ c_lessequals(V_y,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_order__less__le__trans_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Opreorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
% 0.78/0.93 | ~ c_lessequals(V_y,V_z,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_order__le__less__trans_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Opreorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
% 0.78/0.93 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__strict__right__mono_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__less__cancel__right_1,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__less__cancel__right_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__strict__left__mono_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__less__cancel__left_1,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__less__cancel__left_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_order__less__imp__le_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Opreorder(T_a)
% 0.78/0.93 | c_lessequals(V_x,V_y,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_order__le__less_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.93 | c_lessequals(V_x,V_y,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_add__strict__mono_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_less__le__not__le_2,axiom,
% 0.78/0.93 ( ~ class_Orderings_Opreorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.78/0.93 | c_lessequals(V_y,V_x,T_a)
% 0.78/0.93 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__less__iff__disj_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_y,V_z,T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__less__iff_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__right__disj_3,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mult__less__cancel__left__disj_3,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_xt1_I11_J_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.78/0.93 | V_a = V_b
% 0.78/0.93 | ~ c_lessequals(V_b,V_a,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_xt1_I12_J_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.78/0.93 | ~ c_lessequals(V_b,V_a,T_a)
% 0.78/0.93 | V_a = V_b ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_linorder__antisym__conv2_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | V_x = V_y
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.78/0.93 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_linorder__antisym__conv1_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | V_x = V_y
% 0.78/0.93 | ~ c_lessequals(V_x,V_y,T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_order__neq__le__trans_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.93 | ~ c_lessequals(V_a,V_b,T_a)
% 0.78/0.93 | V_a = V_b ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_order__le__neq__trans_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.93 | V_a = V_b
% 0.78/0.93 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_order__le__less_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.93 | V_x = V_y
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.78/0.93 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_order__less__le_2,axiom,
% 0.78/0.93 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.78/0.93 | V_x = V_y
% 0.78/0.93 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__less__iff__conj_2,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_less__le__not__le_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Opreorder(T_a)
% 0.78/0.93 | ~ c_lessequals(V_y,V_x,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_not__leE_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.78/0.93 | c_lessequals(V_y,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_linorder__antisym__conv2_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | ~ c_lessequals(V_x,V_x,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_linorder__antisym__conv1_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,V_x,T_a)
% 0.78/0.93 | c_lessequals(V_x,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_linorder__not__less_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.78/0.93 | ~ c_lessequals(V_y,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_linorder__not__less_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_lessequals(V_y,V_x,T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_linorder__not__le_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.78/0.93 | c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_linorder__not__le_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | ~ c_lessequals(V_x,V_y,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__less__iff__disj_2,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__less__iff__disj_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__less__iff__conj_1,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_z,V_y,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__less__iff__conj_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Oless__infI2_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__max_Oless__infI1_0,axiom,
% 0.78/0.93 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__diff__less__iff_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_less__add__iff2_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_less__add__iff2_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_less__add__iff1_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_less__add__iff1_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Opordered__ring(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__diff__less__iff_2,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.93 | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a)
% 0.78/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__diff__cong_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Oring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_min__diff__distrib__left_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.78/0.93 | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__diff__right__eq_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Oring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__diff__left__eq_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Oring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_mod__diff__eq_0,axiom,
% 0.78/0.93 ( ~ class_Divides_Oring__div(T_a)
% 0.78/0.93 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_abs__minus__commute_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.93 | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_le__eqI_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.78/0.93 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
% 0.78/0.93 | c_lessequals(V_y_H,V_x_H,T_a)
% 0.78/0.93 | ~ c_lessequals(V_y,V_x,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_le__eqI_1,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.78/0.93 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
% 0.78/0.93 | c_lessequals(V_y,V_x,T_a)
% 0.78/0.93 | ~ c_lessequals(V_y_H,V_x_H,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_dvd__diff_0,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
% 0.78/0.93 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a)
% 0.78/0.93 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_eq__iff__diff__eq__0_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Oab__group__add(T_a)
% 0.78/0.93 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_right__minus__eq_1,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Ogroup__add(T_a)
% 0.78/0.93 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_diff__0__right_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Ogroup__add(T_a)
% 0.78/0.93 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_diff__self_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Ogroup__add(T_a)
% 0.78/0.93 | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_class__ringb_Osubr0__iff_1,axiom,
% 0.78/0.93 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.93 | ~ class_Int_Onumber__ring(T_a)
% 0.78/0.93 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_diff__add__cancel_0,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Ogroup__add(T_a)
% 0.78/0.93 | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ).
% 0.78/0.93
% 0.78/0.93 cnf(cls_eq__iff__diff__eq__0_1,axiom,
% 0.78/0.93 ( ~ class_OrderedGroup_Oab__group__add(T_a)
% 0.78/0.94 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.94 | V_a = V_b ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_right__minus__eq_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Ogroup__add(T_a)
% 0.78/0.94 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.94 | V_a = V_b ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_class__ringb_Osubr0__iff_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.78/0.94 | ~ class_Int_Onumber__ring(T_a)
% 0.78/0.94 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.94 | V_x = V_y ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__right_Odiff_0,axiom,
% 0.78/0.94 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult_Odiff__right_0,axiom,
% 0.78/0.94 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult_Odiff__left_0,axiom,
% 0.78/0.94 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__left_Odiff_0,axiom,
% 0.78/0.94 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Deriv_Oadd__diff__add_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Oab__group__add(T_a)
% 0.78/0.94 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_c,V_d,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_add__diff__cancel_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Ogroup__add(T_a)
% 0.78/0.94 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat__add__left__cancel__less_1,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat__add__left__cancel__less_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_add__less__mono1_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_not__add__less1_0,axiom,
% 0.78/0.94 ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_not__add__less2_0,axiom,
% 0.78/0.94 ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_neq0__conv_1,axiom,
% 0.78/0.94 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_gr0I_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.78/0.94 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_termination__basic__simps_I5_J_0,axiom,
% 0.78/0.94 ( c_lessequals(V_x,V_y,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat__less__le_0,axiom,
% 0.78/0.94 ( c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_add__less__mono_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__SucE_0,axiom,
% 0.78/0.94 ( V_m = V_n
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__antisym_0,axiom,
% 0.78/0.94 ( V_m = V_n
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0,axiom,
% 0.78/0.94 c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_dvd__0__right_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.94 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__eq__1__iff_2,axiom,
% 0.78/0.94 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__left_Ozero_0,axiom,
% 0.78/0.94 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult_Ozero__left_0,axiom,
% 0.78/0.94 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__is__0_2,axiom,
% 0.78/0.94 c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__is__0_1,axiom,
% 0.78/0.94 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult_Ozero__right_0,axiom,
% 0.78/0.94 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__right_Ozero_0,axiom,
% 0.78/0.94 ( ~ class_RealVector_Oreal__normed__algebra(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_class__semiring_Omul__0_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__zero__left_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Omult__zero(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__zero__right_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Omult__zero(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__eq__0__iff_1,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__eq__0__iff_2,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
% 0.78/0.94 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__diff__right_0,axiom,
% 0.78/0.94 ( c_HOL_Ominus__class_Ominus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_j,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mod__1_0,axiom,
% 0.78/0.94 c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_abs__mult__pos_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.94 | 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)
% 0.78/0.94 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_dvd__reduce_1,axiom,
% 0.78/0.94 ( c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_dvd__reduce_0,axiom,
% 0.78/0.94 ( c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_abs__dvd__iff_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.94 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_abs__dvd__iff_1,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.94 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_dvd__abs__iff_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.94 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_dvd__abs__iff_1,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.94 | c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_one__is__add_4,axiom,
% 0.78/0.94 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__imp__diff__is__add_1,axiom,
% 0.78/0.94 ( ~ c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),tc_nat)
% 0.78/0.94 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),V_i,tc_nat) = V_k ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_add__pos__pos_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__Suc__ex__iff_1,axiom,
% 0.78/0.94 c_lessequals(V_k,c_HOL_Oplus__class_Oplus(V_k,V_x,tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__iff__add_1,axiom,
% 0.78/0.94 c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__add2_0,axiom,
% 0.78/0.94 c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__add1_0,axiom,
% 0.78/0.94 c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat__dvd__not__less_0,axiom,
% 0.78/0.94 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__iff__diff__le__0_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.78/0.94 | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.94 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__iff__diff__le__0_1,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.78/0.94 | c_lessequals(V_a,V_b,T_a)
% 0.78/0.94 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Suc__neq__Zero_0,axiom,
% 0.78/0.94 c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat_Osimps_I3_J_0,axiom,
% 0.78/0.94 c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_abs__not__less__zero_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__add__diff__inverse2_0,axiom,
% 0.78/0.94 ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m
% 0.78/0.94 | ~ c_lessequals(V_n,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__add__diff__inverse_0,axiom,
% 0.78/0.94 ( c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m
% 0.78/0.94 | ~ c_lessequals(V_n,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__imp__diff__is__add_0,axiom,
% 0.78/0.94 ( ~ c_lessequals(V_i,V_j,tc_nat)
% 0.78/0.94 | V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_dvd__mult__cancel_0,axiom,
% 0.78/0.94 ( c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat__mult__dvd__cancel1_0,axiom,
% 0.78/0.94 ( c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat__mult__dvd__cancel1_1,axiom,
% 0.78/0.94 ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_add__diff__assoc2_0,axiom,
% 0.78/0.94 ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_j,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_add__diff__assoc_0,axiom,
% 0.78/0.94 ( c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_j,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat__mod__eq__iff_1,axiom,
% 0.78/0.94 ( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_n,V_xa,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_y,c_HOL_Otimes__class_Otimes(V_n,V_xb,tc_nat),tc_nat)
% 0.78/0.94 | c_Divides_Odiv__class_Omod(V_x,V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_y,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_of__nat__0__less__iff_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_of__nat__0__less__iff_1,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__le__less__imp__less_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
% 0.78/0.94 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
% 0.78/0.94 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__less__le__imp__less_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.94 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.78/0.94 | ~ c_lessequals(V_c,V_d,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_abs__triangle__ineq4_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.94 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__SucI_0,axiom,
% 0.78/0.94 ( c_lessequals(V_m,c_Suc(V_n),tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Suc__leD_0,axiom,
% 0.78/0.94 ( c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_n__less__n__mult__m_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_n__less__m__mult__n_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Suc__n__not__le__n_0,axiom,
% 0.78/0.94 ~ c_lessequals(c_Suc(V_n),V_n,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mod__mod__cancel_0,axiom,
% 0.78/0.94 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.94 | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(V_a,V_c,T_a)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.78/0.94 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.94 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.78/0.94 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.94 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_abs__if__lattice_1,axiom,
% 0.78/0.94 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.94 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
% 0.78/0.94 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_abs__if_1,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oabs__if(T_a)
% 0.78/0.94 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__dvd__mono_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.78/0.94 | 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)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__0__eq_1,axiom,
% 0.78/0.94 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_abs__add__abs_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.94 | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mod__Suc__eq__Suc__mod_0,axiom,
% 0.78/0.94 c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_abs__eq__0_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.94 | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.78/0.94 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_zero__less__abs__iff_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_one__le__mult__iff_2,axiom,
% 0.78/0.94 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_order__eq__refl_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Opreorder(T_a)
% 0.78/0.94 | c_lessequals(V_x,V_x,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_order__eq__iff_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.94 | c_lessequals(V_x,V_x,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_eq__imp__le_0,axiom,
% 0.78/0.94 c_lessequals(V_x,V_x,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__trans_0,axiom,
% 0.78/0.94 ( c_lessequals(V_i,V_k,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_j,V_k,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_i,V_j,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__refl_0,axiom,
% 0.78/0.94 c_lessequals(V_n,V_n,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__add__right__mono_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.78/0.94 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
% 0.78/0.94 | ~ c_lessequals(V_c,V_d,T_a)
% 0.78/0.94 | ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_order__trans_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Opreorder(T_a)
% 0.78/0.94 | c_lessequals(V_x,V_z,T_a)
% 0.78/0.94 | ~ c_lessequals(V_y,V_z,T_a)
% 0.78/0.94 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_add__nonpos__nonpos_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.78/0.94 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.94 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.94 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_xt1_I6_J_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.94 | c_lessequals(V_z,V_x,T_a)
% 0.78/0.94 | ~ c_lessequals(V_z,V_y,T_a)
% 0.78/0.94 | ~ c_lessequals(V_y,V_x,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_even__product__nat_0,axiom,
% 0.78/0.94 ( c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
% 0.78/0.94 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
% 0.78/0.94 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_add__is__1_5,axiom,
% 0.78/0.94 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mod__eq__0__iff_1,axiom,
% 0.78/0.94 c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mod__mult__self1__is__0_0,axiom,
% 0.78/0.94 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.94 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mod__mult__self2__is__0_0,axiom,
% 0.78/0.94 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.94 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__less__Suc__eq_0,axiom,
% 0.78/0.94 ( V_n = V_m
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_sum__squares__eq__zero__iff_2,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.94 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__less__cancel__left__disj_1,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__less__cancel__left__disj_2,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__less__cancel__right__disj_1,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__less__cancel__right__disj_2,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mod__mult__mult1_0,axiom,
% 0.78/0.94 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.94 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mod__mult__mult2_0,axiom,
% 0.78/0.94 ( ~ class_Divides_Osemiring__div(T_a)
% 0.78/0.94 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_dvd__imp__le_0,axiom,
% 0.78/0.94 ( c_lessequals(V_k,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_abs__ge__zero_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
% 0.78/0.94 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Suc__le__mono_1,axiom,
% 0.78/0.94 ( c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_n,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Suc__le__mono_0,axiom,
% 0.78/0.94 ( c_lessequals(V_n,V_m,tc_nat)
% 0.78/0.94 | ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_dvd__if__abs__eq_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.94 | c_HOL_Oabs__class_Oabs(V_l,T_a) != c_HOL_Oabs__class_Oabs(V_k,T_a)
% 0.78/0.94 | c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_linorder__linear_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.94 | c_lessequals(V_y,V_x,T_a)
% 0.78/0.94 | c_lessequals(V_x,V_y,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_dvd_Oless__le__trans_0,axiom,
% 0.78/0.94 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
% 0.78/0.94 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_dvd_Ole__less__trans_0,axiom,
% 0.78/0.94 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)
% 0.78/0.94 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat__le__linear_0,axiom,
% 0.78/0.94 ( c_lessequals(V_n,V_m,tc_nat)
% 0.78/0.94 | c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_not__less__less__Suc__eq_0,axiom,
% 0.78/0.94 ( V_n = V_m
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__add__eq__less_0,axiom,
% 0.78/0.94 ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_not__less0_0,axiom,
% 0.78/0.94 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_gr__implies__not0_0,axiom,
% 0.78/0.94 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_not__less__eq_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_not__less__eq_1,axiom,
% 0.78/0.94 ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_not__less__less__Suc__eq_1,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat__less__le_2,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | V_m = V_n
% 0.78/0.94 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__eq__less__or__eq_0,axiom,
% 0.78/0.94 ( V_m = V_n
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__neq__implies__less_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | V_m = V_n
% 0.78/0.94 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Suc__lessD_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__SucI_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__less__cancel1_1,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mult__less__cancel2_1,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_lessI_0,axiom,
% 0.78/0.94 c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__Suc__eq_2,axiom,
% 0.78/0.94 c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__trans__Suc_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mod__if_0,axiom,
% 0.78/0.94 ( c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = V_m
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_termination__basic__simps_I1_J_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_termination__basic__simps_I2_J_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_add__lessD1_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_trans__less__add1_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_trans__less__add2_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Suc__lessI_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)
% 0.78/0.94 | c_Suc(V_m) = V_n
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Suc__mono_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Suc__less__eq_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__Suc__eq__0__disj_3,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_of__nat__diff_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oring__1(T_a)
% 0.78/0.94 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
% 0.78/0.94 | ~ c_lessequals(V_n,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__Suc__less_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Suc__pred_0,axiom,
% 0.78/0.94 ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__Suc__Suc_0,axiom,
% 0.78/0.94 c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__cancel_0,axiom,
% 0.78/0.94 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__cancel2_0,axiom,
% 0.78/0.94 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Suc__diff__diff_0,axiom,
% 0.78/0.94 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__diff__cancel_0,axiom,
% 0.78/0.94 ( c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = V_i
% 0.78/0.94 | ~ c_lessequals(V_i,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_min__diff_0,axiom,
% 0.78/0.94 c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_m,V_i,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat),V_i,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diffs0__imp__equal_0,axiom,
% 0.78/0.94 ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.94 | c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
% 0.78/0.94 | V_m = V_n ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_dvd__diff__nat_0,axiom,
% 0.78/0.94 ( c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
% 0.78/0.94 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__self__eq__0_0,axiom,
% 0.78/0.94 c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_minus__nat_Odiff__0_0,axiom,
% 0.78/0.94 c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__diff__iff_0,axiom,
% 0.78/0.94 ( c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_le__diff__iff_1,axiom,
% 0.78/0.94 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__le__mono_0,axiom,
% 0.78/0.94 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_l,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_l,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__le__mono2_0,axiom,
% 0.78/0.94 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__diff__left_0,axiom,
% 0.78/0.94 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_eq__diff__iff_0,axiom,
% 0.78/0.94 ( c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat) != c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_m,tc_nat)
% 0.78/0.94 | V_m = V_n ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__0__eq__0_0,axiom,
% 0.78/0.94 c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_even__difference__nat_4,axiom,
% 0.78/0.94 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_nat),tc_nat)
% 0.78/0.94 | c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
% 0.78/0.94 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_even__difference__nat_3,axiom,
% 0.78/0.94 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
% 0.78/0.94 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__le__self_0,axiom,
% 0.78/0.94 c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__mult__distrib_0,axiom,
% 0.78/0.94 c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__mult__distrib2_0,axiom,
% 0.78/0.94 c_HOL_Otimes__class_Otimes(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_Nat_Odiff__diff__eq_0,axiom,
% 0.78/0.94 ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__add__inverse_0,axiom,
% 0.78/0.94 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat) = V_m ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__add__inverse2_0,axiom,
% 0.78/0.94 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__iff__diff__less__0_1,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__iff__diff__less__0_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_abs__diff__less__iff_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_of__nat__less__iff_1,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_of__nat__less__iff_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_add__diff__inverse_0,axiom,
% 0.78/0.94 ( c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__less_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_even__difference__nat_1,axiom,
% 0.78/0.94 ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
% 0.78/0.94 | c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
% 0.78/0.94 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_nat),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_even__difference__nat_0,axiom,
% 0.78/0.94 ( ~ c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
% 0.78/0.94 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
% 0.78/0.94 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_nat),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__diff__conv_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__diff__conv_1,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__diff__iff_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__diff__iff_1,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_n,tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_k,V_m,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__less__Suc_0,axiom,
% 0.78/0.94 c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_zero__less__diff_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_zero__less__diff_1,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_mod__if_1,axiom,
% 0.78/0.94 ( c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__less__mono_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_c,tc_nat),c_HOL_Ominus__class_Ominus(V_b,V_c,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_lessequals(V_c,V_a,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_even__difference__nat_2,axiom,
% 0.78/0.94 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_xt1_I9_J_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_not__less__iff__gr__or__eq_1,axiom,
% 0.78/0.94 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_order__less__asym_H_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Opreorder(T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_order__less__asym_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Opreorder(T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_order__less__irrefl_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Opreorder(T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_linorder__neq__iff_1,axiom,
% 0.78/0.94 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat__less__le_1,axiom,
% 0.78/0.94 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__not__refl_0,axiom,
% 0.78/0.94 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_order__less__le_1,axiom,
% 0.78/0.94 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__imp__diff__less_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__less__mono2_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__eqI_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.78/0.94 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_less__eqI_1,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.78/0.94 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_linorder__neqE__ordered__idom_0,axiom,
% 0.78/0.94 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.78/0.94 | V_x = V_y ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_not__less__iff__gr__or__eq_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.94 | V_x = V_y
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_linorder__antisym__conv3_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.94 | V_x = V_y
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_linorder__less__linear_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.78/0.94 | V_x = V_y
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_nat__neq__iff_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.78/0.94 | V_m = V_n ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_linorder__neqE__nat_0,axiom,
% 0.78/0.94 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
% 0.78/0.94 | V_x = V_y ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_linorder__neqE_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Olinorder(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.78/0.94 | V_x = V_y ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_assms_0,axiom,
% 0.78/0.94 c_HOL_Oord__class_Oless(v_i,v_n,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_xt1_I10_J_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Oorder(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_order__less__trans_0,axiom,
% 0.78/0.94 ( ~ class_Orderings_Opreorder(T_a)
% 0.78/0.94 | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
% 0.78/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_eq__eqI_0,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Oab__group__add(T_a)
% 0.78/0.94 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
% 0.78/0.94 | V_x_H = V_y_H ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_eq__eqI_1,axiom,
% 0.78/0.94 ( ~ class_OrderedGroup_Oab__group__add(T_a)
% 0.78/0.94 | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
% 0.78/0.94 | V_xa = V_y ) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_diff__commute_0,axiom,
% 0.78/0.94 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_CHAINED_0,axiom,
% 0.78/0.94 c_HOL_Oord__class_Oless(v_i,v_n,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(cls_conjecture_0,negated_conjecture,
% 0.78/0.94 ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
% 0.78/0.94 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
% 0.78/0.94 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
% 0.78/0.94 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
% 0.78/0.94 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
% 0.78/0.94 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
% 0.78/0.94 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
% 0.78/0.94 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
% 0.78/0.94 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
% 0.78/0.94 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
% 0.78/0.94 class_Ring__and__Field_Opordered__semiring(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
% 0.78/0.94 class_Ring__and__Field_Oordered__semiring(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
% 0.78/0.94 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
% 0.78/0.94 class_Ring__and__Field_Oordered__semidom(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
% 0.78/0.94 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
% 0.78/0.94 class_OrderedGroup_Oab__semigroup__mult(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
% 0.78/0.94 class_OrderedGroup_Oab__semigroup__add(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
% 0.78/0.94 class_Ring__and__Field_Ocomm__semiring(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
% 0.78/0.94 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
% 0.78/0.94 class_Ring__and__Field_Osemiring__1(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
% 0.78/0.94 class_Ring__and__Field_Omult__mono1(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
% 0.78/0.94 class_Ring__and__Field_Omult__zero(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom,
% 0.78/0.94 class_Ring__and__Field_Omult__mono(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
% 0.78/0.94 class_Ring__and__Field_Osemiring(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
% 0.78/0.94 class_OrderedGroup_Omonoid__add(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Divides_Osemiring__div,axiom,
% 0.78/0.94 class_Divides_Osemiring__div(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
% 0.78/0.94 class_Nat_Osemiring__char__0(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Ring__and__Field_Odvd,axiom,
% 0.78/0.94 class_Ring__and__Field_Odvd(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Orderings_Opreorder,axiom,
% 0.78/0.94 class_Orderings_Opreorder(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Orderings_Olinorder,axiom,
% 0.78/0.94 class_Orderings_Olinorder(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 cnf(clsarity_nat__Orderings_Oorder,axiom,
% 0.78/0.94 class_Orderings_Oorder(tc_nat) ).
% 0.78/0.94
% 0.78/0.94 %------------------------------------------------------------------------------
% 0.78/0.94 %-------------------------------------------
% 0.78/0.94 % Proof found
% 0.78/0.94 % SZS status Theorem for theBenchmark
% 0.78/0.94 % SZS output start Proof
% 0.78/0.94 %ClaNum:885(EqnAxiom:87)
% 0.78/0.94 %VarNum:5219(SingletonVarNum:1831)
% 0.78/0.94 %MaxLitNum:6
% 0.78/0.94 %MaxfuncDepth:5
% 0.78/0.94 %SharedTerms:52
% 0.78/0.94 %goalClause: 214
% 0.78/0.94 %singleGoalClaCount:1
% 0.78/0.94 [88]P1(a1)
% 0.78/0.94 [89]P2(a1)
% 0.78/0.94 [90]P27(a1)
% 0.78/0.94 [91]P28(a1)
% 0.78/0.94 [92]P29(a1)
% 0.78/0.94 [93]P3(a1)
% 0.78/0.94 [94]P25(a1)
% 0.78/0.94 [95]P4(a1)
% 0.78/0.94 [96]P36(a1)
% 0.78/0.94 [97]P43(a1)
% 0.78/0.94 [98]P10(a1)
% 0.78/0.94 [99]P12(a1)
% 0.78/0.94 [100]P37(a1)
% 0.78/0.94 [101]P44(a1)
% 0.78/0.94 [102]P38(a1)
% 0.78/0.94 [103]P39(a1)
% 0.78/0.94 [104]P48(a1)
% 0.78/0.94 [105]P49(a1)
% 0.78/0.94 [106]P13(a1)
% 0.78/0.94 [107]P30(a1)
% 0.78/0.94 [108]P50(a1)
% 0.78/0.94 [109]P17(a1)
% 0.78/0.94 [110]P18(a1)
% 0.78/0.94 [111]P14(a1)
% 0.78/0.94 [112]P53(a1)
% 0.78/0.95 [113]P45(a1)
% 0.78/0.95 [114]P19(a1)
% 0.78/0.95 [115]P26(a1)
% 0.78/0.95 [116]P31(a1)
% 0.78/0.95 [117]P42(a1)
% 0.78/0.95 [120]P6(a11,a12,a1)
% 0.78/0.95 [118]P5(f2(a1),a1)
% 0.78/0.95 [214]~P6(f3(a11,a13,a1),a12,a1)
% 0.78/0.95 [151]E(f7(f10(f2(a1)),f10(f2(a1)),a1),f10(f2(a1)))
% 0.78/0.95 [121]P7(x1211,x1211,a1)
% 0.78/0.95 [123]P8(x1231,x1231,a1)
% 0.78/0.95 [209]~P6(x2091,x2091,a1)
% 0.78/0.95 [124]E(f3(x1241,x1241,a1),f2(a1))
% 0.78/0.95 [125]P7(x1251,f2(a1),a1)
% 0.78/0.95 [126]P8(f2(a1),x1261,a1)
% 0.78/0.95 [137]P6(x1371,f10(x1371),a1)
% 0.78/0.95 [141]P6(f2(a1),f10(x1411),a1)
% 0.78/0.95 [158]P8(x1581,f7(x1581,x1581,a1),a1)
% 0.78/0.95 [203]~E(f10(x2031),x2031)
% 0.78/0.95 [207]~E(f10(x2071),f2(a1))
% 0.78/0.95 [211]~P6(x2111,f2(a1),a1)
% 0.78/0.95 [212]~P8(f10(x2121),x2121,a1)
% 0.78/0.95 [128]E(f6(x1281,f2(a1),a1),x1281)
% 0.78/0.95 [129]E(f3(x1291,f2(a1),a1),x1291)
% 0.78/0.95 [130]E(f6(f2(a1),x1301,a1),x1301)
% 0.78/0.95 [131]E(f7(x1311,f2(a1),a1),f2(a1))
% 0.78/0.95 [132]E(f8(x1321,f2(a1),a1),f2(a1))
% 0.78/0.95 [133]E(f7(f2(a1),x1331,a1),f2(a1))
% 0.78/0.95 [134]E(f3(f2(a1),x1341,a1),f2(a1))
% 0.78/0.95 [135]E(f8(f2(a1),x1351,a1),f2(a1))
% 0.78/0.95 [143]P7(f10(f2(a1)),x1431,a1)
% 0.78/0.95 [189]P8(x1891,f7(x1891,f7(x1891,x1891,a1),a1),a1)
% 0.78/0.95 [144]E(f4(x1441,f10(f2(a1)),a1),f2(a1))
% 0.78/0.95 [173]P5(f7(f10(f10(f2(a1))),x1731,a1),a1)
% 0.78/0.95 [217]~P5(f10(f7(f10(f10(f2(a1))),x2171,a1)),a1)
% 0.78/0.95 [152]E(f7(x1521,x1522,a1),f7(x1522,x1521,a1))
% 0.78/0.95 [153]E(f6(x1531,x1532,a1),f6(x1532,x1531,a1))
% 0.78/0.95 [159]P8(x1591,f6(x1592,x1591,a1),a1)
% 0.78/0.95 [162]P8(x1621,f6(x1621,x1622,a1),a1)
% 0.78/0.95 [163]P8(f3(x1631,x1632,a1),x1631,a1)
% 0.78/0.95 [164]P8(f4(x1641,x1642,a1),x1641,a1)
% 0.78/0.95 [169]P6(f3(x1691,x1692,a1),f10(x1691),a1)
% 0.78/0.95 [215]~P6(f6(x2151,x2152,a1),x2152,a1)
% 0.78/0.95 [216]~P6(f6(x2161,x2162,a1),x2161,a1)
% 0.78/0.95 [154]E(f7(x1541,f2(a1),a1),f7(x1542,f2(a1),a1))
% 0.78/0.95 [155]E(f7(f2(a1),x1551,a1),f7(f2(a1),x1552,a1))
% 0.78/0.95 [156]E(f6(f10(x1561),x1562,a1),f6(x1561,f10(x1562),a1))
% 0.78/0.95 [157]E(f3(f10(x1571),f10(x1572),a1),f3(x1571,x1572,a1))
% 0.78/0.95 [165]E(f3(f6(x1651,x1652,a1),x1652,a1),x1651)
% 0.78/0.95 [166]E(f3(f6(x1661,x1662,a1),x1661,a1),x1662)
% 0.78/0.95 [167]E(f3(x1671,f6(x1671,x1672,a1),a1),f2(a1))
% 0.78/0.95 [168]E(f4(f7(x1681,x1682,a1),x1681,a1),f2(a1))
% 0.78/0.95 [170]E(f10(f6(x1701,x1702,a1)),f6(x1701,f10(x1702),a1))
% 0.78/0.95 [171]E(f10(f6(x1711,x1712,a1)),f6(f10(x1711),x1712,a1))
% 0.78/0.95 [172]E(f8(f10(x1721),f10(x1722),a1),f10(f8(x1721,x1722,a1)))
% 0.78/0.95 [174]E(f6(x1741,f7(x1741,x1742,a1),a1),f7(x1741,f10(x1742),a1))
% 0.78/0.95 [175]E(f6(x1751,f7(x1752,x1751,a1),a1),f7(f10(x1752),x1751,a1))
% 0.78/0.95 [176]P6(x1761,f10(f6(x1762,x1761,a1)),a1)
% 0.78/0.95 [178]P6(x1781,f10(f6(x1781,x1782,a1)),a1)
% 0.78/0.95 [179]P7(f7(f2(a1),x1791,a1),f7(f2(a1),x1792,a1),a1)
% 0.78/0.95 [187]E(f4(f10(f4(x1871,x1872,a1)),x1872,a1),f4(f10(x1871),x1872,a1))
% 0.78/0.95 [180]E(f6(x1801,f6(x1802,x1803,a1),a1),f6(x1802,f6(x1801,x1803,a1),a1))
% 0.78/0.95 [181]E(f7(f7(x1811,x1812,a1),x1813,a1),f7(x1811,f7(x1812,x1813,a1),a1))
% 0.78/0.95 [182]E(f6(f6(x1821,x1822,a1),x1823,a1),f6(x1821,f6(x1822,x1823,a1),a1))
% 0.78/0.95 [183]E(f3(f3(x1831,x1832,a1),x1833,a1),f3(x1831,f6(x1832,x1833,a1),a1))
% 0.78/0.95 [184]E(f3(f3(x1841,x1842,a1),x1843,a1),f3(f3(x1841,x1843,a1),x1842,a1))
% 0.78/0.95 [185]E(f3(f6(x1851,x1852,a1),f6(x1853,x1852,a1),a1),f3(x1851,x1853,a1))
% 0.78/0.95 [186]E(f3(f6(x1861,x1862,a1),f6(x1861,x1863,a1),a1),f3(x1862,x1863,a1))
% 0.78/0.95 [188]E(f3(f3(f10(x1881),x1882,a1),f10(x1883),a1),f3(f3(x1881,x1882,a1),x1883,a1))
% 0.78/0.95 [191]E(f6(f7(x1911,x1912,a1),f7(x1911,x1913,a1),a1),f7(x1911,f6(x1912,x1913,a1),a1))
% 0.78/0.95 [192]E(f3(f7(x1921,x1922,a1),f7(x1921,x1923,a1),a1),f7(x1921,f3(x1922,x1923,a1),a1))
% 0.78/0.95 [193]E(f4(f7(x1931,x1932,a1),f7(x1931,x1933,a1),a1),f7(x1931,f4(x1932,x1933,a1),a1))
% 0.78/0.95 [194]E(f6(f7(x1941,x1942,a1),f7(x1943,x1942,a1),a1),f7(f6(x1941,x1943,a1),x1942,a1))
% 0.78/0.95 [195]E(f3(f7(x1951,x1952,a1),f7(x1953,x1952,a1),a1),f7(f3(x1951,x1953,a1),x1952,a1))
% 0.78/0.95 [196]E(f4(f7(x1961,x1962,a1),f7(x1963,x1962,a1),a1),f7(f4(x1961,x1963,a1),x1962,a1))
% 0.78/0.95 [197]E(f8(f3(x1971,x1972,a1),f3(x1973,x1972,a1),a1),f3(f8(x1971,x1973,a1),x1972,a1))
% 0.78/0.95 [190]E(f4(f6(f7(x1901,x1902,a1),x1903,a1),x1902,a1),f4(x1903,x1902,a1))
% 0.78/0.95 [200]E(f4(f10(f6(f7(x2001,x2002,a1),x2003,a1)),x2002,a1),f4(f10(x2003),x2002,a1))
% 0.78/0.95 [201]E(f6(f7(x2011,x2012,a1),f6(f7(x2013,x2012,a1),x2014,a1),a1),f6(f7(f6(x2011,x2013,a1),x2012,a1),x2014,a1))
% 0.78/0.95 [222]P5(x2221,a1)+P5(f10(x2221),a1)
% 0.78/0.95 [224]~P5(x2241,a1)+~P5(f10(x2241),a1)
% 0.78/0.95 [226]E(x2261,f2(a1))+P6(f2(a1),x2261,a1)
% 0.78/0.95 [248]P5(x2481,a1)+P6(f2(a1),x2481,a1)
% 0.78/0.95 [271]E(x2711,f2(a1))+~P8(x2711,f2(a1),a1)
% 0.78/0.95 [220]~P48(x2201)+E(f9(f2(a1),x2201),f2(x2201))
% 0.78/0.95 [221]~P23(x2211)+E(f5(f2(x2211),x2211),f2(x2211))
% 0.78/0.95 [263]~P21(x2631)+E(f6(f2(x2631),f2(x2631),x2631),f2(x2631))
% 0.78/0.95 [288]~P23(x2881)+P8(f5(f2(x2881),x2881),f2(x2881),x2881)
% 0.78/0.95 [292]E(x2921,f2(a1))+~P6(x2921,f10(f2(a1)),a1)
% 0.78/0.95 [305]~P7(x3051,f10(f2(a1)),a1)+E(x3051,f10(f2(a1)))
% 0.78/0.95 [388]~P23(x3881)+~P6(f2(x3881),f5(f2(x3881),x3881),x3881)
% 0.78/0.95 [568]~P47(x5681)+E(f6(f7(f2(x5681),f2(x5681),x5681),f7(f2(x5681),f2(x5681),x5681),x5681),f2(x5681))
% 0.78/0.95 [840]~P47(x8401)+P8(f6(f7(f2(x8401),f2(x8401),x8401),f7(f2(x8401),f2(x8401),x8401),x8401),f2(x8401),x8401)
% 0.78/0.95 [861]~P47(x8611)+~P6(f2(x8611),f6(f7(f2(x8611),f2(x8611),x8611),f7(f2(x8611),f2(x8611),x8611),x8611),x8611)
% 0.78/0.95 [286]P5(x2861,a1)+E(f4(x2861,f10(f10(f2(a1))),a1),f10(f2(a1)))
% 0.78/0.95 [290]~P5(x2901,a1)+E(f4(x2901,f10(f10(f2(a1))),a1),f2(a1))
% 0.78/0.95 [357]P5(x3571,a1)+~E(f4(x3571,f10(f10(f2(a1))),a1),f2(a1))
% 0.78/0.95 [389]~P5(x3891,a1)+~E(f4(x3891,f10(f10(f2(a1))),a1),f10(f2(a1)))
% 0.78/0.95 [460]~P6(f2(a1),x4601,a1)+E(f10(f3(x4601,f10(f2(a1)),a1)),x4601)
% 0.78/0.95 [229]~P27(x2292)+P7(x2291,x2291,x2292)
% 0.78/0.95 [230]~P29(x2302)+P8(x2301,x2301,x2302)
% 0.78/0.95 [231]~P31(x2312)+P8(x2311,x2311,x2312)
% 0.78/0.95 [272]~P6(x2722,x2722,x2721)+~P28(x2721)
% 0.78/0.95 [273]~P6(x2732,x2732,x2731)+~P29(x2731)
% 0.78/0.95 [274]~P6(x2742,x2742,x2741)+~P31(x2741)
% 0.78/0.95 [291]P8(x2912,x2911,a1)+P8(x2911,x2912,a1)
% 0.78/0.95 [332]~P6(x3321,x3322,a1)+P8(x3321,x3322,a1)
% 0.78/0.95 [219]E(x2191,x2192)+~E(f10(x2191),f10(x2192))
% 0.78/0.95 [232]~P16(x2322)+E(f7(x2321,x2321,x2322),x2321)
% 0.78/0.95 [233]~P28(x2332)+E(f8(x2331,x2331,x2332),x2331)
% 0.78/0.95 [234]~P15(x2342)+E(f3(x2341,x2341,x2342),f2(x2342))
% 0.78/0.95 [236]~P20(x2362)+E(f3(x2361,x2361,x2362),f2(x2362))
% 0.78/0.95 [237]~P4(x2372)+E(f4(x2371,x2371,x2372),f2(x2372))
% 0.78/0.95 [238]~P27(x2382)+P7(x2381,f2(x2382),x2382)
% 0.78/0.95 [265]~P23(x2652)+P8(x2651,f5(x2651,x2652),x2652)
% 0.78/0.95 [267]~E(f6(x2672,x2671,a1),x2672)+E(x2671,f2(a1))
% 0.78/0.95 [269]E(x2691,f2(a1))+~E(f6(x2692,x2691,a1),f2(a1))
% 0.78/0.95 [270]E(x2701,f2(a1))+~E(f6(x2701,x2702,a1),f2(a1))
% 0.78/0.95 [275]~P23(x2751)+P8(f2(x2751),f5(x2752,x2751),x2751)
% 0.78/0.95 [277]~P44(x2771)+P8(f2(x2771),f9(x2772,x2771),x2771)
% 0.78/0.95 [308]P6(x3081,x3082,a1)+P6(x3082,f10(x3081),a1)
% 0.78/0.95 [310]P8(x3101,x3102,a1)+P8(f10(x3102),x3101,a1)
% 0.78/0.95 [329]~P5(x3292,a1)+P5(f7(x3291,x3292,a1),a1)
% 0.78/0.95 [330]~P5(x3301,a1)+P5(f7(x3301,x3302,a1),a1)
% 0.78/0.95 [333]~P6(x3331,x3332,a1)+E(f4(x3331,x3332,a1),x3331)
% 0.78/0.95 [334]~P8(x3341,x3342,a1)+E(f3(x3341,x3342,a1),f2(a1))
% 0.78/0.95 [338]P8(x3381,x3382,a1)+~E(f3(x3381,x3382,a1),f2(a1))
% 0.78/0.95 [343]~P6(x3431,x3432,a1)+P6(x3431,f10(x3432),a1)
% 0.78/0.95 [344]~P8(x3441,x3442,a1)+P6(x3441,f10(x3442),a1)
% 0.78/0.95 [346]~P8(x3461,x3462,a1)+P8(x3461,f10(x3462),a1)
% 0.78/0.95 [348]~P6(x3481,x3482,a1)+P8(f10(x3481),x3482,a1)
% 0.78/0.95 [349]~P23(x3491)+~P6(f5(x3492,x3491),f2(x3491),x3491)
% 0.78/0.95 [350]~P44(x3501)+~P6(f9(x3502,x3501),f2(x3501),x3501)
% 0.78/0.95 [352]P8(x3521,x3522,a1)+~P6(x3521,f10(x3522),a1)
% 0.78/0.95 [353]P6(x3531,x3532,a1)+~P6(f10(x3531),x3532,a1)
% 0.78/0.95 [355]P6(x3551,x3552,a1)+~P8(f10(x3551),x3552,a1)
% 0.78/0.95 [356]P8(x3561,x3562,a1)+~P8(f10(x3561),x3562,a1)
% 0.78/0.95 [368]~P6(x3681,x3682,a1)+P6(f10(x3681),f10(x3682),a1)
% 0.78/0.95 [369]~P8(x3691,x3692,a1)+P8(f10(x3691),f10(x3692),a1)
% 0.78/0.95 [382]P6(x3821,x3822,a1)+~P6(f10(x3821),f10(x3822),a1)
% 0.78/0.95 [383]P8(x3831,x3832,a1)+~P8(f10(x3831),f10(x3832),a1)
% 0.78/0.95 [416]~P47(x4161)+P8(f2(x4161),f7(x4162,x4162,x4161),x4161)
% 0.78/0.95 [418]~P6(x4181,x4182,a1)+~P6(x4182,f10(x4181),a1)
% 0.78/0.95 [419]~P8(x4191,x4192,a1)+~P8(f10(x4192),x4191,a1)
% 0.78/0.95 [448]~P6(x4481,x4482,a1)+P5(f3(x4481,x4482,a1),a1)
% 0.78/0.95 [488]~P7(x4881,x4882,a1)+P7(x4881,f6(x4882,x4881,a1),a1)
% 0.78/0.95 [498]~P6(x4982,x4981,a1)+P6(f2(a1),f3(x4981,x4982,a1),a1)
% 0.78/0.95 [499]P6(f4(x4991,x4992,a1),x4992,a1)+~P6(f2(a1),x4992,a1)
% 0.78/0.95 [500]P8(f4(x5001,x5002,a1),x5002,a1)+~P6(f2(a1),x5002,a1)
% 0.78/0.95 [528]~P47(x5281)+~P6(f7(x5282,x5282,x5281),f2(x5281),x5281)
% 0.78/0.95 [537]P7(x5371,x5372,a1)+~P7(x5371,f6(x5372,x5371,a1),a1)
% 0.78/0.95 [543]P6(x5431,x5432,a1)+~P6(f2(a1),f3(x5432,x5431,a1),a1)
% 0.78/0.95 [546]P6(f2(a1),x5461,a1)+~P6(f2(a1),f7(x5462,x5461,a1),a1)
% 0.78/0.95 [547]P6(f2(a1),x5471,a1)+~P6(f2(a1),f7(x5471,x5472,a1),a1)
% 0.78/0.95 [227]~P23(x2272)+E(f5(f5(x2271,x2272),x2272),f5(x2271,x2272))
% 0.78/0.95 [228]~P46(x2282)+E(f5(f9(x2281,x2282),x2282),f9(x2281,x2282))
% 0.78/0.95 [239]~P27(x2392)+E(f6(x2391,f2(x2392),x2392),x2391)
% 0.78/0.95 [240]~P12(x2402)+E(f6(x2401,f2(x2402),x2402),x2401)
% 0.78/0.95 [241]~P19(x2412)+E(f6(x2411,f2(x2412),x2412),x2411)
% 0.78/0.95 [242]~P20(x2422)+E(f3(x2421,f2(x2422),x2422),x2421)
% 0.78/0.95 [243]~P4(x2432)+E(f4(x2431,f2(x2432),x2432),x2431)
% 0.78/0.95 [245]~P27(x2451)+E(f6(f2(x2451),x2452,x2451),x2452)
% 0.78/0.95 [246]~P12(x2461)+E(f6(f2(x2461),x2462,x2461),x2462)
% 0.78/0.95 [247]~P19(x2471)+E(f6(f2(x2471),x2472,x2471),x2472)
% 0.78/0.95 [249]~P27(x2492)+E(f7(x2491,f2(x2492),x2492),f2(x2492))
% 0.78/0.95 [250]~P54(x2502)+E(f7(x2501,f2(x2502),x2502),f2(x2502))
% 0.78/0.95 [252]~P32(x2522)+E(f7(x2521,f2(x2522),x2522),f2(x2522))
% 0.78/0.95 [253]~P42(x2532)+E(f7(x2531,f2(x2532),x2532),f2(x2532))
% 0.78/0.95 [255]~P27(x2551)+E(f7(f2(x2551),x2552,x2551),f2(x2551))
% 0.78/0.95 [256]~P54(x2561)+E(f7(f2(x2561),x2562,x2561),f2(x2561))
% 0.78/0.95 [258]~P32(x2581)+E(f7(f2(x2581),x2582,x2581),f2(x2581))
% 0.78/0.95 [259]~P42(x2591)+E(f7(f2(x2591),x2592,x2591),f2(x2591))
% 0.78/0.95 [260]~P4(x2601)+E(f4(f2(x2601),x2602,x2601),f2(x2601))
% 0.78/0.95 [284]E(x2841,f10(f2(a1)))+~E(f7(x2842,x2841,a1),f10(f2(a1)))
% 0.78/0.95 [285]E(x2851,f10(f2(a1)))+~E(f7(x2851,x2852,a1),f10(f2(a1)))
% 0.78/0.95 [390]~P46(x3902)+E(f7(f5(x3901,x3902),f5(x3901,x3902),x3902),f7(x3901,x3901,x3902))
% 0.78/0.95 [451]P6(x4512,x4511,a1)+E(f6(x4511,f3(x4512,x4511,a1),a1),x4512)
% 0.78/0.95 [473]~E(f10(f4(x4731,x4732,a1)),x4732)+E(f4(f10(x4731),x4732,a1),f2(a1))
% 0.78/0.95 [495]~P8(x4951,x4952,a1)+E(f6(x4951,f3(x4952,x4951,a1),a1),x4952)
% 0.78/0.95 [496]~P8(x4962,x4961,a1)+E(f3(x4961,f3(x4961,x4962,a1),a1),x4962)
% 0.78/0.95 [497]~P8(x4972,x4971,a1)+E(f6(f3(x4971,x4972,a1),x4972,a1),x4971)
% 0.78/0.95 [504]~P8(x5042,x5041,a1)+E(f10(f3(x5041,x5042,a1)),f3(f10(x5041),x5042,a1))
% 0.78/0.95 [517]~P6(f2(a1),x5171,a1)+P6(f3(x5171,f10(x5172),a1),x5171,a1)
% 0.78/0.95 [520]P6(x5201,x5202,a1)+E(f4(f3(x5201,x5202,a1),x5202,a1),f4(x5201,x5202,a1))
% 0.78/0.95 [531]E(f10(f4(x5311,x5312,a1)),x5312)+E(f10(f4(x5311,x5312,a1)),f4(f10(x5311),x5312,a1))
% 0.78/0.95 [532]~P8(x5322,x5321,a1)+E(f4(f3(x5321,x5322,a1),x5322,a1),f4(x5321,x5322,a1))
% 0.78/0.95 [586]P8(f10(f2(a1)),x5861,a1)+~P8(f10(f2(a1)),f7(x5862,x5861,a1),a1)
% 0.78/0.95 [587]P8(f10(f2(a1)),x5871,a1)+~P8(f10(f2(a1)),f7(x5871,x5872,a1),a1)
% 0.78/0.95 [312]~P27(x3123)+E(f7(x3121,x3122,x3123),f7(x3122,x3121,x3123))
% 0.78/0.95 [314]~P27(x3143)+E(f6(x3141,x3142,x3143),f6(x3142,x3141,x3143))
% 0.78/0.95 [315]~P12(x3153)+E(f6(x3151,x3152,x3153),f6(x3152,x3151,x3153))
% 0.78/0.95 [316]~P28(x3163)+E(f8(x3161,x3162,x3163),f8(x3162,x3161,x3163))
% 0.78/0.95 [392]E(x3921,x3922)+~E(f6(x3923,x3921,a1),f6(x3923,x3922,a1))
% 0.78/0.95 [393]E(x3931,x3932)+~E(f6(x3931,x3933,a1),f6(x3932,x3933,a1))
% 0.78/0.95 [394]~P27(x3943)+P7(x3941,f7(x3942,x3941,x3943),x3943)
% 0.78/0.95 [395]~P27(x3953)+P7(x3951,f7(x3951,x3952,x3953),x3953)
% 0.78/0.95 [396]~P37(x3963)+P7(x3961,f7(x3961,x3962,x3963),x3963)
% 0.78/0.95 [397]~P28(x3973)+P8(f8(x3971,x3972,x3973),x3972,x3973)
% 0.78/0.95 [398]~P28(x3983)+P8(f8(x3981,x3982,x3983),x3981,x3983)
% 0.78/0.95 [485]~P6(x4851,x4853,a1)+P6(x4851,f6(x4852,x4853,a1),a1)
% 0.78/0.95 [487]~P6(x4871,x4872,a1)+P6(x4871,f6(x4872,x4873,a1),a1)
% 0.78/0.95 [490]~P8(x4901,x4903,a1)+P8(x4901,f6(x4902,x4903,a1),a1)
% 0.78/0.95 [492]~P8(x4921,x4922,a1)+P8(x4921,f6(x4922,x4923,a1),a1)
% 0.78/0.95 [493]~P6(x4931,x4933,a1)+P6(f3(x4931,x4932,a1),x4933,a1)
% 0.78/0.95 [538]P6(x5381,x5382,a1)+~P6(f6(x5381,x5383,a1),x5382,a1)
% 0.78/0.95 [539]P8(x5391,x5392,a1)+~P8(f6(x5393,x5391,a1),x5392,a1)
% 0.78/0.95 [540]P8(x5401,x5402,a1)+~P8(f6(x5401,x5403,a1),x5402,a1)
% 0.78/0.95 [558]P8(f7(x5582,x5581,a1),f7(x5583,x5581,a1),a1)+P6(f2(a1),x5581,a1)
% 0.78/0.95 [559]P8(f7(x5591,x5592,a1),f7(x5591,x5593,a1),a1)+P6(f2(a1),x5591,a1)
% 0.78/0.95 [605]~P6(x6051,x6053,a1)+P6(f6(x6051,x6052,a1),f6(x6053,x6052,a1),a1)
% 0.78/0.95 [606]~P6(x6062,x6063,a1)+P6(f6(x6061,x6062,a1),f6(x6061,x6063,a1),a1)
% 0.78/0.95 [607]~P7(x6072,x6073,a1)+P7(f7(x6071,x6072,a1),f7(x6071,x6073,a1),a1)
% 0.78/0.95 [609]~P8(x6091,x6093,a1)+P8(f7(x6091,x6092,a1),f7(x6093,x6092,a1),a1)
% 0.78/0.95 [611]~P8(x6112,x6113,a1)+P8(f7(x6111,x6112,a1),f7(x6111,x6113,a1),a1)
% 0.78/0.95 [612]~P8(x6121,x6123,a1)+P8(f6(x6121,x6122,a1),f6(x6123,x6122,a1),a1)
% 0.78/0.95 [613]~P8(x6132,x6133,a1)+P8(f6(x6131,x6132,a1),f6(x6131,x6133,a1),a1)
% 0.78/0.95 [614]~P8(x6141,x6143,a1)+P8(f3(x6141,x6142,a1),f3(x6143,x6142,a1),a1)
% 0.78/0.95 [615]~P8(x6153,x6152,a1)+P8(f3(x6151,x6152,a1),f3(x6151,x6153,a1),a1)
% 0.78/0.95 [683]~P6(f6(x6831,x6833,a1),x6832,a1)+P6(x6831,f3(x6832,x6833,a1),a1)
% 0.78/0.95 [684]~P8(f3(x6841,x6843,a1),x6842,a1)+P8(x6841,f6(x6842,x6843,a1),a1)
% 0.78/0.95 [685]~P6(x6851,f3(x6853,x6852,a1),a1)+P6(f6(x6851,x6852,a1),x6853,a1)
% 0.78/0.95 [686]~P8(x6861,f6(x6863,x6862,a1),a1)+P8(f3(x6861,x6862,a1),x6863,a1)
% 0.78/0.95 [750]P6(x7501,x7502,a1)+~P6(f7(x7503,x7501,a1),f7(x7503,x7502,a1),a1)
% 0.78/0.95 [751]P6(x7511,x7512,a1)+~P6(f7(x7511,x7513,a1),f7(x7512,x7513,a1),a1)
% 0.78/0.95 [752]P6(x7521,x7522,a1)+~P6(f6(x7523,x7521,a1),f6(x7523,x7522,a1),a1)
% 0.78/0.95 [753]P8(x7531,x7532,a1)+~P8(f6(x7533,x7531,a1),f6(x7533,x7532,a1),a1)
% 0.78/0.95 [754]~P6(f7(x7542,x7541,a1),f7(x7543,x7541,a1),a1)+P6(f2(a1),x7541,a1)
% 0.78/0.95 [755]~P6(f7(x7551,x7552,a1),f7(x7551,x7553,a1),a1)+P6(f2(a1),x7551,a1)
% 0.78/0.95 [399]~P20(x3993)+E(f6(f3(x3991,x3992,x3993),x3992,x3993),x3991)
% 0.78/0.95 [400]~P20(x4003)+E(f3(f6(x4001,x4002,x4003),x4002,x4003),x4001)
% 0.78/0.95 [409]~P4(x4093)+E(f4(f7(x4091,x4092,x4093),x4092,x4093),f2(x4093))
% 0.78/0.95 [410]~P4(x4103)+E(f4(f7(x4101,x4102,x4103),x4101,x4103),f2(x4103))
% 0.78/0.95 [439]E(x4391,x4392)+~E(f7(f10(x4393),x4391,a1),f7(f10(x4393),x4392,a1))
% 0.78/0.95 [461]~P16(x4613)+E(f7(x4611,f7(x4611,x4612,x4613),x4613),f7(x4611,x4612,x4613))
% 0.78/0.95 [462]~P28(x4623)+E(f8(x4621,f8(x4621,x4622,x4623),x4623),f8(x4621,x4622,x4623))
% 0.78/0.95 [463]~P4(x4633)+E(f4(f6(x4631,x4632,x4633),x4632,x4633),f4(x4631,x4632,x4633))
% 0.78/0.95 [464]~P4(x4643)+E(f4(f6(x4641,x4642,x4643),x4641,x4643),f4(x4642,x4641,x4643))
% 0.78/0.95 [465]~P4(x4653)+E(f4(f4(x4651,x4652,x4653),x4652,x4653),f4(x4651,x4652,x4653))
% 0.78/0.95 [471]~P48(x4712)+E(f7(f9(x4711,x4712),f9(x4713,x4712),x4712),f9(f7(x4711,x4713,a1),x4712))
% 0.78/0.95 [472]~P48(x4722)+E(f6(f9(x4721,x4722),f9(x4723,x4722),x4722),f9(f6(x4721,x4723,a1),x4722))
% 0.78/0.95 [474]~P46(x4742)+E(f7(f5(x4741,x4742),f5(x4743,x4742),x4742),f5(f7(x4741,x4743,x4742),x4742))
% 0.78/0.95 [503]~P23(x5033)+E(f5(f3(x5031,x5032,x5033),x5033),f5(f3(x5032,x5031,x5033),x5033))
% 0.78/0.95 [535]~P40(x5352)+P7(f7(x5351,f2(x5352),x5352),f7(x5353,f2(x5352),x5352),x5352)
% 0.78/0.95 [536]~P40(x5361)+P7(f7(f2(x5361),x5362,x5361),f7(f2(x5361),x5363,x5361),x5361)
% 0.78/0.95 [661]~P6(x6612,x6613,a1)+P6(f7(f10(x6611),x6612,a1),f7(f10(x6611),x6613,a1),a1)
% 0.78/0.95 [676]~P8(x6762,x6763,a1)+E(f3(f6(x6761,x6762,a1),x6763,a1),f3(x6761,f3(x6763,x6762,a1),a1))
% 0.78/0.95 [677]~P8(x6773,x6772,a1)+E(f3(f6(x6771,x6772,a1),x6773,a1),f6(x6771,f3(x6772,x6773,a1),a1))
% 0.78/0.95 [679]~P8(x6793,x6791,a1)+E(f3(f6(x6791,x6792,a1),x6793,a1),f6(f3(x6791,x6793,a1),x6792,a1))
% 0.78/0.95 [731]~P8(x7313,x7312,a1)+P8(x7311,f3(f6(x7312,x7311,a1),x7313,a1),a1)
% 0.78/0.95 [771]P8(x7711,x7712,a1)+~P8(f7(f10(x7713),x7711,a1),f7(f10(x7713),x7712,a1),a1)
% 0.78/0.95 [773]~P41(x7733)+P8(f5(f7(x7731,x7732,x7733),x7733),f7(f5(x7731,x7733),f5(x7732,x7733),x7733),x7733)
% 0.78/0.95 [774]~P23(x7743)+P8(f5(f6(x7741,x7742,x7743),x7743),f6(f5(x7741,x7743),f5(x7742,x7743),x7743),x7743)
% 0.78/0.95 [775]~P23(x7753)+P8(f5(f3(x7751,x7752,x7753),x7753),f6(f5(x7751,x7753),f5(x7752,x7753),x7753),x7753)
% 0.78/0.95 [776]~P23(x7762)+P8(f3(f5(x7761,x7762),f5(x7763,x7762),x7762),f5(f3(x7761,x7763,x7762),x7762),x7762)
% 0.78/0.95 [821]~P47(x8211)+P8(f2(x8211),f6(f7(x8212,x8212,x8211),f7(x8213,x8213,x8211),x8211),x8211)
% 0.78/0.95 [855]~P47(x8551)+~P6(f6(f7(x8552,x8552,x8551),f7(x8553,x8553,x8551),x8551),f2(x8551),x8551)
% 0.78/0.95 [596]~P23(x5962)+E(f5(f6(f5(x5961,x5962),f5(x5963,x5962),x5962),x5962),f6(f5(x5961,x5962),f5(x5963,x5962),x5962))
% 0.78/0.95 [779]~P8(x7792,x7793,a1)+E(f3(f6(x7791,x7792,a1),f10(x7793),a1),f3(x7791,f10(f3(x7793,x7792,a1)),a1))
% 0.78/0.95 [780]~P8(x7802,x7801,a1)+E(f3(f10(f3(x7801,x7802,a1)),x7803,a1),f3(f10(x7801),f6(x7802,x7803,a1),a1))
% 0.78/0.95 [841]~P23(x8412)+P8(f5(f3(f5(x8411,x8412),f5(x8413,x8412),x8412),x8412),f5(f3(x8411,x8413,x8412),x8412),x8412)
% 0.78/0.95 [569]~P27(x5694)+E(f7(x5691,f7(x5692,x5693,x5694),x5694),f7(x5692,f7(x5691,x5693,x5694),x5694))
% 0.78/0.95 [570]~P27(x5704)+E(f6(x5701,f6(x5702,x5703,x5704),x5704),f6(x5702,f6(x5701,x5703,x5704),x5704))
% 0.78/0.95 [571]~P12(x5714)+E(f6(x5711,f6(x5712,x5713,x5714),x5714),f6(x5712,f6(x5711,x5713,x5714),x5714))
% 0.78/0.95 [572]~P15(x5724)+E(f6(x5721,f6(x5722,x5723,x5724),x5724),f6(x5722,f6(x5721,x5723,x5724),x5724))
% 0.78/0.95 [573]~P28(x5734)+E(f8(x5731,f8(x5732,x5733,x5734),x5734),f8(x5732,f8(x5731,x5733,x5734),x5734))
% 0.78/0.95 [578]~P27(x5783)+E(f7(f7(x5781,x5782,x5783),x5784,x5783),f7(x5781,f7(x5782,x5784,x5783),x5783))
% 0.78/0.95 [579]~P13(x5793)+E(f7(f7(x5791,x5792,x5793),x5794,x5793),f7(x5791,f7(x5792,x5794,x5793),x5793))
% 0.78/0.95 [580]~P27(x5803)+E(f6(f6(x5801,x5802,x5803),x5804,x5803),f6(x5801,f6(x5802,x5804,x5803),x5803))
% 0.78/0.95 [581]~P12(x5813)+E(f6(f6(x5811,x5812,x5813),x5814,x5813),f6(x5811,f6(x5812,x5814,x5813),x5813))
% 0.78/0.95 [582]~P14(x5823)+E(f6(f6(x5821,x5822,x5823),x5824,x5823),f6(x5821,f6(x5822,x5824,x5823),x5823))
% 0.78/0.95 [583]~P28(x5833)+E(f8(f8(x5831,x5832,x5833),x5834,x5833),f8(x5831,f8(x5832,x5834,x5833),x5833))
% 0.78/0.95 [584]~P27(x5843)+E(f7(f7(x5841,x5842,x5843),x5844,x5843),f7(f7(x5841,x5844,x5843),x5842,x5843))
% 0.78/0.95 [585]~P27(x5853)+E(f6(f6(x5851,x5852,x5853),x5854,x5853),f6(f6(x5851,x5854,x5853),x5852,x5853))
% 0.78/0.95 [708]~P27(x7083)+E(f6(f7(x7081,x7082,x7083),f7(x7081,x7084,x7083),x7083),f7(x7081,f6(x7082,x7084,x7083),x7083))
% 0.78/0.95 [710]~P32(x7103)+E(f6(f7(x7101,x7102,x7103),f7(x7101,x7104,x7103),x7103),f7(x7101,f6(x7102,x7104,x7103),x7103))
% 0.78/0.95 [712]~P32(x7123)+E(f3(f7(x7121,x7122,x7123),f7(x7121,x7124,x7123),x7123),f7(x7121,f3(x7122,x7124,x7123),x7123))
% 0.78/0.95 [715]~P32(x7153)+E(f6(f7(x7151,x7152,x7153),f7(x7154,x7152,x7153),x7153),f7(f6(x7151,x7154,x7153),x7152,x7153))
% 0.78/0.95 [716]~P30(x7163)+E(f6(f7(x7161,x7162,x7163),f7(x7164,x7162,x7163),x7163),f7(f6(x7161,x7164,x7163),x7162,x7163))
% 0.78/0.95 [718]~P32(x7183)+E(f3(f7(x7181,x7182,x7183),f7(x7184,x7182,x7183),x7183),f7(f3(x7181,x7184,x7183),x7182,x7183))
% 0.78/0.95 [719]~P25(x7193)+E(f8(f6(x7191,x7192,x7193),f6(x7194,x7192,x7193),x7193),f6(f8(x7191,x7194,x7193),x7192,x7193))
% 0.78/0.95 [720]~P24(x7203)+E(f8(f3(x7201,x7202,x7203),f3(x7204,x7202,x7203),x7203),f3(f8(x7201,x7204,x7203),x7202,x7203))
% 0.78/0.95 [721]~P4(x7213)+E(f4(f7(x7211,x7212,x7213),f7(x7211,x7214,x7213),x7213),f7(x7211,f4(x7212,x7214,x7213),x7213))
% 0.78/0.95 [722]~P27(x7223)+E(f6(f7(x7221,x7222,x7223),f7(x7224,x7222,x7223),x7223),f7(f6(x7221,x7224,x7223),x7222,x7223))
% 0.78/0.95 [723]~P4(x7233)+E(f4(f7(x7231,x7232,x7233),f7(x7234,x7232,x7233),x7233),f7(f4(x7231,x7234,x7233),x7232,x7233))
% 0.78/0.95 [706]~P4(x7064)+E(f4(f6(x7061,f7(x7062,x7063,x7064),x7064),x7063,x7064),f4(x7061,x7063,x7064))
% 0.78/0.95 [707]~P4(x7074)+E(f4(f6(x7071,f7(x7072,x7073,x7074),x7074),x7072,x7074),f4(x7071,x7072,x7074))
% 0.78/0.95 [784]~P4(x7844)+E(f4(f7(x7841,f4(x7842,x7843,x7844),x7844),x7843,x7844),f4(f7(x7841,x7842,x7844),x7843,x7844))
% 0.78/0.95 [786]~P9(x7864)+E(f4(f3(x7861,f4(x7862,x7863,x7864),x7864),x7863,x7864),f4(f3(x7861,x7862,x7864),x7863,x7864))
% 0.78/0.95 [789]~P9(x7893)+E(f4(f3(f4(x7891,x7892,x7893),x7894,x7893),x7892,x7893),f4(f3(x7891,x7894,x7893),x7892,x7893))
% 0.78/0.95 [790]~P4(x7904)+E(f4(f6(x7901,f4(x7902,x7903,x7904),x7904),x7903,x7904),f4(f6(x7901,x7902,x7904),x7903,x7904))
% 0.78/0.95 [791]~P4(x7913)+E(f4(f7(f4(x7911,x7912,x7913),x7914,x7913),x7912,x7913),f4(f7(x7911,x7914,x7913),x7912,x7913))
% 0.78/0.95 [792]~P4(x7923)+E(f4(f6(f4(x7921,x7922,x7923),x7924,x7923),x7922,x7923),f4(f6(x7921,x7924,x7923),x7922,x7923))
% 0.78/0.95 [842]~P4(x8423)+E(f4(f7(f4(x8421,x8422,x8423),f4(x8424,x8422,x8423),x8423),x8422,x8423),f4(f7(x8421,x8424,x8423),x8422,x8423))
% 0.78/0.95 [843]~P4(x8433)+E(f4(f6(f4(x8431,x8432,x8433),f4(x8434,x8432,x8433),x8433),x8432,x8433),f4(f6(x8431,x8434,x8433),x8432,x8433))
% 0.78/0.95 [844]~P9(x8443)+E(f4(f3(f4(x8441,x8442,x8443),f4(x8444,x8442,x8443),x8443),x8442,x8443),f4(f3(x8441,x8444,x8443),x8442,x8443))
% 0.78/0.95 [863]~P8(x8631,x8633,a1)+E(f6(f7(x8631,x8632,a1),f6(f7(f3(x8633,x8631,a1),x8632,a1),x8634,a1),a1),f6(f7(x8633,x8632,a1),x8634,a1))
% 0.78/0.95 [793]~P27(x7933)+E(f7(f7(x7931,x7932,x7933),f7(x7934,x7935,x7933),x7933),f7(f7(x7931,x7934,x7933),f7(x7932,x7935,x7933),x7933))
% 0.78/0.95 [794]~P27(x7943)+E(f6(f6(x7941,x7942,x7943),f6(x7944,x7945,x7943),x7943),f6(f6(x7941,x7944,x7943),f6(x7942,x7945,x7943),x7943))
% 0.78/0.95 [795]~P15(x7953)+E(f3(f6(x7951,x7952,x7953),f6(x7954,x7955,x7953),x7953),f6(f3(x7951,x7954,x7953),f3(x7952,x7955,x7953),x7953))
% 0.78/0.95 [820]E(f4(x8201,x8202,a1),f4(x8203,x8202,a1))+~E(f6(x8201,f7(x8202,x8204,a1),a1),f6(x8203,f7(x8202,x8205,a1),a1))
% 0.78/0.95 [850]~P53(x8503)+E(f6(f7(x8501,x8502,x8503),f6(f7(x8504,x8502,x8503),x8505,x8503),x8503),f6(f7(f6(x8501,x8504,x8503),x8502,x8503),x8505,x8503))
% 0.78/0.95 [884]~P23(x8843)+P8(f5(f3(f6(x8841,x8842,x8843),f6(x8844,x8845,x8843),x8843),x8843),f6(f5(f3(x8841,x8844,x8843),x8843),f5(f3(x8842,x8845,x8843),x8843),x8843),x8843)
% 0.78/0.95 [885]~P32(x8853)+E(f6(f6(f7(f3(x8851,x8852,x8853),f3(x8854,x8855,x8853),x8853),f7(f3(x8851,x8852,x8853),x8855,x8853),x8853),f7(x8852,f3(x8854,x8855,x8853),x8853),x8853),f3(f7(x8851,x8854,x8853),f7(x8852,x8855,x8853),x8853))
% 0.78/0.95 [860]~P56(x8603)+E(f6(f7(x8601,x8602,x8603),f6(f7(f3(x8604,x8601,x8603),x8602,x8603),x8605,x8603),x8603),f6(f7(x8604,x8602,x8603),x8605,x8603))
% 0.78/0.95 [866]~P8(x8661,x8664,a1)+E(f3(f6(f7(x8661,x8662,a1),x8663,a1),f6(f7(x8664,x8662,a1),x8665,a1),a1),f3(x8663,f6(f7(f3(x8664,x8661,a1),x8662,a1),x8665,a1),a1))
% 0.78/0.95 [867]~P8(x8674,x8671,a1)+E(f3(f6(f7(x8671,x8672,a1),x8673,a1),f6(f7(x8674,x8672,a1),x8675,a1),a1),f3(f6(f7(f3(x8671,x8674,a1),x8672,a1),x8673,a1),x8675,a1))
% 0.78/0.95 [438]~P2(x4381)+~P8(f2(x4381),f2(x4381),x4381)+E(f6(f2(x4381),f2(x4381),x4381),f2(x4381))
% 0.78/0.95 [351]E(x3511,f2(a1))+E(x3511,f10(f2(a1)))+~P6(x3511,f10(f10(f2(a1))),a1)
% 0.78/0.95 [301]E(x3011,x3012)+P6(x3012,x3011,a1)+P6(x3011,x3012,a1)
% 0.78/0.95 [337]E(x3371,x3372)+P6(x3371,x3372,a1)+~P8(x3371,x3372,a1)
% 0.78/0.95 [407]E(x4071,x4072)+~P7(x4072,x4071,a1)+~P7(x4071,x4072,a1)
% 0.78/0.95 [408]E(x4081,x4082)+~P8(x4082,x4081,a1)+~P8(x4081,x4082,a1)
% 0.78/0.95 [223]~P23(x2232)+~E(f5(x2231,x2232),f2(x2232))+E(x2231,f2(x2232))
% 0.78/0.95 [261]~P40(x2612)+~P11(x2612)+E(f3(x2611,x2611,x2612),f2(x2612))
% 0.78/0.95 [264]~P33(x2642)+P6(x2641,f2(x2642),x2642)+E(f5(x2641,x2642),x2641)
% 0.78/0.95 [278]E(x2781,f2(a1))+E(x2782,f2(a1))+~E(f7(x2782,x2781,a1),f2(a1))
% 0.78/0.95 [279]~P23(x2792)+P6(f2(x2792),f5(x2791,x2792),x2792)+E(x2791,f2(x2792))
% 0.78/0.95 [287]~P21(x2872)+~E(f6(x2871,x2871,x2872),f2(x2872))+E(x2871,f2(x2872))
% 0.78/0.95 [298]~P27(x2982)+~P7(f2(x2982),x2981,x2982)+E(x2981,f2(x2982))
% 0.78/0.95 [322]~P23(x3222)+~P6(f2(x3222),x3221,x3222)+E(f5(x3221,x3222),x3221)
% 0.78/0.95 [323]~P23(x3232)+~P8(f2(x3232),x3231,x3232)+E(f5(x3231,x3232),x3231)
% 0.78/0.95 [341]P5(x3411,a1)+P5(x3412,a1)+P5(f6(x3412,x3411,a1),a1)
% 0.78/0.95 [342]P5(x3421,a1)+P5(x3422,a1)+P5(f3(x3422,x3421,a1),a1)
% 0.78/0.95 [360]~P6(x3601,x3602,a1)+E(f10(x3601),x3602)+P6(f10(x3601),x3602,a1)
% 0.78/0.95 [361]E(x3611,x3612)+P6(x3612,x3611,a1)+~P6(x3612,f10(x3611),a1)
% 0.78/0.95 [363]E(x3631,x3632)+P6(x3631,x3632,a1)+~P6(x3631,f10(x3632),a1)
% 0.78/0.95 [366]~P23(x3662)+~P8(f5(x3661,x3662),f2(x3662),x3662)+E(x3661,f2(x3662))
% 0.78/0.95 [379]P8(x3791,x3792,a1)+E(x3791,f10(x3792))+~P8(x3791,f10(x3792),a1)
% 0.78/0.95 [386]~P5(x3862,a1)+~P5(x3861,a1)+P5(f6(x3861,x3862,a1),a1)
% 0.78/0.95 [387]~P5(x3872,a1)+~P5(x3871,a1)+P5(f3(x3871,x3872,a1),a1)
% 0.78/0.95 [417]E(x4171,x4172)+~E(f3(x4172,x4171,a1),f2(a1))+~E(f3(x4171,x4172,a1),f2(a1))
% 0.78/0.95 [420]E(x4201,x4202)+~P8(x4202,x4201,a1)+~P6(x4201,f10(x4202),a1)
% 0.78/0.95 [437]~P44(x4371)+P6(f2(x4371),f9(x4372,x4371),x4371)+~P6(f2(a1),x4372,a1)
% 0.78/0.95 [447]~P44(x4472)+~P6(f2(x4472),f9(x4471,x4472),x4472)+P6(f2(a1),x4471,a1)
% 0.78/0.95 [450]P5(x4501,a1)+P5(x4502,a1)+~P5(f7(x4501,x4502,a1),a1)
% 0.78/0.95 [455]P5(x4551,a1)+~P5(x4552,a1)+~P5(f6(x4552,x4551,a1),a1)
% 0.78/0.95 [457]P5(x4571,a1)+~P5(x4572,a1)+~P5(f6(x4571,x4572,a1),a1)
% 0.78/0.95 [466]~P7(x4661,x4662,a1)+P8(x4661,x4662,a1)+~P6(f2(a1),x4662,a1)
% 0.78/0.95 [470]~P7(x4701,x4702,a1)+~P6(f2(a1),x4702,a1)+P6(f2(a1),x4701,a1)
% 0.78/0.95 [515]~P7(x5152,x5151,a1)+~P6(x5151,x5152,a1)+~P6(f2(a1),x5151,a1)
% 0.78/0.95 [523]~P21(x5231)+~P6(f2(x5231),x5232,x5231)+P6(f2(x5231),f6(x5232,x5232,x5231),x5231)
% 0.78/0.95 [524]~P21(x5241)+~P8(f2(x5241),x5242,x5241)+P8(f2(x5241),f6(x5242,x5242,x5241),x5241)
% 0.78/0.95 [525]~P46(x5252)+~P6(x5251,f2(x5252),x5252)+P6(f6(x5251,x5251,x5252),f2(x5252),x5252)
% 0.78/0.95 [526]~P21(x5262)+~P6(x5261,f2(x5262),x5262)+P6(f6(x5261,x5261,x5262),f2(x5262),x5262)
% 0.78/0.95 [527]~P21(x5272)+~P8(x5271,f2(x5272),x5272)+P8(f6(x5271,x5271,x5272),f2(x5272),x5272)
% 0.78/0.95 [588]~P46(x5882)+~P6(f6(x5881,x5881,x5882),f2(x5882),x5882)+P6(x5881,f2(x5882),x5882)
% 0.78/0.95 [589]~P21(x5892)+~P6(f6(x5891,x5891,x5892),f2(x5892),x5892)+P6(x5891,f2(x5892),x5892)
% 0.78/0.95 [590]~P21(x5902)+~P8(f6(x5901,x5901,x5902),f2(x5902),x5902)+P8(x5901,f2(x5902),x5902)
% 0.78/0.95 [591]~P21(x5911)+~P6(f2(x5911),f6(x5912,x5912,x5911),x5911)+P6(f2(x5911),x5912,x5911)
% 0.78/0.95 [592]~P21(x5921)+~P8(f2(x5921),f6(x5922,x5922,x5921),x5921)+P8(f2(x5921),x5922,x5921)
% 0.78/0.95 [593]P6(f3(x5931,x5932,a1),x5931,a1)+~P6(f2(a1),x5932,a1)+~P6(f2(a1),x5931,a1)
% 0.78/0.95 [595]~P6(f2(a1),x5952,a1)+~P6(f2(a1),x5951,a1)+P6(f2(a1),f7(x5951,x5952,a1),a1)
% 0.78/0.95 [634]P6(f2(a1),x6341,a1)+P6(f2(a1),x6342,a1)+~P6(f2(a1),f6(x6341,x6342,a1),a1)
% 0.78/0.95 [262]~P40(x2622)+~P11(x2622)+E(f6(x2621,f2(x2622),x2622),x2621)
% 0.78/0.95 [283]E(x2831,f2(a1))+E(x2832,f2(a1))+~E(f6(x2832,x2831,a1),f10(f2(a1)))
% 0.78/0.95 [295]E(x2951,f2(a1))+E(x2951,f10(f2(a1)))+~E(f6(x2952,x2951,a1),f10(f2(a1)))
% 0.78/0.95 [296]E(x2961,f2(a1))+E(x2961,f10(f2(a1)))+~E(f6(x2961,x2962,a1),f10(f2(a1)))
% 0.78/0.95 [307]E(x3071,f10(f2(a1)))+E(x3072,f10(f2(a1)))+~E(f6(x3072,x3071,a1),f10(f2(a1)))
% 0.78/0.95 [632]P6(x6321,f7(x6322,x6321,a1),a1)+~P6(f10(f2(a1)),x6322,a1)+~P6(f10(f2(a1)),x6321,a1)
% 0.78/0.95 [633]P6(x6331,f7(x6331,x6332,a1),a1)+~P6(f10(f2(a1)),x6332,a1)+~P6(f10(f2(a1)),x6331,a1)
% 0.78/0.95 [665]~P6(f10(f2(a1)),x6652,a1)+~P6(f10(f2(a1)),x6651,a1)+P6(f10(f2(a1)),f7(x6651,x6652,a1),a1)
% 0.78/0.95 [666]~P8(f10(f2(a1)),x6662,a1)+~P8(f10(f2(a1)),x6661,a1)+P8(f10(f2(a1)),f7(x6661,x6662,a1),a1)
% 0.78/0.95 [319]P8(x3192,x3191,x3193)+~P28(x3193)+P6(x3191,x3192,x3193)
% 0.78/0.95 [321]P8(x3212,x3211,x3213)+~P28(x3213)+P8(x3211,x3212,x3213)
% 0.78/0.95 [358]~P29(x3583)+~P6(x3581,x3582,x3583)+P8(x3581,x3582,x3583)
% 0.78/0.95 [359]~P31(x3593)+~P6(x3591,x3592,x3593)+P8(x3591,x3592,x3593)
% 0.78/0.95 [421]~P6(x4213,x4212,x4211)+~P28(x4211)+~P6(x4212,x4213,x4211)
% 0.78/0.95 [423]~P8(x4233,x4232,x4231)+~P28(x4231)+~P6(x4232,x4233,x4231)
% 0.78/0.95 [425]~P6(x4253,x4252,x4251)+~P29(x4251)+~P6(x4252,x4253,x4251)
% 0.78/0.95 [427]~P6(x4273,x4272,x4271)+~P31(x4271)+~P6(x4272,x4273,x4271)
% 0.78/0.95 [428]~P8(x4283,x4282,x4281)+~P31(x4281)+~P6(x4282,x4283,x4281)
% 0.78/0.95 [458]~P7(x4581,x4583,a1)+P7(x4581,x4582,a1)+~P7(x4583,x4582,a1)
% 0.78/0.95 [459]~P8(x4591,x4593,a1)+P8(x4591,x4592,a1)+~P8(x4593,x4592,a1)
% 0.78/0.95 [225]~P10(x2253)+E(x2251,x2252)+~E(f9(x2251,x2253),f9(x2252,x2253))
% 0.78/0.95 [280]~P15(x2803)+E(x2801,x2802)+~E(f3(x2801,x2802,x2803),f2(x2803))
% 0.78/0.95 [281]~P20(x2813)+E(x2811,x2812)+~E(f3(x2811,x2812,x2813),f2(x2813))
% 0.78/0.95 [289]~P46(x2893)+P7(x2891,x2892,x2893)+~E(f5(x2891,x2893),f5(x2892,x2893))
% 0.78/0.95 [364]~P28(x3643)+~P8(x3642,x3641,x3643)+E(f8(x3641,x3642,x3643),x3642)
% 0.78/0.95 [365]~P28(x3653)+~P8(x3651,x3652,x3653)+E(f8(x3651,x3652,x3653),x3651)
% 0.78/0.95 [370]~P28(x3703)+P8(x3701,x3702,x3703)+~E(f8(x3701,x3702,x3703),x3701)
% 0.78/0.95 [380]~P4(x3803)+~P7(x3802,x3801,x3803)+E(f4(x3801,x3802,x3803),f2(x3803))
% 0.78/0.95 [381]~P4(x3813)+P7(x3811,x3812,x3813)+~E(f4(x3812,x3811,x3813),f2(x3813))
% 0.78/0.95 [412]E(x4121,x4122)+~E(f7(x4123,x4121,a1),f7(x4123,x4122,a1))+E(x4123,f2(a1))
% 0.78/0.95 [413]E(x4131,x4132)+~E(f7(x4131,x4133,a1),f7(x4132,x4133,a1))+E(x4133,f2(a1))
% 0.78/0.95 [414]~P46(x4143)+~P7(x4141,x4142,x4143)+P7(x4141,f5(x4142,x4143),x4143)
% 0.78/0.95 [415]~P46(x4152)+~P7(x4151,x4153,x4152)+P7(f5(x4151,x4152),x4153,x4152)
% 0.78/0.95 [441]~P46(x4413)+P7(x4411,x4412,x4413)+~P7(x4411,f5(x4412,x4413),x4413)
% 0.78/0.95 [442]~P46(x4423)+P6(x4421,x4422,x4423)+~P6(f5(x4421,x4423),x4422,x4423)
% 0.78/0.95 [443]~P46(x4433)+P7(x4431,x4432,x4433)+~P7(f5(x4431,x4433),x4432,x4433)
% 0.78/0.95 [444]~P23(x4443)+P8(x4441,x4442,x4443)+~P8(f5(x4441,x4443),x4442,x4443)
% 0.78/0.95 [445]~P44(x4452)+~P6(x4451,x4453,a1)+P6(f9(x4451,x4452),f9(x4453,x4452),x4452)
% 0.78/0.95 [446]~P44(x4462)+~P8(x4461,x4463,a1)+P8(f9(x4461,x4462),f9(x4463,x4462),x4462)
% 0.78/0.95 [467]~P6(x4671,x4673,a1)+~P6(x4673,x4672,a1)+P6(f10(x4671),x4672,a1)
% 0.78/0.95 [468]~P44(x4683)+~P6(f9(x4681,x4683),f9(x4682,x4683),x4683)+P6(x4681,x4682,a1)
% 0.78/0.95 [469]~P44(x4693)+~P8(f9(x4691,x4693),f9(x4692,x4693),x4693)+P8(x4691,x4692,a1)
% 0.78/0.95 [516]E(x5161,x5162)+~E(f7(x5163,x5161,a1),f7(x5163,x5162,a1))+~P6(f2(a1),x5163,a1)
% 0.78/0.95 [518]~P24(x5183)+~P6(x5181,x5182,x5183)+P6(f3(x5181,x5182,x5183),f2(x5183),x5183)
% 0.78/0.95 [519]~P24(x5193)+~P8(x5191,x5192,x5193)+P8(f3(x5191,x5192,x5193),f2(x5193),x5193)
% 0.78/0.95 [564]~P7(x5641,x5643,a1)+~P7(x5641,x5642,a1)+P7(x5641,f3(x5642,x5643,a1),a1)
% 0.78/0.95 [565]~P24(x5653)+P6(x5651,x5652,x5653)+~P6(f3(x5651,x5652,x5653),f2(x5653),x5653)
% 0.78/0.95 [566]~P24(x5663)+P8(x5661,x5662,x5663)+~P8(f3(x5661,x5662,x5663),f2(x5663),x5663)
% 0.78/0.95 [695]~P6(x6951,x6953,a1)+~P8(x6952,x6951,a1)+P6(f3(x6951,x6952,a1),f3(x6953,x6952,a1),a1)
% 0.78/0.95 [696]~P6(x6963,x6962,a1)+~P6(x6963,x6961,a1)+P6(f3(x6961,x6962,a1),f3(x6961,x6963,a1),a1)
% 0.78/0.95 [700]~P6(x7001,x7003,a1)+P6(f7(x7001,x7002,a1),f7(x7003,x7002,a1),a1)+~P6(f2(a1),x7002,a1)
% 0.78/0.95 [703]~P6(x7032,x7033,a1)+P6(f7(x7031,x7032,a1),f7(x7031,x7033,a1),a1)+~P6(f2(a1),x7031,a1)
% 0.78/0.95 [756]P7(x7562,x7563,a1)+E(x7561,f2(a1))+~P7(f7(x7561,x7562,a1),f7(x7561,x7563,a1),a1)
% 0.78/0.95 [765]~P8(x7653,x7652,a1)+~P8(f6(x7651,x7653,a1),x7652,a1)+P8(x7651,f3(x7652,x7653,a1),a1)
% 0.78/0.95 [766]~P8(x7662,x7663,a1)+~P8(x7661,f3(x7663,x7662,a1),a1)+P8(f6(x7661,x7662,a1),x7663,a1)
% 0.78/0.95 [806]P7(x8061,x8062,a1)+~P7(f7(x8063,x8061,a1),f7(x8063,x8062,a1),a1)+~P6(f2(a1),x8063,a1)
% 0.78/0.95 [808]P8(x8081,x8082,a1)+~P8(f7(x8083,x8081,a1),f7(x8083,x8082,a1),a1)+~P6(f2(a1),x8083,a1)
% 0.78/0.95 [809]P8(x8091,x8092,a1)+~P8(f7(x8091,x8093,a1),f7(x8092,x8093,a1),a1)+~P6(f2(a1),x8093,a1)
% 0.78/0.95 [542]~P46(x5422)+~P8(f2(x5422),x5423,x5422)+E(f7(f5(x5421,x5422),x5423,x5422),f5(f7(x5421,x5423,x5422),x5422))
% 0.78/0.95 [549]~P55(x5492)+~P8(x5493,x5491,a1)+E(f3(f9(x5491,x5492),f9(x5493,x5492),x5492),f9(f3(x5491,x5493,a1),x5492))
% 0.78/0.95 [724]~P47(x7242)+E(x7241,f2(x7242))+~E(f6(f7(x7243,x7243,x7242),f7(x7241,x7241,x7242),x7242),f2(x7242))
% 0.78/0.95 [725]~P47(x7252)+E(x7251,f2(x7252))+~E(f6(f7(x7251,x7251,x7252),f7(x7253,x7253,x7252),x7252),f2(x7252))
% 0.78/0.95 [760]~P8(x7602,x7603,a1)+~P8(x7602,x7601,a1)+E(f3(f3(x7601,x7602,a1),f3(x7603,x7602,a1),a1),f3(x7601,x7603,a1))
% 0.78/0.95 [822]~P47(x8222)+E(x8221,f2(x8222))+P6(f2(x8222),f6(f7(x8223,x8223,x8222),f7(x8221,x8221,x8222),x8222),x8222)
% 0.78/0.95 [823]~P47(x8232)+E(x8231,f2(x8232))+P6(f2(x8232),f6(f7(x8231,x8231,x8232),f7(x8233,x8233,x8232),x8232),x8232)
% 0.78/0.95 [856]~P47(x8562)+E(x8561,f2(x8562))+~P8(f6(f7(x8563,x8563,x8562),f7(x8561,x8561,x8562),x8562),f2(x8562),x8562)
% 0.78/0.95 [857]~P47(x8572)+E(x8571,f2(x8572))+~P8(f6(f7(x8571,x8571,x8572),f7(x8573,x8573,x8572),x8572),f2(x8572),x8572)
% 0.78/0.95 [429]~P17(x4294)+E(x4291,x4292)+~E(f6(x4293,x4291,x4294),f6(x4293,x4292,x4294))
% 0.78/0.95 [430]~P18(x4304)+E(x4301,x4302)+~E(f6(x4303,x4301,x4304),f6(x4303,x4302,x4304))
% 0.78/0.95 [431]~P15(x4314)+E(x4311,x4312)+~E(f3(x4313,x4313,x4314),f3(x4311,x4312,x4314))
% 0.78/0.95 [432]~P18(x4324)+E(x4321,x4322)+~E(f6(x4321,x4323,x4324),f6(x4322,x4323,x4324))
% 0.78/0.95 [433]~P15(x4333)+E(x4331,x4332)+~E(f3(x4331,x4332,x4333),f3(x4334,x4334,x4333))
% 0.78/0.95 [505]~P27(x5054)+~P7(x5051,x5053,x5054)+P7(x5051,f7(x5052,x5053,x5054),x5054)
% 0.78/0.95 [506]~P27(x5064)+~P7(x5061,x5062,x5064)+P7(x5061,f7(x5062,x5063,x5064),x5064)
% 0.78/0.95 [508]~P28(x5083)+~P6(x5082,x5084,x5083)+P6(f8(x5081,x5082,x5083),x5084,x5083)
% 0.78/0.95 [510]~P28(x5103)+~P6(x5101,x5104,x5103)+P6(f8(x5101,x5102,x5103),x5104,x5103)
% 0.78/0.95 [512]~P28(x5123)+~P8(x5122,x5124,x5123)+P8(f8(x5121,x5122,x5123),x5124,x5123)
% 0.78/0.95 [514]~P28(x5143)+~P8(x5141,x5144,x5143)+P8(f8(x5141,x5142,x5143),x5144,x5143)
% 0.78/0.95 [541]~P6(x5414,x5413,a1)+P6(x5411,x5412,a1)+~E(f6(x5411,x5413,a1),f6(x5414,x5412,a1))
% 0.78/0.95 [550]~P28(x5503)+P6(x5501,x5502,x5503)+~P6(x5501,f8(x5504,x5502,x5503),x5503)
% 0.78/0.95 [551]~P28(x5513)+P6(x5511,x5512,x5513)+~P6(x5511,f8(x5512,x5514,x5513),x5513)
% 0.78/0.95 [553]~P28(x5533)+P8(x5531,x5532,x5533)+~P8(x5531,f8(x5534,x5532,x5533),x5533)
% 0.78/0.95 [555]~P28(x5553)+P8(x5551,x5552,x5553)+~P8(x5551,f8(x5552,x5554,x5553),x5553)
% 0.78/0.95 [556]~P27(x5563)+P7(x5561,x5562,x5563)+~P7(f7(x5564,x5561,x5563),x5562,x5563)
% 0.78/0.95 [557]~P27(x5573)+P7(x5571,x5572,x5573)+~P7(f7(x5571,x5574,x5573),x5572,x5573)
% 0.78/0.95 [622]~P25(x6223)+~P6(x6221,x6224,x6223)+P6(f6(x6221,x6222,x6223),f6(x6224,x6222,x6223),x6223)
% 0.78/0.95 [623]~P26(x6233)+~P6(x6231,x6234,x6233)+P6(f6(x6231,x6232,x6233),f6(x6234,x6232,x6233),x6233)
% 0.78/0.95 [624]~P25(x6243)+~P6(x6242,x6244,x6243)+P6(f6(x6241,x6242,x6243),f6(x6241,x6244,x6243),x6243)
% 0.78/0.95 [625]~P26(x6253)+~P6(x6252,x6254,x6253)+P6(f6(x6251,x6252,x6253),f6(x6251,x6254,x6253),x6253)
% 0.78/0.95 [626]~P40(x6263)+~P7(x6261,x6264,x6263)+P7(f7(x6261,x6262,x6263),f7(x6264,x6262,x6263),x6263)
% 0.78/0.95 [627]~P40(x6273)+~P7(x6272,x6274,x6273)+P7(f7(x6271,x6272,x6273),f7(x6271,x6274,x6273),x6273)
% 0.78/0.95 [628]~P3(x6283)+~P8(x6281,x6284,x6283)+P8(f6(x6281,x6282,x6283),f6(x6284,x6282,x6283),x6283)
% 0.78/0.95 [629]~P25(x6293)+~P8(x6291,x6294,x6293)+P8(f6(x6291,x6292,x6293),f6(x6294,x6292,x6293),x6293)
% 0.78/0.95 [630]~P3(x6303)+~P8(x6302,x6304,x6303)+P8(f6(x6301,x6302,x6303),f6(x6301,x6304,x6303),x6303)
% 0.78/0.95 [631]~P25(x6313)+~P8(x6312,x6314,x6313)+P8(f6(x6311,x6312,x6313),f6(x6311,x6314,x6313),x6313)
% 0.78/0.95 [694]~P6(x6942,x6944,a1)+~P6(x6941,x6943,a1)+P6(f6(x6941,x6942,a1),f6(x6943,x6944,a1),a1)
% 0.78/0.95 [697]~P8(x6972,x6974,a1)+~P8(x6971,x6973,a1)+P8(f7(x6971,x6972,a1),f7(x6973,x6974,a1),a1)
% 0.78/0.95 [698]~P8(x6982,x6984,a1)+~P8(x6981,x6983,a1)+P8(f6(x6981,x6982,a1),f6(x6983,x6984,a1),a1)
% 0.78/0.95 [761]~P25(x7613)+P6(x7611,x7612,x7613)+~P6(f6(x7614,x7611,x7613),f6(x7614,x7612,x7613),x7613)
% 0.78/0.95 [762]~P25(x7623)+P6(x7621,x7622,x7623)+~P6(f6(x7621,x7624,x7623),f6(x7622,x7624,x7623),x7623)
% 0.78/0.95 [763]~P25(x7633)+P8(x7631,x7632,x7633)+~P8(f6(x7634,x7631,x7633),f6(x7634,x7632,x7633),x7633)
% 0.78/0.95 [764]~P25(x7643)+P8(x7641,x7642,x7643)+~P8(f6(x7641,x7644,x7643),f6(x7642,x7644,x7643),x7643)
% 0.78/0.95 [548]~P4(x5483)+~P7(x5484,x5482,x5483)+E(f4(f4(x5481,x5482,x5483),x5484,x5483),f4(x5481,x5484,x5483))
% 0.78/0.95 [759]~P22(x7594)+~P8(f6(x7591,x7593,x7594),x7592,x7594)+P8(x7591,f6(x7592,f5(x7593,x7594),x7594),x7594)
% 0.78/0.95 [769]E(x7691,x7692)+E(x7693,f2(a1))+~E(f6(x7694,f7(x7693,x7691,a1),a1),f6(x7694,f7(x7693,x7692,a1),a1))
% 0.78/0.95 [801]~P40(x8013)+~P11(x8013)+E(f6(f7(x8011,x8012,x8013),f7(x8011,x8014,x8013),x8013),f6(f7(x8011,x8014,x8013),f7(x8011,x8012,x8013),x8013))
% 0.78/0.95 [826]~P46(x8264)+P6(x8261,f6(x8262,x8263,x8264),x8264)+~P6(f5(f3(x8261,x8262,x8264),x8264),x8263,x8264)
% 0.78/0.95 [827]~P46(x8273)+P6(f3(x8271,x8272,x8273),x8274,x8273)+~P6(f5(f3(x8274,x8271,x8273),x8273),x8272,x8273)
% 0.78/0.95 [847]E(x8471,x8472)+E(x8473,x8474)+~E(f6(f7(x8473,x8471,a1),f7(x8474,x8472,a1),a1),f6(f7(x8473,x8472,a1),f7(x8474,x8471,a1),a1))
% 0.78/0.95 [858]~P6(x8584,x8581,a1)+~P6(f2(a1),x8583,a1)+P6(f6(f7(x8581,f4(x8582,x8583,a1),a1),x8584,a1),f7(x8581,x8583,a1),a1)
% 0.78/0.95 [680]~P15(x6803)+E(f6(x6801,x6802,x6803),x6804)+~E(f6(x6801,f6(x6805,x6802,x6803),x6803),f6(x6805,x6804,x6803))
% 0.78/0.95 [853]~P8(x8533,x8532,a1)+~E(f6(f7(x8533,x8534,a1),x8531,a1),f6(f7(x8532,x8534,a1),x8535,a1))+E(x8531,f6(f7(f3(x8532,x8533,a1),x8534,a1),x8535,a1))
% 0.78/0.95 [854]~P8(x8542,x8541,a1)+~E(f6(f7(x8541,x8543,a1),x8544,a1),f6(f7(x8542,x8543,a1),x8545,a1))+E(f6(f7(f3(x8541,x8542,a1),x8543,a1),x8544,a1),x8545)
% 0.78/0.95 [872]~P8(x8723,x8722,a1)+~P6(f6(f7(x8723,x8724,a1),x8721,a1),f6(f7(x8722,x8724,a1),x8725,a1),a1)+P6(x8721,f6(f7(f3(x8722,x8723,a1),x8724,a1),x8725,a1),a1)
% 0.78/0.95 [873]~P8(x8733,x8732,a1)+~P8(f6(f7(x8733,x8734,a1),x8731,a1),f6(f7(x8732,x8734,a1),x8735,a1),a1)+P8(x8731,f6(f7(f3(x8732,x8733,a1),x8734,a1),x8735,a1),a1)
% 0.78/0.95 [874]~P8(x8742,x8741,a1)+~P6(f6(f7(x8741,x8743,a1),x8744,a1),f6(f7(x8742,x8743,a1),x8745,a1),a1)+P6(f6(f7(f3(x8741,x8742,a1),x8743,a1),x8744,a1),x8745,a1)
% 0.78/0.95 [875]~P8(x8752,x8751,a1)+~P8(f6(f7(x8751,x8753,a1),x8754,a1),f6(f7(x8752,x8753,a1),x8755,a1),a1)+P8(f6(f7(f3(x8751,x8752,a1),x8753,a1),x8754,a1),x8755,a1)
% 0.78/0.95 [880]~P8(x8801,x8804,a1)+P6(f6(f7(x8801,x8802,a1),x8803,a1),f6(f7(x8804,x8802,a1),x8805,a1),a1)+~P6(x8803,f6(f7(f3(x8804,x8801,a1),x8802,a1),x8805,a1),a1)
% 0.78/0.95 [881]~P8(x8811,x8814,a1)+P8(f6(f7(x8811,x8812,a1),x8813,a1),f6(f7(x8814,x8812,a1),x8815,a1),a1)+~P8(x8813,f6(f7(f3(x8814,x8811,a1),x8812,a1),x8815,a1),a1)
% 0.78/0.95 [882]~P8(x8824,x8821,a1)+P6(f6(f7(x8821,x8822,a1),x8823,a1),f6(f7(x8824,x8822,a1),x8825,a1),a1)+~P6(f6(f7(f3(x8821,x8824,a1),x8822,a1),x8823,a1),x8825,a1)
% 0.78/0.95 [883]~P8(x8834,x8831,a1)+P8(f6(f7(x8831,x8832,a1),x8833,a1),f6(f7(x8834,x8832,a1),x8835,a1),a1)+~P8(f6(f7(f3(x8831,x8834,a1),x8832,a1),x8833,a1),x8835,a1)
% 0.78/0.95 [851]~P56(x8514)+~E(f6(f7(x8513,x8515,x8514),x8511,x8514),f6(f7(x8512,x8515,x8514),x8516,x8514))+E(x8511,f6(f7(f3(x8512,x8513,x8514),x8515,x8514),x8516,x8514))
% 0.78/0.95 [852]~P56(x8523)+~E(f6(f7(x8521,x8524,x8523),x8525,x8523),f6(f7(x8522,x8524,x8523),x8526,x8523))+E(f6(f7(f3(x8521,x8522,x8523),x8524,x8523),x8525,x8523),x8526)
% 0.78/0.95 [868]~P51(x8684)+~P6(f6(f7(x8683,x8685,x8684),x8681,x8684),f6(f7(x8682,x8685,x8684),x8686,x8684),x8684)+P6(x8681,f6(f7(f3(x8682,x8683,x8684),x8685,x8684),x8686,x8684),x8684)
% 0.78/0.95 [869]~P51(x8694)+~P8(f6(f7(x8693,x8695,x8694),x8691,x8694),f6(f7(x8692,x8695,x8694),x8696,x8694),x8694)+P8(x8691,f6(f7(f3(x8692,x8693,x8694),x8695,x8694),x8696,x8694),x8694)
% 0.78/0.95 [870]~P51(x8703)+~P6(f6(f7(x8701,x8704,x8703),x8705,x8703),f6(f7(x8702,x8704,x8703),x8706,x8703),x8703)+P6(f6(f7(f3(x8701,x8702,x8703),x8704,x8703),x8705,x8703),x8706,x8703)
% 0.78/0.95 [871]~P51(x8713)+~P8(f6(f7(x8711,x8714,x8713),x8715,x8713),f6(f7(x8712,x8714,x8713),x8716,x8713),x8713)+P8(f6(f7(f3(x8711,x8712,x8713),x8714,x8713),x8715,x8713),x8716,x8713)
% 0.78/0.95 [876]~P51(x8763)+P6(f6(f7(x8761,x8762,x8763),x8764,x8763),f6(f7(x8765,x8762,x8763),x8766,x8763),x8763)+~P6(x8764,f6(f7(f3(x8765,x8761,x8763),x8762,x8763),x8766,x8763),x8763)
% 0.78/0.95 [877]~P51(x8773)+P8(f6(f7(x8771,x8772,x8773),x8774,x8773),f6(f7(x8775,x8772,x8773),x8776,x8773),x8773)+~P8(x8774,f6(f7(f3(x8775,x8771,x8773),x8772,x8773),x8776,x8773),x8773)
% 0.78/0.95 [878]~P51(x8783)+P6(f6(f7(x8781,x8782,x8783),x8784,x8783),f6(f7(x8785,x8782,x8783),x8786,x8783),x8783)+~P6(f6(f7(f3(x8781,x8785,x8783),x8782,x8783),x8784,x8783),x8786,x8783)
% 0.78/0.95 [879]~P51(x8793)+P8(f6(f7(x8791,x8792,x8793),x8794,x8793),f6(f7(x8795,x8792,x8793),x8796,x8793),x8793)+~P8(f6(f7(f3(x8791,x8795,x8793),x8792,x8793),x8794,x8793),x8796,x8793)
% 0.78/0.95 [268]~P28(x2682)+~P22(x2682)+P6(x2681,f2(x2682),x2682)+E(f5(x2681,x2682),x2681)
% 0.78/0.95 [521]P6(x5211,x5212,a1)+~P5(x5212,a1)+P5(x5211,a1)+~P5(f3(x5211,x5212,a1),a1)
% 0.78/0.95 [522]P6(x5222,x5221,a1)+~P5(x5222,a1)+P5(x5221,a1)+~P5(f3(x5222,x5221,a1),a1)
% 0.78/0.95 [327]P6(x3271,x3272,x3273)+~P28(x3273)+E(x3271,x3272)+P6(x3272,x3271,x3273)
% 0.78/0.95 [328]P6(x3281,x3282,x3283)+~P46(x3283)+E(x3281,x3282)+P6(x3282,x3281,x3283)
% 0.78/0.95 [372]~P28(x3723)+~P8(x3721,x3722,x3723)+E(x3721,x3722)+P6(x3721,x3722,x3723)
% 0.78/0.95 [378]~P29(x3783)+~P8(x3781,x3782,x3783)+E(x3781,x3782)+P6(x3781,x3782,x3783)
% 0.78/0.95 [436]~P8(x4362,x4361,x4363)+~P8(x4361,x4362,x4363)+E(x4361,x4362)+~P29(x4363)
% 0.78/0.95 [449]P8(x4492,x4491,x4493)+~P31(x4493)+~P8(x4491,x4492,x4493)+P6(x4491,x4492,x4493)
% 0.78/0.95 [297]~P40(x2972)+~P11(x2972)+~E(f6(x2973,x2971,x2972),x2973)+E(x2971,f2(x2972))
% 0.78/0.95 [299]~P40(x2993)+~P11(x2993)+E(x2991,x2992)+~E(f3(x2991,x2992,x2993),f2(x2993))
% 0.78/0.95 [302]~P54(x3022)+~E(f7(x3023,x3021,x3022),f2(x3022))+E(x3021,f2(x3022))+E(x3023,f2(x3022))
% 0.78/0.95 [304]~P36(x3042)+~E(f7(x3043,x3041,x3042),f2(x3042))+E(x3041,f2(x3042))+E(x3043,f2(x3042))
% 0.78/0.95 [594]E(x5941,x5942)+~P8(x5943,x5942,a1)+~P8(x5943,x5941,a1)+~E(f3(x5941,x5943,a1),f3(x5942,x5943,a1))
% 0.78/0.95 [635]~P47(x6351)+~P6(x6353,f2(x6351),x6351)+~P6(x6352,f2(x6351),x6351)+P6(f2(x6351),f7(x6352,x6353,x6351),x6351)
% 0.78/0.95 [636]~P47(x6361)+~P8(x6363,f2(x6361),x6361)+~P8(x6362,f2(x6361),x6361)+P8(f2(x6361),f7(x6362,x6363,x6361),x6361)
% 0.78/0.95 [638]~P51(x6381)+~P8(x6383,f2(x6381),x6381)+~P8(x6382,f2(x6381),x6381)+P8(f2(x6381),f7(x6382,x6383,x6381),x6381)
% 0.78/0.95 [639]~P1(x6391)+~P6(f2(x6391),x6393,x6391)+~P6(f2(x6391),x6392,x6391)+P6(f2(x6391),f7(x6392,x6393,x6391),x6391)
% 0.78/0.95 [640]~P2(x6401)+~P6(f2(x6401),x6403,x6401)+~P6(f2(x6401),x6402,x6401)+P6(f2(x6401),f6(x6402,x6403,x6401),x6401)
% 0.78/0.95 [641]~P2(x6411)+~P6(f2(x6411),x6413,x6411)+~P8(f2(x6411),x6412,x6411)+P6(f2(x6411),f6(x6412,x6413,x6411),x6411)
% 0.78/0.95 [642]~P2(x6421)+~P6(f2(x6421),x6422,x6421)+~P8(f2(x6421),x6423,x6421)+P6(f2(x6421),f6(x6422,x6423,x6421),x6421)
% 0.78/0.95 [643]~P47(x6431)+~P8(f2(x6431),x6433,x6431)+~P8(f2(x6431),x6432,x6431)+P8(f2(x6431),f7(x6432,x6433,x6431),x6431)
% 0.78/0.95 [644]~P51(x6441)+~P8(f2(x6441),x6443,x6441)+~P8(f2(x6441),x6442,x6441)+P8(f2(x6441),f7(x6442,x6443,x6441),x6441)
% 0.78/0.95 [645]~P49(x6451)+~P8(f2(x6451),x6453,x6451)+~P8(f2(x6451),x6452,x6451)+P8(f2(x6451),f7(x6452,x6453,x6451),x6451)
% 0.78/0.95 [646]~P2(x6461)+~P8(f2(x6461),x6463,x6461)+~P8(f2(x6461),x6462,x6461)+P8(f2(x6461),f6(x6462,x6463,x6461),x6461)
% 0.78/0.95 [647]~P2(x6473)+~P6(x6472,f2(x6473),x6473)+~P6(x6471,f2(x6473),x6473)+P6(f6(x6471,x6472,x6473),f2(x6473),x6473)
% 0.78/0.95 [648]~P2(x6483)+~P6(x6482,f2(x6483),x6483)+~P8(x6481,f2(x6483),x6483)+P6(f6(x6481,x6482,x6483),f2(x6483),x6483)
% 0.78/0.95 [649]~P2(x6493)+~P6(x6491,f2(x6493),x6493)+~P8(x6492,f2(x6493),x6493)+P6(f6(x6491,x6492,x6493),f2(x6493),x6493)
% 0.78/0.95 [650]~P2(x6503)+~P8(x6502,f2(x6503),x6503)+~P8(x6501,f2(x6503),x6503)+P8(f6(x6501,x6502,x6503),f2(x6503),x6503)
% 0.78/0.95 [651]~P1(x6513)+~P6(x6512,f2(x6513),x6513)+~P6(f2(x6513),x6511,x6513)+P6(f7(x6511,x6512,x6513),f2(x6513),x6513)
% 0.78/0.95 [653]~P1(x6533)+~P6(x6531,f2(x6533),x6533)+~P6(f2(x6533),x6532,x6533)+P6(f7(x6531,x6532,x6533),f2(x6533),x6533)
% 0.78/0.95 [654]~P47(x6543)+~P8(x6542,f2(x6543),x6543)+~P8(f2(x6543),x6541,x6543)+P8(f7(x6541,x6542,x6543),f2(x6543),x6543)
% 0.78/0.95 [655]~P47(x6553)+~P8(x6551,f2(x6553),x6553)+~P8(f2(x6553),x6552,x6553)+P8(f7(x6551,x6552,x6553),f2(x6553),x6553)
% 0.78/0.95 [657]~P49(x6573)+~P8(x6572,f2(x6573),x6573)+~P8(f2(x6573),x6571,x6573)+P8(f7(x6571,x6572,x6573),f2(x6573),x6573)
% 0.78/0.95 [660]~P49(x6603)+~P8(x6601,f2(x6603),x6603)+~P8(f2(x6603),x6602,x6603)+P8(f7(x6601,x6602,x6603),f2(x6603),x6603)
% 0.78/0.95 [667]~P47(x6672)+~P8(f7(x6673,x6671,x6672),f2(x6672),x6672)+P8(x6671,f2(x6672),x6672)+P8(x6673,f2(x6672),x6672)
% 0.78/0.95 [668]~P47(x6682)+~P8(f2(x6682),f7(x6683,x6681,x6682),x6682)+P8(x6681,f2(x6682),x6682)+P8(f2(x6682),x6683,x6682)
% 0.78/0.95 [669]~P47(x6692)+~P8(f2(x6692),f7(x6691,x6693,x6692),x6692)+P8(x6691,f2(x6692),x6692)+P8(f2(x6692),x6693,x6692)
% 0.78/0.95 [670]~P47(x6702)+~P8(f2(x6702),f7(x6703,x6701,x6702),x6702)+P8(x6701,f2(x6702),x6702)+P8(f2(x6702),x6701,x6702)
% 0.78/0.95 [671]~P47(x6712)+~P8(f2(x6712),f7(x6711,x6713,x6712),x6712)+P8(x6711,f2(x6712),x6712)+P8(f2(x6712),x6711,x6712)
% 0.78/0.95 [672]~P47(x6722)+~P8(f7(x6723,x6721,x6722),f2(x6722),x6722)+P8(x6721,f2(x6722),x6722)+P8(f2(x6722),x6721,x6722)
% 0.78/0.95 [673]~P47(x6732)+~P8(f7(x6731,x6733,x6732),f2(x6732),x6732)+P8(x6731,f2(x6732),x6732)+P8(f2(x6732),x6731,x6732)
% 0.78/0.95 [674]~P47(x6741)+~P8(f7(x6742,x6743,x6741),f2(x6741),x6741)+P8(f2(x6741),x6742,x6741)+P8(f2(x6741),x6743,x6741)
% 0.78/0.95 [692]~P1(x6921)+~P6(f2(x6921),f7(x6923,x6922,x6921),x6921)+P6(f2(x6921),x6922,x6921)+~P6(f2(x6921),x6923,x6921)
% 0.78/0.95 [693]~P1(x6931)+~P6(f2(x6931),f7(x6932,x6933,x6931),x6931)+P6(f2(x6931),x6932,x6931)+~P6(f2(x6931),x6933,x6931)
% 0.78/0.95 [757]~P8(x7573,x7572,a1)+P7(x7571,x7572,a1)+~P7(x7571,x7573,a1)+~P7(x7571,f3(x7572,x7573,a1),a1)
% 0.78/0.95 [758]~P8(x7582,x7583,a1)+P7(x7581,x7582,a1)+~P7(x7581,x7583,a1)+~P7(x7581,f3(x7583,x7582,a1),a1)
% 0.78/0.95 [824]~P8(x8243,x8241,a1)+P6(x8241,x8242,a1)+~P8(x8243,x8242,a1)+~P6(f3(x8241,x8243,a1),f3(x8242,x8243,a1),a1)
% 0.78/0.95 [825]~P8(x8253,x8251,a1)+P8(x8251,x8252,a1)+~P8(x8253,x8252,a1)+~P8(f3(x8251,x8253,a1),f3(x8252,x8253,a1),a1)
% 0.78/0.95 [688]~P52(x6882)+~P8(x6883,f2(x6882),x6882)+~P8(x6881,f2(x6882),x6882)+E(f7(f5(x6881,x6882),f5(x6883,x6882),x6882),f5(f7(x6881,x6883,x6882),x6882))
% 0.78/0.95 [689]~P52(x6892)+~P8(x6893,f2(x6892),x6892)+~P8(f2(x6892),x6891,x6892)+E(f7(f5(x6891,x6892),f5(x6893,x6892),x6892),f5(f7(x6891,x6893,x6892),x6892))
% 0.78/0.95 [690]~P52(x6902)+~P8(x6901,f2(x6902),x6902)+~P8(f2(x6902),x6903,x6902)+E(f7(f5(x6901,x6902),f5(x6903,x6902),x6902),f5(f7(x6901,x6903,x6902),x6902))
% 0.78/0.95 [691]~P52(x6912)+~P8(f2(x6912),x6913,x6912)+~P8(f2(x6912),x6911,x6912)+E(f7(f5(x6911,x6912),f5(x6913,x6912),x6912),f5(f7(x6911,x6913,x6912),x6912))
% 0.78/0.95 [475]~P29(x4753)+~P6(x4751,x4754,x4753)+P6(x4751,x4752,x4753)+~P6(x4754,x4752,x4753)
% 0.78/0.95 [476]~P29(x4763)+~P8(x4761,x4764,x4763)+P6(x4761,x4762,x4763)+~P6(x4764,x4762,x4763)
% 0.78/0.95 [477]~P29(x4773)+~P8(x4774,x4772,x4773)+P6(x4771,x4772,x4773)+~P6(x4771,x4774,x4773)
% 0.78/0.95 [478]~P31(x4783)+~P6(x4781,x4784,x4783)+P6(x4781,x4782,x4783)+~P6(x4784,x4782,x4783)
% 0.78/0.95 [479]~P31(x4793)+~P8(x4791,x4794,x4793)+P6(x4791,x4792,x4793)+~P6(x4794,x4792,x4793)
% 0.78/0.95 [480]~P31(x4803)+~P8(x4804,x4802,x4803)+P6(x4801,x4802,x4803)+~P6(x4801,x4804,x4803)
% 0.78/0.95 [481]~P27(x4813)+~P7(x4811,x4814,x4813)+P7(x4811,x4812,x4813)+~P7(x4814,x4812,x4813)
% 0.78/0.95 [482]~P29(x4823)+~P8(x4821,x4824,x4823)+P8(x4821,x4822,x4823)+~P8(x4824,x4822,x4823)
% 0.78/0.95 [483]~P31(x4833)+~P8(x4831,x4834,x4833)+P8(x4831,x4832,x4833)+~P8(x4834,x4832,x4833)
% 0.78/0.95 [440]~P40(x4404)+~P11(x4404)+E(x4401,x4402)+~E(f6(x4403,x4401,x4404),f6(x4403,x4402,x4404))
% 0.78/0.95 [597]~P28(x5974)+~P6(x5971,x5973,x5974)+~P6(x5971,x5972,x5974)+P6(x5971,f8(x5972,x5973,x5974),x5974)
% 0.78/0.95 [598]~P27(x5984)+~P7(x5981,x5983,x5984)+~P7(x5981,x5982,x5984)+P7(x5981,f6(x5982,x5983,x5984),x5984)
% 0.78/0.95 [599]~P34(x5994)+~P7(x5991,x5993,x5994)+~P7(x5991,x5992,x5994)+P7(x5991,f3(x5992,x5993,x5994),x5994)
% 0.78/0.95 [601]~P4(x6014)+~P7(x6011,x6013,x6014)+~P7(x6011,x6012,x6014)+P7(x6011,f4(x6012,x6013,x6014),x6014)
% 0.78/0.95 [604]~P28(x6044)+~P8(x6041,x6043,x6044)+~P8(x6041,x6042,x6044)+P8(x6041,f8(x6042,x6043,x6044),x6044)
% 0.78/0.95 [616]~P44(x6164)+~P6(x6161,x6163,x6164)+~P6(f2(x6164),x6162,x6164)+P6(x6161,f6(x6162,x6163,x6164),x6164)
% 0.78/0.95 [663]~P28(x6633)+P6(x6631,x6632,x6633)+P6(x6634,x6632,x6633)+~P6(f8(x6631,x6634,x6633),x6632,x6633)
% 0.78/0.95 [664]~P28(x6643)+P8(x6641,x6642,x6643)+P8(x6644,x6642,x6643)+~P8(f8(x6641,x6644,x6643),x6642,x6643)
% 0.78/0.95 [682]~P4(x6823)+P7(x6821,x6822,x6823)+~P7(x6821,x6824,x6823)+~P7(x6821,f4(x6822,x6824,x6823),x6823)
% 0.78/0.95 [733]~P47(x7333)+~P6(x7334,x7331,x7333)+~P6(x7332,f2(x7333),x7333)+P6(f7(x7331,x7332,x7333),f7(x7334,x7332,x7333),x7333)
% 0.78/0.95 [736]~P47(x7363)+~P6(x7364,x7362,x7363)+~P6(x7361,f2(x7363),x7363)+P6(f7(x7361,x7362,x7363),f7(x7361,x7364,x7363),x7363)
% 0.78/0.95 [737]~P51(x7373)+~P8(x7374,x7371,x7373)+~P8(x7372,f2(x7373),x7373)+P8(f7(x7371,x7372,x7373),f7(x7374,x7372,x7373),x7373)
% 0.78/0.95 [738]~P47(x7383)+~P8(x7384,x7382,x7383)+~P6(x7381,f2(x7383),x7383)+P8(f7(x7381,x7382,x7383),f7(x7381,x7384,x7383),x7383)
% 0.78/0.95 [739]~P51(x7393)+~P8(x7394,x7392,x7393)+~P8(x7391,f2(x7393),x7393)+P8(f7(x7391,x7392,x7393),f7(x7391,x7394,x7393),x7393)
% 0.78/0.95 [740]~P1(x7403)+~P6(x7401,x7404,x7403)+~P6(f2(x7403),x7402,x7403)+P6(f7(x7401,x7402,x7403),f7(x7404,x7402,x7403),x7403)
% 0.78/0.95 [741]~P47(x7413)+~P6(x7411,x7414,x7413)+~P6(f2(x7413),x7412,x7413)+P6(f7(x7411,x7412,x7413),f7(x7414,x7412,x7413),x7413)
% 0.78/0.95 [742]~P1(x7423)+~P6(x7422,x7424,x7423)+~P6(f2(x7423),x7421,x7423)+P6(f7(x7421,x7422,x7423),f7(x7421,x7424,x7423),x7423)
% 0.78/0.95 [744]~P47(x7443)+~P6(x7442,x7444,x7443)+~P6(f2(x7443),x7441,x7443)+P6(f7(x7441,x7442,x7443),f7(x7441,x7444,x7443),x7443)
% 0.78/0.95 [745]~P45(x7453)+~P6(x7452,x7454,x7453)+~P6(f2(x7453),x7451,x7453)+P6(f7(x7451,x7452,x7453),f7(x7451,x7454,x7453),x7453)
% 0.78/0.95 [746]~P39(x7463)+~P8(x7461,x7464,x7463)+~P8(f2(x7463),x7462,x7463)+P8(f7(x7461,x7462,x7463),f7(x7464,x7462,x7463),x7463)
% 0.78/0.95 [747]~P47(x7473)+~P8(x7472,x7474,x7473)+~P6(f2(x7473),x7471,x7473)+P8(f7(x7471,x7472,x7473),f7(x7471,x7474,x7473),x7473)
% 0.78/0.95 [748]~P38(x7483)+~P8(x7482,x7484,x7483)+~P8(f2(x7483),x7481,x7483)+P8(f7(x7481,x7482,x7483),f7(x7481,x7484,x7483),x7483)
% 0.78/0.95 [749]~P39(x7493)+~P8(x7492,x7494,x7493)+~P8(f2(x7493),x7491,x7493)+P8(f7(x7491,x7492,x7493),f7(x7491,x7494,x7493),x7493)
% 0.78/0.95 [767]~P40(x7672)+P7(x7673,x7674,x7672)+~P7(f7(x7671,x7673,x7672),f7(x7671,x7674,x7672),x7672)+E(x7671,f2(x7672))
% 0.78/0.95 [768]~P40(x7682)+P7(x7683,x7684,x7682)+~P7(f7(x7683,x7681,x7682),f7(x7684,x7681,x7682),x7682)+E(x7681,f2(x7682))
% 0.78/0.95 [782]P6(x7822,x7821,x7823)+~P47(x7823)+P6(x7821,x7822,x7823)+~P6(f7(x7824,x7821,x7823),f7(x7824,x7822,x7823),x7823)
% 0.78/0.95 [783]P6(x7832,x7831,x7833)+~P47(x7833)+P6(x7831,x7832,x7833)+~P6(f7(x7831,x7834,x7833),f7(x7832,x7834,x7833),x7833)
% 0.78/0.95 [796]~P47(x7963)+P6(x7961,x7962,x7963)+~P6(f7(x7961,x7964,x7963),f7(x7962,x7964,x7963),x7963)+P6(x7964,f2(x7963),x7963)
% 0.78/0.95 [797]~P47(x7973)+P6(x7971,x7972,x7973)+~P6(f7(x7974,x7971,x7973),f7(x7974,x7972,x7973),x7973)+P6(x7974,f2(x7973),x7973)
% 0.78/0.95 [798]~P47(x7983)+P6(x7981,x7982,x7983)+~P6(f7(x7984,x7982,x7983),f7(x7984,x7981,x7983),x7983)+P6(f2(x7983),x7984,x7983)
% 0.78/0.95 [799]~P47(x7993)+P6(x7991,x7992,x7993)+~P6(f7(x7992,x7994,x7993),f7(x7991,x7994,x7993),x7993)+P6(f2(x7993),x7994,x7993)
% 0.78/0.95 [802]~P47(x8022)+~P6(f7(x8023,x8021,x8022),f7(x8024,x8021,x8022),x8022)+P6(x8021,f2(x8022),x8022)+P6(f2(x8022),x8021,x8022)
% 0.78/0.95 [803]~P47(x8032)+~P6(f7(x8031,x8033,x8032),f7(x8031,x8034,x8032),x8032)+P6(x8031,f2(x8032),x8032)+P6(f2(x8032),x8031,x8032)
% 0.78/0.95 [810]~P47(x8103)+P6(x8101,x8102,x8103)+~P6(f7(x8104,x8102,x8103),f7(x8104,x8101,x8103),x8103)+~P6(x8104,f2(x8103),x8103)
% 0.78/0.95 [811]~P47(x8113)+P8(x8111,x8112,x8113)+~P8(f7(x8114,x8112,x8113),f7(x8114,x8111,x8113),x8113)+~P6(x8114,f2(x8113),x8113)
% 0.78/0.95 [812]~P1(x8123)+P6(x8121,x8122,x8123)+~P6(f7(x8124,x8121,x8123),f7(x8124,x8122,x8123),x8123)+~P8(f2(x8123),x8124,x8123)
% 0.78/0.95 [813]~P1(x8133)+P6(x8131,x8132,x8133)+~P6(f7(x8131,x8134,x8133),f7(x8132,x8134,x8133),x8133)+~P8(f2(x8133),x8134,x8133)
% 0.78/0.95 [814]~P47(x8143)+P6(x8141,x8142,x8143)+~P6(f7(x8144,x8141,x8143),f7(x8144,x8142,x8143),x8143)+~P6(f2(x8143),x8144,x8143)
% 0.78/0.95 [815]~P43(x8153)+P6(x8151,x8152,x8153)+~P6(f7(x8154,x8151,x8153),f7(x8154,x8152,x8153),x8153)+~P8(f2(x8153),x8154,x8153)
% 0.78/0.95 [816]~P43(x8163)+P6(x8161,x8162,x8163)+~P6(f7(x8161,x8164,x8163),f7(x8162,x8164,x8163),x8163)+~P8(f2(x8163),x8164,x8163)
% 0.78/0.95 [817]~P1(x8173)+P8(x8171,x8172,x8173)+~P8(f7(x8174,x8171,x8173),f7(x8174,x8172,x8173),x8173)+~P6(f2(x8173),x8174,x8173)
% 0.78/0.95 [818]~P1(x8183)+P8(x8181,x8182,x8183)+~P8(f7(x8181,x8184,x8183),f7(x8182,x8184,x8183),x8183)+~P6(f2(x8183),x8184,x8183)
% 0.78/0.95 [819]~P47(x8193)+P8(x8191,x8192,x8193)+~P8(f7(x8194,x8191,x8193),f7(x8194,x8192,x8193),x8193)+~P6(f2(x8193),x8194,x8193)
% 0.78/0.95 [845]~P46(x8453)+~P6(x8451,f6(x8452,x8454,x8453),x8453)+~P6(f3(x8452,x8454,x8453),x8451,x8453)+P6(f5(f3(x8451,x8452,x8453),x8453),x8454,x8453)
% 0.78/0.95 [560]~P24(x5603)+~P6(x5604,x5605,x5603)+P6(x5601,x5602,x5603)+~E(f3(x5604,x5605,x5603),f3(x5601,x5602,x5603))
% 0.78/0.95 [561]~P24(x5613)+~P6(x5614,x5615,x5613)+P6(x5611,x5612,x5613)+~E(f3(x5611,x5612,x5613),f3(x5614,x5615,x5613))
% 0.78/0.95 [562]~P24(x5623)+~P8(x5625,x5624,x5623)+P8(x5621,x5622,x5623)+~E(f3(x5624,x5625,x5623),f3(x5622,x5621,x5623))
% 0.78/0.95 [563]~P24(x5633)+~P8(x5635,x5634,x5633)+P8(x5631,x5632,x5633)+~E(f3(x5632,x5631,x5633),f3(x5634,x5635,x5633))
% 0.78/0.95 [726]~P26(x7263)+~P6(x7262,x7265,x7263)+~P6(x7261,x7264,x7263)+P6(f6(x7261,x7262,x7263),f6(x7264,x7265,x7263),x7263)
% 0.78/0.95 [727]~P26(x7273)+~P6(x7272,x7275,x7273)+~P8(x7271,x7274,x7273)+P6(f6(x7271,x7272,x7273),f6(x7274,x7275,x7273),x7273)
% 0.78/0.95 [728]~P26(x7283)+~P6(x7281,x7284,x7283)+~P8(x7282,x7285,x7283)+P6(f6(x7281,x7282,x7283),f6(x7284,x7285,x7283),x7283)
% 0.78/0.95 [729]~P27(x7293)+~P7(x7292,x7295,x7293)+~P7(x7291,x7294,x7293)+P7(f7(x7291,x7292,x7293),f7(x7294,x7295,x7293),x7293)
% 0.78/0.95 [730]~P3(x7303)+~P8(x7302,x7305,x7303)+~P8(x7301,x7304,x7303)+P8(f6(x7301,x7302,x7303),f6(x7304,x7305,x7303),x7303)
% 0.78/0.95 [772]~P24(x7724)+~P8(x7725,x7723,x7724)+~P8(x7721,f6(x7722,x7725,x7724),x7724)+P8(x7721,f6(x7722,x7723,x7724),x7724)
% 0.78/0.95 [828]~P46(x8282)+~P6(f5(x8281,x8282),x8284,x8282)+~P6(f5(x8283,x8282),x8285,x8282)+P6(f7(f5(x8281,x8282),f5(x8283,x8282),x8282),f7(x8284,x8285,x8282),x8282)
% 0.78/0.95 [837]~P4(x8373)+~E(f4(x8371,x8374,x8373),f4(x8375,x8374,x8373))+~E(f4(x8372,x8374,x8373),f4(x8376,x8374,x8373))+E(f4(f7(x8371,x8372,x8373),x8374,x8373),f4(f7(x8375,x8376,x8373),x8374,x8373))
% 0.78/0.95 [838]~P4(x8383)+~E(f4(x8381,x8384,x8383),f4(x8385,x8384,x8383))+~E(f4(x8382,x8384,x8383),f4(x8386,x8384,x8383))+E(f4(f6(x8381,x8382,x8383),x8384,x8383),f4(f6(x8385,x8386,x8383),x8384,x8383))
% 0.78/0.95 [839]~P9(x8393)+~E(f4(x8391,x8394,x8393),f4(x8395,x8394,x8393))+~E(f4(x8392,x8394,x8393),f4(x8396,x8394,x8393))+E(f4(f3(x8391,x8392,x8393),x8394,x8393),f4(f3(x8395,x8396,x8393),x8394,x8393))
% 0.78/0.95 [533]~P2(x5332)+~P8(f2(x5332),x5331,x5332)+~P8(f2(x5332),x5333,x5332)+~E(f6(x5333,x5331,x5332),f2(x5332))+E(x5331,f2(x5332))
% 0.78/0.95 [534]~P2(x5342)+~P8(f2(x5342),x5343,x5342)+~P8(f2(x5342),x5341,x5342)+~E(f6(x5341,x5343,x5342),f2(x5342))+E(x5341,f2(x5342))
% 0.78/0.95 [617]~P25(x6174)+~P12(x6174)+~P6(x6171,x6173,x6174)+~P8(f2(x6174),x6172,x6174)+P6(x6171,f6(x6172,x6173,x6174),x6174)
% 0.78/0.95 [618]~P25(x6184)+~P12(x6184)+~P8(x6181,x6183,x6184)+~P6(f2(x6184),x6182,x6184)+P6(x6181,f6(x6182,x6183,x6184),x6184)
% 0.78/0.95 [619]~P25(x6194)+~P12(x6194)+~P8(x6191,x6193,x6194)+~P8(f2(x6194),x6192,x6194)+P8(x6191,f6(x6192,x6193,x6194),x6194)
% 0.78/0.95 [620]~P25(x6204)+~P12(x6204)+~P8(x6201,x6202,x6204)+~P8(f2(x6204),x6203,x6204)+P8(x6201,f6(x6202,x6203,x6204),x6204)
% 0.78/0.95 [781]~P40(x7814)+~P11(x7814)+E(x7811,x7812)+E(x7813,f2(x7814))+~E(f6(x7815,f7(x7813,x7811,x7814),x7814),f6(x7815,f7(x7813,x7812,x7814),x7814))
% 0.78/0.95 [849]~P40(x8495)+~P11(x8495)+E(x8491,x8492)+E(x8493,x8494)+~E(f6(f7(x8493,x8491,x8495),f7(x8494,x8492,x8495),x8495),f6(f7(x8493,x8492,x8495),f7(x8494,x8491,x8495),x8495))
% 0.78/0.95 [864]~P37(x8645)+~P35(x8645)+~P7(x8641,x8644,x8645)+~P7(x8641,f6(x8642,x8646,x8645),x8645)+P7(x8641,f6(f3(x8642,f7(x8643,x8644,x8645),x8645),x8646,x8645),x8645)
% 0.78/0.95 [865]~P37(x8654)+~P35(x8654)+~P7(x8651,x8655,x8654)+P7(x8651,f6(x8652,x8653,x8654),x8654)+~P7(x8651,f6(f3(x8652,f7(x8656,x8655,x8654),x8654),x8653,x8654),x8654)
% 0.78/0.95 [829]~P1(x8293)+~P6(x8292,x8295,x8293)+~P6(x8291,x8294,x8293)+~P6(f2(x8293),x8294,x8293)+~P8(f2(x8293),x8292,x8293)+P6(f7(x8291,x8292,x8293),f7(x8294,x8295,x8293),x8293)
% 0.78/0.95 [830]~P1(x8303)+~P6(x8302,x8305,x8303)+~P6(x8301,x8304,x8303)+~P8(f2(x8303),x8302,x8303)+~P8(f2(x8303),x8301,x8303)+P6(f7(x8301,x8302,x8303),f7(x8304,x8305,x8303),x8303)
% 0.78/0.95 [831]~P1(x8313)+~P6(x8312,x8315,x8313)+~P8(x8311,x8314,x8313)+~P6(f2(x8313),x8311,x8313)+~P8(f2(x8313),x8312,x8313)+P6(f7(x8311,x8312,x8313),f7(x8314,x8315,x8313),x8313)
% 0.78/0.95 [832]~P1(x8323)+~P6(x8321,x8324,x8323)+~P8(x8322,x8325,x8323)+~P6(f2(x8323),x8322,x8323)+~P8(f2(x8323),x8321,x8323)+P6(f7(x8321,x8322,x8323),f7(x8324,x8325,x8323),x8323)
% 0.78/0.95 [833]~P50(x8333)+~P8(x8332,x8335,x8333)+~P8(x8331,x8334,x8333)+~P8(f2(x8333),x8334,x8333)+~P8(f2(x8333),x8332,x8333)+P8(f7(x8331,x8332,x8333),f7(x8334,x8335,x8333),x8333)
% 0.78/0.95 [834]~P50(x8343)+~P8(x8342,x8345,x8343)+~P8(x8341,x8344,x8343)+~P8(f2(x8343),x8342,x8343)+~P8(f2(x8343),x8341,x8343)+P8(f7(x8341,x8342,x8343),f7(x8344,x8345,x8343),x8343)
% 0.78/0.95 %EqnAxiom
% 0.78/0.95 [1]E(x11,x11)
% 0.78/0.95 [2]E(x22,x21)+~E(x21,x22)
% 0.78/0.95 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.78/0.95 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.78/0.95 [5]~E(x51,x52)+E(f3(x51,x53,x54),f3(x52,x53,x54))
% 0.78/0.95 [6]~E(x61,x62)+E(f3(x63,x61,x64),f3(x63,x62,x64))
% 0.78/0.95 [7]~E(x71,x72)+E(f3(x73,x74,x71),f3(x73,x74,x72))
% 0.78/0.95 [8]~E(x81,x82)+E(f4(x81,x83,x84),f4(x82,x83,x84))
% 0.78/0.95 [9]~E(x91,x92)+E(f4(x93,x91,x94),f4(x93,x92,x94))
% 0.78/0.95 [10]~E(x101,x102)+E(f4(x103,x104,x101),f4(x103,x104,x102))
% 0.78/0.95 [11]~E(x111,x112)+E(f7(x111,x113,x114),f7(x112,x113,x114))
% 0.78/0.95 [12]~E(x121,x122)+E(f7(x123,x121,x124),f7(x123,x122,x124))
% 0.78/0.95 [13]~E(x131,x132)+E(f7(x133,x134,x131),f7(x133,x134,x132))
% 0.78/0.95 [14]~E(x141,x142)+E(f5(x141,x143),f5(x142,x143))
% 0.78/0.95 [15]~E(x151,x152)+E(f5(x153,x151),f5(x153,x152))
% 0.78/0.95 [16]~E(x161,x162)+E(f6(x161,x163,x164),f6(x162,x163,x164))
% 0.78/0.95 [17]~E(x171,x172)+E(f6(x173,x171,x174),f6(x173,x172,x174))
% 0.78/0.95 [18]~E(x181,x182)+E(f6(x183,x184,x181),f6(x183,x184,x182))
% 0.78/0.95 [19]~E(x191,x192)+E(f9(x191,x193),f9(x192,x193))
% 0.78/0.95 [20]~E(x201,x202)+E(f9(x203,x201),f9(x203,x202))
% 0.78/0.95 [21]~E(x211,x212)+E(f10(x211),f10(x212))
% 0.78/0.95 [22]~E(x221,x222)+E(f8(x221,x223,x224),f8(x222,x223,x224))
% 0.78/0.95 [23]~E(x231,x232)+E(f8(x233,x231,x234),f8(x233,x232,x234))
% 0.78/0.95 [24]~E(x241,x242)+E(f8(x243,x244,x241),f8(x243,x244,x242))
% 0.78/0.95 [25]~P1(x251)+P1(x252)+~E(x251,x252)
% 0.78/0.95 [26]~P2(x261)+P2(x262)+~E(x261,x262)
% 0.78/0.95 [27]~P27(x271)+P27(x272)+~E(x271,x272)
% 0.78/0.95 [28]~P28(x281)+P28(x282)+~E(x281,x282)
% 0.78/0.95 [29]~P29(x291)+P29(x292)+~E(x291,x292)
% 0.78/0.95 [30]~P3(x301)+P3(x302)+~E(x301,x302)
% 0.78/0.95 [31]~P25(x311)+P25(x312)+~E(x311,x312)
% 0.78/0.95 [32]~P4(x321)+P4(x322)+~E(x321,x322)
% 0.78/0.95 [33]~P36(x331)+P36(x332)+~E(x331,x332)
% 0.78/0.95 [34]~P43(x341)+P43(x342)+~E(x341,x342)
% 0.78/0.95 [35]~P10(x351)+P10(x352)+~E(x351,x352)
% 0.78/0.95 [36]~P12(x361)+P12(x362)+~E(x361,x362)
% 0.78/0.95 [37]~P37(x371)+P37(x372)+~E(x371,x372)
% 0.78/0.95 [38]~P44(x381)+P44(x382)+~E(x381,x382)
% 0.78/0.95 [39]~P38(x391)+P38(x392)+~E(x391,x392)
% 0.78/0.95 [40]~P39(x401)+P39(x402)+~E(x401,x402)
% 0.78/0.95 [41]~P48(x411)+P48(x412)+~E(x411,x412)
% 0.78/0.95 [42]~P49(x421)+P49(x422)+~E(x421,x422)
% 0.78/0.95 [43]~P13(x431)+P13(x432)+~E(x431,x432)
% 0.78/0.95 [44]~P30(x441)+P30(x442)+~E(x441,x442)
% 0.78/0.95 [45]~P50(x451)+P50(x452)+~E(x451,x452)
% 0.78/0.95 [46]~P17(x461)+P17(x462)+~E(x461,x462)
% 0.78/0.95 [47]~P18(x471)+P18(x472)+~E(x471,x472)
% 0.78/0.95 [48]~P14(x481)+P14(x482)+~E(x481,x482)
% 0.78/0.95 [49]~P53(x491)+P53(x492)+~E(x491,x492)
% 0.78/0.95 [50]~P45(x501)+P45(x502)+~E(x501,x502)
% 0.78/0.95 [51]~P19(x511)+P19(x512)+~E(x511,x512)
% 0.78/0.95 [52]~P26(x521)+P26(x522)+~E(x521,x522)
% 0.78/0.95 [53]~P31(x531)+P31(x532)+~E(x531,x532)
% 0.78/0.95 [54]~P42(x541)+P42(x542)+~E(x541,x542)
% 0.78/0.95 [55]P5(x552,x553)+~E(x551,x552)+~P5(x551,x553)
% 0.78/0.95 [56]P5(x563,x562)+~E(x561,x562)+~P5(x563,x561)
% 0.78/0.95 [57]P6(x572,x573,x574)+~E(x571,x572)+~P6(x571,x573,x574)
% 0.78/0.95 [58]P6(x583,x582,x584)+~E(x581,x582)+~P6(x583,x581,x584)
% 0.78/0.95 [59]P6(x593,x594,x592)+~E(x591,x592)+~P6(x593,x594,x591)
% 0.78/0.95 [60]P8(x602,x603,x604)+~E(x601,x602)+~P8(x601,x603,x604)
% 0.78/0.95 [61]P8(x613,x612,x614)+~E(x611,x612)+~P8(x613,x611,x614)
% 0.78/0.95 [62]P8(x623,x624,x622)+~E(x621,x622)+~P8(x623,x624,x621)
% 0.78/0.95 [63]P7(x632,x633,x634)+~E(x631,x632)+~P7(x631,x633,x634)
% 0.78/0.95 [64]P7(x643,x642,x644)+~E(x641,x642)+~P7(x643,x641,x644)
% 0.78/0.95 [65]P7(x653,x654,x652)+~E(x651,x652)+~P7(x653,x654,x651)
% 0.78/0.95 [66]~P20(x661)+P20(x662)+~E(x661,x662)
% 0.78/0.95 [67]~P47(x671)+P47(x672)+~E(x671,x672)
% 0.78/0.95 [68]~P11(x681)+P11(x682)+~E(x681,x682)
% 0.78/0.95 [69]~P40(x691)+P40(x692)+~E(x691,x692)
% 0.78/0.95 [70]~P46(x701)+P46(x702)+~E(x701,x702)
% 0.78/0.95 [71]~P51(x711)+P51(x712)+~E(x711,x712)
% 0.78/0.95 [72]~P23(x721)+P23(x722)+~E(x721,x722)
% 0.78/0.95 [73]~P32(x731)+P32(x732)+~E(x731,x732)
% 0.78/0.95 [74]~P24(x741)+P24(x742)+~E(x741,x742)
% 0.78/0.95 [75]~P21(x751)+P21(x752)+~E(x751,x752)
% 0.78/0.95 [76]~P33(x761)+P33(x762)+~E(x761,x762)
% 0.78/0.95 [77]~P52(x771)+P52(x772)+~E(x771,x772)
% 0.78/0.95 [78]~P56(x781)+P56(x782)+~E(x781,x782)
% 0.78/0.95 [79]~P34(x791)+P34(x792)+~E(x791,x792)
% 0.78/0.95 [80]~P55(x801)+P55(x802)+~E(x801,x802)
% 0.78/0.95 [81]~P9(x811)+P9(x812)+~E(x811,x812)
% 0.78/0.95 [82]~P15(x821)+P15(x822)+~E(x821,x822)
% 0.78/0.95 [83]~P54(x831)+P54(x832)+~E(x831,x832)
% 0.78/0.95 [84]~P35(x841)+P35(x842)+~E(x841,x842)
% 0.78/0.95 [85]~P41(x851)+P41(x852)+~E(x851,x852)
% 0.78/0.95 [86]~P22(x861)+P22(x862)+~E(x861,x862)
% 0.78/0.95 [87]~P16(x871)+P16(x872)+~E(x871,x872)
% 0.78/0.95
% 0.78/0.95 %-------------------------------------------
% 0.78/0.95 cnf(886,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(scs_inference,[],[120,214,493]),
% 0.78/0.95 ['proof']).
% 0.78/0.95 % SZS output end Proof
% 0.78/0.95 % Total time :0.060000s
%------------------------------------------------------------------------------