TSTP Solution File: SWW263+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW263+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n020.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 : Fri Sep 1 00:13:22 EDT 2023
% Result : Theorem 1.61s 1.67s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW263+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 22:49:44 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 1.51/1.59 %-------------------------------------------
% 1.51/1.59 % File :CSE---1.6
% 1.51/1.59 % Problem :theBenchmark
% 1.51/1.59 % Transform :cnf
% 1.51/1.59 % Format :tptp:raw
% 1.51/1.59 % Command :java -jar mcs_scs.jar %d %s
% 1.51/1.59
% 1.51/1.59 % Result :Theorem 0.460000s
% 1.51/1.59 % Output :CNFRefutation 0.460000s
% 1.51/1.59 %-------------------------------------------
% 1.53/1.59 %------------------------------------------------------------------------------
% 1.53/1.59 % File : SWW263+1 : TPTP v8.1.2. Released v5.2.0.
% 1.53/1.59 % Domain : Software Verification
% 1.53/1.59 % Problem : Fundamental Theorem of Algebra 438511, 1000 axioms selected
% 1.53/1.59 % Version : Especial.
% 1.53/1.59 % English :
% 1.53/1.59
% 1.53/1.59 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 1.53/1.59 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 1.53/1.59 % Source : [Bla11]
% 1.53/1.59 % Names : fta_438511.1000.p [Bla11]
% 1.53/1.59
% 1.53/1.59 % Status : Theorem
% 1.53/1.59 % Rating : 0.39 v8.1.0, 0.36 v7.5.0, 0.38 v7.4.0, 0.37 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.30 v7.0.0, 0.37 v6.4.0, 0.38 v6.2.0, 0.44 v6.1.0, 0.50 v6.0.0, 0.52 v5.5.0, 0.59 v5.4.0, 0.68 v5.3.0, 0.74 v5.2.0
% 1.53/1.59 % Syntax : Number of formulae : 1288 ( 386 unt; 0 def)
% 1.53/1.59 % Number of atoms : 2974 ( 769 equ)
% 1.53/1.59 % Maximal formula atoms : 8 ( 2 avg)
% 1.53/1.60 % Number of connectives : 1850 ( 164 ~; 55 |; 98 &)
% 1.53/1.60 % ( 229 <=>;1304 =>; 0 <=; 0 <~>)
% 1.53/1.60 % Maximal formula depth : 13 ( 4 avg)
% 1.53/1.60 % Maximal term depth : 12 ( 2 avg)
% 1.53/1.60 % Number of predicates : 83 ( 82 usr; 0 prp; 1-3 aty)
% 1.53/1.60 % Number of functors : 45 ( 45 usr; 16 con; 0-3 aty)
% 1.53/1.60 % Number of variables : 2695 (2671 !; 24 ?)
% 1.53/1.60 % SPC : FOF_THM_RFO_SEQ
% 1.53/1.60
% 1.53/1.60 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 1.53/1.60 % 2011-03-01 11:59:49
% 1.53/1.60 %------------------------------------------------------------------------------
% 1.53/1.60 %----Relevant facts (998)
% 1.53/1.60 fof(fact_ext,axiom,
% 1.53/1.60 ! [V_g_2,V_f_2] :
% 1.53/1.60 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 1.53/1.60 => V_f_2 = V_g_2 ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_t_I1_J,axiom,
% 1.53/1.60 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_t_I2_J,axiom,
% 1.53/1.60 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_m_I1_J,axiom,
% 1.53/1.60 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_kas_I2_J,axiom,
% 1.53/1.60 v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.53/1.60
% 1.53/1.60 fof(fact__0960_A_060_At_A_094_Ak_096,axiom,
% 1.53/1.60 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)) ).
% 1.53/1.60
% 1.53/1.60 fof(fact__096t_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_060_A1_096,axiom,
% 1.53/1.60 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_t_I3_J,axiom,
% 1.53/1.60 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_inv0,axiom,
% 1.53/1.60 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))) ).
% 1.53/1.60
% 1.53/1.60 fof(fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096,axiom,
% 1.53/1.60 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_power__Suc__less,axiom,
% 1.53/1.60 ! [V_n,V_a,T_a] :
% 1.53/1.60 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.53/1.60 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096,axiom,
% 1.53/1.60 ! [V_d2] :
% 1.53/1.60 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2)
% 1.53/1.60 => ? [B_e] :
% 1.53/1.60 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
% 1.53/1.60 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.53/1.60 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,V_d2) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_norm__mult__less,axiom,
% 1.53/1.60 ! [V_s,V_y,V_r,V_x,T_a] :
% 1.53/1.60 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 1.53/1.60 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)) ) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_zero__less__norm__iff,axiom,
% 1.53/1.60 ! [V_x_2,T_a] :
% 1.53/1.60 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
% 1.53/1.60 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_power__gt1__lemma,axiom,
% 1.53/1.60 ! [V_n,V_a,T_a] :
% 1.53/1.60 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.53/1.60 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_power__less__power__Suc,axiom,
% 1.53/1.60 ! [V_n,V_a,T_a] :
% 1.53/1.60 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.53/1.60 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_power__strict__decreasing,axiom,
% 1.53/1.60 ! [V_a,V_N,V_n,T_a] :
% 1.53/1.60 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.53/1.60 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_zero__less__two,axiom,
% 1.53/1.60 ! [T_a] :
% 1.53/1.60 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.60 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_not__sum__squares__lt__zero,axiom,
% 1.53/1.60 ! [V_y,V_x,T_a] :
% 1.53/1.60 ( class_Rings_Olinordered__ring(T_a)
% 1.53/1.60 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_sum__squares__gt__zero__iff,axiom,
% 1.53/1.60 ! [V_y_2,V_x_2,T_a] :
% 1.53/1.60 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))
% 1.53/1.60 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.60 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_kas_I1_J,axiom,
% 1.53/1.60 v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_w0,axiom,
% 1.53/1.60 v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_w,axiom,
% 1.53/1.60 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_complex__mod__triangle__sub,axiom,
% 1.53/1.60 ! [V_z,V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_inverse__inverse__eq,axiom,
% 1.53/1.60 ! [V_a,T_a] :
% 1.53/1.60 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.53/1.60 => c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_norm__inverse,axiom,
% 1.53/1.60 ! [V_a,T_a] :
% 1.53/1.60 ( ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.53/1.60 & class_Rings_Odivision__ring__inverse__zero(T_a) )
% 1.53/1.60 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_nat__zero__less__power__iff,axiom,
% 1.53/1.60 ! [V_n_2,V_x_2] :
% 1.53/1.60 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
% 1.53/1.60 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 1.53/1.60 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_inverse__eq__iff__eq,axiom,
% 1.53/1.60 ! [V_b_2,V_aa_2,T_a] :
% 1.53/1.60 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.53/1.60 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2) = c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)
% 1.53/1.60 <=> V_aa_2 = V_b_2 ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_nat__power__less__imp__less,axiom,
% 1.53/1.60 ! [V_n,V_m,V_i] :
% 1.53/1.60 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
% 1.53/1.60 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_inverse__eq__imp__eq,axiom,
% 1.53/1.60 ! [V_b,V_a,T_a] :
% 1.53/1.60 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.53/1.60 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b)
% 1.53/1.60 => V_a = V_b ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_nonzero__inverse__eq__imp__eq,axiom,
% 1.53/1.60 ! [V_b,V_a,T_a] :
% 1.53/1.60 ( class_Rings_Odivision__ring(T_a)
% 1.53/1.60 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b)
% 1.53/1.60 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.60 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.60 => V_a = V_b ) ) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_inverse__zero__imp__zero,axiom,
% 1.53/1.60 ! [V_a,T_a] :
% 1.53/1.60 ( class_Rings_Odivision__ring(T_a)
% 1.53/1.60 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.60 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_nonzero__inverse__inverse__eq,axiom,
% 1.53/1.60 ! [V_a,T_a] :
% 1.53/1.60 ( class_Rings_Odivision__ring(T_a)
% 1.53/1.60 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.60 => c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_nonzero__imp__inverse__nonzero,axiom,
% 1.53/1.60 ! [V_a,T_a] :
% 1.53/1.60 ( class_Rings_Odivision__ring(T_a)
% 1.53/1.60 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.60 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_inverse__nonzero__iff__nonzero,axiom,
% 1.53/1.60 ! [V_aa_2,T_a] :
% 1.53/1.60 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.53/1.60 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.60 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_inverse__zero,axiom,
% 1.53/1.60 ! [T_a] :
% 1.53/1.60 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.53/1.60 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_inverse__1,axiom,
% 1.53/1.60 ! [T_a] :
% 1.53/1.60 ( class_Rings_Odivision__ring(T_a)
% 1.53/1.60 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_power__inverse,axiom,
% 1.53/1.60 ! [V_n,V_a,T_a] :
% 1.53/1.60 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.53/1.60 => c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_power__mult,axiom,
% 1.53/1.60 ! [V_n,V_m,V_a,T_a] :
% 1.53/1.60 ( class_Groups_Omonoid__mult(T_a)
% 1.53/1.60 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_nonzero__norm__inverse,axiom,
% 1.53/1.60 ! [V_a,T_a] :
% 1.53/1.60 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.53/1.60 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.60 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) ) ) ).
% 1.53/1.60
% 1.53/1.60 fof(fact_power__eq__imp__eq__base,axiom,
% 1.53/1.60 ! [V_b,V_n,V_a,T_a] :
% 1.53/1.60 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.60 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.60 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.53/1.61 => V_a = V_b ) ) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_power__increasing,axiom,
% 1.53/1.61 ! [V_a,V_N,V_n,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_power__decreasing,axiom,
% 1.53/1.61 ! [V_a,V_N,V_n,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_power__le__imp__le__exp,axiom,
% 1.53/1.61 ! [V_n,V_m,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_power__increasing__iff,axiom,
% 1.53/1.61 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
% 1.53/1.61 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_nonzero__inverse__mult__distrib,axiom,
% 1.53/1.61 ! [V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Odivision__ring(T_a)
% 1.53/1.61 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.61 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.61 => c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_inverse__unique,axiom,
% 1.53/1.61 ! [V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Odivision__ring(T_a)
% 1.53/1.61 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Oone__class_Oone(T_a)
% 1.53/1.61 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) = V_b ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_nonzero__power__inverse,axiom,
% 1.53/1.61 ! [V_n,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Odivision__ring(T_a)
% 1.53/1.61 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.61 => c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_split__mult__neg__le,axiom,
% 1.53/1.61 ! [V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.53/1.61 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.53/1.61 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_split__mult__pos__le,axiom,
% 1.53/1.61 ! [V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__ring(T_a)
% 1.53/1.61 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 1.53/1.61 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__mono,axiom,
% 1.53/1.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__semiring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__mono_H,axiom,
% 1.53/1.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__semiring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__left__mono__neg,axiom,
% 1.53/1.61 ! [V_c,V_a,V_b,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__ring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__right__mono__neg,axiom,
% 1.53/1.61 ! [V_c,V_a,V_b,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__ring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_comm__mult__left__mono,axiom,
% 1.53/1.61 ! [V_c,V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__comm__semiring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__left__mono,axiom,
% 1.53/1.61 ! [V_c,V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__semiring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__right__mono,axiom,
% 1.53/1.61 ! [V_c,V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__semiring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__nonpos__nonpos,axiom,
% 1.53/1.61 ! [V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__ring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__nonpos__nonneg,axiom,
% 1.53/1.61 ! [V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__nonneg__nonpos2,axiom,
% 1.53/1.61 ! [V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__nonneg__nonpos,axiom,
% 1.53/1.61 ! [V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__nonneg__nonneg,axiom,
% 1.53/1.61 ! [V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__le__0__iff,axiom,
% 1.53/1.61 ! [V_b_2,V_aa_2,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
% 1.53/1.61 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.53/1.61 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_zero__le__mult__iff,axiom,
% 1.53/1.61 ! [V_b_2,V_aa_2,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2))
% 1.53/1.61 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
% 1.53/1.61 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 1.53/1.61 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.61 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_zero__le__square,axiom,
% 1.53/1.61 ! [V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__ring(T_a)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_zero__le__one,axiom,
% 1.53/1.61 ! [T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_not__one__le__zero,axiom,
% 1.53/1.61 ! [T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.61 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_power__mono,axiom,
% 1.53/1.61 ! [V_n,V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_zero__le__power,axiom,
% 1.53/1.61 ! [V_n,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_one__le__power,axiom,
% 1.53/1.61 ! [V_n,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_norm__triangle__ineq,axiom,
% 1.53/1.61 ! [V_y,V_x,T_a] :
% 1.53/1.61 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_norm__ge__zero,axiom,
% 1.53/1.61 ! [V_x,T_a] :
% 1.53/1.61 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_power__0,axiom,
% 1.53/1.61 ! [V_a,T_a] :
% 1.53/1.61 ( class_Power_Opower(T_a)
% 1.53/1.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_division__ring__inverse__add,axiom,
% 1.53/1.61 ! [V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Odivision__ring(T_a)
% 1.53/1.61 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.61 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.61 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_left__inverse,axiom,
% 1.53/1.61 ! [V_a,T_a] :
% 1.53/1.61 ( class_Rings_Odivision__ring(T_a)
% 1.53/1.61 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.61 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_right__inverse,axiom,
% 1.53/1.61 ! [V_a,T_a] :
% 1.53/1.61 ( class_Rings_Odivision__ring(T_a)
% 1.53/1.61 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.61 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__left__le__imp__le,axiom,
% 1.53/1.61 ! [V_b,V_a,V_c,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__right__le__imp__le,axiom,
% 1.53/1.61 ! [V_b,V_c,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__less__imp__less__left,axiom,
% 1.53/1.61 ! [V_b,V_a,V_c,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__left__less__imp__less,axiom,
% 1.53/1.61 ! [V_b,V_a,V_c,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semiring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__less__imp__less__right,axiom,
% 1.53/1.61 ! [V_b,V_c,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__right__less__imp__less,axiom,
% 1.53/1.61 ! [V_b,V_c,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semiring(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__le__less__imp__less,axiom,
% 1.53/1.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__less__le__imp__less,axiom,
% 1.53/1.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__strict__mono_H,axiom,
% 1.53/1.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.61 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 1.53/1.61
% 1.53/1.61 fof(fact_mult__strict__mono,axiom,
% 1.53/1.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.53/1.61 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.53/1.61 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.53/1.62 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_mult__le__cancel__left__neg,axiom,
% 1.53/1.62 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.53/1.62 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 1.53/1.62 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_aa_2) ) ) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_mult__le__cancel__left__pos,axiom,
% 1.53/1.62 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.53/1.62 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 1.53/1.62 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_sum__squares__le__zero__iff,axiom,
% 1.53/1.62 ! [V_y_2,V_x_2,T_a] :
% 1.53/1.62 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
% 1.53/1.62 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.53/1.62 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_sum__squares__ge__zero,axiom,
% 1.53/1.62 ! [V_y,V_x,T_a] :
% 1.53/1.62 ( class_Rings_Olinordered__ring(T_a)
% 1.53/1.62 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_mult__left__le__one__le,axiom,
% 1.53/1.62 ! [V_y,V_x,T_a] :
% 1.53/1.62 ( class_Rings_Olinordered__idom(T_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.53/1.62 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_mult__right__le__one__le,axiom,
% 1.53/1.62 ! [V_y,V_x,T_a] :
% 1.53/1.62 ( class_Rings_Olinordered__idom(T_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.53/1.62 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_power__less__imp__less__base,axiom,
% 1.53/1.62 ! [V_b,V_n,V_a,T_a] :
% 1.53/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.53/1.62 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_power__strict__mono,axiom,
% 1.53/1.62 ! [V_n,V_b,V_a,T_a] :
% 1.53/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.53/1.62 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_norm__le__zero__iff,axiom,
% 1.53/1.62 ! [V_x_2,T_a] :
% 1.53/1.62 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.53/1.62 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_norm__mult__ineq,axiom,
% 1.53/1.62 ! [V_y,V_x,T_a] :
% 1.53/1.62 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.53/1.62 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_one__less__power,axiom,
% 1.53/1.62 ! [V_n,V_a,T_a] :
% 1.53/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.53/1.62 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_norm__power__ineq,axiom,
% 1.53/1.62 ! [V_n,V_x,T_a] :
% 1.53/1.62 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.53/1.62 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)) ) ).
% 1.53/1.62
% 1.53/1.62 fof(fact_convex__bound__le,axiom,
% 1.53/1.62 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.53/1.62 ( class_Rings_Olinordered__semiring__1(T_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.53/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.53/1.62 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.53/1.62 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 1.53/1.62
% 1.58/1.62 fof(fact_linorder__neqE__linordered__idom,axiom,
% 1.58/1.62 ! [V_y,V_x,T_a] :
% 1.58/1.62 ( class_Rings_Olinordered__idom(T_a)
% 1.58/1.62 => ( V_x != V_y
% 1.58/1.62 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.58/1.62 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_convex__bound__lt,axiom,
% 1.58/1.62 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.58/1.62 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.58/1.62 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.58/1.62 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_divisors__zero,axiom,
% 1.58/1.62 ! [V_b,V_a,T_a] :
% 1.58/1.62 ( class_Rings_Ono__zero__divisors(T_a)
% 1.58/1.62 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 1.58/1.62 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 1.58/1.62 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_no__zero__divisors,axiom,
% 1.58/1.62 ! [V_b,V_a,T_a] :
% 1.58/1.62 ( class_Rings_Ono__zero__divisors(T_a)
% 1.58/1.62 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.58/1.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__eq__0__iff,axiom,
% 1.58/1.62 ! [V_b_2,V_aa_2,T_a] :
% 1.58/1.62 ( class_Rings_Oring__no__zero__divisors(T_a)
% 1.58/1.62 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.58/1.62 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.58/1.62 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__right_Ozero,axiom,
% 1.58/1.62 ! [V_x,T_a] :
% 1.58/1.62 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult_Ozero__right,axiom,
% 1.58/1.62 ! [V_a,T_a] :
% 1.58/1.62 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__zero__right,axiom,
% 1.58/1.62 ! [V_a,T_a] :
% 1.58/1.62 ( class_Rings_Omult__zero(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__left_Ozero,axiom,
% 1.58/1.62 ! [V_y,T_a] :
% 1.58/1.62 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult_Ozero__left,axiom,
% 1.58/1.62 ! [V_b,T_a] :
% 1.58/1.62 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__zero__left,axiom,
% 1.58/1.62 ! [V_a,T_a] :
% 1.58/1.62 ( class_Rings_Omult__zero(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_zero__neq__one,axiom,
% 1.58/1.62 ! [T_a] :
% 1.58/1.62 ( class_Rings_Ozero__neq__one(T_a)
% 1.58/1.62 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_one__neq__zero,axiom,
% 1.58/1.62 ! [T_a] :
% 1.58/1.62 ( class_Rings_Ozero__neq__one(T_a)
% 1.58/1.62 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_combine__common__factor,axiom,
% 1.58/1.62 ! [V_c,V_b,V_e,V_a,T_a] :
% 1.58/1.62 ( class_Rings_Osemiring(T_a)
% 1.58/1.62 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__left_Oadd,axiom,
% 1.58/1.62 ! [V_ya,V_y,V_x,T_a] :
% 1.58/1.62 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult_Oadd__left,axiom,
% 1.58/1.62 ! [V_b,V_a_H,V_a,T_a] :
% 1.58/1.62 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_comm__semiring__class_Odistrib,axiom,
% 1.58/1.62 ! [V_c,V_b,V_a,T_a] :
% 1.58/1.62 ( class_Rings_Ocomm__semiring(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__right_Oadd,axiom,
% 1.58/1.62 ! [V_y,V_x,V_xa,T_a] :
% 1.58/1.62 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult_Oadd__right,axiom,
% 1.58/1.62 ! [V_b_H,V_b,V_a,T_a] :
% 1.58/1.62 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_field__power__not__zero,axiom,
% 1.58/1.62 ! [V_n,V_a,T_a] :
% 1.58/1.62 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.58/1.62 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_power__eq__0__iff,axiom,
% 1.58/1.62 ! [V_n_2,V_aa_2,T_a] :
% 1.58/1.62 ( ( class_Power_Opower(T_a)
% 1.58/1.62 & class_Rings_Omult__zero(T_a)
% 1.58/1.62 & class_Rings_Ono__zero__divisors(T_a)
% 1.58/1.62 & class_Rings_Ozero__neq__one(T_a) )
% 1.58/1.62 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.58/1.62 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.58/1.62 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_power__mult__distrib,axiom,
% 1.58/1.62 ! [V_n,V_b,V_a,T_a] :
% 1.58/1.62 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_power__commutes,axiom,
% 1.58/1.62 ! [V_n,V_a,T_a] :
% 1.58/1.62 ( class_Groups_Omonoid__mult(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_power__one,axiom,
% 1.58/1.62 ! [V_n,T_a] :
% 1.58/1.62 ( class_Groups_Omonoid__mult(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_power__one__right,axiom,
% 1.58/1.62 ! [V_a,T_a] :
% 1.58/1.62 ( class_Groups_Omonoid__mult(T_a)
% 1.58/1.62 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__strict__left__mono__neg,axiom,
% 1.58/1.62 ! [V_c,V_a,V_b,T_a] :
% 1.58/1.62 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.58/1.62 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__strict__right__mono__neg,axiom,
% 1.58/1.62 ! [V_c,V_a,V_b,T_a] :
% 1.58/1.62 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.58/1.62 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_comm__mult__strict__left__mono,axiom,
% 1.58/1.62 ! [V_c,V_b,V_a,T_a] :
% 1.58/1.62 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.58/1.62 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__strict__left__mono,axiom,
% 1.58/1.62 ! [V_c,V_b,V_a,T_a] :
% 1.58/1.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.58/1.62 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__strict__right__mono,axiom,
% 1.58/1.62 ! [V_c,V_b,V_a,T_a] :
% 1.58/1.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.58/1.62 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__neg__neg,axiom,
% 1.58/1.62 ! [V_b,V_a,T_a] :
% 1.58/1.62 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.58/1.62 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__neg__pos,axiom,
% 1.58/1.62 ! [V_b,V_a,T_a] :
% 1.58/1.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.58/1.62 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_mult__less__cancel__left__neg,axiom,
% 1.58/1.62 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.58/1.62 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.58/1.62 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 1.58/1.62 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ).
% 1.58/1.62
% 1.58/1.62 fof(fact_zero__less__mult__pos2,axiom,
% 1.61/1.62 ! [V_a,V_b,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.62 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_zero__less__mult__pos,axiom,
% 1.61/1.62 ! [V_b,V_a,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.62 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_mult__pos__neg2,axiom,
% 1.61/1.62 ! [V_b,V_a,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.62 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_mult__pos__neg,axiom,
% 1.61/1.62 ! [V_b,V_a,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.62 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_mult__pos__pos,axiom,
% 1.61/1.62 ! [V_b,V_a,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.61/1.62 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_mult__less__cancel__left__pos,axiom,
% 1.61/1.62 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 1.61/1.62 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_mult__less__cancel__left__disj,axiom,
% 1.61/1.62 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 1.61/1.62 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.61/1.62 & c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
% 1.61/1.62 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.62 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_mult__less__cancel__right__disj,axiom,
% 1.61/1.62 ! [V_b_2,V_ca_2,V_aa_2,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
% 1.61/1.62 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.61/1.62 & c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
% 1.61/1.62 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.62 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_not__square__less__zero,axiom,
% 1.61/1.62 ! [V_a,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__ring(T_a)
% 1.61/1.62 => ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_pos__add__strict,axiom,
% 1.61/1.62 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.61/1.62 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_sum__squares__eq__zero__iff,axiom,
% 1.61/1.62 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.61/1.62 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.62 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.62 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_zero__less__one,axiom,
% 1.61/1.62 ! [T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.61/1.62 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_not__one__less__zero,axiom,
% 1.61/1.62 ! [T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.61/1.62 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_less__1__mult,axiom,
% 1.61/1.62 ! [V_n,V_m,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 1.61/1.62 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_zero__less__power,axiom,
% 1.61/1.62 ! [V_n,V_a,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.62 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_less__add__one,axiom,
% 1.61/1.62 ! [V_a,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.61/1.62 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_power__0__left,axiom,
% 1.61/1.62 ! [V_n,T_a] :
% 1.61/1.62 ( ( class_Power_Opower(T_a)
% 1.61/1.62 & class_Rings_Osemiring__0(T_a) )
% 1.61/1.62 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.62 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 1.61/1.62 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.62 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_power__strict__increasing,axiom,
% 1.61/1.62 ! [V_a,V_N,V_n,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.61/1.62 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_power__less__imp__less__exp,axiom,
% 1.61/1.62 ! [V_n,V_m,V_a,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
% 1.61/1.62 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_power__strict__increasing__iff,axiom,
% 1.61/1.62 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
% 1.61/1.62 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_power__inject__exp,axiom,
% 1.61/1.62 ! [V_n_2,V_ma_2,V_aa_2,T_a] :
% 1.61/1.62 ( class_Rings_Olinordered__semidom(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_aa_2)
% 1.61/1.62 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_ma_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2)
% 1.61/1.62 <=> V_ma_2 = V_n_2 ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_norm__zero,axiom,
% 1.61/1.62 ! [T_a] :
% 1.61/1.62 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.62 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_norm__eq__zero,axiom,
% 1.61/1.62 ! [V_x_2,T_a] :
% 1.61/1.62 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.62 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.61/1.62 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_power__add,axiom,
% 1.61/1.62 ! [V_n,V_m,V_a,T_a] :
% 1.61/1.62 ( class_Groups_Omonoid__mult(T_a)
% 1.61/1.62 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_norm__add__less,axiom,
% 1.61/1.62 ! [V_s,V_y,V_r,V_x,T_a] :
% 1.61/1.62 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 1.61/1.62 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_norm__mult,axiom,
% 1.61/1.62 ! [V_y,V_x,T_a] :
% 1.61/1.62 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.61/1.62 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_norm__not__less__zero,axiom,
% 1.61/1.62 ! [V_x,T_a] :
% 1.61/1.62 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.62 => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_norm__one,axiom,
% 1.61/1.62 ! [T_a] :
% 1.61/1.62 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.61/1.62 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_norm__power,axiom,
% 1.61/1.62 ! [V_n,V_x,T_a] :
% 1.61/1.62 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.61/1.62 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact__096_B_Bthesis_O_A_I_B_Bt_O_A_091_124_A0_A_060_At_059_At_A_060_A1_059_At_A_060_Ainverse_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.61/1.62 ~ ! [B_t] :
% 1.61/1.62 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.61/1.62 => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_Bseq__inverse__lemma,axiom,
% 1.61/1.62 ! [V_x,V_r,T_a] :
% 1.61/1.62 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_r,c_RealVector_Onorm__class_Onorm(T_a,V_x))
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 1.61/1.62 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_r)) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_norm__ratiotest__lemma,axiom,
% 1.61/1.62 ! [V_y,V_x,V_c,T_a] :
% 1.61/1.62 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
% 1.61/1.62 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_less__zeroE,axiom,
% 1.61/1.62 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_one__le__inverse,axiom,
% 1.61/1.62 ! [V_a,T_a] :
% 1.61/1.62 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.61/1.62 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_inverse__less__1__iff,axiom,
% 1.61/1.62 ! [V_x_2,T_a] :
% 1.61/1.62 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 1.61/1.62 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.62 | c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_one__le__inverse__iff,axiom,
% 1.61/1.62 ! [V_x_2,T_a] :
% 1.61/1.62 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))
% 1.61/1.62 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.61/1.62 & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_real__mult__inverse__left,axiom,
% 1.61/1.62 ! [V_x] :
% 1.61/1.62 ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.61/1.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_real__mult__inverse__cancel,axiom,
% 1.61/1.62 ! [V_u,V_y,V_x1,V_x] :
% 1.61/1.62 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x1),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_u))
% 1.61/1.62 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)),V_u)) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_real__mult__inverse__cancel2,axiom,
% 1.61/1.62 ! [V_u,V_y,V_x1,V_x] :
% 1.61/1.62 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x1),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_u))
% 1.61/1.62 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1))) ) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_real__mult__le__cancel__iff2,axiom,
% 1.61/1.62 ! [V_y_2,V_x_2,V_z_2] :
% 1.61/1.62 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.61/1.62 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))
% 1.61/1.62 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_le0,axiom,
% 1.61/1.62 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_le__refl,axiom,
% 1.61/1.62 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_le__square,axiom,
% 1.61/1.62 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_le__cube,axiom,
% 1.61/1.62 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_nat__mult__commute,axiom,
% 1.61/1.62 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ).
% 1.61/1.62
% 1.61/1.62 fof(fact_nat__le__linear,axiom,
% 1.61/1.62 ! [V_n,V_m] :
% 1.61/1.62 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.61/1.63 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__mult__assoc,axiom,
% 1.61/1.63 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_eq__imp__le,axiom,
% 1.61/1.63 ! [V_n,V_m] :
% 1.61/1.63 ( V_m = V_n
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__le__mono1,axiom,
% 1.61/1.63 ! [V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__le__mono2,axiom,
% 1.61/1.63 ! [V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__trans,axiom,
% 1.61/1.63 ! [V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__antisym,axiom,
% 1.61/1.63 ! [V_n,V_m] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.61/1.63 => V_m = V_n ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__le__mono,axiom,
% 1.61/1.63 ! [V_l,V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__0__eq,axiom,
% 1.61/1.63 ! [V_n_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.61/1.63 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 1.61/1.63 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__or__eq__imp__le,axiom,
% 1.61/1.63 ! [V_n,V_m] :
% 1.61/1.63 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.61/1.63 | V_m = V_n )
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__neq__implies__less,axiom,
% 1.61/1.63 ! [V_n,V_m] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.61/1.63 => ( V_m != V_n
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__imp__le__nat,axiom,
% 1.61/1.63 ! [V_n,V_m] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__eq__less__or__eq,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.61/1.63 | V_ma_2 = V_n_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__less__le,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.61/1.63 & V_ma_2 != V_n_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__add2,axiom,
% 1.61/1.63 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__add1,axiom,
% 1.61/1.63 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__Suc__ex__iff,axiom,
% 1.61/1.63 ! [V_l_2,V_ka_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_l_2)
% 1.61/1.63 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,B_n) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__iff__add,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.61/1.63 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__add__left__cancel__le,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_trans__le__add1,axiom,
% 1.61/1.63 ! [V_m,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_trans__le__add2,axiom,
% 1.61/1.63 ! [V_m,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__le__mono1,axiom,
% 1.61/1.63 ! [V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__le__mono,axiom,
% 1.61/1.63 ! [V_l,V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__leD2,axiom,
% 1.61/1.63 ! [V_n,V_k,V_m] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__leD1,axiom,
% 1.61/1.63 ! [V_n,V_k,V_m] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__leE,axiom,
% 1.61/1.63 ! [V_n,V_k,V_m] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.61/1.63 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.61/1.63 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__le__cancel2,axiom,
% 1.61/1.63 ! [V_n_2,V_ka_2,V_ma_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2))
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__le__cancel1,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__cancel2,axiom,
% 1.61/1.63 ! [V_n_2,V_ka_2,V_ma_2] :
% 1.61/1.63 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2)
% 1.61/1.63 <=> ( V_ma_2 = V_n_2
% 1.61/1.63 | V_ka_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__cancel1,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.63 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)
% 1.61/1.63 <=> ( V_ma_2 = V_n_2
% 1.61/1.63 | V_ka_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__is__0,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2] :
% 1.61/1.63 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.63 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.63 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__0__right,axiom,
% 1.61/1.63 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__0,axiom,
% 1.61/1.63 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__le__antisym,axiom,
% 1.61/1.63 ! [V_w,V_z] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 1.61/1.63 => V_z = V_w ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__le__trans,axiom,
% 1.61/1.63 ! [V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__add__left__mono,axiom,
% 1.61/1.63 ! [V_z,V_y,V_x] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__le__linear,axiom,
% 1.61/1.63 ! [V_w,V_z] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.61/1.63 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__le__refl,axiom,
% 1.61/1.63 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__less__cases,axiom,
% 1.61/1.63 ! [V_P_2,V_n_2,V_ma_2] :
% 1.61/1.63 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.61/1.63 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 1.61/1.63 => ( ( V_ma_2 = V_n_2
% 1.61/1.63 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 1.61/1.63 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
% 1.61/1.63 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 1.61/1.63 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__not__refl3,axiom,
% 1.61/1.63 ! [V_t,V_s] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 1.61/1.63 => V_s != V_t ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__not__refl2,axiom,
% 1.61/1.63 ! [V_m,V_n] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 1.61/1.63 => V_m != V_n ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__irrefl__nat,axiom,
% 1.61/1.63 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_linorder__neqE__nat,axiom,
% 1.61/1.63 ! [V_y,V_x] :
% 1.61/1.63 ( V_x != V_y
% 1.61/1.63 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__neq__iff,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2] :
% 1.61/1.63 ( V_ma_2 != V_n_2
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.61/1.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__not__refl,axiom,
% 1.61/1.63 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__add__commute,axiom,
% 1.61/1.63 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__add__left__commute,axiom,
% 1.61/1.63 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__add__assoc,axiom,
% 1.61/1.63 ! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__add__left__cancel,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.63 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2)
% 1.61/1.63 <=> V_ma_2 = V_n_2 ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__add__right__cancel,axiom,
% 1.61/1.63 ! [V_n_2,V_ka_2,V_ma_2] :
% 1.61/1.63 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_ka_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_ka_2)
% 1.61/1.63 <=> V_ma_2 = V_n_2 ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__mult__distrib2,axiom,
% 1.61/1.63 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__mult__distrib,axiom,
% 1.61/1.63 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__mult__commute,axiom,
% 1.61/1.63 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__mult__assoc,axiom,
% 1.61/1.63 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__add__mult__distrib,axiom,
% 1.61/1.63 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__mult__1,axiom,
% 1.61/1.63 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__1__eq__mult__iff,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2] :
% 1.61/1.63 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)
% 1.61/1.63 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.61/1.63 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__mult__1__right,axiom,
% 1.61/1.63 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__mult__eq__1__iff,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2] :
% 1.61/1.63 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.61/1.63 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.61/1.63 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_field__inverse__zero,axiom,
% 1.61/1.63 ! [T_a] :
% 1.61/1.63 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.61/1.63 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_gr0I,axiom,
% 1.61/1.63 ! [V_n] :
% 1.61/1.63 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__less__mono2,axiom,
% 1.61/1.63 ! [V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__less__mono1,axiom,
% 1.61/1.63 ! [V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_gr__implies__not0,axiom,
% 1.61/1.63 ! [V_n,V_m] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.61/1.63 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__less__cancel2,axiom,
% 1.61/1.63 ! [V_n_2,V_ka_2,V_ma_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2))
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.61/1.63 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__less__cancel1,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.61/1.63 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__nat__zero__code,axiom,
% 1.61/1.63 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__0__less__mult__iff,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 1.61/1.63 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neq0__conv,axiom,
% 1.61/1.63 ! [V_n_2] :
% 1.61/1.63 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_not__less0,axiom,
% 1.61/1.63 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__less__def,axiom,
% 1.61/1.63 ! [V_y_2,V_x_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.61/1.63 & V_x_2 != V_y_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__eq__real__def,axiom,
% 1.61/1.63 ! [V_y_2,V_x_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.61/1.63 | V_x_2 = V_y_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_plus__nat_Oadd__0,axiom,
% 1.61/1.63 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 1.61/1.63
% 1.61/1.63 fof(fact_Nat_Oadd__0__right,axiom,
% 1.61/1.63 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__is__0,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2] :
% 1.61/1.63 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.63 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.63 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__eq__self__zero,axiom,
% 1.61/1.63 ! [V_n,V_m] :
% 1.61/1.63 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 1.61/1.63 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__mult__distrib,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.61/1.63 => c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__eq__1__iff,axiom,
% 1.61/1.63 ! [V_x_2,T_a] :
% 1.61/1.63 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.61/1.63 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 1.61/1.63 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_not__add__less1,axiom,
% 1.61/1.63 ! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_not__add__less2,axiom,
% 1.61/1.63 ! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__add__left__cancel__less,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_trans__less__add1,axiom,
% 1.61/1.63 ! [V_m,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_trans__less__add2,axiom,
% 1.61/1.63 ! [V_m,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__less__mono1,axiom,
% 1.61/1.63 ! [V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__less__mono,axiom,
% 1.61/1.63 ! [V_l,V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__add__eq__less,axiom,
% 1.61/1.63 ! [V_n,V_m,V_l,V_k] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.61/1.63 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__lessD1,axiom,
% 1.61/1.63 ! [V_k,V_j,V_i] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__mult__right__cancel,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,V_ca_2] :
% 1.61/1.63 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.61/1.63 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_aa_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)
% 1.61/1.63 <=> V_aa_2 = V_b_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__mult__left__cancel,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,V_ca_2] :
% 1.61/1.63 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.61/1.63 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_aa_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)
% 1.61/1.63 <=> V_aa_2 = V_b_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__two__squares__add__zero__iff,axiom,
% 1.61/1.63 ! [V_y_2,V_x_2] :
% 1.61/1.63 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.61/1.63 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.61/1.63 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__eq__self__implies__10,axiom,
% 1.61/1.63 ! [V_n,V_m] :
% 1.61/1.63 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 1.61/1.63 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.61/1.63 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__zero__not__eq__one,axiom,
% 1.61/1.63 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__mult__1,axiom,
% 1.61/1.63 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 1.61/1.63
% 1.61/1.63 fof(fact_INVERSE__ZERO,axiom,
% 1.61/1.63 c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__nonpositive__iff__nonpositive,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__nonnegative__iff__nonnegative,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__positive__iff__positive,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__negative__iff__negative,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_positive__imp__inverse__positive,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__positive__imp__positive,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
% 1.61/1.63 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_negative__imp__inverse__negative,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__imp__inverse__less,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__imp__inverse__less__neg,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__negative__imp__negative,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.63 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__less__imp__less,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__less__imp__less__neg,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__gr__0,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2))
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 1.61/1.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__mult__less__iff1,axiom,
% 1.61/1.63 ! [V_y_2,V_x_2,V_z_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__mult__order,axiom,
% 1.61/1.63 ! [V_y,V_x] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__mult__less__mono2,axiom,
% 1.61/1.63 ! [V_y,V_x,V_z] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__imp__inverse__le,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__imp__inverse__le__neg,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__le__imp__le,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__le__imp__le__neg,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__le__1__iff,axiom,
% 1.61/1.63 ! [V_x_2,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.63 | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__add,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Fields_Ofield(T_a)
% 1.61/1.63 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.63 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.63 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_one__less__inverse__iff,axiom,
% 1.61/1.63 ! [V_x_2,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))
% 1.61/1.63 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.61/1.63 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_one__less__inverse,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_field__inverse,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Fields_Ofield(T_a)
% 1.61/1.63 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_real__mult__le__cancel__iff1,axiom,
% 1.61/1.63 ! [V_y_2,V_x_2,V_z_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact__096_B_Bthesis_O_A_I_B_Bw_O_A1_A_L_Aw_A_094_Ak_A_K_Aa_A_061_A0_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.61/1.63 ~ ! [B_w] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_w),v_k____)),v_a____)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.61/1.63
% 1.61/1.63 fof(fact__0961_A_L_Aw_A_094_Ak_A_K_Aa_A_N_A1_A_061_A0_A_N_A1_096,axiom,
% 1.61/1.63 c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_wm1,axiom,
% 1.61/1.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_tw,axiom,
% 1.61/1.63 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_nat__mult__le__cancel1,axiom,
% 1.61/1.63 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.63 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__pos__nonneg,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__nonneg__pos,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__strict__increasing,axiom,
% 1.61/1.63 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.61/1.63 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_diff__0,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_diff__def,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_ab__diff__minus,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.63 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_diff__minus__eq__add,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_diff__0__right,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_diff__self,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_eq__iff__diff__eq__0,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.63 => ( V_aa_2 = V_b_2
% 1.61/1.63 <=> c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_right__minus__eq,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.63 <=> V_aa_2 = V_b_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__zero,axiom,
% 1.61/1.63 ! [T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neg__0__equal__iff__equal,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
% 1.61/1.63 <=> c_Groups_Ozero__class_Ozero(T_a) = V_aa_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_equal__neg__zero,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.61/1.63 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
% 1.61/1.63 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neg__equal__0__iff__equal,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.63 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neg__equal__zero,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_aa_2
% 1.61/1.63 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_diff__eq__diff__less__eq,axiom,
% 1.61/1.63 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_d_2) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__imp__neg__le,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neg__le__iff__le,axiom,
% 1.61/1.63 ! [V_aa_2,V_b_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__le__iff,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__minus__iff,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_diff__eq__diff__less,axiom,
% 1.61/1.63 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__minus__iff,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__less__iff,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neg__less__iff__less,axiom,
% 1.61/1.63 ! [V_aa_2,V_b_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_diff__add__cancel,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__diff__cancel,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__add__distrib,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.63 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__add,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__minus__cancel,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__add__cancel,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__minus,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__diff__eq,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.63 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_equation__minus__iff,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.61/1.63 <=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__equation__iff,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_b_2
% 1.61/1.63 <=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_aa_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neg__equal__iff__equal,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.61/1.63 <=> V_aa_2 = V_b_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_diff__eq__diff__eq,axiom,
% 1.61/1.63 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.63 => ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
% 1.61/1.63 => ( V_aa_2 = V_b_2
% 1.61/1.63 <=> V_ca_2 = V_d_2 ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_of__real__eq__iff,axiom,
% 1.61/1.63 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.63 => ( c_RealVector_Oof__real(T_a,V_x_2) = c_RealVector_Oof__real(T_a,V_y_2)
% 1.61/1.63 <=> V_x_2 = V_y_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_of__real_Odiff,axiom,
% 1.61/1.63 ! [V_y,V_x,T_a] :
% 1.61/1.63 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.63 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.61/1.63 => c_RealVector_Oof__real(T_a,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_of__real__diff,axiom,
% 1.61/1.63 ! [V_y,V_x,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.63 => c_RealVector_Oof__real(T_a,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_of__real_Ominus,axiom,
% 1.61/1.63 ! [V_x,T_a] :
% 1.61/1.63 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.63 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.61/1.63 => c_RealVector_Oof__real(T_a,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_RealVector_Oof__real(T_a,V_x)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_of__real__minus,axiom,
% 1.61/1.63 ! [V_x,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.63 => c_RealVector_Oof__real(T_a,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_RealVector_Oof__real(T_a,V_x)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_norm__triangle__ineq2,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.63 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__left_Odiff,axiom,
% 1.61/1.63 ! [V_ya,V_y,V_x,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult_Odiff__left,axiom,
% 1.61/1.63 ! [V_b,V_a_H,V_a,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__right_Odiff,axiom,
% 1.61/1.63 ! [V_y,V_x,V_xa,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult_Odiff__right,axiom,
% 1.61/1.63 ! [V_b_H,V_b,V_a,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_square__eq__iff,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Rings_Oidom(T_a)
% 1.61/1.63 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_aa_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
% 1.61/1.63 <=> ( V_aa_2 = V_b_2
% 1.61/1.63 | V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__mult__minus,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Rings_Oring(T_a)
% 1.61/1.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__mult__commute,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Rings_Oring(T_a)
% 1.61/1.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__left_Ominus,axiom,
% 1.61/1.63 ! [V_y,V_x,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult_Ominus__left,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__right_Ominus,axiom,
% 1.61/1.63 ! [V_x,V_xa,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult_Ominus__right,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__mult__left,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Rings_Oring(T_a)
% 1.61/1.63 => c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__mult__right,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Rings_Oring(T_a)
% 1.61/1.63 => c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_norm__minus__commute,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.63 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_norm__minus__cancel,axiom,
% 1.61/1.63 ! [V_x,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.63 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_inverse__minus__eq,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.61/1.63 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__iff__diff__le__0,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__iff__diff__less__0,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neg__0__le__iff__le,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_le__minus__self__iff,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neg__le__0__iff__le,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__le__self__iff,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neg__less__nonneg,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neg__less__0__iff__less,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_neg__0__less__iff__less,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_minus__unique,axiom,
% 1.61/1.63 ! [V_b,V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.63 => c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_ab__left__minus,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.63 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_left__minus,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 1.61/1.63 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.61/1.63 <=> c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_right__minus,axiom,
% 1.61/1.63 ! [V_a,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_less__minus__self__iff,axiom,
% 1.61/1.63 ! [V_aa_2,T_a] :
% 1.61/1.63 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.63 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 1.61/1.63 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_of__real__eq__0__iff,axiom,
% 1.61/1.63 ! [V_x_2,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.63 => ( c_RealVector_Oof__real(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.63 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_of__real_Ozero,axiom,
% 1.61/1.63 ! [T_a] :
% 1.61/1.63 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.63 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.61/1.63 => c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_of__real__0,axiom,
% 1.61/1.63 ! [T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.63 => c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_add__eq__0__iff,axiom,
% 1.61/1.63 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.63 ( class_Groups_Ogroup__add(T_a)
% 1.61/1.63 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.63 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_eq__add__iff1,axiom,
% 1.61/1.63 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Rings_Oring(T_a)
% 1.61/1.63 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
% 1.61/1.63 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2) = V_d_2 ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_eq__add__iff2,axiom,
% 1.61/1.63 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.61/1.63 ( class_Rings_Oring(T_a)
% 1.61/1.63 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
% 1.61/1.63 <=> V_ca_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2) ) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult_Oprod__diff__prod,axiom,
% 1.61/1.63 ! [V_b,V_a,V_y,V_x,T_a] :
% 1.61/1.63 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.63 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_mult__diff__mult,axiom,
% 1.61/1.63 ! [V_b,V_a,V_y,V_x,T_a] :
% 1.61/1.63 ( class_Rings_Oring(T_a)
% 1.61/1.63 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)) ) ).
% 1.61/1.63
% 1.61/1.63 fof(fact_square__eq__1__iff,axiom,
% 1.61/1.63 ! [V_x_2,T_a] :
% 1.61/1.63 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.61/1.63 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 1.61/1.63 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 1.61/1.63 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_of__real__mult,axiom,
% 1.61/1.64 ! [V_y,V_x,T_a] :
% 1.61/1.64 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.64 => c_RealVector_Oof__real(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_RealVector_Oof__real(T_a,V_x)),c_RealVector_Oof__real(T_a,V_y)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_of__real_Oadd,axiom,
% 1.61/1.64 ! [V_y,V_x,T_a] :
% 1.61/1.64 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.64 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.61/1.64 => c_RealVector_Oof__real(T_a,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_of__real__add,axiom,
% 1.61/1.64 ! [V_y,V_x,T_a] :
% 1.61/1.64 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.64 => c_RealVector_Oof__real(T_a,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_of__real__1,axiom,
% 1.61/1.64 ! [T_a] :
% 1.61/1.64 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.64 => c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nonzero__inverse__minus__eq,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Rings_Odivision__ring(T_a)
% 1.61/1.64 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.64 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_of__real__power,axiom,
% 1.61/1.64 ! [V_n,V_x,T_a] :
% 1.61/1.64 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.64 => c_RealVector_Oof__real(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_RealVector_Oof__real(T_a,V_x)),V_n) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_of__real__inverse,axiom,
% 1.61/1.64 ! [V_x,T_a] :
% 1.61/1.64 ( ( class_RealVector_Oreal__div__algebra(T_a)
% 1.61/1.64 & class_Rings_Odivision__ring__inverse__zero(T_a) )
% 1.61/1.64 => c_RealVector_Oof__real(T_a,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)) = c_Rings_Oinverse__class_Oinverse(T_a,c_RealVector_Oof__real(T_a,V_x)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_complex__of__real__power,axiom,
% 1.61/1.64 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_x)),V_n) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_le__add__iff1,axiom,
% 1.61/1.64 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.61/1.64 ( class_Rings_Oordered__ring(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2),V_d_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_le__add__iff2,axiom,
% 1.61/1.64 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.61/1.64 ( class_Rings_Oordered__ring(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_less__add__iff1,axiom,
% 1.61/1.64 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.61/1.64 ( class_Rings_Oordered__ring(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2),V_d_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_less__add__iff2,axiom,
% 1.61/1.64 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.61/1.64 ( class_Rings_Oordered__ring(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_real__squared__diff__one__factored,axiom,
% 1.61/1.64 ! [V_x,T_a] :
% 1.61/1.64 ( class_Rings_Oring__1(T_a)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_division__ring__inverse__diff,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Odivision__ring(T_a)
% 1.61/1.64 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.64 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_power__minus,axiom,
% 1.61/1.64 ! [V_n,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Oring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_norm__triangle__ineq4,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nonzero__of__real__inverse,axiom,
% 1.61/1.64 ! [V_x,T_a] :
% 1.61/1.64 ( class_RealVector_Oreal__div__algebra(T_a)
% 1.61/1.64 => ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.61/1.64 => c_RealVector_Oof__real(T_a,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)) = c_Rings_Oinverse__class_Oinverse(T_a,c_RealVector_Oof__real(T_a,V_x)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_zero__reorient,axiom,
% 1.61/1.64 ! [V_x_2,T_a] :
% 1.61/1.64 ( class_Groups_Ozero(T_a)
% 1.61/1.64 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 1.61/1.64 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oab__semigroup__mult(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__right__imp__eq,axiom,
% 1.61/1.64 ! [V_c,V_a,V_b,T_a] :
% 1.61/1.64 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.61/1.64 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 1.61/1.64 => V_b = V_c ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__imp__eq,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 1.61/1.64 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.61/1.64 => V_b = V_c ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__left__imp__eq,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.61/1.64 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.61/1.64 => V_b = V_c ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__right__cancel,axiom,
% 1.61/1.64 ! [V_ca_2,V_aa_2,V_b_2,T_a] :
% 1.61/1.64 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.61/1.64 => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2)
% 1.61/1.64 <=> V_b_2 = V_ca_2 ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__left__cancel,axiom,
% 1.61/1.64 ! [V_ca_2,V_b_2,V_aa_2,T_a] :
% 1.61/1.64 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.61/1.64 => ( c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2)
% 1.61/1.64 <=> V_b_2 = V_ca_2 ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oab__semigroup__add(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_one__reorient,axiom,
% 1.61/1.64 ! [V_x_2,T_a] :
% 1.61/1.64 ( class_Groups_Oone(T_a)
% 1.61/1.64 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 1.61/1.64 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_norm__diff__triangle__ineq,axiom,
% 1.61/1.64 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add_Ocomm__neutral,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__0__right,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Omonoid__add(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_double__zero__sym,axiom,
% 1.61/1.64 ! [V_aa_2,T_a] :
% 1.61/1.64 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.61/1.64 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)
% 1.61/1.64 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__0,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__0__left,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Omonoid__add(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__le__imp__le__left,axiom,
% 1.61/1.64 ! [V_b,V_a,V_c,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__le__imp__le__right,axiom,
% 1.61/1.64 ! [V_b,V_c,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__mono,axiom,
% 1.61/1.64 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__left__mono,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__right__mono,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__le__cancel__left,axiom,
% 1.61/1.64 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__le__cancel__right,axiom,
% 1.61/1.64 ! [V_b_2,V_ca_2,V_aa_2,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__less__imp__less__left,axiom,
% 1.61/1.64 ! [V_b,V_a,V_c,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__less__imp__less__right,axiom,
% 1.61/1.64 ! [V_b,V_c,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__strict__mono,axiom,
% 1.61/1.64 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__strict__left__mono,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__strict__right__mono,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__less__cancel__left,axiom,
% 1.61/1.64 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__less__cancel__right,axiom,
% 1.61/1.64 ! [V_b_2,V_ca_2,V_aa_2,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_mult_Ocomm__neutral,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_mult__1__right,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Omonoid__mult(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_mult__1,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_mult__1__left,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Omonoid__mult(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.64 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)
% 1.61/1.64 <=> ( V_ka_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 | V_ma_2 = V_n_2 ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_left__add__mult__distrib,axiom,
% 1.61/1.64 ! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__nonpos__nonpos,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__increasing2,axiom,
% 1.61/1.64 ! [V_a,V_b,V_c,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__increasing,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__nonneg__eq__0__iff,axiom,
% 1.61/1.64 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 1.61/1.64 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.64 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.64 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__nonneg__nonneg,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 1.61/1.64 ! [V_aa_2,T_a] :
% 1.61/1.64 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 1.61/1.64 ! [V_aa_2,T_a] :
% 1.61/1.64 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__neg__neg,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__pos__pos,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 1.61/1.64 ! [V_aa_2,T_a] :
% 1.61/1.64 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 1.61/1.64 ! [V_aa_2,T_a] :
% 1.61/1.64 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__le__less__mono,axiom,
% 1.61/1.64 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__less__le__mono,axiom,
% 1.61/1.64 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__mult__eq__cancel1,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.61/1.64 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)
% 1.61/1.64 <=> V_ma_2 = V_n_2 ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__mult__less__cancel1,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__nonpos__neg,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__neg__nonpos,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__strict__increasing2,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_Deriv_Oinverse__diff__inverse,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Odivision__ring(T_a)
% 1.61/1.64 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.64 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b))) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_complex__diff__def,axiom,
% 1.61/1.64 ! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_reduce__poly__simple,axiom,
% 1.61/1.64 ! [V_n,V_b] :
% 1.61/1.64 ( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 1.61/1.64 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 => ? [B_z] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_zero__less__power__nat__eq,axiom,
% 1.61/1.64 ! [V_n_2,V_x_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
% 1.61/1.64 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_not__real__square__gt__zero,axiom,
% 1.61/1.64 ! [V_x_2] :
% 1.61/1.64 ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))
% 1.61/1.64 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 1.61/1.64 ! [V_q,V_p,V_x,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_real__diff__def,axiom,
% 1.61/1.64 ! [V_s,V_r] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_minus__real__def,axiom,
% 1.61/1.64 ! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diffs0__imp__equal,axiom,
% 1.61/1.64 ! [V_n,V_m] :
% 1.61/1.64 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 => V_m = V_n ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__self__eq__0,axiom,
% 1.61/1.64 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_minus__nat_Odiff__0,axiom,
% 1.61/1.64 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__0__eq__0,axiom,
% 1.61/1.64 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__less__mono2,axiom,
% 1.61/1.64 ! [V_l,V_n,V_m] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_less__imp__diff__less,axiom,
% 1.61/1.64 ! [V_n,V_k,V_j] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__add__inverse2,axiom,
% 1.61/1.64 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__add__inverse,axiom,
% 1.61/1.64 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__diff__left,axiom,
% 1.61/1.64 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__cancel,axiom,
% 1.61/1.64 ! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__cancel2,axiom,
% 1.61/1.64 ! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__le__self,axiom,
% 1.61/1.64 ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__le__mono2,axiom,
% 1.61/1.64 ! [V_l,V_n,V_m] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__le__mono,axiom,
% 1.61/1.64 ! [V_l,V_n,V_m] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__diff__cancel,axiom,
% 1.61/1.64 ! [V_n,V_i] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_eq__diff__iff,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_ma_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_n_2)
% 1.61/1.64 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2)
% 1.61/1.64 <=> V_ma_2 = V_n_2 ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_Nat_Odiff__diff__eq,axiom,
% 1.61/1.64 ! [V_n,V_m,V_k] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_le__diff__iff,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_ma_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_n_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__mult__distrib2,axiom,
% 1.61/1.64 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__mult__distrib,axiom,
% 1.61/1.64 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_complex__mod__minus__le__complex__mod,axiom,
% 1.61/1.64 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_real__le__eq__diff,axiom,
% 1.61/1.64 ! [V_y_2,V_x_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__less,axiom,
% 1.61/1.64 ! [V_m,V_n] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_zero__less__diff,axiom,
% 1.61/1.64 ! [V_ma_2,V_n_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ma_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_real__minus__mult__self__le,axiom,
% 1.61/1.64 ! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__add__0,axiom,
% 1.61/1.64 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__is__0__eq,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2] :
% 1.61/1.64 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__is__0__eq_H,axiom,
% 1.61/1.64 ! [V_n,V_m] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__diff__inverse,axiom,
% 1.61/1.64 ! [V_n,V_m] :
% 1.61/1.64 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_less__diff__conv,axiom,
% 1.61/1.64 ! [V_ka_2,V_j_2,V_i_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2),V_j_2) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__less__mono,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_less__diff__iff,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_ma_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_n_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_real__add__minus__iff,axiom,
% 1.61/1.64 ! [V_aa_2,V_x_2] :
% 1.61/1.64 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_aa_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.61/1.64 <=> V_x_2 = V_aa_2 ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_real__add__eq__0__iff,axiom,
% 1.61/1.64 ! [V_y_2,V_x_2] :
% 1.61/1.64 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.61/1.64 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__diff__right,axiom,
% 1.61/1.64 ! [V_i,V_j,V_k] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_le__diff__conv,axiom,
% 1.61/1.64 ! [V_i_2,V_ka_2,V_j_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2),V_i_2)
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_le__add__diff,axiom,
% 1.61/1.64 ! [V_m,V_n,V_k] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_le__add__diff__inverse,axiom,
% 1.61/1.64 ! [V_m,V_n] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__diff__assoc,axiom,
% 1.61/1.64 ! [V_i,V_j,V_k] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_le__diff__conv2,axiom,
% 1.61/1.64 ! [V_i_2,V_j_2,V_ka_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_j_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2),V_j_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_le__add__diff__inverse2,axiom,
% 1.61/1.64 ! [V_m,V_n] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_le__imp__diff__is__add,axiom,
% 1.61/1.64 ! [V_ka_2,V_j_2,V_i_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.61/1.64 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_ka_2
% 1.61/1.64 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_i_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__add__assoc,axiom,
% 1.61/1.64 ! [V_i,V_j,V_k] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__diff__assoc2,axiom,
% 1.61/1.64 ! [V_i,V_j,V_k] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__add__assoc2,axiom,
% 1.61/1.64 ! [V_i,V_j,V_k] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_complex__mod__triangle__ineq2,axiom,
% 1.61/1.64 ! [V_a,V_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_norm__diff__ineq,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__diff__split,axiom,
% 1.61/1.64 ! [V_b_2,V_aa_2,V_P_2] :
% 1.61/1.64 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
% 1.61/1.64 <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)
% 1.61/1.64 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 1.61/1.64 & ! [B_d] :
% 1.61/1.64 ( V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 1.61/1.64 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__diff__split__asm,axiom,
% 1.61/1.64 ! [V_b_2,V_aa_2,V_P_2] :
% 1.61/1.64 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
% 1.61/1.64 <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)
% 1.61/1.64 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 1.61/1.64 | ? [B_d] :
% 1.61/1.64 ( V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 1.61/1.64 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_real__add__le__0__iff,axiom,
% 1.61/1.64 ! [V_y_2,V_x_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_real__0__le__add__iff,axiom,
% 1.61/1.64 ! [V_y_2,V_x_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_real__0__less__add__iff,axiom,
% 1.61/1.64 ! [V_y_2,V_x_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_real__add__less__0__iff,axiom,
% 1.61/1.64 ! [V_y_2,V_x_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__eq__add__iff2,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.61/1.64 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
% 1.61/1.64 <=> V_ma_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__diff__add__eq2,axiom,
% 1.61/1.64 ! [V_n,V_m,V_u,V_j,V_i] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__le__add__iff2,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__eq__add__iff1,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 1.61/1.64 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
% 1.61/1.64 <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2) = V_n_2 ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__diff__add__eq1,axiom,
% 1.61/1.64 ! [V_n,V_m,V_u,V_i,V_j] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__le__add__iff1,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2),V_n_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 1.61/1.64 ! [V_ry,V_rx,V_lx,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 1.61/1.64 ! [V_ry,V_rx,V_lx,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 1.61/1.64 ! [V_rx,V_ly,V_lx,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 1.61/1.64 ! [V_rx,V_ly,V_lx,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 1.61/1.64 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 1.61/1.64 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 1.61/1.64 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 1.61/1.64 ! [V_c,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 1.61/1.64 ! [V_d,V_c,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 1.61/1.64 ! [V_d,V_c,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 1.61/1.64 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_complex__of__real__minus__one,axiom,
% 1.61/1.64 c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__less__add__iff1,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2),V_n_2) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_nat__less__add__iff2,axiom,
% 1.61/1.64 ! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 1.61/1.64 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_mult__eq__if,axiom,
% 1.61/1.64 ! [V_n,V_m] :
% 1.61/1.64 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.61/1.64 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_power__eq__if,axiom,
% 1.61/1.64 ! [V_p,V_m] :
% 1.61/1.64 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 1.61/1.64 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_realpow__num__eq__if,axiom,
% 1.61/1.64 ! [V_m,V_n,T_a] :
% 1.61/1.64 ( class_Power_Opower(T_a)
% 1.61/1.64 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 1.61/1.64 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.64 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_realpow__minus__mult,axiom,
% 1.61/1.64 ! [V_x,V_n,T_a] :
% 1.61/1.64 ( class_Groups_Omonoid__mult(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__0__iff,axiom,
% 1.61/1.64 ! [V_aa_2,V_b_2,T_a] :
% 1.61/1.64 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.61/1.64 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)
% 1.61/1.64 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 1.61/1.64 ! [V_z,V_y,V_x,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_crossproduct__noteq,axiom,
% 1.61/1.64 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 1.61/1.64 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.61/1.64 => ( ( V_aa_2 != V_b_2
% 1.61/1.64 & V_ca_2 != V_d_2 )
% 1.61/1.64 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 1.61/1.64 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 1.61/1.64 ! [V_b,V_m,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_crossproduct__eq,axiom,
% 1.61/1.64 ! [V_z_2,V_x_2,V_y_2,V_wa_2,T_a] :
% 1.61/1.64 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.61/1.64 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
% 1.61/1.64 <=> ( V_wa_2 = V_x_2
% 1.61/1.64 | V_y_2 = V_z_2 ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_Deriv_Oadd__diff__add,axiom,
% 1.61/1.64 ! [V_d,V_b,V_c,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 1.61/1.64 ! [V_q,V_y,V_x,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 1.61/1.64 ! [V_q,V_p,V_x,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 1.61/1.64 ! [V_x,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_add__scale__eq__noteq,axiom,
% 1.61/1.64 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 1.61/1.64 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.61/1.64 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.64 => ( ( V_a = V_b
% 1.61/1.64 & V_c != V_d )
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 1.61/1.64 ! [V_m,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 1.61/1.64 ! [V_a,V_m,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 1.61/1.64 ! [V_m,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 1.61/1.64 ! [V_x,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__ring__1(T_a)
% 1.61/1.64 => c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 1.61/1.64 ! [V_y,V_x,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__ring__1(T_a)
% 1.61/1.64 => c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 1.61/1.64 ! [V_x,T_a] :
% 1.61/1.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_ath,axiom,
% 1.61/1.64 ! [V_t,V_x] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_t)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_t,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.61/1.64 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_t)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact__096cmod_A_I1_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_J_A_061cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096,axiom,
% 1.61/1.64 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))) ).
% 1.61/1.64
% 1.61/1.64 fof(fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096,axiom,
% 1.61/1.64 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) ).
% 1.61/1.64
% 1.61/1.64 fof(fact__0961_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096,axiom,
% 1.61/1.64 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_assms,axiom,
% 1.61/1.64 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_m_I2_J,axiom,
% 1.61/1.64 ! [B_z] :
% 1.61/1.64 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),B_z)),v_m____) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_0611_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096,axiom,
% 1.61/1.64 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) ).
% 1.61/1.64
% 1.61/1.64 fof(fact__096cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_060_061_Acmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_J_A_L_Acmod_A_I_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096,axiom,
% 1.61/1.64 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_th11,axiom,
% 1.61/1.64 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_diff__commute,axiom,
% 1.61/1.64 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__eq__0,axiom,
% 1.61/1.64 ! [V_aa_2,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => ( c_Groups_Oabs__class_Oabs(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.64 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__zero,axiom,
% 1.61/1.64 ! [T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__ge__self,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__le__D1,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__mult,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__mult__self,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__add__abs,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__one,axiom,
% 1.61/1.64 ! [T_a] :
% 1.61/1.64 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__minus__commute,axiom,
% 1.61/1.64 ! [V_b,V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__minus__cancel,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_power__abs,axiom,
% 1.61/1.64 ! [V_n,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__inverse,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__norm__cancel,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_real__norm__def,axiom,
% 1.61/1.64 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__idempotent,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__ge__zero,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__le__zero__iff,axiom,
% 1.61/1.64 ! [V_aa_2,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.64 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__of__nonneg,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__of__pos,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.64 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_zero__less__abs__iff,axiom,
% 1.61/1.64 ! [V_aa_2,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_aa_2))
% 1.61/1.64 <=> V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__not__less__zero,axiom,
% 1.61/1.64 ! [V_a,T_a] :
% 1.61/1.64 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.64 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.61/1.64
% 1.61/1.64 fof(fact_abs__mult__less,axiom,
% 1.61/1.64 ! [V_d,V_b,V_c,V_a,T_a] :
% 1.61/1.64 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
% 1.61/1.64 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
% 1.61/1.64 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__triangle__ineq,axiom,
% 1.61/1.65 ! [V_b,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__triangle__ineq3,axiom,
% 1.61/1.65 ! [V_b,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__triangle__ineq2,axiom,
% 1.61/1.65 ! [V_b,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__triangle__ineq2__sym,axiom,
% 1.61/1.65 ! [V_b,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__ge__minus__self,axiom,
% 1.61/1.65 ! [V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__le__iff,axiom,
% 1.61/1.65 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)
% 1.61/1.65 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
% 1.61/1.65 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__leI,axiom,
% 1.61/1.65 ! [V_b,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__le__D2,axiom,
% 1.61/1.65 ! [V_b,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__less__iff,axiom,
% 1.61/1.65 ! [V_b_2,V_aa_2,T_a] :
% 1.61/1.65 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)
% 1.61/1.65 <=> ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
% 1.61/1.65 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_nonzero__abs__inverse,axiom,
% 1.61/1.65 ! [V_a,T_a] :
% 1.61/1.65 ( class_Fields_Olinordered__field(T_a)
% 1.61/1.65 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__power__minus,axiom,
% 1.61/1.65 ! [V_n,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n)) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__le__interval__iff,axiom,
% 1.61/1.65 ! [V_r_2,V_x_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_r_2)
% 1.61/1.65 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r_2),V_x_2)
% 1.61/1.65 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_r_2) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_norm__of__real,axiom,
% 1.61/1.65 ! [V_r,T_a] :
% 1.61/1.65 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.61/1.65 => c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__minus__add__cancel,axiom,
% 1.61/1.65 ! [V_y,V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__eq__mult,axiom,
% 1.61/1.65 ! [V_b,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Oordered__ring__abs(T_a)
% 1.61/1.65 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.65 | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.61/1.65 & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.61/1.65 | c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__mult__pos,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.61/1.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__of__nonpos,axiom,
% 1.61/1.65 ! [V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__minus__le__zero,axiom,
% 1.61/1.65 ! [V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zero__le__power__abs,axiom,
% 1.61/1.65 ! [V_n,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__if,axiom,
% 1.61/1.65 ! [V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oabs__if(T_a)
% 1.61/1.65 => ( ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) )
% 1.61/1.65 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__of__neg,axiom,
% 1.61/1.65 ! [V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__diff__triangle__ineq,axiom,
% 1.61/1.65 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__triangle__ineq4,axiom,
% 1.61/1.65 ! [V_b,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_rabs__ratiotest__lemma,axiom,
% 1.61/1.65 ! [V_y,V_x,V_c] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
% 1.61/1.65 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__real__def,axiom,
% 1.61/1.65 ! [V_a] :
% 1.61/1.65 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a) )
% 1.61/1.65 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_real__abs__def,axiom,
% 1.61/1.65 ! [V_r] :
% 1.61/1.65 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r) )
% 1.61/1.65 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__add__one__not__less__self,axiom,
% 1.61/1.65 ! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__sum__triangle__ineq,axiom,
% 1.61/1.65 ! [V_m,V_l,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m))))) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_norm__triangle__ineq3,axiom,
% 1.61/1.65 ! [V_b,V_a,T_a] :
% 1.61/1.65 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__add__one__gt__zero,axiom,
% 1.61/1.65 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))) ).
% 1.61/1.65
% 1.61/1.65 fof(fact__096EX_Am_0620_O_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_096,axiom,
% 1.61/1.65 ? [B_m] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)
% 1.61/1.65 & ! [B_z] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),B_z)),B_m) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__diff__less__iff,axiom,
% 1.61/1.65 ! [V_r_2,V_aa_2,V_x_2,T_a] :
% 1.61/1.65 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_aa_2)),V_r_2)
% 1.61/1.65 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_r_2),V_x_2)
% 1.61/1.65 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_r_2)) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_even__less__0__iff,axiom,
% 1.61/1.65 ! [V_aa_2,T_a] :
% 1.61/1.65 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.65 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_less_Oprems,axiom,
% 1.61/1.65 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zero__less__zpower__abs__iff,axiom,
% 1.61/1.65 ! [V_n_2,V_x_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))
% 1.61/1.65 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.61/1.65 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_constant__def,axiom,
% 1.61/1.65 ! [V_f_2,T_b,T_a] :
% 1.61/1.65 ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_a,T_b,V_f_2)
% 1.61/1.65 <=> ! [B_x,B_y] : hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zpower__zadd__distrib,axiom,
% 1.61/1.65 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zpower__zpower,axiom,
% 1.61/1.65 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_double__eq__0__iff,axiom,
% 1.61/1.65 ! [V_aa_2,T_a] :
% 1.61/1.65 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.61/1.65 => ( c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.65 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_of__real_Opos__bounded,axiom,
% 1.61/1.65 ! [T_a] :
% 1.61/1.65 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.65 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.61/1.65 => ? [B_K] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.61/1.65 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),B_K)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_unimodular__reduce__norm,axiom,
% 1.61/1.65 ! [V_z] :
% 1.61/1.65 ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.61/1.65 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.61/1.65 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.61/1.65 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact__096_B_Bthesis_O_A_I_B_Bm_O_A_091_124_A0_A_060_Am_059_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.61/1.65 ~ ! [B_m] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)
% 1.61/1.65 => ~ ! [B_z] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),B_z)),B_m) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_pc0,axiom,
% 1.61/1.65 hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_c,axiom,
% 1.61/1.65 ! [B_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_w))) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_kn,axiom,
% 1.61/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zabs__def,axiom,
% 1.61/1.65 ! [V_i] :
% 1.61/1.65 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i) )
% 1.61/1.65 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = V_i ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_less__bin__lemma,axiom,
% 1.61/1.65 ! [V_l_2,V_ka_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_ka_2,V_l_2)
% 1.61/1.65 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_ka_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zle__diff1__eq,axiom,
% 1.61/1.65 ! [V_z_2,V_wa_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.61/1.65 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zdiff__zmult__distrib2,axiom,
% 1.61/1.65 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zdiff__zmult__distrib,axiom,
% 1.61/1.65 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zero__le__zpower__abs,axiom,
% 1.61/1.65 ! [V_n,V_x] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zabs__less__one__iff,axiom,
% 1.61/1.65 ! [V_z_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))
% 1.61/1.65 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__zmult__eq__1,axiom,
% 1.61/1.65 ! [V_n,V_m] :
% 1.61/1.65 ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zless__linear,axiom,
% 1.61/1.65 ! [V_y,V_x] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 1.61/1.65 | V_x = V_y
% 1.61/1.65 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zadd__zless__mono,axiom,
% 1.61/1.65 ! [V_z,V_z_H,V_w,V_w_H] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zmult__zless__mono2,axiom,
% 1.61/1.65 ! [V_k,V_j,V_i] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zadd__strict__right__mono,axiom,
% 1.61/1.65 ! [V_k,V_j,V_i] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zless__imp__add1__zle,axiom,
% 1.61/1.65 ! [V_z,V_w] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_pos__zmult__eq__1__iff,axiom,
% 1.61/1.65 ! [V_n_2,V_ma_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)
% 1.61/1.65 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.61/1.65 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.61/1.65 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_le__imp__0__less,axiom,
% 1.61/1.65 ! [V_z] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_odd__less__0,axiom,
% 1.61/1.65 ! [V_z_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.61/1.65 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zadd__zmult__distrib,axiom,
% 1.61/1.65 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zmult__assoc,axiom,
% 1.61/1.65 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_add1__zle__eq,axiom,
% 1.61/1.65 ! [V_z_2,V_wa_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)
% 1.61/1.65 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zadd__zmult__distrib2,axiom,
% 1.61/1.65 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zless__add1__eq,axiom,
% 1.61/1.65 ! [V_z_2,V_wa_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.61/1.65 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2)
% 1.61/1.65 | V_wa_2 = V_z_2 ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zle__add1__eq__le,axiom,
% 1.61/1.65 ! [V_z_2,V_wa_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.61/1.65 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_z_2) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zless__le,axiom,
% 1.61/1.65 ! [V_wa_2,V_z_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_wa_2)
% 1.61/1.65 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_wa_2)
% 1.61/1.65 & V_z_2 != V_wa_2 ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zmult__commute,axiom,
% 1.61/1.65 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zmult__1__right,axiom,
% 1.61/1.65 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zadd__0__right,axiom,
% 1.61/1.65 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 1.61/1.65
% 1.61/1.65 fof(fact_int__one__le__iff__zero__less,axiom,
% 1.61/1.65 ! [V_z_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
% 1.61/1.65 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zmult__1,axiom,
% 1.61/1.65 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zadd__0,axiom,
% 1.61/1.65 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 1.61/1.65
% 1.61/1.65 fof(fact_int__0__less__1,axiom,
% 1.61/1.65 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_odd__nonzero,axiom,
% 1.61/1.65 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_int__0__neq__1,axiom,
% 1.61/1.65 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zmult__zminus,axiom,
% 1.61/1.65 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zadd__zminus__inverse2,axiom,
% 1.61/1.65 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zminus__0,axiom,
% 1.61/1.65 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_complex__i__not__one,axiom,
% 1.61/1.65 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_complex__i__not__zero,axiom,
% 1.61/1.65 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_inverse__i,axiom,
% 1.61/1.65 c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_complex__i__mult__minus,axiom,
% 1.61/1.65 ! [V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),V_x)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_x) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_i__mult__eq2,axiom,
% 1.61/1.65 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_k1n,axiom,
% 1.61/1.65 c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_incr__lemma,axiom,
% 1.61/1.65 ! [V_x,V_z,V_d] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_decr__lemma,axiom,
% 1.61/1.65 ! [V_z,V_x,V_d] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zminus__zadd__distrib,axiom,
% 1.61/1.65 ! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zminus__zminus,axiom,
% 1.61/1.65 ! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zle__refl,axiom,
% 1.61/1.65 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zadd__commute,axiom,
% 1.61/1.65 ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zle__linear,axiom,
% 1.61/1.65 ! [V_w,V_z] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.61/1.65 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zadd__left__commute,axiom,
% 1.61/1.65 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zadd__assoc,axiom,
% 1.61/1.65 ! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zadd__left__mono,axiom,
% 1.61/1.65 ! [V_k,V_j,V_i] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zle__trans,axiom,
% 1.61/1.65 ! [V_k,V_j,V_i] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zle__antisym,axiom,
% 1.61/1.65 ! [V_w,V_z] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 1.61/1.65 => V_z = V_w ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_diff__int__def__symmetric,axiom,
% 1.61/1.65 ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_diff__int__def,axiom,
% 1.61/1.65 ! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_psize__eq__0__iff,axiom,
% 1.61/1.65 ! [V_pb_2,T_a] :
% 1.61/1.65 ( class_Groups_Ozero(T_a)
% 1.61/1.65 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.65 <=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_q_I2_J,axiom,
% 1.61/1.65 ! [B_x] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,B_x)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_less_Ohyps,axiom,
% 1.61/1.65 ! [V_pb_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,V_pb_2),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))
% 1.61/1.65 => ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2))
% 1.61/1.65 => ? [B_z] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2),B_z) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096,axiom,
% 1.61/1.65 ? [B_q] :
% 1.61/1.65 ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
% 1.61/1.65 & ! [B_x] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,B_x)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_q_I1_J,axiom,
% 1.61/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_a00,axiom,
% 1.61/1.65 hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.61/1.65
% 1.61/1.65 fof(fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096,axiom,
% 1.61/1.65 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_qnc,axiom,
% 1.61/1.65 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_cq0,axiom,
% 1.61/1.65 ! [B_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_w))) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_pqc0,axiom,
% 1.61/1.65 hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_kas_I3_J,axiom,
% 1.61/1.65 c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact__096poly_Ap_Ac_A_061_A0_A_061_061_062_AEX_Az_O_Apoly_Ap_Az_A_061_A0_096,axiom,
% 1.61/1.65 ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 1.61/1.65 => ? [B_z] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_z) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_self__quotient__aux2,axiom,
% 1.61/1.65 ! [V_q,V_r,V_a] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.61/1.65 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_self__quotient__aux1,axiom,
% 1.61/1.65 ! [V_q,V_r,V_a] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.61/1.65 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact__096poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_096,axiom,
% 1.61/1.65 hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_qr,axiom,
% 1.61/1.65 ! [B_z] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),B_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_z)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_r01,axiom,
% 1.61/1.65 hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_lgqr,axiom,
% 1.61/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_rnc,axiom,
% 1.61/1.65 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_mrmq__eq,axiom,
% 1.61/1.65 ! [V_wa_2] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),V_wa_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.61/1.65 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),V_wa_2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_kas_I4_J,axiom,
% 1.61/1.65 ! [B_z] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),B_z))) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 1.61/1.65 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.61/1.65 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_unique__quotient__lemma__neg,axiom,
% 1.61/1.65 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_zdiv__mono2__lemma,axiom,
% 1.61/1.65 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.61/1.65 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_unique__quotient__lemma,axiom,
% 1.61/1.65 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_q__neg__lemma,axiom,
% 1.61/1.65 ! [V_r_H,V_q_H,V_b_H] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_q__pos__lemma,axiom,
% 1.61/1.65 ! [V_r_H,V_q_H,V_b_H] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact__096psize_Ap_A_061_Ak_A_L_A1_A_061_061_062_AEX_Aw_O_Acmod_A_Ipoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_J_A_060_A1_096,axiom,
% 1.61/1.65 ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 1.61/1.65 => ? [B_w] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_w)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact__096_I_B_Bx_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_061_061_062_AFalse_096,axiom,
% 1.61/1.65 ~ ! [B_x,B_y] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_y) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 1.61/1.65 ! [V_n,V_x] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_offset__poly__eq__0__lemma,axiom,
% 1.61/1.65 ! [V_a,V_p,V_c,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.61/1.65 => V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 1.61/1.65 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 1.61/1.65 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 1.61/1.65 ! [V_y,V_x] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 1.61/1.65 ! [V_y,V_x] :
% 1.61/1.65 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_th01,axiom,
% 1.61/1.65 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_th02,axiom,
% 1.61/1.65 c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__replicate__append,axiom,
% 1.61/1.65 ! [V_x,V_p,V_n,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__ring__1(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,c_Groups_Oone__class_Oone(T_a),V_n)),V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact__096EX_Az_O_Apoly_A_IpCons_A1_A_Imonom_Aa_A_Ik_A_N_A1_J_J_J_Az_A_061_A0_096,axiom,
% 1.61/1.65 ? [B_z] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),B_z) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_monom__0,axiom,
% 1.61/1.65 ! [V_a,T_a] :
% 1.61/1.65 ( class_Groups_Ozero(T_a)
% 1.61/1.65 => c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_abs__poly__def,axiom,
% 1.61/1.65 ! [V_x,T_a] :
% 1.61/1.65 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.65 => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x) )
% 1.61/1.65 & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 1.61/1.65 => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = V_x ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_minus__poly__code_I1_J,axiom,
% 1.61/1.65 ! [T_a] :
% 1.61/1.65 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.65 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_diff__poly__code_I2_J,axiom,
% 1.61/1.65 ! [V_p,T_a] :
% 1.61/1.65 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.65 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_diff__poly__code_I1_J,axiom,
% 1.61/1.65 ! [V_q,T_a] :
% 1.61/1.65 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.65 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_mult__poly__0__right,axiom,
% 1.61/1.65 ! [V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_mult__poly__0__left,axiom,
% 1.61/1.65 ! [V_q,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__eq__iff,axiom,
% 1.61/1.65 ! [V_qa_2,V_pb_2,T_a] :
% 1.61/1.65 ( ( class_Int_Oring__char__0(T_a)
% 1.61/1.65 & class_Rings_Oidom(T_a) )
% 1.61/1.65 => ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,V_qa_2)
% 1.61/1.65 <=> V_pb_2 = V_qa_2 ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_pCons__eq__iff,axiom,
% 1.61/1.65 ! [V_qa_2,V_b_2,V_pb_2,V_aa_2,T_a] :
% 1.61/1.65 ( class_Groups_Ozero(T_a)
% 1.61/1.65 => ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Polynomial_OpCons(T_a,V_b_2,V_qa_2)
% 1.61/1.65 <=> ( V_aa_2 = V_b_2
% 1.61/1.65 & V_pb_2 = V_qa_2 ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__diff__right,axiom,
% 1.61/1.65 ! [V_q,V_p,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__ring(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__minus__right,axiom,
% 1.61/1.65 ! [V_p,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__ring(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,V_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_mult__smult__left,axiom,
% 1.61/1.65 ! [V_q,V_p,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Osmult(T_a,V_a,V_p)),V_q) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_mult__smult__right,axiom,
% 1.61/1.65 ! [V_q,V_a,V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_mult__poly__add__left,axiom,
% 1.61/1.65 ! [V_r,V_q,V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_monom__eq__iff,axiom,
% 1.61/1.65 ! [V_b_2,V_n_2,V_aa_2,T_a] :
% 1.61/1.65 ( class_Groups_Ozero(T_a)
% 1.61/1.65 => ( c_Polynomial_Omonom(T_a,V_aa_2,V_n_2) = c_Polynomial_Omonom(T_a,V_b_2,V_n_2)
% 1.61/1.65 <=> V_aa_2 = V_b_2 ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__mult,axiom,
% 1.61/1.65 ! [V_x,V_q,V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__1,axiom,
% 1.61/1.65 ! [V_x,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__diff,axiom,
% 1.61/1.65 ! [V_x,V_q,V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__ring(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__minus,axiom,
% 1.61/1.65 ! [V_x,V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__ring(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__power,axiom,
% 1.61/1.65 ! [V_x,V_n,V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_diff__pCons,axiom,
% 1.61/1.65 ! [V_q,V_b,V_p,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.65 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__smult,axiom,
% 1.61/1.65 ! [V_p,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Osmult(T_a,V_b,V_p)) = c_Polynomial_Osmult(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_p) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__1__left,axiom,
% 1.61/1.65 ! [V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p) = V_p ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_minus__poly__code_I2_J,axiom,
% 1.61/1.65 ! [V_p,V_a,T_b] :
% 1.61/1.65 ( class_Groups_Oab__group__add(T_b)
% 1.61/1.65 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p)) = c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_minus__pCons,axiom,
% 1.61/1.65 ! [V_p,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.65 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__diff__left,axiom,
% 1.61/1.65 ! [V_p,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__ring(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_p) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__minus__left,axiom,
% 1.61/1.65 ! [V_p,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__ring(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_p) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__zero,axiom,
% 1.61/1.65 ! [V_pb_2,T_a] :
% 1.61/1.65 ( ( class_Int_Oring__char__0(T_a)
% 1.61/1.65 & class_Rings_Oidom(T_a) )
% 1.61/1.65 => ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 1.61/1.65 <=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__0__right,axiom,
% 1.61/1.65 ! [V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_diff__monom,axiom,
% 1.61/1.65 ! [V_b,V_n,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.65 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_n) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_minus__monom,axiom,
% 1.61/1.65 ! [V_n,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.65 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_add__poly__code_I1_J,axiom,
% 1.61/1.65 ! [V_q,T_a] :
% 1.61/1.65 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.61/1.65 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_add__poly__code_I2_J,axiom,
% 1.61/1.65 ! [V_p,T_a] :
% 1.61/1.65 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.61/1.65 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__add__right,axiom,
% 1.61/1.65 ! [V_q,V_p,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__0,axiom,
% 1.61/1.65 ! [V_x,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_pCons__0__0,axiom,
% 1.61/1.65 ! [T_a] :
% 1.61/1.65 ( class_Groups_Ozero(T_a)
% 1.61/1.65 => c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_pCons__eq__0__iff,axiom,
% 1.61/1.65 ! [V_pb_2,V_aa_2,T_a] :
% 1.61/1.65 ( class_Groups_Ozero(T_a)
% 1.61/1.65 => ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.61/1.65 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.65 & V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__0__left,axiom,
% 1.61/1.65 ! [V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__eq__0__iff,axiom,
% 1.61/1.65 ! [V_pb_2,V_aa_2,T_a] :
% 1.61/1.65 ( class_Rings_Oidom(T_a)
% 1.61/1.65 => ( c_Polynomial_Osmult(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.61/1.65 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.65 | V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_one__poly__def,axiom,
% 1.61/1.65 ! [T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.65 => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__smult,axiom,
% 1.61/1.65 ! [V_x,V_p,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__pCons,axiom,
% 1.61/1.65 ! [V_p,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,V_a,c_Polynomial_OpCons(T_a,V_b,V_p)) = c_Polynomial_OpCons(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Polynomial_Osmult(T_a,V_a,V_p)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_mult__monom,axiom,
% 1.61/1.65 ! [V_n,V_b,V_m,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_monom__eq__0,axiom,
% 1.61/1.65 ! [V_n,T_a] :
% 1.61/1.65 ( class_Groups_Ozero(T_a)
% 1.61/1.65 => c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_monom__eq__0__iff,axiom,
% 1.61/1.65 ! [V_n_2,V_aa_2,T_a] :
% 1.61/1.65 ( class_Groups_Ozero(T_a)
% 1.61/1.65 => ( c_Polynomial_Omonom(T_a,V_aa_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.61/1.65 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__add,axiom,
% 1.61/1.65 ! [V_x,V_q,V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_add__pCons,axiom,
% 1.61/1.65 ! [V_q,V_b,V_p,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.61/1.65 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_synthetic__div__unique__lemma,axiom,
% 1.61/1.65 ! [V_a,V_p,V_c,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => ( c_Polynomial_Osmult(T_a,V_c,V_p) = c_Polynomial_OpCons(T_a,V_a,V_p)
% 1.61/1.65 => V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__add__left,axiom,
% 1.61/1.65 ! [V_p,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_smult__monom,axiom,
% 1.61/1.65 ! [V_n,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_add__monom,axiom,
% 1.61/1.65 ! [V_b,V_n,V_a,T_a] :
% 1.61/1.65 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.61/1.65 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__pCons,axiom,
% 1.61/1.65 ! [V_x,V_p,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__monom,axiom,
% 1.61/1.65 ! [V_x,V_n,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_mult__pCons__right,axiom,
% 1.61/1.65 ! [V_q,V_a,V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_mult__pCons__left,axiom,
% 1.61/1.65 ! [V_q,V_p,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,V_p)),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_synthetic__div__correct_H,axiom,
% 1.61/1.65 ! [V_p,V_c,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__ring__1(T_a)
% 1.61/1.65 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = V_p ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_pcompose__pCons,axiom,
% 1.61/1.65 ! [V_q,V_p,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_synthetic__div__0,axiom,
% 1.61/1.65 ! [V_c,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_pcompose__0,axiom,
% 1.61/1.65 ! [V_q,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_poly__pcompose,axiom,
% 1.61/1.65 ! [V_x,V_q,V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_synthetic__div__pCons,axiom,
% 1.61/1.65 ! [V_c,V_p,V_a,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_synthetic__div__correct,axiom,
% 1.61/1.65 ! [V_c,V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_synthetic__div__unique,axiom,
% 1.61/1.65 ! [V_r,V_q,V_c,V_p,T_a] :
% 1.61/1.65 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.65 => ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q)) = c_Polynomial_OpCons(T_a,V_r,V_q)
% 1.61/1.65 => ( V_r = hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)
% 1.61/1.65 & V_q = c_Polynomial_Osynthetic__div(T_a,V_p,V_c) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__root,axiom,
% 1.61/1.65 ! [V_aa_2,V_pb_2,T_a] :
% 1.61/1.65 ( class_Rings_Oidom(T_a)
% 1.61/1.65 => ( hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.65 <=> ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.61/1.65 | c_Polynomial_Oorder(T_a,V_aa_2,V_pb_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__refl,axiom,
% 1.61/1.65 ! [V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_le__fun__def,axiom,
% 1.61/1.65 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.61/1.65 ( class_Orderings_Oord(T_b)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.61/1.65 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_linorder__linear,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Olinorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.61/1.65 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__eq__iff,axiom,
% 1.61/1.65 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( V_x_2 = V_y_2
% 1.61/1.65 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.61/1.65 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__eq__refl,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => ( V_x = V_y
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_le__funD,axiom,
% 1.61/1.65 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.61/1.65 ( class_Orderings_Oord(T_b)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__antisym__conv,axiom,
% 1.61/1.65 ! [V_x_2,V_y_2,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.61/1.65 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_ord__eq__le__trans,axiom,
% 1.61/1.65 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Orderings_Oord(T_a)
% 1.61/1.65 => ( V_a = V_b
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_xt1_I3_J,axiom,
% 1.61/1.65 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( V_a = V_b
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_ord__le__eq__trans,axiom,
% 1.61/1.65 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Orderings_Oord(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.61/1.65 => ( V_b = V_c
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_xt1_I4_J,axiom,
% 1.61/1.65 ! [V_c,V_a,V_b,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.61/1.65 => ( V_b = V_c
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__antisym,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.61/1.65 => V_x = V_y ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__trans,axiom,
% 1.61/1.65 ! [V_z,V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_xt1_I5_J,axiom,
% 1.61/1.65 ! [V_x,V_y,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.61/1.65 => V_x = V_y ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_xt1_I6_J,axiom,
% 1.61/1.65 ! [V_z,V_x,V_y,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_le__funE,axiom,
% 1.61/1.65 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.61/1.65 ( class_Orderings_Oord(T_b)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_linorder__le__cases,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Olinorder(T_a)
% 1.61/1.65 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_linorder__cases,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Olinorder(T_a)
% 1.61/1.65 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 => ( V_x != V_y
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__less__asym,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_xt1_I10_J,axiom,
% 1.61/1.65 ! [V_z,V_x,V_y,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__less__trans,axiom,
% 1.61/1.65 ! [V_z,V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_xt1_I2_J,axiom,
% 1.61/1.65 ! [V_c,V_a,V_b,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.61/1.65 => ( V_b = V_c
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_ord__less__eq__trans,axiom,
% 1.61/1.65 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Orderings_Oord(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.61/1.65 => ( V_b = V_c
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_xt1_I1_J,axiom,
% 1.61/1.65 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( V_a = V_b
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_ord__eq__less__trans,axiom,
% 1.61/1.65 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.65 ( class_Orderings_Oord(T_a)
% 1.61/1.65 => ( V_a = V_b
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_xt1_I9_J,axiom,
% 1.61/1.65 ! [V_a,V_b,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.61/1.65 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__less__asym_H,axiom,
% 1.61/1.65 ! [V_b,V_a,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.61/1.65 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__less__imp__not__eq2,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 => V_y != V_x ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__less__imp__not__eq,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 => V_x != V_y ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__less__imp__not__less,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__less__not__sym,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_less__imp__neq,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 => V_x != V_y ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_linorder__neqE,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Olinorder(T_a)
% 1.61/1.65 => ( V_x != V_y
% 1.61/1.65 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_linorder__antisym__conv3,axiom,
% 1.61/1.65 ! [V_x_2,V_y_2,T_a] :
% 1.61/1.65 ( class_Orderings_Olinorder(T_a)
% 1.61/1.65 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.61/1.65 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.61/1.65 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_linorder__less__linear,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Olinorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 | V_x = V_y
% 1.61/1.65 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_not__less__iff__gr__or__eq,axiom,
% 1.61/1.65 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.65 ( class_Orderings_Olinorder(T_a)
% 1.61/1.65 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.61/1.65 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.61/1.65 | V_x_2 = V_y_2 ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_linorder__neq__iff,axiom,
% 1.61/1.65 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.65 ( class_Orderings_Olinorder(T_a)
% 1.61/1.65 => ( V_x_2 != V_y_2
% 1.61/1.65 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.61/1.65 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__less__irrefl,axiom,
% 1.61/1.65 ! [V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_xt1_I8_J,axiom,
% 1.61/1.65 ! [V_z,V_x,V_y,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__le__less__trans,axiom,
% 1.61/1.65 ! [V_z,V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_xt1_I7_J,axiom,
% 1.61/1.65 ! [V_z,V_x,V_y,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__less__le__trans,axiom,
% 1.61/1.65 ! [V_z,V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_xt1_I11_J,axiom,
% 1.61/1.65 ! [V_a,V_b,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.61/1.65 => ( V_a != V_b
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__le__neq__trans,axiom,
% 1.61/1.65 ! [V_b,V_a,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.61/1.65 => ( V_a != V_b
% 1.61/1.65 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__le__imp__less__or__eq,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Oorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 | V_x = V_y ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_linorder__antisym__conv2,axiom,
% 1.61/1.65 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.65 ( class_Orderings_Olinorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.61/1.65 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.61/1.65 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_order__less__imp__le,axiom,
% 1.61/1.65 ! [V_y,V_x,T_a] :
% 1.61/1.65 ( class_Orderings_Opreorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.65 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.61/1.65
% 1.61/1.65 fof(fact_leD,axiom,
% 1.61/1.65 ! [V_x,V_y,T_a] :
% 1.61/1.65 ( class_Orderings_Olinorder(T_a)
% 1.61/1.65 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.61/1.66 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_xt1_I12_J,axiom,
% 1.61/1.66 ! [V_b,V_a,T_a] :
% 1.61/1.66 ( class_Orderings_Oorder(T_a)
% 1.61/1.66 => ( V_a != V_b
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.61/1.66 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_order__neq__le__trans,axiom,
% 1.61/1.66 ! [V_b,V_a,T_a] :
% 1.61/1.66 ( class_Orderings_Oorder(T_a)
% 1.61/1.66 => ( V_a != V_b
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.61/1.66 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_linorder__antisym__conv1,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Orderings_Olinorder(T_a)
% 1.61/1.66 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.61/1.66 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_not__leE,axiom,
% 1.61/1.66 ! [V_x,V_y,T_a] :
% 1.61/1.66 ( class_Orderings_Olinorder(T_a)
% 1.61/1.66 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.61/1.66 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_leI,axiom,
% 1.61/1.66 ! [V_y,V_x,T_a] :
% 1.61/1.66 ( class_Orderings_Olinorder(T_a)
% 1.61/1.66 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_order__le__less,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Orderings_Oorder(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.61/1.66 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.61/1.66 | V_x_2 = V_y_2 ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_less__le__not__le,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Orderings_Opreorder(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.61/1.66 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.61/1.66 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_order__less__le,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Orderings_Oorder(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.61/1.66 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.61/1.66 & V_x_2 != V_y_2 ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_linorder__le__less__linear,axiom,
% 1.61/1.66 ! [V_y,V_x,T_a] :
% 1.61/1.66 ( class_Orderings_Olinorder(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.61/1.66 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_linorder__not__le,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Orderings_Olinorder(T_a)
% 1.61/1.66 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_linorder__not__less,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Orderings_Olinorder(T_a)
% 1.61/1.66 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096,axiom,
% 1.61/1.66 ? [B_k,B_a] :
% 1.61/1.66 ( B_a != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 1.61/1.66 & B_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.61/1.66 & ? [B_q] :
% 1.61/1.66 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))
% 1.61/1.66 & ! [B_z] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),B_k)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,B_a,B_q)),B_z))) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__add__one,axiom,
% 1.61/1.66 ! [V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.61/1.66 => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_less__fun__def,axiom,
% 1.61/1.66 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.61/1.66 ( class_Orderings_Oord(T_b)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.61/1.66 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.61/1.66 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__zero,axiom,
% 1.61/1.66 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_zero__le__natceiling,axiom,
% 1.61/1.66 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__mono,axiom,
% 1.61/1.66 ! [V_y,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__one,axiom,
% 1.61/1.66 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__neg,axiom,
% 1.61/1.66 ! [V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.61/1.66 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__le__eq__one,axiom,
% 1.61/1.66 ! [V_x_2] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_power__power__power,axiom,
% 1.61/1.66 ! [T_a] :
% 1.61/1.66 ( class_Power_Opower(T_a)
% 1.61/1.66 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_of__real_Ononneg__bounded,axiom,
% 1.61/1.66 ! [T_a] :
% 1.61/1.66 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.66 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.61/1.66 => ? [B_K] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.61/1.66 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),B_K)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_power_Opower_Opower__0,axiom,
% 1.61/1.66 ! [V_aa_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 1.61/1.66
% 1.61/1.66 fof(fact_lemmaCauchy,axiom,
% 1.61/1.66 ! [V_X_2,V_M_2,T_a,T_b] :
% 1.61/1.66 ( ( class_RealVector_Oreal__normed__vector(T_b)
% 1.61/1.66 & class_Orderings_Oord(T_a) )
% 1.61/1.66 => ( ! [B_n] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 1.61/1.66 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
% 1.61/1.66 => ! [B_n] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 1.61/1.66 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_mult__left_Opos__bounded,axiom,
% 1.61/1.66 ! [V_y,T_a] :
% 1.61/1.66 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.66 => ? [B_K] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.61/1.66 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_mult_Opos__bounded,axiom,
% 1.61/1.66 ! [T_a] :
% 1.61/1.66 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.66 => ? [B_K] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.61/1.66 & ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_mult__right_Opos__bounded,axiom,
% 1.61/1.66 ! [V_x,T_a] :
% 1.61/1.66 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.61/1.66 => ? [B_K] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.61/1.66 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.61/1.66 ~ ! [B_q] :
% 1.61/1.66 ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
% 1.61/1.66 => ~ ! [B_x] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,B_x)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natfloor__add__one,axiom,
% 1.61/1.66 ! [V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.61/1.66 => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natfloor__one,axiom,
% 1.61/1.66 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natfloor__zero,axiom,
% 1.61/1.66 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_zero__le__natfloor,axiom,
% 1.61/1.66 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natfloor__mono,axiom,
% 1.61/1.66 ! [V_y,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natfloor__neg,axiom,
% 1.61/1.66 ! [V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.61/1.66 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_le__natfloor__eq__one,axiom,
% 1.61/1.66 ! [V_x_2] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_le__mult__natfloor,axiom,
% 1.61/1.66 ! [V_b,V_a] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_tsub__def,axiom,
% 1.61/1.66 ! [V_x,V_y] :
% 1.61/1.66 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 1.61/1.66 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) )
% 1.61/1.66 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 1.61/1.66 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_termination__basic__simps_I3_J,axiom,
% 1.61/1.66 ! [V_z,V_y,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 1.61/1.66 ! [V_y,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_tsub__eq,axiom,
% 1.61/1.66 ! [V_x,V_y] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 1.61/1.66 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_termination__basic__simps_I2_J,axiom,
% 1.61/1.66 ! [V_y,V_z,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 1.61/1.66 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_termination__basic__simps_I1_J,axiom,
% 1.61/1.66 ! [V_z,V_y,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.61/1.66 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_termination__basic__simps_I5_J,axiom,
% 1.61/1.66 ! [V_y,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_termination__basic__simps_I4_J,axiom,
% 1.61/1.66 ! [V_y,V_z,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__eq,axiom,
% 1.61/1.66 ! [V_x,V_n] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 1.61/1.66 => c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_pos__poly__pCons,axiom,
% 1.61/1.66 ! [V_pb_2,V_aa_2,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2))
% 1.61/1.66 <=> ( c_Polynomial_Opos__poly(T_a,V_pb_2)
% 1.61/1.66 | ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.61/1.66 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__ge__zero,axiom,
% 1.61/1.66 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__diff,axiom,
% 1.61/1.66 ! [V_m,V_n] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.61/1.66 => c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_not__real__of__nat__less__zero,axiom,
% 1.61/1.66 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__less__iff,axiom,
% 1.61/1.66 ! [V_ma_2,V_n_2] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_pos__poly__add,axiom,
% 1.61/1.66 ! [V_q,V_p,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 1.61/1.66 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 1.61/1.66 => c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__mult,axiom,
% 1.61/1.66 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_pos__poly__mult,axiom,
% 1.61/1.66 ! [V_q,V_p,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 1.61/1.66 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 1.61/1.66 => c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_not__pos__poly__0,axiom,
% 1.61/1.66 ! [T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__zero__iff,axiom,
% 1.61/1.66 ! [V_n_2] :
% 1.61/1.66 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.61/1.66 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__zero,axiom,
% 1.61/1.66 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__inject,axiom,
% 1.61/1.66 ! [V_ma_2,V_n_2] :
% 1.61/1.66 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)
% 1.61/1.66 <=> V_n_2 = V_ma_2 ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__add,axiom,
% 1.61/1.66 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__1,axiom,
% 1.61/1.66 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_abs__real__of__nat__cancel,axiom,
% 1.61/1.66 ! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_power__real__of__nat,axiom,
% 1.61/1.66 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__power,axiom,
% 1.61/1.66 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
% 1.61/1.66 ! [V_n_2] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.61/1.66 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_less__eq__poly__def,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
% 1.61/1.66 <=> ( V_x_2 = V_y_2
% 1.61/1.66 | c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__natceiling__ge,axiom,
% 1.61/1.66 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__le__iff,axiom,
% 1.61/1.66 ! [V_ma_2,V_n_2] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__real__of__nat,axiom,
% 1.61/1.66 ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natfloor__real__of__nat,axiom,
% 1.61/1.66 ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__natfloor__le,axiom,
% 1.61/1.66 ! [V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_le__natfloor,axiom,
% 1.61/1.66 ! [V_a,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__le,axiom,
% 1.61/1.66 ! [V_a,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natfloor__power,axiom,
% 1.61/1.66 ! [V_n,V_x] :
% 1.61/1.66 ( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))
% 1.61/1.66 => c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
% 1.61/1.66 ! [V_n_2] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_nat__less__real__le,axiom,
% 1.61/1.66 ! [V_ma_2,V_n_2] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_nat__le__real__less,axiom,
% 1.61/1.66 ! [V_ma_2,V_n_2] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ma_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_le__natfloor__eq,axiom,
% 1.61/1.66 ! [V_aa_2,V_x_2] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_aa_2,c_RComplete_Onatfloor(V_x_2))
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2),V_x_2) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_pos__poly__total,axiom,
% 1.61/1.66 ! [V_p,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.61/1.66 | c_Polynomial_Opos__poly(T_a,V_p)
% 1.61/1.66 | c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__le__eq,axiom,
% 1.61/1.66 ! [V_aa_2,V_x_2] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_aa_2)
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__natfloor__add__one__gt,axiom,
% 1.61/1.66 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natfloor__subtract,axiom,
% 1.61/1.66 ! [V_x,V_a] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 1.61/1.66 => c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_real__natfloor__gt__diff__one,axiom,
% 1.61/1.66 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__subtract,axiom,
% 1.61/1.66 ! [V_x,V_a] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 1.61/1.66 => c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_less__natfloor,axiom,
% 1.61/1.66 ! [V_n,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
% 1.61/1.66 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natfloor__add,axiom,
% 1.61/1.66 ! [V_a,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.61/1.66 => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
% 1.61/1.66 ! [V_n,V_z] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)
% 1.61/1.66 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natfloor__eq,axiom,
% 1.61/1.66 ! [V_x,V_n] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 1.61/1.66 => c_RComplete_Onatfloor(V_x) = V_n ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_natceiling__add,axiom,
% 1.61/1.66 ! [V_a,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.61/1.66 => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_less__poly__def,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
% 1.61/1.66 <=> c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
% 1.61/1.66 ! [V_n,V_x] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_reals__Archimedean6,axiom,
% 1.61/1.66 ! [V_r] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 1.61/1.66 => ? [B_n] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r)
% 1.61/1.66 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_Limits_Ominus__diff__minus,axiom,
% 1.61/1.66 ! [V_b,V_a,T_a] :
% 1.61/1.66 ( class_Groups_Oab__group__add(T_a)
% 1.61/1.66 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_poly__cont,axiom,
% 1.61/1.66 ! [V_p,V_z,V_e] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e)
% 1.61/1.66 => ? [B_d] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 1.61/1.66 & ! [B_w] :
% 1.61/1.66 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z)))
% 1.61/1.66 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z)),B_d) )
% 1.61/1.66 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_w),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),V_z))),V_e) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_decseq__def,axiom,
% 1.61/1.66 ! [V_X_2,T_a] :
% 1.61/1.66 ( class_Orderings_Oorder(T_a)
% 1.61/1.66 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 1.61/1.66 <=> ! [B_m,B_n] :
% 1.61/1.66 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_compl__le__compl__iff,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Lattices_Oboolean__algebra(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_compl__mono,axiom,
% 1.61/1.66 ! [V_y,V_x,T_a] :
% 1.61/1.66 ( class_Lattices_Oboolean__algebra(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.61/1.66 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_minus__apply,axiom,
% 1.61/1.66 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 1.61/1.66 ( class_Groups_Ominus(T_a)
% 1.61/1.66 => hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_times_Oidem,axiom,
% 1.61/1.66 ! [V_a,T_a] :
% 1.61/1.66 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.61/1.66 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_mult__idem,axiom,
% 1.61/1.66 ! [V_x,T_a] :
% 1.61/1.66 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.61/1.66 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_mult__left__idem,axiom,
% 1.61/1.66 ! [V_b,V_a,T_a] :
% 1.61/1.66 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.61/1.66 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_double__compl,axiom,
% 1.61/1.66 ! [V_x,T_a] :
% 1.61/1.66 ( class_Lattices_Oboolean__algebra(T_a)
% 1.61/1.66 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_uminus__apply,axiom,
% 1.61/1.66 ! [V_x_2,V_A_2,T_b,T_a] :
% 1.61/1.66 ( class_Groups_Ouminus(T_a)
% 1.61/1.66 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_compl__eq__compl__iff,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Lattices_Oboolean__algebra(T_a)
% 1.61/1.66 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
% 1.61/1.66 <=> V_x_2 = V_y_2 ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_of__real_Obounded,axiom,
% 1.61/1.66 ! [T_a] :
% 1.61/1.66 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.61/1.66 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.61/1.66 => ? [B_K] :
% 1.61/1.66 ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),B_K)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__poly__def,axiom,
% 1.61/1.66 ! [V_x,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 1.61/1.66 & ( V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.61/1.66 => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) )
% 1.61/1.66 & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) ) ) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__greater,axiom,
% 1.61/1.66 ! [V_aa_2,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__less,axiom,
% 1.61/1.66 ! [V_aa_2,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__mult,axiom,
% 1.61/1.66 ! [V_y,V_x,T_a] :
% 1.61/1.66 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__times,axiom,
% 1.61/1.66 ! [V_b,V_a,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn0,axiom,
% 1.61/1.66 ! [T_a] :
% 1.61/1.66 ( class_Groups_Osgn__if(T_a)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__zero__iff,axiom,
% 1.61/1.66 ! [V_x_2,T_a] :
% 1.61/1.66 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.66 => ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.66 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__0__0,axiom,
% 1.61/1.66 ! [V_aa_2,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.66 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__zero,axiom,
% 1.61/1.66 ! [T_a] :
% 1.61/1.66 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__sgn,axiom,
% 1.61/1.66 ! [V_a,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__of__real,axiom,
% 1.61/1.66 ! [V_r,T_a] :
% 1.61/1.66 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_mult__sgn__abs,axiom,
% 1.61/1.66 ! [V_x,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_abs__sgn,axiom,
% 1.61/1.66 ! [V_k,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__one,axiom,
% 1.61/1.66 ! [T_a] :
% 1.61/1.66 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__minus,axiom,
% 1.61/1.66 ! [V_x,T_a] :
% 1.61/1.66 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__1__pos,axiom,
% 1.61/1.66 ! [V_aa_2,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Oone__class_Oone(T_a)
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__pos,axiom,
% 1.61/1.66 ! [V_a,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__1__neg,axiom,
% 1.61/1.66 ! [V_aa_2,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
% 1.61/1.66 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__neg,axiom,
% 1.61/1.66 ! [V_a,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_sgn__if,axiom,
% 1.61/1.66 ! [V_x,T_a] :
% 1.61/1.66 ( class_Groups_Osgn__if(T_a)
% 1.61/1.66 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 1.61/1.66 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.66 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 1.61/1.66 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.61/1.66 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_norm__sgn,axiom,
% 1.61/1.66 ! [V_x,T_a] :
% 1.61/1.66 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.61/1.66 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.66 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 1.61/1.66 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.66 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_order__1,axiom,
% 1.61/1.66 ! [V_p,V_a,T_a] :
% 1.61/1.66 ( class_Rings_Oidom(T_a)
% 1.61/1.66 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_offset__poly__pCons,axiom,
% 1.61/1.66 ! [V_h,V_p,V_a,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.66 => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__0__right,axiom,
% 1.61/1.66 ! [V_a,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.66 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__diff,axiom,
% 1.61/1.66 ! [V_z,V_y,V_x,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__ring__1(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)
% 1.61/1.66 => c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_minus__dvd__iff,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__ring__1(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)
% 1.61/1.66 <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__minus__iff,axiom,
% 1.61/1.66 ! [V_y_2,V_x_2,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__ring__1(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
% 1.61/1.66 <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_inf__period_I4_J,axiom,
% 1.61/1.66 ! [V_ta_2,V_D_2,V_d_2,T_a] :
% 1.61/1.66 ( ( class_Rings_Ocomm__ring(T_a)
% 1.61/1.66 & class_Rings_Odvd(T_a) )
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
% 1.61/1.66 => ! [B_x,B_k] :
% 1.61/1.66 ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))
% 1.61/1.66 <=> c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_ta_2)) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_inf__period_I3_J,axiom,
% 1.61/1.66 ! [V_ta_2,V_D_2,V_d_2,T_a] :
% 1.61/1.66 ( ( class_Rings_Ocomm__ring(T_a)
% 1.61/1.66 & class_Rings_Odvd(T_a) )
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
% 1.61/1.66 => ! [B_x,B_k] :
% 1.61/1.66 ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))
% 1.61/1.66 <=> c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_ta_2)) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_smult__dvd__iff,axiom,
% 1.61/1.66 ! [V_qa_2,V_pb_2,V_aa_2,T_a] :
% 1.61/1.66 ( class_Fields_Ofield(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_aa_2,V_pb_2),V_qa_2)
% 1.61/1.66 <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.66 => V_qa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 1.61/1.66 & ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.66 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pb_2,V_qa_2) ) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_unity__coeff__ex,axiom,
% 1.61/1.66 ! [V_l_2,V_P_2,T_a] :
% 1.61/1.66 ( ( class_Rings_Odvd(T_a)
% 1.61/1.66 & class_Rings_Osemiring__0(T_a) )
% 1.61/1.66 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
% 1.61/1.66 <=> ? [B_x] :
% 1.61/1.66 ( c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a)))
% 1.61/1.66 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__if__abs__eq,axiom,
% 1.61/1.66 ! [V_k,V_l,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Groups_Oabs__class_Oabs(T_a,V_l) = c_Groups_Oabs__class_Oabs(T_a,V_k)
% 1.61/1.66 => c_Rings_Odvd__class_Odvd(T_a,V_l,V_k) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_abs__dvd__iff,axiom,
% 1.61/1.66 ! [V_ka_2,V_ma_2,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oabs__class_Oabs(T_a,V_ma_2),V_ka_2)
% 1.61/1.66 <=> c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_ka_2) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__abs__iff,axiom,
% 1.61/1.66 ! [V_ka_2,V_ma_2,T_a] :
% 1.61/1.66 ( class_Rings_Olinordered__idom(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,V_ma_2,c_Groups_Oabs__class_Oabs(T_a,V_ka_2))
% 1.61/1.66 <=> c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_ka_2) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__power__same,axiom,
% 1.61/1.66 ! [V_n,V_y,V_x,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 1.61/1.66 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_one__dvd,axiom,
% 1.61/1.66 ! [V_a,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.66 => c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_offset__poly__eq__0__iff,axiom,
% 1.61/1.66 ! [V_h_2,V_pb_2,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.66 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pb_2,V_h_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.61/1.66 <=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_offset__poly__0,axiom,
% 1.61/1.66 ! [V_h,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.61/1.66 => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__add,axiom,
% 1.61/1.66 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
% 1.61/1.66 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__trans,axiom,
% 1.61/1.66 ! [V_c,V_b,V_a,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)
% 1.61/1.66 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__refl,axiom,
% 1.61/1.66 ! [V_a,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.66 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_a) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__0__left,axiom,
% 1.61/1.66 ! [V_a,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.61/1.66 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__mult__cancel__left,axiom,
% 1.61/1.66 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.61/1.66 ( class_Rings_Oidom(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 1.61/1.66 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.66 | c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__mult__cancel__right,axiom,
% 1.61/1.66 ! [V_b_2,V_ca_2,V_aa_2,T_a] :
% 1.61/1.66 ( class_Rings_Oidom(T_a)
% 1.61/1.66 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
% 1.61/1.66 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.61/1.66 | c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2) ) ) ) ).
% 1.61/1.66
% 1.61/1.66 fof(fact_dvd__triv__left,axiom,
% 1.61/1.66 ! [V_b,V_a,T_a] :
% 1.61/1.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.61/1.66 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ).
% 1.61/1.66
% 1.61/1.66 %----Arity declarations (289)
% 1.61/1.66 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 1.61/1.66 ! [T_1] :
% 1.61/1.66 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.61/1.66 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 1.61/1.66 ! [T_2,T_1] :
% 1.61/1.66 ( class_Lattices_Oboolean__algebra(T_1)
% 1.61/1.66 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_fun__Orderings_Opreorder,axiom,
% 1.61/1.66 ! [T_2,T_1] :
% 1.61/1.66 ( class_Orderings_Opreorder(T_1)
% 1.61/1.66 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_fun__Orderings_Oorder,axiom,
% 1.61/1.66 ! [T_2,T_1] :
% 1.61/1.66 ( class_Orderings_Oorder(T_1)
% 1.61/1.66 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_fun__Orderings_Oord,axiom,
% 1.61/1.66 ! [T_2,T_1] :
% 1.61/1.66 ( class_Orderings_Oord(T_1)
% 1.61/1.66 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_fun__Groups_Ouminus,axiom,
% 1.61/1.66 ! [T_2,T_1] :
% 1.61/1.66 ( class_Groups_Ouminus(T_1)
% 1.61/1.66 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_fun__Groups_Ominus,axiom,
% 1.61/1.66 ! [T_2,T_1] :
% 1.61/1.66 ( class_Groups_Ominus(T_1)
% 1.61/1.66 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.61/1.66 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.61/1.66 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.61/1.66 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 1.61/1.66 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 1.61/1.66 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 1.61/1.66 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 1.61/1.66 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 1.61/1.66 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 1.61/1.66 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 1.61/1.66 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 1.61/1.66 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 1.61/1.66 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 1.61/1.66 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 1.61/1.66 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 1.61/1.66 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 1.61/1.66 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 1.61/1.66 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 1.61/1.66 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 1.61/1.66 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 1.61/1.66 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 1.61/1.66 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 1.61/1.66 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 1.61/1.66 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 1.61/1.66 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 1.61/1.66 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 1.61/1.66 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 1.61/1.66 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 1.61/1.66 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 1.61/1.66 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 1.61/1.66 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 1.61/1.66 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 1.61/1.66 class_Orderings_Opreorder(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 1.61/1.66 class_Orderings_Olinorder(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 1.61/1.66 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 1.61/1.66 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 1.61/1.66 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 1.61/1.66 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 1.61/1.66 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 1.61/1.66 class_Rings_Omult__zero(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 1.61/1.66 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 1.61/1.66 class_Orderings_Oorder(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 1.61/1.66 class_Int_Oring__char__0(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 1.61/1.66 class_Rings_Osemiring(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 1.61/1.66 class_Orderings_Oord(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 1.61/1.66 class_Groups_Ouminus(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 1.61/1.66 class_Groups_Osgn__if(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 1.61/1.66 class_Groups_Oabs__if(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 1.61/1.66 class_Rings_Oring__1(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 1.61/1.66 class_Groups_Ominus(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Power_Opower,axiom,
% 1.61/1.66 class_Power_Opower(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 1.61/1.66 class_Groups_Ozero(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Oring,axiom,
% 1.61/1.66 class_Rings_Oring(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 1.61/1.66 class_Rings_Oidom(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Groups_Oone,axiom,
% 1.61/1.66 class_Groups_Oone(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 1.61/1.66 class_Rings_Odvd(tc_Int_Oint) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.61/1.66 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.61/1.66 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.61/1.66 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 1.61/1.66 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 1.61/1.66 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 1.61/1.66 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 1.61/1.66 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 1.61/1.66 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 1.61/1.66 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 1.61/1.66 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 1.61/1.66 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 1.61/1.66 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 1.61/1.66 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 1.61/1.66 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 1.61/1.66 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 1.61/1.66 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 1.61/1.66 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 1.61/1.66 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 1.61/1.66 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 1.61/1.66 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 1.61/1.66 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 1.61/1.66 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 1.61/1.66 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 1.61/1.66 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 1.61/1.66 class_Orderings_Oorder(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 1.61/1.66 class_Rings_Osemiring(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 1.61/1.66 class_Orderings_Oord(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 1.61/1.66 class_Groups_Ominus(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Power_Opower,axiom,
% 1.61/1.66 class_Power_Opower(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 1.61/1.66 class_Groups_Ozero(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 1.61/1.66 class_Groups_Oone(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 1.61/1.66 class_Rings_Odvd(tc_Nat_Onat) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 1.61/1.66 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 1.61/1.66 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 1.61/1.66 class_Orderings_Oorder(tc_HOL_Obool) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 1.61/1.66 class_Orderings_Oord(tc_HOL_Obool) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 1.61/1.66 class_Groups_Ouminus(tc_HOL_Obool) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 1.61/1.66 class_Groups_Ominus(tc_HOL_Obool) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.61/1.66 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.61/1.66 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.61/1.66 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
% 1.61/1.66 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 1.61/1.66 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 1.61/1.66 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 1.61/1.66 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
% 1.61/1.66 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 1.61/1.66 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 1.61/1.66 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 1.61/1.66 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 1.61/1.66 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 1.61/1.66 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 1.61/1.66 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 1.61/1.66 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 1.61/1.66 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 1.61/1.66 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 1.61/1.66 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 1.61/1.66 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 1.61/1.66 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__RealVector_Oreal__div__algebra,axiom,
% 1.61/1.66 class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 1.61/1.66 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 1.61/1.66 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
% 1.61/1.66 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
% 1.61/1.66 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 1.61/1.66 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 1.61/1.66 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 1.61/1.66 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
% 1.61/1.66 class_Fields_Olinordered__field(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 1.61/1.66 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
% 1.61/1.66 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 1.61/1.66 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 1.61/1.66 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 1.61/1.66 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 1.61/1.66 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 1.61/1.66 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
% 1.61/1.66 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
% 1.61/1.66 class_Rings_Odivision__ring(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 1.61/1.66 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 1.61/1.66 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 1.61/1.66 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 1.61/1.66 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 1.61/1.66 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 1.61/1.66 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 1.61/1.66 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 1.61/1.66 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 1.61/1.66 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 1.61/1.66 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 1.61/1.66 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 1.61/1.66 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 1.61/1.66 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 1.61/1.66 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 1.61/1.66 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 1.61/1.66 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 1.61/1.66 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
% 1.61/1.66 class_Groups_Ouminus(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom,
% 1.61/1.66 class_Groups_Osgn__if(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Oabs__if,axiom,
% 1.61/1.66 class_Groups_Oabs__if(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 1.61/1.66 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
% 1.61/1.66 class_Groups_Ominus(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 1.61/1.66 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 1.61/1.66 class_Power_Opower(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 1.61/1.66 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 1.61/1.66 class_Rings_Oring(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 1.61/1.66 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 1.61/1.66 class_Groups_Oone(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
% 1.61/1.66 class_Rings_Odvd(tc_RealDef_Oreal) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.61/1.66 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 1.61/1.66 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
% 1.61/1.66 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 1.61/1.66 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 1.61/1.66 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 1.61/1.66 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 1.61/1.66 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 1.61/1.66 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__RealVector_Oreal__div__algebra,axiom,
% 1.61/1.66 class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
% 1.61/1.66 class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
% 1.61/1.66 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 1.61/1.66 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 1.61/1.66 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 1.61/1.66 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 1.61/1.66 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 1.61/1.66 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 1.61/1.66
% 1.61/1.66 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 1.61/1.67 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 1.61/1.67 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
% 1.61/1.67 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 1.61/1.67 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 1.61/1.67 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 1.61/1.67 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 1.61/1.67 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 1.61/1.67 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 1.61/1.67 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 1.61/1.67 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 1.61/1.67 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 1.61/1.67 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 1.61/1.67 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 1.61/1.67 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 1.61/1.67 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
% 1.61/1.67 class_Groups_Ouminus(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 1.61/1.67 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
% 1.61/1.67 class_Groups_Ominus(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 1.61/1.67 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 1.61/1.67 class_Power_Opower(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 1.61/1.67 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 1.61/1.67 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 1.61/1.67 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 1.61/1.67 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
% 1.61/1.67 class_Rings_Odvd(tc_Complex_Ocomplex) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Oidom(T_1)
% 1.61/1.67 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.61/1.67 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Oidom(T_1)
% 1.61/1.67 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Oidom(T_1)
% 1.61/1.67 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.61/1.67 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.61/1.67 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.61/1.67 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.61/1.67 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Oidom(T_1)
% 1.61/1.67 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.61/1.67 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.61/1.67 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.61/1.67 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.61/1.67 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Groups_Oab__group__add(T_1)
% 1.61/1.67 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.61/1.67 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.61/1.67 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__ring__1(T_1)
% 1.61/1.67 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.61/1.67 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.61/1.67 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Groups_Oab__group__add(T_1)
% 1.61/1.67 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.61/1.67 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__ring(T_1)
% 1.61/1.67 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.61/1.67 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Groups_Oab__group__add(T_1)
% 1.61/1.67 => class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Olinordered__idom(T_1)
% 1.61/1.67 => class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__ring__1(T_1)
% 1.61/1.67 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Groups_Oab__group__add(T_1)
% 1.61/1.67 => class_Groups_Ominus(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Power_Opower,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.61/1.67 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Groups_Ozero(T_1)
% 1.61/1.67 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__ring(T_1)
% 1.61/1.67 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Oidom(T_1)
% 1.61/1.67 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.61/1.67 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
% 1.61/1.67 ! [T_1] :
% 1.61/1.67 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.61/1.67 => class_Rings_Odvd(tc_Polynomial_Opoly(T_1)) ) ).
% 1.61/1.67
% 1.61/1.67 %----Conjectures (1)
% 1.61/1.67 fof(conj_0,conjecture,
% 1.61/1.67 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 1.61/1.67
% 1.61/1.67 %------------------------------------------------------------------------------
% 1.61/1.67 %-------------------------------------------
% 1.61/1.67 % Proof found
% 1.61/1.67 % SZS status Theorem for theBenchmark
% 1.61/1.67 % SZS output start Proof
% 1.61/1.67 %ClaNum:1813(EqnAxiom:204)
% 1.61/1.67 %VarNum:8820(SingletonVarNum:3025)
% 1.61/1.67 %MaxLitNum:7
% 1.61/1.67 %MaxfuncDepth:9
% 1.61/1.67 %SharedTerms:456
% 1.61/1.67 %goalClause: 603
% 1.61/1.67 %singleGoalClaCount:1
% 1.61/1.67 [205]P1(a1)
% 1.61/1.67 [206]P1(a2)
% 1.61/1.67 [207]P1(a3)
% 1.61/1.67 [208]P2(a1)
% 1.61/1.67 [209]P2(a4)
% 1.61/1.67 [210]P47(a1)
% 1.61/1.67 [211]P47(a4)
% 1.61/1.67 [212]P50(a1)
% 1.61/1.67 [213]P50(a3)
% 1.61/1.67 [214]P62(a1)
% 1.61/1.67 [215]P62(a3)
% 1.61/1.67 [216]P51(a1)
% 1.61/1.67 [217]P51(a4)
% 1.61/1.67 [218]P48(a1)
% 1.61/1.67 [219]P48(a4)
% 1.61/1.67 [220]P52(a1)
% 1.61/1.67 [221]P52(a4)
% 1.61/1.67 [222]P3(a1)
% 1.61/1.67 [223]P3(a2)
% 1.61/1.67 [224]P3(a4)
% 1.61/1.67 [225]P3(a3)
% 1.61/1.67 [226]P63(a1)
% 1.61/1.67 [227]P63(a2)
% 1.61/1.67 [228]P63(a3)
% 1.61/1.67 [229]P70(a1)
% 1.61/1.67 [230]P70(a3)
% 1.61/1.67 [231]P72(a1)
% 1.61/1.67 [232]P72(a2)
% 1.61/1.67 [233]P72(a3)
% 1.61/1.67 [234]P71(a1)
% 1.61/1.67 [235]P71(a2)
% 1.61/1.67 [236]P71(a3)
% 1.61/1.67 [237]P27(a1)
% 1.61/1.67 [238]P27(a2)
% 1.61/1.67 [239]P27(a4)
% 1.61/1.67 [240]P27(a3)
% 1.61/1.67 [241]P64(a1)
% 1.61/1.67 [242]P64(a2)
% 1.61/1.67 [243]P64(a3)
% 1.61/1.67 [244]P65(a1)
% 1.61/1.67 [245]P65(a2)
% 1.61/1.67 [246]P65(a3)
% 1.61/1.67 [247]P58(a1)
% 1.61/1.67 [248]P58(a3)
% 1.61/1.67 [249]P49(a1)
% 1.61/1.67 [250]P49(a4)
% 1.61/1.67 [251]P66(a1)
% 1.61/1.67 [252]P66(a3)
% 1.61/1.67 [253]P67(a1)
% 1.61/1.67 [254]P67(a3)
% 1.61/1.67 [255]P68(a1)
% 1.61/1.67 [256]P68(a2)
% 1.61/1.67 [257]P68(a4)
% 1.61/1.67 [258]P68(a3)
% 1.61/1.67 [259]P74(a1)
% 1.61/1.67 [260]P74(a4)
% 1.61/1.67 [261]P74(a3)
% 1.61/1.67 [262]P69(a1)
% 1.61/1.67 [263]P69(a2)
% 1.61/1.67 [264]P69(a4)
% 1.61/1.67 [265]P69(a3)
% 1.61/1.67 [266]P78(a1)
% 1.61/1.67 [267]P78(a2)
% 1.61/1.67 [268]P78(a4)
% 1.61/1.67 [269]P78(a3)
% 1.61/1.67 [270]P79(a1)
% 1.61/1.67 [271]P79(a2)
% 1.61/1.67 [272]P79(a4)
% 1.61/1.67 [273]P79(a3)
% 1.61/1.67 [274]P53(a1)
% 1.61/1.67 [275]P53(a2)
% 1.61/1.67 [276]P53(a4)
% 1.61/1.67 [277]P53(a3)
% 1.61/1.67 [278]P75(a1)
% 1.61/1.67 [279]P75(a4)
% 1.61/1.67 [280]P75(a3)
% 1.61/1.67 [281]P4(a1)
% 1.61/1.67 [282]P4(a2)
% 1.61/1.67 [283]P4(a4)
% 1.61/1.67 [284]P4(a3)
% 1.61/1.67 [285]P59(a1)
% 1.61/1.67 [286]P59(a2)
% 1.61/1.67 [287]P59(a3)
% 1.61/1.67 [288]P80(a1)
% 1.61/1.67 [289]P80(a2)
% 1.61/1.67 [290]P80(a4)
% 1.61/1.67 [291]P80(a3)
% 1.61/1.67 [292]P5(a1)
% 1.61/1.67 [293]P14(a1)
% 1.61/1.67 [294]P6(a1)
% 1.61/1.67 [295]P6(a4)
% 1.61/1.67 [296]P7(a1)
% 1.61/1.67 [297]P7(a4)
% 1.61/1.67 [298]P28(a1)
% 1.61/1.67 [299]P28(a2)
% 1.61/1.67 [300]P28(a3)
% 1.61/1.67 [301]P23(a1)
% 1.61/1.67 [302]P23(a4)
% 1.61/1.67 [303]P23(a3)
% 1.61/1.67 [304]P15(a1)
% 1.61/1.67 [305]P15(a4)
% 1.61/1.67 [306]P15(a3)
% 1.61/1.67 [307]P24(a1)
% 1.61/1.67 [308]P24(a3)
% 1.61/1.67 [309]P29(a1)
% 1.61/1.67 [310]P29(a3)
% 1.61/1.67 [311]P45(a1)
% 1.61/1.67 [312]P45(a4)
% 1.61/1.67 [313]P60(a1)
% 1.61/1.67 [314]P60(a4)
% 1.61/1.67 [315]P60(a3)
% 1.61/1.67 [316]P76(a1)
% 1.61/1.67 [317]P76(a4)
% 1.61/1.67 [318]P76(a3)
% 1.61/1.67 [319]P46(a1)
% 1.61/1.67 [320]P46(a4)
% 1.61/1.67 [321]P77(a1)
% 1.61/1.67 [322]P77(a4)
% 1.61/1.67 [323]P77(a3)
% 1.61/1.67 [324]P35(a1)
% 1.61/1.67 [325]P35(a2)
% 1.61/1.67 [326]P35(a4)
% 1.61/1.67 [327]P35(a3)
% 1.61/1.67 [328]P16(a1)
% 1.61/1.67 [329]P16(a2)
% 1.61/1.67 [330]P16(a4)
% 1.61/1.67 [331]P16(a3)
% 1.61/1.67 [332]P18(a1)
% 1.61/1.67 [333]P18(a2)
% 1.61/1.67 [334]P18(a4)
% 1.61/1.67 [335]P18(a3)
% 1.61/1.67 [336]P19(a1)
% 1.61/1.67 [337]P19(a2)
% 1.61/1.67 [338]P19(a4)
% 1.61/1.67 [339]P19(a3)
% 1.61/1.67 [340]P17(a1)
% 1.61/1.67 [341]P17(a2)
% 1.61/1.67 [342]P17(a4)
% 1.61/1.67 [343]P17(a3)
% 1.61/1.67 [344]P30(a1)
% 1.61/1.67 [345]P30(a2)
% 1.61/1.67 [346]P30(a4)
% 1.61/1.67 [347]P30(a3)
% 1.61/1.67 [348]P22(a1)
% 1.61/1.67 [349]P22(a2)
% 1.61/1.67 [350]P22(a4)
% 1.61/1.67 [351]P22(a3)
% 1.61/1.67 [352]P25(a1)
% 1.61/1.67 [353]P25(a2)
% 1.61/1.67 [354]P25(a4)
% 1.61/1.67 [355]P25(a3)
% 1.61/1.67 [356]P31(a1)
% 1.61/1.67 [357]P31(a2)
% 1.61/1.67 [358]P31(a3)
% 1.61/1.67 [359]P32(a1)
% 1.61/1.67 [360]P32(a2)
% 1.61/1.67 [361]P32(a3)
% 1.61/1.67 [362]P34(a1)
% 1.61/1.67 [363]P34(a2)
% 1.61/1.67 [364]P34(a3)
% 1.61/1.67 [365]P56(a1)
% 1.61/1.67 [366]P56(a2)
% 1.61/1.67 [367]P56(a4)
% 1.61/1.67 [368]P56(a3)
% 1.61/1.67 [369]P81(a1)
% 1.61/1.67 [370]P81(a2)
% 1.61/1.67 [371]P81(a4)
% 1.61/1.67 [372]P81(a3)
% 1.61/1.67 [373]P54(a1)
% 1.61/1.67 [374]P54(a4)
% 1.61/1.67 [375]P54(a3)
% 1.61/1.67 [376]P33(a1)
% 1.61/1.67 [377]P33(a3)
% 1.61/1.67 [378]P73(a1)
% 1.61/1.67 [379]P73(a3)
% 1.61/1.67 [380]P20(a1)
% 1.61/1.67 [381]P20(a3)
% 1.61/1.67 [382]P57(a1)
% 1.61/1.67 [383]P57(a2)
% 1.61/1.67 [384]P57(a4)
% 1.61/1.67 [385]P57(a3)
% 1.61/1.67 [386]P38(a1)
% 1.61/1.67 [387]P38(a4)
% 1.61/1.67 [388]P38(a3)
% 1.61/1.67 [389]P55(a1)
% 1.61/1.67 [390]P55(a4)
% 1.61/1.67 [391]P55(a3)
% 1.61/1.67 [392]P39(a1)
% 1.61/1.67 [393]P39(a2)
% 1.61/1.67 [394]P39(a3)
% 1.61/1.67 [395]P39(a71)
% 1.61/1.67 [396]P40(a1)
% 1.61/1.67 [397]P40(a2)
% 1.61/1.67 [398]P40(a3)
% 1.61/1.67 [399]P40(a71)
% 1.61/1.67 [400]P41(a1)
% 1.61/1.67 [401]P41(a2)
% 1.61/1.67 [402]P41(a3)
% 1.61/1.67 [403]P44(a1)
% 1.61/1.67 [404]P44(a2)
% 1.61/1.67 [405]P44(a3)
% 1.61/1.67 [406]P44(a71)
% 1.61/1.67 [407]P42(a71)
% 1.61/1.67 [408]P26(a1)
% 1.61/1.67 [409]P26(a2)
% 1.61/1.67 [410]P26(a4)
% 1.61/1.67 [411]P26(a3)
% 1.61/1.67 [412]P26(a71)
% 1.61/1.67 [413]P36(a1)
% 1.61/1.67 [414]P36(a4)
% 1.61/1.67 [415]P36(a3)
% 1.61/1.67 [416]P36(a71)
% 1.61/1.67 [417]P37(a1)
% 1.61/1.67 [418]P37(a3)
% 1.61/1.67 [419]P61(a1)
% 1.61/1.67 [420]P61(a2)
% 1.61/1.67 [421]P61(a4)
% 1.61/1.67 [422]P61(a3)
% 1.61/1.67 [423]P21(a1)
% 1.61/1.67 [424]P21(a2)
% 1.61/1.67 [425]P21(a4)
% 1.61/1.67 [426]P21(a3)
% 1.61/1.67 [435]E(f28(a4,a7),f12(a4,a7))
% 1.61/1.67 [436]E(f8(a4,a73),f8(a4,a80))
% 1.61/1.67 [437]E(f8(a4,a32),f8(a4,a73))
% 1.61/1.67 [438]E(f8(a4,a39),f8(a4,a73))
% 1.61/1.67 [453]P9(a1,a81,f6(a1))
% 1.61/1.67 [454]P9(a1,a57,f6(a1))
% 1.61/1.67 [455]P9(a1,f5(a1),a81)
% 1.61/1.67 [456]P9(a1,f5(a1),a74)
% 1.61/1.67 [457]P9(a1,f5(a1),a57)
% 1.61/1.67 [458]P9(a1,f5(a1),a33)
% 1.61/1.67 [459]P9(a1,f5(a1),a34)
% 1.61/1.67 [472]P9(a3,f5(a3),f6(a3))
% 1.61/1.67 [474]P8(a3,f5(a3),f6(a3))
% 1.61/1.67 [574]~E(f5(a2),a78)
% 1.61/1.67 [575]~E(f5(a4),a83)
% 1.61/1.67 [576]~E(f5(a4),a76)
% 1.61/1.67 [577]~E(f5(a4),a7)
% 1.61/1.67 [578]~E(f6(a4),a7)
% 1.61/1.67 [579]~E(f5(a2),a41)
% 1.61/1.67 [580]~E(f5(a4),a49)
% 1.61/1.67 [581]~E(f6(a1),f5(a1))
% 1.61/1.67 [582]~E(f6(a3),f5(a3))
% 1.61/1.67 [591]~P10(a4,a4,f17(a4,a79))
% 1.61/1.67 [592]~P10(a4,a4,f17(a4,a73))
% 1.61/1.67 [594]~P10(a4,a4,f17(a4,a80))
% 1.61/1.67 [427]E(f16(f5(a1)),f5(a2))
% 1.61/1.67 [428]E(f16(f6(a1)),f6(a2))
% 1.61/1.67 [429]E(f27(f5(a1)),f5(a2))
% 1.61/1.67 [430]E(f27(f6(a1)),f6(a2))
% 1.61/1.67 [431]E(f28(a1,f5(a1)),f5(a1))
% 1.61/1.67 [432]E(f12(a3,f5(a3)),f5(a3))
% 1.61/1.67 [433]E(f29(a2,f5(a2)),f5(a1))
% 1.61/1.67 [434]E(f29(a2,f6(a2)),f6(a1))
% 1.61/1.67 [477]E(f56(f17(a4,a80),f5(a4)),f56(f17(a4,a73),a75))
% 1.61/1.67 [504]P9(a2,f14(a2,a78,f6(a2)),f8(a4,a73))
% 1.61/1.67 [526]P8(a1,f56(f56(f13(a1),a81),f30(a4,a83)),f56(f56(f13(a1),f6(a1)),f30(a4,a83)))
% 1.61/1.67 [555]E(f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),f5(a4)),f6(a4))
% 1.61/1.67 [557]E(f11(a4,f14(a4,f6(a4),f56(f56(f13(a4),f56(f56(f23(a4),a83),a78)),a76)),f6(a4)),f11(a4,f5(a4),f6(a4)))
% 1.61/1.67 [583]~E(f56(f17(a4,a73),a75),f5(a4))
% 1.61/1.67 [584]~E(f56(f17(a4,a80),f5(a4)),f5(a4))
% 1.61/1.67 [590]~E(f14(a2,a78,f6(a2)),f8(a4,a73))
% 1.61/1.67 [469]E(f31(a4,f12(a1,f6(a1))),f12(a4,f6(a4)))
% 1.61/1.67 [470]E(f56(f56(f13(a4),a7),a7),f12(a4,f6(a4)))
% 1.61/1.67 [491]P9(a1,f5(a1),f56(f56(f23(a1),a81),a78))
% 1.61/1.67 [540]P8(a1,f30(a4,f56(f56(f13(a4),f31(a4,a81)),a83)),f30(a4,a83))
% 1.61/1.67 [514]E(f56(f56(f13(a4),f56(f56(f23(a4),a83),a78)),a76),f12(a4,f6(a4)))
% 1.61/1.67 [541]E(f8(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),f8(a4,a80))
% 1.61/1.67 [550]E(f8(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),f14(a2,f14(a2,f8(a4,a82),a78),f6(a2)))
% 1.61/1.67 [551]E(f8(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),f14(a2,f14(a2,f8(a4,a40),a41),f6(a2)))
% 1.61/1.67 [554]E(f8(a4,f20(a4,f6(a4),f18(a4,a76,f11(a2,a78,f6(a2))))),f14(a2,a78,f6(a2)))
% 1.61/1.67 [600]~P10(a4,a4,f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)))
% 1.61/1.67 [601]~P10(a4,a4,f17(a4,f20(a4,f6(a4),f18(a4,a76,f11(a2,a78,f6(a2))))))
% 1.61/1.67 [543]E(f14(a4,f6(a4),f56(f56(f13(a4),f56(f56(f23(a4),a83),a78)),a76)),f5(a4))
% 1.61/1.67 [544]E(f14(a4,f6(a4),f56(f56(f13(a4),f56(f56(f23(a4),a65),a78)),a76)),f5(a4))
% 1.61/1.67 [558]E(f56(f17(a4,f20(a4,f6(a4),f18(a4,a76,f11(a2,a78,f6(a2))))),a42),f5(a4))
% 1.61/1.67 [560]P9(a1,a81,f28(a1,f56(f56(f13(a1),f56(f56(f23(a1),f30(a4,a83)),f14(a2,a78,f6(a2)))),a74)))
% 1.61/1.67 [561]P9(a1,a57,f28(a1,f56(f56(f13(a1),f56(f56(f23(a1),f30(a4,a83)),f14(a2,a78,f6(a2)))),a74)))
% 1.61/1.67 [562]P9(a1,f5(a1),f28(a1,f56(f56(f13(a1),f56(f56(f23(a1),f30(a4,a83)),f14(a2,a78,f6(a2)))),a74)))
% 1.61/1.67 [563]P9(a1,f56(f56(f13(a1),a81),f56(f56(f13(a1),f56(f56(f23(a1),f30(a4,a83)),f14(a2,a78,f6(a2)))),a74)),f6(a1))
% 1.61/1.67 [570]E(f14(a4,f14(a4,f6(a4),f56(f56(f13(a4),f56(f56(f23(a4),f31(a4,a81)),a78)),f56(f56(f13(a4),f56(f56(f23(a4),a83),a78)),a76))),f56(f56(f13(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f56(f56(f13(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83)))),f14(a4,f31(a4,f11(a1,f6(a1),f56(f56(f23(a1),a81),a78))),f56(f56(f13(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f56(f56(f13(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83)))))
% 1.61/1.67 [602]~E(f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),a43),f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),a46))
% 1.61/1.67 [573]P8(a1,f30(a4,f14(a4,f31(a4,f11(a1,f6(a1),f56(f56(f23(a1),a81),a78))),f56(f56(f13(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f56(f56(f13(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83))))),f14(a1,f30(a4,f31(a4,f11(a1,f6(a1),f56(f56(f23(a1),a81),a78)))),f30(a4,f56(f56(f13(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f56(f56(f13(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83))))))
% 1.61/1.67 [603]~P9(a1,f56(f56(f13(a1),f56(f56(f23(a1),a81),a78)),f56(f56(f13(a1),a81),f56(f56(f13(a1),f56(f56(f23(a1),f30(a4,a83)),f14(a2,a78,f6(a2)))),a74))),f56(f56(f13(a1),f56(f56(f23(a1),a81),a78)),f6(a1)))
% 1.61/1.67 [568]E(f14(a4,f31(a4,f11(a1,f6(a1),f56(f56(f23(a1),a81),a78))),f56(f56(f13(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f56(f56(f13(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83)))),f14(a4,f6(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f14(a4,a76,f56(f56(f13(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83)))))))
% 1.61/1.67 [569]E(f14(a4,f14(a4,f6(a4),f56(f56(f13(a4),f56(f56(f23(a4),f31(a4,a81)),a78)),f56(f56(f13(a4),f56(f56(f23(a4),a83),a78)),a76))),f56(f56(f13(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f56(f56(f13(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83)))),f14(a4,f6(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f14(a4,a76,f56(f56(f13(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83)))))))
% 1.61/1.67 [571]E(f30(a4,f14(a4,f31(a4,f11(a1,f6(a1),f56(f56(f23(a1),a81),a78))),f56(f56(f13(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f56(f56(f13(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83))))),f30(a4,f14(a4,f6(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f14(a4,a76,f56(f56(f13(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83))))))))
% 1.61/1.67 [572]P8(a1,f30(a4,f14(a4,f6(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f14(a4,a76,f56(f56(f13(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83))))))),f14(a1,f10(a1,f11(a1,f6(a1),f56(f56(f23(a1),a81),a78))),f30(a4,f56(f56(f13(a4),f56(f56(f13(a4),f56(f56(f23(a4),f56(f56(f13(a4),f31(a4,a81)),a83)),a78)),f56(f56(f13(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f13(a4),f31(a4,a81)),a83))))))
% 1.61/1.67 [447]P8(a1,x4471,x4471)
% 1.61/1.67 [448]P8(a2,x4481,x4481)
% 1.61/1.67 [449]P8(a3,x4491,x4491)
% 1.61/1.67 [586]~P9(a2,x5861,x5861)
% 1.61/1.67 [439]E(f30(a1,x4391),f10(a1,x4391))
% 1.61/1.67 [461]E(f11(a2,x4611,x4611),f5(a2))
% 1.61/1.67 [463]P8(a2,f5(a2),x4631)
% 1.61/1.67 [479]P8(a1,f5(a1),f29(a2,x4791))
% 1.61/1.67 [589]~P9(a2,x5891,f5(a2))
% 1.61/1.67 [595]~P9(a1,f29(a2,x5951),f5(a1))
% 1.61/1.67 [440]E(f16(f29(a2,x4401)),x4401)
% 1.61/1.67 [441]E(f27(f29(a2,x4411)),x4411)
% 1.61/1.67 [442]E(f12(a3,f12(a3,x4421)),x4421)
% 1.61/1.67 [443]E(f10(a1,f29(a2,x4431)),f29(a2,x4431))
% 1.61/1.67 [444]E(f56(f56(f13(a2),x4441),f6(a2)),x4441)
% 1.61/1.67 [445]E(f56(f56(f13(a3),x4451),f6(a3)),x4451)
% 1.61/1.67 [446]E(f56(f56(f13(a2),x4461),f5(a2)),f5(a2))
% 1.61/1.67 [464]E(f14(a2,x4641,f5(a2)),x4641)
% 1.61/1.67 [465]E(f14(a3,x4651,f5(a3)),x4651)
% 1.61/1.67 [466]E(f11(a2,x4661,f5(a2)),x4661)
% 1.61/1.67 [467]E(f14(a2,f5(a2),x4671),x4671)
% 1.61/1.67 [468]E(f14(a3,f5(a3),x4681),x4681)
% 1.61/1.67 [471]E(f11(a2,f5(a2),x4711),f5(a2))
% 1.61/1.67 [478]E(f14(a3,f12(a3,x4781),x4781),f5(a3))
% 1.61/1.67 [480]P8(a1,x4801,f29(a2,f16(x4801)))
% 1.61/1.67 [494]P8(a1,f12(a1,f30(a4,x4941)),f30(a4,x4941))
% 1.61/1.67 [501]E(f56(f17(a4,a73),f14(a4,a75,x5011)),f56(f17(a4,a80),x5011))
% 1.61/1.67 [502]E(f56(f17(a4,a73),f14(a4,a75,x5021)),f56(f17(a4,a32),x5021))
% 1.61/1.67 [503]E(f56(f17(a4,a73),f14(a4,a75,x5031)),f56(f17(a4,a39),x5031))
% 1.61/1.67 [509]P9(a1,f11(a1,x5091,f6(a1)),f29(a2,f27(x5091)))
% 1.61/1.67 [510]P9(a1,f5(a1),f14(a1,f6(a1),f10(a1,x5101)))
% 1.61/1.67 [515]P9(a1,x5151,f14(a1,f29(a2,f27(x5151)),f6(a1)))
% 1.61/1.67 [599]~P9(a1,f14(a1,f10(a1,x5991),f6(a1)),x5991)
% 1.61/1.67 [450]E(f56(f56(f13(a1),f6(a1)),x4501),x4501)
% 1.61/1.67 [451]E(f56(f56(f13(a2),f6(a2)),x4511),x4511)
% 1.61/1.67 [452]E(f56(f56(f13(a3),f6(a3)),x4521),x4521)
% 1.61/1.67 [460]E(f56(f56(f13(a2),f5(a2)),x4601),f5(a2))
% 1.61/1.67 [493]P8(a2,x4931,f56(f56(f13(a2),x4931),x4931))
% 1.61/1.67 [530]P8(a1,f30(a4,f56(f17(a4,a73),a75)),f30(a4,f56(f17(a4,a73),x5301)))
% 1.61/1.67 [535]P8(a1,f30(a4,f56(f17(a4,a80),f5(a4))),f30(a4,f56(f17(a4,a73),x5351)))
% 1.61/1.67 [564]E(f56(f56(f13(a4),f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),x5641)),f56(f17(a4,a80),f5(a4))),f56(f17(a4,a80),x5641))
% 1.61/1.67 [598]~E(f14(a3,f14(a3,f6(a3),x5981),x5981),f5(a3))
% 1.61/1.67 [492]E(f56(f56(f13(a4),a7),f56(f56(f13(a4),a7),x4921)),f12(a4,x4921))
% 1.61/1.67 [527]P8(a2,x5271,f56(f56(f13(a2),x5271),f56(f56(f13(a2),x5271),x5271)))
% 1.61/1.67 [566]E(f14(a4,f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),f5(a4)),f56(f56(f13(a4),f56(f56(f23(a4),x5661),a78)),f56(f17(a4,f20(a4,a76,a82)),x5661))),f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),x5661))
% 1.61/1.67 [567]E(f14(a4,f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),f5(a4)),f56(f56(f13(a4),f56(f56(f23(a4),x5671),a41)),f56(f17(a4,f20(a4,a49,a40)),x5671))),f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),x5671))
% 1.61/1.67 [484]E(f14(a2,x4841,x4842),f14(a2,x4842,x4841))
% 1.61/1.67 [485]E(f14(a3,x4851,x4852),f14(a3,x4852,x4851))
% 1.61/1.67 [495]P8(a2,x4951,f14(a2,x4952,x4951))
% 1.61/1.67 [496]P8(a2,x4961,f14(a2,x4961,x4962))
% 1.61/1.67 [497]P8(a2,f11(a2,x4971,x4972),x4971)
% 1.61/1.67 [596]~P9(a2,f14(a2,x5961,x5962),x5962)
% 1.61/1.67 [597]~P9(a2,f14(a2,x5971,x5972),x5971)
% 1.61/1.67 [487]E(f14(a1,x4871,f12(a1,x4872)),f11(a1,x4871,x4872))
% 1.61/1.67 [488]E(f14(a4,x4881,f12(a4,x4882)),f11(a4,x4881,x4882))
% 1.61/1.67 [490]E(f14(a3,x4901,f12(a3,x4902)),f11(a3,x4901,x4902))
% 1.61/1.67 [498]E(f11(a2,f14(a2,x4981,x4982),x4982),x4981)
% 1.61/1.67 [499]E(f11(a2,f14(a2,x4991,x4992),x4991),x4992)
% 1.61/1.67 [500]E(f11(a2,x5001,f14(a2,x5001,x5002)),f5(a2))
% 1.61/1.67 [511]E(f14(a3,f12(a3,x5111),f12(a3,x5112)),f12(a3,f14(a3,x5111,x5112)))
% 1.61/1.67 [512]E(f14(a1,f29(a2,x5121),f29(a2,x5122)),f29(a2,f14(a2,x5121,x5122)))
% 1.61/1.67 [552]P8(a1,f30(a4,x5521),f14(a1,f30(a4,f14(a4,x5521,x5522)),f30(a4,x5522)))
% 1.61/1.67 [553]P8(a1,f11(a1,f30(a4,f14(a4,x5531,x5532)),f30(a4,x5531)),f30(a4,x5532))
% 1.61/1.67 [481]E(f56(f56(f13(a1),x4811),x4812),f56(f56(f13(a1),x4812),x4811))
% 1.61/1.67 [482]E(f56(f56(f13(a2),x4821),x4822),f56(f56(f13(a2),x4822),x4821))
% 1.61/1.67 [483]E(f56(f56(f13(a3),x4831),x4832),f56(f56(f13(a3),x4832),x4831))
% 1.61/1.67 [516]P8(a3,f5(a3),f56(f56(f23(a3),f10(a3,x5161)),x5162))
% 1.61/1.67 [528]E(f10(a1,f14(a1,x5281,f12(a1,x5282))),f10(a1,f14(a1,x5282,f12(a1,x5281))))
% 1.61/1.67 [506]E(f56(f56(f23(a1),f29(a2,x5061)),x5062),f29(a2,f56(f56(f23(a2),x5061),x5062)))
% 1.61/1.67 [507]E(f31(a4,f56(f56(f23(a1),x5071),x5072)),f56(f56(f23(a4),f31(a4,x5071)),x5072))
% 1.61/1.67 [508]E(f56(f56(f13(a3),f12(a3,x5081)),x5082),f12(a3,f56(f56(f13(a3),x5081),x5082)))
% 1.61/1.67 [513]E(f56(f56(f13(a1),f29(a2,x5131)),f29(a2,x5132)),f29(a2,f56(f56(f13(a2),x5131),x5132)))
% 1.61/1.67 [529]P8(a1,f12(a1,f56(f56(f13(a1),x5291),x5291)),f56(f56(f13(a1),x5292),x5292))
% 1.61/1.67 [518]E(f14(a2,x5181,f14(a2,x5182,x5183)),f14(a2,x5182,f14(a2,x5181,x5183)))
% 1.61/1.67 [519]E(f14(a3,x5191,f14(a3,x5192,x5193)),f14(a3,x5192,f14(a3,x5191,x5193)))
% 1.61/1.67 [520]E(f14(a2,f14(a2,x5201,x5202),x5203),f14(a2,x5201,f14(a2,x5202,x5203)))
% 1.61/1.67 [521]E(f14(a3,f14(a3,x5211,x5212),x5213),f14(a3,x5211,f14(a3,x5212,x5213)))
% 1.61/1.67 [522]E(f11(a2,f11(a2,x5221,x5222),x5223),f11(a2,x5221,f14(a2,x5222,x5223)))
% 1.61/1.67 [523]E(f11(a2,f11(a2,x5231,x5232),x5233),f11(a2,f11(a2,x5231,x5233),x5232))
% 1.61/1.67 [524]E(f11(a2,f14(a2,x5241,x5242),f14(a2,x5243,x5242)),f11(a2,x5241,x5243))
% 1.61/1.67 [525]E(f11(a2,f14(a2,x5251,x5252),f14(a2,x5251,x5253)),f11(a2,x5252,x5253))
% 1.61/1.67 [536]E(f14(a2,f56(f56(f13(a2),x5361),x5362),f56(f56(f13(a2),x5361),x5363)),f56(f56(f13(a2),x5361),f14(a2,x5362,x5363)))
% 1.61/1.67 [537]E(f11(a2,f56(f56(f13(a2),x5371),x5372),f56(f56(f13(a2),x5371),x5373)),f56(f56(f13(a2),x5371),f11(a2,x5372,x5373)))
% 1.61/1.67 [538]E(f14(a3,f56(f56(f13(a3),x5381),x5382),f56(f56(f13(a3),x5381),x5383)),f56(f56(f13(a3),x5381),f14(a3,x5382,x5383)))
% 1.61/1.67 [539]E(f11(a3,f56(f56(f13(a3),x5391),x5392),f56(f56(f13(a3),x5391),x5393)),f56(f56(f13(a3),x5391),f11(a3,x5392,x5393)))
% 1.61/1.67 [542]E(f56(f56(f13(a3),f56(f56(f23(a3),x5421),x5422)),f56(f56(f23(a3),x5421),x5423)),f56(f56(f23(a3),x5421),f14(a2,x5422,x5423)))
% 1.61/1.67 [545]E(f14(a1,f56(f56(f13(a1),x5451),x5452),f56(f56(f13(a1),x5453),x5452)),f56(f56(f13(a1),f14(a1,x5451,x5453)),x5452))
% 1.61/1.67 [546]E(f14(a2,f56(f56(f13(a2),x5461),x5462),f56(f56(f13(a2),x5463),x5462)),f56(f56(f13(a2),f14(a2,x5461,x5463)),x5462))
% 1.61/1.67 [547]E(f11(a2,f56(f56(f13(a2),x5471),x5472),f56(f56(f13(a2),x5473),x5472)),f56(f56(f13(a2),f11(a2,x5471,x5473)),x5472))
% 1.61/1.67 [548]E(f14(a3,f56(f56(f13(a3),x5481),x5482),f56(f56(f13(a3),x5483),x5482)),f56(f56(f13(a3),f14(a3,x5481,x5483)),x5482))
% 1.61/1.67 [549]E(f11(a3,f56(f56(f13(a3),x5491),x5492),f56(f56(f13(a3),x5493),x5492)),f56(f56(f13(a3),f11(a3,x5491,x5493)),x5492))
% 1.61/1.67 [531]E(f56(f56(f23(a3),f56(f56(f23(a3),x5311),x5312)),x5313),f56(f56(f23(a3),x5311),f56(f56(f13(a2),x5312),x5313)))
% 1.61/1.67 [532]E(f56(f56(f13(a1),f56(f56(f13(a1),x5321),x5322)),x5323),f56(f56(f13(a1),x5321),f56(f56(f13(a1),x5322),x5323)))
% 1.61/1.67 [533]E(f56(f56(f13(a2),f56(f56(f13(a2),x5331),x5332)),x5333),f56(f56(f13(a2),x5331),f56(f56(f13(a2),x5332),x5333)))
% 1.61/1.67 [534]E(f56(f56(f13(a3),f56(f56(f13(a3),x5341),x5342)),x5343),f56(f56(f13(a3),x5341),f56(f56(f13(a3),x5342),x5343)))
% 1.61/1.67 [517]E(f56(f56(f24(x5171,x5172,x5173),x5174),f5(a2)),x5172)
% 1.61/1.67 [559]P8(a1,f10(a1,f14(a1,f14(a1,x5591,x5592),f14(a1,f12(a1,x5593),f12(a1,x5594)))),f14(a1,f10(a1,f14(a1,x5591,f12(a1,x5593))),f10(a1,f14(a1,x5592,f12(a1,x5594)))))
% 1.61/1.67 [556]E(f14(a2,f56(f56(f13(a2),x5561),x5562),f14(a2,f56(f56(f13(a2),x5563),x5562),x5564)),f14(a2,f56(f56(f13(a2),f14(a2,x5561,x5563)),x5562),x5564))
% 1.61/1.67 [604]~P58(x6041)+P1(f72(x6041))
% 1.61/1.67 [605]~P58(x6051)+P50(f72(x6051))
% 1.61/1.67 [606]~P58(x6061)+P62(f72(x6061))
% 1.61/1.67 [607]~P56(x6071)+P3(f72(x6071))
% 1.61/1.67 [608]~P58(x6081)+P63(f72(x6081))
% 1.61/1.67 [609]~P58(x6091)+P70(f72(x6091))
% 1.61/1.67 [610]~P58(x6101)+P72(f72(x6101))
% 1.61/1.67 [611]~P58(x6111)+P71(f72(x6111))
% 1.61/1.67 [612]~P56(x6121)+P27(f72(x6121))
% 1.61/1.67 [613]~P58(x6131)+P64(f72(x6131))
% 1.61/1.67 [614]~P58(x6141)+P65(f72(x6141))
% 1.61/1.67 [615]~P58(x6151)+P58(f72(x6151))
% 1.61/1.67 [616]~P58(x6161)+P66(f72(x6161))
% 1.61/1.67 [617]~P58(x6171)+P67(f72(x6171))
% 1.61/1.67 [618]~P60(x6181)+P68(f72(x6181))
% 1.61/1.67 [619]~P60(x6191)+P74(f72(x6191))
% 1.61/1.67 [620]~P57(x6201)+P69(f72(x6201))
% 1.61/1.67 [621]~P56(x6211)+P78(f72(x6211))
% 1.61/1.67 [622]~P57(x6221)+P79(f72(x6221))
% 1.61/1.67 [623]~P57(x6231)+P53(f72(x6231))
% 1.61/1.67 [624]~P60(x6241)+P75(f72(x6241))
% 1.61/1.67 [625]~P56(x6251)+P4(f72(x6251))
% 1.61/1.67 [626]~P58(x6261)+P59(f72(x6261))
% 1.61/1.67 [627]~P57(x6271)+P80(f72(x6271))
% 1.61/1.67 [628]~P58(x6281)+P28(f72(x6281))
% 1.61/1.67 [629]~P15(x6291)+P23(f72(x6291))
% 1.61/1.67 [630]~P15(x6301)+P15(f72(x6301))
% 1.61/1.67 [631]~P58(x6311)+P24(f72(x6311))
% 1.61/1.67 [632]~P58(x6321)+P29(f72(x6321))
% 1.61/1.67 [633]~P60(x6331)+P60(f72(x6331))
% 1.61/1.67 [634]~P55(x6341)+P76(f72(x6341))
% 1.61/1.67 [635]~P54(x6351)+P77(f72(x6351))
% 1.61/1.67 [636]~P35(x6361)+P35(f72(x6361))
% 1.61/1.67 [637]~P57(x6371)+P16(f72(x6371))
% 1.61/1.67 [638]~P21(x6381)+P18(f72(x6381))
% 1.61/1.67 [639]~P21(x6391)+P19(f72(x6391))
% 1.61/1.67 [640]~P22(x6401)+P17(f72(x6401))
% 1.61/1.67 [641]~P56(x6411)+P30(f72(x6411))
% 1.61/1.67 [642]~P22(x6421)+P22(f72(x6421))
% 1.61/1.67 [643]~P22(x6431)+P25(f72(x6431))
% 1.61/1.67 [644]~P58(x6441)+P31(f72(x6441))
% 1.61/1.67 [645]~P58(x6451)+P32(f72(x6451))
% 1.61/1.67 [646]~P58(x6461)+P34(f72(x6461))
% 1.61/1.67 [647]~P56(x6471)+P56(f72(x6471))
% 1.61/1.67 [648]~P60(x6481)+P81(f72(x6481))
% 1.61/1.67 [649]~P54(x6491)+P54(f72(x6491))
% 1.61/1.67 [650]~P58(x6501)+P33(f72(x6501))
% 1.61/1.67 [651]~P58(x6511)+P73(f72(x6511))
% 1.61/1.67 [652]~P58(x6521)+P20(f72(x6521))
% 1.61/1.67 [653]~P57(x6531)+P57(f72(x6531))
% 1.61/1.67 [654]~P58(x6541)+P38(f72(x6541))
% 1.61/1.67 [655]~P55(x6551)+P55(f72(x6551))
% 1.61/1.67 [656]~P58(x6561)+P39(f72(x6561))
% 1.61/1.67 [657]~P58(x6571)+P40(f72(x6571))
% 1.61/1.67 [658]~P58(x6581)+P41(f72(x6581))
% 1.61/1.67 [659]~P58(x6591)+P44(f72(x6591))
% 1.61/1.67 [660]~P15(x6601)+P26(f72(x6601))
% 1.61/1.67 [661]~P15(x6611)+P36(f72(x6611))
% 1.61/1.67 [662]~P58(x6621)+P37(f72(x6621))
% 1.61/1.67 [663]~P56(x6631)+P61(f72(x6631))
% 1.61/1.67 [664]~P21(x6641)+P21(f72(x6641))
% 1.61/1.67 [666]~P78(x6661)+~E(f6(x6661),f5(x6661))
% 1.61/1.67 [667]~E(x6671,f5(a2))+E(f29(a2,x6671),f5(a1))
% 1.61/1.67 [668]E(x6681,f5(a2))+~E(f29(a2,x6681),f5(a1))
% 1.61/1.67 [746]E(x7461,f5(a2))+P9(a2,f5(a2),x7461)
% 1.61/1.67 [787]~P2(x7871)+P9(a1,f5(a1),f50(x7871))
% 1.61/1.67 [794]E(f10(a1,x7941),x7941)+P9(a1,x7941,f5(a1))
% 1.61/1.67 [795]E(f10(a3,x7951),x7951)+P9(a3,x7951,f5(a3))
% 1.61/1.67 [804]~P1(x8041)+P9(x8041,f5(x8041),f6(x8041))
% 1.61/1.67 [805]~P1(x8051)+P8(x8051,f5(x8051),f6(x8051))
% 1.61/1.67 [832]~E(x8321,f5(a3))+P9(a3,f10(a3,x8321),f6(a3))
% 1.61/1.67 [833]~E(x8331,f5(a2))+P8(a1,f29(a2,x8331),f5(a1))
% 1.61/1.67 [876]E(x8761,f5(a2))+~P8(a2,x8761,f5(a2))
% 1.61/1.67 [885]E(f16(x8851),f5(a2))+~P8(a1,x8851,f5(a1))
% 1.61/1.67 [886]E(f27(x8861),f5(a2))+~P8(a1,x8861,f5(a1))
% 1.61/1.67 [934]~P1(x9341)+~P9(x9341,f6(x9341),f5(x9341))
% 1.61/1.67 [935]~P1(x9351)+~P8(x9351,f6(x9351),f5(x9351))
% 1.61/1.67 [937]E(f12(a1,x9371),f10(a1,x9371))+~P9(a1,x9371,f5(a1))
% 1.61/1.67 [938]E(f12(a3,x9381),f10(a3,x9381))+~P9(a3,x9381,f5(a3))
% 1.61/1.67 [980]E(x9801,f5(a2))+~P8(a1,f29(a2,x9801),f5(a1))
% 1.61/1.67 [981]E(x9811,f5(a3))+~P9(a3,f10(a3,x9811),f6(a3))
% 1.61/1.67 [1019]~P8(a3,f6(a3),x10191)+P9(a3,f5(a3),x10191)
% 1.61/1.67 [1020]~P9(a3,f5(a3),x10201)+P8(a3,f6(a3),x10201)
% 1.61/1.67 [1022]P9(a1,f55(x10221),x10221)+~P9(a1,f5(a1),x10221)
% 1.61/1.67 [1049]~P8(a1,x10491,f6(a1))+P8(a2,f16(x10491),f6(a2))
% 1.61/1.67 [1050]~P9(a1,f5(a1),x10501)+P9(a1,f55(x10501),f6(a1))
% 1.61/1.67 [1051]~P9(a1,f5(a1),x10511)+P9(a1,f5(a1),f55(x10511))
% 1.61/1.67 [1052]~P8(a1,f6(a1),x10521)+P8(a2,f6(a2),f27(x10521))
% 1.61/1.67 [1057]~P8(a2,f16(x10571),f6(a2))+P8(a1,x10571,f6(a1))
% 1.61/1.67 [1058]~P8(a2,f6(a2),f27(x10581))+P8(a1,f6(a1),x10581)
% 1.61/1.67 [1064]~P9(a2,f5(a2),x10641)+P9(a1,f5(a1),f29(a2,x10641))
% 1.61/1.67 [1108]P9(a2,f5(a2),x11081)+~P9(a1,f5(a1),f29(a2,x11081))
% 1.61/1.67 [669]~P45(x6691)+E(f31(x6691,f5(a1)),f5(x6691))
% 1.61/1.67 [670]~P45(x6701)+E(f31(x6701,f6(a1)),f6(x6701))
% 1.61/1.67 [671]~P47(x6711)+E(f30(x6711,f5(x6711)),f5(a1))
% 1.61/1.67 [672]~P49(x6721)+E(f30(x6721,f6(x6721)),f6(a1))
% 1.61/1.67 [676]~P51(x6761)+E(f28(x6761,f5(x6761)),f5(x6761))
% 1.61/1.67 [677]~P6(x6771)+E(f28(x6771,f5(x6771)),f5(x6771))
% 1.61/1.67 [678]~P52(x6781)+E(f28(x6781,f6(x6781)),f6(x6781))
% 1.61/1.67 [679]~P23(x6791)+E(f12(x6791,f5(x6791)),f5(x6791))
% 1.61/1.67 [680]~P33(x6801)+E(f10(x6801,f5(x6801)),f5(x6801))
% 1.61/1.67 [681]~P58(x6811)+E(f10(x6811,f6(x6811)),f6(x6811))
% 1.61/1.67 [682]~P47(x6821)+E(f15(x6821,f5(x6821)),f5(x6821))
% 1.61/1.67 [683]~P37(x6831)+E(f15(x6831,f5(x6831)),f5(x6831))
% 1.61/1.67 [684]~P49(x6841)+E(f15(x6841,f6(x6841)),f6(x6841))
% 1.61/1.67 [742]~P58(x7421)+~P11(x7421,f5(f72(x7421)))
% 1.61/1.67 [816]~P27(x8161)+E(f24(x8161,f6(x8161),f13(x8161)),f23(x8161))
% 1.61/1.67 [1082]~P8(a1,f5(a1),x10821)+P9(a1,x10821,f29(a2,f59(x10821)))
% 1.61/1.67 [1083]~P8(a1,f5(a1),x10831)+P8(a1,f29(a2,f27(x10831)),x10831)
% 1.61/1.67 [1160]~P1(x11601)+P9(x11601,f5(x11601),f14(x11601,f6(x11601),f6(x11601)))
% 1.61/1.67 [1290]~P8(a3,f5(a3),x12901)+P9(a3,f5(a3),f14(a3,f6(a3),x12901))
% 1.61/1.67 [736]~P15(x7361)+E(f12(f72(x7361),f5(f72(x7361))),f5(f72(x7361)))
% 1.61/1.67 [887]~P56(x8871)+E(f20(x8871,f6(x8871),f5(f72(x8871))),f6(f72(x8871)))
% 1.61/1.67 [888]~P35(x8881)+E(f20(x8881,f5(x8881),f5(f72(x8881))),f5(f72(x8881)))
% 1.61/1.67 [903]E(x9031,f5(a1))+E(f56(f56(f13(a1),f28(a1,x9031)),x9031),f6(a1))
% 1.61/1.67 [1032]E(x10321,f5(a1))+P9(a1,f5(a1),f56(f56(f13(a1),x10321),x10321))
% 1.61/1.67 [1245]~E(x12451,f5(a1))+~P9(a1,f5(a1),f56(f56(f13(a1),x12451),x12451))
% 1.61/1.67 [1299]~P8(a1,f5(a1),x12991)+E(f16(f14(a1,x12991,f6(a1))),f14(a2,f16(x12991),f6(a2)))
% 1.61/1.67 [1300]~P8(a1,f5(a1),x13001)+E(f27(f14(a1,x13001,f6(a1))),f14(a2,f27(x13001),f6(a2)))
% 1.61/1.67 [1439]~P8(a1,f30(a4,x14391),f30(a4,a83))+P8(a1,f30(a4,f56(f17(a4,a82),x14391)),a74)
% 1.61/1.67 [1440]~P8(a1,f30(a4,x14401),f30(a4,a83))+P8(a1,f30(a4,f56(f17(a4,a82),x14401)),a33)
% 1.61/1.67 [1441]~P8(a1,f30(a4,x14411),f30(a4,a83))+P8(a1,f30(a4,f56(f17(a4,a82),x14411)),a34)
% 1.61/1.67 [1520]~P8(a1,f5(a1),x15201)+P8(a1,f29(a2,f11(a2,f59(x15201),f6(a2))),x15201)
% 1.61/1.67 [1604]~P9(a3,x16041,f5(a3))+P9(a3,f14(a3,f14(a3,f6(a3),x16041),x16041),f5(a3))
% 1.61/1.67 [1719]P9(a3,x17191,f5(a3))+~P9(a3,f14(a3,f14(a3,f6(a3),x17191),x17191),f5(a3))
% 1.61/1.67 [1809]~P9(a1,f30(a4,f56(f17(a4,a80),x18091)),f30(a4,f56(f17(a4,a80),f5(a4))))+P9(a1,f30(a4,f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),x18091)),f6(a1))
% 1.61/1.67 [1812]P9(a1,f30(a4,f56(f17(a4,a80),x18121)),f30(a4,f56(f17(a4,a80),f5(a4))))+~P9(a1,f30(a4,f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f5(a4))),a80)),x18121)),f6(a1))
% 1.61/1.67 [737]~E(x7371,x7372)+P8(a1,x7371,x7372)
% 1.61/1.67 [740]~E(x7401,x7402)+P8(a2,x7401,x7402)
% 1.61/1.67 [756]~P39(x7561)+P8(x7561,x7562,x7562)
% 1.61/1.67 [757]~P56(x7571)+P12(x7571,x7572,x7572)
% 1.61/1.67 [842]~E(x8421,x8422)+~P9(a1,x8421,x8422)
% 1.61/1.67 [847]~E(x8471,x8472)+~P9(a2,x8471,x8472)
% 1.61/1.67 [848]~E(x8481,x8482)+~P9(a3,x8481,x8482)
% 1.61/1.67 [880]~P9(x8801,x8802,x8802)+~P39(x8801)
% 1.61/1.67 [921]P8(a1,x9212,x9211)+P8(a1,x9211,x9212)
% 1.61/1.67 [922]P8(a2,x9222,x9221)+P8(a2,x9221,x9222)
% 1.61/1.67 [923]P8(a3,x9232,x9231)+P8(a3,x9231,x9232)
% 1.61/1.67 [989]~P9(a1,x9891,x9892)+P8(a1,x9891,x9892)
% 1.61/1.67 [994]~P9(a2,x9941,x9942)+P8(a2,x9941,x9942)
% 1.61/1.67 [995]~P9(a3,x9951,x9952)+P8(a3,x9951,x9952)
% 1.61/1.67 [697]~P39(x6972)+P39(f77(x6971,x6972))
% 1.61/1.67 [698]~P40(x6982)+P40(f77(x6981,x6982))
% 1.61/1.67 [699]~P44(x6992)+P44(f77(x6991,x6992))
% 1.61/1.67 [700]~P42(x7002)+P42(f77(x7001,x7002))
% 1.61/1.67 [701]~P26(x7012)+P26(f77(x7011,x7012))
% 1.61/1.67 [702]~P36(x7022)+P36(f77(x7021,x7022))
% 1.61/1.67 [714]E(x7141,x7142)+~E(f29(a2,x7141),f29(a2,x7142))
% 1.61/1.67 [766]~P23(x7661)+E(f11(x7661,x7662,x7662),f5(x7661))
% 1.61/1.67 [773]~P56(x7731)+P12(x7731,x7732,f5(x7731))
% 1.61/1.67 [774]~P56(x7741)+P12(x7741,f6(x7741),x7742)
% 1.61/1.67 [792]P8(a3,x7922,x7921)+E(f19(x7921,x7922),f5(a3))
% 1.61/1.67 [815]~E(x8152,f12(a1,x8151))+E(f14(a1,x8151,x8152),f5(a1))
% 1.61/1.67 [849]~P33(x8491)+P8(x8491,x8492,f10(x8491,x8492))
% 1.61/1.67 [853]~E(f14(a2,x8532,x8531),x8532)+E(x8531,f5(a2))
% 1.61/1.67 [855]~P2(x8552)+P9(a1,f5(a1),f52(x8551,x8552))
% 1.61/1.67 [856]~P2(x8562)+P9(a1,f5(a1),f54(x8561,x8562))
% 1.61/1.67 [857]~P47(x8571)+P8(a1,f5(a1),f30(x8571,x8572))
% 1.61/1.67 [860]~P9(a2,x8602,x8601)+~E(x8601,f5(a2))
% 1.61/1.67 [869]E(x8691,f5(a2))+~E(f14(a2,x8692,x8691),f5(a2))
% 1.61/1.67 [870]E(x8701,f5(a2))+~E(f14(a2,x8701,x8702),f5(a2))
% 1.61/1.67 [881]~P33(x8811)+P8(x8811,f5(x8811),f10(x8811,x8812))
% 1.61/1.67 [909]E(x9091,f12(a1,x9092))+~E(f14(a1,x9092,x9091),f5(a1))
% 1.61/1.67 [939]~P33(x9391)+P8(x9391,f12(x9391,x9392),f10(x9391,x9392))
% 1.61/1.67 [987]~P47(x9871)+~P9(a1,f30(x9871,x9872),f5(a1))
% 1.61/1.67 [1004]~P8(a2,x10041,x10042)+E(f11(a2,x10041,x10042),f5(a2))
% 1.61/1.67 [1011]P8(a2,x10111,x10112)+~E(f11(a2,x10111,x10112),f5(a2))
% 1.61/1.67 [1017]~P33(x10171)+~P9(x10171,f10(x10171,x10172),f5(x10171))
% 1.61/1.67 [1028]~P8(a1,x10281,x10282)+P8(a2,f16(x10281),f16(x10282))
% 1.61/1.67 [1029]~P8(a1,x10291,x10292)+P8(a2,f27(x10291),f27(x10292))
% 1.61/1.67 [1043]~P8(a3,x10432,x10431)+E(f11(a3,x10431,x10432),f19(x10431,x10432))
% 1.61/1.67 [1076]P8(a1,x10761,x10762)+~P8(a1,f10(a1,x10761),x10762)
% 1.61/1.67 [1086]P8(a2,x10861,f27(x10862))+~P8(a1,f29(a2,x10861),x10862)
% 1.61/1.67 [1087]P8(a2,f16(x10871),x10872)+~P8(a1,x10871,f29(a2,x10872))
% 1.61/1.67 [1114]~P9(a2,x11141,x11142)+P9(a1,f29(a2,x11141),f29(a2,x11142))
% 1.61/1.67 [1115]~P8(a2,x11151,x11152)+P8(a1,f29(a2,x11151),f29(a2,x11152))
% 1.61/1.67 [1159]~P8(a1,f10(a1,x11592),x11591)+P8(a1,f12(a1,x11591),x11592)
% 1.61/1.67 [1185]P9(a2,x11851,x11852)+~P9(a1,f29(a2,x11851),f29(a2,x11852))
% 1.61/1.67 [1186]P8(a2,x11861,x11862)+~P8(a1,f29(a2,x11861),f29(a2,x11862))
% 1.61/1.67 [1269]~P9(a2,x12692,x12691)+P9(a2,f5(a2),f11(a2,x12691,x12692))
% 1.61/1.67 [1270]~P9(a3,x12701,x12702)+P9(a3,f11(a3,x12701,x12702),f5(a3))
% 1.61/1.67 [1271]~P8(a1,x12711,x12712)+P8(a1,f11(a1,x12711,x12712),f5(a1))
% 1.61/1.67 [1324]~P9(a1,f12(a1,x13241),x13242)+P9(a1,f5(a1),f14(a1,x13241,x13242))
% 1.61/1.67 [1325]~P8(a1,f12(a1,x13251),x13252)+P8(a1,f5(a1),f14(a1,x13251,x13252))
% 1.61/1.67 [1326]~P9(a1,x13262,f12(a1,x13261))+P9(a1,f14(a1,x13261,x13262),f5(a1))
% 1.61/1.67 [1327]~P8(a1,x13272,f12(a1,x13271))+P8(a1,f14(a1,x13271,x13272),f5(a1))
% 1.61/1.67 [1362]P9(a2,x13621,x13622)+~P9(a2,f5(a2),f11(a2,x13622,x13621))
% 1.61/1.67 [1363]P9(a3,x13631,x13632)+~P9(a3,f11(a3,x13631,x13632),f5(a3))
% 1.61/1.67 [1364]P8(a1,x13641,x13642)+~P8(a1,f11(a1,x13641,x13642),f5(a1))
% 1.61/1.67 [1392]P9(a1,x13921,f12(a1,x13922))+~P9(a1,f14(a1,x13922,x13921),f5(a1))
% 1.61/1.67 [1393]P8(a1,x13931,f12(a1,x13932))+~P8(a1,f14(a1,x13932,x13931),f5(a1))
% 1.61/1.67 [1394]P9(a1,f12(a1,x13941),x13942)+~P9(a1,f5(a1),f14(a1,x13941,x13942))
% 1.61/1.67 [1395]P8(a1,f12(a1,x13951),x13952)+~P8(a1,f5(a1),f14(a1,x13951,x13952))
% 1.61/1.67 [721]~P51(x7211)+E(f28(x7211,f28(x7211,x7212)),x7212)
% 1.61/1.67 [722]~P23(x7221)+E(f12(x7221,f12(x7221,x7222)),x7222)
% 1.61/1.67 [723]~P42(x7231)+E(f12(x7231,f12(x7231,x7232)),x7232)
% 1.61/1.67 [743]~P49(x7431)+E(f30(x7431,f31(x7431,x7432)),f10(a1,x7432))
% 1.61/1.67 [744]~P47(x7441)+E(f10(a1,f30(x7441,x7442)),f30(x7441,x7442))
% 1.61/1.67 [752]~P47(x7521)+E(f30(x7521,f12(x7521,x7522)),f30(x7521,x7522))
% 1.61/1.67 [753]~P33(x7531)+E(f10(x7531,f12(x7531,x7532)),f10(x7531,x7532))
% 1.61/1.67 [754]~P33(x7541)+E(f10(x7541,f10(x7541,x7542)),f10(x7541,x7542))
% 1.61/1.67 [755]~P58(x7551)+E(f15(x7551,f15(x7551,x7552)),f15(x7551,x7552))
% 1.61/1.67 [759]~P3(x7591)+E(f56(f56(f23(x7591),x7592),f6(a2)),x7592)
% 1.61/1.67 [760]~P56(x7601)+E(f56(f56(f23(x7601),x7602),f6(a2)),x7602)
% 1.61/1.67 [767]~P3(x7671)+E(f56(f56(f13(x7671),x7672),f6(x7671)),x7672)
% 1.61/1.67 [768]~P4(x7681)+E(f56(f56(f13(x7681),x7682),f6(x7681)),x7682)
% 1.61/1.67 [769]~P56(x7691)+E(f56(f56(f13(x7691),x7692),f6(x7691)),x7692)
% 1.61/1.67 [770]~P27(x7701)+E(f56(f56(f23(x7701),x7702),f5(a2)),f6(x7701))
% 1.61/1.67 [771]~P56(x7711)+E(f56(f56(f23(x7711),x7712),f5(a2)),f6(x7711))
% 1.61/1.67 [775]~P22(x7751)+E(f14(x7751,x7752,f5(x7751)),x7752)
% 1.61/1.67 [776]~P25(x7761)+E(f14(x7761,x7762,f5(x7761)),x7762)
% 1.61/1.67 [777]~P56(x7771)+E(f14(x7771,x7772,f5(x7771)),x7772)
% 1.61/1.67 [778]~P23(x7781)+E(f11(x7781,x7782,f5(x7781)),x7782)
% 1.61/1.67 [779]~P22(x7791)+E(f14(x7791,f5(x7791),x7792),x7792)
% 1.61/1.67 [780]~P25(x7801)+E(f14(x7801,f5(x7801),x7802),x7802)
% 1.61/1.67 [781]~P56(x7811)+E(f14(x7811,f5(x7811),x7812),x7812)
% 1.61/1.67 [782]~P56(x7821)+E(f25(x7821,f6(x7821),x7822),x7822)
% 1.61/1.67 [789]~P2(x7891)+E(f56(f56(f13(x7891),x7892),f5(x7891)),f5(x7891))
% 1.61/1.67 [790]~P69(x7901)+E(f56(f56(f13(x7901),x7902),f5(x7901)),f5(x7901))
% 1.61/1.67 [791]~P56(x7911)+E(f56(f56(f13(x7911),x7912),f5(x7911)),f5(x7911))
% 1.61/1.67 [817]~P57(x8171)+E(f25(x8171,f5(x8171),x8172),f5(f72(x8171)))
% 1.61/1.67 [818]~P35(x8181)+E(f18(x8181,f5(x8181),x8182),f5(f72(x8181)))
% 1.61/1.67 [825]~P23(x8251)+E(f11(x8251,f5(x8251),x8252),f12(x8251,x8252))
% 1.61/1.67 [827]~E(x8271,x8272)+E(f14(a1,x8271,f12(a1,x8272)),f5(a1))
% 1.61/1.67 [829]~P49(x8291)+E(f15(x8291,f31(x8291,x8292)),f31(x8291,f15(a1,x8292)))
% 1.61/1.67 [830]~P45(x8301)+E(f31(x8301,f12(a1,x8302)),f12(x8301,f31(x8301,x8302)))
% 1.61/1.67 [839]~P51(x8391)+E(f28(x8391,f12(x8391,x8392)),f12(x8391,f28(x8391,x8392)))
% 1.61/1.67 [840]~P14(x8401)+E(f28(x8401,f10(x8401,x8402)),f10(x8401,f28(x8401,x8402)))
% 1.61/1.67 [841]~P47(x8411)+E(f15(x8411,f12(x8411,x8412)),f12(x8411,f15(x8411,x8412)))
% 1.61/1.67 [873]~P23(x8731)+E(f14(x8731,x8732,f12(x8731,x8732)),f5(x8731))
% 1.61/1.67 [874]~P23(x8741)+E(f14(x8741,f12(x8741,x8742),x8742),f5(x8741))
% 1.61/1.67 [875]~P15(x8751)+E(f14(x8751,f12(x8751,x8752),x8752),f5(x8751))
% 1.61/1.67 [906]~P58(x9061)+E(f56(f56(f13(x9061),x9062),f15(x9061,x9062)),f10(x9061,x9062))
% 1.61/1.67 [975]E(x9751,x9752)+~E(f14(a1,x9751,f12(a1,x9752)),f5(a1))
% 1.61/1.67 [979]E(x9791,x9792)+~E(f56(x9791,f47(x9792,x9791)),f56(x9792,f47(x9792,x9791)))
% 1.61/1.67 [999]~P58(x9991)+E(f56(f56(f13(x9991),f15(x9991,x9992)),f10(x9991,x9992)),x9992)
% 1.61/1.67 [1021]~P33(x10211)+P8(x10211,f12(x10211,f10(x10211,x10212)),f5(x10211))
% 1.61/1.67 [1060]~P8(a2,x10601,x10602)+E(f14(a2,x10601,f66(x10602,x10601)),x10602)
% 1.61/1.67 [1061]~P8(a2,x10611,x10612)+E(f14(a2,x10611,f67(x10612,x10611)),x10612)
% 1.61/1.67 [1063]~E(x10631,x10632)+P9(a3,x10631,f14(a3,x10632,f6(a3)))
% 1.61/1.67 [1107]~P1(x11071)+P9(x11071,x11072,f14(x11071,x11072,f6(x11071)))
% 1.61/1.67 [1189]P9(a2,x11892,x11891)+E(f14(a2,x11891,f11(a2,x11892,x11891)),x11892)
% 1.61/1.67 [1264]~P8(a2,x12641,x12642)+E(f14(a2,x12641,f11(a2,x12642,x12641)),x12642)
% 1.61/1.67 [1265]~P8(a2,x12652,x12651)+E(f11(a2,x12651,f11(a2,x12651,x12652)),x12652)
% 1.61/1.67 [1266]~P8(a2,x12662,x12661)+E(f14(a2,f11(a2,x12661,x12662),x12662),x12661)
% 1.61/1.67 [1272]~P9(a3,x12721,x12722)+P9(a3,x12721,f14(a3,x12722,f6(a3)))
% 1.61/1.67 [1273]~P8(a3,x12731,x12732)+P9(a3,x12731,f14(a3,x12732,f6(a3)))
% 1.61/1.67 [1274]~P9(a3,x12741,x12742)+P8(a3,x12741,f11(a3,x12742,f6(a3)))
% 1.61/1.67 [1276]~P9(a3,x12761,x12762)+P8(a3,f14(a3,x12761,f6(a3)),x12762)
% 1.61/1.67 [1350]~P8(a2,x13502,x13501)+E(f11(a1,f29(a2,x13501),f29(a2,x13502)),f29(a2,f11(a2,x13501,x13502)))
% 1.61/1.67 [1365]P9(a3,x13651,x13652)+~P8(a3,x13651,f11(a3,x13652,f6(a3)))
% 1.61/1.67 [1366]P8(a3,x13661,x13662)+~P9(a3,x13661,f14(a3,x13662,f6(a3)))
% 1.61/1.67 [1367]P9(a3,x13671,x13672)+~P8(a3,f14(a3,x13671,f6(a3)),x13672)
% 1.61/1.67 [1369]~P8(a2,x13691,x13692)+P9(a1,f29(a2,x13691),f14(a1,f29(a2,x13692),f6(a1)))
% 1.61/1.67 [1370]~P9(a2,x13701,x13702)+P8(a1,f14(a1,f29(a2,x13701),f6(a1)),f29(a2,x13702))
% 1.61/1.67 [1433]P9(a1,x14331,f29(a2,x14332))+~P8(a2,f14(a2,f27(x14331),f6(a2)),x14332)
% 1.61/1.67 [1523]P8(a2,x15231,x15232)+~P9(a1,f29(a2,x15231),f14(a1,f29(a2,x15232),f6(a1)))
% 1.61/1.67 [1524]P9(a2,x15241,x15242)+~P8(a1,f14(a1,f29(a2,x15241),f6(a1)),f29(a2,x15242))
% 1.61/1.67 [730]~E(x7302,f5(a2))+E(f56(f56(f23(a2),x7301),x7302),f6(a2))
% 1.61/1.67 [731]~E(x7312,f5(a2))+E(f56(f56(f13(a2),x7311),x7312),f5(a2))
% 1.61/1.67 [733]~E(x7331,f5(a2))+E(f56(f56(f13(a2),x7331),x7332),f5(a2))
% 1.61/1.67 [748]~P43(x7481)+E(f56(f56(f13(x7481),x7482),x7482),x7482)
% 1.61/1.67 [801]~P3(x8011)+E(f56(f56(f13(x8011),f6(x8011)),x8012),x8012)
% 1.61/1.67 [802]~P4(x8021)+E(f56(f56(f13(x8021),f6(x8021)),x8022),x8022)
% 1.61/1.67 [803]~P56(x8031)+E(f56(f56(f13(x8031),f6(x8031)),x8032),x8032)
% 1.61/1.67 [808]~P3(x8081)+E(f56(f56(f23(x8081),f6(x8081)),x8082),f6(x8081))
% 1.61/1.67 [810]~P2(x8101)+E(f56(f56(f13(x8101),f5(x8101)),x8102),f5(x8101))
% 1.61/1.67 [811]~P69(x8111)+E(f56(f56(f13(x8111),f5(x8111)),x8112),f5(x8111))
% 1.61/1.67 [812]~P56(x8121)+E(f56(f56(f13(x8121),f5(x8121)),x8122),f5(x8121))
% 1.61/1.67 [823]E(x8231,f6(a2))+~E(f56(f56(f13(a2),x8232),x8231),f6(a2))
% 1.61/1.67 [824]E(x8241,f6(a2))+~E(f56(f56(f13(a2),x8241),x8242),f6(a2))
% 1.61/1.67 [836]~P22(x8361)+E(f14(f72(x8361),x8362,f5(f72(x8361))),x8362)
% 1.61/1.67 [837]~P15(x8371)+E(f11(f72(x8371),x8372,f5(f72(x8371))),x8372)
% 1.61/1.67 [838]~P22(x8381)+E(f14(f72(x8381),f5(f72(x8381)),x8382),x8382)
% 1.61/1.67 [864]~P57(x8641)+E(f25(x8641,x8642,f5(f72(x8641))),f5(f72(x8641)))
% 1.61/1.67 [865]~P57(x8651)+E(f26(x8651,f5(f72(x8651)),x8652),f5(f72(x8651)))
% 1.61/1.67 [866]~P57(x8661)+E(f22(x8661,f5(f72(x8661)),x8662),f5(f72(x8661)))
% 1.61/1.67 [867]~P57(x8671)+E(f9(x8671,f5(f72(x8671)),x8672),f5(f72(x8671)))
% 1.61/1.67 [916]~P15(x9161)+E(f11(f72(x9161),f5(f72(x9161)),x9162),f12(f72(x9161),x9162))
% 1.61/1.67 [933]~P57(x9331)+E(f56(f56(f13(f72(x9331)),x9332),f5(f72(x9331))),f5(f72(x9331)))
% 1.61/1.67 [998]~P35(x9981)+E(f20(x9981,x9982,f5(f72(x9981))),f18(x9981,x9982,f5(a2)))
% 1.61/1.67 [1056]~E(x10562,f5(a2))+P9(a2,f5(a2),f56(f56(f23(a2),x10561),x10562))
% 1.61/1.67 [1074]~P50(x10741)+P8(x10741,f5(x10741),f56(f56(f13(x10741),x10742),x10742))
% 1.61/1.67 [1135]~P58(x11351)+E(f56(f56(f13(x11351),f10(x11351,x11352)),f10(x11351,x11352)),f56(f56(f13(x11351),x11352),x11352))
% 1.61/1.67 [1242]~P9(a2,f5(a2),x12421)+P9(a2,f5(a2),f56(f56(f23(a2),x12421),x12422))
% 1.61/1.67 [1243]~P8(a3,f5(a3),x12431)+P8(a3,f5(a3),f56(f56(f23(a3),x12431),x12432))
% 1.61/1.67 [1263]E(x12631,f5(a3))+P9(a3,f5(a3),f56(f56(f23(a3),f10(a3,x12631)),x12632))
% 1.61/1.67 [1268]~E(x12682,f5(a2))+P9(a3,f5(a3),f56(f56(f23(a3),f10(a3,x12681)),x12682))
% 1.61/1.67 [1297]~P50(x12971)+~P9(x12971,f56(f56(f13(x12971),x12972),x12972),f5(x12971))
% 1.61/1.67 [1334]P9(a2,f5(a2),x13341)+~P9(a2,f5(a2),f56(f56(f13(a2),x13342),x13341))
% 1.61/1.67 [1335]P9(a2,f5(a2),x13351)+~P9(a2,f5(a2),f56(f56(f13(a2),x13351),x13352))
% 1.61/1.67 [1359]~P8(a1,f5(a1),x13591)+E(f16(f14(a1,x13591,f29(a2,x13592))),f14(a2,f16(x13591),x13592))
% 1.61/1.67 [1360]~P8(a1,f5(a1),x13601)+E(f27(f14(a1,x13601,f29(a2,x13602))),f14(a2,f27(x13601),x13602))
% 1.61/1.67 [1406]~P8(a1,f29(a2,x14062),x14061)+E(f16(f11(a1,x14061,f29(a2,x14062))),f11(a2,f16(x14061),x14062))
% 1.61/1.67 [1407]~P8(a1,f29(a2,x14072),x14071)+E(f27(f11(a1,x14071,f29(a2,x14072))),f11(a2,f27(x14071),x14072))
% 1.61/1.67 [1696]~P77(x16961)+E(f56(f56(f13(x16961),f14(x16961,x16962,f6(x16961))),f11(x16961,x16962,f6(x16961))),f11(x16961,f56(f56(f13(x16961),x16962),x16962),f6(x16961)))
% 1.61/1.67 [850]~P57(x8501)+E(f56(f17(x8501,f5(f72(x8501))),x8502),f5(x8501))
% 1.61/1.67 [851]~P56(x8511)+E(f56(f17(x8511,f6(f72(x8511))),x8512),f6(x8511))
% 1.61/1.67 [982]~P57(x9821)+E(f56(f56(f13(f72(x9821)),f5(f72(x9821))),x9822),f5(f72(x9821)))
% 1.61/1.68 [1031]~P54(x10311)+E(f56(f56(f13(x10311),f12(x10311,f6(x10311))),x10312),f12(x10311,x10312))
% 1.61/1.68 [1098]E(f10(a3,x10981),f6(a3))+~E(f10(a3,f56(f56(f13(a3),x10981),x10982)),f6(a3))
% 1.61/1.68 [1117]~E(f29(a2,f27(x11171)),x11171)+E(f27(f56(f56(f23(a1),x11171),x11172)),f56(f56(f23(a2),f27(x11171)),x11172))
% 1.61/1.68 [1478]E(x14781,f5(a1))+~E(f14(a1,f56(f56(f13(a1),x14782),x14782),f56(f56(f13(a1),x14781),x14781)),f5(a1))
% 1.61/1.68 [1479]E(x14791,f5(a1))+~E(f14(a1,f56(f56(f13(a1),x14791),x14791),f56(f56(f13(a1),x14792),x14792)),f5(a1))
% 1.61/1.68 [1481]~P56(x14811)+E(f14(x14811,x14812,x14812),f56(f56(f13(x14811),f14(x14811,f6(x14811),f6(x14811))),x14812))
% 1.61/1.68 [1505]E(x15051,f5(a2))+E(f56(f56(f13(a2),x15052),f56(f56(f23(a2),x15052),f11(a2,x15051,f6(a2)))),f56(f56(f23(a2),x15052),x15051))
% 1.61/1.68 [1765]~P8(a1,f5(a1),x17652)+P8(a1,f14(a1,f56(f56(f13(a1),f29(a2,x17651)),x17652),f6(a1)),f56(f56(f23(a1),f14(a1,x17652,f6(a1))),x17651))
% 1.61/1.68 [1716]E(x17161,f5(a2))+E(f14(a2,x17162,f56(f56(f13(a2),f11(a2,x17161,f6(a2))),x17162)),f56(f56(f13(a2),x17161),x17162))
% 1.61/1.68 [946]~P56(x9461)+E(f14(x9461,x9462,x9463),f14(x9461,x9463,x9462))
% 1.61/1.68 [1001]P8(a2,x10011,x10012)+~E(x10012,f14(a2,x10011,x10013))
% 1.61/1.68 [1065]E(x10651,x10652)+~E(f14(a2,x10653,x10651),f14(a2,x10653,x10652))
% 1.61/1.68 [1066]E(x10661,x10662)+~E(f14(a2,x10661,x10663),f14(a2,x10662,x10663))
% 1.61/1.68 [1251]~P9(a2,x12511,x12513)+P9(a2,x12511,f14(a2,x12512,x12513))
% 1.61/1.68 [1253]~P9(a2,x12531,x12532)+P9(a2,x12531,f14(a2,x12532,x12533))
% 1.61/1.68 [1255]~P8(a2,x12551,x12553)+P8(a2,x12551,f14(a2,x12552,x12553))
% 1.61/1.68 [1257]~P8(a2,x12571,x12572)+P8(a2,x12571,f14(a2,x12572,x12573))
% 1.61/1.68 [1258]~P9(a2,x12581,x12583)+P9(a2,f11(a2,x12581,x12582),x12583)
% 1.61/1.68 [1283]~P9(a1,f5(a1),x12833)+P9(a1,f5(a1),f60(x12831,x12832,x12833))
% 1.61/1.68 [1351]P9(a2,x13511,x13512)+~P9(a2,f14(a2,x13511,x13513),x13512)
% 1.61/1.68 [1354]P8(a2,x13541,x13542)+~P8(a2,f14(a2,x13543,x13541),x13542)
% 1.61/1.68 [1355]P8(a2,x13551,x13552)+~P8(a2,f14(a2,x13551,x13553),x13552)
% 1.61/1.68 [1419]~P9(a2,x14192,x14193)+P9(a2,f14(a2,x14191,x14192),f14(a2,x14191,x14193))
% 1.61/1.68 [1420]~P9(a2,x14201,x14203)+P9(a2,f14(a2,x14201,x14202),f14(a2,x14203,x14202))
% 1.61/1.68 [1421]~P9(a3,x14211,x14213)+P9(a3,f14(a3,x14211,x14212),f14(a3,x14213,x14212))
% 1.61/1.68 [1422]~P8(a1,x14222,x14223)+P8(a1,f14(a1,x14221,x14222),f14(a1,x14221,x14223))
% 1.61/1.68 [1423]~P8(a2,x14232,x14233)+P8(a2,f14(a2,x14231,x14232),f14(a2,x14231,x14233))
% 1.61/1.68 [1424]~P8(a2,x14241,x14243)+P8(a2,f14(a2,x14241,x14242),f14(a2,x14243,x14242))
% 1.61/1.68 [1425]~P8(a2,x14253,x14252)+P8(a2,f11(a2,x14251,x14252),f11(a2,x14251,x14253))
% 1.61/1.68 [1426]~P8(a2,x14261,x14263)+P8(a2,f11(a2,x14261,x14262),f11(a2,x14263,x14262))
% 1.61/1.68 [1427]~P8(a3,x14272,x14273)+P8(a3,f14(a3,x14271,x14272),f14(a3,x14271,x14273))
% 1.61/1.68 [1501]~P9(a2,f14(a2,x15011,x15013),x15012)+P9(a2,x15011,f11(a2,x15012,x15013))
% 1.61/1.68 [1502]~P8(a2,f11(a2,x15021,x15023),x15022)+P8(a2,x15021,f14(a2,x15022,x15023))
% 1.61/1.68 [1503]~P9(a2,x15031,f11(a2,x15033,x15032))+P9(a2,f14(a2,x15031,x15032),x15033)
% 1.61/1.68 [1504]~P8(a2,x15041,f14(a2,x15043,x15042))+P8(a2,f11(a2,x15041,x15042),x15043)
% 1.61/1.68 [1601]P9(a2,x16011,x16012)+~P9(a2,f14(a2,x16013,x16011),f14(a2,x16013,x16012))
% 1.61/1.68 [1602]P8(a2,x16021,x16022)+~P8(a2,f14(a2,x16023,x16021),f14(a2,x16023,x16022))
% 1.61/1.68 [956]P10(x9561,x9562,x9563)+~E(f56(x9563,f36(x9563)),f56(x9563,f37(x9563)))
% 1.61/1.68 [1013]~P23(x10131)+E(f14(x10131,x10132,f12(x10131,x10133)),f11(x10131,x10132,x10133))
% 1.61/1.68 [1014]~P15(x10141)+E(f14(x10141,x10142,f12(x10141,x10143)),f11(x10141,x10142,x10143))
% 1.61/1.68 [1015]~P54(x10151)+E(f14(x10151,x10152,f12(x10151,x10153)),f11(x10151,x10152,x10153))
% 1.61/1.68 [1016]~P23(x10161)+E(f11(x10161,x10162,f12(x10161,x10163)),f14(x10161,x10162,x10163))
% 1.61/1.68 [1069]~P23(x10691)+E(f14(x10691,f11(x10691,x10692,x10693),x10693),x10692)
% 1.61/1.68 [1070]~P23(x10701)+E(f11(x10701,f14(x10701,x10702,x10703),x10703),x10702)
% 1.61/1.68 [1113]~P15(x11131)+E(f12(x11131,f11(x11131,x11132,x11133)),f11(x11131,x11133,x11132))
% 1.61/1.68 [1158]~P23(x11581)+E(f14(x11581,f12(x11581,x11582),f14(x11581,x11582,x11583)),x11583)
% 1.61/1.68 [1191]~P55(x11911)+E(f12(f72(x11911),f25(x11911,x11912,x11913)),f25(x11911,f12(x11911,x11912),x11913))
% 1.61/1.68 [1192]~P15(x11921)+E(f12(f72(x11921),f18(x11921,x11922,x11923)),f18(x11921,f12(x11921,x11922),x11923))
% 1.61/1.68 [1226]~P45(x12261)+E(f14(x12261,f31(x12261,x12262),f31(x12261,x12263)),f31(x12261,f14(a1,x12262,x12263)))
% 1.61/1.68 [1227]~P45(x12271)+E(f11(x12271,f31(x12271,x12272),f31(x12271,x12273)),f31(x12271,f11(a1,x12272,x12273)))
% 1.61/1.68 [1229]~P23(x12291)+E(f14(x12291,f12(x12291,x12292),f12(x12291,x12293)),f12(x12291,f14(x12291,x12293,x12292)))
% 1.61/1.68 [1230]~P15(x12301)+E(f14(x12301,f12(x12301,x12302),f12(x12301,x12303)),f12(x12301,f14(x12301,x12302,x12303)))
% 1.61/1.68 [1231]~P15(x12311)+E(f11(x12311,f12(x12311,x12312),f12(x12311,x12313)),f12(x12311,f11(x12311,x12312,x12313)))
% 1.61/1.68 [1281]~P47(x12811)+E(f30(x12811,f11(x12811,x12812,x12813)),f30(x12811,f11(x12811,x12813,x12812)))
% 1.61/1.68 [1282]~P33(x12821)+E(f10(x12821,f11(x12821,x12822,x12823)),f10(x12821,f11(x12821,x12823,x12822)))
% 1.61/1.68 [1496]~P8(a2,x14962,x14963)+E(f11(a2,f14(a2,x14961,x14962),x14963),f11(a2,x14961,f11(a2,x14963,x14962)))
% 1.61/1.68 [1497]~P8(a2,x14973,x14972)+E(f14(a2,x14971,f11(a2,x14972,x14973)),f11(a2,f14(a2,x14971,x14972),x14973))
% 1.61/1.68 [1499]~P8(a2,x14992,x14991)+E(f14(a2,f11(a2,x14991,x14992),x14993),f11(a2,f14(a2,x14991,x14993),x14992))
% 1.61/1.68 [1566]~P8(a2,x15663,x15662)+P8(a2,x15661,f11(a2,f14(a2,x15662,x15661),x15663))
% 1.61/1.68 [1627]~P47(x16271)+P8(a1,f30(x16271,f14(x16271,x16272,x16273)),f14(a1,f30(x16271,x16272),f30(x16271,x16273)))
% 1.61/1.68 [1628]~P47(x16281)+P8(a1,f30(x16281,f11(x16281,x16282,x16283)),f14(a1,f30(x16281,x16282),f30(x16281,x16283)))
% 1.61/1.68 [1629]~P47(x16291)+P8(a1,f11(a1,f30(x16291,x16292),f30(x16291,x16293)),f30(x16291,f14(x16291,x16292,x16293)))
% 1.61/1.68 [1630]~P47(x16301)+P8(a1,f11(a1,f30(x16301,x16302),f30(x16301,x16303)),f30(x16301,f11(x16301,x16302,x16303)))
% 1.61/1.68 [1641]~P33(x16411)+P8(x16411,f10(x16411,f14(x16411,x16412,x16413)),f14(x16411,f10(x16411,x16412),f10(x16411,x16413)))
% 1.61/1.68 [1642]~P33(x16421)+P8(x16421,f10(x16421,f11(x16421,x16422,x16423)),f14(x16421,f10(x16421,x16422),f10(x16421,x16423)))
% 1.61/1.68 [1643]~P33(x16431)+P8(x16431,f11(x16431,f10(x16431,x16432),f10(x16431,x16433)),f10(x16431,f11(x16431,x16433,x16432)))
% 1.61/1.68 [1644]~P33(x16441)+P8(x16441,f11(x16441,f10(x16441,x16442),f10(x16441,x16443)),f10(x16441,f11(x16441,x16442,x16443)))
% 1.61/1.68 [1796]~P60(x17961)+P12(f72(x17961),f56(f56(f23(f72(x17961)),f20(x17961,f12(x17961,x17962),f20(x17961,f6(x17961),f5(f72(x17961))))),f21(x17961,x17962,x17963)),x17963)
% 1.61/1.68 [900]~E(x9002,f5(a2))+E(f56(f56(f13(a2),x9001),x9002),f56(f56(f13(a2),x9003),x9002))
% 1.61/1.68 [902]~E(x9021,f5(a2))+E(f56(f56(f13(a2),x9021),x9022),f56(f56(f13(a2),x9021),x9023))
% 1.61/1.68 [932]~P56(x9321)+E(f56(f56(f13(x9321),x9322),x9323),f56(f56(f13(x9321),x9323),x9322))
% 1.61/1.68 [1062]~P56(x10621)+P12(x10621,x10622,f56(f56(f13(x10621),x10622),x10623))
% 1.61/1.68 [1133]~P76(x11331)+E(f56(f56(f13(x11331),f12(x11331,x11332)),x11333),f56(f56(f13(x11331),x11332),f12(x11331,x11333)))
% 1.61/1.68 [1134]~P76(x11341)+E(f56(f56(f13(x11341),f12(x11341,x11342)),f12(x11341,x11343)),f56(f56(f13(x11341),x11342),x11343))
% 1.61/1.68 [1212]~P23(x12121)+E(f14(x12121,x12122,f14(x12121,f12(x12121,x12122),x12123)),x12123)
% 1.61/1.68 [1217]~P55(x12171)+E(f25(x12171,x12172,f12(f72(x12171),x12173)),f12(f72(x12171),f25(x12171,x12172,x12173)))
% 1.61/1.68 [1285]~P15(x12851)+E(f20(x12851,f12(x12851,x12852),f12(f72(x12851),x12853)),f12(f72(x12851),f20(x12851,x12852,x12853)))
% 1.61/1.68 [1317]~P58(x13171)+P8(x13171,f5(x13171),f56(f56(f23(x13171),f10(x13171,x13172)),x13173))
% 1.61/1.68 [1338]P9(a2,f5(a2),x13381)+P8(a2,f56(f56(f13(a2),x13382),x13381),f56(f56(f13(a2),x13383),x13381))
% 1.61/1.68 [1339]P9(a2,f5(a2),x13391)+P8(a2,f56(f56(f13(a2),x13391),x13392),f56(f56(f13(a2),x13391),x13393))
% 1.61/1.68 [1373]~P8(a2,x13732,x13733)+P8(a2,f56(f56(f13(a2),x13731),x13732),f56(f56(f13(a2),x13731),x13733))
% 1.61/1.68 [1375]~P8(a2,x13751,x13753)+P8(a2,f56(f56(f13(a2),x13751),x13752),f56(f56(f13(a2),x13753),x13752))
% 1.61/1.68 [1412]~P33(x14121)+E(f10(x14121,f14(x14121,f10(x14121,x14122),f10(x14121,x14123))),f14(x14121,f10(x14121,x14122),f10(x14121,x14123)))
% 1.61/1.68 [1529]P9(a2,x15291,x15292)+~P9(a2,f56(f56(f13(a2),x15293),x15291),f56(f56(f13(a2),x15293),x15292))
% 1.61/1.68 [1530]P9(a2,x15301,x15302)+~P9(a2,f56(f56(f13(a2),x15301),x15303),f56(f56(f13(a2),x15302),x15303))
% 1.61/1.68 [1533]P9(a2,f5(a2),x15331)+~P9(a2,f56(f56(f13(a2),x15332),x15331),f56(f56(f13(a2),x15333),x15331))
% 1.61/1.68 [1534]P9(a2,f5(a2),x15341)+~P9(a2,f56(f56(f13(a2),x15341),x15342),f56(f56(f13(a2),x15341),x15343))
% 1.61/1.68 [1703]~P57(x17031)+E(f20(x17031,f56(f17(x17031,x17032),x17033),f26(x17031,x17032,x17033)),f14(f72(x17031),x17032,f25(x17031,x17033,f26(x17031,x17032,x17033))))
% 1.61/1.68 [1731]~P47(x17311)+P8(a1,f10(a1,f11(a1,f30(x17311,x17312),f30(x17311,x17313))),f30(x17311,f11(x17311,x17312,x17313)))
% 1.61/1.68 [1732]~P33(x17321)+P8(x17321,f10(x17321,f11(x17321,f10(x17321,x17322),f10(x17321,x17323))),f10(x17321,f11(x17321,x17322,x17323)))
% 1.61/1.68 [1167]~P76(x11671)+E(f56(f56(f13(x11671),x11672),f12(x11671,x11673)),f12(x11671,f56(f56(f13(x11671),x11672),x11673)))
% 1.61/1.68 [1169]~P2(x11691)+E(f56(f56(f13(x11691),x11692),f12(x11691,x11693)),f12(x11691,f56(f56(f13(x11691),x11692),x11693)))
% 1.61/1.68 [1190]~P43(x11901)+E(f56(f56(f13(x11901),x11902),f56(f56(f13(x11901),x11902),x11903)),f56(f56(f13(x11901),x11902),x11903))
% 1.61/1.68 [1205]~P55(x12051)+E(f56(f17(x12051,f12(f72(x12051),x12052)),x12053),f12(x12051,f56(f17(x12051,x12052),x12053)))
% 1.61/1.68 [1206]~P45(x12061)+E(f31(x12061,f56(f56(f23(a1),x12062),x12063)),f56(f56(f23(x12061),f31(x12061,x12062)),x12063))
% 1.61/1.68 [1213]~P48(x12131)+E(f30(x12131,f56(f56(f23(x12131),x12132),x12133)),f56(f56(f23(a1),f30(x12131,x12132)),x12133))
% 1.61/1.68 [1218]~P51(x12181)+E(f56(f56(f23(x12181),f28(x12181,x12182)),x12183),f28(x12181,f56(f56(f23(x12181),x12182),x12183)))
% 1.61/1.68 [1219]~P76(x12191)+E(f56(f56(f13(x12191),f12(x12191,x12192)),x12193),f12(x12191,f56(f56(f13(x12191),x12192),x12193)))
% 1.61/1.68 [1220]~P58(x12201)+E(f56(f56(f23(x12201),f10(x12201,x12202)),x12203),f10(x12201,f56(f56(f23(x12201),x12202),x12203)))
% 1.61/1.68 [1222]~P2(x12221)+E(f56(f56(f13(x12221),f12(x12221,x12222)),x12223),f12(x12221,f56(f56(f13(x12221),x12222),x12223)))
% 1.61/1.68 [1262]~P45(x12621)+E(f56(f56(f13(x12621),f31(x12621,x12622)),f31(x12621,x12623)),f31(x12621,f56(f56(f13(a1),x12622),x12623)))
% 1.61/1.68 [1277]~P48(x12771)+E(f56(f56(f13(a1),f30(x12771,x12772)),f30(x12771,x12773)),f30(x12771,f56(f56(f13(x12771),x12772),x12773)))
% 1.61/1.68 [1286]~P6(x12861)+E(f56(f56(f13(x12861),f28(x12861,x12862)),f28(x12861,x12863)),f28(x12861,f56(f56(f13(x12861),x12862),x12863)))
% 1.61/1.68 [1287]~P58(x12871)+E(f56(f56(f13(x12871),f10(x12871,x12872)),f10(x12871,x12873)),f10(x12871,f56(f56(f13(x12871),x12872),x12873)))
% 1.61/1.68 [1288]~P48(x12881)+E(f56(f56(f13(x12881),f15(x12881,x12882)),f15(x12881,x12883)),f15(x12881,f56(f56(f13(x12881),x12882),x12883)))
% 1.61/1.68 [1289]~P58(x12891)+E(f56(f56(f13(x12891),f15(x12891,x12892)),f15(x12891,x12893)),f15(x12891,f56(f56(f13(x12891),x12892),x12893)))
% 1.61/1.68 [1418]~P58(x14181)+E(f10(x14181,f56(f56(f23(x14181),f12(x14181,x14182)),x14183)),f10(x14181,f56(f56(f23(x14181),x14182),x14183)))
% 1.61/1.68 [1592]~P56(x15921)+E(f14(x15921,x15922,f56(f56(f13(x15921),x15923),x15922)),f56(f56(f13(x15921),f14(x15921,x15923,f6(x15921))),x15922))
% 1.61/1.68 [1593]~P56(x15931)+E(f14(x15931,f56(f56(f13(x15931),x15932),x15933),x15933),f56(f56(f13(x15931),f14(x15931,x15932,f6(x15931))),x15933))
% 1.61/1.68 [1617]~P49(x16171)+P8(a1,f30(x16171,f56(f56(f23(x16171),x16172),x16173)),f56(f56(f23(a1),f30(x16171,x16172)),x16173))
% 1.61/1.68 [1665]~P2(x16651)+P8(a1,f30(x16651,f56(f56(f13(x16651),x16652),x16653)),f56(f56(f13(a1),f30(x16651,x16653)),f54(x16652,x16651)))
% 1.61/1.68 [1666]~P2(x16661)+P8(a1,f30(x16661,f56(f56(f13(x16661),x16662),x16663)),f56(f56(f13(a1),f30(x16661,x16662)),f30(x16661,x16663)))
% 1.61/1.68 [1667]~P2(x16671)+P8(a1,f30(x16671,f56(f56(f13(x16671),x16672),x16673)),f56(f56(f13(a1),f30(x16671,x16672)),f52(x16673,x16671)))
% 1.61/1.68 [1697]~P50(x16971)+P8(x16971,f5(x16971),f14(x16971,f56(f56(f13(x16971),x16972),x16972),f56(f56(f13(x16971),x16973),x16973)))
% 1.61/1.68 [1736]~P77(x17361)+E(f56(f56(f13(x17361),f56(f56(f23(x17361),f12(x17361,f6(x17361))),x17362)),f56(f56(f23(x17361),x17363),x17362)),f56(f56(f23(x17361),f12(x17361,x17363)),x17362))
% 1.61/1.68 [1746]~P50(x17461)+~P9(x17461,f14(x17461,f56(f56(f13(x17461),x17462),x17462),f56(f56(f13(x17461),x17463),x17463)),f5(x17461))
% 1.61/1.68 [1775]~P2(x17751)+P8(a1,f30(x17751,f56(f56(f13(x17751),x17752),x17753)),f56(f56(f13(a1),f56(f56(f13(a1),f30(x17751,x17752)),f30(x17751,x17753))),f50(x17751)))
% 1.61/1.68 [1805]~P54(x18051)+E(f14(f72(x18051),f56(f56(f13(f72(x18051)),f20(x18051,f12(x18051,x18052),f20(x18051,f6(x18051),f5(f72(x18051))))),f26(x18051,x18053,x18052)),f20(x18051,f56(f17(x18051,x18053),x18052),f5(f72(x18051)))),x18053)
% 1.61/1.68 [1526]~P3(x15261)+E(f56(f56(f13(x15261),f56(f56(f23(x15261),x15262),x15263)),x15262),f56(f56(f13(x15261),x15262),f56(f56(f23(x15261),x15262),x15263)))
% 1.61/1.68 [1810]~P9(a3,f5(a3),x18103)+P9(a3,x18101,f14(a3,x18102,f56(f56(f13(a3),f14(a3,f10(a3,f11(a3,x18102,x18101)),f6(a3))),x18103)))
% 1.61/1.68 [1811]~P9(a3,f5(a3),x18113)+P9(a3,f11(a3,x18111,f56(f56(f13(a3),f14(a3,f10(a3,f11(a3,x18111,x18112)),f6(a3))),x18113)),x18112)
% 1.61/1.68 [1396]~P56(x13961)+E(f14(x13961,x13962,f14(x13961,x13963,x13964)),f14(x13961,x13963,f14(x13961,x13962,x13964)))
% 1.61/1.68 [1398]~P17(x13981)+E(f14(x13981,f14(x13981,x13982,x13983),x13984),f14(x13981,x13982,f14(x13981,x13983,x13984)))
% 1.61/1.68 [1399]~P56(x13991)+E(f14(x13991,f14(x13991,x13992,x13993),x13994),f14(x13991,x13992,f14(x13991,x13993,x13994)))
% 1.61/1.68 [1400]~P56(x14001)+E(f14(x14001,f14(x14001,x14002,x14003),x14004),f14(x14001,f14(x14001,x14002,x14004),x14003))
% 1.61/1.68 [1519]~P57(x15191)+E(f26(x15191,f20(x15191,x15192,x15193),x15194),f20(x15191,f56(f17(x15191,x15193),x15194),f26(x15191,x15193,x15194)))
% 1.61/1.68 [1548]~P57(x15481)+E(f20(x15481,f56(f56(f13(x15481),x15482),x15483),f25(x15481,x15482,x15484)),f25(x15481,x15482,f20(x15481,x15483,x15484)))
% 1.61/1.68 [1550]~P57(x15501)+E(f14(f72(x15501),f25(x15501,x15502,x15503),f25(x15501,x15504,x15503)),f25(x15501,f14(x15501,x15502,x15504),x15503))
% 1.61/1.68 [1551]~P55(x15511)+E(f11(f72(x15511),f25(x15511,x15512,x15513),f25(x15511,x15514,x15513)),f25(x15511,f11(x15511,x15512,x15514),x15513))
% 1.61/1.68 [1552]~P22(x15521)+E(f14(f72(x15521),f18(x15521,x15522,x15523),f18(x15521,x15524,x15523)),f18(x15521,f14(x15521,x15522,x15524),x15523))
% 1.61/1.68 [1553]~P15(x15531)+E(f11(f72(x15531),f18(x15531,x15532,x15533),f18(x15531,x15534,x15533)),f18(x15531,f11(x15531,x15532,x15534),x15533))
% 1.61/1.68 [1002]~P36(x10022)+E(f56(f12(f77(x10021,x10022),x10023),x10024),f12(x10022,f56(x10023,x10024)))
% 1.61/1.68 [1482]~P57(x14821)+E(f56(f17(x14821,x14822),f56(f17(x14821,x14823),x14824)),f56(f17(x14821,f22(x14821,x14822,x14823)),x14824))
% 1.61/1.68 [1492]~P57(x14921)+E(f56(f56(f13(x14921),x14922),f56(f17(x14921,x14923),x14924)),f56(f17(x14921,f25(x14921,x14922,x14923)),x14924))
% 1.61/1.68 [1595]~P57(x15951)+E(f14(f72(x15951),f25(x15951,x15952,x15953),f25(x15951,x15952,x15954)),f25(x15951,x15952,f14(f72(x15951),x15953,x15954)))
% 1.61/1.68 [1596]~P55(x15961)+E(f11(f72(x15961),f25(x15961,x15962,x15963),f25(x15961,x15962,x15964)),f25(x15961,x15962,f11(f72(x15961),x15963,x15964)))
% 1.61/1.68 [1730]~P57(x17301)+E(f14(f72(x17301),f20(x17301,x17302,f5(f72(x17301))),f56(f56(f13(f72(x17301)),x17303),f22(x17301,x17304,x17303))),f22(x17301,f20(x17301,x17302,x17304),x17303))
% 1.61/1.68 [1743]~P57(x17431)+E(f14(f72(x17431),f25(x17431,x17432,f9(x17431,x17433,x17432)),f20(x17431,x17434,f9(x17431,x17433,x17432))),f9(x17431,f20(x17431,x17434,x17433),x17432))
% 1.61/1.68 [1371]~P56(x13711)+E(f56(f56(f13(x13711),x13712),f56(f56(f13(x13711),x13713),x13714)),f56(f56(f13(x13711),x13713),f56(f56(f13(x13711),x13712),x13714)))
% 1.61/1.68 [1384]~P57(x13841)+E(f25(x13841,f56(f56(f13(x13841),x13842),x13843),x13844),f25(x13841,x13842,f25(x13841,x13843,x13844)))
% 1.61/1.68 [1385]~P57(x13851)+E(f18(x13851,f56(f56(f13(x13851),x13852),x13853),x13854),f25(x13851,x13852,f18(x13851,x13853,x13854)))
% 1.61/1.68 [1522]~P56(x15221)+E(f56(f56(f13(x15221),x15222),f56(f56(f23(x15221),x15223),x15224)),f56(f17(x15221,f18(x15221,x15222,x15224)),x15223))
% 1.61/1.68 [1536]~P2(x15361)+E(f14(x15361,f56(f56(f13(x15361),x15362),x15363),f56(f56(f13(x15361),x15362),x15364)),f56(f56(f13(x15361),x15362),f14(x15361,x15363,x15364)))
% 1.61/1.68 [1537]~P56(x15371)+E(f14(x15371,f56(f56(f13(x15371),x15372),x15373),f56(f56(f13(x15371),x15372),x15374)),f56(f56(f13(x15371),x15372),f14(x15371,x15373,x15374)))
% 1.61/1.68 [1539]~P2(x15391)+E(f11(x15391,f56(f56(f13(x15391),x15392),x15393),f56(f56(f13(x15391),x15392),x15394)),f56(f56(f13(x15391),x15392),f11(x15391,x15393,x15394)))
% 1.61/1.68 [1624]~P57(x16241)+E(f14(x16241,f56(f17(x16241,x16242),x16243),f56(f17(x16241,x16244),x16243)),f56(f17(x16241,f14(f72(x16241),x16242,x16244)),x16243))
% 1.61/1.68 [1625]~P55(x16251)+E(f11(x16251,f56(f17(x16251,x16252),x16253),f56(f17(x16251,x16254),x16253)),f56(f17(x16251,f11(f72(x16251),x16252,x16254)),x16253))
% 1.61/1.68 [1648]~P3(x16481)+E(f56(f56(f13(x16481),f56(f56(f23(x16481),x16482),x16483)),f56(f56(f23(x16481),x16482),x16484)),f56(f56(f23(x16481),x16482),f14(a2,x16483,x16484)))
% 1.61/1.68 [1649]~P56(x16491)+E(f56(f56(f13(x16491),f56(f56(f23(x16491),x16492),x16493)),f56(f56(f23(x16491),x16492),x16494)),f56(f56(f23(x16491),x16492),f14(a2,x16493,x16494)))
% 1.61/1.68 [1659]~P2(x16591)+E(f14(x16591,f56(f56(f13(x16591),x16592),x16593),f56(f56(f13(x16591),x16594),x16593)),f56(f56(f13(x16591),f14(x16591,x16592,x16594)),x16593))
% 1.61/1.68 [1660]~P53(x16601)+E(f14(x16601,f56(f56(f13(x16601),x16602),x16603),f56(f56(f13(x16601),x16604),x16603)),f56(f56(f13(x16601),f14(x16601,x16602,x16604)),x16603))
% 1.61/1.68 [1663]~P2(x16631)+E(f11(x16631,f56(f56(f13(x16631),x16632),x16633),f56(f56(f13(x16631),x16634),x16633)),f56(f56(f13(x16631),f11(x16631,x16632,x16634)),x16633))
% 1.61/1.68 [1664]~P56(x16641)+E(f14(x16641,f56(f56(f13(x16641),x16642),x16643),f56(f56(f13(x16641),x16644),x16643)),f56(f56(f13(x16641),f14(x16641,x16642,x16644)),x16643))
% 1.61/1.68 [1695]~P57(x16951)+E(f14(x16951,x16952,f56(f56(f13(x16951),x16953),f56(f17(x16951,x16954),x16953))),f56(f17(x16951,f20(x16951,x16952,x16954)),x16953))
% 1.61/1.68 [1493]~P57(x14931)+E(f25(x14931,x14932,f56(f56(f13(f72(x14931)),x14933),x14934)),f56(f56(f13(f72(x14931)),x14933),f25(x14931,x14932,x14934)))
% 1.61/1.68 [1517]~P56(x15171)+E(f56(f56(f23(x15171),f56(f56(f23(x15171),x15172),x15173)),x15174),f56(f56(f23(x15171),x15172),f56(f56(f13(a2),x15173),x15174)))
% 1.61/1.68 [1518]~P3(x15181)+E(f56(f56(f23(x15181),f56(f56(f23(x15181),x15182),x15183)),x15184),f56(f56(f23(x15181),x15182),f56(f56(f13(a2),x15183),x15184)))
% 1.61/1.68 [1527]~P16(x15271)+E(f56(f56(f13(x15271),f56(f56(f13(x15271),x15272),x15273)),x15274),f56(f56(f13(x15271),x15272),f56(f56(f13(x15271),x15273),x15274)))
% 1.61/1.68 [1528]~P56(x15281)+E(f56(f56(f13(x15281),f56(f56(f13(x15281),x15282),x15283)),x15284),f56(f56(f13(x15281),x15282),f56(f56(f13(x15281),x15283),x15284)))
% 1.61/1.68 [1626]~P57(x16261)+E(f25(x16261,x16262,f56(f56(f13(f72(x16261)),x16263),x16264)),f56(f56(f13(f72(x16261)),f25(x16261,x16262,x16263)),x16264))
% 1.61/1.68 [1647]~P56(x16471)+E(f56(f56(f13(x16471),f56(f56(f13(x16471),x16472),x16473)),x16474),f56(f56(f13(x16471),f56(f56(f13(x16471),x16472),x16474)),x16473))
% 1.61/1.68 [1701]~P4(x17011)+E(f56(f56(f13(x17011),f56(f56(f23(x17011),x17012),x17013)),f56(f56(f23(x17011),x17014),x17013)),f56(f56(f23(x17011),f56(f56(f13(x17011),x17012),x17014)),x17013))
% 1.61/1.68 [1702]~P56(x17021)+E(f56(f56(f13(x17021),f56(f56(f23(x17021),x17022),x17023)),f56(f56(f23(x17021),x17024),x17023)),f56(f56(f23(x17021),f56(f56(f13(x17021),x17022),x17024)),x17023))
% 1.61/1.68 [1727]~P57(x17271)+E(f14(f72(x17271),f56(f56(f13(f72(x17271)),x17272),x17273),f56(f56(f13(f72(x17271)),x17274),x17273)),f56(f56(f13(f72(x17271)),f14(f72(x17271),x17272,x17274)),x17273))
% 1.61/1.68 [1676]~P56(x16761)+E(f56(f17(x16761,f56(f56(f23(f72(x16761)),x16762),x16763)),x16764),f56(f56(f23(x16761),f56(f17(x16761,x16762),x16764)),x16763))
% 1.61/1.68 [1717]~P57(x17171)+E(f56(f56(f13(x17171),f56(f17(x17171,x17172),x17173)),f56(f17(x17171,x17174),x17173)),f56(f17(x17171,f56(f56(f13(f72(x17171)),x17172),x17174)),x17173))
% 1.61/1.68 [1737]~P57(x17371)+E(f14(f72(x17371),f25(x17371,x17372,x17373),f20(x17371,f5(x17371),f56(f56(f13(f72(x17371)),x17373),x17374))),f56(f56(f13(f72(x17371)),x17373),f20(x17371,x17372,x17374)))
% 1.61/1.68 [1744]~P57(x17441)+E(f14(f72(x17441),f25(x17441,x17442,x17443),f20(x17441,f5(x17441),f56(f56(f13(f72(x17441)),x17444),x17443))),f56(f56(f13(f72(x17441)),f20(x17441,x17442,x17444)),x17443))
% 1.61/1.68 [1780]~P54(x17801)+E(f56(f17(x17801,f56(f56(f13(f72(x17801)),f18(x17801,f6(x17801),x17802)),x17803)),x17804),f56(f56(f13(x17801),f56(f56(f23(x17801),x17804),x17802)),f56(f17(x17801,x17803),x17804)))
% 1.61/1.68 [942]~P10(x9424,x9425,x9421)+E(f56(x9421,x9422),f56(x9421,x9423))
% 1.61/1.68 [1673]~P56(x16731)+E(f14(x16731,f14(x16731,x16732,x16733),f14(x16731,x16734,x16735)),f14(x16731,f14(x16731,x16732,x16734),f14(x16731,x16733,x16735)))
% 1.61/1.68 [1674]~P15(x16741)+E(f14(x16741,f11(x16741,x16742,x16743),f11(x16741,x16744,x16745)),f11(x16741,f14(x16741,x16742,x16744),f14(x16741,x16743,x16745)))
% 1.61/1.68 [1721]~P57(x17211)+E(f56(f56(f13(f72(x17211)),f18(x17211,x17212,x17213)),f18(x17211,x17214,x17215)),f18(x17211,f56(f56(f13(x17211),x17212),x17214),f14(a2,x17213,x17215)))
% 1.61/1.68 [1333]~P26(x13332)+E(f56(f11(f77(x13331,x13332),x13333,x13334),x13335),f11(x13332,f56(x13333,x13335),f56(x13334,x13335)))
% 1.61/1.68 [1677]~P22(x16771)+E(f20(x16771,f14(x16771,x16772,x16773),f14(f72(x16771),x16774,x16775)),f14(f72(x16771),f20(x16771,x16772,x16774),f20(x16771,x16773,x16775)))
% 1.61/1.68 [1678]~P15(x16781)+E(f20(x16781,f11(x16781,x16782,x16783),f11(f72(x16781),x16784,x16785)),f11(f72(x16781),f20(x16781,x16782,x16784),f20(x16781,x16783,x16785)))
% 1.61/1.68 [1785]~P47(x17851)+P8(a1,f30(x17851,f11(x17851,f14(x17851,x17852,x17853),f14(x17851,x17854,x17855))),f14(a1,f30(x17851,f11(x17851,x17852,x17854)),f30(x17851,f11(x17851,x17853,x17855))))
% 1.61/1.68 [1787]~P33(x17871)+P8(x17871,f10(x17871,f11(x17871,f14(x17871,x17872,x17873),f14(x17871,x17874,x17875))),f14(x17871,f10(x17871,f11(x17871,x17872,x17874)),f10(x17871,f11(x17871,x17873,x17875))))
% 1.61/1.68 [1729]~P56(x17291)+E(f56(f56(f13(x17291),f56(f56(f13(x17291),x17292),x17293)),f56(f56(f13(x17291),x17294),x17295)),f56(f56(f13(x17291),f56(f56(f13(x17291),x17292),x17294)),f56(f56(f13(x17291),x17293),x17295)))
% 1.61/1.68 [1766]~P76(x17661)+E(f14(x17661,f56(f56(f13(x17661),x17662),f11(x17661,x17663,x17664)),f56(f56(f13(x17661),f11(x17661,x17662,x17665)),x17664)),f11(x17661,f56(f56(f13(x17661),x17662),x17663),f56(f56(f13(x17661),x17665),x17664)))
% 1.61/1.68 [1806]~P2(x18061)+E(f14(x18061,f14(x18061,f56(f56(f13(x18061),f11(x18061,x18062,x18063)),f11(x18061,x18064,x18065)),f56(f56(f13(x18061),f11(x18061,x18062,x18063)),x18065)),f56(f56(f13(x18061),x18063),f11(x18061,x18064,x18065))),f11(x18061,f56(f56(f13(x18061),x18062),x18064),f56(f56(f13(x18061),x18063),x18065)))
% 1.61/1.68 [1758]~P79(x17581)+E(f14(x17581,f56(f56(f13(x17581),x17582),x17583),f14(x17581,f56(f56(f13(x17581),x17584),x17583),x17585)),f14(x17581,f56(f56(f13(x17581),f14(x17581,x17582,x17584)),x17583),x17585))
% 1.61/1.68 [1781]~P8(a2,x17811,x17814)+E(f11(a2,f14(a2,f56(f56(f13(a2),x17811),x17812),x17813),f14(a2,f56(f56(f13(a2),x17814),x17812),x17815)),f11(a2,x17813,f14(a2,f56(f56(f13(a2),f11(a2,x17814,x17811)),x17812),x17815)))
% 1.61/1.68 [1782]~P8(a2,x17824,x17821)+E(f11(a2,f14(a2,f56(f56(f13(a2),x17821),x17822),x17823),f14(a2,f56(f56(f13(a2),x17824),x17822),x17825)),f11(a2,f14(a2,f56(f56(f13(a2),f11(a2,x17821,x17824)),x17822),x17823),x17825))
% 1.61/1.68 [813]~P47(x8131)+~P45(x8131)+P9(a1,f5(a1),f35(x8131))
% 1.61/1.68 [814]~P47(x8141)+~P45(x8141)+P8(a1,f5(a1),f51(x8141))
% 1.61/1.68 [1315]~P9(a2,f8(a4,x13151),f8(a4,a73))+P10(a4,a4,f17(a4,x13151))+E(f56(f17(a4,x13151),f38(x13151)),f5(a4))
% 1.61/1.68 [929]E(x9291,x9292)+P9(a2,x9292,x9291)+P9(a2,x9291,x9292)
% 1.61/1.68 [930]E(x9301,x9302)+P9(a3,x9302,x9301)+P9(a3,x9301,x9302)
% 1.61/1.68 [1006]E(x10061,x10062)+P9(a1,x10061,x10062)+~P8(a1,x10061,x10062)
% 1.61/1.68 [1009]E(x10091,x10092)+P9(a2,x10091,x10092)+~P8(a2,x10091,x10092)
% 1.61/1.68 [1010]E(x10101,x10102)+P9(a3,x10101,x10102)+~P8(a3,x10101,x10102)
% 1.61/1.68 [1071]E(x10711,x10712)+~P8(a1,x10712,x10711)+~P8(a1,x10711,x10712)
% 1.61/1.68 [1072]E(x10721,x10722)+~P8(a2,x10722,x10721)+~P8(a2,x10721,x10722)
% 1.61/1.68 [1073]E(x10731,x10732)+~P8(a3,x10732,x10731)+~P8(a3,x10731,x10732)
% 1.61/1.68 [674]~P24(x6741)+~E(x6742,f5(x6741))+E(f12(x6741,x6742),x6742)
% 1.61/1.68 [675]~P45(x6751)+E(f31(x6751,x6752),f5(x6751))+~E(x6752,f5(a1))
% 1.61/1.68 [685]~P47(x6851)+~E(x6852,f5(x6851))+E(f30(x6851,x6852),f5(a1))
% 1.61/1.68 [686]~P23(x6861)+~E(f5(x6861),x6862)+E(f12(x6861,x6862),f5(x6861))
% 1.61/1.68 [687]~P51(x6871)+~E(x6872,f5(x6871))+E(f28(x6871,x6872),f5(x6871))
% 1.61/1.68 [688]~P6(x6881)+~E(x6882,f6(x6881))+E(f28(x6881,x6882),f6(x6881))
% 1.61/1.68 [689]~P23(x6891)+~E(x6892,f5(x6891))+E(f12(x6891,x6892),f5(x6891))
% 1.61/1.68 [690]~P33(x6901)+~E(x6902,f5(x6901))+E(f10(x6901,x6902),f5(x6901))
% 1.61/1.68 [691]~P47(x6911)+~E(x6912,f5(x6911))+E(f15(x6911,x6912),f5(x6911))
% 1.61/1.68 [692]~P58(x6921)+~E(x6922,f5(x6921))+E(f15(x6921,x6922),f5(x6921))
% 1.61/1.68 [693]~P37(x6931)+~E(x6932,f5(x6931))+E(f15(x6931,x6932),f5(x6931))
% 1.61/1.68 [696]~P24(x6962)+~E(f12(x6962,x6961),x6961)+E(x6961,f5(x6962))
% 1.61/1.68 [703]~P47(x7032)+E(x7031,f5(x7032))+~E(f30(x7032,x7031),f5(a1))
% 1.61/1.68 [704]~P45(x7042)+~E(f31(x7042,x7041),f5(x7042))+E(x7041,f5(a1))
% 1.61/1.68 [705]~P51(x7052)+~E(f28(x7052,x7051),f5(x7052))+E(x7051,f5(x7052))
% 1.61/1.68 [707]~P52(x7072)+~E(f28(x7072,x7071),f5(x7072))+E(x7071,f5(x7072))
% 1.61/1.68 [708]~P23(x7082)+~E(f12(x7082,x7081),f5(x7082))+E(x7081,f5(x7082))
% 1.61/1.68 [709]~P33(x7092)+~E(f10(x7092,x7091),f5(x7092))+E(x7091,f5(x7092))
% 1.61/1.68 [710]~P47(x7102)+~E(f15(x7102,x7101),f5(x7102))+E(x7101,f5(x7102))
% 1.61/1.68 [711]~P58(x7112)+~E(f15(x7112,x7111),f5(x7112))+E(x7111,f5(x7112))
% 1.61/1.68 [712]~P6(x7122)+~E(f28(x7122,x7121),f6(x7122))+E(x7121,f6(x7122))
% 1.61/1.68 [713]~P23(x7131)+~E(f12(x7131,x7132),f5(x7131))+E(f5(x7131),x7132)
% 1.61/1.68 [772]~E(x7722,f5(a2))+~E(x7721,f5(a2))+E(f14(a2,x7721,x7722),f5(a2))
% 1.61/1.68 [807]~P24(x8071)+~E(x8072,f5(x8071))+E(f14(x8071,x8072,x8072),f5(x8071))
% 1.61/1.68 [828]~P20(x8281)+P9(x8281,x8282,f5(x8281))+E(f10(x8281,x8282),x8282)
% 1.61/1.68 [883]~P47(x8832)+E(x8831,f5(x8832))+P9(a1,f5(a1),f30(x8832,x8831))
% 1.61/1.68 [889]~P58(x8891)+P9(x8891,f5(x8891),x8892)+~E(f15(x8891,x8892),f6(x8891))
% 1.61/1.68 [899]~P47(x8991)+~E(x8992,f5(x8991))+P8(a1,f30(x8991,x8992),f5(a1))
% 1.61/1.68 [907]~P33(x9072)+P9(x9072,f5(x9072),f10(x9072,x9071))+E(x9071,f5(x9072))
% 1.61/1.68 [913]~P33(x9131)+P8(x9131,f10(x9131,x9132),f5(x9131))+~E(x9132,f5(x9131))
% 1.61/1.68 [915]~P24(x9152)+~E(f14(x9152,x9151,x9151),f5(x9152))+E(x9151,f5(x9152))
% 1.61/1.68 [926]~P56(x9262)+~P12(x9262,f5(x9262),x9261)+E(x9261,f5(x9262))
% 1.61/1.68 [954]~P33(x9541)+~P9(x9541,f5(x9541),x9542)+E(f10(x9541,x9542),x9542)
% 1.61/1.68 [955]~P33(x9551)+~P8(x9551,f5(x9551),x9552)+E(f10(x9551,x9552),x9552)
% 1.61/1.68 [970]~P58(x9701)+~P9(x9701,f5(x9701),x9702)+E(f15(x9701,x9702),f6(x9701))
% 1.61/1.68 [978]~P44(x9781)+P13(x9781,x9782)+P8(a2,f58(x9782,x9781),f61(x9782,x9781))
% 1.61/1.68 [983]~P33(x9831)+~P9(x9831,x9832,f5(x9831))+E(f12(x9831,x9832),f10(x9831,x9832))
% 1.61/1.68 [984]~P33(x9841)+~P8(x9841,x9842,f5(x9841))+E(f12(x9841,x9842),f10(x9841,x9842))
% 1.61/1.68 [985]~P20(x9851)+~P9(x9851,x9852,f5(x9851))+E(f12(x9851,x9852),f10(x9851,x9852))
% 1.61/1.68 [1012]~P47(x10122)+E(x10121,f5(x10122))+~P8(a1,f30(x10122,x10121),f5(a1))
% 1.61/1.68 [1018]~P47(x10182)+~E(x10181,f5(x10182))+~P9(a1,f5(a1),f30(x10182,x10181))
% 1.61/1.68 [1027]~P33(x10272)+~P8(x10272,f10(x10272,x10271),f5(x10272))+E(x10271,f5(x10272))
% 1.61/1.68 [1054]~P33(x10542)+~P9(x10542,f5(x10542),f10(x10542,x10541))+~E(x10541,f5(x10542))
% 1.61/1.68 [1084]E(x10841,x10842)+~E(f11(a2,x10842,x10841),f5(a2))+~E(f11(a2,x10841,x10842),f5(a2))
% 1.61/1.68 [1118]~P58(x11181)+~P9(x11181,x11182,f5(x11181))+P9(x11181,x11182,f12(x11181,x11182))
% 1.61/1.68 [1119]~P24(x11191)+~P8(x11191,x11192,f5(x11191))+P8(x11191,x11192,f12(x11191,x11192))
% 1.61/1.68 [1120]~P24(x11201)+~P9(x11201,f5(x11201),x11202)+P9(x11201,f12(x11201,x11202),x11202)
% 1.61/1.68 [1121]~P24(x11211)+~P8(x11211,f5(x11211),x11212)+P8(x11211,f12(x11211,x11212),x11212)
% 1.61/1.68 [1137]~P29(x11371)+~P9(x11371,x11372,f5(x11371))+P9(x11371,f5(x11371),f12(x11371,x11372))
% 1.61/1.68 [1138]~P29(x11381)+~P8(x11381,x11382,f5(x11381))+P8(x11381,f5(x11381),f12(x11381,x11382))
% 1.61/1.68 [1139]~P5(x11391)+~P9(x11391,f5(x11391),x11392)+P9(x11391,f5(x11391),f28(x11391,x11392))
% 1.61/1.68 [1140]~P14(x11401)+~P9(x11401,f5(x11401),x11402)+P9(x11401,f5(x11401),f28(x11401,x11402))
% 1.61/1.68 [1141]~P58(x11411)+~P9(x11411,f5(x11411),x11412)+P9(x11411,f5(x11411),f15(x11411,x11412))
% 1.61/1.68 [1142]~P14(x11421)+~P8(x11421,f5(x11421),x11422)+P8(x11421,f5(x11421),f28(x11421,x11422))
% 1.61/1.68 [1143]~P5(x11431)+~P9(x11431,x11432,f5(x11431))+P9(x11431,f28(x11431,x11432),f5(x11431))
% 1.61/1.68 [1144]~P14(x11441)+~P9(x11441,x11442,f5(x11441))+P9(x11441,f28(x11441,x11442),f5(x11441))
% 1.61/1.68 [1145]~P14(x11451)+~P8(x11451,x11452,f5(x11451))+P9(x11451,f28(x11451,x11452),f6(x11451))
% 1.61/1.68 [1146]~P58(x11461)+~P9(x11461,x11462,f5(x11461))+P9(x11461,f15(x11461,x11462),f5(x11461))
% 1.61/1.68 [1147]~P14(x11471)+~P8(x11471,x11472,f5(x11471))+P8(x11471,f28(x11471,x11472),f5(x11471))
% 1.61/1.68 [1148]~P14(x11481)+~P8(x11481,x11482,f5(x11481))+P8(x11481,f28(x11481,x11482),f6(x11481))
% 1.61/1.68 [1149]~P14(x11491)+~P9(x11491,f6(x11491),x11492)+P9(x11491,f28(x11491,x11492),f6(x11491))
% 1.61/1.68 [1150]~P29(x11501)+~P9(x11501,f5(x11501),x11502)+P9(x11501,f12(x11501,x11502),f5(x11501))
% 1.61/1.68 [1151]~P14(x11511)+~P8(x11511,f6(x11511),x11512)+P8(x11511,f28(x11511,x11512),f6(x11511))
% 1.61/1.68 [1152]~P29(x11521)+~P8(x11521,f5(x11521),x11522)+P8(x11521,f12(x11521,x11522),f5(x11521))
% 1.61/1.68 [1154]~P58(x11541)+~P9(x11541,x11542,f12(x11541,x11542))+P9(x11541,x11542,f5(x11541))
% 1.61/1.68 [1155]~P24(x11551)+~P8(x11551,x11552,f12(x11551,x11552))+P8(x11551,x11552,f5(x11551))
% 1.61/1.68 [1156]~P24(x11561)+~P9(x11561,f12(x11561,x11562),x11562)+P9(x11561,f5(x11561),x11562)
% 1.61/1.68 [1157]~P24(x11571)+~P8(x11571,f12(x11571,x11572),x11572)+P8(x11571,f5(x11571),x11572)
% 1.61/1.68 [1171]~P29(x11711)+~P9(x11711,f5(x11711),f12(x11711,x11712))+P9(x11711,x11712,f5(x11711))
% 1.61/1.68 [1172]~P14(x11721)+~P9(x11721,f6(x11721),f28(x11721,x11722))+P9(x11721,x11722,f6(x11721))
% 1.61/1.68 [1173]~P29(x11731)+~P8(x11731,f5(x11731),f12(x11731,x11732))+P8(x11731,x11732,f5(x11731))
% 1.61/1.68 [1174]~P14(x11741)+~P8(x11741,f6(x11741),f28(x11741,x11742))+P8(x11741,x11742,f6(x11741))
% 1.61/1.68 [1175]~P58(x11751)+~P9(x11751,f15(x11751,x11752),f5(x11751))+P9(x11751,x11752,f5(x11751))
% 1.61/1.68 [1176]~P14(x11761)+~P9(x11761,f28(x11761,x11762),f5(x11761))+P9(x11761,x11762,f5(x11761))
% 1.61/1.68 [1177]~P14(x11771)+~P8(x11771,f28(x11771,x11772),f5(x11771))+P8(x11771,x11772,f5(x11771))
% 1.61/1.68 [1178]~P58(x11781)+~P9(x11781,f5(x11781),f15(x11781,x11782))+P9(x11781,f5(x11781),x11782)
% 1.61/1.68 [1179]~P14(x11791)+~P9(x11791,f5(x11791),f28(x11791,x11792))+P9(x11791,f5(x11791),x11792)
% 1.61/1.68 [1180]~P14(x11801)+~P9(x11801,f6(x11801),f28(x11801,x11802))+P9(x11801,f5(x11801),x11802)
% 1.61/1.68 [1181]~P14(x11811)+~P8(x11811,f6(x11811),f28(x11811,x11812))+P9(x11811,f5(x11811),x11812)
% 1.61/1.68 [1182]~P14(x11821)+~P8(x11821,f5(x11821),f28(x11821,x11822))+P8(x11821,f5(x11821),x11822)
% 1.61/1.68 [1183]~P29(x11831)+~P9(x11831,f12(x11831,x11832),f5(x11831))+P9(x11831,f5(x11831),x11832)
% 1.61/1.68 [1184]~P29(x11841)+~P8(x11841,f12(x11841,x11842),f5(x11841))+P8(x11841,f5(x11841),x11842)
% 1.61/1.68 [1291]~P8(a2,f16(x12911),x12912)+P8(a1,x12911,f29(a2,x12912))+~P8(a1,f5(a1),x12911)
% 1.61/1.68 [1292]~P8(a2,x12921,f27(x12922))+P8(a1,f29(a2,x12921),x12922)+~P8(a1,f5(a1),x12922)
% 1.61/1.68 [1293]~P8(a3,f5(a3),x12932)+~P8(a3,f5(a3),x12931)+P8(a3,f5(a3),f19(x12931,x12932))
% 1.61/1.68 [1307]P9(a2,f27(x13071),x13072)+~P9(a1,x13071,f29(a2,x13072))+~P8(a1,f5(a1),x13071)
% 1.61/1.68 [1310]~P24(x13101)+~P9(x13101,f5(x13101),x13102)+P9(x13101,f5(x13101),f14(x13101,x13102,x13102))
% 1.61/1.68 [1311]~P24(x13111)+~P8(x13111,f5(x13111),x13112)+P8(x13111,f5(x13111),f14(x13111,x13112,x13112))
% 1.61/1.68 [1312]~P58(x13121)+~P9(x13121,x13122,f5(x13121))+P9(x13121,f14(x13121,x13122,x13122),f5(x13121))
% 1.61/1.68 [1313]~P24(x13131)+~P9(x13131,x13132,f5(x13131))+P9(x13131,f14(x13131,x13132,x13132),f5(x13131))
% 1.61/1.68 [1314]~P24(x13141)+~P8(x13141,x13142,f5(x13141))+P8(x13141,f14(x13141,x13142,x13142),f5(x13141))
% 1.61/1.68 [1328]~P8(a1,x13281,x13282)+~P8(a1,f12(a1,x13282),x13281)+P8(a1,f10(a1,x13281),x13282)
% 1.61/1.68 [1401]~P58(x14011)+~P9(x14011,f14(x14011,x14012,x14012),f5(x14011))+P9(x14011,x14012,f5(x14011))
% 1.61/1.68 [1402]~P24(x14021)+~P9(x14021,f14(x14021,x14022,x14022),f5(x14021))+P9(x14021,x14022,f5(x14021))
% 1.61/1.68 [1403]~P24(x14031)+~P8(x14031,f14(x14031,x14032,x14032),f5(x14031))+P8(x14031,x14032,f5(x14031))
% 1.61/1.68 [1404]~P24(x14041)+~P9(x14041,f5(x14041),f14(x14041,x14042,x14042))+P9(x14041,f5(x14041),x14042)
% 1.61/1.68 [1405]~P24(x14051)+~P8(x14051,f5(x14051),f14(x14051,x14052,x14052))+P8(x14051,f5(x14051),x14052)
% 1.61/1.68 [1408]P9(a2,f11(a2,x14081,x14082),x14081)+~P9(a2,f5(a2),x14081)+~P9(a2,f5(a2),x14082)
% 1.61/1.68 [1411]~P8(a3,f5(a3),x14112)+~P8(a3,f5(a3),x14111)+P8(a3,f5(a3),f14(a3,x14111,x14112))
% 1.61/1.68 [1469]P9(a2,f5(a2),x14691)+P9(a2,f5(a2),x14692)+~P9(a2,f5(a2),f14(a2,x14692,x14691))
% 1.61/1.68 [715]~P35(x7151)+E(f8(x7151,x7152),f5(a2))+~E(x7152,f5(f72(x7151)))
% 1.61/1.68 [716]~P35(x7162)+~E(f8(x7162,x7161),f5(a2))+E(x7161,f5(f72(x7162)))
% 1.61/1.68 [724]~P52(x7242)+E(x7241,f5(x7242))+E(f28(x7242,f28(x7242,x7241)),x7241)
% 1.61/1.68 [734]~P47(x7342)+E(x7341,f5(x7342))+E(f30(x7342,f15(x7342,x7341)),f6(a1))
% 1.61/1.68 [735]~P58(x7351)+~E(x7352,f5(f72(x7351)))+E(f15(f72(x7351),x7352),f5(f72(x7351)))
% 1.61/1.68 [741]~P47(x7411)+~E(x7412,f5(x7411))+E(f30(x7411,f15(x7411,x7412)),f5(a1))
% 1.61/1.68 [852]~P46(x8522)+E(x8521,f5(a1))+E(f31(x8522,f28(a1,x8521)),f28(x8522,f31(x8522,x8521)))
% 1.61/1.68 [868]~P48(x8682)+E(x8681,f5(x8682))+E(f30(x8682,f28(x8682,x8681)),f28(a1,f30(x8682,x8681)))
% 1.61/1.68 [871]~P51(x8711)+~P46(x8711)+E(f31(x8711,f28(a1,x8712)),f28(x8711,f31(x8711,x8712)))
% 1.61/1.68 [877]~P52(x8772)+E(x8771,f5(x8772))+E(f28(x8772,f12(x8772,x8771)),f12(x8772,f28(x8772,x8771)))
% 1.61/1.68 [878]~P5(x8782)+E(x8781,f5(x8782))+E(f28(x8782,f10(x8782,x8781)),f10(x8782,f28(x8782,x8781)))
% 1.61/1.68 [879]~P51(x8791)+~P48(x8791)+E(f30(x8791,f28(x8791,x8792)),f28(a1,f30(x8791,x8792)))
% 1.61/1.68 [884]~P52(x8842)+E(x8841,f5(x8842))+E(f56(f56(f13(x8842),x8841),f28(x8842,x8841)),f6(x8842))
% 1.61/1.68 [924]~P58(x9241)+P9(f72(x9241),x9242,f5(f72(x9241)))+E(f10(f72(x9241),x9242),x9242)
% 1.61/1.68 [971]~P58(x9711)+P9(x9711,x9712,f5(x9711))+~E(f15(x9711,x9712),f12(x9711,f6(x9711)))
% 1.61/1.68 [997]~P58(x9971)+~P9(x9971,x9972,f5(x9971))+E(f15(x9971,x9972),f12(x9971,f6(x9971)))
% 1.61/1.68 [1075]~P58(x10751)+~P9(f72(x10751),x10752,f5(f72(x10751)))+E(f12(f72(x10751),x10752),f10(f72(x10751),x10752))
% 1.61/1.68 [1368]E(x13681,x13682)+P9(a3,x13681,x13682)+~P9(a3,x13681,f14(a3,x13682,f6(a3)))
% 1.61/1.68 [1413]~P47(x14131)+~P45(x14131)+P8(a1,f30(x14131,f31(x14131,x14132)),f56(f56(f13(a1),f30(a1,x14132)),f35(x14131)))
% 1.61/1.68 [1414]~P47(x14141)+~P45(x14141)+P8(a1,f30(x14141,f31(x14141,x14142)),f56(f56(f13(a1),f30(a1,x14142)),f51(x14141)))
% 1.61/1.68 [1415]~P47(x14151)+~P45(x14151)+P8(a1,f30(x14151,f31(x14151,x14152)),f56(f56(f13(a1),f30(a1,x14152)),f62(x14151)))
% 1.61/1.68 [1434]~P44(x14341)+P13(x14341,x14342)+~P8(x14341,f56(x14342,f61(x14342,x14341)),f56(x14342,f58(x14342,x14341)))
% 1.61/1.68 [1591]E(f27(x15911),x15912)+~P8(a1,f29(a2,x15912),x15911)+~P9(a1,x15911,f14(a1,f29(a2,x15912),f6(a1)))
% 1.61/1.68 [1631]~P9(a1,f29(a2,x16312),x16311)+~P8(a1,x16311,f14(a1,f29(a2,x16312),f6(a1)))+E(f16(x16311),f14(a2,x16312,f6(a2)))
% 1.61/1.68 [750]~E(x7502,f6(a2))+~E(x7501,f6(a2))+E(f56(f56(f13(a2),x7501),x7502),f6(a2))
% 1.61/1.68 [800]~P75(x8001)+~E(x8002,f6(x8001))+E(f56(f56(f13(x8001),x8002),x8002),f6(x8001))
% 1.61/1.68 [826]E(x8261,f6(a2))+E(x8262,f5(a2))+~E(f56(f56(f13(a2),x8262),x8261),x8262)
% 1.61/1.68 [831]E(x8311,f5(a2))+E(x8312,f5(a2))+~E(f56(f56(f13(a2),x8312),x8311),f5(a2))
% 1.61/1.68 [897]~P75(x8971)+~E(x8972,f12(x8971,f6(x8971)))+E(f56(f56(f13(x8971),x8972),x8972),f6(x8971))
% 1.61/1.68 [967]~P52(x9672)+E(x9671,f5(x9672))+E(f56(f56(f13(x9672),f28(x9672,x9671)),x9671),f6(x9672))
% 1.61/1.68 [968]~P7(x9682)+E(x9681,f5(x9682))+E(f56(f56(f13(x9682),f28(x9682,x9681)),x9681),f6(x9682))
% 1.61/1.68 [1067]E(x10671,f6(a3))+~P9(a3,f5(a3),x10672)+~E(f56(f56(f13(a3),x10672),x10671),f6(a3))
% 1.61/1.68 [1068]E(x10681,f6(a3))+~P9(a3,f5(a3),x10681)+~E(f56(f56(f13(a3),x10681),x10682),f6(a3))
% 1.61/1.68 [1341]E(x13411,f5(a2))+P9(a2,f5(a2),x13412)+~P9(a2,f5(a2),f56(f56(f23(a2),x13412),x13411))
% 1.61/1.68 [1381]~P9(a1,f5(a1),x13812)+~P9(a1,f5(a1),x13811)+P9(a1,f5(a1),f56(f56(f13(a1),x13811),x13812))
% 1.61/1.68 [1382]~P9(a2,f5(a2),x13822)+~P9(a2,f5(a2),x13821)+P9(a2,f5(a2),f56(f56(f13(a2),x13821),x13822))
% 1.61/1.68 [1383]~P8(a3,f5(a3),x13832)+~P8(a3,f5(a3),x13831)+P8(a3,f5(a3),f56(f56(f13(a3),x13831),x13832))
% 1.61/1.68 [1483]E(x14831,f5(a2))+~E(x14832,f5(a3))+~P9(a3,f5(a3),f56(f56(f23(a3),f10(a3,x14832)),x14831))
% 1.61/1.68 [1278]~E(x12782,f5(a1))+~E(x12781,f5(a1))+E(f14(a1,f56(f56(f13(a1),x12781),x12781),f56(f56(f13(a1),x12782),x12782)),f5(a1))
% 1.61/1.68 [1675]~P8(a1,f5(a1),x16752)+~P8(a1,f5(a1),x16751)+P8(a2,f56(f56(f13(a2),f27(x16751)),f27(x16752)),f27(f56(f56(f13(a1),x16751),x16752)))
% 1.61/1.68 [1786]E(x17861,f5(a2))+E(x17862,f5(a4))+P9(a1,f30(a4,f14(a4,f6(a4),f56(f56(f13(a4),x17862),f56(f56(f23(a4),f69(x17861,x17862)),x17861)))),f6(a1))
% 1.61/1.68 [763]~E(x7632,x7633)+~P39(x7631)+P8(x7631,x7632,x7633)
% 1.61/1.68 [765]~E(x7652,x7653)+~P44(x7651)+P8(x7651,x7652,x7653)
% 1.61/1.68 [895]~P9(x8953,x8951,x8952)+~E(x8951,x8952)+~P41(x8953)
% 1.61/1.68 [896]~P9(x8963,x8961,x8962)+~E(x8961,x8962)+~P44(x8963)
% 1.61/1.68 [951]P8(x9511,x9513,x9512)+~P41(x9511)+P9(x9511,x9512,x9513)
% 1.61/1.68 [953]P8(x9531,x9533,x9532)+~P41(x9531)+P8(x9531,x9532,x9533)
% 1.61/1.68 [1024]~P39(x10241)+~P9(x10241,x10242,x10243)+P8(x10241,x10242,x10243)
% 1.61/1.68 [1026]~P44(x10261)+~P9(x10261,x10262,x10263)+P8(x10261,x10262,x10263)
% 1.61/1.68 [1091]~P9(x10911,x10913,x10912)+~P39(x10911)+~P9(x10911,x10912,x10913)
% 1.61/1.68 [1092]~P8(x10921,x10923,x10922)+~P39(x10921)+~P9(x10921,x10922,x10923)
% 1.61/1.68 [1093]~P9(x10931,x10933,x10932)+~P41(x10931)+~P9(x10931,x10932,x10933)
% 1.61/1.68 [1096]~P8(x10961,x10963,x10962)+~P41(x10961)+~P9(x10961,x10962,x10963)
% 1.61/1.68 [1097]~P9(x10971,x10973,x10972)+~P44(x10971)+~P9(x10971,x10972,x10973)
% 1.61/1.68 [1209]~P8(a1,x12091,x12093)+P8(a1,x12091,x12092)+~P8(a1,x12093,x12092)
% 1.61/1.68 [1210]~P8(a2,x12101,x12103)+P8(a2,x12101,x12102)+~P8(a2,x12103,x12102)
% 1.61/1.68 [1211]~P8(a3,x12111,x12113)+P8(a3,x12111,x12112)+~P8(a3,x12113,x12112)
% 1.61/1.68 [718]~P23(x7182)+~E(x7183,f12(x7182,x7181))+E(x7181,f12(x7182,x7183))
% 1.61/1.68 [720]~P23(x7201)+~E(f12(x7201,x7203),x7202)+E(f12(x7201,x7202),x7203)
% 1.61/1.68 [726]~P51(x7263)+E(x7261,x7262)+~E(f28(x7263,x7261),f28(x7263,x7262))
% 1.61/1.68 [727]~P23(x7273)+E(x7271,x7272)+~E(f12(x7273,x7271),f12(x7273,x7272))
% 1.61/1.68 [728]~P42(x7283)+E(x7281,x7282)+~E(f12(x7283,x7281),f12(x7283,x7282))
% 1.61/1.68 [729]~P45(x7293)+E(x7291,x7292)+~E(f31(x7293,x7291),f31(x7293,x7292))
% 1.61/1.68 [784]~E(x7842,x7843)+~P23(x7841)+E(f11(x7841,x7842,x7843),f5(x7841))
% 1.61/1.68 [785]~E(x7852,x7853)+~P15(x7851)+E(f11(x7851,x7852,x7853),f5(x7851))
% 1.61/1.68 [796]~P81(x7961)+~E(x7963,f5(x7961))+E(f14(x7961,x7962,x7963),x7962)
% 1.61/1.68 [797]~E(x7972,x7973)+~P58(x7971)+P8(f72(x7971),x7972,x7973)
% 1.61/1.68 [858]~P23(x8581)+~E(x8583,f12(x8581,x8582))+E(f14(x8581,x8582,x8583),f5(x8581))
% 1.61/1.68 [859]~P23(x8591)+~E(x8592,f12(x8591,x8593))+E(f14(x8591,x8592,x8593),f5(x8591))
% 1.61/1.68 [908]~P81(x9082)+~E(f14(x9082,x9083,x9081),x9083)+E(x9081,f5(x9082))
% 1.61/1.68 [911]~P23(x9113)+E(x9111,x9112)+~E(f11(x9113,x9111,x9112),f5(x9113))
% 1.61/1.68 [912]~P15(x9123)+E(x9121,x9122)+~E(f11(x9123,x9121,x9122),f5(x9123))
% 1.61/1.68 [917]~P58(x9171)+P12(x9171,x9172,x9173)+~E(f10(x9171,x9172),f10(x9171,x9173))
% 1.61/1.68 [943]~P23(x9432)+~E(f14(x9432,x9433,x9431),f5(x9432))+E(x9431,f12(x9432,x9433))
% 1.61/1.68 [944]~P23(x9442)+~E(f14(x9442,x9441,x9443),f5(x9442))+E(x9441,f12(x9442,x9443))
% 1.61/1.68 [945]~P23(x9451)+~E(f14(x9451,x9452,x9453),f5(x9451))+E(f12(x9451,x9452),x9453)
% 1.61/1.68 [1053]~P58(x10531)+~P11(x10531,x10533)+P11(x10531,f20(x10531,x10532,x10533))
% 1.61/1.68 [1078]~P54(x10781)+~P12(x10781,x10782,x10783)+P12(x10781,x10782,f12(x10781,x10783))
% 1.61/1.68 [1079]~P58(x10791)+~P12(x10791,x10792,x10793)+P12(x10791,x10792,f10(x10791,x10793))
% 1.61/1.68 [1080]~P54(x10801)+~P12(x10801,x10802,x10803)+P12(x10801,f12(x10801,x10802),x10803)
% 1.61/1.68 [1081]~P58(x10811)+~P12(x10811,x10812,x10813)+P12(x10811,f10(x10811,x10812),x10813)
% 1.61/1.68 [1126]~P58(x11261)+P12(x11261,x11262,x11263)+~P12(x11261,x11262,f10(x11261,x11263))
% 1.61/1.68 [1127]~P54(x11271)+P12(x11271,x11272,x11273)+~P12(x11271,x11272,f12(x11271,x11273))
% 1.61/1.68 [1128]~P58(x11281)+P9(x11281,x11282,x11283)+~P9(x11281,f10(x11281,x11282),x11283)
% 1.61/1.68 [1130]~P33(x11301)+P8(x11301,x11302,x11303)+~P8(x11301,f10(x11301,x11302),x11303)
% 1.61/1.68 [1131]~P58(x11311)+P12(x11311,x11312,x11313)+~P12(x11311,f10(x11311,x11312),x11313)
% 1.61/1.68 [1132]~P54(x11321)+P12(x11321,x11322,x11323)+~P12(x11321,f12(x11321,x11322),x11323)
% 1.61/1.68 [1161]~P29(x11611)+~P9(x11611,x11613,x11612)+P9(x11611,f12(x11611,x11612),f12(x11611,x11613))
% 1.61/1.68 [1163]~P29(x11631)+~P8(x11631,x11633,x11632)+P8(x11631,f12(x11631,x11632),f12(x11631,x11633))
% 1.61/1.68 [1165]~P42(x11651)+~P8(x11651,x11653,x11652)+P8(x11651,f12(x11651,x11652),f12(x11651,x11653))
% 1.61/1.68 [1194]~P29(x11941)+~P9(x11941,x11943,f12(x11941,x11942))+P9(x11941,x11942,f12(x11941,x11943))
% 1.61/1.68 [1196]~P29(x11961)+~P8(x11961,x11963,f12(x11961,x11962))+P8(x11961,x11962,f12(x11961,x11963))
% 1.61/1.68 [1198]~P29(x11981)+~P9(x11981,f12(x11981,x11983),x11982)+P9(x11981,f12(x11981,x11982),x11983)
% 1.61/1.68 [1199]~P58(x11991)+~P9(x11991,f10(x11991,x11992),x11993)+P9(x11991,f12(x11991,x11992),x11993)
% 1.61/1.68 [1201]~P29(x12011)+~P8(x12011,f12(x12011,x12013),x12012)+P8(x12011,f12(x12011,x12012),x12013)
% 1.61/1.68 [1203]~P33(x12031)+~P8(x12031,f10(x12031,x12032),x12033)+P8(x12031,f12(x12031,x12032),x12033)
% 1.61/1.68 [1214]~P8(a2,x12143,x12141)+~E(f11(a2,x12141,x12143),x12142)+E(x12141,f14(a2,x12142,x12143))
% 1.61/1.68 [1215]~P8(a2,x12152,x12151)+~E(x12151,f14(a2,x12153,x12152))+E(f11(a2,x12151,x12152),x12153)
% 1.61/1.68 [1223]~P29(x12231)+P9(x12231,x12232,x12233)+~P9(x12231,f12(x12231,x12233),f12(x12231,x12232))
% 1.61/1.68 [1224]~P29(x12241)+P8(x12241,x12242,x12243)+~P8(x12241,f12(x12241,x12243),f12(x12241,x12242))
% 1.61/1.68 [1225]~P42(x12251)+P8(x12251,x12252,x12253)+~P8(x12251,f12(x12251,x12253),f12(x12251,x12252))
% 1.61/1.68 [1294]~P29(x12941)+~P9(x12941,x12942,x12943)+P9(x12941,f11(x12941,x12942,x12943),f5(x12941))
% 1.61/1.68 [1295]~P29(x12951)+~P8(x12951,x12952,x12953)+P8(x12951,f11(x12951,x12952,x12953),f5(x12951))
% 1.61/1.68 [1386]~P29(x13861)+P9(x13861,x13862,x13863)+~P9(x13861,f11(x13861,x13862,x13863),f5(x13861))
% 1.61/1.68 [1387]~P29(x13871)+P8(x13871,x13872,x13873)+~P8(x13871,f11(x13871,x13872,x13873),f5(x13871))
% 1.61/1.68 [1544]~P9(a2,x15443,x15441)+~P9(a2,x15443,x15442)+P9(a2,f11(a2,x15441,x15442),f11(a2,x15441,x15443))
% 1.61/1.68 [1545]~P9(a2,x15451,x15453)+~P8(a2,x15452,x15451)+P9(a2,f11(a2,x15451,x15452),f11(a2,x15453,x15452))
% 1.61/1.68 [1618]~P8(a2,x16183,x16182)+~P8(a2,f14(a2,x16181,x16183),x16182)+P8(a2,x16181,f11(a2,x16182,x16183))
% 1.61/1.68 [1619]~P8(a2,x16192,x16193)+~P8(a2,x16191,f11(a2,x16193,x16192))+P8(a2,f14(a2,x16191,x16192),x16193)
% 1.61/1.68 [783]~P60(x7831)+~E(x7832,f5(f72(x7831)))+E(f56(f17(x7831,x7832),x7833),f5(x7831))
% 1.61/1.68 [819]~P60(x8191)+~E(x8192,f5(x8191))+E(f25(x8191,x8192,x8193),f5(f72(x8191)))
% 1.61/1.68 [820]~P35(x8201)+~E(x8202,f5(x8201))+E(f18(x8201,x8202,x8203),f5(f72(x8201)))
% 1.61/1.68 [861]~P60(x8611)+~E(x8613,f5(f72(x8611)))+E(f25(x8611,x8612,x8613),f5(f72(x8611)))
% 1.61/1.68 [862]~P57(x8621)+~E(x8622,f5(f72(x8621)))+E(f9(x8621,x8622,x8623),f5(f72(x8621)))
% 1.61/1.68 [927]~P60(x9271)+E(f21(x9271,x9272,x9273),f5(a2))+E(f56(f17(x9271,x9273),x9272),f5(x9271))
% 1.61/1.68 [940]~P35(x9402)+E(x9401,f5(x9402))+~E(f18(x9402,x9401,x9403),f5(f72(x9402)))
% 1.61/1.68 [941]~P35(x9412)+E(x9411,f5(x9412))+~E(f20(x9412,x9411,x9413),f5(f72(x9412)))
% 1.61/1.68 [964]~P57(x9642)+~E(f9(x9642,x9641,x9643),f5(f72(x9642)))+E(x9641,f5(f72(x9642)))
% 1.61/1.68 [965]~P35(x9652)+~E(f20(x9652,x9653,x9651),f5(f72(x9652)))+E(x9651,f5(f72(x9652)))
% 1.61/1.68 [1246]~P58(x12461)+~P9(f72(x12461),x12463,x12462)+P11(x12461,f11(f72(x12461),x12462,x12463))
% 1.61/1.68 [1322]~P58(x13221)+P9(f72(x13221),x13222,x13223)+~P11(x13221,f11(f72(x13221),x13223,x13222))
% 1.61/1.68 [1323]~P58(x13231)+P8(f72(x13231),x13232,x13233)+~P11(x13231,f11(f72(x13231),x13233,x13232))
% 1.61/1.68 [1540]E(x15401,f5(a1))+~P8(a1,x15402,f5(a1))+~P8(a1,f10(a1,x15401),f56(f56(f13(a1),x15402),f10(a1,x15403)))
% 1.61/1.68 [1589]P9(a2,x15892,x15891)+E(f14(a2,x15891,f68(x15891,x15892,x15893)),x15892)+P82(f56(x15893,f11(a2,x15892,x15891)))
% 1.61/1.68 [1590]P9(a2,x15902,x15901)+E(f14(a2,x15901,f70(x15901,x15902,x15903)),x15902)+P82(f56(x15903,f11(a2,x15902,x15901)))
% 1.61/1.68 [1598]E(f14(a2,x15981,f68(x15981,x15982,x15983)),x15982)+P82(f56(x15983,f11(a2,x15982,x15981)))+~P82(f56(x15983,f5(a2)))
% 1.61/1.68 [1599]E(f14(a2,x15991,f70(x15991,x15992,x15993)),x15992)+P82(f56(x15993,f11(a2,x15992,x15991)))+~P82(f56(x15993,f5(a2)))
% 1.61/1.68 [1608]~P8(a2,x16082,x16083)+~P8(a2,x16082,x16081)+E(f11(a2,f11(a2,x16081,x16082),f11(a2,x16083,x16082)),f11(a2,x16081,x16083))
% 1.61/1.68 [1623]~P9(a2,x16232,x16233)+~P82(f56(x16231,f11(a2,x16232,x16233)))+P82(f56(x16231,f5(a2)))
% 1.61/1.68 [1722]P9(a2,x17221,x17222)+~P82(f56(x17223,f68(x17222,x17221,x17223)))+P82(f56(x17223,f11(a2,x17221,x17222)))
% 1.61/1.68 [1723]P9(a2,x17231,x17232)+~P82(f56(x17233,f70(x17232,x17231,x17233)))+P82(f56(x17233,f11(a2,x17231,x17232)))
% 1.61/1.68 [1725]~P82(f56(x17251,f68(x17253,x17252,x17251)))+P82(f56(x17251,f11(a2,x17252,x17253)))+~P82(f56(x17251,f5(a2)))
% 1.61/1.68 [1726]~P82(f56(x17261,f70(x17263,x17262,x17261)))+P82(f56(x17261,f11(a2,x17262,x17263)))+~P82(f56(x17261,f5(a2)))
% 1.61/1.68 [786]~P27(x7861)+~E(x7863,f5(a2))+E(f56(f56(f23(x7861),x7862),x7863),f6(x7861))
% 1.61/1.68 [798]~P74(x7981)+~E(x7983,f5(x7981))+E(f56(f56(f13(x7981),x7982),x7983),f5(x7981))
% 1.61/1.68 [799]~P74(x7991)+~E(x7992,f5(x7991))+E(f56(f56(f13(x7991),x7992),x7993),f5(x7991))
% 1.61/1.68 [910]~P75(x9102)+E(x9101,f5(x9102))+~E(f56(f56(f23(x9102),x9101),x9103),f5(x9102))
% 1.61/1.68 [931]~P52(x9311)+E(f28(x9311,x9312),x9313)+~E(f56(f56(f13(x9311),x9312),x9313),f6(x9311))
% 1.61/1.68 [986]~P60(x9861)+~E(x9862,f12(x9861,x9863))+E(f56(f56(f13(x9861),x9862),x9862),f56(f56(f13(x9861),x9863),x9863))
% 1.61/1.68 [1044]E(x10441,x10442)+E(x10443,f5(a1))+~E(f56(f56(f13(a1),x10443),x10441),f56(f56(f13(a1),x10443),x10442))
% 1.61/1.68 [1046]E(x10461,x10462)+E(x10463,f5(a2))+~E(f56(f56(f13(a2),x10463),x10461),f56(f56(f13(a2),x10463),x10462))
% 1.61/1.68 [1047]E(x10471,x10472)+E(x10473,f5(a1))+~E(f56(f56(f13(a1),x10471),x10473),f56(f56(f13(a1),x10472),x10473))
% 1.61/1.68 [1048]E(x10481,x10482)+E(x10483,f5(a2))+~E(f56(f56(f13(a2),x10481),x10483),f56(f56(f13(a2),x10482),x10483))
% 1.61/1.68 [1244]E(x12441,x12442)+~P9(a2,f5(a2),x12443)+~E(f56(f56(f13(a2),x12443),x12441),f56(f56(f13(a2),x12443),x12442))
% 1.61/1.68 [1303]~P1(x13031)+~P9(x13031,f5(x13031),x13032)+P9(x13031,f5(x13031),f56(f56(f23(x13031),x13032),x13033))
% 1.61/1.68 [1304]~P1(x13041)+~P8(x13041,f5(x13041),x13042)+P8(x13041,f5(x13041),f56(f56(f23(x13041),x13042),x13043))
% 1.61/1.68 [1305]~P1(x13051)+~P8(x13051,f6(x13051),x13052)+P8(x13051,f6(x13051),f56(f56(f23(x13051),x13052),x13053))
% 1.61/1.68 [1506]~P9(a1,x15061,x15063)+~P9(a1,f5(a1),x15062)+P9(a1,f56(f56(f13(a1),x15061),x15062),f56(f56(f13(a1),x15063),x15062))
% 1.61/1.68 [1507]~P9(a1,x15072,x15073)+~P9(a1,f5(a1),x15071)+P9(a1,f56(f56(f13(a1),x15071),x15072),f56(f56(f13(a1),x15071),x15073))
% 1.61/1.68 [1511]~P9(a2,x15111,x15113)+~P9(a2,f5(a2),x15112)+P9(a2,f56(f56(f13(a2),x15111),x15112),f56(f56(f13(a2),x15113),x15112))
% 1.61/1.68 [1512]~P9(a2,x15122,x15123)+~P9(a2,f5(a2),x15121)+P9(a2,f56(f56(f13(a2),x15121),x15122),f56(f56(f13(a2),x15121),x15123))
% 1.61/1.68 [1513]~P9(a3,x15132,x15133)+~P9(a3,f5(a3),x15131)+P9(a3,f56(f56(f13(a3),x15131),x15132),f56(f56(f13(a3),x15131),x15133))
% 1.61/1.68 [1514]~P8(a1,x15142,x15143)+~P9(a1,f5(a1),x15141)+P8(a1,f56(f56(f13(a1),x15141),x15142),f56(f56(f13(a1),x15141),x15143))
% 1.61/1.68 [1515]~P8(a1,x15151,x15153)+~P9(a1,f5(a1),x15152)+P8(a1,f56(f56(f13(a1),x15151),x15152),f56(f56(f13(a1),x15153),x15152))
% 1.61/1.68 [1632]P9(a1,x16321,x16322)+~P9(a1,f5(a1),x16323)+~P9(a1,f56(f56(f13(a1),x16321),x16323),f56(f56(f13(a1),x16322),x16323))
% 1.61/1.68 [1633]P9(a2,x16331,x16332)+~P9(a2,f5(a2),x16333)+~P9(a2,f56(f56(f23(a2),x16333),x16331),f56(f56(f23(a2),x16333),x16332))
% 1.61/1.68 [1635]P8(a1,x16351,x16352)+~P9(a1,f5(a1),x16353)+~P8(a1,f56(f56(f13(a1),x16353),x16351),f56(f56(f13(a1),x16353),x16352))
% 1.61/1.68 [1636]P8(a1,x16361,x16362)+~P9(a1,f5(a1),x16363)+~P8(a1,f56(f56(f13(a1),x16361),x16363),f56(f56(f13(a1),x16362),x16363))
% 1.61/1.68 [1638]P8(a2,x16381,x16382)+~P9(a2,f5(a2),x16383)+~P8(a2,f56(f56(f13(a2),x16383),x16381),f56(f56(f13(a2),x16383),x16382))
% 1.61/1.68 [1639]P8(a2,x16391,x16392)+~P9(a2,f5(a2),x16393)+~P8(a2,f56(f56(f13(a2),x16391),x16393),f56(f56(f13(a2),x16392),x16393))
% 1.61/1.68 [1228]~P52(x12282)+E(x12281,f5(x12282))+E(f56(f56(f23(x12282),f28(x12282,x12281)),x12283),f28(x12282,f56(f56(f23(x12282),x12281),x12283)))
% 1.61/1.68 [1380]~P58(x13801)+~P8(x13801,f5(x13801),x13803)+E(f56(f56(f13(x13801),f10(x13801,x13802)),x13803),f10(x13801,f56(f56(f13(x13801),x13802),x13803)))
% 1.61/1.68 [1541]~P62(x15412)+E(x15411,f5(x15412))+~E(f14(x15412,f56(f56(f13(x15412),x15413),x15413),f56(f56(f13(x15412),x15411),x15411)),f5(x15412))
% 1.61/1.68 [1542]~P62(x15422)+E(x15421,f5(x15422))+~E(f14(x15422,f56(f56(f13(x15422),x15421),x15421),f56(f56(f13(x15422),x15423),x15423)),f5(x15422))
% 1.61/1.68 [1549]~P27(x15492)+E(x15491,f5(a2))+E(f56(f56(f13(x15492),x15493),f56(f56(f23(x15492),x15493),f11(a2,x15491,f6(a2)))),f56(f56(f23(x15492),x15493),x15491))
% 1.61/1.68 [1605]~P1(x16051)+~P9(x16051,f6(x16051),x16052)+P9(x16051,f6(x16051),f56(f56(f13(x16051),x16052),f56(f56(f23(x16051),x16052),x16053)))
% 1.61/1.68 [1694]~P1(x16941)+~P9(x16941,f6(x16941),x16942)+P9(x16941,f56(f56(f23(x16941),x16942),x16943),f56(f56(f13(x16941),x16942),f56(f56(f23(x16941),x16942),x16943)))
% 1.61/1.68 [1698]~P62(x16982)+E(x16981,f5(x16982))+P9(x16982,f5(x16982),f14(x16982,f56(f56(f13(x16982),x16983),x16983),f56(f56(f13(x16982),x16981),x16981)))
% 1.61/1.68 [1699]~P62(x16992)+E(x16991,f5(x16992))+P9(x16992,f5(x16992),f14(x16992,f56(f56(f13(x16992),x16991),x16991),f56(f56(f13(x16992),x16993),x16993)))
% 1.61/1.68 [1747]~P62(x17472)+E(x17471,f5(x17472))+~P8(x17472,f14(x17472,f56(f56(f13(x17472),x17473),x17473),f56(f56(f13(x17472),x17471),x17471)),f5(x17472))
% 1.61/1.68 [1748]~P62(x17482)+E(x17481,f5(x17482))+~P8(x17482,f14(x17482,f56(f56(f13(x17482),x17481),x17481),f56(f56(f13(x17482),x17483),x17483)),f5(x17482))
% 1.61/1.68 [1741]~P3(x17411)+~P9(a2,f5(a2),x17413)+E(f56(f56(f13(x17411),f56(f56(f23(x17411),x17412),f11(a2,x17413,f6(a2)))),x17412),f56(f56(f23(x17411),x17412),x17413))
% 1.61/1.68 [1100]~P18(x11003)+E(x11001,x11002)+~E(f14(x11003,x11004,x11001),f14(x11003,x11004,x11002))
% 1.61/1.68 [1101]~P19(x11013)+E(x11011,x11012)+~E(f14(x11013,x11014,x11011),f14(x11013,x11014,x11012))
% 1.61/1.68 [1103]~P18(x11033)+E(x11031,x11032)+~E(f14(x11033,x11031,x11034),f14(x11033,x11032,x11034))
% 1.61/1.68 [1104]~P35(x11043)+E(x11041,x11042)+~E(f18(x11043,x11041,x11044),f18(x11043,x11042,x11044))
% 1.61/1.68 [1204]~P40(x12042)+~P9(f77(x12041,x12042),x12043,x12044)+P8(f77(x12041,x12042),x12043,x12044)
% 1.61/1.68 [1296]~P40(x12961)+~P8(f77(x12962,x12961),x12964,x12963)+~P9(f77(x12962,x12961),x12963,x12964)
% 1.61/1.68 [1361]~P9(a2,x13613,x13614)+P9(a2,x13611,x13612)+~E(f14(a2,x13613,x13612),f14(a2,x13611,x13614))
% 1.61/1.68 [1442]~P31(x14421)+~P9(x14421,x14423,x14424)+P9(x14421,f14(x14421,x14422,x14423),f14(x14421,x14422,x14424))
% 1.61/1.68 [1443]~P34(x14431)+~P9(x14431,x14433,x14434)+P9(x14431,f14(x14431,x14432,x14433),f14(x14431,x14432,x14434))
% 1.61/1.68 [1444]~P31(x14441)+~P9(x14441,x14442,x14444)+P9(x14441,f14(x14441,x14442,x14443),f14(x14441,x14444,x14443))
% 1.61/1.68 [1445]~P34(x14451)+~P9(x14451,x14452,x14454)+P9(x14451,f14(x14451,x14452,x14453),f14(x14451,x14454,x14453))
% 1.61/1.68 [1446]~P31(x14461)+~P8(x14461,x14463,x14464)+P8(x14461,f14(x14461,x14462,x14463),f14(x14461,x14462,x14464))
% 1.61/1.68 [1447]~P32(x14471)+~P8(x14471,x14473,x14474)+P8(x14471,f14(x14471,x14472,x14473),f14(x14471,x14472,x14474))
% 1.61/1.68 [1448]~P31(x14481)+~P8(x14481,x14482,x14484)+P8(x14481,f14(x14481,x14482,x14483),f14(x14481,x14484,x14483))
% 1.61/1.68 [1449]~P32(x14491)+~P8(x14491,x14492,x14494)+P8(x14491,f14(x14491,x14492,x14493),f14(x14491,x14494,x14493))
% 1.61/1.68 [1543]~P9(a2,x15432,x15434)+~P9(a2,x15431,x15433)+P9(a2,f14(a2,x15431,x15432),f14(a2,x15433,x15434))
% 1.61/1.68 [1546]~P9(a3,x15461,x15463)+~P8(a3,x15462,x15464)+P9(a3,f14(a3,x15461,x15462),f14(a3,x15463,x15464))
% 1.61/1.68 [1547]~P8(a2,x15472,x15474)+~P8(a2,x15471,x15473)+P8(a2,f14(a2,x15471,x15472),f14(a2,x15473,x15474))
% 1.61/1.68 [1610]~P31(x16101)+P9(x16101,x16102,x16103)+~P9(x16101,f14(x16101,x16104,x16102),f14(x16101,x16104,x16103))
% 1.61/1.68 [1612]~P31(x16121)+P9(x16121,x16122,x16123)+~P9(x16121,f14(x16121,x16122,x16124),f14(x16121,x16123,x16124))
% 1.61/1.68 [1614]~P31(x16141)+P8(x16141,x16142,x16143)+~P8(x16141,f14(x16141,x16144,x16142),f14(x16141,x16144,x16143))
% 1.61/1.68 [1616]~P31(x16161)+P8(x16161,x16162,x16163)+~P8(x16161,f14(x16161,x16162,x16164),f14(x16161,x16163,x16164))
% 1.61/1.68 [1136]~P57(x11362)+~E(f20(x11362,x11363,x11361),f25(x11362,x11364,x11361))+E(x11361,f5(f72(x11362)))
% 1.61/1.68 [1603]~P57(x16032)+~E(f14(f72(x16032),f25(x16032,x16033,x16031),f20(x16032,x16034,x16031)),f5(f72(x16032)))+E(x16031,f5(f72(x16032)))
% 1.61/1.68 [1621]~E(x16213,f14(a2,x16214,x16212))+P82(f56(x16211,x16212))+~P82(f56(x16211,f11(a2,x16213,x16214)))
% 1.61/1.68 [1714]~P58(x17141)+P9(x17141,x17142,f14(x17141,x17143,x17144))+~P9(x17141,f10(x17141,f11(x17141,x17142,x17143)),x17144)
% 1.61/1.68 [1715]~P58(x17151)+P9(x17151,f11(x17151,x17152,x17153),x17154)+~P9(x17151,f10(x17151,f11(x17151,x17154,x17152)),x17153)
% 1.61/1.68 [1807]~P40(x18072)+P8(f77(x18071,x18072),x18073,x18074)+~P8(x18072,f56(x18073,f48(x18074,x18073,x18071,x18072)),f56(x18074,f48(x18074,x18073,x18071,x18072)))
% 1.61/1.68 [1319]~P60(x13191)+~E(x13193,f5(x13191))+P12(x13191,f56(f56(f13(x13191),x13192),x13193),f56(f56(f13(x13191),x13194),x13193))
% 1.61/1.68 [1320]~P60(x13201)+~E(x13202,f5(x13201))+P12(x13201,f56(f56(f13(x13201),x13202),x13203),f56(f56(f13(x13201),x13202),x13204))
% 1.61/1.68 [1435]~P56(x14351)+~P12(x14351,x14352,x14354)+P12(x14351,f56(f56(f23(x14351),x14352),x14353),f56(f56(f23(x14351),x14354),x14353))
% 1.61/1.68 [1436]~P60(x14361)+~P12(x14361,x14363,x14364)+P12(x14361,f56(f56(f13(x14361),x14362),x14363),f56(f56(f13(x14361),x14362),x14364))
% 1.61/1.68 [1437]~P60(x14371)+~P12(x14371,x14372,x14374)+P12(x14371,f56(f56(f13(x14371),x14372),x14373),f56(f56(f13(x14371),x14374),x14373))
% 1.61/1.68 [1500]~P8(a2,x15002,x15004)+~P8(a2,x15001,x15003)+P8(a2,f56(f56(f13(a2),x15001),x15002),f56(f56(f13(a2),x15003),x15004))
% 1.61/1.68 [1105]~P35(x11053)+E(x11051,x11052)+~E(f20(x11053,x11054,x11051),f20(x11053,x11055,x11052))
% 1.61/1.68 [1106]~P35(x11063)+E(x11061,x11062)+~E(f20(x11063,x11061,x11064),f20(x11063,x11062,x11065))
% 1.61/1.68 [1261]~P40(x12611)+P8(x12611,f56(x12612,x12613),f56(x12614,x12613))+~P8(f77(x12615,x12611),x12612,x12614)
% 1.61/1.68 [1494]~P57(x14942)+~E(f14(f72(x14942),x14943,f25(x14942,x14944,x14945)),f20(x14942,x14941,x14945))+E(x14941,f56(f17(x14942,x14943),x14944))
% 1.61/1.68 [1521]~P57(x15212)+E(x15211,f26(x15212,x15213,x15214))+~E(f14(f72(x15212),x15213,f25(x15212,x15214,x15211)),f20(x15212,x15215,x15211))
% 1.61/1.68 [1653]~E(x16532,x16534)+~P81(x16531)+E(f14(x16531,f56(f56(f13(x16531),x16532),x16533),f56(f56(f13(x16531),x16534),x16535)),f14(x16531,f56(f56(f13(x16531),x16532),x16535),f56(f56(f13(x16531),x16534),x16533)))
% 1.61/1.68 [1761]~P8(a2,x17613,x17612)+E(x17611,f14(a2,f56(f56(f13(a2),f11(a2,x17612,x17613)),x17614),x17615))+~E(f14(a2,f56(f56(f13(a2),x17613),x17614),x17611),f14(a2,f56(f56(f13(a2),x17612),x17614),x17615))
% 1.61/1.68 [1762]~P8(a2,x17622,x17621)+E(f14(a2,f56(f56(f13(a2),f11(a2,x17621,x17622)),x17623),x17624),x17625)+~E(f14(a2,f56(f56(f13(a2),x17621),x17623),x17624),f14(a2,f56(f56(f13(a2),x17622),x17623),x17625))
% 1.61/1.68 [1770]~P8(a2,x17704,x17701)+~E(x17705,f14(a2,f56(f56(f13(a2),f11(a2,x17701,x17704)),x17702),x17703))+E(f14(a2,f56(f56(f13(a2),x17701),x17702),x17703),f14(a2,f56(f56(f13(a2),x17704),x17702),x17705))
% 1.61/1.68 [1771]~P8(a2,x17714,x17711)+~E(f14(a2,f56(f56(f13(a2),f11(a2,x17711,x17714)),x17712),x17713),x17715)+E(f14(a2,f56(f56(f13(a2),x17711),x17712),x17713),f14(a2,f56(f56(f13(a2),x17714),x17712),x17715))
% 1.61/1.68 [1788]~P8(a2,x17883,x17882)+P9(a2,x17881,f14(a2,f56(f56(f13(a2),f11(a2,x17882,x17883)),x17884),x17885))+~P9(a2,f14(a2,f56(f56(f13(a2),x17883),x17884),x17881),f14(a2,f56(f56(f13(a2),x17882),x17884),x17885))
% 1.61/1.68 [1789]~P8(a2,x17893,x17892)+P8(a2,x17891,f14(a2,f56(f56(f13(a2),f11(a2,x17892,x17893)),x17894),x17895))+~P8(a2,f14(a2,f56(f56(f13(a2),x17893),x17894),x17891),f14(a2,f56(f56(f13(a2),x17892),x17894),x17895))
% 1.61/1.68 [1790]~P8(a2,x17902,x17901)+P9(a2,f14(a2,f56(f56(f13(a2),f11(a2,x17901,x17902)),x17903),x17904),x17905)+~P9(a2,f14(a2,f56(f56(f13(a2),x17901),x17903),x17904),f14(a2,f56(f56(f13(a2),x17902),x17903),x17905))
% 1.61/1.68 [1791]~P8(a2,x17912,x17911)+P8(a2,f14(a2,f56(f56(f13(a2),f11(a2,x17911,x17912)),x17913),x17914),x17915)+~P8(a2,f14(a2,f56(f56(f13(a2),x17911),x17913),x17914),f14(a2,f56(f56(f13(a2),x17912),x17913),x17915))
% 1.61/1.68 [1797]~P8(a2,x17971,x17974)+~P9(a2,x17973,f14(a2,f56(f56(f13(a2),f11(a2,x17974,x17971)),x17972),x17975))+P9(a2,f14(a2,f56(f56(f13(a2),x17971),x17972),x17973),f14(a2,f56(f56(f13(a2),x17974),x17972),x17975))
% 1.61/1.68 [1798]~P8(a2,x17981,x17984)+~P8(a2,x17983,f14(a2,f56(f56(f13(a2),f11(a2,x17984,x17981)),x17982),x17985))+P8(a2,f14(a2,f56(f56(f13(a2),x17981),x17982),x17983),f14(a2,f56(f56(f13(a2),x17984),x17982),x17985))
% 1.61/1.68 [1799]~P8(a2,x17994,x17991)+~P9(a2,f14(a2,f56(f56(f13(a2),f11(a2,x17991,x17994)),x17992),x17993),x17995)+P9(a2,f14(a2,f56(f56(f13(a2),x17991),x17992),x17993),f14(a2,f56(f56(f13(a2),x17994),x17992),x17995))
% 1.61/1.68 [1800]~P8(a2,x18004,x18001)+~P8(a2,f14(a2,f56(f56(f13(a2),f11(a2,x18001,x18004)),x18002),x18003),x18005)+P8(a2,f14(a2,f56(f56(f13(a2),x18001),x18002),x18003),f14(a2,f56(f56(f13(a2),x18004),x18002),x18005))
% 1.61/1.68 [1759]~P76(x17592)+~E(f14(x17592,f56(f56(f13(x17592),x17594),x17595),x17591),f14(x17592,f56(f56(f13(x17592),x17593),x17595),x17596))+E(x17591,f14(x17592,f56(f56(f13(x17592),f11(x17592,x17593,x17594)),x17595),x17596))
% 1.61/1.68 [1760]~P76(x17601)+~E(f14(x17601,f56(f56(f13(x17601),x17602),x17604),x17605),f14(x17601,f56(f56(f13(x17601),x17603),x17604),x17606))+E(f14(x17601,f56(f56(f13(x17601),f11(x17601,x17602,x17603)),x17604),x17605),x17606)
% 1.61/1.68 [1768]~P76(x17681)+~E(x17686,f14(x17681,f56(f56(f13(x17681),f11(x17681,x17682,x17685)),x17683),x17684))+E(f14(x17681,f56(f56(f13(x17681),x17682),x17683),x17684),f14(x17681,f56(f56(f13(x17681),x17685),x17683),x17686))
% 1.61/1.68 [1769]~P76(x17691)+~E(f14(x17691,f56(f56(f13(x17691),f11(x17691,x17692,x17695)),x17693),x17694),x17696)+E(f14(x17691,f56(f56(f13(x17691),x17692),x17693),x17694),f14(x17691,f56(f56(f13(x17691),x17695),x17693),x17696))
% 1.61/1.68 [1792]~P70(x17921)+~P9(x17921,f14(x17921,f56(f56(f13(x17921),x17924),x17925),x17922),f14(x17921,f56(f56(f13(x17921),x17923),x17925),x17926))+P9(x17921,x17922,f14(x17921,f56(f56(f13(x17921),f11(x17921,x17923,x17924)),x17925),x17926))
% 1.61/1.68 [1793]~P70(x17931)+~P8(x17931,f14(x17931,f56(f56(f13(x17931),x17934),x17935),x17932),f14(x17931,f56(f56(f13(x17931),x17933),x17935),x17936))+P8(x17931,x17932,f14(x17931,f56(f56(f13(x17931),f11(x17931,x17933,x17934)),x17935),x17936))
% 1.61/1.68 [1794]~P70(x17941)+~P9(x17941,f14(x17941,f56(f56(f13(x17941),x17942),x17944),x17945),f14(x17941,f56(f56(f13(x17941),x17943),x17944),x17946))+P9(x17941,f14(x17941,f56(f56(f13(x17941),f11(x17941,x17942,x17943)),x17944),x17945),x17946)
% 1.61/1.68 [1795]~P70(x17951)+~P8(x17951,f14(x17951,f56(f56(f13(x17951),x17952),x17954),x17955),f14(x17951,f56(f56(f13(x17951),x17953),x17954),x17956))+P8(x17951,f14(x17951,f56(f56(f13(x17951),f11(x17951,x17952,x17953)),x17954),x17955),x17956)
% 1.61/1.68 [1801]~P70(x18011)+~P9(x18011,x18014,f14(x18011,f56(f56(f13(x18011),f11(x18011,x18015,x18012)),x18013),x18016))+P9(x18011,f14(x18011,f56(f56(f13(x18011),x18012),x18013),x18014),f14(x18011,f56(f56(f13(x18011),x18015),x18013),x18016))
% 1.61/1.68 [1802]~P70(x18021)+~P8(x18021,x18024,f14(x18021,f56(f56(f13(x18021),f11(x18021,x18025,x18022)),x18023),x18026))+P8(x18021,f14(x18021,f56(f56(f13(x18021),x18022),x18023),x18024),f14(x18021,f56(f56(f13(x18021),x18025),x18023),x18026))
% 1.61/1.68 [1803]~P70(x18031)+~P9(x18031,f14(x18031,f56(f56(f13(x18031),f11(x18031,x18032,x18035)),x18033),x18034),x18036)+P9(x18031,f14(x18031,f56(f56(f13(x18031),x18032),x18033),x18034),f14(x18031,f56(f56(f13(x18031),x18035),x18033),x18036))
% 1.61/1.68 [1804]~P70(x18041)+~P8(x18041,f14(x18041,f56(f56(f13(x18041),f11(x18041,x18042,x18045)),x18043),x18044),x18046)+P8(x18041,f14(x18041,f56(f56(f13(x18041),x18042),x18043),x18044),f14(x18041,f56(f56(f13(x18041),x18045),x18043),x18046))
% 1.61/1.68 [977]~P37(x9772)+~P9(x9772,f5(x9772),x9771)+E(f15(x9772,x9771),f6(x9772))+E(x9771,f5(x9772))
% 1.61/1.68 [1187]~P5(x11872)+~P9(x11872,f28(x11872,x11871),f5(x11872))+P9(x11872,x11871,f5(x11872))+E(x11871,f5(x11872))
% 1.61/1.68 [1188]~P5(x11882)+~P9(x11882,f5(x11882),f28(x11882,x11881))+P9(x11882,f5(x11882),x11881)+E(x11881,f5(x11882))
% 1.61/1.68 [1301]~P14(x13011)+P9(x13011,f6(x13011),x13012)+~P9(x13011,f28(x13011,x13012),f6(x13011))+P8(x13011,x13012,f5(x13011))
% 1.61/1.68 [1302]~P14(x13021)+P8(x13021,f6(x13021),x13022)+~P8(x13021,f28(x13021,x13022),f6(x13021))+P8(x13021,x13022,f5(x13021))
% 1.61/1.68 [1329]~P5(x13291)+~P9(x13291,x13292,f6(x13291))+~P9(x13291,f5(x13291),x13292)+P9(x13291,f6(x13291),f28(x13291,x13292))
% 1.61/1.68 [1330]~P14(x13301)+~P9(x13301,x13302,f6(x13301))+~P9(x13301,f5(x13301),x13302)+P9(x13301,f6(x13301),f28(x13301,x13302))
% 1.61/1.68 [1331]~P5(x13311)+~P8(x13311,x13312,f6(x13311))+~P9(x13311,f5(x13311),x13312)+P8(x13311,f6(x13311),f28(x13311,x13312))
% 1.61/1.68 [1332]~P14(x13321)+~P8(x13321,x13322,f6(x13321))+~P9(x13321,f5(x13321),x13322)+P8(x13321,f6(x13321),f28(x13321,x13322))
% 1.61/1.68 [834]P11(x8342,x8341)+~P58(x8342)+P11(x8342,f12(f72(x8342),x8341))+E(x8341,f5(f72(x8342)))
% 1.61/1.68 [925]~P37(x9252)+P9(x9252,f5(x9252),x9251)+E(x9251,f5(x9252))+E(f15(x9252,x9251),f12(x9252,f6(x9252)))
% 1.61/1.68 [1077]~P58(x10772)+~P9(f72(x10772),f5(f72(x10772)),x10771)+E(f15(f72(x10772),x10771),f6(f72(x10772)))+E(x10771,f5(f72(x10772)))
% 1.61/1.68 [835]~P27(x8352)+~P80(x8352)+E(x8351,f5(a2))+E(f56(f56(f23(x8352),f5(x8352)),x8351),f5(x8352))
% 1.61/1.68 [972]~P75(x9722)+E(x9721,f6(x9722))+E(x9721,f12(x9722,f6(x9722)))+~E(f56(f56(f13(x9722),x9721),x9721),f6(x9722))
% 1.61/1.68 [1030]~E(x10302,f6(a3))+~E(x10301,f6(a3))+~P9(a3,f5(a3),x10301)+E(f56(f56(f13(a3),x10301),x10302),f6(a3))
% 1.61/1.68 [1059]~P58(x10592)+P9(f72(x10592),f5(f72(x10592)),x10591)+E(x10591,f5(f72(x10592)))+E(f15(f72(x10592),x10591),f12(f72(x10592),f6(f72(x10592))))
% 1.61/1.68 [1745]~P9(a1,x17452,x17451)+~P8(a1,x17451,f6(a1))+~P8(a1,f5(a1),x17452)+P9(a1,f14(a1,f10(a1,f11(a1,f6(a1),x17451)),x17452),f6(a1))
% 1.61/1.68 [957]P9(x9573,x9571,x9572)+~P58(x9573)+E(x9571,x9572)+P9(x9573,x9572,x9571)
% 1.61/1.68 [963]P9(x9633,x9631,x9632)+~P41(x9633)+E(x9631,x9632)+P9(x9633,x9632,x9631)
% 1.61/1.68 [966]P8(x9661,x9662,x9663)+~E(x9662,x9663)+~P41(x9661)+P9(x9661,x9662,x9663)
% 1.61/1.68 [1033]~P44(x10333)+~P8(x10333,x10332,x10331)+E(x10331,x10332)+P9(x10333,x10332,x10331)
% 1.61/1.68 [1035]~P41(x10353)+~P8(x10353,x10351,x10352)+E(x10351,x10352)+P9(x10353,x10351,x10352)
% 1.61/1.68 [1041]~P44(x10413)+~P8(x10413,x10411,x10412)+E(x10411,x10412)+P9(x10413,x10411,x10412)
% 1.61/1.68 [1112]~P8(x11123,x11122,x11121)+~P8(x11123,x11121,x11122)+E(x11121,x11122)+~P44(x11123)
% 1.61/1.68 [1170]P8(x11701,x11703,x11702)+~P39(x11701)+~P8(x11701,x11702,x11703)+P9(x11701,x11702,x11703)
% 1.61/1.68 [751]~P60(x7513)+~P38(x7513)+E(x7511,x7512)+~E(f17(x7513,x7511),f17(x7513,x7512))
% 1.61/1.68 [1316]~P58(x13161)+P11(x13161,x13162)+P9(x13161,f5(x13161),x13163)+~P11(x13161,f20(x13161,x13163,x13162))
% 1.61/1.68 [1344]~P5(x13441)+~P9(x13441,x13443,x13442)+~P9(x13441,x13442,f5(x13441))+P9(x13441,f28(x13441,x13442),f28(x13441,x13443))
% 1.61/1.68 [1345]~P5(x13451)+~P8(x13451,x13453,x13452)+~P9(x13451,x13452,f5(x13451))+P8(x13451,f28(x13451,x13452),f28(x13451,x13453))
% 1.61/1.68 [1346]~P5(x13461)+~P9(x13461,x13463,x13462)+~P9(x13461,f5(x13461),x13463)+P9(x13461,f28(x13461,x13462),f28(x13461,x13463))
% 1.61/1.68 [1347]~P5(x13471)+~P8(x13471,x13473,x13472)+~P9(x13471,f5(x13471),x13473)+P8(x13471,f28(x13471,x13472),f28(x13471,x13473))
% 1.61/1.68 [1356]~P58(x13561)+~P9(x13561,x13562,x13563)+~P9(x13561,f12(x13561,x13562),x13563)+P9(x13561,f10(x13561,x13562),x13563)
% 1.61/1.68 [1358]~P33(x13581)+~P8(x13581,x13582,x13583)+~P8(x13581,f12(x13581,x13582),x13583)+P8(x13581,f10(x13581,x13582),x13583)
% 1.61/1.68 [1388]~P5(x13881)+P9(x13881,x13882,x13883)+~P9(x13881,x13882,f5(x13881))+~P9(x13881,f28(x13881,x13883),f28(x13881,x13882))
% 1.61/1.68 [1389]~P5(x13891)+P8(x13891,x13892,x13893)+~P9(x13891,x13892,f5(x13891))+~P8(x13891,f28(x13891,x13893),f28(x13891,x13892))
% 1.61/1.68 [1390]~P5(x13901)+P9(x13901,x13902,x13903)+~P9(x13901,f5(x13901),x13903)+~P9(x13901,f28(x13901,x13903),f28(x13901,x13902))
% 1.61/1.68 [1391]~P5(x13911)+P8(x13911,x13912,x13913)+~P9(x13911,f5(x13911),x13913)+~P8(x13911,f28(x13911,x13913),f28(x13911,x13912))
% 1.61/1.68 [1409]E(x14091,x14092)+~P8(a2,x14093,x14092)+~P8(a2,x14093,x14091)+~E(f11(a2,x14091,x14093),f11(a2,x14092,x14093))
% 1.61/1.68 [1470]~P28(x14701)+~P9(x14701,f5(x14701),x14703)+~P9(x14701,f5(x14701),x14702)+P9(x14701,f5(x14701),f14(x14701,x14702,x14703))
% 1.61/1.68 [1474]~P28(x14741)+~P9(x14741,x14743,f5(x14741))+~P9(x14741,x14742,f5(x14741))+P9(x14741,f14(x14741,x14742,x14743),f5(x14741))
% 1.61/1.68 [1475]~P28(x14751)+~P9(x14751,x14753,f5(x14751))+~P8(x14751,x14752,f5(x14751))+P9(x14751,f14(x14751,x14752,x14753),f5(x14751))
% 1.61/1.68 [1476]~P28(x14761)+~P9(x14761,x14762,f5(x14761))+~P8(x14761,x14763,f5(x14761))+P9(x14761,f14(x14761,x14762,x14763),f5(x14761))
% 1.61/1.68 [1477]~P28(x14771)+~P8(x14771,x14773,f5(x14771))+~P8(x14771,x14772,f5(x14771))+P8(x14771,f14(x14771,x14772,x14773),f5(x14771))
% 1.61/1.68 [1712]~P8(a2,x17123,x17121)+P9(a2,x17121,x17122)+~P8(a2,x17123,x17122)+~P9(a2,f11(a2,x17121,x17123),f11(a2,x17122,x17123))
% 1.61/1.68 [1713]~P8(a2,x17133,x17131)+P8(a2,x17131,x17132)+~P8(a2,x17133,x17132)+~P8(a2,f11(a2,x17131,x17133),f11(a2,x17132,x17133))
% 1.61/1.68 [904]~P35(x9041)+~E(x9042,f5(x9041))+~E(x9043,f5(f72(x9041)))+E(f20(x9041,x9042,x9043),f5(f72(x9041)))
% 1.61/1.68 [976]~P60(x9762)+E(x9761,f5(x9762))+~E(f25(x9762,x9761,x9763),f5(f72(x9762)))+E(x9763,f5(f72(x9762)))
% 1.61/1.68 [1085]~P60(x10852)+~E(f21(x10852,x10853,x10851),f5(a2))+~E(f56(f17(x10852,x10851),x10853),f5(x10852))+E(x10851,f5(f72(x10852)))
% 1.61/1.68 [1124]~P58(x11241)+~P11(x11241,x11243)+~P11(x11241,x11242)+P11(x11241,f14(f72(x11241),x11242,x11243))
% 1.61/1.68 [1216]P11(x12162,x12161)+~P58(x12162)+~P11(x12162,f20(x12162,x12163,x12161))+E(x12161,f5(f72(x12162)))
% 1.61/1.68 [1249]~P58(x12493)+E(x12491,x12492)+~P8(f72(x12493),x12491,x12492)+P11(x12493,f11(f72(x12493),x12492,x12491))
% 1.61/1.68 [1267]~P58(x12671)+~P9(x12671,f5(x12671),x12672)+P11(x12671,f20(x12671,x12672,x12673))+~E(x12673,f5(f72(x12671)))
% 1.61/1.68 [1480]~P48(x14801)+~P8(a1,x14803,f30(x14801,x14802))+~P9(a1,f5(a1),x14803)+P8(a1,f30(x14801,f28(x14801,x14802)),f28(a1,x14803))
% 1.61/1.68 [1755]~P52(x17552)+E(x17551,f5(x17552))+E(x17553,f5(x17552))+E(f56(f56(f13(x17552),f56(f56(f13(x17552),f28(x17552,x17553)),f14(x17552,x17553,x17551))),f28(x17552,x17551)),f14(x17552,f28(x17552,x17553),f28(x17552,x17551)))
% 1.61/1.68 [1756]~P52(x17562)+E(x17561,f5(x17562))+E(x17563,f5(x17562))+E(f56(f56(f13(x17562),f56(f56(f13(x17562),f28(x17562,x17563)),f11(x17562,x17561,x17563))),f28(x17562,x17561)),f11(x17562,f28(x17562,x17563),f28(x17562,x17561)))
% 1.61/1.68 [1774]~P7(x17742)+E(x17741,f5(x17742))+E(x17743,f5(x17742))+E(f56(f56(f13(x17742),f56(f56(f13(x17742),f14(x17742,x17743,x17741)),f28(x17742,x17743))),f28(x17742,x17741)),f14(x17742,f28(x17742,x17743),f28(x17742,x17741)))
% 1.61/1.68 [919]~P68(x9192)+E(x9191,f5(x9192))+E(x9193,f5(x9192))+~E(f56(f56(f13(x9192),x9193),x9191),f5(x9192))
% 1.61/1.68 [920]~P74(x9202)+E(x9201,f5(x9202))+E(x9203,f5(x9202))+~E(f56(f56(f13(x9202),x9203),x9201),f5(x9202))
% 1.61/1.68 [1125]~P60(x11253)+E(x11251,x11252)+E(x11251,f12(x11253,x11252))+~E(f56(f56(f13(x11253),x11251),x11251),f56(f56(f13(x11253),x11252),x11252))
% 1.61/1.68 [1438]~P1(x14381)+~P9(x14381,f6(x14381),x14382)+~P9(a2,f5(a2),x14383)+P9(x14381,f6(x14381),f56(f56(f23(x14381),x14382),x14383))
% 1.61/1.68 [1450]~P62(x14501)+~P9(x14501,x14503,f5(x14501))+~P9(x14501,x14502,f5(x14501))+P9(x14501,f5(x14501),f56(f56(f13(x14501),x14502),x14503))
% 1.61/1.68 [1451]~P62(x14511)+~P8(x14511,x14513,f5(x14511))+~P8(x14511,x14512,f5(x14511))+P8(x14511,f5(x14511),f56(f56(f13(x14511),x14512),x14513))
% 1.61/1.68 [1453]~P70(x14531)+~P8(x14531,x14533,f5(x14531))+~P8(x14531,x14532,f5(x14531))+P8(x14531,f5(x14531),f56(f56(f13(x14531),x14532),x14533))
% 1.61/1.68 [1454]~P64(x14541)+~P9(x14541,f5(x14541),x14543)+~P9(x14541,f5(x14541),x14542)+P9(x14541,f5(x14541),f56(f56(f13(x14541),x14542),x14543))
% 1.61/1.68 [1455]~P1(x14551)+~P9(x14551,f6(x14551),x14553)+~P9(x14551,f6(x14551),x14552)+P9(x14551,f6(x14551),f56(f56(f13(x14551),x14552),x14553))
% 1.61/1.68 [1456]~P62(x14561)+~P8(x14561,f5(x14561),x14563)+~P8(x14561,f5(x14561),x14562)+P8(x14561,f5(x14561),f56(f56(f13(x14561),x14562),x14563))
% 1.61/1.68 [1457]~P63(x14571)+~P8(x14571,f5(x14571),x14573)+~P8(x14571,f5(x14571),x14572)+P8(x14571,f5(x14571),f56(f56(f13(x14571),x14572),x14573))
% 1.61/1.68 [1458]~P70(x14581)+~P8(x14581,f5(x14581),x14583)+~P8(x14581,f5(x14581),x14582)+P8(x14581,f5(x14581),f56(f56(f13(x14581),x14582),x14583))
% 1.61/1.68 [1460]~P64(x14601)+~P9(x14601,x14603,f5(x14601))+~P9(x14601,f5(x14601),x14602)+P9(x14601,f56(f56(f13(x14601),x14602),x14603),f5(x14601))
% 1.61/1.68 [1461]~P64(x14611)+~P9(x14611,x14612,f5(x14611))+~P9(x14611,f5(x14611),x14613)+P9(x14611,f56(f56(f13(x14611),x14612),x14613),f5(x14611))
% 1.61/1.68 [1463]~P62(x14631)+~P8(x14631,x14633,f5(x14631))+~P8(x14631,f5(x14631),x14632)+P8(x14631,f56(f56(f13(x14631),x14632),x14633),f5(x14631))
% 1.61/1.68 [1464]~P62(x14641)+~P8(x14641,x14642,f5(x14641))+~P8(x14641,f5(x14641),x14643)+P8(x14641,f56(f56(f13(x14641),x14642),x14643),f5(x14641))
% 1.61/1.68 [1466]~P63(x14661)+~P8(x14661,x14663,f5(x14661))+~P8(x14661,f5(x14661),x14662)+P8(x14661,f56(f56(f13(x14661),x14662),x14663),f5(x14661))
% 1.61/1.68 [1468]~P63(x14681)+~P8(x14681,x14682,f5(x14681))+~P8(x14681,f5(x14681),x14683)+P8(x14681,f56(f56(f13(x14681),x14682),x14683),f5(x14681))
% 1.61/1.68 [1484]~P62(x14841)+P8(x14841,x14842,f5(x14841))+P8(x14841,x14843,f5(x14841))+~P8(x14841,f56(f56(f13(x14841),x14843),x14842),f5(x14841))
% 1.61/1.68 [1485]~P62(x14851)+P8(x14851,x14852,f5(x14851))+P8(x14851,f5(x14851),x14853)+~P8(x14851,f5(x14851),f56(f56(f13(x14851),x14853),x14852))
% 1.61/1.68 [1486]~P62(x14861)+P8(x14861,x14862,f5(x14861))+P8(x14861,f5(x14861),x14863)+~P8(x14861,f5(x14861),f56(f56(f13(x14861),x14862),x14863))
% 1.61/1.68 [1487]~P62(x14871)+P8(x14871,f5(x14871),x14872)+P8(x14871,x14872,f5(x14871))+~P8(x14871,f5(x14871),f56(f56(f13(x14871),x14873),x14872))
% 1.61/1.68 [1488]~P62(x14881)+P8(x14881,f5(x14881),x14882)+P8(x14881,x14882,f5(x14881))+~P8(x14881,f5(x14881),f56(f56(f13(x14881),x14882),x14883))
% 1.61/1.68 [1489]~P62(x14891)+P8(x14891,f5(x14891),x14892)+P8(x14891,x14892,f5(x14891))+~P8(x14891,f56(f56(f13(x14891),x14893),x14892),f5(x14891))
% 1.61/1.68 [1490]~P62(x14901)+P8(x14901,f5(x14901),x14902)+P8(x14901,x14902,f5(x14901))+~P8(x14901,f56(f56(f13(x14901),x14902),x14903),f5(x14901))
% 1.61/1.68 [1491]~P62(x14911)+P8(x14911,f5(x14911),x14912)+P8(x14911,f5(x14911),x14913)+~P8(x14911,f56(f56(f13(x14911),x14912),x14913),f5(x14911))
% 1.61/1.68 [1531]~P64(x15311)+P9(x15311,f5(x15311),x15312)+~P9(x15311,f5(x15311),x15313)+~P9(x15311,f5(x15311),f56(f56(f13(x15311),x15313),x15312))
% 1.61/1.68 [1532]~P64(x15321)+P9(x15321,f5(x15321),x15322)+~P9(x15321,f5(x15321),x15323)+~P9(x15321,f5(x15321),f56(f56(f13(x15321),x15322),x15323))
% 1.61/1.68 [1783]~P52(x17832)+E(x17831,f5(x17832))+E(x17833,f5(x17832))+E(f12(x17832,f56(f56(f13(x17832),f56(f56(f13(x17832),f28(x17832,x17833)),f11(x17832,x17833,x17831))),f28(x17832,x17831))),f11(x17832,f28(x17832,x17833),f28(x17832,x17831)))
% 1.61/1.68 [1207]~P58(x12071)+~P11(x12071,x12073)+~P11(x12071,x12072)+P11(x12071,f56(f56(f13(f72(x12071)),x12072),x12073))
% 1.61/1.68 [1298]~P52(x12982)+E(x12981,f5(x12982))+E(x12983,f5(x12982))+E(f56(f56(f13(x12982),f28(x12982,x12981)),f28(x12982,x12983)),f28(x12982,f56(f56(f13(x12982),x12983),x12981)))
% 1.61/1.68 [1336]~P62(x13361)+~E(x13363,f5(x13361))+~E(x13362,f5(x13361))+E(f14(x13361,f56(f56(f13(x13361),x13362),x13362),f56(f56(f13(x13361),x13363),x13363)),f5(x13361))
% 1.61/1.68 [1554]~P73(x15541)+~P8(x15541,x15542,f5(x15541))+~P8(x15541,x15543,f5(x15541))+E(f56(f56(f13(x15541),f10(x15541,x15542)),f10(x15541,x15543)),f10(x15541,f56(f56(f13(x15541),x15542),x15543)))
% 1.61/1.68 [1555]~P73(x15551)+~P8(x15551,x15552,f5(x15551))+~P8(x15551,f5(x15551),x15553)+E(f56(f56(f13(x15551),f10(x15551,x15552)),f10(x15551,x15553)),f10(x15551,f56(f56(f13(x15551),x15552),x15553)))
% 1.61/1.68 [1556]~P73(x15561)+~P8(x15561,x15563,f5(x15561))+~P8(x15561,f5(x15561),x15562)+E(f56(f56(f13(x15561),f10(x15561,x15562)),f10(x15561,x15563)),f10(x15561,f56(f56(f13(x15561),x15562),x15563)))
% 1.61/1.68 [1557]~P73(x15571)+~P8(x15571,f5(x15571),x15572)+~P8(x15571,f5(x15571),x15573)+E(f56(f56(f13(x15571),f10(x15571,x15572)),f10(x15571,x15573)),f10(x15571,f56(f56(f13(x15571),x15572),x15573)))
% 1.61/1.68 [1597]~P9(a3,x15972,x15973)+~P9(a3,f5(a3),x15973)+P8(a3,f6(a3),x15971)+~E(f14(a3,x15972,f56(f56(f13(a3),x15973),x15971)),x15973)
% 1.61/1.68 [1600]~P9(a3,f5(a3),x16003)+~P8(a3,f5(a3),x16002)+P8(a3,x16001,f6(a3))+~E(f14(a3,x16002,f56(f56(f13(a3),x16003),x16001)),x16003)
% 1.61/1.68 [1700]~P62(x17001)+~E(x17003,f5(x17001))+~E(x17002,f5(x17001))+P8(x17001,f14(x17001,f56(f56(f13(x17001),x17002),x17002),f56(f56(f13(x17001),x17003),x17003)),f5(x17001))
% 1.61/1.68 [1720]~P1(x17201)+~P9(x17201,x17202,f6(x17201))+~P9(x17201,f5(x17201),x17202)+P9(x17201,f56(f56(f13(x17201),x17202),f56(f56(f23(x17201),x17202),x17203)),f56(f56(f23(x17201),x17202),x17203))
% 1.61/1.68 [1733]~P9(a3,x17332,x17333)+~P9(a3,f5(a3),x17333)+P8(a3,f5(a3),x17331)+~P8(a3,f5(a3),f14(a3,f56(f56(f13(a3),x17333),x17331),x17332))
% 1.61/1.68 [1734]P8(a3,x17341,f5(a3))+~P9(a3,f5(a3),x17342)+~P8(a3,f5(a3),x17343)+~P9(a3,f14(a3,f56(f56(f13(a3),x17342),x17341),x17343),f5(a3))
% 1.61/1.68 [1750]~P62(x17502)+~E(x17501,f5(x17502))+~E(x17503,f5(x17502))+~P9(x17502,f5(x17502),f14(x17502,f56(f56(f13(x17502),x17503),x17503),f56(f56(f13(x17502),x17501),x17501)))
% 1.61/1.68 [1232]~P44(x12321)+~P9(x12321,x12324,x12323)+P9(x12321,x12322,x12323)+~P9(x12321,x12322,x12324)
% 1.61/1.68 [1233]~P44(x12331)+~P8(x12331,x12334,x12333)+P9(x12331,x12332,x12333)+~P9(x12331,x12332,x12334)
% 1.61/1.68 [1234]~P44(x12341)+~P8(x12341,x12342,x12344)+P9(x12341,x12342,x12343)+~P9(x12341,x12344,x12343)
% 1.61/1.68 [1235]~P39(x12351)+~P9(x12351,x12352,x12354)+P9(x12351,x12352,x12353)+~P9(x12351,x12354,x12353)
% 1.61/1.68 [1236]~P39(x12361)+~P8(x12361,x12362,x12364)+P9(x12361,x12362,x12363)+~P9(x12361,x12364,x12363)
% 1.61/1.68 [1237]~P39(x12371)+~P8(x12371,x12374,x12373)+P9(x12371,x12372,x12373)+~P9(x12371,x12372,x12374)
% 1.61/1.68 [1238]~P44(x12381)+~P8(x12381,x12384,x12383)+P8(x12381,x12382,x12383)+~P8(x12381,x12382,x12384)
% 1.61/1.68 [1239]~P39(x12391)+~P8(x12391,x12392,x12394)+P8(x12391,x12392,x12393)+~P8(x12391,x12394,x12393)
% 1.61/1.68 [1240]~P56(x12401)+~P12(x12401,x12402,x12404)+P12(x12401,x12402,x12403)+~P12(x12401,x12404,x12403)
% 1.61/1.68 [1208]~P44(x12081)+~P13(x12081,x12082)+~P8(a2,x12084,x12083)+P8(x12081,f56(x12082,x12083),f56(x12082,x12084))
% 1.61/1.68 [1321]~P7(x13212)+~P12(f72(x13212),x13213,x13214)+P12(f72(x13212),f25(x13212,x13211,x13213),x13214)+E(x13211,f5(x13212))
% 1.61/1.68 [1343]~P40(x13432)+P8(f77(x13431,x13432),x13434,x13433)+~P8(f77(x13431,x13432),x13433,x13434)+P9(f77(x13431,x13432),x13433,x13434)
% 1.61/1.68 [1410]~P7(x14102)+~P12(f72(x14102),f25(x14102,x14101,x14103),x14104)+P12(f72(x14102),x14103,x14104)+E(x14101,f5(x14102))
% 1.61/1.68 [1416]~P56(x14161)+~P12(x14161,x14162,x14164)+~P12(x14161,x14162,x14163)+P12(x14161,x14162,f14(x14161,x14163,x14164))
% 1.61/1.68 [1417]~P54(x14171)+~P12(x14171,x14172,x14174)+~P12(x14171,x14172,x14173)+P12(x14171,x14172,f11(x14171,x14173,x14174))
% 1.61/1.68 [1428]~P1(x14281)+~P9(x14281,x14282,x14284)+~P9(x14281,f5(x14281),x14283)+P9(x14281,x14282,f14(x14281,x14283,x14284))
% 1.61/1.68 [1429]~P28(x14291)+~P9(x14291,x14292,x14294)+~P8(x14291,f5(x14291),x14293)+P9(x14291,x14292,f14(x14291,x14293,x14294))
% 1.61/1.68 [1430]~P28(x14301)+~P8(x14301,x14302,x14304)+~P9(x14301,f5(x14301),x14303)+P9(x14301,x14302,f14(x14301,x14303,x14304))
% 1.61/1.68 [1431]~P28(x14311)+~P8(x14311,x14312,x14313)+~P8(x14311,f5(x14311),x14314)+P8(x14311,x14312,f14(x14311,x14313,x14314))
% 1.61/1.68 [1432]~P28(x14321)+~P8(x14321,x14322,x14324)+~P8(x14321,f5(x14321),x14323)+P8(x14321,x14322,f14(x14321,x14323,x14324))
% 1.61/1.68 [1166]~P7(x11661)+P12(f72(x11661),f25(x11661,x11662,x11663),x11664)+~E(x11662,f5(x11661))+~E(x11664,f5(f72(x11661)))
% 1.61/1.68 [1337]~P7(x13371)+~P12(f72(x13371),x13373,x13374)+P12(f72(x13371),f25(x13371,x13372,x13373),x13374)+~E(x13374,f5(f72(x13371)))
% 1.61/1.68 [1342]~P7(x13422)+~P12(f72(x13422),f25(x13422,x13423,x13424),x13421)+~E(x13423,f5(x13422))+E(x13421,f5(f72(x13422)))
% 1.61/1.68 [1586]~P47(x15862)+E(x15861,f5(x15862))+~P8(a1,x15863,f5(a1))+~P8(a1,f30(x15862,x15861),f56(f56(f13(a1),x15863),f30(x15862,x15864)))
% 1.61/1.68 [1738]~P58(x17381)+~P9(x17381,x17382,f14(x17381,x17383,x17384))+~P9(x17381,f11(x17381,x17383,x17384),x17382)+P9(x17381,f10(x17381,f11(x17381,x17382,x17383)),x17384)
% 1.61/1.68 [1309]~P1(x13093)+E(x13091,x13092)+~P9(x13093,f6(x13093),x13094)+~E(f56(f56(f23(x13093),x13094),x13091),f56(f56(f23(x13093),x13094),x13092))
% 1.61/1.68 [1559]~P1(x15591)+~P9(a2,x15593,x15594)+~P9(x15591,f6(x15591),x15592)+P9(x15591,f56(f56(f23(x15591),x15592),x15593),f56(f56(f23(x15591),x15592),x15594))
% 1.61/1.68 [1560]~P1(x15601)+~P8(a2,x15603,x15604)+~P9(x15601,f6(x15601),x15602)+P8(x15601,f56(f56(f23(x15601),x15602),x15603),f56(f56(f23(x15601),x15602),x15604))
% 1.61/1.68 [1561]~P1(x15611)+~P8(a2,x15613,x15614)+~P8(x15611,f6(x15611),x15612)+P8(x15611,f56(f56(f23(x15611),x15612),x15613),f56(f56(f23(x15611),x15612),x15614))
% 1.61/1.68 [1570]~P62(x15701)+~P9(x15701,x15704,x15702)+~P9(x15701,x15703,f5(x15701))+P9(x15701,f56(f56(f13(x15701),x15702),x15703),f56(f56(f13(x15701),x15704),x15703))
% 1.61/1.68 [1571]~P62(x15711)+~P9(x15711,x15714,x15713)+~P9(x15711,x15712,f5(x15711))+P9(x15711,f56(f56(f13(x15711),x15712),x15713),f56(f56(f13(x15711),x15712),x15714))
% 1.61/1.68 [1572]~P62(x15721)+~P8(x15721,x15724,x15723)+~P9(x15721,x15722,f5(x15721))+P8(x15721,f56(f56(f13(x15721),x15722),x15723),f56(f56(f13(x15721),x15722),x15724))
% 1.61/1.68 [1573]~P70(x15731)+~P8(x15731,x15734,x15733)+~P8(x15731,x15732,f5(x15731))+P8(x15731,f56(f56(f13(x15731),x15732),x15733),f56(f56(f13(x15731),x15732),x15734))
% 1.61/1.68 [1574]~P70(x15741)+~P8(x15741,x15744,x15742)+~P8(x15741,x15743,f5(x15741))+P8(x15741,f56(f56(f13(x15741),x15742),x15743),f56(f56(f13(x15741),x15744),x15743))
% 1.61/1.68 [1576]~P64(x15761)+~P9(x15761,x15763,x15764)+~P9(x15761,f5(x15761),x15762)+P9(x15761,f56(f56(f13(x15761),x15762),x15763),f56(f56(f13(x15761),x15762),x15764))
% 1.61/1.68 [1577]~P59(x15771)+~P9(x15771,x15773,x15774)+~P9(x15771,f5(x15771),x15772)+P9(x15771,f56(f56(f13(x15771),x15772),x15773),f56(f56(f13(x15771),x15772),x15774))
% 1.61/1.68 [1578]~P62(x15781)+~P9(x15781,x15782,x15784)+~P9(x15781,f5(x15781),x15783)+P9(x15781,f56(f56(f13(x15781),x15782),x15783),f56(f56(f13(x15781),x15784),x15783))
% 1.61/1.68 [1579]~P64(x15791)+~P9(x15791,x15792,x15794)+~P9(x15791,f5(x15791),x15793)+P9(x15791,f56(f56(f13(x15791),x15792),x15793),f56(f56(f13(x15791),x15794),x15793))
% 1.61/1.68 [1580]~P62(x15801)+~P9(x15801,x15803,x15804)+~P9(x15801,f5(x15801),x15802)+P9(x15801,f56(f56(f13(x15801),x15802),x15803),f56(f56(f13(x15801),x15802),x15804))
% 1.61/1.68 [1581]~P1(x15811)+~P8(x15811,x15812,x15814)+~P8(x15811,f5(x15811),x15812)+P8(x15811,f56(f56(f23(x15811),x15812),x15813),f56(f56(f23(x15811),x15814),x15813))
% 1.61/1.68 [1582]~P62(x15821)+~P8(x15821,x15823,x15824)+~P9(x15821,f5(x15821),x15822)+P8(x15821,f56(f56(f13(x15821),x15822),x15823),f56(f56(f13(x15821),x15822),x15824))
% 1.61/1.68 [1583]~P72(x15831)+~P8(x15831,x15833,x15834)+~P8(x15831,f5(x15831),x15832)+P8(x15831,f56(f56(f13(x15831),x15832),x15833),f56(f56(f13(x15831),x15832),x15834))
% 1.61/1.68 [1584]~P71(x15841)+~P8(x15841,x15843,x15844)+~P8(x15841,f5(x15841),x15842)+P8(x15841,f56(f56(f13(x15841),x15842),x15843),f56(f56(f13(x15841),x15842),x15844))
% 1.61/1.68 [1585]~P72(x15851)+~P8(x15851,x15852,x15854)+~P8(x15851,f5(x15851),x15853)+P8(x15851,f56(f56(f13(x15851),x15852),x15853),f56(f56(f13(x15851),x15854),x15853))
% 1.61/1.68 [1606]~P60(x16062)+P12(x16062,x16063,x16064)+E(x16061,f5(x16062))+~P12(x16062,f56(f56(f13(x16062),x16063),x16061),f56(f56(f13(x16062),x16064),x16061))
% 1.61/1.68 [1607]~P60(x16072)+P12(x16072,x16073,x16074)+E(x16071,f5(x16072))+~P12(x16072,f56(f56(f13(x16072),x16071),x16073),f56(f56(f13(x16072),x16071),x16074))
% 1.61/1.68 [1650]P9(x16501,x16503,x16502)+~P62(x16501)+P9(x16501,x16502,x16503)+~P9(x16501,f56(f56(f13(x16501),x16504),x16502),f56(f56(f13(x16501),x16504),x16503))
% 1.61/1.68 [1651]P9(x16511,x16513,x16512)+~P62(x16511)+P9(x16511,x16512,x16513)+~P9(x16511,f56(f56(f13(x16511),x16512),x16514),f56(f56(f13(x16511),x16513),x16514))
% 1.61/1.68 [1654]~P62(x16541)+P9(x16541,x16542,x16543)+P9(x16541,x16544,f5(x16541))+~P9(x16541,f56(f56(f13(x16541),x16542),x16544),f56(f56(f13(x16541),x16543),x16544))
% 1.61/1.68 [1655]~P62(x16551)+P9(x16551,x16552,x16553)+P9(x16551,x16554,f5(x16551))+~P9(x16551,f56(f56(f13(x16551),x16554),x16552),f56(f56(f13(x16551),x16554),x16553))
% 1.61/1.68 [1656]~P62(x16561)+P9(x16561,x16562,x16563)+P9(x16561,f5(x16561),x16564)+~P9(x16561,f56(f56(f13(x16561),x16564),x16563),f56(f56(f13(x16561),x16564),x16562))
% 1.61/1.68 [1657]~P62(x16571)+P9(x16571,x16572,x16573)+P9(x16571,f5(x16571),x16574)+~P9(x16571,f56(f56(f13(x16571),x16573),x16574),f56(f56(f13(x16571),x16572),x16574))
% 1.61/1.68 [1668]~P62(x16681)+P9(x16681,f5(x16681),x16682)+P9(x16681,x16682,f5(x16681))+~P9(x16681,f56(f56(f13(x16681),x16683),x16682),f56(f56(f13(x16681),x16684),x16682))
% 1.61/1.68 [1669]~P62(x16691)+P9(x16691,f5(x16691),x16692)+P9(x16691,x16692,f5(x16691))+~P9(x16691,f56(f56(f13(x16691),x16692),x16693),f56(f56(f13(x16691),x16692),x16694))
% 1.61/1.68 [1680]~P1(x16803)+P9(a2,x16801,x16802)+~P9(x16803,f6(x16803),x16804)+~P9(x16803,f56(f56(f23(x16803),x16804),x16801),f56(f56(f23(x16803),x16804),x16802))
% 1.61/1.68 [1682]~P1(x16823)+P8(a2,x16821,x16822)+~P9(x16823,f6(x16823),x16824)+~P8(x16823,f56(f56(f23(x16823),x16824),x16821),f56(f56(f23(x16823),x16824),x16822))
% 1.61/1.68 [1683]~P62(x16831)+P9(x16831,x16832,x16833)+~P9(x16831,x16834,f5(x16831))+~P9(x16831,f56(f56(f13(x16831),x16834),x16833),f56(f56(f13(x16831),x16834),x16832))
% 1.61/1.68 [1684]~P62(x16841)+P8(x16841,x16842,x16843)+~P9(x16841,x16844,f5(x16841))+~P8(x16841,f56(f56(f13(x16841),x16844),x16843),f56(f56(f13(x16841),x16844),x16842))
% 1.61/1.68 [1685]~P62(x16851)+P9(x16851,x16852,x16853)+~P9(x16851,f5(x16851),x16854)+~P9(x16851,f56(f56(f13(x16851),x16854),x16852),f56(f56(f13(x16851),x16854),x16853))
% 1.61/1.68 [1686]~P64(x16861)+P9(x16861,x16862,x16863)+~P8(x16861,f5(x16861),x16864)+~P9(x16861,f56(f56(f13(x16861),x16864),x16862),f56(f56(f13(x16861),x16864),x16863))
% 1.61/1.68 [1687]~P65(x16871)+P9(x16871,x16872,x16873)+~P8(x16871,f5(x16871),x16874)+~P9(x16871,f56(f56(f13(x16871),x16874),x16872),f56(f56(f13(x16871),x16874),x16873))
% 1.61/1.68 [1688]~P1(x16881)+P9(x16881,x16882,x16883)+~P8(x16881,f5(x16881),x16883)+~P9(x16881,f56(f56(f23(x16881),x16882),x16884),f56(f56(f23(x16881),x16883),x16884))
% 1.61/1.68 [1689]~P64(x16891)+P9(x16891,x16892,x16893)+~P8(x16891,f5(x16891),x16894)+~P9(x16891,f56(f56(f13(x16891),x16892),x16894),f56(f56(f13(x16891),x16893),x16894))
% 1.61/1.68 [1690]~P65(x16901)+P9(x16901,x16902,x16903)+~P8(x16901,f5(x16901),x16904)+~P9(x16901,f56(f56(f13(x16901),x16902),x16904),f56(f56(f13(x16901),x16903),x16904))
% 1.61/1.68 [1691]~P62(x16911)+P8(x16911,x16912,x16913)+~P9(x16911,f5(x16911),x16914)+~P8(x16911,f56(f56(f13(x16911),x16914),x16912),f56(f56(f13(x16911),x16914),x16913))
% 1.61/1.68 [1692]~P64(x16921)+P8(x16921,x16922,x16923)+~P9(x16921,f5(x16921),x16924)+~P8(x16921,f56(f56(f13(x16921),x16924),x16922),f56(f56(f13(x16921),x16924),x16923))
% 1.61/1.68 [1693]~P64(x16931)+P8(x16931,x16932,x16933)+~P9(x16931,f5(x16931),x16934)+~P8(x16931,f56(f56(f13(x16931),x16932),x16934),f56(f56(f13(x16931),x16933),x16934))
% 1.61/1.68 [1742]~P9(a1,f5(a1),x17424)+~P9(a1,f5(a1),x17422)+P9(a1,f56(f56(f13(a1),x17421),f28(a1,x17422)),f56(f56(f13(a1),x17423),f28(a1,x17424)))+~P9(a1,f56(f56(f13(a1),x17424),x17421),f56(f56(f13(a1),x17422),x17423))
% 1.61/1.68 [1751]~P9(a1,f5(a1),x17513)+~P9(a1,f5(a1),x17511)+~P9(a1,f56(f56(f13(a1),x17513),x17512),f56(f56(f13(a1),x17511),x17514))+P9(a1,f56(f56(f13(a1),f28(a1,x17511)),x17512),f56(f56(f13(a1),f28(a1,x17513)),x17514))
% 1.61/1.68 [1704]~P80(x17043)+~P61(x17043)+P82(f56(x17041,f63(x17042,x17041,x17043)))+~P82(f56(x17041,f56(f56(f13(x17043),x17042),x17044)))
% 1.61/1.68 [1735]~P80(x17351)+~P61(x17351)+P12(x17351,x17352,f14(x17351,f63(x17352,x17353,x17351),f5(x17351)))+~P82(f56(x17353,f56(f56(f13(x17351),x17352),x17354)))
% 1.61/1.68 [1784]~P9(a1,f5(a1),x17844)+~P9(a1,f30(a4,f11(a4,x17842,x17843)),f60(x17841,x17843,x17844))+~P9(a1,f5(a1),f30(a4,f11(a4,x17842,x17843)))+P9(a1,f30(a4,f11(a4,f56(f17(a4,x17841),x17842),f56(f17(a4,x17841),x17843))),x17844)
% 1.61/1.68 [1123]~P15(x11235)+E(x11231,x11232)+~E(x11233,x11234)+~E(f11(x11235,x11233,x11234),f11(x11235,x11231,x11232))
% 1.61/1.68 [1377]~P29(x13771)+~P9(x13771,x13774,x13775)+P9(x13771,x13772,x13773)+~E(f11(x13771,x13774,x13775),f11(x13771,x13772,x13773))
% 1.61/1.68 [1379]~P29(x13791)+~P8(x13791,x13794,x13795)+P8(x13791,x13792,x13793)+~E(f11(x13791,x13794,x13795),f11(x13791,x13792,x13793))
% 1.61/1.68 [1562]~P34(x15621)+~P9(x15621,x15623,x15625)+~P9(x15621,x15622,x15624)+P9(x15621,f14(x15621,x15622,x15623),f14(x15621,x15624,x15625))
% 1.61/1.68 [1563]~P34(x15631)+~P9(x15631,x15633,x15635)+~P8(x15631,x15632,x15634)+P9(x15631,f14(x15631,x15632,x15633),f14(x15631,x15634,x15635))
% 1.61/1.68 [1564]~P34(x15641)+~P9(x15641,x15642,x15644)+~P8(x15641,x15643,x15645)+P9(x15641,f14(x15641,x15642,x15643),f14(x15641,x15644,x15645))
% 1.61/1.68 [1565]~P32(x15651)+~P8(x15651,x15653,x15655)+~P8(x15651,x15652,x15654)+P8(x15651,f14(x15651,x15652,x15653),f14(x15651,x15654,x15655))
% 1.61/1.68 [1718]~P47(x17181)+~P9(a1,f30(x17181,x17183),x17185)+~P9(a1,f30(x17181,x17182),x17184)+P9(a1,f30(x17181,f14(x17181,x17182,x17183)),f14(a1,x17184,x17185))
% 1.61/1.68 [1724]~P58(x17241)+~P9(x17241,f10(x17241,x17242),x17244)+~P9(x17241,f10(x17241,x17243),x17245)+P9(x17241,f56(f56(f13(x17241),f10(x17241,x17242)),f10(x17241,x17243)),f56(f56(f13(x17241),x17244),x17245))
% 1.61/1.68 [1705]~P2(x17051)+~P9(a1,f30(x17051,x17053),x17055)+~P9(a1,f30(x17051,x17052),x17054)+P9(a1,f30(x17051,f56(f56(f13(x17051),x17052),x17053)),f56(f56(f13(a1),x17054),x17055))
% 1.61/1.68 [1740]~P81(x17405)+E(x17401,x17402)+E(x17403,x17404)+~E(f14(x17405,f56(f56(f13(x17405),x17403),x17401),f56(f56(f13(x17405),x17404),x17402)),f14(x17405,f56(f56(f13(x17405),x17403),x17402),f56(f56(f13(x17405),x17404),x17401)))
% 1.61/1.68 [1767]~E(f30(a4,x17671),f6(a1))+P9(a1,f30(a4,f11(a4,x17671,a7)),f6(a1))+P9(a1,f30(a4,f14(a4,x17671,a7)),f6(a1))+P9(a1,f30(a4,f14(a4,x17671,f6(a4))),f6(a1))+P9(a1,f30(a4,f11(a4,x17671,f6(a4))),f6(a1))
% 1.61/1.68 [761]~P52(x7613)+E(x7611,x7612)+~E(f28(x7613,x7611),f28(x7613,x7612))+E(x7612,f5(x7613))+E(x7611,f5(x7613))
% 1.61/1.68 [1348]~P28(x13482)+~P8(x13482,f5(x13482),x13483)+~P8(x13482,f5(x13482),x13481)+~E(f14(x13482,x13483,x13481),f5(x13482))+E(x13481,f5(x13482))
% 1.61/1.68 [1349]~P28(x13492)+~P8(x13492,f5(x13492),x13493)+~P8(x13492,f5(x13492),x13491)+~E(f14(x13492,x13491,x13493),f5(x13492))+E(x13491,f5(x13492))
% 1.61/1.68 [1587]~P58(x15871)+~P8(x15871,x15872,f6(x15871))+~P8(x15871,f5(x15871),x15872)+~P8(x15871,f5(x15871),x15873)+P8(x15871,f56(f56(f13(x15871),x15872),x15873),x15873)
% 1.61/1.68 [1588]~P58(x15881)+~P8(x15881,x15883,f6(x15881))+~P8(x15881,f5(x15881),x15883)+~P8(x15881,f5(x15881),x15882)+P8(x15881,f56(f56(f13(x15881),x15882),x15883),x15882)
% 1.61/1.68 [1670]~P1(x16701)+~P9(x16701,x16702,x16704)+~P8(x16701,f5(x16701),x16702)+~P9(a2,f5(a2),x16703)+P9(x16701,f56(f56(f23(x16701),x16702),x16703),f56(f56(f23(x16701),x16704),x16703))
% 1.61/1.68 [1671]~P1(x16711)+~P9(a2,x16714,x16713)+~P9(x16711,x16712,f6(x16711))+~P9(x16711,f5(x16711),x16712)+P9(x16711,f56(f56(f23(x16711),x16712),x16713),f56(f56(f23(x16711),x16712),x16714))
% 1.61/1.68 [1672]~P1(x16721)+~P8(a2,x16724,x16723)+~P8(x16721,x16722,f6(x16721))+~P8(x16721,f5(x16721),x16722)+P8(x16721,f56(f56(f23(x16721),x16722),x16723),f56(f56(f23(x16721),x16722),x16724))
% 1.61/1.68 [1752]~P80(x17522)+~P61(x17522)+~P12(x17522,x17523,f14(x17522,x17524,f5(x17522)))+~P82(f56(x17521,x17524))+P82(f56(x17521,f56(f56(f13(x17522),x17523),f64(x17523,x17521,x17522))))
% 1.61/1.68 [1757]~P47(x17574)+~P40(x17571)+~P8(x17571,x17572,x17575)+P8(x17571,x17572,f53(x17573,x17572,x17571,x17574))+P9(a1,f30(x17574,f56(x17573,x17575)),f14(a1,f6(a1),f30(x17574,f56(x17573,x17572))))
% 1.61/1.68 [1772]P8(a3,x17721,x17722)+~P9(a3,x17723,x17724)+~P9(a3,x17723,x17725)+~P8(a3,x17724,f5(a3))+~P8(a3,f14(a3,f56(f56(f13(a3),x17723),x17722),x17725),f14(a3,f56(f56(f13(a3),x17723),x17721),x17724))
% 1.61/1.68 [1773]P8(a3,x17731,x17732)+~P9(a3,x17733,x17734)+~P9(a3,x17735,x17734)+~P8(a3,f5(a3),x17735)+~P8(a3,f14(a3,f56(f56(f13(a3),x17734),x17731),x17735),f14(a3,f56(f56(f13(a3),x17734),x17732),x17733))
% 1.61/1.68 [1813]~P47(x18131)+~P8(x18135,x18134,x18133)+~P40(x18135)+P9(a1,f30(x18131,f56(x18132,x18133)),f14(a1,f6(a1),f30(x18131,f56(x18132,x18134))))+~P9(a1,f30(x18131,f11(x18131,f56(x18132,x18134),f56(x18132,f53(x18132,x18134,x18135,x18131)))),f6(a1))
% 1.61/1.68 [1640]~P81(x16404)+E(x16401,x16402)+~E(x16405,x16406)+E(x16403,f5(x16404))+~E(f14(x16404,x16405,f56(f56(f13(x16404),x16403),x16401)),f14(x16404,x16406,f56(f56(f13(x16404),x16403),x16402)))
% 1.61/1.68 [1764]~P55(x17641)+~P61(x17641)+~P12(x17641,x17642,x17645)+~P12(x17641,x17642,f14(x17641,x17643,x17646))+P12(x17641,x17642,f14(x17641,f11(x17641,x17643,f56(f56(f13(x17641),x17644),x17645)),x17646))
% 1.61/1.68 [1779]~P55(x17791)+~P61(x17791)+~P12(x17791,x17792,x17795)+P12(x17791,x17792,f14(x17791,x17793,x17794))+~P12(x17791,x17792,f14(x17791,f11(x17791,x17793,f56(f56(f13(x17791),x17796),x17795)),x17794))
% 1.61/1.68 [1318]~P28(x13181)+~P8(x13181,f5(x13181),x13183)+~P8(x13181,f5(x13181),x13182)+~E(x13183,f5(x13181))+~E(x13182,f5(x13181))+E(f14(x13181,x13182,x13183),f5(x13181))
% 1.61/1.68 [973]~P27(x9732)+~P68(x9732)+~P69(x9732)+~P78(x9732)+E(x9731,f5(x9732))+~E(f56(f56(f23(x9732),x9731),x9733),f5(x9732))
% 1.61/1.68 [974]~P27(x9742)+~P68(x9742)+~P69(x9742)+~P78(x9742)+~E(x9741,f5(a2))+~E(f56(f56(f23(x9742),x9743),x9741),f5(x9742))
% 1.61/1.68 [1594]~P1(x15943)+E(x15941,x15942)+~P8(x15943,f5(x15943),x15942)+~P8(x15943,f5(x15943),x15941)+~P9(a2,f5(a2),x15944)+~E(f56(f56(f23(x15943),x15941),x15944),f56(f56(f23(x15943),x15942),x15944))
% 1.61/1.68 [1706]~P64(x17061)+~P9(x17061,x17063,x17065)+~P9(x17061,x17062,x17064)+~P9(x17061,f5(x17061),x17064)+~P8(x17061,f5(x17061),x17063)+P9(x17061,f56(f56(f13(x17061),x17062),x17063),f56(f56(f13(x17061),x17064),x17065))
% 1.61/1.68 [1707]~P64(x17071)+~P9(x17071,x17073,x17075)+~P9(x17071,x17072,x17074)+~P8(x17071,f5(x17071),x17073)+~P8(x17071,f5(x17071),x17072)+P9(x17071,f56(f56(f13(x17071),x17072),x17073),f56(f56(f13(x17071),x17074),x17075))
% 1.61/1.68 [1708]~P64(x17081)+~P9(x17081,x17083,x17085)+~P8(x17081,x17082,x17084)+~P9(x17081,f5(x17081),x17082)+~P8(x17081,f5(x17081),x17083)+P9(x17081,f56(f56(f13(x17081),x17082),x17083),f56(f56(f13(x17081),x17084),x17085))
% 1.61/1.68 [1709]~P64(x17091)+~P9(x17091,x17092,x17094)+~P8(x17091,x17093,x17095)+~P9(x17091,f5(x17091),x17093)+~P8(x17091,f5(x17091),x17092)+P9(x17091,f56(f56(f13(x17091),x17092),x17093),f56(f56(f13(x17091),x17094),x17095))
% 1.61/1.68 [1710]~P72(x17101)+~P8(x17101,x17103,x17105)+~P8(x17101,x17102,x17104)+~P8(x17101,f5(x17101),x17103)+~P8(x17101,f5(x17101),x17104)+P8(x17101,f56(f56(f13(x17101),x17102),x17103),f56(f56(f13(x17101),x17104),x17105))
% 1.61/1.68 [1711]~P72(x17111)+~P8(x17111,x17113,x17115)+~P8(x17111,x17112,x17114)+~P8(x17111,f5(x17111),x17113)+~P8(x17111,f5(x17111),x17112)+P8(x17111,f56(f56(f13(x17111),x17112),x17113),f56(f56(f13(x17111),x17114),x17115))
% 1.61/1.68 [898]~P27(x8982)+~P68(x8982)+~P69(x8982)+~P78(x8982)+~E(x8983,f5(x8982))+E(x8981,f5(a2))+E(f56(f56(f23(x8982),x8983),x8981),f5(x8982))
% 1.61/1.68 [1753]~P67(x17531)+~P9(x17531,x17535,x17536)+~P9(x17531,x17533,x17536)+~P8(x17531,f5(x17531),x17534)+~P8(x17531,f5(x17531),x17532)+~E(f14(x17531,x17532,x17534),f6(x17531))+P9(x17531,f14(x17531,f56(f56(f13(x17531),x17532),x17533),f56(f56(f13(x17531),x17534),x17535)),x17536)
% 1.61/1.68 [1754]~P66(x17541)+~P8(x17541,x17545,x17546)+~P8(x17541,x17543,x17546)+~P8(x17541,f5(x17541),x17544)+~P8(x17541,f5(x17541),x17542)+~E(f14(x17541,x17542,x17544),f6(x17541))+P8(x17541,f14(x17541,f56(f56(f13(x17541),x17542),x17543),f56(f56(f13(x17541),x17544),x17545)),x17546)
% 1.61/1.68 [1776]~P9(a3,x17766,x17765)+~P8(a3,x17765,x17763)+P8(a3,x17761,x17762)+~P9(a3,f5(a3),x17765)+~P8(a3,f5(a3),x17764)+~P8(a3,f5(a3),f14(a3,f56(f56(f13(a3),x17765),x17762),x17766))+~E(f14(a3,f56(f56(f13(a3),x17763),x17761),x17764),f14(a3,f56(f56(f13(a3),x17765),x17762),x17766))
% 1.61/1.68 [1777]~P9(a3,x17774,x17773)+~P8(a3,x17775,x17773)+P8(a3,x17771,x17772)+~P9(a3,f5(a3),x17775)+~P8(a3,f5(a3),x17776)+~P9(a3,f14(a3,f56(f56(f13(a3),x17775),x17771),x17776),f5(a3))+~E(f14(a3,f56(f56(f13(a3),x17773),x17772),x17774),f14(a3,f56(f56(f13(a3),x17775),x17771),x17776))
% 1.61/1.68 %EqnAxiom
% 1.61/1.68 [1]E(x11,x11)
% 1.61/1.68 [2]E(x22,x21)+~E(x21,x22)
% 1.61/1.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.61/1.68 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 1.61/1.68 [5]~E(x51,x52)+E(f16(x51),f16(x52))
% 1.61/1.68 [6]~E(x61,x62)+E(f6(x61),f6(x62))
% 1.61/1.68 [7]~E(x71,x72)+E(f56(x71,x73),f56(x72,x73))
% 1.61/1.68 [8]~E(x81,x82)+E(f56(x83,x81),f56(x83,x82))
% 1.61/1.68 [9]~E(x91,x92)+E(f11(x91,x93,x94),f11(x92,x93,x94))
% 1.61/1.68 [10]~E(x101,x102)+E(f11(x103,x101,x104),f11(x103,x102,x104))
% 1.61/1.68 [11]~E(x111,x112)+E(f11(x113,x114,x111),f11(x113,x114,x112))
% 1.61/1.68 [12]~E(x121,x122)+E(f13(x121),f13(x122))
% 1.61/1.68 [13]~E(x131,x132)+E(f30(x131,x133),f30(x132,x133))
% 1.61/1.68 [14]~E(x141,x142)+E(f30(x143,x141),f30(x143,x142))
% 1.61/1.68 [15]~E(x151,x152)+E(f27(x151),f27(x152))
% 1.61/1.68 [16]~E(x161,x162)+E(f23(x161),f23(x162))
% 1.61/1.68 [17]~E(x171,x172)+E(f14(x171,x173,x174),f14(x172,x173,x174))
% 1.61/1.68 [18]~E(x181,x182)+E(f14(x183,x181,x184),f14(x183,x182,x184))
% 1.61/1.68 [19]~E(x191,x192)+E(f14(x193,x194,x191),f14(x193,x194,x192))
% 1.61/1.68 [20]~E(x201,x202)+E(f28(x201,x203),f28(x202,x203))
% 1.61/1.68 [21]~E(x211,x212)+E(f28(x213,x211),f28(x213,x212))
% 1.61/1.68 [22]~E(x221,x222)+E(f19(x221,x223),f19(x222,x223))
% 1.61/1.68 [23]~E(x231,x232)+E(f19(x233,x231),f19(x233,x232))
% 1.61/1.68 [24]~E(x241,x242)+E(f25(x241,x243,x244),f25(x242,x243,x244))
% 1.61/1.68 [25]~E(x251,x252)+E(f25(x253,x251,x254),f25(x253,x252,x254))
% 1.61/1.68 [26]~E(x261,x262)+E(f25(x263,x264,x261),f25(x263,x264,x262))
% 1.61/1.68 [27]~E(x271,x272)+E(f72(x271),f72(x272))
% 1.61/1.68 [28]~E(x281,x282)+E(f53(x281,x283,x284,x285),f53(x282,x283,x284,x285))
% 1.61/1.68 [29]~E(x291,x292)+E(f53(x293,x291,x294,x295),f53(x293,x292,x294,x295))
% 1.61/1.68 [30]~E(x301,x302)+E(f53(x303,x304,x301,x305),f53(x303,x304,x302,x305))
% 1.61/1.68 [31]~E(x311,x312)+E(f53(x313,x314,x315,x311),f53(x313,x314,x315,x312))
% 1.61/1.68 [32]~E(x321,x322)+E(f20(x321,x323,x324),f20(x322,x323,x324))
% 1.61/1.68 [33]~E(x331,x332)+E(f20(x333,x331,x334),f20(x333,x332,x334))
% 1.61/1.68 [34]~E(x341,x342)+E(f20(x343,x344,x341),f20(x343,x344,x342))
% 1.61/1.68 [35]~E(x351,x352)+E(f12(x351,x353),f12(x352,x353))
% 1.61/1.68 [36]~E(x361,x362)+E(f12(x363,x361),f12(x363,x362))
% 1.61/1.68 [37]~E(x371,x372)+E(f18(x371,x373,x374),f18(x372,x373,x374))
% 1.61/1.68 [38]~E(x381,x382)+E(f18(x383,x381,x384),f18(x383,x382,x384))
% 1.61/1.68 [39]~E(x391,x392)+E(f18(x393,x394,x391),f18(x393,x394,x392))
% 1.61/1.68 [40]~E(x401,x402)+E(f9(x401,x403,x404),f9(x402,x403,x404))
% 1.61/1.68 [41]~E(x411,x412)+E(f9(x413,x411,x414),f9(x413,x412,x414))
% 1.61/1.68 [42]~E(x421,x422)+E(f9(x423,x424,x421),f9(x423,x424,x422))
% 1.61/1.68 [43]~E(x431,x432)+E(f29(x431,x433),f29(x432,x433))
% 1.61/1.68 [44]~E(x441,x442)+E(f29(x443,x441),f29(x443,x442))
% 1.61/1.68 [45]~E(x451,x452)+E(f17(x451,x453),f17(x452,x453))
% 1.61/1.68 [46]~E(x461,x462)+E(f17(x463,x461),f17(x463,x462))
% 1.61/1.68 [47]~E(x471,x472)+E(f10(x471,x473),f10(x472,x473))
% 1.61/1.68 [48]~E(x481,x482)+E(f10(x483,x481),f10(x483,x482))
% 1.61/1.68 [49]~E(x491,x492)+E(f69(x491,x493),f69(x492,x493))
% 1.61/1.68 [50]~E(x501,x502)+E(f69(x503,x501),f69(x503,x502))
% 1.61/1.68 [51]~E(x511,x512)+E(f31(x511,x513),f31(x512,x513))
% 1.61/1.68 [52]~E(x521,x522)+E(f31(x523,x521),f31(x523,x522))
% 1.61/1.68 [53]~E(x531,x532)+E(f26(x531,x533,x534),f26(x532,x533,x534))
% 1.61/1.68 [54]~E(x541,x542)+E(f26(x543,x541,x544),f26(x543,x542,x544))
% 1.61/1.68 [55]~E(x551,x552)+E(f26(x553,x554,x551),f26(x553,x554,x552))
% 1.61/1.68 [56]~E(x561,x562)+E(f77(x561,x563),f77(x562,x563))
% 1.61/1.68 [57]~E(x571,x572)+E(f77(x573,x571),f77(x573,x572))
% 1.61/1.68 [58]~E(x581,x582)+E(f8(x581,x583),f8(x582,x583))
% 1.61/1.68 [59]~E(x591,x592)+E(f8(x593,x591),f8(x593,x592))
% 1.61/1.68 [60]~E(x601,x602)+E(f15(x601,x603),f15(x602,x603))
% 1.61/1.68 [61]~E(x611,x612)+E(f15(x613,x611),f15(x613,x612))
% 1.61/1.68 [62]~E(x621,x622)+E(f60(x621,x623,x624),f60(x622,x623,x624))
% 1.61/1.68 [63]~E(x631,x632)+E(f60(x633,x631,x634),f60(x633,x632,x634))
% 1.61/1.68 [64]~E(x641,x642)+E(f60(x643,x644,x641),f60(x643,x644,x642))
% 1.61/1.68 [65]~E(x651,x652)+E(f52(x651,x653),f52(x652,x653))
% 1.61/1.68 [66]~E(x661,x662)+E(f52(x663,x661),f52(x663,x662))
% 1.61/1.68 [67]~E(x671,x672)+E(f48(x671,x673,x674,x675),f48(x672,x673,x674,x675))
% 1.61/1.68 [68]~E(x681,x682)+E(f48(x683,x681,x684,x685),f48(x683,x682,x684,x685))
% 1.61/1.68 [69]~E(x691,x692)+E(f48(x693,x694,x691,x695),f48(x693,x694,x692,x695))
% 1.61/1.68 [70]~E(x701,x702)+E(f48(x703,x704,x705,x701),f48(x703,x704,x705,x702))
% 1.61/1.68 [71]~E(x711,x712)+E(f47(x711,x713),f47(x712,x713))
% 1.61/1.68 [72]~E(x721,x722)+E(f47(x723,x721),f47(x723,x722))
% 1.61/1.68 [73]~E(x731,x732)+E(f58(x731,x733),f58(x732,x733))
% 1.61/1.68 [74]~E(x741,x742)+E(f58(x743,x741),f58(x743,x742))
% 1.61/1.68 [75]~E(x751,x752)+E(f61(x751,x753),f61(x752,x753))
% 1.61/1.68 [76]~E(x761,x762)+E(f61(x763,x761),f61(x763,x762))
% 1.61/1.68 [77]~E(x771,x772)+E(f59(x771),f59(x772))
% 1.61/1.68 [78]~E(x781,x782)+E(f54(x781,x783),f54(x782,x783))
% 1.61/1.68 [79]~E(x791,x792)+E(f54(x793,x791),f54(x793,x792))
% 1.61/1.68 [80]~E(x801,x802)+E(f35(x801),f35(x802))
% 1.61/1.68 [81]~E(x811,x812)+E(f64(x811,x813,x814),f64(x812,x813,x814))
% 1.61/1.68 [82]~E(x821,x822)+E(f64(x823,x821,x824),f64(x823,x822,x824))
% 1.61/1.68 [83]~E(x831,x832)+E(f64(x833,x834,x831),f64(x833,x834,x832))
% 1.61/1.68 [84]~E(x841,x842)+E(f22(x841,x843,x844),f22(x842,x843,x844))
% 1.61/1.68 [85]~E(x851,x852)+E(f22(x853,x851,x854),f22(x853,x852,x854))
% 1.61/1.68 [86]~E(x861,x862)+E(f22(x863,x864,x861),f22(x863,x864,x862))
% 1.61/1.68 [87]~E(x871,x872)+E(f63(x871,x873,x874),f63(x872,x873,x874))
% 1.61/1.68 [88]~E(x881,x882)+E(f63(x883,x881,x884),f63(x883,x882,x884))
% 1.61/1.68 [89]~E(x891,x892)+E(f63(x893,x894,x891),f63(x893,x894,x892))
% 1.61/1.68 [90]~E(x901,x902)+E(f38(x901),f38(x902))
% 1.61/1.68 [91]~E(x911,x912)+E(f21(x911,x913,x914),f21(x912,x913,x914))
% 1.61/1.68 [92]~E(x921,x922)+E(f21(x923,x921,x924),f21(x923,x922,x924))
% 1.61/1.68 [93]~E(x931,x932)+E(f21(x933,x934,x931),f21(x933,x934,x932))
% 1.61/1.68 [94]~E(x941,x942)+E(f70(x941,x943,x944),f70(x942,x943,x944))
% 1.61/1.68 [95]~E(x951,x952)+E(f70(x953,x951,x954),f70(x953,x952,x954))
% 1.61/1.68 [96]~E(x961,x962)+E(f70(x963,x964,x961),f70(x963,x964,x962))
% 1.61/1.68 [97]~E(x971,x972)+E(f51(x971),f51(x972))
% 1.61/1.68 [98]~E(x981,x982)+E(f36(x981),f36(x982))
% 1.61/1.68 [99]~E(x991,x992)+E(f68(x991,x993,x994),f68(x992,x993,x994))
% 1.61/1.68 [100]~E(x1001,x1002)+E(f68(x1003,x1001,x1004),f68(x1003,x1002,x1004))
% 1.61/1.68 [101]~E(x1011,x1012)+E(f68(x1013,x1014,x1011),f68(x1013,x1014,x1012))
% 1.61/1.68 [102]~E(x1021,x1022)+E(f37(x1021),f37(x1022))
% 1.61/1.68 [103]~E(x1031,x1032)+E(f55(x1031),f55(x1032))
% 1.61/1.68 [104]~E(x1041,x1042)+E(f67(x1041,x1043),f67(x1042,x1043))
% 1.61/1.68 [105]~E(x1051,x1052)+E(f67(x1053,x1051),f67(x1053,x1052))
% 1.61/1.68 [106]~E(x1061,x1062)+E(f62(x1061),f62(x1062))
% 1.61/1.68 [107]~E(x1071,x1072)+E(f66(x1071,x1073),f66(x1072,x1073))
% 1.61/1.68 [108]~E(x1081,x1082)+E(f66(x1083,x1081),f66(x1083,x1082))
% 1.61/1.68 [109]~E(x1091,x1092)+E(f50(x1091),f50(x1092))
% 1.61/1.68 [110]~E(x1101,x1102)+E(f24(x1101,x1103,x1104),f24(x1102,x1103,x1104))
% 1.61/1.68 [111]~E(x1111,x1112)+E(f24(x1113,x1111,x1114),f24(x1113,x1112,x1114))
% 1.61/1.68 [112]~E(x1121,x1122)+E(f24(x1123,x1124,x1121),f24(x1123,x1124,x1122))
% 1.61/1.68 [113]~P1(x1131)+P1(x1132)+~E(x1131,x1132)
% 1.61/1.68 [114]P9(x1142,x1143,x1144)+~E(x1141,x1142)+~P9(x1141,x1143,x1144)
% 1.61/1.68 [115]P9(x1153,x1152,x1154)+~E(x1151,x1152)+~P9(x1153,x1151,x1154)
% 1.61/1.68 [116]P9(x1163,x1164,x1162)+~E(x1161,x1162)+~P9(x1163,x1164,x1161)
% 1.61/1.68 [117]P8(x1172,x1173,x1174)+~E(x1171,x1172)+~P8(x1171,x1173,x1174)
% 1.61/1.68 [118]P8(x1183,x1182,x1184)+~E(x1181,x1182)+~P8(x1183,x1181,x1184)
% 1.61/1.68 [119]P8(x1193,x1194,x1192)+~E(x1191,x1192)+~P8(x1193,x1194,x1191)
% 1.61/1.68 [120]~P2(x1201)+P2(x1202)+~E(x1201,x1202)
% 1.61/1.68 [121]~P55(x1211)+P55(x1212)+~E(x1211,x1212)
% 1.61/1.68 [122]~P47(x1221)+P47(x1222)+~E(x1221,x1222)
% 1.61/1.68 [123]P11(x1232,x1233)+~E(x1231,x1232)+~P11(x1231,x1233)
% 1.61/1.68 [124]P11(x1243,x1242)+~E(x1241,x1242)+~P11(x1243,x1241)
% 1.61/1.68 [125]~P50(x1251)+P50(x1252)+~E(x1251,x1252)
% 1.61/1.68 [126]~P48(x1261)+P48(x1262)+~E(x1261,x1262)
% 1.61/1.68 [127]~P62(x1271)+P62(x1272)+~E(x1271,x1272)
% 1.61/1.68 [128]P12(x1282,x1283,x1284)+~E(x1281,x1282)+~P12(x1281,x1283,x1284)
% 1.61/1.68 [129]P12(x1293,x1292,x1294)+~E(x1291,x1292)+~P12(x1293,x1291,x1294)
% 1.61/1.68 [130]P12(x1303,x1304,x1302)+~E(x1301,x1302)+~P12(x1303,x1304,x1301)
% 1.61/1.68 [131]~P51(x1311)+P51(x1312)+~E(x1311,x1312)
% 1.61/1.68 [132]~P61(x1321)+P61(x1322)+~E(x1321,x1322)
% 1.61/1.68 [133]~P3(x1331)+P3(x1332)+~E(x1331,x1332)
% 1.61/1.68 [134]~P44(x1341)+P44(x1342)+~E(x1341,x1342)
% 1.61/1.68 [135]~P52(x1351)+P52(x1352)+~E(x1351,x1352)
% 1.61/1.68 [136]~P39(x1361)+P39(x1362)+~E(x1361,x1362)
% 1.61/1.68 [137]~P82(x1371)+P82(x1372)+~E(x1371,x1372)
% 1.61/1.68 [138]~P18(x1381)+P18(x1382)+~E(x1381,x1382)
% 1.61/1.68 [139]~P49(x1391)+P49(x1392)+~E(x1391,x1392)
% 1.61/1.68 [140]~P24(x1401)+P24(x1402)+~E(x1401,x1402)
% 1.61/1.68 [141]~P63(x1411)+P63(x1412)+~E(x1411,x1412)
% 1.61/1.68 [142]~P58(x1421)+P58(x1422)+~E(x1421,x1422)
% 1.61/1.68 [143]~P29(x1431)+P29(x1432)+~E(x1431,x1432)
% 1.61/1.68 [144]~P70(x1441)+P70(x1442)+~E(x1441,x1442)
% 1.61/1.68 [145]~P53(x1451)+P53(x1452)+~E(x1451,x1452)
% 1.61/1.68 [146]~P72(x1461)+P72(x1462)+~E(x1461,x1462)
% 1.61/1.68 [147]~P76(x1471)+P76(x1472)+~E(x1471,x1472)
% 1.61/1.68 [148]~P41(x1481)+P41(x1482)+~E(x1481,x1482)
% 1.61/1.68 [149]~P71(x1491)+P71(x1492)+~E(x1491,x1492)
% 1.61/1.68 [150]~P14(x1501)+P14(x1502)+~E(x1501,x1502)
% 1.61/1.68 [151]~P56(x1511)+P56(x1512)+~E(x1511,x1512)
% 1.61/1.68 [152]~P27(x1521)+P27(x1522)+~E(x1521,x1522)
% 1.61/1.68 [153]~P31(x1531)+P31(x1532)+~E(x1531,x1532)
% 1.61/1.68 [154]P13(x1542,x1543)+~E(x1541,x1542)+~P13(x1541,x1543)
% 1.61/1.68 [155]P13(x1553,x1552)+~E(x1551,x1552)+~P13(x1553,x1551)
% 1.61/1.68 [156]~P32(x1561)+P32(x1562)+~E(x1561,x1562)
% 1.61/1.68 [157]~P64(x1571)+P64(x1572)+~E(x1571,x1572)
% 1.61/1.68 [158]~P23(x1581)+P23(x1582)+~E(x1581,x1582)
% 1.61/1.68 [159]~P35(x1591)+P35(x1592)+~E(x1591,x1592)
% 1.61/1.68 [160]~P65(x1601)+P65(x1602)+~E(x1601,x1602)
% 1.61/1.68 [161]~P80(x1611)+P80(x1612)+~E(x1611,x1612)
% 1.61/1.68 [162]~P73(x1621)+P73(x1622)+~E(x1621,x1622)
% 1.61/1.68 [163]~P60(x1631)+P60(x1632)+~E(x1631,x1632)
% 1.61/1.68 [164]~P15(x1641)+P15(x1642)+~E(x1641,x1642)
% 1.61/1.68 [165]~P57(x1651)+P57(x1652)+~E(x1651,x1652)
% 1.61/1.68 [166]~P28(x1661)+P28(x1662)+~E(x1661,x1662)
% 1.61/1.68 [167]~P66(x1671)+P66(x1672)+~E(x1671,x1672)
% 1.61/1.68 [168]~P54(x1681)+P54(x1682)+~E(x1681,x1682)
% 1.61/1.68 [169]~P67(x1691)+P67(x1692)+~E(x1691,x1692)
% 1.61/1.68 [170]~P22(x1701)+P22(x1702)+~E(x1701,x1702)
% 1.61/1.68 [171]~P68(x1711)+P68(x1712)+~E(x1711,x1712)
% 1.61/1.68 [172]~P37(x1721)+P37(x1722)+~E(x1721,x1722)
% 1.61/1.68 [173]~P17(x1731)+P17(x1732)+~E(x1731,x1732)
% 1.61/1.68 [174]~P33(x1741)+P33(x1742)+~E(x1741,x1742)
% 1.61/1.68 [175]~P74(x1751)+P74(x1752)+~E(x1751,x1752)
% 1.61/1.68 [176]~P40(x1761)+P40(x1762)+~E(x1761,x1762)
% 1.61/1.68 [177]P10(x1772,x1773,x1774)+~E(x1771,x1772)+~P10(x1771,x1773,x1774)
% 1.61/1.68 [178]P10(x1783,x1782,x1784)+~E(x1781,x1782)+~P10(x1783,x1781,x1784)
% 1.61/1.68 [179]P10(x1793,x1794,x1792)+~E(x1791,x1792)+~P10(x1793,x1794,x1791)
% 1.61/1.68 [180]~P69(x1801)+P69(x1802)+~E(x1801,x1802)
% 1.61/1.68 [181]~P45(x1811)+P45(x1812)+~E(x1811,x1812)
% 1.61/1.68 [182]~P26(x1821)+P26(x1822)+~E(x1821,x1822)
% 1.61/1.68 [183]~P81(x1831)+P81(x1832)+~E(x1831,x1832)
% 1.61/1.68 [184]~P78(x1841)+P78(x1842)+~E(x1841,x1842)
% 1.61/1.68 [185]~P36(x1851)+P36(x1852)+~E(x1851,x1852)
% 1.61/1.68 [186]~P5(x1861)+P5(x1862)+~E(x1861,x1862)
% 1.61/1.68 [187]~P21(x1871)+P21(x1872)+~E(x1871,x1872)
% 1.61/1.68 [188]~P79(x1881)+P79(x1882)+~E(x1881,x1882)
% 1.61/1.68 [189]~P42(x1891)+P42(x1892)+~E(x1891,x1892)
% 1.61/1.68 [190]~P34(x1901)+P34(x1902)+~E(x1901,x1902)
% 1.61/1.68 [191]~P43(x1911)+P43(x1912)+~E(x1911,x1912)
% 1.61/1.68 [192]~P19(x1921)+P19(x1922)+~E(x1921,x1922)
% 1.61/1.68 [193]~P20(x1931)+P20(x1932)+~E(x1931,x1932)
% 1.61/1.68 [194]~P46(x1941)+P46(x1942)+~E(x1941,x1942)
% 1.61/1.68 [195]~P77(x1951)+P77(x1952)+~E(x1951,x1952)
% 1.61/1.68 [196]~P75(x1961)+P75(x1962)+~E(x1961,x1962)
% 1.61/1.68 [197]~P25(x1971)+P25(x1972)+~E(x1971,x1972)
% 1.61/1.68 [198]~P16(x1981)+P16(x1982)+~E(x1981,x1982)
% 1.61/1.68 [199]~P4(x1991)+P4(x1992)+~E(x1991,x1992)
% 1.61/1.68 [200]~P30(x2001)+P30(x2002)+~E(x2001,x2002)
% 1.61/1.68 [201]~P6(x2011)+P6(x2012)+~E(x2011,x2012)
% 1.61/1.68 [202]~P59(x2021)+P59(x2022)+~E(x2021,x2022)
% 1.61/1.68 [203]~P7(x2031)+P7(x2032)+~E(x2031,x2032)
% 1.61/1.68 [204]~P38(x2041)+P38(x2042)+~E(x2041,x2042)
% 1.61/1.68
% 1.61/1.68 %-------------------------------------------
% 1.61/1.69 cnf(1824,plain,
% 1.61/1.69 (P8(a3,x18241,x18241)),
% 1.61/1.69 inference(rename_variables,[],[449])).
% 1.61/1.69 cnf(1827,plain,
% 1.61/1.69 (P8(a3,x18271,x18271)),
% 1.61/1.69 inference(rename_variables,[],[449])).
% 1.61/1.69 cnf(1830,plain,
% 1.61/1.69 (P8(a2,x18301,f14(a2,x18302,x18301))),
% 1.61/1.69 inference(rename_variables,[],[495])).
% 1.61/1.69 cnf(1838,plain,
% 1.61/1.69 (~P9(a2,x18381,x18381)),
% 1.61/1.69 inference(rename_variables,[],[586])).
% 1.61/1.69 cnf(1841,plain,
% 1.61/1.69 (~P9(a2,f14(a2,x18411,x18412),x18412)),
% 1.61/1.69 inference(rename_variables,[],[596])).
% 1.61/1.69 cnf(1847,plain,
% 1.61/1.69 (P8(a1,x18471,x18471)),
% 1.61/1.69 inference(rename_variables,[],[447])).
% 1.61/1.69 cnf(1854,plain,
% 1.61/1.69 (~P9(a1,f14(a1,f10(a1,x18541),f6(a1)),x18541)),
% 1.61/1.69 inference(rename_variables,[],[599])).
% 1.61/1.69 cnf(1862,plain,
% 1.61/1.69 (P8(a1,x18621,f29(a2,f16(x18621)))),
% 1.61/1.69 inference(rename_variables,[],[480])).
% 1.61/1.69 cnf(1865,plain,
% 1.61/1.69 (P9(a1,x18651,f14(a1,f29(a2,f27(x18651)),f6(a1)))),
% 1.61/1.69 inference(rename_variables,[],[515])).
% 1.61/1.69 cnf(1868,plain,
% 1.61/1.69 (P8(a2,x18681,x18681)),
% 1.61/1.69 inference(rename_variables,[],[448])).
% 1.61/1.69 cnf(1873,plain,
% 1.61/1.69 (P8(a1,x18731,f29(a2,f16(x18731)))),
% 1.61/1.69 inference(rename_variables,[],[480])).
% 1.61/1.69 cnf(1878,plain,
% 1.61/1.69 (P8(a1,x18781,x18781)),
% 1.61/1.69 inference(rename_variables,[],[447])).
% 1.61/1.69 cnf(1891,plain,
% 1.61/1.69 (~P9(a1,f14(a1,f10(a1,x18911),f6(a1)),x18911)),
% 1.61/1.69 inference(rename_variables,[],[599])).
% 1.61/1.69 cnf(1894,plain,
% 1.61/1.69 (P9(a1,x18941,f14(a1,f29(a2,f27(x18941)),f6(a1)))),
% 1.61/1.69 inference(rename_variables,[],[515])).
% 1.61/1.69 cnf(1897,plain,
% 1.61/1.69 (~P9(a2,x18971,x18971)),
% 1.61/1.69 inference(rename_variables,[],[586])).
% 1.61/1.69 cnf(1900,plain,
% 1.61/1.69 (~P9(a2,x19001,x19001)),
% 1.61/1.69 inference(rename_variables,[],[586])).
% 1.61/1.69 cnf(1903,plain,
% 1.61/1.69 (P8(a1,x19031,x19031)),
% 1.61/1.69 inference(rename_variables,[],[447])).
% 1.61/1.69 cnf(1905,plain,
% 1.61/1.69 (P8(a1,x19051,x19051)),
% 1.61/1.69 inference(rename_variables,[],[447])).
% 1.61/1.69 cnf(1924,plain,
% 1.61/1.69 (P8(a2,f5(a2),x19241)),
% 1.61/1.69 inference(rename_variables,[],[463])).
% 1.61/1.69 cnf(1948,plain,
% 1.61/1.69 (P8(a1,x19481,x19481)),
% 1.61/1.69 inference(rename_variables,[],[447])).
% 1.61/1.69 cnf(1952,plain,
% 1.61/1.69 (P8(a1,x19521,x19521)),
% 1.61/1.69 inference(rename_variables,[],[447])).
% 1.61/1.69 cnf(1972,plain,
% 1.61/1.69 (E(f11(a2,f5(a2),x19721),f5(a2))),
% 1.61/1.69 inference(rename_variables,[],[471])).
% 1.61/1.69 cnf(1979,plain,
% 1.61/1.69 ($false),
% 1.61/1.69 inference(scs_inference,[],[603,447,1847,1878,1903,1905,1948,1952,448,1868,449,1824,1827,586,1838,1897,1900,247,311,334,365,377,392,393,394,400,401,403,404,463,1924,453,455,574,438,437,472,474,581,582,590,504,427,431,491,554,563,602,570,495,1830,497,596,1841,480,1862,1873,498,467,599,1854,1891,494,471,1972,515,1865,1894,2,880,848,842,860,1367,1365,1355,1354,1351,1258,1253,1251,1076,1001,1022,794,1283,8,1602,1524,1523,1433,1419,1186,1185,1087,1086,1011,942,938,1326,1394,1503,1501,119,118,116,115,3,1097,1096,1093,1092,1091,1073,1072,1009,953,951,896,895,765,1408,1130,1128,1307,1292,704,675,1543,1361,1328,1103,926,912,911,1635,1507]),
% 1.61/1.69 ['proof']).
% 1.61/1.69 % SZS output end Proof
% 1.61/1.69 % Total time :0.460000s
%------------------------------------------------------------------------------