TSTP Solution File: SWW262+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW262+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 1.96s 1.90s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW262+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
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 20:20:44 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 1.72/1.82 %-------------------------------------------
% 1.72/1.82 % File :CSE---1.6
% 1.72/1.82 % Problem :theBenchmark
% 1.72/1.82 % Transform :cnf
% 1.72/1.82 % Format :tptp:raw
% 1.72/1.82 % Command :java -jar mcs_scs.jar %d %s
% 1.72/1.83
% 1.72/1.83 % Result :Theorem 0.680000s
% 1.72/1.83 % Output :CNFRefutation 0.680000s
% 1.72/1.83 %-------------------------------------------
% 1.72/1.83 %------------------------------------------------------------------------------
% 1.72/1.83 % File : SWW262+1 : TPTP v8.1.2. Released v5.2.0.
% 1.72/1.83 % Domain : Software Verification
% 1.72/1.83 % Problem : Fundamental Theorem of Algebra 438508, 1000 axioms selected
% 1.72/1.83 % Version : Especial.
% 1.72/1.83 % English :
% 1.72/1.83
% 1.72/1.83 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 1.72/1.83 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 1.72/1.83 % Source : [Bla11]
% 1.72/1.83 % Names : fta_438508.1000.p [Bla11]
% 1.72/1.83
% 1.72/1.83 % Status : Theorem
% 1.72/1.83 % Rating : 0.39 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, 0.53 v6.0.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.71 v5.3.0, 0.78 v5.2.0
% 1.72/1.83 % Syntax : Number of formulae : 1288 ( 386 unt; 0 def)
% 1.72/1.83 % Number of atoms : 2977 ( 767 equ)
% 1.72/1.83 % Maximal formula atoms : 8 ( 2 avg)
% 1.72/1.83 % Number of connectives : 1856 ( 167 ~; 54 |; 98 &)
% 1.72/1.83 % ( 226 <=>;1311 =>; 0 <=; 0 <~>)
% 1.72/1.83 % Maximal formula depth : 13 ( 4 avg)
% 1.72/1.83 % Maximal term depth : 12 ( 2 avg)
% 1.72/1.83 % Number of predicates : 83 ( 82 usr; 0 prp; 1-3 aty)
% 1.72/1.83 % Number of functors : 45 ( 45 usr; 16 con; 0-3 aty)
% 1.72/1.83 % Number of variables : 2707 (2683 !; 24 ?)
% 1.72/1.83 % SPC : FOF_THM_RFO_SEQ
% 1.72/1.83
% 1.72/1.83 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 1.72/1.83 % 2011-03-01 11:59:38
% 1.72/1.83 %------------------------------------------------------------------------------
% 1.72/1.83 %----Relevant facts (998)
% 1.72/1.83 fof(fact_ext,axiom,
% 1.72/1.83 ! [V_g_2,V_f_2] :
% 1.72/1.83 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 1.72/1.83 => V_f_2 = V_g_2 ) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_t_I2_J,axiom,
% 1.72/1.83 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.72/1.83
% 1.72/1.83 fof(fact__0960_A_060_At_A_094_Ak_096,axiom,
% 1.72/1.83 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____)) ).
% 1.72/1.83
% 1.72/1.83 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,
% 1.72/1.83 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)) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_kas_I2_J,axiom,
% 1.72/1.83 v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_t_I1_J,axiom,
% 1.72/1.83 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_m_I1_J,axiom,
% 1.72/1.83 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_t_I3_J,axiom,
% 1.72/1.83 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____))) ).
% 1.72/1.83
% 1.72/1.83 fof(fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096,axiom,
% 1.72/1.83 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____))) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_norm__mult__less,axiom,
% 1.72/1.83 ! [V_s,V_y,V_r,V_x,T_a] :
% 1.72/1.83 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.72/1.83 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 1.72/1.83 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 1.72/1.83 => 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)) ) ) ) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_power__gt1__lemma,axiom,
% 1.72/1.83 ! [V_n,V_a,T_a] :
% 1.72/1.83 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.72/1.83 => 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))) ) ) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_power__less__power__Suc,axiom,
% 1.72/1.83 ! [V_n,V_a,T_a] :
% 1.72/1.83 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.72/1.83 => 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))) ) ) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_norm__power,axiom,
% 1.72/1.83 ! [V_n,V_x,T_a] :
% 1.72/1.83 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.72/1.83 => 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) ) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_norm__one,axiom,
% 1.72/1.83 ! [T_a] :
% 1.72/1.83 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.72/1.83 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_norm__mult,axiom,
% 1.72/1.83 ! [V_y,V_x,T_a] :
% 1.72/1.83 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.72/1.83 => 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)) ) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_norm__add__less,axiom,
% 1.72/1.83 ! [V_s,V_y,V_r,V_x,T_a] :
% 1.72/1.83 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.72/1.83 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 1.72/1.83 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 1.72/1.83 => 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)) ) ) ) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_power__add,axiom,
% 1.72/1.83 ! [V_n,V_m,V_a,T_a] :
% 1.72/1.83 ( class_Groups_Omonoid__mult(T_a)
% 1.72/1.83 => 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)) ) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 1.72/1.83 ! [V_q,V_p,V_x,T_a] :
% 1.72/1.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.83 => 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)) ) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_power__inject__exp,axiom,
% 1.72/1.83 ! [V_n_2,V_ma_2,V_aa_2,T_a] :
% 1.72/1.83 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_aa_2)
% 1.72/1.83 => ( 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)
% 1.72/1.83 <=> V_ma_2 = V_n_2 ) ) ) ).
% 1.72/1.83
% 1.72/1.83 fof(fact_power__strict__increasing__iff,axiom,
% 1.72/1.83 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 1.72/1.84 => ( 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))
% 1.72/1.84 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_inv0,axiom,
% 1.72/1.84 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____))) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_norm__ge__zero,axiom,
% 1.72/1.84 ! [V_x,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.72/1.84 => 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)) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_norm__zero,axiom,
% 1.72/1.84 ! [T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.72/1.84 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_complex__mod__triangle__sub,axiom,
% 1.72/1.84 ! [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))) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_norm__inverse,axiom,
% 1.72/1.84 ! [V_a,T_a] :
% 1.72/1.84 ( ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.72/1.84 & class_Rings_Odivision__ring__inverse__zero(T_a) )
% 1.72/1.84 => 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)) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_nat__zero__less__power__iff,axiom,
% 1.72/1.84 ! [V_n_2,V_x_2] :
% 1.72/1.84 ( 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))
% 1.72/1.84 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 1.72/1.84 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_norm__eq__zero,axiom,
% 1.72/1.84 ! [V_x_2,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.72/1.84 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.72/1.84 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_norm__le__zero__iff,axiom,
% 1.72/1.84 ! [V_x_2,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.72/1.84 => ( 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))
% 1.72/1.84 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__eq__0__iff,axiom,
% 1.72/1.84 ! [V_n_2,V_aa_2,T_a] :
% 1.72/1.84 ( ( class_Power_Opower(T_a)
% 1.72/1.84 & class_Rings_Omult__zero(T_a)
% 1.72/1.84 & class_Rings_Ono__zero__divisors(T_a)
% 1.72/1.84 & class_Rings_Ozero__neq__one(T_a) )
% 1.72/1.84 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.84 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.84 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_nonzero__norm__inverse,axiom,
% 1.72/1.84 ! [V_a,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.72/1.84 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.84 => 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)) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_nonzero__power__inverse,axiom,
% 1.72/1.84 ! [V_n,V_a,T_a] :
% 1.72/1.84 ( class_Rings_Odivision__ring(T_a)
% 1.72/1.84 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.84 => 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) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_zero__le__power,axiom,
% 1.72/1.84 ! [V_n,V_a,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.84 => 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)) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_nat__power__less__imp__less,axiom,
% 1.72/1.84 ! [V_n,V_m,V_i] :
% 1.72/1.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 1.72/1.84 => ( 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))
% 1.72/1.84 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__mono,axiom,
% 1.72/1.84 ! [V_n,V_b,V_a,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.84 => 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)) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__eq__imp__eq__base,axiom,
% 1.72/1.84 ! [V_b,V_n,V_a,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( 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)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.72/1.84 => V_a = V_b ) ) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__decreasing,axiom,
% 1.72/1.84 ! [V_a,V_N,V_n,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.72/1.84 => 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)) ) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__strict__mono,axiom,
% 1.72/1.84 ! [V_n,V_b,V_a,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.72/1.84 => 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)) ) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__inverse,axiom,
% 1.72/1.84 ! [V_n,V_a,T_a] :
% 1.72/1.84 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.72/1.84 => 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) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 1.72/1.84 ! [V_q,V_p,V_x,T_a] :
% 1.72/1.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.84 => 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)) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__mult,axiom,
% 1.72/1.84 ! [V_n,V_m,V_a,T_a] :
% 1.72/1.84 ( class_Groups_Omonoid__mult(T_a)
% 1.72/1.84 => 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) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_mult__right_Ozero,axiom,
% 1.72/1.84 ! [V_x,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.72/1.84 => 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) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_mult_Ozero__right,axiom,
% 1.72/1.84 ! [V_a,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.72/1.84 => 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) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 1.72/1.84 ! [V_a,T_a] :
% 1.72/1.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.84 => 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) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_mult__left_Ozero,axiom,
% 1.72/1.84 ! [V_y,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.72/1.84 => 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) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_mult_Ozero__left,axiom,
% 1.72/1.84 ! [V_b,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.72/1.84 => 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) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 1.72/1.84 ! [V_a,T_a] :
% 1.72/1.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.84 => 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) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_add__0__iff,axiom,
% 1.72/1.84 ! [V_aa_2,V_b_2,T_a] :
% 1.72/1.84 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.72/1.84 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)
% 1.72/1.84 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 1.72/1.84 ! [V_a,T_a] :
% 1.72/1.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.84 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 1.72/1.84 ! [V_a,T_a] :
% 1.72/1.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.84 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_field__power__not__zero,axiom,
% 1.72/1.84 ! [V_n,V_a,T_a] :
% 1.72/1.84 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.72/1.84 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__increasing,axiom,
% 1.72/1.84 ! [V_a,V_N,V_n,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.72/1.84 => 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)) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__less__imp__less__base,axiom,
% 1.72/1.84 ! [V_b,V_n,V_a,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( 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))
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.84 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__0__left,axiom,
% 1.72/1.84 ! [V_n,T_a] :
% 1.72/1.84 ( ( class_Power_Opower(T_a)
% 1.72/1.84 & class_Rings_Osemiring__0(T_a) )
% 1.72/1.84 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.72/1.84 => 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) )
% 1.72/1.84 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.72/1.84 => 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) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_zero__less__norm__iff,axiom,
% 1.72/1.84 ! [V_x_2,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.72/1.84 => ( 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))
% 1.72/1.84 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__le__imp__le__exp,axiom,
% 1.72/1.84 ! [V_n,V_m,V_a,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.72/1.84 => ( 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))
% 1.72/1.84 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__increasing__iff,axiom,
% 1.72/1.84 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 1.72/1.84 => ( 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))
% 1.72/1.84 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_one__le__power,axiom,
% 1.72/1.84 ! [V_n,V_a,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.72/1.84 => 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)) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_add__scale__eq__noteq,axiom,
% 1.72/1.84 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 1.72/1.84 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.72/1.84 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.84 => ( ( V_a = V_b
% 1.72/1.84 & V_c != V_d )
% 1.72/1.84 => 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)) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_norm__triangle__ineq,axiom,
% 1.72/1.84 ! [V_y,V_x,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.72/1.84 => 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))) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_zero__less__power,axiom,
% 1.72/1.84 ! [V_n,V_a,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.84 => 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)) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 1.72/1.84 ! [V_x,T_a] :
% 1.72/1.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.84 => 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) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__0,axiom,
% 1.72/1.84 ! [V_a,T_a] :
% 1.72/1.84 ( class_Power_Opower(T_a)
% 1.72/1.84 => 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) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_norm__not__less__zero,axiom,
% 1.72/1.84 ! [V_x,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.72/1.84 => ~ 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)) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_power__strict__decreasing,axiom,
% 1.72/1.84 ! [V_a,V_N,V_n,T_a] :
% 1.72/1.84 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.84 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.72/1.84 => 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)) ) ) ) ) ).
% 1.72/1.84
% 1.72/1.84 fof(fact_norm__mult__ineq,axiom,
% 1.72/1.84 ! [V_y,V_x,T_a] :
% 1.72/1.84 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.72/1.85 => 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))) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_one__less__power,axiom,
% 1.72/1.85 ! [V_n,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.72/1.85 => 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)) ) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_norm__power__ineq,axiom,
% 1.72/1.85 ! [V_n,V_x,T_a] :
% 1.72/1.85 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_power__Suc__less,axiom,
% 1.72/1.85 ! [V_n,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.72/1.85 => 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)) ) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 1.72/1.85 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 1.72/1.85 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 1.72/1.85 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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))) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 1.72/1.85 ! [V_rx,V_ly,V_lx,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 1.72/1.85 ! [V_rx,V_ly,V_lx,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 1.72/1.85 ! [V_ry,V_rx,V_lx,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 1.72/1.85 ! [V_ry,V_rx,V_lx,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 1.72/1.85 ! [V_b,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 1.72/1.85 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 1.72/1.85 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 1.72/1.85 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 1.72/1.85 ! [V_d,V_c,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 1.72/1.85 ! [V_d,V_c,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 1.72/1.85 ! [V_c,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_crossproduct__eq,axiom,
% 1.72/1.85 ! [V_z_2,V_x_2,V_y_2,V_wa_2,T_a] :
% 1.72/1.85 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.72/1.85 => ( 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))
% 1.72/1.85 <=> ( V_wa_2 = V_x_2
% 1.72/1.85 | V_y_2 = V_z_2 ) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 1.72/1.85 ! [V_b,V_m,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_mult__left_Oadd,axiom,
% 1.72/1.85 ! [V_ya,V_y,V_x,T_a] :
% 1.72/1.85 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_mult_Oadd__left,axiom,
% 1.72/1.85 ! [V_b,V_a_H,V_a,T_a] :
% 1.72/1.85 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 1.72/1.85 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_crossproduct__noteq,axiom,
% 1.72/1.85 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 1.72/1.85 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.72/1.85 => ( ( V_aa_2 != V_b_2
% 1.72/1.85 & V_ca_2 != V_d_2 )
% 1.72/1.85 <=> 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)) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_mult__right_Oadd,axiom,
% 1.72/1.85 ! [V_y,V_x,V_xa,T_a] :
% 1.72/1.85 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 1.72/1.85 ! [V_z,V_y,V_x,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_mult_Oadd__right,axiom,
% 1.72/1.85 ! [V_b_H,V_b,V_a,T_a] :
% 1.72/1.85 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 1.72/1.85 ! [V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 1.72/1.85 ! [V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 1.72/1.85 ! [V_q,V_y,V_x,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_power__mult__distrib,axiom,
% 1.72/1.85 ! [V_n,V_b,V_a,T_a] :
% 1.72/1.85 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_power__commutes,axiom,
% 1.72/1.85 ! [V_n,V_a,T_a] :
% 1.72/1.85 ( class_Groups_Omonoid__mult(T_a)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_power__one,axiom,
% 1.72/1.85 ! [V_n,T_a] :
% 1.72/1.85 ( class_Groups_Omonoid__mult(T_a)
% 1.72/1.85 => 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) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 1.72/1.85 ! [V_x,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_power__one__right,axiom,
% 1.72/1.85 ! [V_a,T_a] :
% 1.72/1.85 ( class_Groups_Omonoid__mult(T_a)
% 1.72/1.85 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 1.72/1.85 ! [V_m,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 1.72/1.85 ! [V_a,V_m,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 1.72/1.85 ! [V_m,T_a] :
% 1.72/1.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.72/1.85 => 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) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_power__strict__increasing,axiom,
% 1.72/1.85 ! [V_a,V_N,V_n,T_a] :
% 1.72/1.85 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.72/1.85 => 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)) ) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_power__less__imp__less__exp,axiom,
% 1.72/1.85 ! [V_n,V_m,V_a,T_a] :
% 1.72/1.85 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.72/1.85 => ( 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))
% 1.72/1.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.72/1.85
% 1.72/1.85 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,
% 1.72/1.85 ~ ! [B_t] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.72/1.85 => ~ 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____))) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_Bseq__inverse__lemma,axiom,
% 1.72/1.85 ! [V_x,V_r,T_a] :
% 1.72/1.85 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_r,c_RealVector_Onorm__class_Onorm(T_a,V_x))
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 1.72/1.85 => 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)) ) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_convex__bound__lt,axiom,
% 1.72/1.85 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.72/1.85 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.72/1.85 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.72/1.85 => 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) ) ) ) ) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_norm__ratiotest__lemma,axiom,
% 1.72/1.85 ! [V_y,V_x,V_c,T_a] :
% 1.72/1.85 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.72/1.85 => ( 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)))
% 1.72/1.85 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_less__zeroE,axiom,
% 1.72/1.85 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_one__le__inverse,axiom,
% 1.72/1.85 ! [V_a,T_a] :
% 1.72/1.85 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.72/1.85 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_inverse__less__1__iff,axiom,
% 1.72/1.85 ! [V_x_2,T_a] :
% 1.72/1.85 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 1.72/1.85 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.85 | c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2) ) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_one__le__inverse__iff,axiom,
% 1.72/1.85 ! [V_x_2,T_a] :
% 1.72/1.85 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.72/1.85 => ( 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))
% 1.72/1.85 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.72/1.85 & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_convex__bound__le,axiom,
% 1.72/1.85 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.72/1.85 ( class_Rings_Olinordered__semiring__1(T_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.72/1.85 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.72/1.85 => 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) ) ) ) ) ) ) ).
% 1.72/1.85
% 1.72/1.85 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,
% 1.72/1.85 ! [V_d2] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2)
% 1.72/1.85 => ? [B_e] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
% 1.72/1.85 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.72/1.85 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,V_d2) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_real__mult__inverse__left,axiom,
% 1.72/1.85 ! [V_x] :
% 1.72/1.85 ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.72/1.85 => 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) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_kas_I1_J,axiom,
% 1.72/1.85 v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_w0,axiom,
% 1.72/1.85 v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le0,axiom,
% 1.72/1.85 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_w,axiom,
% 1.72/1.85 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) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__refl,axiom,
% 1.72/1.85 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__square,axiom,
% 1.72/1.85 ! [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)) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__cube,axiom,
% 1.72/1.85 ! [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))) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_nat__mult__commute,axiom,
% 1.72/1.85 ! [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) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_nat__le__linear,axiom,
% 1.72/1.85 ! [V_n,V_m] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.72/1.85 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_nat__mult__assoc,axiom,
% 1.72/1.85 ! [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)) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_eq__imp__le,axiom,
% 1.72/1.85 ! [V_n,V_m] :
% 1.72/1.85 ( V_m = V_n
% 1.72/1.85 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_mult__le__mono1,axiom,
% 1.72/1.85 ! [V_k,V_j,V_i] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_mult__le__mono2,axiom,
% 1.72/1.85 ! [V_k,V_j,V_i] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__trans,axiom,
% 1.72/1.85 ! [V_k,V_j,V_i] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 1.72/1.85 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__antisym,axiom,
% 1.72/1.85 ! [V_n,V_m] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.72/1.85 => V_m = V_n ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_mult__le__mono,axiom,
% 1.72/1.85 ! [V_l,V_k,V_j,V_i] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.72/1.85 => 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)) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__0__eq,axiom,
% 1.72/1.85 ! [V_n_2] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.72/1.85 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 1.72/1.85 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_less__or__eq__imp__le,axiom,
% 1.72/1.85 ! [V_n,V_m] :
% 1.72/1.85 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.72/1.85 | V_m = V_n )
% 1.72/1.85 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__neq__implies__less,axiom,
% 1.72/1.85 ! [V_n,V_m] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.72/1.85 => ( V_m != V_n
% 1.72/1.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_less__imp__le__nat,axiom,
% 1.72/1.85 ! [V_n,V_m] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.72/1.85 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__eq__less__or__eq,axiom,
% 1.72/1.85 ! [V_n_2,V_ma_2] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.72/1.85 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.72/1.85 | V_ma_2 = V_n_2 ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_nat__less__le,axiom,
% 1.72/1.85 ! [V_n_2,V_ma_2] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.72/1.85 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.72/1.85 & V_ma_2 != V_n_2 ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__add2,axiom,
% 1.72/1.85 ! [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)) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__add1,axiom,
% 1.72/1.85 ! [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)) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__Suc__ex__iff,axiom,
% 1.72/1.85 ! [V_l_2,V_ka_2] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_l_2)
% 1.72/1.85 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,B_n) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_le__iff__add,axiom,
% 1.72/1.85 ! [V_n_2,V_ma_2] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.72/1.85 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_nat__add__left__cancel__le,axiom,
% 1.72/1.85 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.72/1.85 ( 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))
% 1.72/1.85 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_trans__le__add1,axiom,
% 1.72/1.85 ! [V_m,V_j,V_i] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.72/1.85 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_trans__le__add2,axiom,
% 1.72/1.85 ! [V_m,V_j,V_i] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.72/1.85 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_add__le__mono1,axiom,
% 1.72/1.85 ! [V_k,V_j,V_i] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.72/1.85 => 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)) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_add__le__mono,axiom,
% 1.72/1.85 ! [V_l,V_k,V_j,V_i] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.72/1.85 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.72/1.85 => 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)) ) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_add__leD2,axiom,
% 1.72/1.85 ! [V_n,V_k,V_m] :
% 1.72/1.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.72/1.85 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 1.72/1.85
% 1.72/1.85 fof(fact_add__leD1,axiom,
% 1.72/1.86 ! [V_n,V_k,V_m] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.72/1.86 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_add__leE,axiom,
% 1.72/1.86 ! [V_n,V_k,V_m] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.72/1.86 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.72/1.86 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__le__cancel2,axiom,
% 1.72/1.86 ! [V_n_2,V_ka_2,V_ma_2] :
% 1.72/1.86 ( 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))
% 1.72/1.86 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.72/1.86 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__le__cancel1,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.72/1.86 ( 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))
% 1.72/1.86 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.72/1.86 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_linorder__neqE__linordered__idom,axiom,
% 1.72/1.86 ! [V_y,V_x,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__idom(T_a)
% 1.72/1.86 => ( V_x != V_y
% 1.72/1.86 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__cancel2,axiom,
% 1.72/1.86 ! [V_n_2,V_ka_2,V_ma_2] :
% 1.72/1.86 ( 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)
% 1.72/1.86 <=> ( V_ma_2 = V_n_2
% 1.72/1.86 | V_ka_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__cancel1,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.72/1.86 ( 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)
% 1.72/1.86 <=> ( V_ma_2 = V_n_2
% 1.72/1.86 | V_ka_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__is__0,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2] :
% 1.72/1.86 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.72/1.86 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.72/1.86 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__0__right,axiom,
% 1.72/1.86 ! [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) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__0,axiom,
% 1.72/1.86 ! [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) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__le__antisym,axiom,
% 1.72/1.86 ! [V_w,V_z] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 1.72/1.86 => V_z = V_w ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__le__trans,axiom,
% 1.72/1.86 ! [V_k,V_j,V_i] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 1.72/1.86 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__le__linear,axiom,
% 1.72/1.86 ! [V_w,V_z] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.72/1.86 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__le__refl,axiom,
% 1.72/1.86 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__less__cases,axiom,
% 1.72/1.86 ! [V_P_2,V_n_2,V_ma_2] :
% 1.72/1.86 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.72/1.86 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 1.72/1.86 => ( ( V_ma_2 = V_n_2
% 1.72/1.86 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 1.72/1.86 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
% 1.72/1.86 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 1.72/1.86 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_less__not__refl3,axiom,
% 1.72/1.86 ! [V_t,V_s] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 1.72/1.86 => V_s != V_t ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_less__not__refl2,axiom,
% 1.72/1.86 ! [V_m,V_n] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 1.72/1.86 => V_m != V_n ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_less__irrefl__nat,axiom,
% 1.72/1.86 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_linorder__neqE__nat,axiom,
% 1.72/1.86 ! [V_y,V_x] :
% 1.72/1.86 ( V_x != V_y
% 1.72/1.86 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__neq__iff,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2] :
% 1.72/1.86 ( V_ma_2 != V_n_2
% 1.72/1.86 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.72/1.86 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_less__not__refl,axiom,
% 1.72/1.86 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__add__commute,axiom,
% 1.72/1.86 ! [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) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__add__left__commute,axiom,
% 1.72/1.86 ! [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)) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__add__assoc,axiom,
% 1.72/1.86 ! [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)) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__add__left__cancel,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.72/1.86 ( 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)
% 1.72/1.86 <=> V_ma_2 = V_n_2 ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__add__right__cancel,axiom,
% 1.72/1.86 ! [V_n_2,V_ka_2,V_ma_2] :
% 1.72/1.86 ( 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)
% 1.72/1.86 <=> V_ma_2 = V_n_2 ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_add__mult__distrib2,axiom,
% 1.72/1.86 ! [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)) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_add__mult__distrib,axiom,
% 1.72/1.86 ! [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)) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__mult__commute,axiom,
% 1.72/1.86 ! [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) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__mult__assoc,axiom,
% 1.72/1.86 ! [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)) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__eq__imp__eq,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.72/1.86 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b)
% 1.72/1.86 => V_a = V_b ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__eq__iff__eq,axiom,
% 1.72/1.86 ! [V_b_2,V_aa_2,T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.72/1.86 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2) = c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)
% 1.72/1.86 <=> V_aa_2 = V_b_2 ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__inverse__eq,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.72/1.86 => c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__mult__1,axiom,
% 1.72/1.86 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__1__eq__mult__iff,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2] :
% 1.72/1.86 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)
% 1.72/1.86 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.72/1.86 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__mult__1__right,axiom,
% 1.72/1.86 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__mult__eq__1__iff,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2] :
% 1.72/1.86 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.72/1.86 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.72/1.86 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__zero__left,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Rings_Omult__zero(T_a)
% 1.72/1.86 => 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) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__zero__right,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Rings_Omult__zero(T_a)
% 1.72/1.86 => 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) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__eq__0__iff,axiom,
% 1.72/1.86 ! [V_b_2,V_aa_2,T_a] :
% 1.72/1.86 ( class_Rings_Oring__no__zero__divisors(T_a)
% 1.72/1.86 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_no__zero__divisors,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Ono__zero__divisors(T_a)
% 1.72/1.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_divisors__zero,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Ono__zero__divisors(T_a)
% 1.72/1.86 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_one__neq__zero,axiom,
% 1.72/1.86 ! [T_a] :
% 1.72/1.86 ( class_Rings_Ozero__neq__one(T_a)
% 1.72/1.86 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_zero__neq__one,axiom,
% 1.72/1.86 ! [T_a] :
% 1.72/1.86 ( class_Rings_Ozero__neq__one(T_a)
% 1.72/1.86 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_comm__semiring__class_Odistrib,axiom,
% 1.72/1.86 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Ocomm__semiring(T_a)
% 1.72/1.86 => 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)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_combine__common__factor,axiom,
% 1.72/1.86 ! [V_c,V_b,V_e,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Osemiring(T_a)
% 1.72/1.86 => 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) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nonzero__inverse__eq__imp__eq,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring(T_a)
% 1.72/1.86 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b)
% 1.72/1.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => V_a = V_b ) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__zero__imp__zero,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring(T_a)
% 1.72/1.86 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nonzero__inverse__inverse__eq,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring(T_a)
% 1.72/1.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nonzero__imp__inverse__nonzero,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring(T_a)
% 1.72/1.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__nonzero__iff__nonzero,axiom,
% 1.72/1.86 ! [V_aa_2,T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.72/1.86 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__zero,axiom,
% 1.72/1.86 ! [T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.72/1.86 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_field__inverse__zero,axiom,
% 1.72/1.86 ! [T_a] :
% 1.72/1.86 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.72/1.86 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_gr0I,axiom,
% 1.72/1.86 ! [V_n] :
% 1.72/1.86 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__less__mono2,axiom,
% 1.72/1.86 ! [V_k,V_j,V_i] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.72/1.86 => 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)) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__less__mono1,axiom,
% 1.72/1.86 ! [V_k,V_j,V_i] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.72/1.86 => 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)) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_gr__implies__not0,axiom,
% 1.72/1.86 ! [V_n,V_m] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.72/1.86 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__less__cancel2,axiom,
% 1.72/1.86 ! [V_n_2,V_ka_2,V_ma_2] :
% 1.72/1.86 ( 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))
% 1.72/1.86 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.72/1.86 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__less__cancel1,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.72/1.86 ( 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))
% 1.72/1.86 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.72/1.86 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_less__nat__zero__code,axiom,
% 1.72/1.86 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__0__less__mult__iff,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2] :
% 1.72/1.86 ( 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))
% 1.72/1.86 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 1.72/1.86 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_neq0__conv,axiom,
% 1.72/1.86 ! [V_n_2] :
% 1.72/1.86 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.72/1.86 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_not__less0,axiom,
% 1.72/1.86 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__less__def,axiom,
% 1.72/1.86 ! [V_y_2,V_x_2] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.72/1.86 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.72/1.86 & V_x_2 != V_y_2 ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_less__eq__real__def,axiom,
% 1.72/1.86 ! [V_y_2,V_x_2] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.72/1.86 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.72/1.86 | V_x_2 = V_y_2 ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_plus__nat_Oadd__0,axiom,
% 1.72/1.86 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 1.72/1.86
% 1.72/1.86 fof(fact_Nat_Oadd__0__right,axiom,
% 1.72/1.86 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.72/1.86
% 1.72/1.86 fof(fact_add__is__0,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2] :
% 1.72/1.86 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.72/1.86 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.72/1.86 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_add__eq__self__zero,axiom,
% 1.72/1.86 ! [V_n,V_m] :
% 1.72/1.86 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 1.72/1.86 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__mult__distrib,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.72/1.86 => 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)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__1,axiom,
% 1.72/1.86 ! [T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring(T_a)
% 1.72/1.86 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__eq__1__iff,axiom,
% 1.72/1.86 ! [V_x_2,T_a] :
% 1.72/1.86 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.72/1.86 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 1.72/1.86 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_not__add__less1,axiom,
% 1.72/1.86 ! [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) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_not__add__less2,axiom,
% 1.72/1.86 ! [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) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nat__add__left__cancel__less,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.72/1.86 ( 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))
% 1.72/1.86 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_trans__less__add1,axiom,
% 1.72/1.86 ! [V_m,V_j,V_i] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_trans__less__add2,axiom,
% 1.72/1.86 ! [V_m,V_j,V_i] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_add__less__mono1,axiom,
% 1.72/1.86 ! [V_k,V_j,V_i] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.72/1.86 => 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)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_add__less__mono,axiom,
% 1.72/1.86 ! [V_l,V_k,V_j,V_i] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.72/1.86 => 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)) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_less__add__eq__less,axiom,
% 1.72/1.86 ! [V_n,V_m,V_l,V_k] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.72/1.86 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_add__lessD1,axiom,
% 1.72/1.86 ! [V_k,V_j,V_i] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__mult__right__cancel,axiom,
% 1.72/1.86 ! [V_b_2,V_aa_2,V_ca_2] :
% 1.72/1.86 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.72/1.86 => ( 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)
% 1.72/1.86 <=> V_aa_2 = V_b_2 ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__mult__left__cancel,axiom,
% 1.72/1.86 ! [V_b_2,V_aa_2,V_ca_2] :
% 1.72/1.86 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.72/1.86 => ( 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)
% 1.72/1.86 <=> V_aa_2 = V_b_2 ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__eq__self__implies__10,axiom,
% 1.72/1.86 ! [V_n,V_m] :
% 1.72/1.86 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 1.72/1.86 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.72/1.86 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__zero__not__eq__one,axiom,
% 1.72/1.86 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__add__left__mono,axiom,
% 1.72/1.86 ! [V_z,V_y,V_x] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.72/1.86 => 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)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__mult__1,axiom,
% 1.72/1.86 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__add__mult__distrib,axiom,
% 1.72/1.86 ! [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)) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_INVERSE__ZERO,axiom,
% 1.72/1.86 c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_split__mult__neg__le,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.72/1.86 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.72/1.86 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 1.72/1.86 => 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)) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_split__mult__pos__le,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__ring(T_a)
% 1.72/1.86 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 1.72/1.86 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 1.72/1.86 => 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)) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__mono,axiom,
% 1.72/1.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__semiring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.86 => 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)) ) ) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__mono_H,axiom,
% 1.72/1.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__semiring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.86 => 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)) ) ) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__left__mono__neg,axiom,
% 1.72/1.86 ! [V_c,V_a,V_b,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__ring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__right__mono__neg,axiom,
% 1.72/1.86 ! [V_c,V_a,V_b,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__ring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_comm__mult__left__mono,axiom,
% 1.72/1.86 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__comm__semiring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__left__mono,axiom,
% 1.72/1.86 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__semiring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__right__mono,axiom,
% 1.72/1.86 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__semiring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__nonpos__nonpos,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__ring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__nonpos__nonneg,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__nonneg__nonpos2,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__nonneg__nonpos,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__nonneg__nonneg,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__le__0__iff,axiom,
% 1.72/1.86 ! [V_b_2,V_aa_2,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.86 => ( 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))
% 1.72/1.86 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
% 1.72/1.86 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.72/1.86 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_zero__le__mult__iff,axiom,
% 1.72/1.86 ! [V_b_2,V_aa_2,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.86 => ( 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))
% 1.72/1.86 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
% 1.72/1.86 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 1.72/1.86 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_zero__le__square,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring(T_a)
% 1.72/1.86 => 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)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_not__square__less__zero,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring(T_a)
% 1.72/1.86 => ~ 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)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__less__cancel__right__disj,axiom,
% 1.72/1.86 ! [V_b_2,V_ca_2,V_aa_2,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.86 => ( 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))
% 1.72/1.86 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.72/1.86 & c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
% 1.72/1.86 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__less__cancel__left__disj,axiom,
% 1.72/1.86 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.86 => ( 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))
% 1.72/1.86 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.72/1.86 & c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
% 1.72/1.86 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__less__cancel__left__pos,axiom,
% 1.72/1.86 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.72/1.86 => ( 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))
% 1.72/1.86 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__pos__pos,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__pos__neg,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__pos__neg2,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_zero__less__mult__pos,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.86 => ( 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))
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_zero__less__mult__pos2,axiom,
% 1.72/1.86 ! [V_a,V_b,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.86 => ( 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))
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__less__cancel__left__neg,axiom,
% 1.72/1.86 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => ( 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))
% 1.72/1.86 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__neg__pos,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__neg__neg,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__strict__right__mono,axiom,
% 1.72/1.86 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__strict__left__mono,axiom,
% 1.72/1.86 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_comm__mult__strict__left__mono,axiom,
% 1.72/1.86 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__strict__right__mono__neg,axiom,
% 1.72/1.86 ! [V_c,V_a,V_b,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__strict__left__mono__neg,axiom,
% 1.72/1.86 ! [V_c,V_a,V_b,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_pos__add__strict,axiom,
% 1.72/1.86 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_zero__le__one,axiom,
% 1.72/1.86 ! [T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.86 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_not__one__le__zero,axiom,
% 1.72/1.86 ! [T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.86 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_not__one__less__zero,axiom,
% 1.72/1.86 ! [T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.86 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_zero__less__one,axiom,
% 1.72/1.86 ! [T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_less__1__mult,axiom,
% 1.72/1.86 ! [V_n,V_m,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_less__add__one,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.86 => 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))) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__nonpositive__iff__nonpositive,axiom,
% 1.72/1.86 ! [V_aa_2,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.72/1.86 => ( 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))
% 1.72/1.86 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__nonnegative__iff__nonnegative,axiom,
% 1.72/1.86 ! [V_aa_2,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.72/1.86 => ( 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))
% 1.72/1.86 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__less__imp__less__neg,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.86 => ( 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))
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__less__imp__less,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.86 => ( 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))
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__negative__imp__negative,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_less__imp__inverse__less__neg,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_less__imp__inverse__less,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_negative__imp__inverse__negative,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__positive__imp__positive,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
% 1.72/1.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_positive__imp__inverse__positive,axiom,
% 1.72/1.86 ! [V_a,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__negative__iff__negative,axiom,
% 1.72/1.86 ! [V_aa_2,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__positive__iff__positive,axiom,
% 1.72/1.86 ! [V_aa_2,T_a] :
% 1.72/1.86 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))
% 1.72/1.86 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_nonzero__inverse__mult__distrib,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring(T_a)
% 1.72/1.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.86 => 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)) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_inverse__unique,axiom,
% 1.72/1.86 ! [V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Odivision__ring(T_a)
% 1.72/1.86 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Oone__class_Oone(T_a)
% 1.72/1.86 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) = V_b ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_add__gr__0,axiom,
% 1.72/1.86 ! [V_n_2,V_ma_2] :
% 1.72/1.86 ( 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))
% 1.72/1.86 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 1.72/1.86 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__mult__less__iff1,axiom,
% 1.72/1.86 ! [V_y_2,V_x_2,V_z_2] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.72/1.86 => ( 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))
% 1.72/1.86 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__mult__order,axiom,
% 1.72/1.86 ! [V_y,V_x] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 1.72/1.86 => 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)) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__mult__less__mono2,axiom,
% 1.72/1.86 ! [V_y,V_x,V_z] :
% 1.72/1.86 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.72/1.86 => 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)) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_real__two__squares__add__zero__iff,axiom,
% 1.72/1.86 ! [V_y_2,V_x_2] :
% 1.72/1.86 ( 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)
% 1.72/1.86 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.72/1.86 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__le__cancel__left__pos,axiom,
% 1.72/1.86 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.72/1.86 => ( 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))
% 1.72/1.86 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__le__cancel__left__neg,axiom,
% 1.72/1.86 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.86 => ( 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))
% 1.72/1.86 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_aa_2) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__strict__mono,axiom,
% 1.72/1.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.86 => 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)) ) ) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__strict__mono_H,axiom,
% 1.72/1.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.86 => 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)) ) ) ) ) ) ).
% 1.72/1.86
% 1.72/1.86 fof(fact_mult__less__le__imp__less,axiom,
% 1.72/1.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.72/1.86 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.87 => 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)) ) ) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__le__less__imp__less,axiom,
% 1.72/1.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.87 => 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)) ) ) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__right__less__imp__less,axiom,
% 1.72/1.87 ! [V_b,V_c,V_a,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__semiring(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.87 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__less__imp__less__right,axiom,
% 1.72/1.87 ! [V_b,V_c,V_a,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.87 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__left__less__imp__less,axiom,
% 1.72/1.87 ! [V_b,V_a,V_c,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__semiring(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.87 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__less__imp__less__left,axiom,
% 1.72/1.87 ! [V_b,V_a,V_c,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.87 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__right__le__imp__le,axiom,
% 1.72/1.87 ! [V_b,V_c,V_a,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.87 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__left__le__imp__le,axiom,
% 1.72/1.87 ! [V_b,V_a,V_c,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.87 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__right__le__one__le,axiom,
% 1.72/1.87 ! [V_y,V_x,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__idom(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.72/1.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__left__le__one__le,axiom,
% 1.72/1.87 ! [V_y,V_x,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__idom(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.72/1.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_zero__less__two,axiom,
% 1.72/1.87 ! [T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__semidom(T_a)
% 1.72/1.87 => 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))) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_inverse__le__imp__le__neg,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.87 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_inverse__le__imp__le,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.87 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_le__imp__inverse__le__neg,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_le__imp__inverse__le,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_inverse__le__1__iff,axiom,
% 1.72/1.87 ! [V_x_2,T_a] :
% 1.72/1.87 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.87 | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_division__ring__inverse__add,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Rings_Odivision__ring(T_a)
% 1.72/1.87 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.87 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_inverse__add,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Fields_Ofield(T_a)
% 1.72/1.87 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.87 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_one__less__inverse__iff,axiom,
% 1.72/1.87 ! [V_x_2,T_a] :
% 1.72/1.87 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))
% 1.72/1.87 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.72/1.87 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_one__less__inverse,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Fields_Olinordered__field(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.72/1.87 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_right__inverse,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Rings_Odivision__ring(T_a)
% 1.72/1.87 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.87 => 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) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_field__inverse,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Fields_Ofield(T_a)
% 1.72/1.87 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.87 => 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) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_left__inverse,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Rings_Odivision__ring(T_a)
% 1.72/1.87 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.87 => 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) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_real__mult__le__cancel__iff1,axiom,
% 1.72/1.87 ! [V_y_2,V_x_2,V_z_2] :
% 1.72/1.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.72/1.87 => ( 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))
% 1.72/1.87 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_real__mult__le__cancel__iff2,axiom,
% 1.72/1.87 ! [V_y_2,V_x_2,V_z_2] :
% 1.72/1.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.72/1.87 => ( 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))
% 1.72/1.87 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_real__mult__inverse__cancel2,axiom,
% 1.72/1.87 ! [V_u,V_y,V_x1,V_x] :
% 1.72/1.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => 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))) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_real__mult__inverse__cancel,axiom,
% 1.72/1.87 ! [V_u,V_y,V_x1,V_x] :
% 1.72/1.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_nat__mult__le__cancel1,axiom,
% 1.72/1.87 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.72/1.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.72/1.87 => ( 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))
% 1.72/1.87 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_not__sum__squares__lt__zero,axiom,
% 1.72/1.87 ! [V_y,V_x,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__ring(T_a)
% 1.72/1.87 => ~ 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)) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_sum__squares__gt__zero__iff,axiom,
% 1.72/1.87 ! [V_y_2,V_x_2,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.87 => ( 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)))
% 1.72/1.87 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.87 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_sum__squares__ge__zero,axiom,
% 1.72/1.87 ! [V_y,V_x,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__ring(T_a)
% 1.72/1.87 => 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))) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_sum__squares__le__zero__iff,axiom,
% 1.72/1.87 ! [V_y_2,V_x_2,T_a] :
% 1.72/1.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.87 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__pos__nonneg,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__nonneg__pos,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_zero__reorient,axiom,
% 1.72/1.87 ! [V_x_2,T_a] :
% 1.72/1.87 ( class_Groups_Ozero(T_a)
% 1.72/1.87 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 1.72/1.87 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 1.72/1.87 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oab__semigroup__mult(T_a)
% 1.72/1.87 => 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)) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__right__imp__eq,axiom,
% 1.72/1.87 ! [V_c,V_a,V_b,T_a] :
% 1.72/1.87 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.72/1.87 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 1.72/1.87 => V_b = V_c ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__imp__eq,axiom,
% 1.72/1.87 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 1.72/1.87 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.72/1.87 => V_b = V_c ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__left__imp__eq,axiom,
% 1.72/1.87 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.72/1.87 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.72/1.87 => V_b = V_c ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__right__cancel,axiom,
% 1.72/1.87 ! [V_ca_2,V_aa_2,V_b_2,T_a] :
% 1.72/1.87 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.72/1.87 => ( 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)
% 1.72/1.87 <=> V_b_2 = V_ca_2 ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__left__cancel,axiom,
% 1.72/1.87 ! [V_ca_2,V_b_2,V_aa_2,T_a] :
% 1.72/1.87 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.72/1.87 => ( 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)
% 1.72/1.87 <=> V_b_2 = V_ca_2 ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 1.72/1.87 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oab__semigroup__add(T_a)
% 1.72/1.87 => 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)) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_one__reorient,axiom,
% 1.72/1.87 ! [V_x_2,T_a] :
% 1.72/1.87 ( class_Groups_Oone(T_a)
% 1.72/1.87 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 1.72/1.87 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add_Ocomm__neutral,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.72/1.87 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__0__right,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Groups_Omonoid__add(T_a)
% 1.72/1.87 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_double__zero__sym,axiom,
% 1.72/1.87 ! [V_aa_2,T_a] :
% 1.72/1.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.72/1.87 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)
% 1.72/1.87 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__0,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.72/1.87 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__0__left,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Groups_Omonoid__add(T_a)
% 1.72/1.87 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__le__imp__le__left,axiom,
% 1.72/1.87 ! [V_b,V_a,V_c,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__le__imp__le__right,axiom,
% 1.72/1.87 ! [V_b,V_c,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__mono,axiom,
% 1.72/1.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__left__mono,axiom,
% 1.72/1.87 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.87 => 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)) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__right__mono,axiom,
% 1.72/1.87 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.72/1.87 => 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)) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__le__cancel__left,axiom,
% 1.72/1.87 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__le__cancel__right,axiom,
% 1.72/1.87 ! [V_b_2,V_ca_2,V_aa_2,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__less__imp__less__left,axiom,
% 1.72/1.87 ! [V_b,V_a,V_c,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__less__imp__less__right,axiom,
% 1.72/1.87 ! [V_b,V_c,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__strict__mono,axiom,
% 1.72/1.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__strict__left__mono,axiom,
% 1.72/1.87 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.87 => 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)) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__strict__right__mono,axiom,
% 1.72/1.87 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.72/1.87 => 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)) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__less__cancel__left,axiom,
% 1.72/1.87 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__less__cancel__right,axiom,
% 1.72/1.87 ! [V_b_2,V_ca_2,V_aa_2,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult_Ocomm__neutral,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.72/1.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__1__right,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Groups_Omonoid__mult(T_a)
% 1.72/1.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__1,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.72/1.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_mult__1__left,axiom,
% 1.72/1.87 ! [V_a,T_a] :
% 1.72/1.87 ( class_Groups_Omonoid__mult(T_a)
% 1.72/1.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 1.72/1.87 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.72/1.87 ( 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)
% 1.72/1.87 <=> ( V_ka_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.72/1.87 | V_ma_2 = V_n_2 ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_left__add__mult__distrib,axiom,
% 1.72/1.87 ! [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) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 1.72/1.87 ! [V_aa_2,T_a] :
% 1.72/1.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 1.72/1.87 ! [V_aa_2,T_a] :
% 1.72/1.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.72/1.87 => ( 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))
% 1.72/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__nonneg__nonneg,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__nonneg__eq__0__iff,axiom,
% 1.72/1.87 ! [V_y_2,V_x_2,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 1.72/1.87 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.87 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.72/1.87 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__increasing,axiom,
% 1.72/1.87 ! [V_c,V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.72/1.87 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__increasing2,axiom,
% 1.72/1.87 ! [V_a,V_b,V_c,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.72/1.87 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__nonpos__nonpos,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__neg__neg,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_add__pos__pos,axiom,
% 1.72/1.87 ! [V_b,V_a,T_a] :
% 1.72/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.72/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.72/1.87 => 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)) ) ) ) ).
% 1.72/1.87
% 1.72/1.87 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.88/1.87 => ( 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))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.88/1.87 => ( 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))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_add__le__less__mono,axiom,
% 1.88/1.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.88/1.87 => 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)) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_add__less__le__mono,axiom,
% 1.88/1.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.88/1.87 => 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)) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_sum__squares__eq__zero__iff,axiom,
% 1.88/1.87 ! [V_y_2,V_x_2,T_a] :
% 1.88/1.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.88/1.87 => ( 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)
% 1.88/1.87 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.87 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_nat__mult__eq__cancel1,axiom,
% 1.88/1.87 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.88/1.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.88/1.87 => ( 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)
% 1.88/1.87 <=> V_ma_2 = V_n_2 ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_nat__mult__less__cancel1,axiom,
% 1.88/1.87 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.88/1.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 1.88/1.87 => ( 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))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_add__nonpos__neg,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.88/1.87 => 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)) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_add__neg__nonpos,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.88/1.87 => 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)) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_add__strict__increasing2,axiom,
% 1.88/1.87 ! [V_c,V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.88/1.87 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_add__strict__increasing,axiom,
% 1.88/1.87 ! [V_c,V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.88/1.87 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 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,
% 1.88/1.87 ~ ! [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) ).
% 1.88/1.87
% 1.88/1.87 fof(fact__0961_A_L_Aw_A_094_Ak_A_K_Aa_A_N_A1_A_061_A0_A_N_A1_096,axiom,
% 1.88/1.87 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)) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_wm1,axiom,
% 1.88/1.87 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)) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_tw,axiom,
% 1.88/1.87 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____)) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_reduce__poly__simple,axiom,
% 1.88/1.87 ! [V_n,V_b] :
% 1.88/1.87 ( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 1.88/1.87 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.87 => ? [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)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_zero__less__power__nat__eq,axiom,
% 1.88/1.87 ! [V_n_2,V_x_2] :
% 1.88/1.87 ( 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))
% 1.88/1.87 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.87 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_diff__0,axiom,
% 1.88/1.87 ! [V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => 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) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_diff__def,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_ab__diff__minus,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_diff__minus__eq__add,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => 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) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__minus,axiom,
% 1.88/1.87 ! [V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__diff__eq,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.87 => 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) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_equation__minus__iff,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.88/1.87 <=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__equation__iff,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_b_2
% 1.88/1.87 <=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_aa_2 ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_neg__equal__iff__equal,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.88/1.87 <=> V_aa_2 = V_b_2 ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_diff__eq__diff__eq,axiom,
% 1.88/1.87 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.87 => ( 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)
% 1.88/1.87 => ( V_aa_2 = V_b_2
% 1.88/1.87 <=> V_ca_2 = V_d_2 ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_norm__triangle__ineq2,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.88/1.87 => 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))) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real__minus,axiom,
% 1.88/1.87 ! [V_x,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real_Ominus,axiom,
% 1.88/1.87 ! [V_x,T_a] :
% 1.88/1.87 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real__diff,axiom,
% 1.88/1.87 ! [V_y,V_x,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real_Odiff,axiom,
% 1.88/1.87 ! [V_y,V_x,T_a] :
% 1.88/1.87 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real__eq__iff,axiom,
% 1.88/1.87 ! [V_y_2,V_x_2,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 => ( c_RealVector_Oof__real(T_a,V_x_2) = c_RealVector_Oof__real(T_a,V_y_2)
% 1.88/1.87 <=> V_x_2 = V_y_2 ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 1.88/1.87 ! [V_y,V_x,T_a] :
% 1.88/1.87 ( class_Rings_Ocomm__ring__1(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_diff__0__right,axiom,
% 1.88/1.87 ! [V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_diff__self,axiom,
% 1.88/1.87 ! [V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_eq__iff__diff__eq__0,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.87 => ( V_aa_2 = V_b_2
% 1.88/1.87 <=> c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_right__minus__eq,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.87 <=> V_aa_2 = V_b_2 ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_diff__eq__diff__less__eq,axiom,
% 1.88/1.87 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( 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)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_d_2) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__zero,axiom,
% 1.88/1.87 ! [T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_neg__0__equal__iff__equal,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
% 1.88/1.87 <=> c_Groups_Ozero__class_Ozero(T_a) = V_aa_2 ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_equal__neg__zero,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.88/1.87 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
% 1.88/1.87 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_neg__equal__0__iff__equal,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.87 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_neg__equal__zero,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_aa_2
% 1.88/1.87 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_diff__eq__diff__less,axiom,
% 1.88/1.87 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( 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)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_le__minus__iff,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__le__iff,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_neg__le__iff__le,axiom,
% 1.88/1.87 ! [V_aa_2,V_b_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( 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))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_le__imp__neg__le,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.88/1.87 => 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)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_neg__less__iff__less,axiom,
% 1.88/1.87 ! [V_aa_2,V_b_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( 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))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__less__iff,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_less__minus__iff,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_mult_Odiff__right,axiom,
% 1.88/1.87 ! [V_b_H,V_b,V_a,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_mult__right_Odiff,axiom,
% 1.88/1.87 ! [V_y,V_x,V_xa,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_mult_Odiff__left,axiom,
% 1.88/1.87 ! [V_b,V_a_H,V_a,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_mult__left_Odiff,axiom,
% 1.88/1.87 ! [V_ya,V_y,V_x,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__mult__right,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Rings_Oring(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__mult__left,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Rings_Oring(T_a)
% 1.88/1.87 => 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) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__mult__commute,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Rings_Oring(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__mult__minus,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Rings_Oring(T_a)
% 1.88/1.87 => 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) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_square__eq__iff,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Rings_Oidom(T_a)
% 1.88/1.87 => ( 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)
% 1.88/1.87 <=> ( V_aa_2 = V_b_2
% 1.88/1.87 | V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_mult_Ominus__right,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_mult__right_Ominus,axiom,
% 1.88/1.87 ! [V_x,V_xa,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_mult_Ominus__left,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_mult__left_Ominus,axiom,
% 1.88/1.87 ! [V_y,V_x,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_add__diff__cancel,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_diff__add__cancel,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__add__cancel,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => 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 ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_add__minus__cancel,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => 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 ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__add,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__add__distrib,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_norm__minus__commute,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_norm__minus__cancel,axiom,
% 1.88/1.87 ! [V_x,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.88/1.87 => 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) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_inverse__minus__eq,axiom,
% 1.88/1.87 ! [V_a,T_a] :
% 1.88/1.87 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_le__iff__diff__le__0,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
% 1.88/1.87 <=> 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)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_less__iff__diff__less__0,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
% 1.88/1.87 <=> 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)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__le__self__iff,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_neg__le__0__iff__le,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( 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))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_le__minus__self__iff,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_neg__0__le__iff__le,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( 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))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_less__minus__self__iff,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_neg__less__nonneg,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_neg__less__0__iff__less,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_neg__0__less__iff__less,axiom,
% 1.88/1.87 ! [V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.88/1.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 1.88/1.87 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real__eq__0__iff,axiom,
% 1.88/1.87 ! [V_x_2,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 => ( c_RealVector_Oof__real(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.87 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real_Ozero,axiom,
% 1.88/1.87 ! [T_a] :
% 1.88/1.87 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.88/1.87 => c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real__0,axiom,
% 1.88/1.87 ! [T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 => c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_add__eq__0__iff,axiom,
% 1.88/1.87 ! [V_y_2,V_x_2,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.87 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_minus__unique,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.87 => c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_ab__left__minus,axiom,
% 1.88/1.87 ! [V_a,T_a] :
% 1.88/1.87 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.87 => 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) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_left__minus,axiom,
% 1.88/1.87 ! [V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => 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) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 1.88/1.87 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.88/1.87 <=> c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_right__minus,axiom,
% 1.88/1.87 ! [V_a,T_a] :
% 1.88/1.87 ( class_Groups_Ogroup__add(T_a)
% 1.88/1.87 => 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) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_mult__diff__mult,axiom,
% 1.88/1.87 ! [V_b,V_a,V_y,V_x,T_a] :
% 1.88/1.87 ( class_Rings_Oring(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_eq__add__iff2,axiom,
% 1.88/1.87 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Rings_Oring(T_a)
% 1.88/1.87 => ( 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)
% 1.88/1.87 <=> 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) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_eq__add__iff1,axiom,
% 1.88/1.87 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Rings_Oring(T_a)
% 1.88/1.87 => ( 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)
% 1.88/1.87 <=> 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 ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_mult_Oprod__diff__prod,axiom,
% 1.88/1.87 ! [V_b,V_a,V_y,V_x,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.88/1.87 => 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))) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_square__eq__1__iff,axiom,
% 1.88/1.87 ! [V_x_2,T_a] :
% 1.88/1.87 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.88/1.87 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 1.88/1.87 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 1.88/1.87 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 1.88/1.87 ! [V_x,T_a] :
% 1.88/1.87 ( class_Rings_Ocomm__ring__1(T_a)
% 1.88/1.87 => 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) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real__mult,axiom,
% 1.88/1.87 ! [V_y,V_x,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real__add,axiom,
% 1.88/1.87 ! [V_y,V_x,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real_Oadd,axiom,
% 1.88/1.87 ! [V_y,V_x,T_a] :
% 1.88/1.87 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real__1,axiom,
% 1.88/1.87 ! [T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 => c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_nonzero__inverse__minus__eq,axiom,
% 1.88/1.87 ! [V_a,T_a] :
% 1.88/1.87 ( class_Rings_Odivision__ring(T_a)
% 1.88/1.87 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.87 => 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)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real__power,axiom,
% 1.88/1.87 ! [V_n,V_x,T_a] :
% 1.88/1.87 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.87 => 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) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_of__real__inverse,axiom,
% 1.88/1.87 ! [V_x,T_a] :
% 1.88/1.87 ( ( class_RealVector_Oreal__div__algebra(T_a)
% 1.88/1.87 & class_Rings_Odivision__ring__inverse__zero(T_a) )
% 1.88/1.87 => 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)) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_complex__of__real__power,axiom,
% 1.88/1.87 ! [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)) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_le__add__iff2,axiom,
% 1.88/1.87 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Rings_Oordered__ring(T_a)
% 1.88/1.87 => ( 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))
% 1.88/1.87 <=> 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)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_le__add__iff1,axiom,
% 1.88/1.87 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Rings_Oordered__ring(T_a)
% 1.88/1.87 => ( 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))
% 1.88/1.87 <=> 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) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_less__add__iff2,axiom,
% 1.88/1.87 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Rings_Oordered__ring(T_a)
% 1.88/1.87 => ( 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))
% 1.88/1.87 <=> 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)) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_less__add__iff1,axiom,
% 1.88/1.87 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 1.88/1.87 ( class_Rings_Oordered__ring(T_a)
% 1.88/1.87 => ( 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))
% 1.88/1.87 <=> 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) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_real__squared__diff__one__factored,axiom,
% 1.88/1.87 ! [V_x,T_a] :
% 1.88/1.87 ( class_Rings_Oring__1(T_a)
% 1.88/1.87 => 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))) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_division__ring__inverse__diff,axiom,
% 1.88/1.87 ! [V_b,V_a,T_a] :
% 1.88/1.87 ( class_Rings_Odivision__ring(T_a)
% 1.88/1.87 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.87 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.87 => 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)) ) ) ) ).
% 1.88/1.87
% 1.88/1.87 fof(fact_power__minus,axiom,
% 1.88/1.87 ! [V_n,V_a,T_a] :
% 1.88/1.87 ( class_Rings_Oring__1(T_a)
% 1.88/1.87 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_norm__triangle__ineq4,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.88/1.88 => 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))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nonzero__of__real__inverse,axiom,
% 1.88/1.88 ! [V_x,T_a] :
% 1.88/1.88 ( class_RealVector_Oreal__div__algebra(T_a)
% 1.88/1.88 => ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.88/1.88 => 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_norm__diff__triangle__ineq,axiom,
% 1.88/1.88 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.88/1.88 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.88/1.88 => 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)))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_Deriv_Oinverse__diff__inverse,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Rings_Odivision__ring(T_a)
% 1.88/1.88 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.88 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.88 => 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))) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_complex__diff__def,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_not__real__square__gt__zero,axiom,
% 1.88/1.88 ! [V_x_2] :
% 1.88/1.88 ( ~ 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))
% 1.88/1.88 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_even__less__0__iff,axiom,
% 1.88/1.88 ! [V_aa_2,T_a] :
% 1.88/1.88 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.88 => ( 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))
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_unimodular__reduce__norm,axiom,
% 1.88/1.88 ! [V_z] :
% 1.88/1.88 ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 1.88/1.88 => ( 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))
% 1.88/1.88 | 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))
% 1.88/1.88 | 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))
% 1.88/1.88 | 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_minus__real__def,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_real__diff__def,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_inverse__i,axiom,
% 1.88/1.88 c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diffs0__imp__equal,axiom,
% 1.88/1.88 ! [V_n,V_m] :
% 1.88/1.88 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.88 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.88 => V_m = V_n ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__self__eq__0,axiom,
% 1.88/1.88 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_minus__nat_Odiff__0,axiom,
% 1.88/1.88 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__0__eq__0,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__less__mono2,axiom,
% 1.88/1.88 ! [V_l,V_n,V_m] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
% 1.88/1.88 => 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_less__imp__diff__less,axiom,
% 1.88/1.88 ! [V_n,V_k,V_j] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 1.88/1.88 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__add__inverse2,axiom,
% 1.88/1.88 ! [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 ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__add__inverse,axiom,
% 1.88/1.88 ! [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 ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__diff__left,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__cancel,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__cancel2,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__le__self,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__le__mono2,axiom,
% 1.88/1.88 ! [V_l,V_n,V_m] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__le__mono,axiom,
% 1.88/1.88 ! [V_l,V_n,V_m] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__diff__cancel,axiom,
% 1.88/1.88 ! [V_n,V_i] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
% 1.88/1.88 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_eq__diff__iff,axiom,
% 1.88/1.88 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_ma_2)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_n_2)
% 1.88/1.88 => ( 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)
% 1.88/1.88 <=> V_ma_2 = V_n_2 ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_Nat_Odiff__diff__eq,axiom,
% 1.88/1.88 ! [V_n,V_m,V_k] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 1.88/1.88 => 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) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_le__diff__iff,axiom,
% 1.88/1.88 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_ma_2)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_n_2)
% 1.88/1.88 => ( 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))
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__mult__distrib2,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__mult__distrib,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_complex__i__not__one,axiom,
% 1.88/1.88 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_complex__i__not__zero,axiom,
% 1.88/1.88 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_complex__mod__minus__le__complex__mod,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_complex__i__mult__minus,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_real__le__eq__diff,axiom,
% 1.88/1.88 ! [V_y_2,V_x_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.88/1.88 <=> 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zero__less__diff,axiom,
% 1.88/1.88 ! [V_ma_2,V_n_2] :
% 1.88/1.88 ( 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))
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__less,axiom,
% 1.88/1.88 ! [V_m,V_n] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 1.88/1.88 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_real__minus__mult__self__le,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__add__0,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__is__0__eq_H,axiom,
% 1.88/1.88 ! [V_n,V_m] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.88/1.88 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__is__0__eq,axiom,
% 1.88/1.88 ! [V_n_2,V_ma_2] :
% 1.88/1.88 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_less__diff__conv,axiom,
% 1.88/1.88 ! [V_ka_2,V_j_2,V_i_2] :
% 1.88/1.88 ( 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))
% 1.88/1.88 <=> 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_add__diff__inverse,axiom,
% 1.88/1.88 ! [V_n,V_m] :
% 1.88/1.88 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.88/1.88 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_less__diff__iff,axiom,
% 1.88/1.88 ! [V_n_2,V_ma_2,V_ka_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_ma_2)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_n_2)
% 1.88/1.88 => ( 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))
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__less__mono,axiom,
% 1.88/1.88 ! [V_c,V_b,V_a] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
% 1.88/1.88 => 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_real__add__eq__0__iff,axiom,
% 1.88/1.88 ! [V_y_2,V_x_2] :
% 1.88/1.88 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.88/1.88 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_real__add__minus__iff,axiom,
% 1.88/1.88 ! [V_aa_2,V_x_2] :
% 1.88/1.88 ( 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)
% 1.88/1.88 <=> V_x_2 = V_aa_2 ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__add__assoc2,axiom,
% 1.88/1.88 ! [V_i,V_j,V_k] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_add__diff__assoc2,axiom,
% 1.88/1.88 ! [V_i,V_j,V_k] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__add__assoc,axiom,
% 1.88/1.88 ! [V_i,V_j,V_k] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_le__imp__diff__is__add,axiom,
% 1.88/1.88 ! [V_ka_2,V_j_2,V_i_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.88/1.88 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_ka_2
% 1.88/1.88 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_i_2) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_le__add__diff__inverse2,axiom,
% 1.88/1.88 ! [V_m,V_n] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.88/1.88 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_le__diff__conv2,axiom,
% 1.88/1.88 ! [V_i_2,V_j_2,V_ka_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_j_2)
% 1.88/1.88 => ( 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))
% 1.88/1.88 <=> 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) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_add__diff__assoc,axiom,
% 1.88/1.88 ! [V_i,V_j,V_k] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_le__add__diff__inverse,axiom,
% 1.88/1.88 ! [V_m,V_n] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.88/1.88 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_le__add__diff,axiom,
% 1.88/1.88 ! [V_m,V_n,V_k] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_le__diff__conv,axiom,
% 1.88/1.88 ! [V_i_2,V_ka_2,V_j_2] :
% 1.88/1.88 ( 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)
% 1.88/1.88 <=> 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__diff__right,axiom,
% 1.88/1.88 ! [V_i,V_j,V_k] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_complex__mod__triangle__ineq2,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_norm__diff__ineq,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.88/1.88 => 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))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nat__diff__split__asm,axiom,
% 1.88/1.88 ! [V_b_2,V_aa_2,V_P_2] :
% 1.88/1.88 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
% 1.88/1.88 <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)
% 1.88/1.88 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 1.88/1.88 | ? [B_d] :
% 1.88/1.88 ( V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 1.88/1.88 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nat__diff__split,axiom,
% 1.88/1.88 ! [V_b_2,V_aa_2,V_P_2] :
% 1.88/1.88 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
% 1.88/1.88 <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)
% 1.88/1.88 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 1.88/1.88 & ! [B_d] :
% 1.88/1.88 ( V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 1.88/1.88 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_real__0__le__add__iff,axiom,
% 1.88/1.88 ! [V_y_2,V_x_2] :
% 1.88/1.88 ( 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))
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_real__add__le__0__iff,axiom,
% 1.88/1.88 ! [V_y_2,V_x_2] :
% 1.88/1.88 ( 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))
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_real__0__less__add__iff,axiom,
% 1.88/1.88 ! [V_y_2,V_x_2] :
% 1.88/1.88 ( 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))
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_real__add__less__0__iff,axiom,
% 1.88/1.88 ! [V_y_2,V_x_2] :
% 1.88/1.88 ( 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))
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nat__le__add__iff1,axiom,
% 1.88/1.88 ! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 1.88/1.88 => ( 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))
% 1.88/1.88 <=> 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) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nat__diff__add__eq1,axiom,
% 1.88/1.88 ! [V_n,V_m,V_u,V_i,V_j] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nat__eq__add__iff1,axiom,
% 1.88/1.88 ! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 1.88/1.88 => ( 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)
% 1.88/1.88 <=> 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 ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nat__le__add__iff2,axiom,
% 1.88/1.88 ! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.88/1.88 => ( 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))
% 1.88/1.88 <=> 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nat__diff__add__eq2,axiom,
% 1.88/1.88 ! [V_n,V_m,V_u,V_j,V_i] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nat__eq__add__iff2,axiom,
% 1.88/1.88 ! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.88/1.88 => ( 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)
% 1.88/1.88 <=> 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) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_i__mult__eq2,axiom,
% 1.88/1.88 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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_complex__of__real__minus__one,axiom,
% 1.88/1.88 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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zpower__zadd__distrib,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zpower__zpower,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nat__less__add__iff2,axiom,
% 1.88/1.88 ! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.88/1.88 => ( 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))
% 1.88/1.88 <=> 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nat__less__add__iff1,axiom,
% 1.88/1.88 ! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 1.88/1.88 => ( 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))
% 1.88/1.88 <=> 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) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_mult__eq__if,axiom,
% 1.88/1.88 ! [V_n,V_m] :
% 1.88/1.88 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.88/1.88 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.88 => 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_power__eq__if,axiom,
% 1.88/1.88 ! [V_p,V_m] :
% 1.88/1.88 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.88 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 1.88/1.88 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.88 => 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)))) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_realpow__num__eq__if,axiom,
% 1.88/1.88 ! [V_m,V_n,T_a] :
% 1.88/1.88 ( class_Power_Opower(T_a)
% 1.88/1.88 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.88 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 1.88/1.88 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.88 => 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)))) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_realpow__minus__mult,axiom,
% 1.88/1.88 ! [V_x,V_n,T_a] :
% 1.88/1.88 ( class_Groups_Omonoid__mult(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.88/1.88 => 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) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_double__eq__0__iff,axiom,
% 1.88/1.88 ! [V_aa_2,T_a] :
% 1.88/1.88 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.88/1.88 => ( c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.88 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_Deriv_Oadd__diff__add,axiom,
% 1.88/1.88 ! [V_d,V_b,V_c,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_ath,axiom,
% 1.88/1.88 ! [V_t,V_x] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_t)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_t,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.88/1.88 => 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)) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 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____))))) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 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____)))) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 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____)))) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_assms,axiom,
% 1.88/1.88 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_m_I2_J,axiom,
% 1.88/1.88 ! [B_z] :
% 1.88/1.88 ( 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____))
% 1.88/1.88 => 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____) ) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 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____)))) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 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____)))))) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_th11,axiom,
% 1.88/1.88 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____)))))) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zdiff__zmult__distrib2,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zmult__zminus,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zdiff__zmult__distrib,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__minus__cancel,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__minus__commute,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__commute,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zmult__zless__mono2,axiom,
% 1.88/1.88 ! [V_k,V_j,V_i] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 1.88/1.88 => 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_pos__zmult__eq__1__iff,axiom,
% 1.88/1.88 ! [V_n_2,V_ma_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)
% 1.88/1.88 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.88/1.88 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.88/1.88 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zadd__zmult__distrib,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zmult__assoc,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zadd__zmult__distrib2,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zmult__commute,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zmult__1__right,axiom,
% 1.88/1.88 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zmult__1,axiom,
% 1.88/1.88 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__eq__0,axiom,
% 1.88/1.88 ! [V_aa_2,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ( c_Groups_Oabs__class_Oabs(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.88 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__zero,axiom,
% 1.88/1.88 ! [T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__le__D1,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__ge__self,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__add__abs,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__idempotent,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__mult__self,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__mult,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__one,axiom,
% 1.88/1.88 ! [T_a] :
% 1.88/1.88 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_real__norm__def,axiom,
% 1.88/1.88 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__norm__cancel,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__inverse,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_power__abs,axiom,
% 1.88/1.88 ! [V_n,V_a,T_a] :
% 1.88/1.88 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__of__nonneg,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__le__zero__iff,axiom,
% 1.88/1.88 ! [V_aa_2,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ( 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))
% 1.88/1.88 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__ge__zero,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__of__pos,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zero__less__abs__iff,axiom,
% 1.88/1.88 ! [V_aa_2,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_aa_2))
% 1.88/1.88 <=> V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__not__less__zero,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__mult__less,axiom,
% 1.88/1.88 ! [V_d,V_b,V_c,V_a,T_a] :
% 1.88/1.88 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
% 1.88/1.88 => 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)) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__triangle__ineq,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__triangle__ineq3,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__triangle__ineq2,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__triangle__ineq2__sym,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__ge__minus__self,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__le__iff,axiom,
% 1.88/1.88 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)
% 1.88/1.88 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
% 1.88/1.88 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__leI,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__le__D2,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__less__iff,axiom,
% 1.88/1.88 ! [V_b_2,V_aa_2,T_a] :
% 1.88/1.88 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)
% 1.88/1.88 <=> ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
% 1.88/1.88 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_nonzero__abs__inverse,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Fields_Olinordered__field(T_a)
% 1.88/1.88 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.88 => 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__power__minus,axiom,
% 1.88/1.88 ! [V_n,V_a,T_a] :
% 1.88/1.88 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__le__interval__iff,axiom,
% 1.88/1.88 ! [V_r_2,V_x_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_r_2)
% 1.88/1.88 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r_2),V_x_2)
% 1.88/1.88 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_r_2) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_norm__of__real,axiom,
% 1.88/1.88 ! [V_r,T_a] :
% 1.88/1.88 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__minus__add__cancel,axiom,
% 1.88/1.88 ! [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))) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__eq__mult,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Rings_Oordered__ring__abs(T_a)
% 1.88/1.88 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.88/1.88 | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.88/1.88 & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.88/1.88 | c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 1.88/1.88 => 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__mult__pos,axiom,
% 1.88/1.88 ! [V_y,V_x,T_a] :
% 1.88/1.88 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.88/1.88 => 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__minus__le__zero,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__of__nonpos,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zero__le__power__abs,axiom,
% 1.88/1.88 ! [V_n,V_a,T_a] :
% 1.88/1.88 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__if,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oabs__if(T_a)
% 1.88/1.88 => ( ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) )
% 1.88/1.88 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__of__neg,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__triangle__ineq4,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__diff__triangle__ineq,axiom,
% 1.88/1.88 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.88/1.88 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.88/1.88 => 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)))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_rabs__ratiotest__lemma,axiom,
% 1.88/1.88 ! [V_y,V_x,V_c] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.88/1.88 => ( 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)))
% 1.88/1.88 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_real__abs__def,axiom,
% 1.88/1.88 ! [V_r] :
% 1.88/1.88 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r) )
% 1.88/1.88 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__real__def,axiom,
% 1.88/1.88 ! [V_a] :
% 1.88/1.88 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a) )
% 1.88/1.88 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__add__one__not__less__self,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__sum__triangle__ineq,axiom,
% 1.88/1.88 ! [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))))) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_norm__triangle__ineq3,axiom,
% 1.88/1.88 ! [V_b,V_a,T_a] :
% 1.88/1.88 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.88/1.88 => 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))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__add__one__gt__zero,axiom,
% 1.88/1.88 ! [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))) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 ? [B_m] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)
% 1.88/1.88 & ! [B_z] :
% 1.88/1.88 ( 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____))
% 1.88/1.88 => 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) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__diff__less__iff,axiom,
% 1.88/1.88 ! [V_r_2,V_aa_2,V_x_2,T_a] :
% 1.88/1.88 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.88 => ( 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)
% 1.88/1.88 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_r_2),V_x_2)
% 1.88/1.88 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_r_2)) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 ~ ! [B_m] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)
% 1.88/1.88 => ~ ! [B_z] :
% 1.88/1.88 ( 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____))
% 1.88/1.88 => 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) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_less_Oprems,axiom,
% 1.88/1.88 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zabs__def,axiom,
% 1.88/1.88 ! [V_i] :
% 1.88/1.88 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i) )
% 1.88/1.88 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = V_i ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_less__bin__lemma,axiom,
% 1.88/1.88 ! [V_l_2,V_ka_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_ka_2,V_l_2)
% 1.88/1.88 <=> 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zle__diff1__eq,axiom,
% 1.88/1.88 ! [V_z_2,V_wa_2] :
% 1.88/1.88 ( 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)))
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__int__def__symmetric,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__int__def,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_abs__zmult__eq__1,axiom,
% 1.88/1.88 ! [V_n,V_m] :
% 1.88/1.88 ( 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)
% 1.88/1.88 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zabs__less__one__iff,axiom,
% 1.88/1.88 ! [V_z_2] :
% 1.88/1.88 ( 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))
% 1.88/1.88 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zero__le__zpower__abs,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_constant__def,axiom,
% 1.88/1.88 ! [V_f_2,T_b,T_a] :
% 1.88/1.88 ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_a,T_b,V_f_2)
% 1.88/1.88 <=> ! [B_x,B_y] : hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_int__0__neq__1,axiom,
% 1.88/1.88 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_odd__nonzero,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_int__0__less__1,axiom,
% 1.88/1.88 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zadd__0,axiom,
% 1.88/1.88 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 1.88/1.88
% 1.88/1.88 fof(fact_int__one__le__iff__zero__less,axiom,
% 1.88/1.88 ! [V_z_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zadd__0__right,axiom,
% 1.88/1.88 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zle__add1__eq__le,axiom,
% 1.88/1.88 ! [V_z_2,V_wa_2] :
% 1.88/1.88 ( 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)))
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_z_2) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zless__add1__eq,axiom,
% 1.88/1.88 ! [V_z_2,V_wa_2] :
% 1.88/1.88 ( 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)))
% 1.88/1.88 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2)
% 1.88/1.88 | V_wa_2 = V_z_2 ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_add1__zle__eq,axiom,
% 1.88/1.88 ! [V_z_2,V_wa_2] :
% 1.88/1.88 ( 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)
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_odd__less__0,axiom,
% 1.88/1.88 ! [V_z_2] :
% 1.88/1.88 ( 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))
% 1.88/1.88 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_le__imp__0__less,axiom,
% 1.88/1.88 ! [V_z] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zless__imp__add1__zle,axiom,
% 1.88/1.88 ! [V_z,V_w] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zless__linear,axiom,
% 1.88/1.88 ! [V_y,V_x] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 1.88/1.88 | V_x = V_y
% 1.88/1.88 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zadd__zless__mono,axiom,
% 1.88/1.88 ! [V_z,V_z_H,V_w,V_w_H] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 1.88/1.88 => 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zadd__left__mono,axiom,
% 1.88/1.88 ! [V_k,V_j,V_i] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zadd__strict__right__mono,axiom,
% 1.88/1.88 ! [V_k,V_j,V_i] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zadd__assoc,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zadd__left__commute,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zless__le,axiom,
% 1.88/1.88 ! [V_wa_2,V_z_2] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_wa_2)
% 1.88/1.88 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_wa_2)
% 1.88/1.88 & V_z_2 != V_wa_2 ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zadd__commute,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zminus__zadd__distrib,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zminus__zminus,axiom,
% 1.88/1.88 ! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zadd__zminus__inverse2,axiom,
% 1.88/1.88 ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zminus__0,axiom,
% 1.88/1.88 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zero__less__zpower__abs__iff,axiom,
% 1.88/1.88 ! [V_n_2,V_x_2] :
% 1.88/1.88 ( 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))
% 1.88/1.88 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.88/1.88 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_incr__lemma,axiom,
% 1.88/1.88 ! [V_x,V_z,V_d] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 1.88/1.88 => 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))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_decr__lemma,axiom,
% 1.88/1.88 ! [V_z,V_x,V_d] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_self__quotient__aux1,axiom,
% 1.88/1.88 ! [V_q,V_r,V_a] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.88/1.88 => ( 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))
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_pc0,axiom,
% 1.88/1.88 hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_c,axiom,
% 1.88/1.88 ! [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))) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_kn,axiom,
% 1.88/1.88 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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zle__refl,axiom,
% 1.88/1.88 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zle__linear,axiom,
% 1.88/1.88 ! [V_w,V_z] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.88/1.88 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zle__trans,axiom,
% 1.88/1.88 ! [V_k,V_j,V_i] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zle__antisym,axiom,
% 1.88/1.88 ! [V_w,V_z] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 1.88/1.88 => V_z = V_w ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_q__pos__lemma,axiom,
% 1.88/1.88 ! [V_r_H,V_q_H,V_b_H] :
% 1.88/1.88 ( 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))
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_q__neg__lemma,axiom,
% 1.88/1.88 ! [V_r_H,V_q_H,V_b_H] :
% 1.88/1.88 ( 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))
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_unique__quotient__lemma,axiom,
% 1.88/1.88 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.88/1.88 ( 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))
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zdiv__mono2__lemma,axiom,
% 1.88/1.88 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.88/1.88 ( 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)
% 1.88/1.88 => ( 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))
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_unique__quotient__lemma__neg,axiom,
% 1.88/1.88 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.88/1.88 ( 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))
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 1.88/1.88 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.88/1.88 ( 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)
% 1.88/1.88 => ( 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))
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_self__quotient__aux2,axiom,
% 1.88/1.88 ! [V_q,V_r,V_a] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.88/1.88 => ( 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))
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.88/1.88 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_k1n,axiom,
% 1.88/1.88 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____)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 1.88/1.88 ! [V_n,V_x] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 1.88/1.88 ! [V_y,V_x] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.88/1.88 => 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_psize__eq__0__iff,axiom,
% 1.88/1.88 ! [V_pb_2,T_a] :
% 1.88/1.88 ( class_Groups_Ozero(T_a)
% 1.88/1.88 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.88 <=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 1.88/1.88 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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 1.88/1.88 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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 1.88/1.88 ! [V_y,V_x] :
% 1.88/1.88 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.88/1.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.88/1.88 => 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)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_q_I2_J,axiom,
% 1.88/1.88 ! [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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_less_Ohyps,axiom,
% 1.88/1.88 ! [V_pb_2] :
% 1.88/1.88 ( 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____))
% 1.88/1.88 => ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2))
% 1.88/1.88 => ? [B_z] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2),B_z) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 ? [B_q] :
% 1.88/1.88 ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
% 1.88/1.88 & ! [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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_q_I1_J,axiom,
% 1.88/1.88 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_a00,axiom,
% 1.88/1.88 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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_qnc,axiom,
% 1.88/1.88 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096,axiom,
% 1.88/1.88 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_cq0,axiom,
% 1.88/1.88 ! [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))) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_pqc0,axiom,
% 1.88/1.88 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)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_kas_I3_J,axiom,
% 1.88/1.88 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____)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact__096poly_Ap_Ac_A_061_A0_A_061_061_062_AEX_Az_O_Apoly_Ap_Az_A_061_A0_096,axiom,
% 1.88/1.88 ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 1.88/1.88 => ? [B_z] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_z) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_mrmq__eq,axiom,
% 1.88/1.88 ! [V_wa_2] :
% 1.88/1.88 ( 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))
% 1.88/1.88 <=> 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)))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_rnc,axiom,
% 1.88/1.88 ~ 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____))) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 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))) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_qr,axiom,
% 1.88/1.88 ! [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))) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_r01,axiom,
% 1.88/1.88 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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_lgqr,axiom,
% 1.88/1.88 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____)) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_kas_I4_J,axiom,
% 1.88/1.88 ! [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))) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 ( 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))
% 1.88/1.88 => ? [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)) ) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 ~ ! [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_offset__poly__eq__0__lemma,axiom,
% 1.88/1.88 ! [V_a,V_p,V_c,T_a] :
% 1.88/1.88 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.88 => ( 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))
% 1.88/1.88 => V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_th01,axiom,
% 1.88/1.88 ~ 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)))))) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_th02,axiom,
% 1.88/1.88 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))))) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_poly__replicate__append,axiom,
% 1.88/1.88 ! [V_x,V_p,V_n,T_a] :
% 1.88/1.88 ( class_Rings_Ocomm__ring__1(T_a)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 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,
% 1.88/1.88 ? [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) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_monom__0,axiom,
% 1.88/1.88 ! [V_a,T_a] :
% 1.88/1.88 ( class_Groups_Ozero(T_a)
% 1.88/1.88 => 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))) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__poly__code_I1_J,axiom,
% 1.88/1.88 ! [V_q,T_a] :
% 1.88/1.88 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.88 => 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) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_diff__poly__code_I2_J,axiom,
% 1.88/1.88 ! [V_p,T_a] :
% 1.88/1.88 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.88 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_mult__poly__0__left,axiom,
% 1.88/1.88 ! [V_q,T_a] :
% 1.88/1.88 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.88 => 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)) ) ).
% 1.88/1.88
% 1.88/1.88 fof(fact_mult__poly__0__right,axiom,
% 1.88/1.89 ! [V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_minus__poly__code_I1_J,axiom,
% 1.88/1.89 ! [T_a] :
% 1.88/1.89 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_abs__poly__def,axiom,
% 1.88/1.89 ! [V_x,T_a] :
% 1.88/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.88/1.89 => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 1.88/1.89 => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x) )
% 1.88/1.89 & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 1.88/1.89 => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = V_x ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__eq__iff,axiom,
% 1.88/1.89 ! [V_qa_2,V_pb_2,T_a] :
% 1.88/1.89 ( ( class_Int_Oring__char__0(T_a)
% 1.88/1.89 & class_Rings_Oidom(T_a) )
% 1.88/1.89 => ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,V_qa_2)
% 1.88/1.89 <=> V_pb_2 = V_qa_2 ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_pCons__eq__iff,axiom,
% 1.88/1.89 ! [V_qa_2,V_b_2,V_pb_2,V_aa_2,T_a] :
% 1.88/1.89 ( class_Groups_Ozero(T_a)
% 1.88/1.89 => ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Polynomial_OpCons(T_a,V_b_2,V_qa_2)
% 1.88/1.89 <=> ( V_aa_2 = V_b_2
% 1.88/1.89 & V_pb_2 = V_qa_2 ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__diff__right,axiom,
% 1.88/1.89 ! [V_q,V_p,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__ring(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__minus__right,axiom,
% 1.88/1.89 ! [V_p,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__ring(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_mult__smult__left,axiom,
% 1.88/1.89 ! [V_q,V_p,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_mult__smult__right,axiom,
% 1.88/1.89 ! [V_q,V_a,V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_mult__poly__add__left,axiom,
% 1.88/1.89 ! [V_r,V_q,V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_monom__eq__iff,axiom,
% 1.88/1.89 ! [V_b_2,V_n_2,V_aa_2,T_a] :
% 1.88/1.89 ( class_Groups_Ozero(T_a)
% 1.88/1.89 => ( c_Polynomial_Omonom(T_a,V_aa_2,V_n_2) = c_Polynomial_Omonom(T_a,V_b_2,V_n_2)
% 1.88/1.89 <=> V_aa_2 = V_b_2 ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__mult,axiom,
% 1.88/1.89 ! [V_x,V_q,V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__1,axiom,
% 1.88/1.89 ! [V_x,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.88/1.89 => 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) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__diff,axiom,
% 1.88/1.89 ! [V_x,V_q,V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__ring(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__minus,axiom,
% 1.88/1.89 ! [V_x,V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__ring(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__power,axiom,
% 1.88/1.89 ! [V_x,V_n,V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.88/1.89 => 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) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_diff__pCons,axiom,
% 1.88/1.89 ! [V_q,V_b,V_p,V_a,T_a] :
% 1.88/1.89 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__smult,axiom,
% 1.88/1.89 ! [V_p,V_b,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__1__left,axiom,
% 1.88/1.89 ! [V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.88/1.89 => c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p) = V_p ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_minus__pCons,axiom,
% 1.88/1.89 ! [V_p,V_a,T_a] :
% 1.88/1.89 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_minus__poly__code_I2_J,axiom,
% 1.88/1.89 ! [V_p,V_a,T_b] :
% 1.88/1.89 ( class_Groups_Oab__group__add(T_b)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__diff__left,axiom,
% 1.88/1.89 ! [V_p,V_b,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__ring(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__minus__left,axiom,
% 1.88/1.89 ! [V_p,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__ring(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__zero,axiom,
% 1.88/1.89 ! [V_pb_2,T_a] :
% 1.88/1.89 ( ( class_Int_Oring__char__0(T_a)
% 1.88/1.89 & class_Rings_Oidom(T_a) )
% 1.88/1.89 => ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 1.88/1.89 <=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__0__right,axiom,
% 1.88/1.89 ! [V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_diff__monom,axiom,
% 1.88/1.89 ! [V_b,V_n,V_a,T_a] :
% 1.88/1.89 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.89 => 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) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_minus__monom,axiom,
% 1.88/1.89 ! [V_n,V_a,T_a] :
% 1.88/1.89 ( class_Groups_Oab__group__add(T_a)
% 1.88/1.89 => 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) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_add__poly__code_I2_J,axiom,
% 1.88/1.89 ! [V_p,T_a] :
% 1.88/1.89 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.88/1.89 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_add__poly__code_I1_J,axiom,
% 1.88/1.89 ! [V_q,T_a] :
% 1.88/1.89 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.88/1.89 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__add__right,axiom,
% 1.88/1.89 ! [V_q,V_p,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__0,axiom,
% 1.88/1.89 ! [V_x,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_pCons__eq__0__iff,axiom,
% 1.88/1.89 ! [V_pb_2,V_aa_2,T_a] :
% 1.88/1.89 ( class_Groups_Ozero(T_a)
% 1.88/1.89 => ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.88/1.89 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.89 & V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_pCons__0__0,axiom,
% 1.88/1.89 ! [T_a] :
% 1.88/1.89 ( class_Groups_Ozero(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__eq__0__iff,axiom,
% 1.88/1.89 ! [V_pb_2,V_aa_2,T_a] :
% 1.88/1.89 ( class_Rings_Oidom(T_a)
% 1.88/1.89 => ( c_Polynomial_Osmult(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.88/1.89 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.89 | V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__0__left,axiom,
% 1.88/1.89 ! [V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_one__poly__def,axiom,
% 1.88/1.89 ! [T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.88/1.89 => 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))) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__smult,axiom,
% 1.88/1.89 ! [V_x,V_p,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__pCons,axiom,
% 1.88/1.89 ! [V_p,V_b,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_mult__monom,axiom,
% 1.88/1.89 ! [V_n,V_b,V_m,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_monom__eq__0,axiom,
% 1.88/1.89 ! [V_n,T_a] :
% 1.88/1.89 ( class_Groups_Ozero(T_a)
% 1.88/1.89 => c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_monom__eq__0__iff,axiom,
% 1.88/1.89 ! [V_n_2,V_aa_2,T_a] :
% 1.88/1.89 ( class_Groups_Ozero(T_a)
% 1.88/1.89 => ( c_Polynomial_Omonom(T_a,V_aa_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.88/1.89 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__add,axiom,
% 1.88/1.89 ! [V_x,V_q,V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_add__pCons,axiom,
% 1.88/1.89 ! [V_q,V_b,V_p,V_a,T_a] :
% 1.88/1.89 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_synthetic__div__unique__lemma,axiom,
% 1.88/1.89 ! [V_a,V_p,V_c,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => ( c_Polynomial_Osmult(T_a,V_c,V_p) = c_Polynomial_OpCons(T_a,V_a,V_p)
% 1.88/1.89 => V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__add__left,axiom,
% 1.88/1.89 ! [V_p,V_b,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_smult__monom,axiom,
% 1.88/1.89 ! [V_n,V_b,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_add__monom,axiom,
% 1.88/1.89 ! [V_b,V_n,V_a,T_a] :
% 1.88/1.89 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.88/1.89 => 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) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__pCons,axiom,
% 1.88/1.89 ! [V_x,V_p,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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))) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__monom,axiom,
% 1.88/1.89 ! [V_x,V_n,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_mult__pCons__right,axiom,
% 1.88/1.89 ! [V_q,V_a,V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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))) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_mult__pCons__left,axiom,
% 1.88/1.89 ! [V_q,V_p,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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))) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_synthetic__div__correct_H,axiom,
% 1.88/1.89 ! [V_p,V_c,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__ring__1(T_a)
% 1.88/1.89 => 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 ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_pcompose__pCons,axiom,
% 1.88/1.89 ! [V_q,V_p,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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))) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_synthetic__div__0,axiom,
% 1.88/1.89 ! [V_c,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_pcompose__0,axiom,
% 1.88/1.89 ! [V_q,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_poly__pcompose,axiom,
% 1.88/1.89 ! [V_x,V_q,V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_synthetic__div__pCons,axiom,
% 1.88/1.89 ! [V_c,V_p,V_a,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_synthetic__div__unique,axiom,
% 1.88/1.89 ! [V_r,V_q,V_c,V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => ( 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)
% 1.88/1.89 => ( V_r = hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)
% 1.88/1.89 & V_q = c_Polynomial_Osynthetic__div(T_a,V_p,V_c) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_synthetic__div__correct,axiom,
% 1.88/1.89 ! [V_c,V_p,T_a] :
% 1.88/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.88/1.89 => 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)) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_of__real_Opos__bounded,axiom,
% 1.88/1.89 ! [T_a] :
% 1.88/1.89 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.88/1.89 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.88/1.89 => ? [B_K] :
% 1.88/1.89 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.88/1.89 & ! [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)) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__root,axiom,
% 1.88/1.89 ! [V_aa_2,V_pb_2,T_a] :
% 1.88/1.89 ( class_Rings_Oidom(T_a)
% 1.88/1.89 => ( hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.88/1.89 <=> ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.88/1.89 | c_Polynomial_Oorder(T_a,V_aa_2,V_pb_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__refl,axiom,
% 1.88/1.89 ! [V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 1.88/1.89
% 1.88/1.89 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,
% 1.88/1.89 ? [B_k,B_a] :
% 1.88/1.89 ( B_a != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 1.88/1.89 & B_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.88/1.89 & ? [B_q] :
% 1.88/1.89 ( 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____))
% 1.88/1.89 & ! [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))) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_le__fun__def,axiom,
% 1.88/1.89 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.88/1.89 ( class_Orderings_Oord(T_b)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.88/1.89 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_linorder__linear,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Olinorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.88/1.89 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__eq__iff,axiom,
% 1.88/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( V_x_2 = V_y_2
% 1.88/1.89 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.88/1.89 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__eq__refl,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => ( V_x = V_y
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_le__funD,axiom,
% 1.88/1.89 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.88/1.89 ( class_Orderings_Oord(T_b)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__antisym__conv,axiom,
% 1.88/1.89 ! [V_x_2,V_y_2,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.88/1.89 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_ord__eq__le__trans,axiom,
% 1.88/1.89 ! [V_c,V_b,V_a,T_a] :
% 1.88/1.89 ( class_Orderings_Oord(T_a)
% 1.88/1.89 => ( V_a = V_b
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I3_J,axiom,
% 1.88/1.89 ! [V_c,V_b,V_a,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( V_a = V_b
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_ord__le__eq__trans,axiom,
% 1.88/1.89 ! [V_c,V_b,V_a,T_a] :
% 1.88/1.89 ( class_Orderings_Oord(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.88/1.89 => ( V_b = V_c
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I4_J,axiom,
% 1.88/1.89 ! [V_c,V_a,V_b,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.88/1.89 => ( V_b = V_c
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__antisym,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.88/1.89 => V_x = V_y ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__trans,axiom,
% 1.88/1.89 ! [V_z,V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I5_J,axiom,
% 1.88/1.89 ! [V_x,V_y,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.88/1.89 => V_x = V_y ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I6_J,axiom,
% 1.88/1.89 ! [V_z,V_x,V_y,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_le__funE,axiom,
% 1.88/1.89 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.88/1.89 ( class_Orderings_Oord(T_b)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_linorder__le__cases,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Olinorder(T_a)
% 1.88/1.89 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_linorder__cases,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Olinorder(T_a)
% 1.88/1.89 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 => ( V_x != V_y
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__less__asym,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I10_J,axiom,
% 1.88/1.89 ! [V_z,V_x,V_y,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__less__trans,axiom,
% 1.88/1.89 ! [V_z,V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I2_J,axiom,
% 1.88/1.89 ! [V_c,V_a,V_b,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.88/1.89 => ( V_b = V_c
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_ord__less__eq__trans,axiom,
% 1.88/1.89 ! [V_c,V_b,V_a,T_a] :
% 1.88/1.89 ( class_Orderings_Oord(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.88/1.89 => ( V_b = V_c
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I1_J,axiom,
% 1.88/1.89 ! [V_c,V_b,V_a,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( V_a = V_b
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_ord__eq__less__trans,axiom,
% 1.88/1.89 ! [V_c,V_b,V_a,T_a] :
% 1.88/1.89 ( class_Orderings_Oord(T_a)
% 1.88/1.89 => ( V_a = V_b
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I9_J,axiom,
% 1.88/1.89 ! [V_a,V_b,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.88/1.89 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__less__asym_H,axiom,
% 1.88/1.89 ! [V_b,V_a,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.88/1.89 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__less__imp__not__eq2,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 => V_y != V_x ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__less__imp__not__eq,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 => V_x != V_y ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__less__imp__not__less,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__less__not__sym,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_less__imp__neq,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 => V_x != V_y ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_linorder__neqE,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Olinorder(T_a)
% 1.88/1.89 => ( V_x != V_y
% 1.88/1.89 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_linorder__antisym__conv3,axiom,
% 1.88/1.89 ! [V_x_2,V_y_2,T_a] :
% 1.88/1.89 ( class_Orderings_Olinorder(T_a)
% 1.88/1.89 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.88/1.89 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.88/1.89 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_linorder__less__linear,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Olinorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 | V_x = V_y
% 1.88/1.89 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_not__less__iff__gr__or__eq,axiom,
% 1.88/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.88/1.89 ( class_Orderings_Olinorder(T_a)
% 1.88/1.89 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.88/1.89 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.88/1.89 | V_x_2 = V_y_2 ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_linorder__neq__iff,axiom,
% 1.88/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.88/1.89 ( class_Orderings_Olinorder(T_a)
% 1.88/1.89 => ( V_x_2 != V_y_2
% 1.88/1.89 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.88/1.89 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__less__irrefl,axiom,
% 1.88/1.89 ! [V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I8_J,axiom,
% 1.88/1.89 ! [V_z,V_x,V_y,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__le__less__trans,axiom,
% 1.88/1.89 ! [V_z,V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I7_J,axiom,
% 1.88/1.89 ! [V_z,V_x,V_y,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__less__le__trans,axiom,
% 1.88/1.89 ! [V_z,V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I11_J,axiom,
% 1.88/1.89 ! [V_a,V_b,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.88/1.89 => ( V_a != V_b
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__le__neq__trans,axiom,
% 1.88/1.89 ! [V_b,V_a,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.88/1.89 => ( V_a != V_b
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__le__imp__less__or__eq,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 | V_x = V_y ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_linorder__antisym__conv2,axiom,
% 1.88/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.88/1.89 ( class_Orderings_Olinorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.88/1.89 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.88/1.89 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__less__imp__le,axiom,
% 1.88/1.89 ! [V_y,V_x,T_a] :
% 1.88/1.89 ( class_Orderings_Opreorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.88/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_leD,axiom,
% 1.88/1.89 ! [V_x,V_y,T_a] :
% 1.88/1.89 ( class_Orderings_Olinorder(T_a)
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.88/1.89 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_xt1_I12_J,axiom,
% 1.88/1.89 ! [V_b,V_a,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( V_a != V_b
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.88/1.89 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.88/1.89
% 1.88/1.89 fof(fact_order__neq__le__trans,axiom,
% 1.88/1.89 ! [V_b,V_a,T_a] :
% 1.88/1.89 ( class_Orderings_Oorder(T_a)
% 1.88/1.89 => ( V_a != V_b
% 1.88/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.96/1.89 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_linorder__antisym__conv1,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Orderings_Olinorder(T_a)
% 1.96/1.89 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.96/1.89 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_not__leE,axiom,
% 1.96/1.89 ! [V_x,V_y,T_a] :
% 1.96/1.89 ( class_Orderings_Olinorder(T_a)
% 1.96/1.89 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.96/1.89 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_leI,axiom,
% 1.96/1.89 ! [V_y,V_x,T_a] :
% 1.96/1.89 ( class_Orderings_Olinorder(T_a)
% 1.96/1.89 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.96/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_order__le__less,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Orderings_Oorder(T_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.96/1.89 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.96/1.89 | V_x_2 = V_y_2 ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_less__le__not__le,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Orderings_Opreorder(T_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.96/1.89 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.96/1.89 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_order__less__le,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Orderings_Oorder(T_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.96/1.89 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.96/1.89 & V_x_2 != V_y_2 ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_linorder__le__less__linear,axiom,
% 1.96/1.89 ! [V_y,V_x,T_a] :
% 1.96/1.89 ( class_Orderings_Olinorder(T_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.96/1.89 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_linorder__not__le,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Orderings_Olinorder(T_a)
% 1.96/1.89 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_linorder__not__less,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Orderings_Olinorder(T_a)
% 1.96/1.89 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__add__one,axiom,
% 1.96/1.89 ! [V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_power__power__power,axiom,
% 1.96/1.89 ! [T_a] :
% 1.96/1.89 ( class_Power_Opower(T_a)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_less__fun__def,axiom,
% 1.96/1.89 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.96/1.89 ( class_Orderings_Oord(T_b)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.96/1.89 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.96/1.89 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__zero,axiom,
% 1.96/1.89 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_zero__le__natceiling,axiom,
% 1.96/1.89 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__mono,axiom,
% 1.96/1.89 ! [V_y,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.96/1.89 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__one,axiom,
% 1.96/1.89 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_power_Opower_Opower__0,axiom,
% 1.96/1.89 ! [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 ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__neg,axiom,
% 1.96/1.89 ! [V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.96/1.89 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__le__eq__one,axiom,
% 1.96/1.89 ! [V_x_2] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_of__real_Ononneg__bounded,axiom,
% 1.96/1.89 ! [T_a] :
% 1.96/1.89 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.96/1.89 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.96/1.89 => ? [B_K] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.96/1.89 & ! [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)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_lemmaCauchy,axiom,
% 1.96/1.89 ! [V_X_2,V_M_2,T_a,T_b] :
% 1.96/1.89 ( ( class_RealVector_Oreal__normed__vector(T_b)
% 1.96/1.89 & class_Orderings_Oord(T_a) )
% 1.96/1.89 => ( ! [B_n] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 1.96/1.89 => 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)) )
% 1.96/1.89 => ! [B_n] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 1.96/1.89 => 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)))) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_mult__left_Opos__bounded,axiom,
% 1.96/1.89 ! [V_y,T_a] :
% 1.96/1.89 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.96/1.89 => ? [B_K] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.96/1.89 & ! [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)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_mult__right_Opos__bounded,axiom,
% 1.96/1.89 ! [V_x,T_a] :
% 1.96/1.89 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.96/1.89 => ? [B_K] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.96/1.89 & ! [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)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_mult_Opos__bounded,axiom,
% 1.96/1.89 ! [T_a] :
% 1.96/1.89 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.96/1.89 => ? [B_K] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.96/1.89 & ! [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)) ) ) ).
% 1.96/1.89
% 1.96/1.89 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,
% 1.96/1.89 ~ ! [B_q] :
% 1.96/1.89 ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
% 1.96/1.89 => ~ ! [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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natfloor__add__one,axiom,
% 1.96/1.89 ! [V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_tsub__def,axiom,
% 1.96/1.89 ! [V_x,V_y] :
% 1.96/1.89 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 1.96/1.89 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) )
% 1.96/1.89 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 1.96/1.89 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natfloor__zero,axiom,
% 1.96/1.89 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natfloor__one,axiom,
% 1.96/1.89 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natfloor__mono,axiom,
% 1.96/1.89 ! [V_y,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.96/1.89 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_zero__le__natfloor,axiom,
% 1.96/1.89 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natfloor__neg,axiom,
% 1.96/1.89 ! [V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.96/1.89 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 1.96/1.89 ! [V_y,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.96/1.89 => 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)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_le__natfloor__eq__one,axiom,
% 1.96/1.89 ! [V_x_2] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_tsub__eq,axiom,
% 1.96/1.89 ! [V_x,V_y] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 1.96/1.89 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_le__mult__natfloor,axiom,
% 1.96/1.89 ! [V_b,V_a] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
% 1.96/1.89 => 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))) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_termination__basic__simps_I3_J,axiom,
% 1.96/1.89 ! [V_z,V_y,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
% 1.96/1.89 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_termination__basic__simps_I4_J,axiom,
% 1.96/1.89 ! [V_y,V_z,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
% 1.96/1.89 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_termination__basic__simps_I2_J,axiom,
% 1.96/1.89 ! [V_y,V_z,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 1.96/1.89 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_termination__basic__simps_I1_J,axiom,
% 1.96/1.89 ! [V_z,V_y,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.96/1.89 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_termination__basic__simps_I5_J,axiom,
% 1.96/1.89 ! [V_y,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.96/1.89 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__eq,axiom,
% 1.96/1.89 ! [V_x,V_n] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 1.96/1.89 => ( 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)))
% 1.96/1.89 => c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_pos__poly__pCons,axiom,
% 1.96/1.89 ! [V_pb_2,V_aa_2,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2))
% 1.96/1.89 <=> ( c_Polynomial_Opos__poly(T_a,V_pb_2)
% 1.96/1.89 | ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.96/1.89 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__ge__zero,axiom,
% 1.96/1.89 ! [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)) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__diff,axiom,
% 1.96/1.89 ! [V_m,V_n] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__less__iff,axiom,
% 1.96/1.89 ! [V_ma_2,V_n_2] :
% 1.96/1.89 ( 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))
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_not__real__of__nat__less__zero,axiom,
% 1.96/1.89 ! [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)) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_abs__real__of__nat__cancel,axiom,
% 1.96/1.89 ! [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) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__1,axiom,
% 1.96/1.89 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_power__real__of__nat,axiom,
% 1.96/1.89 ! [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)) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__power,axiom,
% 1.96/1.89 ! [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) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__add,axiom,
% 1.96/1.89 ! [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)) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__inject,axiom,
% 1.96/1.89 ! [V_ma_2,V_n_2] :
% 1.96/1.89 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)
% 1.96/1.89 <=> V_n_2 = V_ma_2 ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__zero__iff,axiom,
% 1.96/1.89 ! [V_n_2] :
% 1.96/1.89 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.96/1.89 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__zero,axiom,
% 1.96/1.89 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_not__pos__poly__0,axiom,
% 1.96/1.89 ! [T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__mult,axiom,
% 1.96/1.89 ! [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)) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_pos__poly__mult,axiom,
% 1.96/1.89 ! [V_q,V_p,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 1.96/1.89 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 1.96/1.89 => c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_pos__poly__add,axiom,
% 1.96/1.89 ! [V_q,V_p,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 1.96/1.89 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 1.96/1.89 => c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
% 1.96/1.89 ! [V_n_2] :
% 1.96/1.89 ( 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))
% 1.96/1.89 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__natceiling__ge,axiom,
% 1.96/1.89 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__le__iff,axiom,
% 1.96/1.89 ! [V_ma_2,V_n_2] :
% 1.96/1.89 ( 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))
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__real__of__nat,axiom,
% 1.96/1.89 ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 1.96/1.89
% 1.96/1.89 fof(fact_less__eq__poly__def,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
% 1.96/1.89 <=> ( V_x_2 = V_y_2
% 1.96/1.89 | c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natfloor__real__of__nat,axiom,
% 1.96/1.89 ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__natfloor__le,axiom,
% 1.96/1.89 ! [V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.96/1.89 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_le__natfloor,axiom,
% 1.96/1.89 ! [V_a,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)
% 1.96/1.89 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__le,axiom,
% 1.96/1.89 ! [V_a,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))
% 1.96/1.89 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natfloor__power,axiom,
% 1.96/1.89 ! [V_n,V_x] :
% 1.96/1.89 ( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))
% 1.96/1.89 => 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) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
% 1.96/1.89 ! [V_n_2] :
% 1.96/1.89 ( 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))
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_nat__less__real__le,axiom,
% 1.96/1.89 ! [V_ma_2,V_n_2] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
% 1.96/1.89 <=> 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_nat__le__real__less,axiom,
% 1.96/1.89 ! [V_ma_2,V_n_2] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
% 1.96/1.89 <=> 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))) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_le__natfloor__eq,axiom,
% 1.96/1.89 ! [V_aa_2,V_x_2] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_aa_2,c_RComplete_Onatfloor(V_x_2))
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2),V_x_2) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_pos__poly__total,axiom,
% 1.96/1.89 ! [V_p,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.96/1.89 | c_Polynomial_Opos__poly(T_a,V_p)
% 1.96/1.89 | c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__le__eq,axiom,
% 1.96/1.89 ! [V_aa_2,V_x_2] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_aa_2)
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__natfloor__add__one__gt,axiom,
% 1.96/1.89 ! [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))) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natfloor__subtract,axiom,
% 1.96/1.89 ! [V_x,V_a] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 1.96/1.89 => 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) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_real__natfloor__gt__diff__one,axiom,
% 1.96/1.89 ! [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))) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__subtract,axiom,
% 1.96/1.89 ! [V_x,V_a] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 1.96/1.89 => 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) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_less__natfloor,axiom,
% 1.96/1.89 ! [V_n,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
% 1.96/1.89 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natfloor__add,axiom,
% 1.96/1.89 ! [V_a,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.96/1.89 => 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) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
% 1.96/1.89 ! [V_n,V_z] :
% 1.96/1.89 ( 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)
% 1.96/1.89 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natfloor__eq,axiom,
% 1.96/1.89 ! [V_x,V_n] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 1.96/1.89 => ( 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)))
% 1.96/1.89 => c_RComplete_Onatfloor(V_x) = V_n ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_natceiling__add,axiom,
% 1.96/1.89 ! [V_a,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.96/1.89 => 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) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_less__poly__def,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
% 1.96/1.89 <=> c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
% 1.96/1.89 ! [V_n,V_x] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_reals__Archimedean6,axiom,
% 1.96/1.89 ! [V_r] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 1.96/1.89 => ? [B_n] :
% 1.96/1.89 ( 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)
% 1.96/1.89 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_Limits_Ominus__diff__minus,axiom,
% 1.96/1.89 ! [V_b,V_a,T_a] :
% 1.96/1.89 ( class_Groups_Oab__group__add(T_a)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_poly__cont,axiom,
% 1.96/1.89 ! [V_p,V_z,V_e] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e)
% 1.96/1.89 => ? [B_d] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 1.96/1.89 & ! [B_w] :
% 1.96/1.89 ( ( 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)))
% 1.96/1.89 & 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) )
% 1.96/1.89 => 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) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_decseq__def,axiom,
% 1.96/1.89 ! [V_X_2,T_a] :
% 1.96/1.89 ( class_Orderings_Oorder(T_a)
% 1.96/1.89 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 1.96/1.89 <=> ! [B_m,B_n] :
% 1.96/1.89 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 1.96/1.89 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_compl__le__compl__iff,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Lattices_Oboolean__algebra(T_a)
% 1.96/1.89 => ( 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))
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_compl__mono,axiom,
% 1.96/1.89 ! [V_y,V_x,T_a] :
% 1.96/1.89 ( class_Lattices_Oboolean__algebra(T_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.96/1.89 => 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)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_minus__apply,axiom,
% 1.96/1.89 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 1.96/1.89 ( class_Groups_Ominus(T_a)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_times_Oidem,axiom,
% 1.96/1.89 ! [V_a,T_a] :
% 1.96/1.89 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.96/1.89 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_mult__idem,axiom,
% 1.96/1.89 ! [V_x,T_a] :
% 1.96/1.89 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.96/1.89 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_mult__left__idem,axiom,
% 1.96/1.89 ! [V_b,V_a,T_a] :
% 1.96/1.89 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.96/1.89 => 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) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_double__compl,axiom,
% 1.96/1.89 ! [V_x,T_a] :
% 1.96/1.89 ( class_Lattices_Oboolean__algebra(T_a)
% 1.96/1.89 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_uminus__apply,axiom,
% 1.96/1.89 ! [V_x_2,V_A_2,T_b,T_a] :
% 1.96/1.89 ( class_Groups_Ouminus(T_a)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_compl__eq__compl__iff,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Lattices_Oboolean__algebra(T_a)
% 1.96/1.89 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
% 1.96/1.89 <=> V_x_2 = V_y_2 ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_of__real_Obounded,axiom,
% 1.96/1.89 ! [T_a] :
% 1.96/1.89 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.96/1.89 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.96/1.89 => ? [B_K] :
% 1.96/1.89 ! [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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__poly__def,axiom,
% 1.96/1.89 ! [V_x,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.96/1.89 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 1.96/1.89 & ( V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.96/1.89 => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 1.96/1.89 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) )
% 1.96/1.89 & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 1.96/1.89 => 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))) ) ) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__less,axiom,
% 1.96/1.89 ! [V_aa_2,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__greater,axiom,
% 1.96/1.89 ! [V_aa_2,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__one,axiom,
% 1.96/1.89 ! [T_a] :
% 1.96/1.89 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.96/1.89 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__minus,axiom,
% 1.96/1.89 ! [V_x,T_a] :
% 1.96/1.89 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_mult__sgn__abs,axiom,
% 1.96/1.89 ! [V_x,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => 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 ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_abs__sgn,axiom,
% 1.96/1.89 ! [V_k,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__of__real,axiom,
% 1.96/1.89 ! [V_r,T_a] :
% 1.96/1.89 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__sgn,axiom,
% 1.96/1.89 ! [V_a,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => 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) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn0,axiom,
% 1.96/1.89 ! [T_a] :
% 1.96/1.89 ( class_Groups_Osgn__if(T_a)
% 1.96/1.89 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__zero,axiom,
% 1.96/1.89 ! [T_a] :
% 1.96/1.89 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.96/1.89 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__zero__iff,axiom,
% 1.96/1.89 ! [V_x_2,T_a] :
% 1.96/1.89 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.96/1.89 => ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.89 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__0__0,axiom,
% 1.96/1.89 ! [V_aa_2,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.89 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__mult,axiom,
% 1.96/1.89 ! [V_y,V_x,T_a] :
% 1.96/1.89 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__times,axiom,
% 1.96/1.89 ! [V_b,V_a,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => 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)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__1__pos,axiom,
% 1.96/1.89 ! [V_aa_2,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Oone__class_Oone(T_a)
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__pos,axiom,
% 1.96/1.89 ! [V_a,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.96/1.89 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__1__neg,axiom,
% 1.96/1.89 ! [V_aa_2,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
% 1.96/1.89 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__neg,axiom,
% 1.96/1.89 ! [V_a,T_a] :
% 1.96/1.89 ( class_Rings_Olinordered__idom(T_a)
% 1.96/1.89 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.96/1.89 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_sgn__if,axiom,
% 1.96/1.89 ! [V_x,T_a] :
% 1.96/1.89 ( class_Groups_Osgn__if(T_a)
% 1.96/1.89 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.89 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 1.96/1.89 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.89 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.96/1.89 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 1.96/1.89 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.96/1.89 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_norm__sgn,axiom,
% 1.96/1.89 ! [V_x,T_a] :
% 1.96/1.89 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.96/1.89 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.89 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 1.96/1.89 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.89 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_order__1,axiom,
% 1.96/1.89 ! [V_p,V_a,T_a] :
% 1.96/1.89 ( class_Rings_Oidom(T_a)
% 1.96/1.89 => 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) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_offset__poly__pCons,axiom,
% 1.96/1.89 ! [V_h,V_p,V_a,T_a] :
% 1.96/1.89 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.96/1.89 => 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))) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_dvd__0__right,axiom,
% 1.96/1.89 ! [V_a,T_a] :
% 1.96/1.89 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.96/1.89 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_dvd__minus__iff,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Rings_Ocomm__ring__1(T_a)
% 1.96/1.89 => ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
% 1.96/1.89 <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_minus__dvd__iff,axiom,
% 1.96/1.89 ! [V_y_2,V_x_2,T_a] :
% 1.96/1.89 ( class_Rings_Ocomm__ring__1(T_a)
% 1.96/1.89 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)
% 1.96/1.89 <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_dvd__diff,axiom,
% 1.96/1.89 ! [V_z,V_y,V_x,T_a] :
% 1.96/1.89 ( class_Rings_Ocomm__ring__1(T_a)
% 1.96/1.89 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 1.96/1.89 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)
% 1.96/1.89 => c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_inf__period_I3_J,axiom,
% 1.96/1.89 ! [V_ta_2,V_D_2,V_d_2,T_a] :
% 1.96/1.89 ( ( class_Rings_Ocomm__ring(T_a)
% 1.96/1.89 & class_Rings_Odvd(T_a) )
% 1.96/1.89 => ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
% 1.96/1.89 => ! [B_x,B_k] :
% 1.96/1.89 ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))
% 1.96/1.89 <=> 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)) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_inf__period_I4_J,axiom,
% 1.96/1.89 ! [V_ta_2,V_D_2,V_d_2,T_a] :
% 1.96/1.89 ( ( class_Rings_Ocomm__ring(T_a)
% 1.96/1.89 & class_Rings_Odvd(T_a) )
% 1.96/1.89 => ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
% 1.96/1.89 => ! [B_x,B_k] :
% 1.96/1.89 ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))
% 1.96/1.89 <=> 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)) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_smult__dvd__iff,axiom,
% 1.96/1.89 ! [V_qa_2,V_pb_2,V_aa_2,T_a] :
% 1.96/1.89 ( class_Fields_Ofield(T_a)
% 1.96/1.89 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_aa_2,V_pb_2),V_qa_2)
% 1.96/1.89 <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.89 => V_qa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 1.96/1.89 & ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.89 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pb_2,V_qa_2) ) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_unity__coeff__ex,axiom,
% 1.96/1.89 ! [V_l_2,V_P_2,T_a] :
% 1.96/1.89 ( ( class_Rings_Odvd(T_a)
% 1.96/1.89 & class_Rings_Osemiring__0(T_a) )
% 1.96/1.89 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
% 1.96/1.89 <=> ? [B_x] :
% 1.96/1.89 ( 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)))
% 1.96/1.89 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_smult__dvd__cancel,axiom,
% 1.96/1.89 ! [V_q,V_p,V_a,T_a] :
% 1.96/1.89 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.96/1.89 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)
% 1.96/1.89 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_dvd__smult,axiom,
% 1.96/1.89 ! [V_a,V_q,V_p,T_a] :
% 1.96/1.89 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.96/1.89 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
% 1.96/1.89 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q)) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_dvd__smult__iff,axiom,
% 1.96/1.89 ! [V_qa_2,V_pb_2,V_aa_2,T_a] :
% 1.96/1.89 ( class_Fields_Ofield(T_a)
% 1.96/1.89 => ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.89 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pb_2,c_Polynomial_Osmult(T_a,V_aa_2,V_qa_2))
% 1.96/1.89 <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pb_2,V_qa_2) ) ) ) ).
% 1.96/1.89
% 1.96/1.89 fof(fact_smult__dvd,axiom,
% 1.96/1.90 ! [V_a,V_q,V_p,T_a] :
% 1.96/1.90 ( class_Fields_Ofield(T_a)
% 1.96/1.90 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
% 1.96/1.90 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.90 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q) ) ) ) ).
% 1.96/1.90
% 1.96/1.90 fof(fact_dvd__smult__cancel,axiom,
% 1.96/1.90 ! [V_q,V_a,V_p,T_a] :
% 1.96/1.90 ( class_Fields_Ofield(T_a)
% 1.96/1.90 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q))
% 1.96/1.90 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.90 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) ) ) ) ).
% 1.96/1.90
% 1.96/1.90 fof(fact_dvd__triv__left,axiom,
% 1.96/1.90 ! [V_b,V_a,T_a] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.96/1.90 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(fact_dvd__triv__right,axiom,
% 1.96/1.90 ! [V_b,V_a,T_a] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.96/1.90 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(fact_dvd__mult2,axiom,
% 1.96/1.90 ! [V_c,V_b,V_a,T_a] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.96/1.90 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 1.96/1.90 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ).
% 1.96/1.90
% 1.96/1.90 fof(fact_dvd__mult,axiom,
% 1.96/1.90 ! [V_b,V_c,V_a,T_a] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.96/1.90 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
% 1.96/1.90 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ).
% 1.96/1.90
% 1.96/1.90 fof(fact_mult__dvd__mono,axiom,
% 1.96/1.90 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.96/1.90 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 1.96/1.90 => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)
% 1.96/1.90 => c_Rings_Odvd__class_Odvd(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)) ) ) ) ).
% 1.96/1.90
% 1.96/1.90 fof(fact_dvdI,axiom,
% 1.96/1.90 ! [V_k,V_b,V_a,T_a] :
% 1.96/1.90 ( class_Rings_Odvd(T_a)
% 1.96/1.90 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 1.96/1.90 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_a) ) ) ).
% 1.96/1.90
% 1.96/1.90 fof(fact_dvd__mult__left,axiom,
% 1.96/1.90 ! [V_c,V_b,V_a,T_a] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.96/1.90 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
% 1.96/1.90 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ).
% 1.96/1.90
% 1.96/1.90 fof(fact_dvd__mult__right,axiom,
% 1.96/1.90 ! [V_c,V_b,V_a,T_a] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.96/1.90 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
% 1.96/1.90 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_c) ) ) ).
% 1.96/1.90
% 1.96/1.90 fof(fact_dvd__mult__cancel__left,axiom,
% 1.96/1.90 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 1.96/1.90 ( class_Rings_Oidom(T_a)
% 1.96/1.90 => ( 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))
% 1.96/1.90 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.96/1.90 | c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2) ) ) ) ).
% 1.96/1.90
% 1.96/1.90 %----Arity declarations (289)
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.96/1.90 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 1.96/1.90 ! [T_2,T_1] :
% 1.96/1.90 ( class_Lattices_Oboolean__algebra(T_1)
% 1.96/1.90 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_fun__Orderings_Opreorder,axiom,
% 1.96/1.90 ! [T_2,T_1] :
% 1.96/1.90 ( class_Orderings_Opreorder(T_1)
% 1.96/1.90 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_fun__Orderings_Oorder,axiom,
% 1.96/1.90 ! [T_2,T_1] :
% 1.96/1.90 ( class_Orderings_Oorder(T_1)
% 1.96/1.90 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_fun__Orderings_Oord,axiom,
% 1.96/1.90 ! [T_2,T_1] :
% 1.96/1.90 ( class_Orderings_Oord(T_1)
% 1.96/1.90 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_fun__Groups_Ouminus,axiom,
% 1.96/1.90 ! [T_2,T_1] :
% 1.96/1.90 ( class_Groups_Ouminus(T_1)
% 1.96/1.90 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_fun__Groups_Ominus,axiom,
% 1.96/1.90 ! [T_2,T_1] :
% 1.96/1.90 ( class_Groups_Ominus(T_1)
% 1.96/1.90 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.96/1.90 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.96/1.90 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.96/1.90 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 1.96/1.90 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 1.96/1.90 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 1.96/1.90 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 1.96/1.90 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 1.96/1.90 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 1.96/1.90 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 1.96/1.90 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 1.96/1.90 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 1.96/1.90 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 1.96/1.90 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 1.96/1.90 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 1.96/1.90 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 1.96/1.90 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 1.96/1.90 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 1.96/1.90 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 1.96/1.90 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 1.96/1.90 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 1.96/1.90 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 1.96/1.90 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 1.96/1.90 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 1.96/1.90 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 1.96/1.90 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 1.96/1.90 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 1.96/1.90 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 1.96/1.90 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 1.96/1.90 class_Orderings_Opreorder(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 1.96/1.90 class_Orderings_Olinorder(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 1.96/1.90 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 1.96/1.90 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 1.96/1.90 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 1.96/1.90 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 1.96/1.90 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 1.96/1.90 class_Rings_Omult__zero(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 1.96/1.90 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 1.96/1.90 class_Orderings_Oorder(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 1.96/1.90 class_Int_Oring__char__0(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 1.96/1.90 class_Rings_Osemiring(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 1.96/1.90 class_Orderings_Oord(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 1.96/1.90 class_Groups_Ouminus(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 1.96/1.90 class_Groups_Osgn__if(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 1.96/1.90 class_Groups_Oabs__if(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 1.96/1.90 class_Rings_Oring__1(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 1.96/1.90 class_Groups_Ominus(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Power_Opower,axiom,
% 1.96/1.90 class_Power_Opower(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 1.96/1.90 class_Groups_Ozero(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Oring,axiom,
% 1.96/1.90 class_Rings_Oring(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 1.96/1.90 class_Rings_Oidom(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Groups_Oone,axiom,
% 1.96/1.90 class_Groups_Oone(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 1.96/1.90 class_Rings_Odvd(tc_Int_Oint) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.96/1.90 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.96/1.90 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.96/1.90 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 1.96/1.90 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 1.96/1.90 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 1.96/1.90 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 1.96/1.90 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 1.96/1.90 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 1.96/1.90 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 1.96/1.90 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 1.96/1.90 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 1.96/1.90 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 1.96/1.90 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 1.96/1.90 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 1.96/1.90 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 1.96/1.90 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 1.96/1.90 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 1.96/1.90 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 1.96/1.90 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 1.96/1.90 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 1.96/1.90 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 1.96/1.90 class_Orderings_Oorder(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 1.96/1.90 class_Rings_Osemiring(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 1.96/1.90 class_Orderings_Oord(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 1.96/1.90 class_Groups_Ominus(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Power_Opower,axiom,
% 1.96/1.90 class_Power_Opower(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 1.96/1.90 class_Groups_Ozero(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 1.96/1.90 class_Groups_Oone(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 1.96/1.90 class_Rings_Odvd(tc_Nat_Onat) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 1.96/1.90 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 1.96/1.90 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 1.96/1.90 class_Orderings_Oorder(tc_HOL_Obool) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 1.96/1.90 class_Orderings_Oord(tc_HOL_Obool) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 1.96/1.90 class_Groups_Ouminus(tc_HOL_Obool) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 1.96/1.90 class_Groups_Ominus(tc_HOL_Obool) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.96/1.90 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.96/1.90 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.96/1.90 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
% 1.96/1.90 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 1.96/1.90 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 1.96/1.90 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 1.96/1.90 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
% 1.96/1.90 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 1.96/1.90 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 1.96/1.90 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 1.96/1.90 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 1.96/1.90 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 1.96/1.90 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 1.96/1.90 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 1.96/1.90 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 1.96/1.90 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 1.96/1.90 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 1.96/1.90 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 1.96/1.90 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 1.96/1.90 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__RealVector_Oreal__div__algebra,axiom,
% 1.96/1.90 class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 1.96/1.90 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 1.96/1.90 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
% 1.96/1.90 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
% 1.96/1.90 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 1.96/1.90 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 1.96/1.90 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 1.96/1.90 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
% 1.96/1.90 class_Fields_Olinordered__field(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 1.96/1.90 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
% 1.96/1.90 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 1.96/1.90 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 1.96/1.90 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 1.96/1.90 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 1.96/1.90 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
% 1.96/1.90 class_Rings_Odivision__ring(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 1.96/1.90 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 1.96/1.90 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 1.96/1.90 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 1.96/1.90 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 1.96/1.90 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 1.96/1.90 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 1.96/1.90 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 1.96/1.90 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 1.96/1.90 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 1.96/1.90 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 1.96/1.90 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 1.96/1.90 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 1.96/1.90 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 1.96/1.90 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 1.96/1.90 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 1.96/1.90 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
% 1.96/1.90 class_Groups_Ouminus(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom,
% 1.96/1.90 class_Groups_Osgn__if(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Oabs__if,axiom,
% 1.96/1.90 class_Groups_Oabs__if(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 1.96/1.90 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
% 1.96/1.90 class_Groups_Ominus(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 1.96/1.90 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 1.96/1.90 class_Power_Opower(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 1.96/1.90 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 1.96/1.90 class_Rings_Oring(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 1.96/1.90 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 1.96/1.90 class_Groups_Oone(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
% 1.96/1.90 class_Rings_Odvd(tc_RealDef_Oreal) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.96/1.90 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 1.96/1.90 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
% 1.96/1.90 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 1.96/1.90 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 1.96/1.90 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 1.96/1.90 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 1.96/1.90 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 1.96/1.90 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__RealVector_Oreal__div__algebra,axiom,
% 1.96/1.90 class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
% 1.96/1.90 class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
% 1.96/1.90 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 1.96/1.90 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 1.96/1.90 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 1.96/1.90 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 1.96/1.90 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 1.96/1.90 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
% 1.96/1.90 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 1.96/1.90 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 1.96/1.90 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 1.96/1.90 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 1.96/1.90 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 1.96/1.90 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 1.96/1.90 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 1.96/1.90 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 1.96/1.90 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 1.96/1.90 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 1.96/1.90 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 1.96/1.90 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 1.96/1.90 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
% 1.96/1.90 class_Groups_Ouminus(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 1.96/1.90 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
% 1.96/1.90 class_Groups_Ominus(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 1.96/1.90 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 1.96/1.90 class_Power_Opower(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 1.96/1.90 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 1.96/1.90 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 1.96/1.90 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 1.96/1.90 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
% 1.96/1.90 class_Rings_Odvd(tc_Complex_Ocomplex) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Oidom(T_1)
% 1.96/1.90 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.96/1.90 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Oidom(T_1)
% 1.96/1.90 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Oidom(T_1)
% 1.96/1.90 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.96/1.90 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.96/1.90 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.96/1.90 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.96/1.90 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Oidom(T_1)
% 1.96/1.90 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.96/1.90 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.96/1.90 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.96/1.90 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.96/1.90 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Groups_Oab__group__add(T_1)
% 1.96/1.90 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.96/1.90 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.96/1.90 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__ring__1(T_1)
% 1.96/1.90 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.96/1.90 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.96/1.90 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Groups_Oab__group__add(T_1)
% 1.96/1.90 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.96/1.90 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__ring(T_1)
% 1.96/1.90 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.96/1.90 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Groups_Oab__group__add(T_1)
% 1.96/1.90 => class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Olinordered__idom(T_1)
% 1.96/1.90 => class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__ring__1(T_1)
% 1.96/1.90 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Groups_Oab__group__add(T_1)
% 1.96/1.90 => class_Groups_Ominus(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Power_Opower,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.96/1.90 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Groups_Ozero(T_1)
% 1.96/1.90 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__ring(T_1)
% 1.96/1.90 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Oidom(T_1)
% 1.96/1.90 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.96/1.90 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
% 1.96/1.90 ! [T_1] :
% 1.96/1.90 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.96/1.90 => class_Rings_Odvd(tc_Polynomial_Opoly(T_1)) ) ).
% 1.96/1.90
% 1.96/1.90 %----Conjectures (1)
% 1.96/1.90 fof(conj_0,conjecture,
% 1.96/1.90 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))) ).
% 1.96/1.90
% 1.96/1.90 %------------------------------------------------------------------------------
% 1.96/1.90 %-------------------------------------------
% 1.96/1.90 % Proof found
% 1.96/1.90 % SZS status Theorem for theBenchmark
% 1.96/1.90 % SZS output start Proof
% 1.96/1.90 %ClaNum:1809(EqnAxiom:204)
% 1.96/1.90 %VarNum:8784(SingletonVarNum:3016)
% 1.96/1.90 %MaxLitNum:7
% 1.96/1.90 %MaxfuncDepth:9
% 1.96/1.90 %SharedTerms:456
% 1.96/1.90 %goalClause: 603
% 1.96/1.90 %singleGoalClaCount:1
% 1.96/1.90 [205]P1(a1)
% 1.96/1.90 [206]P1(a2)
% 1.96/1.90 [207]P46(a1)
% 1.96/1.90 [208]P46(a69)
% 1.96/1.90 [209]P46(a70)
% 1.96/1.90 [210]P47(a1)
% 1.96/1.90 [211]P47(a2)
% 1.96/1.90 [212]P48(a1)
% 1.96/1.90 [213]P48(a2)
% 1.96/1.90 [214]P49(a1)
% 1.96/1.90 [215]P49(a2)
% 1.96/1.90 [216]P2(a1)
% 1.96/1.90 [217]P2(a2)
% 1.96/1.90 [218]P2(a69)
% 1.96/1.90 [219]P2(a70)
% 1.96/1.90 [220]P50(a1)
% 1.96/1.90 [221]P50(a2)
% 1.96/1.90 [222]P50(a69)
% 1.96/1.90 [223]P50(a70)
% 1.96/1.90 [224]P55(a1)
% 1.96/1.90 [225]P55(a2)
% 1.96/1.90 [226]P26(a1)
% 1.96/1.90 [227]P26(a2)
% 1.96/1.90 [228]P26(a69)
% 1.96/1.90 [229]P26(a70)
% 1.96/1.90 [230]P63(a1)
% 1.96/1.90 [231]P63(a2)
% 1.96/1.90 [232]P63(a69)
% 1.96/1.90 [233]P63(a70)
% 1.96/1.90 [234]P68(a1)
% 1.96/1.90 [235]P68(a2)
% 1.96/1.90 [236]P68(a69)
% 1.96/1.90 [237]P68(a70)
% 1.96/1.90 [238]P69(a1)
% 1.96/1.90 [239]P69(a2)
% 1.96/1.90 [240]P69(a69)
% 1.96/1.90 [241]P69(a70)
% 1.96/1.90 [242]P56(a1)
% 1.96/1.90 [243]P56(a2)
% 1.96/1.90 [244]P81(a1)
% 1.96/1.90 [245]P81(a2)
% 1.96/1.90 [246]P81(a69)
% 1.96/1.90 [247]P81(a70)
% 1.96/1.90 [248]P70(a1)
% 1.96/1.90 [249]P70(a2)
% 1.96/1.90 [250]P70(a70)
% 1.96/1.90 [251]P78(a1)
% 1.96/1.90 [252]P78(a2)
% 1.96/1.90 [253]P78(a69)
% 1.96/1.90 [254]P78(a70)
% 1.96/1.90 [255]P3(a1)
% 1.96/1.90 [256]P3(a2)
% 1.96/1.90 [257]P3(a69)
% 1.96/1.90 [258]P3(a70)
% 1.96/1.90 [259]P64(a1)
% 1.96/1.90 [260]P64(a70)
% 1.96/1.90 [261]P4(a1)
% 1.96/1.90 [262]P13(a1)
% 1.96/1.90 [263]P65(a1)
% 1.96/1.90 [264]P65(a70)
% 1.96/1.90 [265]P57(a1)
% 1.96/1.90 [266]P57(a70)
% 1.96/1.90 [267]P79(a1)
% 1.96/1.90 [268]P79(a2)
% 1.96/1.90 [269]P79(a70)
% 1.96/1.90 [270]P51(a1)
% 1.96/1.90 [271]P51(a2)
% 1.96/1.90 [272]P51(a69)
% 1.96/1.90 [273]P51(a70)
% 1.96/1.90 [274]P80(a1)
% 1.96/1.90 [275]P80(a2)
% 1.96/1.90 [276]P80(a69)
% 1.96/1.90 [277]P80(a70)
% 1.96/1.90 [278]P5(a1)
% 1.96/1.90 [279]P5(a2)
% 1.96/1.90 [280]P71(a1)
% 1.96/1.90 [281]P71(a69)
% 1.96/1.90 [282]P71(a70)
% 1.96/1.90 [283]P72(a1)
% 1.96/1.90 [284]P72(a70)
% 1.96/1.90 [285]P74(a1)
% 1.96/1.90 [286]P74(a69)
% 1.96/1.90 [287]P74(a70)
% 1.96/1.90 [288]P73(a1)
% 1.96/1.90 [289]P73(a69)
% 1.96/1.90 [290]P73(a70)
% 1.96/1.90 [291]P61(a1)
% 1.96/1.90 [292]P61(a70)
% 1.96/1.90 [293]P62(a1)
% 1.96/1.90 [294]P62(a70)
% 1.96/1.90 [295]P67(a1)
% 1.96/1.90 [296]P67(a69)
% 1.96/1.90 [297]P67(a70)
% 1.96/1.90 [298]P58(a1)
% 1.96/1.90 [299]P58(a69)
% 1.96/1.90 [300]P58(a70)
% 1.96/1.90 [301]P66(a1)
% 1.96/1.90 [302]P66(a69)
% 1.96/1.90 [303]P66(a70)
% 1.96/1.90 [304]P6(a1)
% 1.96/1.90 [305]P6(a2)
% 1.96/1.90 [306]P27(a1)
% 1.96/1.90 [307]P27(a69)
% 1.96/1.90 [308]P27(a70)
% 1.96/1.90 [309]P34(a1)
% 1.96/1.90 [310]P34(a2)
% 1.96/1.90 [311]P34(a69)
% 1.96/1.90 [312]P34(a70)
% 1.96/1.90 [313]P14(a1)
% 1.96/1.90 [314]P14(a2)
% 1.96/1.90 [315]P14(a69)
% 1.96/1.90 [316]P14(a70)
% 1.96/1.90 [317]P17(a1)
% 1.96/1.90 [318]P17(a2)
% 1.96/1.90 [319]P17(a69)
% 1.96/1.90 [320]P17(a70)
% 1.96/1.90 [321]P18(a1)
% 1.96/1.90 [322]P18(a2)
% 1.96/1.90 [323]P18(a69)
% 1.96/1.90 [324]P18(a70)
% 1.96/1.90 [325]P15(a1)
% 1.96/1.90 [326]P15(a2)
% 1.96/1.90 [327]P15(a69)
% 1.96/1.90 [328]P15(a70)
% 1.96/1.90 [329]P28(a1)
% 1.96/1.90 [330]P28(a2)
% 1.96/1.90 [331]P28(a69)
% 1.96/1.90 [332]P28(a70)
% 1.96/1.90 [333]P21(a1)
% 1.96/1.90 [334]P21(a2)
% 1.96/1.90 [335]P21(a69)
% 1.96/1.90 [336]P21(a70)
% 1.96/1.90 [337]P22(a1)
% 1.96/1.90 [338]P22(a2)
% 1.96/1.90 [339]P22(a69)
% 1.96/1.90 [340]P22(a70)
% 1.96/1.90 [341]P23(a1)
% 1.96/1.90 [342]P23(a70)
% 1.96/1.90 [343]P29(a1)
% 1.96/1.90 [344]P29(a69)
% 1.96/1.90 [345]P29(a70)
% 1.96/1.90 [346]P30(a1)
% 1.96/1.90 [347]P30(a69)
% 1.96/1.90 [348]P30(a70)
% 1.96/1.90 [349]P33(a1)
% 1.96/1.90 [350]P33(a69)
% 1.96/1.90 [351]P33(a70)
% 1.96/1.90 [352]P24(a1)
% 1.96/1.90 [353]P24(a2)
% 1.96/1.90 [354]P24(a70)
% 1.96/1.90 [355]P16(a1)
% 1.96/1.91 [356]P16(a2)
% 1.96/1.91 [357]P16(a70)
% 1.96/1.91 [358]P44(a1)
% 1.96/1.91 [359]P44(a2)
% 1.96/1.91 [360]P52(a1)
% 1.96/1.91 [361]P52(a2)
% 1.96/1.91 [362]P52(a70)
% 1.96/1.91 [363]P31(a1)
% 1.96/1.91 [364]P31(a70)
% 1.96/1.91 [365]P76(a1)
% 1.96/1.91 [366]P76(a2)
% 1.96/1.91 [367]P76(a70)
% 1.96/1.91 [368]P59(a1)
% 1.96/1.91 [369]P59(a2)
% 1.96/1.91 [370]P59(a70)
% 1.96/1.91 [371]P45(a1)
% 1.96/1.91 [372]P45(a2)
% 1.96/1.91 [373]P77(a1)
% 1.96/1.91 [374]P77(a2)
% 1.96/1.91 [375]P77(a70)
% 1.96/1.91 [376]P32(a1)
% 1.96/1.91 [377]P32(a70)
% 1.96/1.91 [378]P75(a1)
% 1.96/1.91 [379]P75(a70)
% 1.96/1.91 [380]P19(a1)
% 1.96/1.91 [381]P19(a70)
% 1.96/1.91 [382]P54(a1)
% 1.96/1.91 [383]P54(a2)
% 1.96/1.91 [384]P54(a69)
% 1.96/1.91 [385]P54(a70)
% 1.96/1.91 [386]P37(a1)
% 1.96/1.91 [387]P37(a2)
% 1.96/1.91 [388]P37(a70)
% 1.96/1.91 [389]P53(a1)
% 1.96/1.91 [390]P53(a2)
% 1.96/1.91 [391]P53(a70)
% 1.96/1.91 [392]P38(a1)
% 1.96/1.91 [393]P38(a69)
% 1.96/1.91 [394]P38(a70)
% 1.96/1.91 [395]P38(a71)
% 1.96/1.91 [396]P39(a1)
% 1.96/1.91 [397]P39(a69)
% 1.96/1.91 [398]P39(a70)
% 1.96/1.91 [399]P39(a71)
% 1.96/1.91 [400]P40(a1)
% 1.96/1.91 [401]P40(a69)
% 1.96/1.91 [402]P40(a70)
% 1.96/1.91 [403]P43(a1)
% 1.96/1.91 [404]P43(a69)
% 1.96/1.91 [405]P43(a70)
% 1.96/1.91 [406]P43(a71)
% 1.96/1.91 [407]P41(a71)
% 1.96/1.91 [408]P25(a1)
% 1.96/1.91 [409]P25(a2)
% 1.96/1.91 [410]P25(a69)
% 1.96/1.91 [411]P25(a70)
% 1.96/1.91 [412]P25(a71)
% 1.96/1.91 [413]P35(a1)
% 1.96/1.91 [414]P35(a2)
% 1.96/1.91 [415]P35(a70)
% 1.96/1.91 [416]P35(a71)
% 1.96/1.91 [417]P36(a1)
% 1.96/1.91 [418]P36(a70)
% 1.96/1.91 [419]P60(a1)
% 1.96/1.91 [420]P60(a2)
% 1.96/1.91 [421]P60(a69)
% 1.96/1.91 [422]P60(a70)
% 1.96/1.91 [423]P20(a1)
% 1.96/1.91 [424]P20(a2)
% 1.96/1.91 [425]P20(a69)
% 1.96/1.91 [426]P20(a70)
% 1.96/1.91 [435]E(f26(a2,a4),f11(a2,a4))
% 1.96/1.91 [436]E(f5(a2,a73),f5(a2,a80))
% 1.96/1.91 [437]E(f5(a2,a30),f5(a2,a73))
% 1.96/1.91 [438]E(f5(a2,a36),f5(a2,a73))
% 1.96/1.91 [453]P8(a1,a81,f3(a1))
% 1.96/1.91 [454]P8(a1,a37,f3(a1))
% 1.96/1.91 [455]P8(a1,f10(a1),a81)
% 1.96/1.91 [456]P8(a1,f10(a1),a74)
% 1.96/1.91 [457]P8(a1,f10(a1),a37)
% 1.96/1.91 [458]P8(a1,f10(a1),a31)
% 1.96/1.91 [459]P8(a1,f10(a1),a32)
% 1.96/1.91 [472]P8(a70,f10(a70),f3(a70))
% 1.96/1.91 [473]P7(a70,f10(a70),f3(a70))
% 1.96/1.91 [574]~E(f10(a69),a78)
% 1.96/1.91 [575]~E(f10(a2),a83)
% 1.96/1.91 [576]~E(f10(a2),a76)
% 1.96/1.91 [577]~E(f3(a2),a4)
% 1.96/1.91 [578]~E(f10(a2),a4)
% 1.96/1.91 [579]~E(f10(a69),a39)
% 1.96/1.91 [580]~E(f10(a2),a47)
% 1.96/1.91 [581]~E(f10(a1),f3(a1))
% 1.96/1.91 [582]~E(f10(a70),f3(a70))
% 1.96/1.91 [591]~P9(a2,a2,f15(a2,a79))
% 1.96/1.91 [592]~P9(a2,a2,f15(a2,a73))
% 1.96/1.91 [594]~P9(a2,a2,f15(a2,a80))
% 1.96/1.91 [427]E(f9(f3(a1)),f3(a69))
% 1.96/1.91 [428]E(f9(f10(a1)),f10(a69))
% 1.96/1.91 [429]E(f25(f3(a1)),f3(a69))
% 1.96/1.91 [430]E(f25(f10(a1)),f10(a69))
% 1.96/1.91 [431]E(f26(a1,f10(a1)),f10(a1))
% 1.96/1.91 [432]E(f11(a70,f10(a70)),f10(a70))
% 1.96/1.91 [433]E(f27(a69,f3(a69)),f3(a1))
% 1.96/1.91 [434]E(f27(a69,f10(a69)),f10(a1))
% 1.96/1.91 [477]E(f54(f15(a2,a80),f10(a2)),f54(f15(a2,a73),a75))
% 1.96/1.91 [504]P8(a69,f13(a69,a78,f3(a69)),f5(a2,a73))
% 1.96/1.91 [526]P7(a1,f54(f54(f12(a1),a81),f28(a2,a83)),f54(f54(f12(a1),f3(a1)),f28(a2,a83)))
% 1.96/1.91 [555]E(f54(f15(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),f10(a2)),f3(a2))
% 1.96/1.91 [557]E(f8(a2,f13(a2,f3(a2),f54(f54(f12(a2),f54(f54(f21(a2),a83),a78)),a76)),f3(a2)),f8(a2,f10(a2),f3(a2)))
% 1.96/1.91 [583]~E(f54(f15(a2,a73),a75),f10(a2))
% 1.96/1.91 [584]~E(f54(f15(a2,a80),f10(a2)),f10(a2))
% 1.96/1.91 [590]~E(f13(a69,a78,f3(a69)),f5(a2,a73))
% 1.96/1.91 [469]E(f29(a2,f11(a1,f3(a1))),f11(a2,f3(a2)))
% 1.96/1.91 [470]E(f54(f54(f12(a2),a4),a4),f11(a2,f3(a2)))
% 1.96/1.91 [491]P8(a1,f10(a1),f54(f54(f21(a1),a81),a78))
% 1.96/1.91 [540]P7(a1,f28(a2,f54(f54(f12(a2),f29(a2,a81)),a83)),f28(a2,a83))
% 1.96/1.91 [514]E(f54(f54(f12(a2),f54(f54(f21(a2),a83),a78)),a76),f11(a2,f3(a2)))
% 1.96/1.91 [541]E(f5(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),f5(a2,a80))
% 1.96/1.91 [550]E(f5(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),f13(a69,f13(a69,f5(a2,a82),a78),f3(a69)))
% 1.96/1.91 [551]E(f5(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),f13(a69,f13(a69,f5(a2,a38),a39),f3(a69)))
% 1.96/1.91 [554]E(f5(a2,f18(a2,f3(a2),f16(a2,a76,f8(a69,a78,f3(a69))))),f13(a69,a78,f3(a69)))
% 1.96/1.91 [600]~P9(a2,a2,f15(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)))
% 1.96/1.91 [601]~P9(a2,a2,f15(a2,f18(a2,f3(a2),f16(a2,a76,f8(a69,a78,f3(a69))))))
% 1.96/1.91 [543]E(f13(a2,f3(a2),f54(f54(f12(a2),f54(f54(f21(a2),a83),a78)),a76)),f10(a2))
% 1.96/1.91 [544]E(f13(a2,f3(a2),f54(f54(f12(a2),f54(f54(f21(a2),a55),a78)),a76)),f10(a2))
% 1.96/1.91 [558]E(f54(f15(a2,f18(a2,f3(a2),f16(a2,a76,f8(a69,a78,f3(a69))))),a40),f10(a2))
% 1.96/1.91 [560]P8(a1,a81,f26(a1,f54(f54(f12(a1),f54(f54(f21(a1),f28(a2,a83)),f13(a69,a78,f3(a69)))),a74)))
% 1.96/1.91 [561]P8(a1,a37,f26(a1,f54(f54(f12(a1),f54(f54(f21(a1),f28(a2,a83)),f13(a69,a78,f3(a69)))),a74)))
% 1.96/1.91 [562]P8(a1,f10(a1),f26(a1,f54(f54(f12(a1),f54(f54(f21(a1),f28(a2,a83)),f13(a69,a78,f3(a69)))),a74)))
% 1.96/1.91 [563]P8(a1,f54(f54(f12(a1),a81),f54(f54(f12(a1),f54(f54(f21(a1),f28(a2,a83)),f13(a69,a78,f3(a69)))),a74)),f3(a1))
% 1.96/1.91 [570]E(f13(a2,f13(a2,f3(a2),f54(f54(f12(a2),f54(f54(f21(a2),f29(a2,a81)),a78)),f54(f54(f12(a2),f54(f54(f21(a2),a83),a78)),a76))),f54(f54(f12(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f54(f54(f12(a2),f29(a2,a81)),a83))),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83)))),f13(a2,f29(a2,f8(a1,f3(a1),f54(f54(f21(a1),a81),a78))),f54(f54(f12(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f54(f54(f12(a2),f29(a2,a81)),a83))),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83)))))
% 1.96/1.91 [602]~E(f54(f15(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),a41),f54(f15(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),a44))
% 1.96/1.91 [573]P7(a1,f28(a2,f13(a2,f29(a2,f8(a1,f3(a1),f54(f54(f21(a1),a81),a78))),f54(f54(f12(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f54(f54(f12(a2),f29(a2,a81)),a83))),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83))))),f13(a1,f28(a2,f29(a2,f8(a1,f3(a1),f54(f54(f21(a1),a81),a78)))),f28(a2,f54(f54(f12(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f54(f54(f12(a2),f29(a2,a81)),a83))),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83))))))
% 1.96/1.91 [603]~P8(a1,f54(f54(f12(a1),f54(f54(f21(a1),a81),a78)),f54(f54(f12(a1),a81),f54(f54(f12(a1),f54(f54(f21(a1),f28(a2,a83)),f13(a69,a78,f3(a69)))),a74))),f54(f54(f12(a1),f54(f54(f21(a1),a81),a78)),f3(a1)))
% 1.96/1.91 [568]E(f13(a2,f29(a2,f8(a1,f3(a1),f54(f54(f21(a1),a81),a78))),f54(f54(f12(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f54(f54(f12(a2),f29(a2,a81)),a83))),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83)))),f13(a2,f3(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f13(a2,a76,f54(f54(f12(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83)))))))
% 1.96/1.91 [569]E(f13(a2,f13(a2,f3(a2),f54(f54(f12(a2),f54(f54(f21(a2),f29(a2,a81)),a78)),f54(f54(f12(a2),f54(f54(f21(a2),a83),a78)),a76))),f54(f54(f12(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f54(f54(f12(a2),f29(a2,a81)),a83))),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83)))),f13(a2,f3(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f13(a2,a76,f54(f54(f12(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83)))))))
% 1.96/1.91 [571]E(f28(a2,f13(a2,f29(a2,f8(a1,f3(a1),f54(f54(f21(a1),a81),a78))),f54(f54(f12(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f54(f54(f12(a2),f29(a2,a81)),a83))),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83))))),f28(a2,f13(a2,f3(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f13(a2,a76,f54(f54(f12(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83))))))))
% 1.96/1.91 [572]P7(a1,f28(a2,f13(a2,f3(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f13(a2,a76,f54(f54(f12(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83))))))),f13(a1,f7(a1,f8(a1,f3(a1),f54(f54(f21(a1),a81),a78))),f28(a2,f54(f54(f12(a2),f54(f54(f12(a2),f54(f54(f21(a2),f54(f54(f12(a2),f29(a2,a81)),a83)),a78)),f54(f54(f12(a2),f29(a2,a81)),a83))),f54(f15(a2,a82),f54(f54(f12(a2),f29(a2,a81)),a83))))))
% 1.96/1.91 [447]P7(a1,x4471,x4471)
% 1.96/1.91 [448]P7(a69,x4481,x4481)
% 1.96/1.91 [449]P7(a70,x4491,x4491)
% 1.96/1.91 [586]~P8(a69,x5861,x5861)
% 1.96/1.91 [439]E(f28(a1,x4391),f7(a1,x4391))
% 1.96/1.91 [461]E(f8(a69,x4611,x4611),f10(a69))
% 1.96/1.91 [463]P7(a69,f10(a69),x4631)
% 1.96/1.91 [479]P7(a1,f10(a1),f27(a69,x4791))
% 1.96/1.91 [589]~P8(a69,x5891,f10(a69))
% 1.96/1.91 [595]~P8(a1,f27(a69,x5951),f10(a1))
% 1.96/1.91 [440]E(f9(f27(a69,x4401)),x4401)
% 1.96/1.91 [441]E(f25(f27(a69,x4411)),x4411)
% 1.96/1.91 [442]E(f11(a70,f11(a70,x4421)),x4421)
% 1.96/1.91 [443]E(f7(a1,f27(a69,x4431)),f27(a69,x4431))
% 1.96/1.91 [444]E(f54(f54(f12(a69),x4441),f3(a69)),x4441)
% 1.96/1.91 [445]E(f54(f54(f12(a70),x4451),f3(a70)),x4451)
% 1.96/1.91 [446]E(f54(f54(f12(a69),x4461),f10(a69)),f10(a69))
% 1.96/1.91 [464]E(f13(a69,x4641,f10(a69)),x4641)
% 1.96/1.91 [465]E(f13(a70,x4651,f10(a70)),x4651)
% 1.96/1.91 [466]E(f8(a69,x4661,f10(a69)),x4661)
% 1.96/1.91 [467]E(f13(a69,f10(a69),x4671),x4671)
% 1.96/1.91 [468]E(f13(a70,f10(a70),x4681),x4681)
% 1.96/1.91 [471]E(f8(a69,f10(a69),x4711),f10(a69))
% 1.96/1.91 [478]E(f13(a70,f11(a70,x4781),x4781),f10(a70))
% 1.96/1.91 [480]P7(a1,x4801,f27(a69,f9(x4801)))
% 1.96/1.91 [494]P7(a1,f11(a1,f28(a2,x4941)),f28(a2,x4941))
% 1.96/1.91 [501]E(f54(f15(a2,a73),f13(a2,a75,x5011)),f54(f15(a2,a80),x5011))
% 1.96/1.91 [502]E(f54(f15(a2,a73),f13(a2,a75,x5021)),f54(f15(a2,a30),x5021))
% 1.96/1.91 [503]E(f54(f15(a2,a73),f13(a2,a75,x5031)),f54(f15(a2,a36),x5031))
% 1.96/1.91 [509]P8(a1,f8(a1,x5091,f3(a1)),f27(a69,f25(x5091)))
% 1.96/1.91 [510]P8(a1,f10(a1),f13(a1,f3(a1),f7(a1,x5101)))
% 1.96/1.91 [515]P8(a1,x5151,f13(a1,f27(a69,f25(x5151)),f3(a1)))
% 1.96/1.91 [599]~P8(a1,f13(a1,f7(a1,x5991),f3(a1)),x5991)
% 1.96/1.91 [450]E(f54(f54(f12(a1),f3(a1)),x4501),x4501)
% 1.96/1.91 [451]E(f54(f54(f12(a69),f3(a69)),x4511),x4511)
% 1.96/1.91 [452]E(f54(f54(f12(a70),f3(a70)),x4521),x4521)
% 1.96/1.91 [460]E(f54(f54(f12(a69),f10(a69)),x4601),f10(a69))
% 1.96/1.91 [493]P7(a69,x4931,f54(f54(f12(a69),x4931),x4931))
% 1.96/1.91 [530]P7(a1,f28(a2,f54(f15(a2,a73),a75)),f28(a2,f54(f15(a2,a73),x5301)))
% 1.96/1.91 [535]P7(a1,f28(a2,f54(f15(a2,a80),f10(a2))),f28(a2,f54(f15(a2,a73),x5351)))
% 1.96/1.91 [564]E(f54(f54(f12(a2),f54(f15(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),x5641)),f54(f15(a2,a80),f10(a2))),f54(f15(a2,a80),x5641))
% 1.96/1.91 [598]~E(f13(a70,f13(a70,f3(a70),x5981),x5981),f10(a70))
% 1.96/1.91 [492]E(f54(f54(f12(a2),a4),f54(f54(f12(a2),a4),x4921)),f11(a2,x4921))
% 1.96/1.91 [527]P7(a69,x5271,f54(f54(f12(a69),x5271),f54(f54(f12(a69),x5271),x5271)))
% 1.96/1.91 [566]E(f13(a2,f54(f15(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),f10(a2)),f54(f54(f12(a2),f54(f54(f21(a2),x5661),a78)),f54(f15(a2,f18(a2,a76,a82)),x5661))),f54(f15(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),x5661))
% 1.96/1.91 [567]E(f13(a2,f54(f15(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),f10(a2)),f54(f54(f12(a2),f54(f54(f21(a2),x5671),a39)),f54(f15(a2,f18(a2,a47,a38)),x5671))),f54(f15(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),x5671))
% 1.96/1.91 [484]E(f13(a69,x4841,x4842),f13(a69,x4842,x4841))
% 1.96/1.91 [485]E(f13(a70,x4851,x4852),f13(a70,x4852,x4851))
% 1.96/1.91 [495]P7(a69,x4951,f13(a69,x4952,x4951))
% 1.96/1.91 [496]P7(a69,x4961,f13(a69,x4961,x4962))
% 1.96/1.91 [497]P7(a69,f8(a69,x4971,x4972),x4971)
% 1.96/1.91 [596]~P8(a69,f13(a69,x5961,x5962),x5962)
% 1.96/1.91 [597]~P8(a69,f13(a69,x5971,x5972),x5971)
% 1.96/1.91 [487]E(f13(a1,x4871,f11(a1,x4872)),f8(a1,x4871,x4872))
% 1.96/1.91 [488]E(f13(a2,x4881,f11(a2,x4882)),f8(a2,x4881,x4882))
% 1.96/1.91 [490]E(f13(a70,x4901,f11(a70,x4902)),f8(a70,x4901,x4902))
% 1.96/1.91 [498]E(f8(a69,f13(a69,x4981,x4982),x4982),x4981)
% 1.96/1.91 [499]E(f8(a69,f13(a69,x4991,x4992),x4991),x4992)
% 1.96/1.91 [500]E(f8(a69,x5001,f13(a69,x5001,x5002)),f10(a69))
% 1.96/1.91 [511]E(f13(a70,f11(a70,x5111),f11(a70,x5112)),f11(a70,f13(a70,x5111,x5112)))
% 1.96/1.91 [512]E(f13(a1,f27(a69,x5121),f27(a69,x5122)),f27(a69,f13(a69,x5121,x5122)))
% 1.96/1.91 [552]P7(a1,f28(a2,x5521),f13(a1,f28(a2,f13(a2,x5521,x5522)),f28(a2,x5522)))
% 1.96/1.91 [553]P7(a1,f8(a1,f28(a2,f13(a2,x5531,x5532)),f28(a2,x5531)),f28(a2,x5532))
% 1.96/1.91 [481]E(f54(f54(f12(a1),x4811),x4812),f54(f54(f12(a1),x4812),x4811))
% 1.96/1.91 [482]E(f54(f54(f12(a69),x4821),x4822),f54(f54(f12(a69),x4822),x4821))
% 1.96/1.91 [483]E(f54(f54(f12(a70),x4831),x4832),f54(f54(f12(a70),x4832),x4831))
% 1.96/1.91 [516]P7(a70,f10(a70),f54(f54(f21(a70),f7(a70,x5161)),x5162))
% 1.96/1.91 [528]E(f7(a1,f13(a1,x5281,f11(a1,x5282))),f7(a1,f13(a1,x5282,f11(a1,x5281))))
% 1.96/1.91 [506]E(f54(f54(f21(a1),f27(a69,x5061)),x5062),f27(a69,f54(f54(f21(a69),x5061),x5062)))
% 1.96/1.91 [507]E(f29(a2,f54(f54(f21(a1),x5071),x5072)),f54(f54(f21(a2),f29(a2,x5071)),x5072))
% 1.96/1.91 [508]E(f54(f54(f12(a70),f11(a70,x5081)),x5082),f11(a70,f54(f54(f12(a70),x5081),x5082)))
% 1.96/1.91 [513]E(f54(f54(f12(a1),f27(a69,x5131)),f27(a69,x5132)),f27(a69,f54(f54(f12(a69),x5131),x5132)))
% 1.96/1.91 [529]P7(a1,f11(a1,f54(f54(f12(a1),x5291),x5291)),f54(f54(f12(a1),x5292),x5292))
% 1.96/1.91 [518]E(f13(a69,x5181,f13(a69,x5182,x5183)),f13(a69,x5182,f13(a69,x5181,x5183)))
% 1.96/1.91 [519]E(f13(a70,x5191,f13(a70,x5192,x5193)),f13(a70,x5192,f13(a70,x5191,x5193)))
% 1.96/1.91 [520]E(f13(a69,f13(a69,x5201,x5202),x5203),f13(a69,x5201,f13(a69,x5202,x5203)))
% 1.96/1.91 [521]E(f13(a70,f13(a70,x5211,x5212),x5213),f13(a70,x5211,f13(a70,x5212,x5213)))
% 1.96/1.91 [522]E(f8(a69,f8(a69,x5221,x5222),x5223),f8(a69,x5221,f13(a69,x5222,x5223)))
% 1.96/1.91 [523]E(f8(a69,f8(a69,x5231,x5232),x5233),f8(a69,f8(a69,x5231,x5233),x5232))
% 1.96/1.91 [524]E(f8(a69,f13(a69,x5241,x5242),f13(a69,x5243,x5242)),f8(a69,x5241,x5243))
% 1.96/1.91 [525]E(f8(a69,f13(a69,x5251,x5252),f13(a69,x5251,x5253)),f8(a69,x5252,x5253))
% 1.96/1.91 [536]E(f13(a69,f54(f54(f12(a69),x5361),x5362),f54(f54(f12(a69),x5361),x5363)),f54(f54(f12(a69),x5361),f13(a69,x5362,x5363)))
% 1.96/1.91 [537]E(f8(a69,f54(f54(f12(a69),x5371),x5372),f54(f54(f12(a69),x5371),x5373)),f54(f54(f12(a69),x5371),f8(a69,x5372,x5373)))
% 1.96/1.91 [538]E(f13(a70,f54(f54(f12(a70),x5381),x5382),f54(f54(f12(a70),x5381),x5383)),f54(f54(f12(a70),x5381),f13(a70,x5382,x5383)))
% 1.96/1.91 [539]E(f8(a70,f54(f54(f12(a70),x5391),x5392),f54(f54(f12(a70),x5391),x5393)),f54(f54(f12(a70),x5391),f8(a70,x5392,x5393)))
% 1.96/1.91 [542]E(f54(f54(f12(a70),f54(f54(f21(a70),x5421),x5422)),f54(f54(f21(a70),x5421),x5423)),f54(f54(f21(a70),x5421),f13(a69,x5422,x5423)))
% 1.96/1.91 [545]E(f13(a1,f54(f54(f12(a1),x5451),x5452),f54(f54(f12(a1),x5453),x5452)),f54(f54(f12(a1),f13(a1,x5451,x5453)),x5452))
% 1.96/1.91 [546]E(f13(a69,f54(f54(f12(a69),x5461),x5462),f54(f54(f12(a69),x5463),x5462)),f54(f54(f12(a69),f13(a69,x5461,x5463)),x5462))
% 1.96/1.91 [547]E(f8(a69,f54(f54(f12(a69),x5471),x5472),f54(f54(f12(a69),x5473),x5472)),f54(f54(f12(a69),f8(a69,x5471,x5473)),x5472))
% 1.96/1.91 [548]E(f13(a70,f54(f54(f12(a70),x5481),x5482),f54(f54(f12(a70),x5483),x5482)),f54(f54(f12(a70),f13(a70,x5481,x5483)),x5482))
% 1.96/1.91 [549]E(f8(a70,f54(f54(f12(a70),x5491),x5492),f54(f54(f12(a70),x5493),x5492)),f54(f54(f12(a70),f8(a70,x5491,x5493)),x5492))
% 1.96/1.91 [531]E(f54(f54(f21(a70),f54(f54(f21(a70),x5311),x5312)),x5313),f54(f54(f21(a70),x5311),f54(f54(f12(a69),x5312),x5313)))
% 1.96/1.91 [532]E(f54(f54(f12(a1),f54(f54(f12(a1),x5321),x5322)),x5323),f54(f54(f12(a1),x5321),f54(f54(f12(a1),x5322),x5323)))
% 1.96/1.91 [533]E(f54(f54(f12(a69),f54(f54(f12(a69),x5331),x5332)),x5333),f54(f54(f12(a69),x5331),f54(f54(f12(a69),x5332),x5333)))
% 1.96/1.91 [534]E(f54(f54(f12(a70),f54(f54(f12(a70),x5341),x5342)),x5343),f54(f54(f12(a70),x5341),f54(f54(f12(a70),x5342),x5343)))
% 1.96/1.91 [517]E(f54(f54(f22(x5171,x5172,x5173),x5174),f10(a69)),x5172)
% 1.96/1.91 [559]P7(a1,f7(a1,f13(a1,f13(a1,x5591,x5592),f13(a1,f11(a1,x5593),f11(a1,x5594)))),f13(a1,f7(a1,f13(a1,x5591,f11(a1,x5593))),f7(a1,f13(a1,x5592,f11(a1,x5594)))))
% 1.96/1.91 [556]E(f13(a69,f54(f54(f12(a69),x5561),x5562),f13(a69,f54(f54(f12(a69),x5563),x5562),x5564)),f13(a69,f54(f54(f12(a69),f13(a69,x5561,x5563)),x5562),x5564))
% 1.96/1.91 [604]~P57(x6041)+P46(f72(x6041))
% 1.96/1.91 [605]~P50(x6051)+P2(f72(x6051))
% 1.96/1.91 [606]~P50(x6061)+P50(f72(x6061))
% 1.96/1.91 [607]~P50(x6071)+P26(f72(x6071))
% 1.96/1.91 [608]~P54(x6081)+P63(f72(x6081))
% 1.96/1.91 [609]~P59(x6091)+P68(f72(x6091))
% 1.96/1.91 [610]~P50(x6101)+P69(f72(x6101))
% 1.96/1.91 [611]~P59(x6111)+P81(f72(x6111))
% 1.96/1.91 [612]~P59(x6121)+P70(f72(x6121))
% 1.96/1.91 [613]~P54(x6131)+P78(f72(x6131))
% 1.96/1.91 [614]~P50(x6141)+P3(f72(x6141))
% 1.96/1.91 [615]~P57(x6151)+P64(f72(x6151))
% 1.96/1.91 [616]~P57(x6161)+P65(f72(x6161))
% 1.96/1.91 [617]~P57(x6171)+P57(f72(x6171))
% 1.96/1.91 [618]~P59(x6181)+P79(f72(x6181))
% 1.96/1.91 [619]~P54(x6191)+P51(f72(x6191))
% 1.96/1.91 [620]~P54(x6201)+P80(f72(x6201))
% 1.96/1.91 [621]~P57(x6211)+P71(f72(x6211))
% 1.96/1.91 [622]~P57(x6221)+P72(f72(x6221))
% 1.96/1.91 [623]~P57(x6231)+P74(f72(x6231))
% 1.96/1.91 [624]~P57(x6241)+P73(f72(x6241))
% 1.96/1.91 [625]~P57(x6251)+P61(f72(x6251))
% 1.96/1.91 [626]~P57(x6261)+P62(f72(x6261))
% 1.96/1.91 [627]~P57(x6271)+P67(f72(x6271))
% 1.96/1.91 [628]~P57(x6281)+P58(f72(x6281))
% 1.96/1.91 [629]~P57(x6291)+P66(f72(x6291))
% 1.96/1.91 [630]~P57(x6301)+P27(f72(x6301))
% 1.96/1.91 [631]~P34(x6311)+P34(f72(x6311))
% 1.96/1.91 [632]~P54(x6321)+P14(f72(x6321))
% 1.96/1.91 [633]~P20(x6331)+P17(f72(x6331))
% 1.96/1.91 [634]~P20(x6341)+P18(f72(x6341))
% 1.96/1.91 [635]~P21(x6351)+P15(f72(x6351))
% 1.96/1.91 [636]~P50(x6361)+P28(f72(x6361))
% 1.96/1.91 [637]~P21(x6371)+P21(f72(x6371))
% 1.96/1.91 [638]~P21(x6381)+P22(f72(x6381))
% 1.96/1.91 [639]~P57(x6391)+P23(f72(x6391))
% 1.96/1.91 [640]~P57(x6401)+P29(f72(x6401))
% 1.96/1.91 [641]~P57(x6411)+P30(f72(x6411))
% 1.96/1.91 [642]~P57(x6421)+P33(f72(x6421))
% 1.96/1.91 [643]~P16(x6431)+P24(f72(x6431))
% 1.96/1.91 [644]~P16(x6441)+P16(f72(x6441))
% 1.96/1.91 [645]~P52(x6451)+P52(f72(x6451))
% 1.96/1.91 [646]~P57(x6461)+P31(f72(x6461))
% 1.96/1.91 [647]~P53(x6471)+P76(f72(x6471))
% 1.96/1.91 [648]~P59(x6481)+P59(f72(x6481))
% 1.96/1.91 [649]~P52(x6491)+P77(f72(x6491))
% 1.96/1.91 [650]~P57(x6501)+P32(f72(x6501))
% 1.96/1.91 [651]~P57(x6511)+P75(f72(x6511))
% 1.96/1.91 [652]~P57(x6521)+P19(f72(x6521))
% 1.96/1.91 [653]~P54(x6531)+P54(f72(x6531))
% 1.96/1.91 [654]~P57(x6541)+P37(f72(x6541))
% 1.96/1.91 [655]~P53(x6551)+P53(f72(x6551))
% 1.96/1.91 [656]~P57(x6561)+P38(f72(x6561))
% 1.96/1.91 [657]~P57(x6571)+P39(f72(x6571))
% 1.96/1.91 [658]~P57(x6581)+P40(f72(x6581))
% 1.96/1.91 [659]~P57(x6591)+P43(f72(x6591))
% 1.96/1.91 [660]~P16(x6601)+P25(f72(x6601))
% 1.96/1.91 [661]~P16(x6611)+P35(f72(x6611))
% 1.96/1.91 [662]~P57(x6621)+P36(f72(x6621))
% 1.96/1.91 [663]~P50(x6631)+P60(f72(x6631))
% 1.96/1.91 [664]~P20(x6641)+P20(f72(x6641))
% 1.96/1.91 [666]~P69(x6661)+~E(f10(x6661),f3(x6661))
% 1.96/1.91 [667]~E(x6671,f10(a69))+E(f27(a69,x6671),f10(a1))
% 1.96/1.91 [668]E(x6681,f10(a69))+~E(f27(a69,x6681),f10(a1))
% 1.96/1.91 [746]E(x7461,f10(a69))+P8(a69,f10(a69),x7461)
% 1.96/1.91 [785]~P1(x7851)+P8(a1,f10(a1),f53(x7851))
% 1.96/1.91 [792]E(f7(a1,x7921),x7921)+P8(a1,x7921,f10(a1))
% 1.96/1.91 [793]E(f7(a70,x7931),x7931)+P8(a70,x7931,f10(a70))
% 1.96/1.91 [802]~P46(x8021)+P8(x8021,f10(x8021),f3(x8021))
% 1.96/1.91 [803]~P46(x8031)+P7(x8031,f10(x8031),f3(x8031))
% 1.96/1.91 [830]~E(x8301,f10(a70))+P8(a70,f7(a70,x8301),f3(a70))
% 1.96/1.91 [831]~E(x8311,f10(a69))+P7(a1,f27(a69,x8311),f10(a1))
% 1.96/1.91 [872]E(x8721,f10(a69))+~P7(a69,x8721,f10(a69))
% 1.96/1.91 [881]E(f9(x8811),f10(a69))+~P7(a1,x8811,f10(a1))
% 1.96/1.91 [882]E(f25(x8821),f10(a69))+~P7(a1,x8821,f10(a1))
% 1.96/1.91 [928]~P46(x9281)+~P8(x9281,f3(x9281),f10(x9281))
% 1.96/1.91 [929]~P46(x9291)+~P7(x9291,f3(x9291),f10(x9291))
% 1.96/1.91 [931]E(f11(a1,x9311),f7(a1,x9311))+~P8(a1,x9311,f10(a1))
% 1.96/1.91 [932]E(f11(a70,x9321),f7(a70,x9321))+~P8(a70,x9321,f10(a70))
% 1.96/1.91 [973]E(x9731,f10(a69))+~P7(a1,f27(a69,x9731),f10(a1))
% 1.96/1.91 [974]E(x9741,f10(a70))+~P8(a70,f7(a70,x9741),f3(a70))
% 1.96/1.91 [1012]~P7(a70,f3(a70),x10121)+P8(a70,f10(a70),x10121)
% 1.96/1.91 [1013]~P8(a70,f10(a70),x10131)+P7(a70,f3(a70),x10131)
% 1.96/1.91 [1016]P8(a1,f60(x10161),x10161)+~P8(a1,f10(a1),x10161)
% 1.96/1.91 [1043]~P7(a1,x10431,f3(a1))+P7(a69,f9(x10431),f3(a69))
% 1.96/1.91 [1044]~P8(a1,f10(a1),x10441)+P8(a1,f60(x10441),f3(a1))
% 1.96/1.91 [1045]~P8(a1,f10(a1),x10451)+P8(a1,f10(a1),f60(x10451))
% 1.96/1.91 [1046]~P7(a1,f3(a1),x10461)+P7(a69,f3(a69),f25(x10461))
% 1.96/1.91 [1051]~P7(a69,f9(x10511),f3(a69))+P7(a1,x10511,f3(a1))
% 1.96/1.91 [1052]~P7(a69,f3(a69),f25(x10521))+P7(a1,f3(a1),x10521)
% 1.96/1.91 [1059]~P8(a69,f10(a69),x10591)+P8(a1,f10(a1),f27(a69,x10591))
% 1.96/1.91 [1101]P8(a69,f10(a69),x11011)+~P8(a1,f10(a1),f27(a69,x11011))
% 1.96/1.91 [669]~P44(x6691)+E(f29(x6691,f3(a1)),f3(x6691))
% 1.96/1.91 [670]~P44(x6701)+E(f29(x6701,f10(a1)),f10(x6701))
% 1.96/1.91 [671]~P48(x6711)+E(f28(x6711,f3(x6711)),f3(a1))
% 1.96/1.91 [672]~P49(x6721)+E(f28(x6721,f10(x6721)),f10(a1))
% 1.96/1.91 [676]~P56(x6761)+E(f26(x6761,f3(x6761)),f3(x6761))
% 1.96/1.91 [677]~P55(x6771)+E(f26(x6771,f10(x6771)),f10(x6771))
% 1.96/1.91 [678]~P5(x6781)+E(f26(x6781,f10(x6781)),f10(x6781))
% 1.96/1.91 [679]~P24(x6791)+E(f11(x6791,f10(x6791)),f10(x6791))
% 1.96/1.91 [680]~P57(x6801)+E(f7(x6801,f3(x6801)),f3(x6801))
% 1.96/1.91 [681]~P32(x6811)+E(f7(x6811,f10(x6811)),f10(x6811))
% 1.96/1.91 [682]~P48(x6821)+E(f14(x6821,f3(x6821)),f3(x6821))
% 1.96/1.91 [683]~P49(x6831)+E(f14(x6831,f10(x6831)),f10(x6831))
% 1.96/1.91 [684]~P36(x6841)+E(f14(x6841,f10(x6841)),f10(x6841))
% 1.96/1.91 [742]~P57(x7421)+~P10(x7421,f10(f72(x7421)))
% 1.96/1.91 [814]~P26(x8141)+E(f22(x8141,f3(x8141),f12(x8141)),f21(x8141))
% 1.96/1.91 [1075]~P7(a1,f10(a1),x10751)+P8(a1,x10751,f27(a69,f57(x10751)))
% 1.96/1.91 [1076]~P7(a1,f10(a1),x10761)+P7(a1,f27(a69,f25(x10761)),x10761)
% 1.96/1.91 [1151]~P46(x11511)+P8(x11511,f10(x11511),f13(x11511,f3(x11511),f3(x11511)))
% 1.96/1.91 [1282]~P7(a70,f10(a70),x12821)+P8(a70,f10(a70),f13(a70,f3(a70),x12821))
% 1.96/1.91 [736]~P16(x7361)+E(f11(f72(x7361),f10(f72(x7361))),f10(f72(x7361)))
% 1.96/1.91 [883]~P50(x8831)+E(f18(x8831,f3(x8831),f10(f72(x8831))),f3(f72(x8831)))
% 1.96/1.91 [884]~P34(x8841)+E(f18(x8841,f10(x8841),f10(f72(x8841))),f10(f72(x8841)))
% 1.96/1.91 [899]E(x8991,f10(a1))+E(f54(f54(f12(a1),f26(a1,x8991)),x8991),f3(a1))
% 1.96/1.91 [1026]E(x10261,f10(a1))+P8(a1,f10(a1),f54(f54(f12(a1),x10261),x10261))
% 1.96/1.91 [1235]~E(x12351,f10(a1))+~P8(a1,f10(a1),f54(f54(f12(a1),x12351),x12351))
% 1.96/1.91 [1291]~P7(a1,f10(a1),x12911)+E(f9(f13(a1,x12911,f3(a1))),f13(a69,f9(x12911),f3(a69)))
% 1.96/1.91 [1292]~P7(a1,f10(a1),x12921)+E(f25(f13(a1,x12921,f3(a1))),f13(a69,f25(x12921),f3(a69)))
% 1.96/1.91 [1435]~P7(a1,f28(a2,x14351),f28(a2,a83))+P7(a1,f28(a2,f54(f15(a2,a82),x14351)),a74)
% 1.96/1.91 [1436]~P7(a1,f28(a2,x14361),f28(a2,a83))+P7(a1,f28(a2,f54(f15(a2,a82),x14361)),a31)
% 1.96/1.91 [1437]~P7(a1,f28(a2,x14371),f28(a2,a83))+P7(a1,f28(a2,f54(f15(a2,a82),x14371)),a32)
% 1.96/1.91 [1516]~P7(a1,f10(a1),x15161)+P7(a1,f27(a69,f8(a69,f57(x15161),f3(a69))),x15161)
% 1.96/1.91 [1601]~P8(a70,x16011,f10(a70))+P8(a70,f13(a70,f13(a70,f3(a70),x16011),x16011),f10(a70))
% 1.96/1.91 [1715]P8(a70,x17151,f10(a70))+~P8(a70,f13(a70,f13(a70,f3(a70),x17151),x17151),f10(a70))
% 1.96/1.91 [1805]~P8(a1,f28(a2,f54(f15(a2,a80),x18051)),f28(a2,f54(f15(a2,a80),f10(a2))))+P8(a1,f28(a2,f54(f15(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),x18051)),f3(a1))
% 1.96/1.91 [1808]P8(a1,f28(a2,f54(f15(a2,a80),x18081)),f28(a2,f54(f15(a2,a80),f10(a2))))+~P8(a1,f28(a2,f54(f15(a2,f23(a2,f26(a2,f54(f15(a2,a80),f10(a2))),a80)),x18081)),f3(a1))
% 1.96/1.91 [737]~E(x7371,x7372)+P7(a1,x7371,x7372)
% 1.96/1.91 [740]~E(x7401,x7402)+P7(a69,x7401,x7402)
% 1.96/1.91 [756]~P38(x7561)+P7(x7561,x7562,x7562)
% 1.96/1.91 [840]~E(x8401,x8402)+~P8(a1,x8401,x8402)
% 1.96/1.91 [845]~E(x8451,x8452)+~P8(a69,x8451,x8452)
% 1.96/1.91 [846]~E(x8461,x8462)+~P8(a70,x8461,x8462)
% 1.96/1.91 [876]~P8(x8761,x8762,x8762)+~P38(x8761)
% 1.96/1.91 [916]P7(a1,x9162,x9161)+P7(a1,x9161,x9162)
% 1.96/1.91 [917]P7(a69,x9172,x9171)+P7(a69,x9171,x9172)
% 1.96/1.91 [918]P7(a70,x9182,x9181)+P7(a70,x9181,x9182)
% 1.96/1.91 [982]~P8(a1,x9821,x9822)+P7(a1,x9821,x9822)
% 1.96/1.91 [987]~P8(a69,x9871,x9872)+P7(a69,x9871,x9872)
% 1.96/1.91 [988]~P8(a70,x9881,x9882)+P7(a70,x9881,x9882)
% 1.96/1.91 [697]~P38(x6972)+P38(f77(x6971,x6972))
% 1.96/1.91 [698]~P39(x6982)+P39(f77(x6981,x6982))
% 1.96/1.91 [699]~P43(x6992)+P43(f77(x6991,x6992))
% 1.96/1.91 [700]~P41(x7002)+P41(f77(x7001,x7002))
% 1.96/1.91 [701]~P25(x7012)+P25(f77(x7011,x7012))
% 1.96/1.91 [702]~P35(x7022)+P35(f77(x7021,x7022))
% 1.96/1.91 [714]E(x7141,x7142)+~E(f27(a69,x7141),f27(a69,x7142))
% 1.96/1.91 [765]~P24(x7651)+E(f8(x7651,x7652,x7652),f10(x7651))
% 1.96/1.91 [772]~P50(x7721)+P11(x7721,x7722,f10(x7721))
% 1.96/1.91 [790]P7(a70,x7902,x7901)+E(f17(x7901,x7902),f10(a70))
% 1.96/1.91 [813]~E(x8132,f11(a1,x8131))+E(f13(a1,x8131,x8132),f10(a1))
% 1.96/1.91 [847]~P32(x8471)+P7(x8471,x8472,f7(x8471,x8472))
% 1.96/1.91 [851]~E(f13(a69,x8512,x8511),x8512)+E(x8511,f10(a69))
% 1.96/1.91 [853]~P1(x8532)+P8(a1,f10(a1),f50(x8531,x8532))
% 1.96/1.91 [854]~P1(x8542)+P8(a1,f10(a1),f52(x8541,x8542))
% 1.96/1.91 [855]~P49(x8551)+P7(a1,f10(a1),f28(x8551,x8552))
% 1.96/1.91 [858]~P8(a69,x8582,x8581)+~E(x8581,f10(a69))
% 1.96/1.91 [865]E(x8651,f10(a69))+~E(f13(a69,x8652,x8651),f10(a69))
% 1.96/1.91 [866]E(x8661,f10(a69))+~E(f13(a69,x8661,x8662),f10(a69))
% 1.96/1.91 [877]~P32(x8771)+P7(x8771,f10(x8771),f7(x8771,x8772))
% 1.96/1.91 [905]E(x9051,f11(a1,x9052))+~E(f13(a1,x9052,x9051),f10(a1))
% 1.96/1.91 [933]~P32(x9331)+P7(x9331,f11(x9331,x9332),f7(x9331,x9332))
% 1.96/1.91 [980]~P49(x9801)+~P8(a1,f28(x9801,x9802),f10(a1))
% 1.96/1.91 [997]~P7(a69,x9971,x9972)+E(f8(a69,x9971,x9972),f10(a69))
% 1.96/1.91 [1004]P7(a69,x10041,x10042)+~E(f8(a69,x10041,x10042),f10(a69))
% 1.96/1.91 [1010]~P32(x10101)+~P8(x10101,f7(x10101,x10102),f10(x10101))
% 1.96/1.91 [1022]~P7(a1,x10221,x10222)+P7(a69,f9(x10221),f9(x10222))
% 1.96/1.91 [1023]~P7(a1,x10231,x10232)+P7(a69,f25(x10231),f25(x10232))
% 1.96/1.91 [1037]~P7(a70,x10372,x10371)+E(f8(a70,x10371,x10372),f17(x10371,x10372))
% 1.96/1.91 [1071]P7(a1,x10711,x10712)+~P7(a1,f7(a1,x10711),x10712)
% 1.96/1.91 [1079]P7(a69,x10791,f25(x10792))+~P7(a1,f27(a69,x10791),x10792)
% 1.96/1.91 [1080]P7(a69,f9(x10801),x10802)+~P7(a1,x10801,f27(a69,x10802))
% 1.96/1.91 [1107]~P8(a69,x11071,x11072)+P8(a1,f27(a69,x11071),f27(a69,x11072))
% 1.96/1.91 [1108]~P7(a69,x11081,x11082)+P7(a1,f27(a69,x11081),f27(a69,x11082))
% 1.96/1.91 [1150]~P7(a1,f7(a1,x11502),x11501)+P7(a1,f11(a1,x11501),x11502)
% 1.96/1.91 [1176]P8(a69,x11761,x11762)+~P8(a1,f27(a69,x11761),f27(a69,x11762))
% 1.96/1.91 [1177]P7(a69,x11771,x11772)+~P7(a1,f27(a69,x11771),f27(a69,x11772))
% 1.96/1.91 [1259]~P8(a69,x12592,x12591)+P8(a69,f10(a69),f8(a69,x12591,x12592))
% 1.96/1.91 [1260]~P8(a70,x12601,x12602)+P8(a70,f8(a70,x12601,x12602),f10(a70))
% 1.96/1.91 [1261]~P7(a1,x12611,x12612)+P7(a1,f8(a1,x12611,x12612),f10(a1))
% 1.96/1.91 [1318]~P8(a1,f11(a1,x13181),x13182)+P8(a1,f10(a1),f13(a1,x13181,x13182))
% 1.96/1.91 [1319]~P7(a1,f11(a1,x13191),x13192)+P7(a1,f10(a1),f13(a1,x13191,x13192))
% 1.96/1.91 [1320]~P8(a1,x13202,f11(a1,x13201))+P8(a1,f13(a1,x13201,x13202),f10(a1))
% 1.96/1.91 [1321]~P7(a1,x13212,f11(a1,x13211))+P7(a1,f13(a1,x13211,x13212),f10(a1))
% 1.96/1.91 [1356]P8(a69,x13561,x13562)+~P8(a69,f10(a69),f8(a69,x13562,x13561))
% 1.96/1.91 [1357]P8(a70,x13571,x13572)+~P8(a70,f8(a70,x13571,x13572),f10(a70))
% 1.96/1.91 [1358]P7(a1,x13581,x13582)+~P7(a1,f8(a1,x13581,x13582),f10(a1))
% 1.96/1.91 [1388]P8(a1,x13881,f11(a1,x13882))+~P8(a1,f13(a1,x13882,x13881),f10(a1))
% 1.96/1.91 [1389]P7(a1,x13891,f11(a1,x13892))+~P7(a1,f13(a1,x13892,x13891),f10(a1))
% 1.96/1.91 [1390]P8(a1,f11(a1,x13901),x13902)+~P8(a1,f10(a1),f13(a1,x13901,x13902))
% 1.96/1.91 [1391]P7(a1,f11(a1,x13911),x13912)+~P7(a1,f10(a1),f13(a1,x13911,x13912))
% 1.96/1.91 [721]~P55(x7211)+E(f26(x7211,f26(x7211,x7212)),x7212)
% 1.96/1.91 [722]~P24(x7221)+E(f11(x7221,f11(x7221,x7222)),x7222)
% 1.96/1.91 [723]~P41(x7231)+E(f11(x7231,f11(x7231,x7232)),x7232)
% 1.96/1.91 [743]~P48(x7431)+E(f28(x7431,f29(x7431,x7432)),f7(a1,x7432))
% 1.96/1.91 [744]~P49(x7441)+E(f7(a1,f28(x7441,x7442)),f28(x7441,x7442))
% 1.96/1.91 [752]~P49(x7521)+E(f28(x7521,f11(x7521,x7522)),f28(x7521,x7522))
% 1.96/1.91 [753]~P32(x7531)+E(f7(x7531,f11(x7531,x7532)),f7(x7531,x7532))
% 1.96/1.91 [754]~P32(x7541)+E(f7(x7541,f7(x7541,x7542)),f7(x7541,x7542))
% 1.96/1.91 [755]~P57(x7551)+E(f14(x7551,f14(x7551,x7552)),f14(x7551,x7552))
% 1.96/1.91 [758]~P2(x7581)+E(f54(f54(f21(x7581),x7582),f3(a69)),x7582)
% 1.96/1.91 [759]~P50(x7591)+E(f54(f54(f21(x7591),x7592),f3(a69)),x7592)
% 1.96/1.91 [766]~P2(x7661)+E(f54(f54(f12(x7661),x7662),f3(x7661)),x7662)
% 1.96/1.91 [767]~P50(x7671)+E(f54(f54(f12(x7671),x7672),f3(x7671)),x7672)
% 1.96/1.91 [768]~P3(x7681)+E(f54(f54(f12(x7681),x7682),f3(x7681)),x7682)
% 1.96/1.91 [769]~P50(x7691)+E(f54(f54(f21(x7691),x7692),f10(a69)),f3(x7691))
% 1.96/1.91 [770]~P26(x7701)+E(f54(f54(f21(x7701),x7702),f10(a69)),f3(x7701))
% 1.96/1.91 [773]~P50(x7731)+E(f13(x7731,x7732,f10(x7731)),x7732)
% 1.96/1.91 [774]~P21(x7741)+E(f13(x7741,x7742,f10(x7741)),x7742)
% 1.96/1.91 [775]~P22(x7751)+E(f13(x7751,x7752,f10(x7751)),x7752)
% 1.96/1.91 [776]~P24(x7761)+E(f8(x7761,x7762,f10(x7761)),x7762)
% 1.96/1.91 [777]~P50(x7771)+E(f13(x7771,f10(x7771),x7772),x7772)
% 1.96/1.91 [778]~P21(x7781)+E(f13(x7781,f10(x7781),x7782),x7782)
% 1.96/1.91 [779]~P22(x7791)+E(f13(x7791,f10(x7791),x7792),x7792)
% 1.96/1.91 [780]~P50(x7801)+E(f23(x7801,f3(x7801),x7802),x7802)
% 1.96/1.91 [787]~P1(x7871)+E(f54(f54(f12(x7871),x7872),f10(x7871)),f10(x7871))
% 1.96/1.91 [788]~P50(x7881)+E(f54(f54(f12(x7881),x7882),f10(x7881)),f10(x7881))
% 1.96/1.91 [789]~P63(x7891)+E(f54(f54(f12(x7891),x7892),f10(x7891)),f10(x7891))
% 1.96/1.91 [815]~P54(x8151)+E(f23(x8151,f10(x8151),x8152),f10(f72(x8151)))
% 1.96/1.91 [816]~P34(x8161)+E(f16(x8161,f10(x8161),x8162),f10(f72(x8161)))
% 1.96/1.91 [823]~P24(x8231)+E(f8(x8231,f10(x8231),x8232),f11(x8231,x8232))
% 1.96/1.91 [825]~E(x8251,x8252)+E(f13(a1,x8251,f11(a1,x8252)),f10(a1))
% 1.96/1.91 [827]~P48(x8271)+E(f14(x8271,f29(x8271,x8272)),f29(x8271,f14(a1,x8272)))
% 1.96/1.91 [828]~P44(x8281)+E(f29(x8281,f11(a1,x8282)),f11(x8281,f29(x8281,x8282)))
% 1.96/1.91 [837]~P55(x8371)+E(f26(x8371,f11(x8371,x8372)),f11(x8371,f26(x8371,x8372)))
% 1.96/1.91 [838]~P13(x8381)+E(f26(x8381,f7(x8381,x8382)),f7(x8381,f26(x8381,x8382)))
% 1.96/1.91 [839]~P49(x8391)+E(f14(x8391,f11(x8391,x8392)),f11(x8391,f14(x8391,x8392)))
% 1.96/1.91 [869]~P24(x8691)+E(f13(x8691,x8692,f11(x8691,x8692)),f10(x8691))
% 1.96/1.91 [870]~P24(x8701)+E(f13(x8701,f11(x8701,x8702),x8702),f10(x8701))
% 1.96/1.91 [871]~P16(x8711)+E(f13(x8711,f11(x8711,x8712),x8712),f10(x8711))
% 1.96/1.91 [902]~P57(x9021)+E(f54(f54(f12(x9021),x9022),f14(x9021,x9022)),f7(x9021,x9022))
% 1.96/1.91 [968]E(x9681,x9682)+~E(f13(a1,x9681,f11(a1,x9682)),f10(a1))
% 1.96/1.91 [972]E(x9721,x9722)+~E(f54(x9721,f45(x9722,x9721)),f54(x9722,f45(x9722,x9721)))
% 1.96/1.91 [992]~P57(x9921)+E(f54(f54(f12(x9921),f14(x9921,x9922)),f7(x9921,x9922)),x9922)
% 1.96/1.91 [1014]~P32(x10141)+P7(x10141,f11(x10141,f7(x10141,x10142)),f10(x10141))
% 1.96/1.91 [1054]~P7(a69,x10541,x10542)+E(f13(a69,x10541,f64(x10542,x10541)),x10542)
% 1.96/1.91 [1055]~P7(a69,x10551,x10552)+E(f13(a69,x10551,f65(x10552,x10551)),x10552)
% 1.96/1.91 [1058]~E(x10581,x10582)+P8(a70,x10581,f13(a70,x10582,f3(a70)))
% 1.96/1.91 [1100]~P46(x11001)+P8(x11001,x11002,f13(x11001,x11002,f3(x11001)))
% 1.96/1.91 [1180]P8(a69,x11802,x11801)+E(f13(a69,x11801,f8(a69,x11802,x11801)),x11802)
% 1.96/1.91 [1254]~P7(a69,x12541,x12542)+E(f13(a69,x12541,f8(a69,x12542,x12541)),x12542)
% 1.96/1.91 [1255]~P7(a69,x12552,x12551)+E(f8(a69,x12551,f8(a69,x12551,x12552)),x12552)
% 1.96/1.91 [1256]~P7(a69,x12562,x12561)+E(f13(a69,f8(a69,x12561,x12562),x12562),x12561)
% 1.96/1.91 [1262]~P8(a70,x12621,x12622)+P8(a70,x12621,f13(a70,x12622,f3(a70)))
% 1.96/1.91 [1263]~P7(a70,x12631,x12632)+P8(a70,x12631,f13(a70,x12632,f3(a70)))
% 1.96/1.91 [1264]~P8(a70,x12641,x12642)+P7(a70,x12641,f8(a70,x12642,f3(a70)))
% 1.96/1.91 [1266]~P8(a70,x12661,x12662)+P7(a70,f13(a70,x12661,f3(a70)),x12662)
% 1.96/1.91 [1344]~P7(a69,x13442,x13441)+E(f8(a1,f27(a69,x13441),f27(a69,x13442)),f27(a69,f8(a69,x13441,x13442)))
% 1.96/1.91 [1361]P8(a70,x13611,x13612)+~P7(a70,x13611,f8(a70,x13612,f3(a70)))
% 1.96/1.91 [1362]P7(a70,x13621,x13622)+~P8(a70,x13621,f13(a70,x13622,f3(a70)))
% 1.96/1.91 [1363]P8(a70,x13631,x13632)+~P7(a70,f13(a70,x13631,f3(a70)),x13632)
% 1.96/1.91 [1365]~P7(a69,x13651,x13652)+P8(a1,f27(a69,x13651),f13(a1,f27(a69,x13652),f3(a1)))
% 1.96/1.91 [1366]~P8(a69,x13661,x13662)+P7(a1,f13(a1,f27(a69,x13661),f3(a1)),f27(a69,x13662))
% 1.96/1.91 [1431]P8(a1,x14311,f27(a69,x14312))+~P7(a69,f13(a69,f25(x14311),f3(a69)),x14312)
% 1.96/1.91 [1519]P7(a69,x15191,x15192)+~P8(a1,f27(a69,x15191),f13(a1,f27(a69,x15192),f3(a1)))
% 1.96/1.91 [1520]P8(a69,x15201,x15202)+~P7(a1,f13(a1,f27(a69,x15201),f3(a1)),f27(a69,x15202))
% 1.96/1.91 [730]~E(x7302,f10(a69))+E(f54(f54(f21(a69),x7301),x7302),f3(a69))
% 1.96/1.91 [731]~E(x7312,f10(a69))+E(f54(f54(f12(a69),x7311),x7312),f10(a69))
% 1.96/1.91 [733]~E(x7331,f10(a69))+E(f54(f54(f12(a69),x7331),x7332),f10(a69))
% 1.96/1.91 [748]~P42(x7481)+E(f54(f54(f12(x7481),x7482),x7482),x7482)
% 1.96/1.91 [799]~P2(x7991)+E(f54(f54(f12(x7991),f3(x7991)),x7992),x7992)
% 1.96/1.91 [800]~P50(x8001)+E(f54(f54(f12(x8001),f3(x8001)),x8002),x8002)
% 1.96/1.91 [801]~P3(x8011)+E(f54(f54(f12(x8011),f3(x8011)),x8012),x8012)
% 1.96/1.91 [806]~P2(x8061)+E(f54(f54(f21(x8061),f3(x8061)),x8062),f3(x8061))
% 1.96/1.91 [808]~P1(x8081)+E(f54(f54(f12(x8081),f10(x8081)),x8082),f10(x8081))
% 1.96/1.91 [809]~P50(x8091)+E(f54(f54(f12(x8091),f10(x8091)),x8092),f10(x8091))
% 1.96/1.91 [810]~P63(x8101)+E(f54(f54(f12(x8101),f10(x8101)),x8102),f10(x8101))
% 1.96/1.91 [821]E(x8211,f3(a69))+~E(f54(f54(f12(a69),x8212),x8211),f3(a69))
% 1.96/1.91 [822]E(x8221,f3(a69))+~E(f54(f54(f12(a69),x8221),x8222),f3(a69))
% 1.96/1.91 [834]~P21(x8341)+E(f13(f72(x8341),x8342,f10(f72(x8341))),x8342)
% 1.96/1.91 [835]~P16(x8351)+E(f8(f72(x8351),x8352,f10(f72(x8351))),x8352)
% 1.96/1.91 [836]~P21(x8361)+E(f13(f72(x8361),f10(f72(x8361)),x8362),x8362)
% 1.96/1.91 [861]~P54(x8611)+E(f23(x8611,x8612,f10(f72(x8611))),f10(f72(x8611)))
% 1.96/1.91 [862]~P54(x8621)+E(f24(x8621,f10(f72(x8621)),x8622),f10(f72(x8621)))
% 1.96/1.91 [863]~P54(x8631)+E(f20(x8631,f10(f72(x8631)),x8632),f10(f72(x8631)))
% 1.96/1.91 [912]~P16(x9121)+E(f8(f72(x9121),f10(f72(x9121)),x9122),f11(f72(x9121),x9122))
% 1.96/1.91 [927]~P54(x9271)+E(f54(f54(f12(f72(x9271)),x9272),f10(f72(x9271))),f10(f72(x9271)))
% 1.96/1.91 [991]~P34(x9911)+E(f18(x9911,x9912,f10(f72(x9911))),f16(x9911,x9912,f10(a69)))
% 1.96/1.91 [1050]~E(x10502,f10(a69))+P8(a69,f10(a69),f54(f54(f21(a69),x10501),x10502))
% 1.96/1.91 [1069]~P62(x10691)+P7(x10691,f10(x10691),f54(f54(f12(x10691),x10692),x10692))
% 1.96/1.91 [1126]~P57(x11261)+E(f54(f54(f12(x11261),f7(x11261,x11262)),f7(x11261,x11262)),f54(f54(f12(x11261),x11262),x11262))
% 1.96/1.91 [1232]~P8(a69,f10(a69),x12321)+P8(a69,f10(a69),f54(f54(f21(a69),x12321),x12322))
% 1.96/1.91 [1233]~P7(a70,f10(a70),x12331)+P7(a70,f10(a70),f54(f54(f21(a70),x12331),x12332))
% 1.96/1.91 [1253]E(x12531,f10(a70))+P8(a70,f10(a70),f54(f54(f21(a70),f7(a70,x12531)),x12532))
% 1.96/1.91 [1258]~E(x12582,f10(a69))+P8(a70,f10(a70),f54(f54(f21(a70),f7(a70,x12581)),x12582))
% 1.96/1.91 [1289]~P62(x12891)+~P8(x12891,f54(f54(f12(x12891),x12892),x12892),f10(x12891))
% 1.96/1.91 [1328]P8(a69,f10(a69),x13281)+~P8(a69,f10(a69),f54(f54(f12(a69),x13282),x13281))
% 1.96/1.91 [1329]P8(a69,f10(a69),x13291)+~P8(a69,f10(a69),f54(f54(f12(a69),x13291),x13292))
% 1.96/1.91 [1353]~P7(a1,f10(a1),x13531)+E(f9(f13(a1,x13531,f27(a69,x13532))),f13(a69,f9(x13531),x13532))
% 1.96/1.91 [1354]~P7(a1,f10(a1),x13541)+E(f25(f13(a1,x13541,f27(a69,x13542))),f13(a69,f25(x13541),x13542))
% 1.96/1.91 [1403]~P7(a1,f27(a69,x14032),x14031)+E(f9(f8(a1,x14031,f27(a69,x14032))),f8(a69,f9(x14031),x14032))
% 1.96/1.91 [1404]~P7(a1,f27(a69,x14042),x14041)+E(f25(f8(a1,x14041,f27(a69,x14042))),f8(a69,f25(x14041),x14042))
% 1.96/1.91 [1692]~P77(x16921)+E(f54(f54(f12(x16921),f13(x16921,x16922,f3(x16921))),f8(x16921,x16922,f3(x16921))),f8(x16921,f54(f54(f12(x16921),x16922),x16922),f3(x16921)))
% 1.96/1.91 [848]~P50(x8481)+E(f54(f15(x8481,f3(f72(x8481))),x8482),f3(x8481))
% 1.96/1.91 [849]~P54(x8491)+E(f54(f15(x8491,f10(f72(x8491))),x8492),f10(x8491))
% 1.96/1.91 [975]~P54(x9751)+E(f54(f54(f12(f72(x9751)),f10(f72(x9751))),x9752),f10(f72(x9751)))
% 1.96/1.91 [1025]~P52(x10251)+E(f54(f54(f12(x10251),f11(x10251,f3(x10251))),x10252),f11(x10251,x10252))
% 1.96/1.91 [1091]E(f7(a70,x10911),f3(a70))+~E(f7(a70,f54(f54(f12(a70),x10911),x10912)),f3(a70))
% 1.96/1.91 [1110]~E(f27(a69,f25(x11101)),x11101)+E(f25(f54(f54(f21(a1),x11101),x11102)),f54(f54(f21(a69),f25(x11101)),x11102))
% 1.96/1.91 [1474]E(x14741,f10(a1))+~E(f13(a1,f54(f54(f12(a1),x14742),x14742),f54(f54(f12(a1),x14741),x14741)),f10(a1))
% 1.96/1.91 [1475]E(x14751,f10(a1))+~E(f13(a1,f54(f54(f12(a1),x14751),x14751),f54(f54(f12(a1),x14752),x14752)),f10(a1))
% 1.96/1.91 [1477]~P50(x14771)+E(f13(x14771,x14772,x14772),f54(f54(f12(x14771),f13(x14771,f3(x14771),f3(x14771))),x14772))
% 1.96/1.91 [1501]E(x15011,f10(a69))+E(f54(f54(f12(a69),x15012),f54(f54(f21(a69),x15012),f8(a69,x15011,f3(a69)))),f54(f54(f21(a69),x15012),x15011))
% 1.96/1.91 [1761]~P7(a1,f10(a1),x17612)+P7(a1,f13(a1,f54(f54(f12(a1),f27(a69,x17611)),x17612),f3(a1)),f54(f54(f21(a1),f13(a1,x17612,f3(a1))),x17611))
% 1.96/1.91 [1712]E(x17121,f10(a69))+E(f13(a69,x17122,f54(f54(f12(a69),f8(a69,x17121,f3(a69))),x17122)),f54(f54(f12(a69),x17121),x17122))
% 1.96/1.91 [940]~P50(x9401)+E(f13(x9401,x9402,x9403),f13(x9401,x9403,x9402))
% 1.96/1.91 [994]P7(a69,x9941,x9942)+~E(x9942,f13(a69,x9941,x9943))
% 1.96/1.91 [1060]E(x10601,x10602)+~E(f13(a69,x10603,x10601),f13(a69,x10603,x10602))
% 1.96/1.91 [1061]E(x10611,x10612)+~E(f13(a69,x10611,x10613),f13(a69,x10612,x10613))
% 1.96/1.91 [1241]~P8(a69,x12411,x12413)+P8(a69,x12411,f13(a69,x12412,x12413))
% 1.96/1.91 [1243]~P8(a69,x12431,x12432)+P8(a69,x12431,f13(a69,x12432,x12433))
% 1.96/1.91 [1245]~P7(a69,x12451,x12453)+P7(a69,x12451,f13(a69,x12452,x12453))
% 1.96/1.91 [1247]~P7(a69,x12471,x12472)+P7(a69,x12471,f13(a69,x12472,x12473))
% 1.96/1.91 [1248]~P8(a69,x12481,x12483)+P8(a69,f8(a69,x12481,x12482),x12483)
% 1.96/1.91 [1275]~P8(a1,f10(a1),x12753)+P8(a1,f10(a1),f58(x12751,x12752,x12753))
% 1.96/1.91 [1345]P8(a69,x13451,x13452)+~P8(a69,f13(a69,x13451,x13453),x13452)
% 1.96/1.91 [1348]P7(a69,x13481,x13482)+~P7(a69,f13(a69,x13483,x13481),x13482)
% 1.96/1.91 [1349]P7(a69,x13491,x13492)+~P7(a69,f13(a69,x13491,x13493),x13492)
% 1.96/1.91 [1417]~P8(a69,x14172,x14173)+P8(a69,f13(a69,x14171,x14172),f13(a69,x14171,x14173))
% 1.96/1.91 [1418]~P8(a69,x14181,x14183)+P8(a69,f13(a69,x14181,x14182),f13(a69,x14183,x14182))
% 1.96/1.91 [1419]~P8(a70,x14191,x14193)+P8(a70,f13(a70,x14191,x14192),f13(a70,x14193,x14192))
% 1.96/1.91 [1420]~P7(a1,x14202,x14203)+P7(a1,f13(a1,x14201,x14202),f13(a1,x14201,x14203))
% 1.96/1.91 [1421]~P7(a69,x14212,x14213)+P7(a69,f13(a69,x14211,x14212),f13(a69,x14211,x14213))
% 1.96/1.91 [1422]~P7(a69,x14221,x14223)+P7(a69,f13(a69,x14221,x14222),f13(a69,x14223,x14222))
% 1.96/1.91 [1423]~P7(a69,x14233,x14232)+P7(a69,f8(a69,x14231,x14232),f8(a69,x14231,x14233))
% 1.96/1.91 [1424]~P7(a69,x14241,x14243)+P7(a69,f8(a69,x14241,x14242),f8(a69,x14243,x14242))
% 1.96/1.91 [1425]~P7(a70,x14252,x14253)+P7(a70,f13(a70,x14251,x14252),f13(a70,x14251,x14253))
% 1.96/1.91 [1497]~P8(a69,f13(a69,x14971,x14973),x14972)+P8(a69,x14971,f8(a69,x14972,x14973))
% 1.96/1.91 [1498]~P7(a69,f8(a69,x14981,x14983),x14982)+P7(a69,x14981,f13(a69,x14982,x14983))
% 1.96/1.91 [1499]~P8(a69,x14991,f8(a69,x14993,x14992))+P8(a69,f13(a69,x14991,x14992),x14993)
% 1.96/1.91 [1500]~P7(a69,x15001,f13(a69,x15003,x15002))+P7(a69,f8(a69,x15001,x15002),x15003)
% 1.96/1.91 [1598]P8(a69,x15981,x15982)+~P8(a69,f13(a69,x15983,x15981),f13(a69,x15983,x15982))
% 1.96/1.91 [1599]P7(a69,x15991,x15992)+~P7(a69,f13(a69,x15993,x15991),f13(a69,x15993,x15992))
% 1.96/1.91 [950]P9(x9501,x9502,x9503)+~E(f54(x9503,f33(x9503)),f54(x9503,f34(x9503)))
% 1.96/1.91 [1006]~P24(x10061)+E(f13(x10061,x10062,f11(x10061,x10063)),f8(x10061,x10062,x10063))
% 1.96/1.91 [1007]~P16(x10071)+E(f13(x10071,x10072,f11(x10071,x10073)),f8(x10071,x10072,x10073))
% 1.96/1.91 [1008]~P52(x10081)+E(f13(x10081,x10082,f11(x10081,x10083)),f8(x10081,x10082,x10083))
% 1.96/1.91 [1009]~P24(x10091)+E(f8(x10091,x10092,f11(x10091,x10093)),f13(x10091,x10092,x10093))
% 1.96/1.91 [1064]~P24(x10641)+E(f13(x10641,f8(x10641,x10642,x10643),x10643),x10642)
% 1.96/1.91 [1065]~P24(x10651)+E(f8(x10651,f13(x10651,x10652,x10653),x10653),x10652)
% 1.96/1.91 [1106]~P16(x11061)+E(f11(x11061,f8(x11061,x11062,x11063)),f8(x11061,x11063,x11062))
% 1.96/1.91 [1149]~P24(x11491)+E(f13(x11491,f11(x11491,x11492),f13(x11491,x11492,x11493)),x11493)
% 1.96/1.91 [1182]~P53(x11821)+E(f11(f72(x11821),f23(x11821,x11822,x11823)),f23(x11821,f11(x11821,x11822),x11823))
% 1.96/1.91 [1183]~P16(x11831)+E(f11(f72(x11831),f16(x11831,x11832,x11833)),f16(x11831,f11(x11831,x11832),x11833))
% 1.96/1.91 [1217]~P44(x12171)+E(f13(x12171,f29(x12171,x12172),f29(x12171,x12173)),f29(x12171,f13(a1,x12172,x12173)))
% 1.96/1.91 [1218]~P44(x12181)+E(f8(x12181,f29(x12181,x12182),f29(x12181,x12183)),f29(x12181,f8(a1,x12182,x12183)))
% 1.96/1.91 [1220]~P24(x12201)+E(f13(x12201,f11(x12201,x12202),f11(x12201,x12203)),f11(x12201,f13(x12201,x12203,x12202)))
% 1.96/1.91 [1221]~P16(x12211)+E(f13(x12211,f11(x12211,x12212),f11(x12211,x12213)),f11(x12211,f13(x12211,x12212,x12213)))
% 1.96/1.91 [1222]~P16(x12221)+E(f8(x12221,f11(x12221,x12222),f11(x12221,x12223)),f11(x12221,f8(x12221,x12222,x12223)))
% 1.96/1.91 [1271]~P49(x12711)+E(f28(x12711,f8(x12711,x12712,x12713)),f28(x12711,f8(x12711,x12713,x12712)))
% 1.96/1.91 [1272]~P32(x12721)+E(f7(x12721,f8(x12721,x12722,x12723)),f7(x12721,f8(x12721,x12723,x12722)))
% 1.96/1.91 [1492]~P7(a69,x14922,x14923)+E(f8(a69,f13(a69,x14921,x14922),x14923),f8(a69,x14921,f8(a69,x14923,x14922)))
% 1.96/1.91 [1493]~P7(a69,x14933,x14932)+E(f13(a69,x14931,f8(a69,x14932,x14933)),f8(a69,f13(a69,x14931,x14932),x14933))
% 1.96/1.91 [1495]~P7(a69,x14952,x14951)+E(f13(a69,f8(a69,x14951,x14952),x14953),f8(a69,f13(a69,x14951,x14953),x14952))
% 1.96/1.91 [1563]~P7(a69,x15633,x15632)+P7(a69,x15631,f8(a69,f13(a69,x15632,x15631),x15633))
% 1.96/1.91 [1623]~P49(x16231)+P7(a1,f28(x16231,f13(x16231,x16232,x16233)),f13(a1,f28(x16231,x16232),f28(x16231,x16233)))
% 1.96/1.91 [1624]~P49(x16241)+P7(a1,f28(x16241,f8(x16241,x16242,x16243)),f13(a1,f28(x16241,x16242),f28(x16241,x16243)))
% 1.96/1.91 [1625]~P49(x16251)+P7(a1,f8(a1,f28(x16251,x16252),f28(x16251,x16253)),f28(x16251,f13(x16251,x16252,x16253)))
% 1.96/1.91 [1626]~P49(x16261)+P7(a1,f8(a1,f28(x16261,x16262),f28(x16261,x16263)),f28(x16261,f8(x16261,x16262,x16263)))
% 1.96/1.91 [1637]~P32(x16371)+P7(x16371,f7(x16371,f13(x16371,x16372,x16373)),f13(x16371,f7(x16371,x16372),f7(x16371,x16373)))
% 1.96/1.91 [1638]~P32(x16381)+P7(x16381,f7(x16381,f8(x16381,x16382,x16383)),f13(x16381,f7(x16381,x16382),f7(x16381,x16383)))
% 1.96/1.91 [1639]~P32(x16391)+P7(x16391,f8(x16391,f7(x16391,x16392),f7(x16391,x16393)),f7(x16391,f8(x16391,x16393,x16392)))
% 1.96/1.91 [1640]~P32(x16401)+P7(x16401,f8(x16401,f7(x16401,x16402),f7(x16401,x16403)),f7(x16401,f8(x16401,x16402,x16403)))
% 1.96/1.91 [1792]~P59(x17921)+P11(f72(x17921),f54(f54(f21(f72(x17921)),f18(x17921,f11(x17921,x17922),f18(x17921,f3(x17921),f10(f72(x17921))))),f19(x17921,x17922,x17923)),x17923)
% 1.96/1.91 [896]~E(x8962,f10(a69))+E(f54(f54(f12(a69),x8961),x8962),f54(f54(f12(a69),x8963),x8962))
% 1.96/1.91 [898]~E(x8981,f10(a69))+E(f54(f54(f12(a69),x8981),x8982),f54(f54(f12(a69),x8981),x8983))
% 1.96/1.91 [926]~P50(x9261)+E(f54(f54(f12(x9261),x9262),x9263),f54(f54(f12(x9261),x9263),x9262))
% 1.96/1.91 [1056]~P50(x10561)+P11(x10561,x10562,f54(f54(f12(x10561),x10563),x10562))
% 1.96/1.91 [1057]~P50(x10571)+P11(x10571,x10572,f54(f54(f12(x10571),x10572),x10573))
% 1.96/1.91 [1124]~P76(x11241)+E(f54(f54(f12(x11241),f11(x11241,x11242)),x11243),f54(f54(f12(x11241),x11242),f11(x11241,x11243)))
% 1.96/1.91 [1125]~P76(x11251)+E(f54(f54(f12(x11251),f11(x11251,x11252)),f11(x11251,x11253)),f54(f54(f12(x11251),x11252),x11253))
% 1.96/1.91 [1203]~P24(x12031)+E(f13(x12031,x12032,f13(x12031,f11(x12031,x12032),x12033)),x12033)
% 1.96/1.91 [1208]~P53(x12081)+E(f23(x12081,x12082,f11(f72(x12081),x12083)),f11(f72(x12081),f23(x12081,x12082,x12083)))
% 1.96/1.91 [1277]~P16(x12771)+E(f18(x12771,f11(x12771,x12772),f11(f72(x12771),x12773)),f11(f72(x12771),f18(x12771,x12772,x12773)))
% 1.96/1.91 [1310]~P57(x13101)+P7(x13101,f10(x13101),f54(f54(f21(x13101),f7(x13101,x13102)),x13103))
% 1.96/1.91 [1332]P8(a69,f10(a69),x13321)+P7(a69,f54(f54(f12(a69),x13322),x13321),f54(f54(f12(a69),x13323),x13321))
% 1.96/1.91 [1333]P8(a69,f10(a69),x13331)+P7(a69,f54(f54(f12(a69),x13331),x13332),f54(f54(f12(a69),x13331),x13333))
% 1.96/1.91 [1369]~P7(a69,x13692,x13693)+P7(a69,f54(f54(f12(a69),x13691),x13692),f54(f54(f12(a69),x13691),x13693))
% 1.96/1.91 [1371]~P7(a69,x13711,x13713)+P7(a69,f54(f54(f12(a69),x13711),x13712),f54(f54(f12(a69),x13713),x13712))
% 1.96/1.91 [1411]~P32(x14111)+E(f7(x14111,f13(x14111,f7(x14111,x14112),f7(x14111,x14113))),f13(x14111,f7(x14111,x14112),f7(x14111,x14113)))
% 1.96/1.91 [1525]P8(a69,x15251,x15252)+~P8(a69,f54(f54(f12(a69),x15253),x15251),f54(f54(f12(a69),x15253),x15252))
% 1.96/1.91 [1526]P8(a69,x15261,x15262)+~P8(a69,f54(f54(f12(a69),x15261),x15263),f54(f54(f12(a69),x15262),x15263))
% 1.96/1.91 [1529]P8(a69,f10(a69),x15291)+~P8(a69,f54(f54(f12(a69),x15292),x15291),f54(f54(f12(a69),x15293),x15291))
% 1.96/1.91 [1530]P8(a69,f10(a69),x15301)+~P8(a69,f54(f54(f12(a69),x15301),x15302),f54(f54(f12(a69),x15301),x15303))
% 1.96/1.91 [1699]~P54(x16991)+E(f18(x16991,f54(f15(x16991,x16992),x16993),f24(x16991,x16992,x16993)),f13(f72(x16991),x16992,f23(x16991,x16993,f24(x16991,x16992,x16993))))
% 1.96/1.91 [1727]~P49(x17271)+P7(a1,f7(a1,f8(a1,f28(x17271,x17272),f28(x17271,x17273))),f28(x17271,f8(x17271,x17272,x17273)))
% 1.96/1.91 [1728]~P32(x17281)+P7(x17281,f7(x17281,f8(x17281,f7(x17281,x17282),f7(x17281,x17283))),f7(x17281,f8(x17281,x17282,x17283)))
% 1.96/1.91 [1158]~P76(x11581)+E(f54(f54(f12(x11581),x11582),f11(x11581,x11583)),f11(x11581,f54(f54(f12(x11581),x11582),x11583)))
% 1.96/1.91 [1160]~P1(x11601)+E(f54(f54(f12(x11601),x11602),f11(x11601,x11603)),f11(x11601,f54(f54(f12(x11601),x11602),x11603)))
% 1.96/1.91 [1181]~P42(x11811)+E(f54(f54(f12(x11811),x11812),f54(f54(f12(x11811),x11812),x11813)),f54(f54(f12(x11811),x11812),x11813))
% 1.96/1.91 [1196]~P53(x11961)+E(f54(f15(x11961,f11(f72(x11961),x11962)),x11963),f11(x11961,f54(f15(x11961,x11962),x11963)))
% 1.96/1.91 [1197]~P44(x11971)+E(f29(x11971,f54(f54(f21(a1),x11972),x11973)),f54(f54(f21(x11971),f29(x11971,x11972)),x11973))
% 1.96/1.91 [1204]~P47(x12041)+E(f28(x12041,f54(f54(f21(x12041),x12042),x12043)),f54(f54(f21(a1),f28(x12041,x12042)),x12043))
% 1.96/1.91 [1209]~P55(x12091)+E(f54(f54(f21(x12091),f26(x12091,x12092)),x12093),f26(x12091,f54(f54(f21(x12091),x12092),x12093)))
% 1.96/1.91 [1210]~P76(x12101)+E(f54(f54(f12(x12101),f11(x12101,x12102)),x12103),f11(x12101,f54(f54(f12(x12101),x12102),x12103)))
% 1.96/1.91 [1211]~P57(x12111)+E(f54(f54(f21(x12111),f7(x12111,x12112)),x12113),f7(x12111,f54(f54(f21(x12111),x12112),x12113)))
% 1.96/1.91 [1213]~P1(x12131)+E(f54(f54(f12(x12131),f11(x12131,x12132)),x12133),f11(x12131,f54(f54(f12(x12131),x12132),x12133)))
% 1.96/1.91 [1252]~P44(x12521)+E(f54(f54(f12(x12521),f29(x12521,x12522)),f29(x12521,x12523)),f29(x12521,f54(f54(f12(a1),x12522),x12523)))
% 1.96/1.91 [1267]~P47(x12671)+E(f54(f54(f12(a1),f28(x12671,x12672)),f28(x12671,x12673)),f28(x12671,f54(f54(f12(x12671),x12672),x12673)))
% 1.96/1.91 [1278]~P5(x12781)+E(f54(f54(f12(x12781),f26(x12781,x12782)),f26(x12781,x12783)),f26(x12781,f54(f54(f12(x12781),x12782),x12783)))
% 1.96/1.91 [1279]~P57(x12791)+E(f54(f54(f12(x12791),f7(x12791,x12792)),f7(x12791,x12793)),f7(x12791,f54(f54(f12(x12791),x12792),x12793)))
% 1.96/1.91 [1280]~P47(x12801)+E(f54(f54(f12(x12801),f14(x12801,x12802)),f14(x12801,x12803)),f14(x12801,f54(f54(f12(x12801),x12802),x12803)))
% 1.96/1.91 [1281]~P57(x12811)+E(f54(f54(f12(x12811),f14(x12811,x12812)),f14(x12811,x12813)),f14(x12811,f54(f54(f12(x12811),x12812),x12813)))
% 1.96/1.91 [1416]~P57(x14161)+E(f7(x14161,f54(f54(f21(x14161),f11(x14161,x14162)),x14163)),f7(x14161,f54(f54(f21(x14161),x14162),x14163)))
% 1.96/1.91 [1589]~P50(x15891)+E(f13(x15891,x15892,f54(f54(f12(x15891),x15893),x15892)),f54(f54(f12(x15891),f13(x15891,x15893,f3(x15891))),x15892))
% 1.96/1.91 [1590]~P50(x15901)+E(f13(x15901,f54(f54(f12(x15901),x15902),x15903),x15903),f54(f54(f12(x15901),f13(x15901,x15902,f3(x15901))),x15903))
% 1.96/1.91 [1613]~P48(x16131)+P7(a1,f28(x16131,f54(f54(f21(x16131),x16132),x16133)),f54(f54(f21(a1),f28(x16131,x16132)),x16133))
% 1.96/1.91 [1661]~P1(x16611)+P7(a1,f28(x16611,f54(f54(f12(x16611),x16612),x16613)),f54(f54(f12(a1),f28(x16611,x16613)),f52(x16612,x16611)))
% 1.96/1.91 [1662]~P1(x16621)+P7(a1,f28(x16621,f54(f54(f12(x16621),x16622),x16623)),f54(f54(f12(a1),f28(x16621,x16622)),f28(x16621,x16623)))
% 1.96/1.91 [1663]~P1(x16631)+P7(a1,f28(x16631,f54(f54(f12(x16631),x16632),x16633)),f54(f54(f12(a1),f28(x16631,x16632)),f50(x16633,x16631)))
% 1.96/1.91 [1693]~P62(x16931)+P7(x16931,f10(x16931),f13(x16931,f54(f54(f12(x16931),x16932),x16932),f54(f54(f12(x16931),x16933),x16933)))
% 1.96/1.91 [1732]~P77(x17321)+E(f54(f54(f12(x17321),f54(f54(f21(x17321),f11(x17321,f3(x17321))),x17322)),f54(f54(f21(x17321),x17323),x17322)),f54(f54(f21(x17321),f11(x17321,x17323)),x17322))
% 1.96/1.91 [1742]~P62(x17421)+~P8(x17421,f13(x17421,f54(f54(f12(x17421),x17422),x17422),f54(f54(f12(x17421),x17423),x17423)),f10(x17421))
% 1.96/1.91 [1771]~P1(x17711)+P7(a1,f28(x17711,f54(f54(f12(x17711),x17712),x17713)),f54(f54(f12(a1),f54(f54(f12(a1),f28(x17711,x17712)),f28(x17711,x17713))),f53(x17711)))
% 1.96/1.91 [1801]~P52(x18011)+E(f13(f72(x18011),f54(f54(f12(f72(x18011)),f18(x18011,f11(x18011,x18012),f18(x18011,f3(x18011),f10(f72(x18011))))),f24(x18011,x18013,x18012)),f18(x18011,f54(f15(x18011,x18013),x18012),f10(f72(x18011)))),x18013)
% 1.96/1.91 [1522]~P2(x15221)+E(f54(f54(f12(x15221),f54(f54(f21(x15221),x15222),x15223)),x15222),f54(f54(f12(x15221),x15222),f54(f54(f21(x15221),x15222),x15223)))
% 1.96/1.91 [1806]~P8(a70,f10(a70),x18063)+P8(a70,x18061,f13(a70,x18062,f54(f54(f12(a70),f13(a70,f7(a70,f8(a70,x18062,x18061)),f3(a70))),x18063)))
% 1.96/1.91 [1807]~P8(a70,f10(a70),x18073)+P8(a70,f8(a70,x18071,f54(f54(f12(a70),f13(a70,f7(a70,f8(a70,x18071,x18072)),f3(a70))),x18073)),x18072)
% 1.96/1.91 [1392]~P50(x13921)+E(f13(x13921,x13922,f13(x13921,x13923,x13924)),f13(x13921,x13923,f13(x13921,x13922,x13924)))
% 1.96/1.91 [1394]~P50(x13941)+E(f13(x13941,f13(x13941,x13942,x13943),x13944),f13(x13941,x13942,f13(x13941,x13943,x13944)))
% 1.96/1.91 [1395]~P15(x13951)+E(f13(x13951,f13(x13951,x13952,x13953),x13954),f13(x13951,x13952,f13(x13951,x13953,x13954)))
% 1.96/1.91 [1396]~P50(x13961)+E(f13(x13961,f13(x13961,x13962,x13963),x13964),f13(x13961,f13(x13961,x13962,x13964),x13963))
% 1.96/1.91 [1515]~P54(x15151)+E(f24(x15151,f18(x15151,x15152,x15153),x15154),f18(x15151,f54(f15(x15151,x15153),x15154),f24(x15151,x15153,x15154)))
% 1.96/1.91 [1544]~P54(x15441)+E(f18(x15441,f54(f54(f12(x15441),x15442),x15443),f23(x15441,x15442,x15444)),f23(x15441,x15442,f18(x15441,x15443,x15444)))
% 1.96/1.91 [1547]~P54(x15471)+E(f13(f72(x15471),f23(x15471,x15472,x15473),f23(x15471,x15474,x15473)),f23(x15471,f13(x15471,x15472,x15474),x15473))
% 1.96/1.91 [1548]~P53(x15481)+E(f8(f72(x15481),f23(x15481,x15482,x15483),f23(x15481,x15484,x15483)),f23(x15481,f8(x15481,x15482,x15484),x15483))
% 1.96/1.91 [1549]~P21(x15491)+E(f13(f72(x15491),f16(x15491,x15492,x15493),f16(x15491,x15494,x15493)),f16(x15491,f13(x15491,x15492,x15494),x15493))
% 1.96/1.91 [1550]~P16(x15501)+E(f8(f72(x15501),f16(x15501,x15502,x15503),f16(x15501,x15504,x15503)),f16(x15501,f8(x15501,x15502,x15504),x15503))
% 1.96/1.91 [995]~P35(x9952)+E(f54(f11(f77(x9951,x9952),x9953),x9954),f11(x9952,f54(x9953,x9954)))
% 1.96/1.91 [1478]~P54(x14781)+E(f54(f15(x14781,x14782),f54(f15(x14781,x14783),x14784)),f54(f15(x14781,f20(x14781,x14782,x14783)),x14784))
% 1.96/1.91 [1488]~P54(x14881)+E(f54(f54(f12(x14881),x14882),f54(f15(x14881,x14883),x14884)),f54(f15(x14881,f23(x14881,x14882,x14883)),x14884))
% 1.96/1.91 [1592]~P54(x15921)+E(f13(f72(x15921),f23(x15921,x15922,x15923),f23(x15921,x15922,x15924)),f23(x15921,x15922,f13(f72(x15921),x15923,x15924)))
% 1.96/1.91 [1593]~P53(x15931)+E(f8(f72(x15931),f23(x15931,x15932,x15933),f23(x15931,x15932,x15934)),f23(x15931,x15932,f8(f72(x15931),x15933,x15934)))
% 1.96/1.91 [1726]~P54(x17261)+E(f13(f72(x17261),f18(x17261,x17262,f10(f72(x17261))),f54(f54(f12(f72(x17261)),x17263),f20(x17261,x17264,x17263))),f20(x17261,f18(x17261,x17262,x17264),x17263))
% 1.96/1.91 [1739]~P54(x17391)+E(f13(f72(x17391),f23(x17391,x17392,f6(x17391,x17393,x17392)),f18(x17391,x17394,f6(x17391,x17393,x17392))),f6(x17391,f18(x17391,x17394,x17393),x17392))
% 1.96/1.91 [1367]~P50(x13671)+E(f54(f54(f12(x13671),x13672),f54(f54(f12(x13671),x13673),x13674)),f54(f54(f12(x13671),x13673),f54(f54(f12(x13671),x13672),x13674)))
% 1.96/1.91 [1380]~P54(x13801)+E(f23(x13801,f54(f54(f12(x13801),x13802),x13803),x13804),f23(x13801,x13802,f23(x13801,x13803,x13804)))
% 1.96/1.91 [1381]~P54(x13811)+E(f16(x13811,f54(f54(f12(x13811),x13812),x13813),x13814),f23(x13811,x13812,f16(x13811,x13813,x13814)))
% 1.96/1.91 [1518]~P50(x15181)+E(f54(f54(f12(x15181),x15182),f54(f54(f21(x15181),x15183),x15184)),f54(f15(x15181,f16(x15181,x15182,x15184)),x15183))
% 1.96/1.91 [1532]~P1(x15321)+E(f13(x15321,f54(f54(f12(x15321),x15322),x15323),f54(f54(f12(x15321),x15322),x15324)),f54(f54(f12(x15321),x15322),f13(x15321,x15323,x15324)))
% 1.96/1.91 [1533]~P50(x15331)+E(f13(x15331,f54(f54(f12(x15331),x15332),x15333),f54(f54(f12(x15331),x15332),x15334)),f54(f54(f12(x15331),x15332),f13(x15331,x15333,x15334)))
% 1.96/1.91 [1535]~P1(x15351)+E(f8(x15351,f54(f54(f12(x15351),x15352),x15353),f54(f54(f12(x15351),x15352),x15354)),f54(f54(f12(x15351),x15352),f8(x15351,x15353,x15354)))
% 1.96/1.91 [1620]~P54(x16201)+E(f13(x16201,f54(f15(x16201,x16202),x16203),f54(f15(x16201,x16204),x16203)),f54(f15(x16201,f13(f72(x16201),x16202,x16204)),x16203))
% 1.96/1.91 [1621]~P53(x16211)+E(f8(x16211,f54(f15(x16211,x16212),x16213),f54(f15(x16211,x16214),x16213)),f54(f15(x16211,f8(f72(x16211),x16212,x16214)),x16213))
% 1.96/1.91 [1644]~P2(x16441)+E(f54(f54(f12(x16441),f54(f54(f21(x16441),x16442),x16443)),f54(f54(f21(x16441),x16442),x16444)),f54(f54(f21(x16441),x16442),f13(a69,x16443,x16444)))
% 1.96/1.91 [1645]~P50(x16451)+E(f54(f54(f12(x16451),f54(f54(f21(x16451),x16452),x16453)),f54(f54(f21(x16451),x16452),x16454)),f54(f54(f21(x16451),x16452),f13(a69,x16453,x16454)))
% 1.96/1.91 [1655]~P1(x16551)+E(f13(x16551,f54(f54(f12(x16551),x16552),x16553),f54(f54(f12(x16551),x16554),x16553)),f54(f54(f12(x16551),f13(x16551,x16552,x16554)),x16553))
% 1.96/1.91 [1657]~P51(x16571)+E(f13(x16571,f54(f54(f12(x16571),x16572),x16573),f54(f54(f12(x16571),x16574),x16573)),f54(f54(f12(x16571),f13(x16571,x16572,x16574)),x16573))
% 1.96/1.91 [1659]~P1(x16591)+E(f8(x16591,f54(f54(f12(x16591),x16592),x16593),f54(f54(f12(x16591),x16594),x16593)),f54(f54(f12(x16591),f8(x16591,x16592,x16594)),x16593))
% 1.96/1.91 [1660]~P50(x16601)+E(f13(x16601,f54(f54(f12(x16601),x16602),x16603),f54(f54(f12(x16601),x16604),x16603)),f54(f54(f12(x16601),f13(x16601,x16602,x16604)),x16603))
% 1.96/1.91 [1691]~P54(x16911)+E(f13(x16911,x16912,f54(f54(f12(x16911),x16913),f54(f15(x16911,x16914),x16913))),f54(f15(x16911,f18(x16911,x16912,x16914)),x16913))
% 1.96/1.91 [1489]~P54(x14891)+E(f23(x14891,x14892,f54(f54(f12(f72(x14891)),x14893),x14894)),f54(f54(f12(f72(x14891)),x14893),f23(x14891,x14892,x14894)))
% 1.96/1.91 [1513]~P50(x15131)+E(f54(f54(f21(x15131),f54(f54(f21(x15131),x15132),x15133)),x15134),f54(f54(f21(x15131),x15132),f54(f54(f12(a69),x15133),x15134)))
% 1.96/1.91 [1514]~P2(x15141)+E(f54(f54(f21(x15141),f54(f54(f21(x15141),x15142),x15143)),x15144),f54(f54(f21(x15141),x15142),f54(f54(f12(a69),x15143),x15144)))
% 1.96/1.91 [1523]~P50(x15231)+E(f54(f54(f12(x15231),f54(f54(f12(x15231),x15232),x15233)),x15234),f54(f54(f12(x15231),x15232),f54(f54(f12(x15231),x15233),x15234)))
% 1.96/1.91 [1524]~P14(x15241)+E(f54(f54(f12(x15241),f54(f54(f12(x15241),x15242),x15243)),x15244),f54(f54(f12(x15241),x15242),f54(f54(f12(x15241),x15243),x15244)))
% 1.96/1.91 [1622]~P54(x16221)+E(f23(x16221,x16222,f54(f54(f12(f72(x16221)),x16223),x16224)),f54(f54(f12(f72(x16221)),f23(x16221,x16222,x16223)),x16224))
% 1.96/1.91 [1643]~P50(x16431)+E(f54(f54(f12(x16431),f54(f54(f12(x16431),x16432),x16433)),x16434),f54(f54(f12(x16431),f54(f54(f12(x16431),x16432),x16434)),x16433))
% 1.96/1.91 [1697]~P50(x16971)+E(f54(f54(f12(x16971),f54(f54(f21(x16971),x16972),x16973)),f54(f54(f21(x16971),x16974),x16973)),f54(f54(f21(x16971),f54(f54(f12(x16971),x16972),x16974)),x16973))
% 1.96/1.91 [1698]~P3(x16981)+E(f54(f54(f12(x16981),f54(f54(f21(x16981),x16982),x16983)),f54(f54(f21(x16981),x16984),x16983)),f54(f54(f21(x16981),f54(f54(f12(x16981),x16982),x16984)),x16983))
% 1.96/1.91 [1723]~P54(x17231)+E(f13(f72(x17231),f54(f54(f12(f72(x17231)),x17232),x17233),f54(f54(f12(f72(x17231)),x17234),x17233)),f54(f54(f12(f72(x17231)),f13(f72(x17231),x17232,x17234)),x17233))
% 1.96/1.91 [1672]~P50(x16721)+E(f54(f15(x16721,f54(f54(f21(f72(x16721)),x16722),x16723)),x16724),f54(f54(f21(x16721),f54(f15(x16721,x16722),x16724)),x16723))
% 1.96/1.91 [1713]~P54(x17131)+E(f54(f54(f12(x17131),f54(f15(x17131,x17132),x17133)),f54(f15(x17131,x17134),x17133)),f54(f15(x17131,f54(f54(f12(f72(x17131)),x17132),x17134)),x17133))
% 1.96/1.91 [1733]~P54(x17331)+E(f13(f72(x17331),f23(x17331,x17332,x17333),f18(x17331,f10(x17331),f54(f54(f12(f72(x17331)),x17333),x17334))),f54(f54(f12(f72(x17331)),x17333),f18(x17331,x17332,x17334)))
% 1.96/1.91 [1740]~P54(x17401)+E(f13(f72(x17401),f23(x17401,x17402,x17403),f18(x17401,f10(x17401),f54(f54(f12(f72(x17401)),x17404),x17403))),f54(f54(f12(f72(x17401)),f18(x17401,x17402,x17404)),x17403))
% 1.96/1.91 [1776]~P52(x17761)+E(f54(f15(x17761,f54(f54(f12(f72(x17761)),f16(x17761,f3(x17761),x17762)),x17763)),x17764),f54(f54(f12(x17761),f54(f54(f21(x17761),x17764),x17762)),f54(f15(x17761,x17763),x17764)))
% 1.96/1.91 [936]~P9(x9364,x9365,x9361)+E(f54(x9361,x9362),f54(x9361,x9363))
% 1.96/1.91 [1669]~P50(x16691)+E(f13(x16691,f13(x16691,x16692,x16693),f13(x16691,x16694,x16695)),f13(x16691,f13(x16691,x16692,x16694),f13(x16691,x16693,x16695)))
% 1.96/1.91 [1670]~P16(x16701)+E(f13(x16701,f8(x16701,x16702,x16703),f8(x16701,x16704,x16705)),f8(x16701,f13(x16701,x16702,x16704),f13(x16701,x16703,x16705)))
% 1.96/1.91 [1717]~P54(x17171)+E(f54(f54(f12(f72(x17171)),f16(x17171,x17172,x17173)),f16(x17171,x17174,x17175)),f16(x17171,f54(f54(f12(x17171),x17172),x17174),f13(a69,x17173,x17175)))
% 1.96/1.91 [1327]~P25(x13272)+E(f54(f8(f77(x13271,x13272),x13273,x13274),x13275),f8(x13272,f54(x13273,x13275),f54(x13274,x13275)))
% 1.96/1.91 [1673]~P21(x16731)+E(f18(x16731,f13(x16731,x16732,x16733),f13(f72(x16731),x16734,x16735)),f13(f72(x16731),f18(x16731,x16732,x16734),f18(x16731,x16733,x16735)))
% 1.96/1.91 [1674]~P16(x16741)+E(f18(x16741,f8(x16741,x16742,x16743),f8(f72(x16741),x16744,x16745)),f8(f72(x16741),f18(x16741,x16742,x16744),f18(x16741,x16743,x16745)))
% 1.96/1.91 [1781]~P49(x17811)+P7(a1,f28(x17811,f8(x17811,f13(x17811,x17812,x17813),f13(x17811,x17814,x17815))),f13(a1,f28(x17811,f8(x17811,x17812,x17814)),f28(x17811,f8(x17811,x17813,x17815))))
% 1.96/1.91 [1783]~P32(x17831)+P7(x17831,f7(x17831,f8(x17831,f13(x17831,x17832,x17833),f13(x17831,x17834,x17835))),f13(x17831,f7(x17831,f8(x17831,x17832,x17834)),f7(x17831,f8(x17831,x17833,x17835))))
% 1.96/1.91 [1725]~P50(x17251)+E(f54(f54(f12(x17251),f54(f54(f12(x17251),x17252),x17253)),f54(f54(f12(x17251),x17254),x17255)),f54(f54(f12(x17251),f54(f54(f12(x17251),x17252),x17254)),f54(f54(f12(x17251),x17253),x17255)))
% 1.96/1.91 [1762]~P76(x17621)+E(f13(x17621,f54(f54(f12(x17621),x17622),f8(x17621,x17623,x17624)),f54(f54(f12(x17621),f8(x17621,x17622,x17625)),x17624)),f8(x17621,f54(f54(f12(x17621),x17622),x17623),f54(f54(f12(x17621),x17625),x17624)))
% 1.96/1.91 [1802]~P1(x18021)+E(f13(x18021,f13(x18021,f54(f54(f12(x18021),f8(x18021,x18022,x18023)),f8(x18021,x18024,x18025)),f54(f54(f12(x18021),f8(x18021,x18022,x18023)),x18025)),f54(f54(f12(x18021),x18023),f8(x18021,x18024,x18025))),f8(x18021,f54(f54(f12(x18021),x18022),x18024),f54(f54(f12(x18021),x18023),x18025)))
% 1.96/1.91 [1754]~P80(x17541)+E(f13(x17541,f54(f54(f12(x17541),x17542),x17543),f13(x17541,f54(f54(f12(x17541),x17544),x17543),x17545)),f13(x17541,f54(f54(f12(x17541),f13(x17541,x17542,x17544)),x17543),x17545))
% 1.96/1.91 [1777]~P7(a69,x17771,x17774)+E(f8(a69,f13(a69,f54(f54(f12(a69),x17771),x17772),x17773),f13(a69,f54(f54(f12(a69),x17774),x17772),x17775)),f8(a69,x17773,f13(a69,f54(f54(f12(a69),f8(a69,x17774,x17771)),x17772),x17775)))
% 1.96/1.91 [1778]~P7(a69,x17784,x17781)+E(f8(a69,f13(a69,f54(f54(f12(a69),x17781),x17782),x17783),f13(a69,f54(f54(f12(a69),x17784),x17782),x17785)),f8(a69,f13(a69,f54(f54(f12(a69),f8(a69,x17781,x17784)),x17782),x17783),x17785))
% 1.96/1.91 [811]~P49(x8111)+~P44(x8111)+P8(a1,f10(a1),f46(x8111))
% 1.96/1.91 [812]~P49(x8121)+~P44(x8121)+P7(a1,f10(a1),f48(x8121))
% 1.96/1.91 [1308]~P8(a69,f5(a2,x13081),f5(a2,a73))+P9(a2,a2,f15(a2,x13081))+E(f54(f15(a2,x13081),f35(x13081)),f10(a2))
% 1.96/1.91 [923]E(x9231,x9232)+P8(a69,x9232,x9231)+P8(a69,x9231,x9232)
% 1.96/1.91 [924]E(x9241,x9242)+P8(a70,x9242,x9241)+P8(a70,x9241,x9242)
% 1.96/1.91 [999]E(x9991,x9992)+P8(a1,x9991,x9992)+~P7(a1,x9991,x9992)
% 1.96/1.91 [1002]E(x10021,x10022)+P8(a69,x10021,x10022)+~P7(a69,x10021,x10022)
% 1.96/1.91 [1003]E(x10031,x10032)+P8(a70,x10031,x10032)+~P7(a70,x10031,x10032)
% 1.96/1.91 [1066]E(x10661,x10662)+~P7(a1,x10662,x10661)+~P7(a1,x10661,x10662)
% 1.96/1.91 [1067]E(x10671,x10672)+~P7(a69,x10672,x10671)+~P7(a69,x10671,x10672)
% 1.96/1.91 [1068]E(x10681,x10682)+~P7(a70,x10682,x10681)+~P7(a70,x10681,x10682)
% 1.96/1.91 [674]~P23(x6741)+~E(x6742,f10(x6741))+E(f11(x6741,x6742),x6742)
% 1.96/1.91 [675]~P44(x6751)+E(f29(x6751,x6752),f10(x6751))+~E(x6752,f10(a1))
% 1.96/1.91 [685]~P49(x6851)+~E(x6852,f10(x6851))+E(f28(x6851,x6852),f10(a1))
% 1.96/1.91 [686]~P24(x6861)+~E(f10(x6861),x6862)+E(f11(x6861,x6862),f10(x6861))
% 1.96/1.91 [687]~P5(x6871)+~E(x6872,f3(x6871))+E(f26(x6871,x6872),f3(x6871))
% 1.96/1.91 [688]~P55(x6881)+~E(x6882,f10(x6881))+E(f26(x6881,x6882),f10(x6881))
% 1.96/1.91 [689]~P24(x6891)+~E(x6892,f10(x6891))+E(f11(x6891,x6892),f10(x6891))
% 1.96/1.91 [690]~P32(x6901)+~E(x6902,f10(x6901))+E(f7(x6901,x6902),f10(x6901))
% 1.96/1.91 [691]~P49(x6911)+~E(x6912,f10(x6911))+E(f14(x6911,x6912),f10(x6911))
% 1.96/1.91 [692]~P57(x6921)+~E(x6922,f10(x6921))+E(f14(x6921,x6922),f10(x6921))
% 1.96/1.91 [693]~P36(x6931)+~E(x6932,f10(x6931))+E(f14(x6931,x6932),f10(x6931))
% 1.96/1.91 [696]~P23(x6962)+~E(f11(x6962,x6961),x6961)+E(x6961,f10(x6962))
% 1.96/1.91 [703]~P49(x7032)+E(x7031,f10(x7032))+~E(f28(x7032,x7031),f10(a1))
% 1.96/1.91 [704]~P44(x7042)+~E(f29(x7042,x7041),f10(x7042))+E(x7041,f10(a1))
% 1.96/1.91 [705]~P5(x7052)+~E(f26(x7052,x7051),f3(x7052))+E(x7051,f3(x7052))
% 1.96/1.91 [706]~P55(x7062)+~E(f26(x7062,x7061),f10(x7062))+E(x7061,f10(x7062))
% 1.96/1.91 [708]~P56(x7082)+~E(f26(x7082,x7081),f10(x7082))+E(x7081,f10(x7082))
% 1.96/1.91 [709]~P24(x7092)+~E(f11(x7092,x7091),f10(x7092))+E(x7091,f10(x7092))
% 1.96/1.91 [710]~P32(x7102)+~E(f7(x7102,x7101),f10(x7102))+E(x7101,f10(x7102))
% 1.96/1.91 [711]~P49(x7112)+~E(f14(x7112,x7111),f10(x7112))+E(x7111,f10(x7112))
% 1.96/1.91 [712]~P57(x7122)+~E(f14(x7122,x7121),f10(x7122))+E(x7121,f10(x7122))
% 1.96/1.91 [713]~P24(x7131)+~E(f11(x7131,x7132),f10(x7131))+E(f10(x7131),x7132)
% 1.96/1.91 [771]~E(x7712,f10(a69))+~E(x7711,f10(a69))+E(f13(a69,x7711,x7712),f10(a69))
% 1.96/1.91 [805]~P23(x8051)+~E(x8052,f10(x8051))+E(f13(x8051,x8052,x8052),f10(x8051))
% 1.96/1.91 [826]~P19(x8261)+P8(x8261,x8262,f10(x8261))+E(f7(x8261,x8262),x8262)
% 1.96/1.91 [879]~P49(x8792)+E(x8791,f10(x8792))+P8(a1,f10(a1),f28(x8792,x8791))
% 1.96/1.91 [885]~P57(x8851)+P8(x8851,f10(x8851),x8852)+~E(f14(x8851,x8852),f3(x8851))
% 1.96/1.91 [895]~P49(x8951)+~E(x8952,f10(x8951))+P7(a1,f28(x8951,x8952),f10(a1))
% 1.96/1.91 [903]~P32(x9032)+P8(x9032,f10(x9032),f7(x9032,x9031))+E(x9031,f10(x9032))
% 1.96/1.91 [909]~P32(x9091)+P7(x9091,f7(x9091,x9092),f10(x9091))+~E(x9092,f10(x9091))
% 1.96/1.91 [911]~P23(x9112)+~E(f13(x9112,x9111,x9111),f10(x9112))+E(x9111,f10(x9112))
% 1.96/1.91 [948]~P32(x9481)+~P8(x9481,f10(x9481),x9482)+E(f7(x9481,x9482),x9482)
% 1.96/1.91 [949]~P32(x9491)+~P7(x9491,f10(x9491),x9492)+E(f7(x9491,x9492),x9492)
% 1.96/1.91 [963]~P57(x9631)+~P8(x9631,f10(x9631),x9632)+E(f14(x9631,x9632),f3(x9631))
% 1.96/1.91 [971]~P43(x9711)+P12(x9711,x9712)+P7(a69,f56(x9712,x9711),f59(x9712,x9711))
% 1.96/1.91 [976]~P32(x9761)+~P8(x9761,x9762,f10(x9761))+E(f11(x9761,x9762),f7(x9761,x9762))
% 1.96/1.91 [977]~P32(x9771)+~P7(x9771,x9772,f10(x9771))+E(f11(x9771,x9772),f7(x9771,x9772))
% 1.96/1.91 [978]~P19(x9781)+~P8(x9781,x9782,f10(x9781))+E(f11(x9781,x9782),f7(x9781,x9782))
% 1.96/1.91 [1005]~P49(x10052)+E(x10051,f10(x10052))+~P7(a1,f28(x10052,x10051),f10(a1))
% 1.96/1.91 [1011]~P49(x10112)+~E(x10111,f10(x10112))+~P8(a1,f10(a1),f28(x10112,x10111))
% 1.96/1.91 [1021]~P32(x10212)+~P7(x10212,f7(x10212,x10211),f10(x10212))+E(x10211,f10(x10212))
% 1.96/1.91 [1048]~P32(x10482)+~P8(x10482,f10(x10482),f7(x10482,x10481))+~E(x10481,f10(x10482))
% 1.96/1.91 [1077]E(x10771,x10772)+~E(f8(a69,x10772,x10771),f10(a69))+~E(f8(a69,x10771,x10772),f10(a69))
% 1.96/1.91 [1111]~P57(x11111)+~P8(x11111,x11112,f10(x11111))+P8(x11111,x11112,f11(x11111,x11112))
% 1.96/1.91 [1112]~P23(x11121)+~P7(x11121,x11122,f10(x11121))+P7(x11121,x11122,f11(x11121,x11122))
% 1.96/1.91 [1113]~P23(x11131)+~P8(x11131,f10(x11131),x11132)+P8(x11131,f11(x11131,x11132),x11132)
% 1.96/1.91 [1114]~P23(x11141)+~P7(x11141,f10(x11141),x11142)+P7(x11141,f11(x11141,x11142),x11142)
% 1.96/1.91 [1128]~P31(x11281)+~P8(x11281,x11282,f10(x11281))+P8(x11281,f10(x11281),f11(x11281,x11282))
% 1.96/1.91 [1129]~P31(x11291)+~P7(x11291,x11292,f10(x11291))+P7(x11291,f10(x11291),f11(x11291,x11292))
% 1.96/1.91 [1130]~P4(x11301)+~P8(x11301,f10(x11301),x11302)+P8(x11301,f10(x11301),f26(x11301,x11302))
% 1.96/1.91 [1131]~P13(x11311)+~P8(x11311,f10(x11311),x11312)+P8(x11311,f10(x11311),f26(x11311,x11312))
% 1.96/1.91 [1132]~P57(x11321)+~P8(x11321,f10(x11321),x11322)+P8(x11321,f10(x11321),f14(x11321,x11322))
% 1.96/1.91 [1133]~P13(x11331)+~P7(x11331,f10(x11331),x11332)+P7(x11331,f10(x11331),f26(x11331,x11332))
% 1.96/1.91 [1134]~P13(x11341)+~P7(x11341,x11342,f10(x11341))+P8(x11341,f26(x11341,x11342),f3(x11341))
% 1.96/1.91 [1135]~P4(x11351)+~P8(x11351,x11352,f10(x11351))+P8(x11351,f26(x11351,x11352),f10(x11351))
% 1.96/1.91 [1136]~P13(x11361)+~P8(x11361,x11362,f10(x11361))+P8(x11361,f26(x11361,x11362),f10(x11361))
% 1.96/1.91 [1137]~P57(x11371)+~P8(x11371,x11372,f10(x11371))+P8(x11371,f14(x11371,x11372),f10(x11371))
% 1.96/1.91 [1138]~P13(x11381)+~P7(x11381,x11382,f10(x11381))+P7(x11381,f26(x11381,x11382),f3(x11381))
% 1.96/1.91 [1139]~P13(x11391)+~P7(x11391,x11392,f10(x11391))+P7(x11391,f26(x11391,x11392),f10(x11391))
% 1.96/1.91 [1140]~P13(x11401)+~P8(x11401,f3(x11401),x11402)+P8(x11401,f26(x11401,x11402),f3(x11401))
% 1.96/1.91 [1141]~P31(x11411)+~P8(x11411,f10(x11411),x11412)+P8(x11411,f11(x11411,x11412),f10(x11411))
% 1.96/1.91 [1142]~P13(x11421)+~P7(x11421,f3(x11421),x11422)+P7(x11421,f26(x11421,x11422),f3(x11421))
% 1.96/1.91 [1143]~P31(x11431)+~P7(x11431,f10(x11431),x11432)+P7(x11431,f11(x11431,x11432),f10(x11431))
% 1.96/1.91 [1145]~P57(x11451)+~P8(x11451,x11452,f11(x11451,x11452))+P8(x11451,x11452,f10(x11451))
% 1.96/1.91 [1146]~P23(x11461)+~P7(x11461,x11462,f11(x11461,x11462))+P7(x11461,x11462,f10(x11461))
% 1.96/1.91 [1147]~P23(x11471)+~P8(x11471,f11(x11471,x11472),x11472)+P8(x11471,f10(x11471),x11472)
% 1.96/1.91 [1148]~P23(x11481)+~P7(x11481,f11(x11481,x11482),x11482)+P7(x11481,f10(x11481),x11482)
% 1.96/1.91 [1162]~P13(x11621)+~P8(x11621,f3(x11621),f26(x11621,x11622))+P8(x11621,x11622,f3(x11621))
% 1.96/1.91 [1163]~P31(x11631)+~P8(x11631,f10(x11631),f11(x11631,x11632))+P8(x11631,x11632,f10(x11631))
% 1.96/1.91 [1164]~P13(x11641)+~P7(x11641,f3(x11641),f26(x11641,x11642))+P7(x11641,x11642,f3(x11641))
% 1.96/1.91 [1165]~P31(x11651)+~P7(x11651,f10(x11651),f11(x11651,x11652))+P7(x11651,x11652,f10(x11651))
% 1.96/1.91 [1166]~P13(x11661)+~P8(x11661,f26(x11661,x11662),f10(x11661))+P8(x11661,x11662,f10(x11661))
% 1.96/1.91 [1167]~P57(x11671)+~P8(x11671,f14(x11671,x11672),f10(x11671))+P8(x11671,x11672,f10(x11671))
% 1.96/1.91 [1168]~P13(x11681)+~P7(x11681,f26(x11681,x11682),f10(x11681))+P7(x11681,x11682,f10(x11681))
% 1.96/1.91 [1169]~P13(x11691)+~P8(x11691,f3(x11691),f26(x11691,x11692))+P8(x11691,f10(x11691),x11692)
% 1.96/1.91 [1170]~P13(x11701)+~P8(x11701,f10(x11701),f26(x11701,x11702))+P8(x11701,f10(x11701),x11702)
% 1.96/1.91 [1171]~P13(x11711)+~P7(x11711,f3(x11711),f26(x11711,x11712))+P8(x11711,f10(x11711),x11712)
% 1.96/1.91 [1172]~P57(x11721)+~P8(x11721,f10(x11721),f14(x11721,x11722))+P8(x11721,f10(x11721),x11722)
% 1.96/1.91 [1173]~P13(x11731)+~P7(x11731,f10(x11731),f26(x11731,x11732))+P7(x11731,f10(x11731),x11732)
% 1.96/1.91 [1174]~P31(x11741)+~P8(x11741,f11(x11741,x11742),f10(x11741))+P8(x11741,f10(x11741),x11742)
% 1.96/1.91 [1175]~P31(x11751)+~P7(x11751,f11(x11751,x11752),f10(x11751))+P7(x11751,f10(x11751),x11752)
% 1.96/1.91 [1283]~P7(a69,f9(x12831),x12832)+P7(a1,x12831,f27(a69,x12832))+~P7(a1,f10(a1),x12831)
% 1.96/1.91 [1284]~P7(a69,x12841,f25(x12842))+P7(a1,f27(a69,x12841),x12842)+~P7(a1,f10(a1),x12842)
% 1.96/1.91 [1285]~P7(a70,f10(a70),x12852)+~P7(a70,f10(a70),x12851)+P7(a70,f10(a70),f17(x12851,x12852))
% 1.96/1.91 [1299]P8(a69,f25(x12991),x12992)+~P8(a1,x12991,f27(a69,x12992))+~P7(a1,f10(a1),x12991)
% 1.96/1.91 [1302]~P23(x13021)+~P8(x13021,f10(x13021),x13022)+P8(x13021,f10(x13021),f13(x13021,x13022,x13022))
% 1.96/1.91 [1303]~P23(x13031)+~P7(x13031,f10(x13031),x13032)+P7(x13031,f10(x13031),f13(x13031,x13032,x13032))
% 1.96/1.91 [1304]~P57(x13041)+~P8(x13041,x13042,f10(x13041))+P8(x13041,f13(x13041,x13042,x13042),f10(x13041))
% 1.96/1.91 [1305]~P23(x13051)+~P8(x13051,x13052,f10(x13051))+P8(x13051,f13(x13051,x13052,x13052),f10(x13051))
% 1.96/1.91 [1306]~P23(x13061)+~P7(x13061,x13062,f10(x13061))+P7(x13061,f13(x13061,x13062,x13062),f10(x13061))
% 1.96/1.91 [1322]~P7(a1,x13221,x13222)+~P7(a1,f11(a1,x13222),x13221)+P7(a1,f7(a1,x13221),x13222)
% 1.96/1.91 [1397]~P57(x13971)+~P8(x13971,f13(x13971,x13972,x13972),f10(x13971))+P8(x13971,x13972,f10(x13971))
% 1.96/1.91 [1398]~P23(x13981)+~P8(x13981,f13(x13981,x13982,x13982),f10(x13981))+P8(x13981,x13982,f10(x13981))
% 1.96/1.91 [1399]~P23(x13991)+~P7(x13991,f13(x13991,x13992,x13992),f10(x13991))+P7(x13991,x13992,f10(x13991))
% 1.96/1.91 [1400]~P23(x14001)+~P8(x14001,f10(x14001),f13(x14001,x14002,x14002))+P8(x14001,f10(x14001),x14002)
% 1.96/1.91 [1401]~P23(x14011)+~P7(x14011,f10(x14011),f13(x14011,x14012,x14012))+P7(x14011,f10(x14011),x14012)
% 1.96/1.91 [1405]P8(a69,f8(a69,x14051,x14052),x14051)+~P8(a69,f10(a69),x14051)+~P8(a69,f10(a69),x14052)
% 1.96/1.91 [1410]~P7(a70,f10(a70),x14102)+~P7(a70,f10(a70),x14101)+P7(a70,f10(a70),f13(a70,x14101,x14102))
% 1.96/1.91 [1465]P8(a69,f10(a69),x14651)+P8(a69,f10(a69),x14652)+~P8(a69,f10(a69),f13(a69,x14652,x14651))
% 1.96/1.91 [715]~P34(x7151)+E(f5(x7151,x7152),f10(a69))+~E(x7152,f10(f72(x7151)))
% 1.96/1.91 [716]~P34(x7162)+~E(f5(x7162,x7161),f10(a69))+E(x7161,f10(f72(x7162)))
% 1.96/1.91 [724]~P56(x7242)+E(x7241,f10(x7242))+E(f26(x7242,f26(x7242,x7241)),x7241)
% 1.96/1.91 [734]~P49(x7342)+E(x7341,f10(x7342))+E(f28(x7342,f14(x7342,x7341)),f3(a1))
% 1.96/1.91 [735]~P57(x7351)+~E(x7352,f10(f72(x7351)))+E(f14(f72(x7351),x7352),f10(f72(x7351)))
% 1.96/1.91 [741]~P49(x7411)+~E(x7412,f10(x7411))+E(f28(x7411,f14(x7411,x7412)),f10(a1))
% 1.96/1.91 [850]~P45(x8502)+E(x8501,f10(a1))+E(f29(x8502,f26(a1,x8501)),f26(x8502,f29(x8502,x8501)))
% 1.96/1.91 [864]~P47(x8642)+E(x8641,f10(x8642))+E(f28(x8642,f26(x8642,x8641)),f26(a1,f28(x8642,x8641)))
% 1.96/1.91 [867]~P55(x8671)+~P45(x8671)+E(f29(x8671,f26(a1,x8672)),f26(x8671,f29(x8671,x8672)))
% 1.96/1.91 [873]~P56(x8732)+E(x8731,f10(x8732))+E(f26(x8732,f11(x8732,x8731)),f11(x8732,f26(x8732,x8731)))
% 1.96/1.91 [874]~P4(x8742)+E(x8741,f10(x8742))+E(f26(x8742,f7(x8742,x8741)),f7(x8742,f26(x8742,x8741)))
% 1.96/1.91 [875]~P47(x8751)+~P55(x8751)+E(f28(x8751,f26(x8751,x8752)),f26(a1,f28(x8751,x8752)))
% 1.96/1.91 [880]~P56(x8802)+E(x8801,f10(x8802))+E(f54(f54(f12(x8802),x8801),f26(x8802,x8801)),f3(x8802))
% 1.96/1.91 [919]~P57(x9191)+P8(f72(x9191),x9192,f10(f72(x9191)))+E(f7(f72(x9191),x9192),x9192)
% 1.96/1.91 [964]~P57(x9641)+P8(x9641,x9642,f10(x9641))+~E(f14(x9641,x9642),f11(x9641,f3(x9641)))
% 1.96/1.91 [990]~P57(x9901)+~P8(x9901,x9902,f10(x9901))+E(f14(x9901,x9902),f11(x9901,f3(x9901)))
% 1.96/1.91 [1070]~P57(x10701)+~P8(f72(x10701),x10702,f10(f72(x10701)))+E(f11(f72(x10701),x10702),f7(f72(x10701),x10702))
% 1.96/1.91 [1364]E(x13641,x13642)+P8(a70,x13641,x13642)+~P8(a70,x13641,f13(a70,x13642,f3(a70)))
% 1.96/1.91 [1412]~P49(x14121)+~P44(x14121)+P7(a1,f28(x14121,f29(x14121,x14122)),f54(f54(f12(a1),f28(a1,x14122)),f46(x14121)))
% 1.96/1.91 [1413]~P49(x14131)+~P44(x14131)+P7(a1,f28(x14131,f29(x14131,x14132)),f54(f54(f12(a1),f28(a1,x14132)),f48(x14131)))
% 1.96/1.91 [1414]~P49(x14141)+~P44(x14141)+P7(a1,f28(x14141,f29(x14141,x14142)),f54(f54(f12(a1),f28(a1,x14142)),f61(x14141)))
% 1.96/1.91 [1432]~P43(x14321)+P12(x14321,x14322)+~P7(x14321,f54(x14322,f59(x14322,x14321)),f54(x14322,f56(x14322,x14321)))
% 1.96/1.91 [1588]E(f25(x15881),x15882)+~P7(a1,f27(a69,x15882),x15881)+~P8(a1,x15881,f13(a1,f27(a69,x15882),f3(a1)))
% 1.96/1.91 [1627]~P8(a1,f27(a69,x16272),x16271)+~P7(a1,x16271,f13(a1,f27(a69,x16272),f3(a1)))+E(f9(x16271),f13(a69,x16272,f3(a69)))
% 1.96/1.91 [750]~E(x7502,f3(a69))+~E(x7501,f3(a69))+E(f54(f54(f12(a69),x7501),x7502),f3(a69))
% 1.96/1.91 [798]~P70(x7981)+~E(x7982,f3(x7981))+E(f54(f54(f12(x7981),x7982),x7982),f3(x7981))
% 1.96/1.91 [824]E(x8241,f3(a69))+E(x8242,f10(a69))+~E(f54(f54(f12(a69),x8242),x8241),x8242)
% 1.96/1.91 [829]E(x8291,f10(a69))+E(x8292,f10(a69))+~E(f54(f54(f12(a69),x8292),x8291),f10(a69))
% 1.96/1.91 [893]~P70(x8931)+~E(x8932,f11(x8931,f3(x8931)))+E(f54(f54(f12(x8931),x8932),x8932),f3(x8931))
% 1.96/1.91 [960]~P56(x9602)+E(x9601,f10(x9602))+E(f54(f54(f12(x9602),f26(x9602,x9601)),x9601),f3(x9602))
% 1.96/1.91 [961]~P6(x9612)+E(x9611,f10(x9612))+E(f54(f54(f12(x9612),f26(x9612,x9611)),x9611),f3(x9612))
% 1.96/1.91 [1062]E(x10621,f3(a70))+~P8(a70,f10(a70),x10622)+~E(f54(f54(f12(a70),x10622),x10621),f3(a70))
% 1.96/1.91 [1063]E(x10631,f3(a70))+~P8(a70,f10(a70),x10631)+~E(f54(f54(f12(a70),x10631),x10632),f3(a70))
% 1.96/1.91 [1335]E(x13351,f10(a69))+P8(a69,f10(a69),x13352)+~P8(a69,f10(a69),f54(f54(f21(a69),x13352),x13351))
% 1.96/1.91 [1377]~P8(a1,f10(a1),x13772)+~P8(a1,f10(a1),x13771)+P8(a1,f10(a1),f54(f54(f12(a1),x13771),x13772))
% 1.96/1.91 [1378]~P8(a69,f10(a69),x13782)+~P8(a69,f10(a69),x13781)+P8(a69,f10(a69),f54(f54(f12(a69),x13781),x13782))
% 1.96/1.91 [1379]~P7(a70,f10(a70),x13792)+~P7(a70,f10(a70),x13791)+P7(a70,f10(a70),f54(f54(f12(a70),x13791),x13792))
% 1.96/1.91 [1479]E(x14791,f10(a69))+~E(x14792,f10(a70))+~P8(a70,f10(a70),f54(f54(f21(a70),f7(a70,x14792)),x14791))
% 1.96/1.91 [1268]~E(x12682,f10(a1))+~E(x12681,f10(a1))+E(f13(a1,f54(f54(f12(a1),x12681),x12681),f54(f54(f12(a1),x12682),x12682)),f10(a1))
% 1.96/1.91 [1671]~P7(a1,f10(a1),x16712)+~P7(a1,f10(a1),x16711)+P7(a69,f54(f54(f12(a69),f25(x16711)),f25(x16712)),f25(f54(f54(f12(a1),x16711),x16712)))
% 1.96/1.91 [1782]E(x17821,f10(a69))+E(x17822,f10(a2))+P8(a1,f28(a2,f13(a2,f3(a2),f54(f54(f12(a2),x17822),f54(f54(f21(a2),f67(x17821,x17822)),x17821)))),f3(a1))
% 1.96/1.91 [762]~E(x7622,x7623)+~P38(x7621)+P7(x7621,x7622,x7623)
% 1.96/1.91 [764]~E(x7642,x7643)+~P43(x7641)+P7(x7641,x7642,x7643)
% 1.96/1.91 [891]~P8(x8913,x8911,x8912)+~E(x8911,x8912)+~P40(x8913)
% 1.96/1.91 [892]~P8(x8923,x8921,x8922)+~E(x8921,x8922)+~P43(x8923)
% 1.96/1.91 [945]P7(x9451,x9453,x9452)+~P40(x9451)+P8(x9451,x9452,x9453)
% 1.96/1.91 [947]P7(x9471,x9473,x9472)+~P40(x9471)+P7(x9471,x9472,x9473)
% 1.96/1.91 [1018]~P38(x10181)+~P8(x10181,x10182,x10183)+P7(x10181,x10182,x10183)
% 1.96/1.91 [1020]~P43(x10201)+~P8(x10201,x10202,x10203)+P7(x10201,x10202,x10203)
% 1.96/1.91 [1084]~P8(x10841,x10843,x10842)+~P38(x10841)+~P8(x10841,x10842,x10843)
% 1.96/1.91 [1085]~P7(x10851,x10853,x10852)+~P38(x10851)+~P8(x10851,x10852,x10853)
% 1.96/1.91 [1086]~P8(x10861,x10863,x10862)+~P40(x10861)+~P8(x10861,x10862,x10863)
% 1.96/1.91 [1089]~P7(x10891,x10893,x10892)+~P40(x10891)+~P8(x10891,x10892,x10893)
% 1.96/1.91 [1090]~P8(x10901,x10903,x10902)+~P43(x10901)+~P8(x10901,x10902,x10903)
% 1.96/1.91 [1200]~P7(a1,x12001,x12003)+P7(a1,x12001,x12002)+~P7(a1,x12003,x12002)
% 1.96/1.91 [1201]~P7(a69,x12011,x12013)+P7(a69,x12011,x12012)+~P7(a69,x12013,x12012)
% 1.96/1.91 [1202]~P7(a70,x12021,x12023)+P7(a70,x12021,x12022)+~P7(a70,x12023,x12022)
% 1.96/1.91 [718]~P24(x7182)+~E(x7183,f11(x7182,x7181))+E(x7181,f11(x7182,x7183))
% 1.96/1.91 [720]~P24(x7201)+~E(f11(x7201,x7203),x7202)+E(f11(x7201,x7202),x7203)
% 1.96/1.91 [726]~P55(x7263)+E(x7261,x7262)+~E(f26(x7263,x7261),f26(x7263,x7262))
% 1.96/1.91 [727]~P24(x7273)+E(x7271,x7272)+~E(f11(x7273,x7271),f11(x7273,x7272))
% 1.96/1.91 [728]~P41(x7283)+E(x7281,x7282)+~E(f11(x7283,x7281),f11(x7283,x7282))
% 1.96/1.91 [729]~P44(x7293)+E(x7291,x7292)+~E(f29(x7293,x7291),f29(x7293,x7292))
% 1.96/1.91 [782]~E(x7822,x7823)+~P24(x7821)+E(f8(x7821,x7822,x7823),f10(x7821))
% 1.96/1.91 [783]~E(x7832,x7833)+~P16(x7831)+E(f8(x7831,x7832,x7833),f10(x7831))
% 1.96/1.91 [794]~P81(x7941)+~E(x7943,f10(x7941))+E(f13(x7941,x7942,x7943),x7942)
% 1.96/1.91 [795]~E(x7952,x7953)+~P57(x7951)+P7(f72(x7951),x7952,x7953)
% 1.96/1.91 [856]~P24(x8561)+~E(x8563,f11(x8561,x8562))+E(f13(x8561,x8562,x8563),f10(x8561))
% 1.96/1.91 [857]~P24(x8571)+~E(x8572,f11(x8571,x8573))+E(f13(x8571,x8572,x8573),f10(x8571))
% 1.96/1.91 [904]~P81(x9042)+~E(f13(x9042,x9043,x9041),x9043)+E(x9041,f10(x9042))
% 1.96/1.91 [907]~P24(x9073)+E(x9071,x9072)+~E(f8(x9073,x9071,x9072),f10(x9073))
% 1.96/1.91 [908]~P16(x9083)+E(x9081,x9082)+~E(f8(x9083,x9081,x9082),f10(x9083))
% 1.96/1.91 [937]~P24(x9372)+~E(f13(x9372,x9373,x9371),f10(x9372))+E(x9371,f11(x9372,x9373))
% 1.96/1.91 [938]~P24(x9382)+~E(f13(x9382,x9381,x9383),f10(x9382))+E(x9381,f11(x9382,x9383))
% 1.96/1.91 [939]~P24(x9391)+~E(f13(x9391,x9392,x9393),f10(x9391))+E(f11(x9391,x9392),x9393)
% 1.96/1.91 [1047]~P57(x10471)+~P10(x10471,x10473)+P10(x10471,f18(x10471,x10472,x10473))
% 1.96/1.91 [1073]~P52(x10731)+~P11(x10731,x10732,x10733)+P11(x10731,x10732,f11(x10731,x10733))
% 1.96/1.91 [1074]~P52(x10741)+~P11(x10741,x10742,x10743)+P11(x10741,f11(x10741,x10742),x10743)
% 1.96/1.91 [1119]~P52(x11191)+P11(x11191,x11192,x11193)+~P11(x11191,x11192,f11(x11191,x11193))
% 1.96/1.91 [1120]~P57(x11201)+P8(x11201,x11202,x11203)+~P8(x11201,f7(x11201,x11202),x11203)
% 1.96/1.91 [1122]~P32(x11221)+P7(x11221,x11222,x11223)+~P7(x11221,f7(x11221,x11222),x11223)
% 1.96/1.91 [1123]~P52(x11231)+P11(x11231,x11232,x11233)+~P11(x11231,f11(x11231,x11232),x11233)
% 1.96/1.91 [1152]~P31(x11521)+~P8(x11521,x11523,x11522)+P8(x11521,f11(x11521,x11522),f11(x11521,x11523))
% 1.96/1.91 [1154]~P31(x11541)+~P7(x11541,x11543,x11542)+P7(x11541,f11(x11541,x11542),f11(x11541,x11543))
% 1.96/1.91 [1156]~P41(x11561)+~P7(x11561,x11563,x11562)+P7(x11561,f11(x11561,x11562),f11(x11561,x11563))
% 1.96/1.91 [1185]~P31(x11851)+~P8(x11851,x11853,f11(x11851,x11852))+P8(x11851,x11852,f11(x11851,x11853))
% 1.96/1.91 [1187]~P31(x11871)+~P7(x11871,x11873,f11(x11871,x11872))+P7(x11871,x11872,f11(x11871,x11873))
% 1.96/1.91 [1189]~P31(x11891)+~P8(x11891,f11(x11891,x11893),x11892)+P8(x11891,f11(x11891,x11892),x11893)
% 1.96/1.91 [1190]~P57(x11901)+~P8(x11901,f7(x11901,x11902),x11903)+P8(x11901,f11(x11901,x11902),x11903)
% 1.96/1.91 [1192]~P31(x11921)+~P7(x11921,f11(x11921,x11923),x11922)+P7(x11921,f11(x11921,x11922),x11923)
% 1.96/1.91 [1194]~P32(x11941)+~P7(x11941,f7(x11941,x11942),x11943)+P7(x11941,f11(x11941,x11942),x11943)
% 1.96/1.91 [1205]~P7(a69,x12053,x12051)+~E(f8(a69,x12051,x12053),x12052)+E(x12051,f13(a69,x12052,x12053))
% 1.96/1.91 [1206]~P7(a69,x12062,x12061)+~E(x12061,f13(a69,x12063,x12062))+E(f8(a69,x12061,x12062),x12063)
% 1.96/1.91 [1214]~P31(x12141)+P8(x12141,x12142,x12143)+~P8(x12141,f11(x12141,x12143),f11(x12141,x12142))
% 1.96/1.91 [1215]~P31(x12151)+P7(x12151,x12152,x12153)+~P7(x12151,f11(x12151,x12153),f11(x12151,x12152))
% 1.96/1.91 [1216]~P41(x12161)+P7(x12161,x12162,x12163)+~P7(x12161,f11(x12161,x12163),f11(x12161,x12162))
% 1.96/1.91 [1286]~P31(x12861)+~P8(x12861,x12862,x12863)+P8(x12861,f8(x12861,x12862,x12863),f10(x12861))
% 1.96/1.91 [1287]~P31(x12871)+~P7(x12871,x12872,x12873)+P7(x12871,f8(x12871,x12872,x12873),f10(x12871))
% 1.96/1.91 [1382]~P31(x13821)+P8(x13821,x13822,x13823)+~P8(x13821,f8(x13821,x13822,x13823),f10(x13821))
% 1.96/1.91 [1383]~P31(x13831)+P7(x13831,x13832,x13833)+~P7(x13831,f8(x13831,x13832,x13833),f10(x13831))
% 1.96/1.91 [1540]~P8(a69,x15403,x15401)+~P8(a69,x15403,x15402)+P8(a69,f8(a69,x15401,x15402),f8(a69,x15401,x15403))
% 1.96/1.91 [1541]~P8(a69,x15411,x15413)+~P7(a69,x15412,x15411)+P8(a69,f8(a69,x15411,x15412),f8(a69,x15413,x15412))
% 1.96/1.91 [1614]~P7(a69,x16143,x16142)+~P7(a69,f13(a69,x16141,x16143),x16142)+P7(a69,x16141,f8(a69,x16142,x16143))
% 1.96/1.91 [1615]~P7(a69,x16152,x16153)+~P7(a69,x16151,f8(a69,x16153,x16152))+P7(a69,f13(a69,x16151,x16152),x16153)
% 1.96/1.91 [781]~P59(x7811)+~E(x7812,f10(f72(x7811)))+E(f54(f15(x7811,x7812),x7813),f10(x7811))
% 1.96/1.91 [817]~P59(x8171)+~E(x8172,f10(x8171))+E(f23(x8171,x8172,x8173),f10(f72(x8171)))
% 1.96/1.91 [818]~P34(x8181)+~E(x8182,f10(x8181))+E(f16(x8181,x8182,x8183),f10(f72(x8181)))
% 1.96/1.91 [859]~P59(x8591)+~E(x8593,f10(f72(x8591)))+E(f23(x8591,x8592,x8593),f10(f72(x8591)))
% 1.96/1.91 [921]~P59(x9211)+E(f19(x9211,x9212,x9213),f10(a69))+E(f54(f15(x9211,x9213),x9212),f10(x9211))
% 1.96/1.91 [934]~P34(x9342)+E(x9341,f10(x9342))+~E(f16(x9342,x9341,x9343),f10(f72(x9342)))
% 1.96/1.91 [935]~P34(x9352)+E(x9351,f10(x9352))+~E(f18(x9352,x9351,x9353),f10(f72(x9352)))
% 1.96/1.91 [958]~P34(x9582)+~E(f18(x9582,x9583,x9581),f10(f72(x9582)))+E(x9581,f10(f72(x9582)))
% 1.96/1.91 [1236]~P57(x12361)+~P8(f72(x12361),x12363,x12362)+P10(x12361,f8(f72(x12361),x12362,x12363))
% 1.96/1.91 [1316]~P57(x13161)+P8(f72(x13161),x13162,x13163)+~P10(x13161,f8(f72(x13161),x13163,x13162))
% 1.96/1.91 [1317]~P57(x13171)+P7(f72(x13171),x13172,x13173)+~P10(x13171,f8(f72(x13171),x13173,x13172))
% 1.96/1.91 [1536]E(x15361,f10(a1))+~P7(a1,x15362,f10(a1))+~P7(a1,f7(a1,x15361),f54(f54(f12(a1),x15362),f7(a1,x15363)))
% 1.96/1.91 [1586]P8(a69,x15862,x15861)+E(f13(a69,x15861,f66(x15861,x15862,x15863)),x15862)+P82(f54(x15863,f8(a69,x15862,x15861)))
% 1.96/1.91 [1587]P8(a69,x15872,x15871)+E(f13(a69,x15871,f68(x15871,x15872,x15873)),x15872)+P82(f54(x15873,f8(a69,x15872,x15871)))
% 1.96/1.91 [1595]E(f13(a69,x15951,f66(x15951,x15952,x15953)),x15952)+P82(f54(x15953,f8(a69,x15952,x15951)))+~P82(f54(x15953,f10(a69)))
% 1.96/1.91 [1596]E(f13(a69,x15961,f68(x15961,x15962,x15963)),x15962)+P82(f54(x15963,f8(a69,x15962,x15961)))+~P82(f54(x15963,f10(a69)))
% 1.96/1.91 [1604]~P7(a69,x16042,x16043)+~P7(a69,x16042,x16041)+E(f8(a69,f8(a69,x16041,x16042),f8(a69,x16043,x16042)),f8(a69,x16041,x16043))
% 1.96/1.91 [1619]~P8(a69,x16192,x16193)+~P82(f54(x16191,f8(a69,x16192,x16193)))+P82(f54(x16191,f10(a69)))
% 1.96/1.91 [1718]P8(a69,x17181,x17182)+~P82(f54(x17183,f66(x17182,x17181,x17183)))+P82(f54(x17183,f8(a69,x17181,x17182)))
% 1.96/1.91 [1719]P8(a69,x17191,x17192)+~P82(f54(x17193,f68(x17192,x17191,x17193)))+P82(f54(x17193,f8(a69,x17191,x17192)))
% 1.96/1.91 [1721]~P82(f54(x17211,f66(x17213,x17212,x17211)))+P82(f54(x17211,f8(a69,x17212,x17213)))+~P82(f54(x17211,f10(a69)))
% 1.96/1.91 [1722]~P82(f54(x17221,f68(x17223,x17222,x17221)))+P82(f54(x17221,f8(a69,x17222,x17223)))+~P82(f54(x17221,f10(a69)))
% 1.96/1.91 [784]~P26(x7841)+~E(x7843,f10(a69))+E(f54(f54(f21(x7841),x7842),x7843),f3(x7841))
% 1.96/1.91 [796]~P79(x7961)+~E(x7963,f10(x7961))+E(f54(f54(f12(x7961),x7962),x7963),f10(x7961))
% 1.96/1.91 [797]~P79(x7971)+~E(x7972,f10(x7971))+E(f54(f54(f12(x7971),x7972),x7973),f10(x7971))
% 1.96/1.91 [906]~P70(x9062)+E(x9061,f10(x9062))+~E(f54(f54(f21(x9062),x9061),x9063),f10(x9062))
% 1.96/1.91 [925]~P56(x9251)+E(f26(x9251,x9252),x9253)+~E(f54(f54(f12(x9251),x9252),x9253),f3(x9251))
% 1.96/1.91 [979]~P59(x9791)+~E(x9792,f11(x9791,x9793))+E(f54(f54(f12(x9791),x9792),x9792),f54(f54(f12(x9791),x9793),x9793))
% 1.96/1.91 [1038]E(x10381,x10382)+E(x10383,f10(a1))+~E(f54(f54(f12(a1),x10383),x10381),f54(f54(f12(a1),x10383),x10382))
% 1.96/1.91 [1040]E(x10401,x10402)+E(x10403,f10(a69))+~E(f54(f54(f12(a69),x10403),x10401),f54(f54(f12(a69),x10403),x10402))
% 1.96/1.91 [1041]E(x10411,x10412)+E(x10413,f10(a1))+~E(f54(f54(f12(a1),x10411),x10413),f54(f54(f12(a1),x10412),x10413))
% 1.96/1.91 [1042]E(x10421,x10422)+E(x10423,f10(a69))+~E(f54(f54(f12(a69),x10421),x10423),f54(f54(f12(a69),x10422),x10423))
% 1.96/1.91 [1234]E(x12341,x12342)+~P8(a69,f10(a69),x12343)+~E(f54(f54(f12(a69),x12343),x12341),f54(f54(f12(a69),x12343),x12342))
% 1.96/1.91 [1295]~P46(x12951)+~P8(x12951,f10(x12951),x12952)+P8(x12951,f10(x12951),f54(f54(f21(x12951),x12952),x12953))
% 1.96/1.91 [1296]~P46(x12961)+~P7(x12961,f3(x12961),x12962)+P7(x12961,f3(x12961),f54(f54(f21(x12961),x12962),x12963))
% 1.96/1.91 [1297]~P46(x12971)+~P7(x12971,f10(x12971),x12972)+P7(x12971,f10(x12971),f54(f54(f21(x12971),x12972),x12973))
% 1.96/1.91 [1502]~P8(a1,x15021,x15023)+~P8(a1,f10(a1),x15022)+P8(a1,f54(f54(f12(a1),x15021),x15022),f54(f54(f12(a1),x15023),x15022))
% 1.96/1.91 [1503]~P8(a1,x15032,x15033)+~P8(a1,f10(a1),x15031)+P8(a1,f54(f54(f12(a1),x15031),x15032),f54(f54(f12(a1),x15031),x15033))
% 1.96/1.91 [1507]~P8(a69,x15071,x15073)+~P8(a69,f10(a69),x15072)+P8(a69,f54(f54(f12(a69),x15071),x15072),f54(f54(f12(a69),x15073),x15072))
% 1.96/1.91 [1508]~P8(a69,x15082,x15083)+~P8(a69,f10(a69),x15081)+P8(a69,f54(f54(f12(a69),x15081),x15082),f54(f54(f12(a69),x15081),x15083))
% 1.96/1.91 [1509]~P8(a70,x15092,x15093)+~P8(a70,f10(a70),x15091)+P8(a70,f54(f54(f12(a70),x15091),x15092),f54(f54(f12(a70),x15091),x15093))
% 1.96/1.91 [1510]~P7(a1,x15102,x15103)+~P8(a1,f10(a1),x15101)+P7(a1,f54(f54(f12(a1),x15101),x15102),f54(f54(f12(a1),x15101),x15103))
% 1.96/1.91 [1511]~P7(a1,x15111,x15113)+~P8(a1,f10(a1),x15112)+P7(a1,f54(f54(f12(a1),x15111),x15112),f54(f54(f12(a1),x15113),x15112))
% 1.96/1.91 [1628]P8(a1,x16281,x16282)+~P8(a1,f10(a1),x16283)+~P8(a1,f54(f54(f12(a1),x16281),x16283),f54(f54(f12(a1),x16282),x16283))
% 1.96/1.91 [1629]P8(a69,x16291,x16292)+~P8(a69,f10(a69),x16293)+~P8(a69,f54(f54(f21(a69),x16293),x16291),f54(f54(f21(a69),x16293),x16292))
% 1.96/1.91 [1631]P7(a1,x16311,x16312)+~P8(a1,f10(a1),x16313)+~P7(a1,f54(f54(f12(a1),x16313),x16311),f54(f54(f12(a1),x16313),x16312))
% 1.96/1.91 [1632]P7(a1,x16321,x16322)+~P8(a1,f10(a1),x16323)+~P7(a1,f54(f54(f12(a1),x16321),x16323),f54(f54(f12(a1),x16322),x16323))
% 1.96/1.91 [1634]P7(a69,x16341,x16342)+~P8(a69,f10(a69),x16343)+~P7(a69,f54(f54(f12(a69),x16343),x16341),f54(f54(f12(a69),x16343),x16342))
% 1.96/1.91 [1635]P7(a69,x16351,x16352)+~P8(a69,f10(a69),x16353)+~P7(a69,f54(f54(f12(a69),x16351),x16353),f54(f54(f12(a69),x16352),x16353))
% 1.96/1.91 [1219]~P56(x12192)+E(x12191,f10(x12192))+E(f54(f54(f21(x12192),f26(x12192,x12191)),x12193),f26(x12192,f54(f54(f21(x12192),x12191),x12193)))
% 1.96/1.91 [1376]~P57(x13761)+~P7(x13761,f10(x13761),x13763)+E(f54(f54(f12(x13761),f7(x13761,x13762)),x13763),f7(x13761,f54(f54(f12(x13761),x13762),x13763)))
% 1.96/1.91 [1537]~P61(x15372)+E(x15371,f10(x15372))+~E(f13(x15372,f54(f54(f12(x15372),x15373),x15373),f54(f54(f12(x15372),x15371),x15371)),f10(x15372))
% 1.96/1.91 [1538]~P61(x15382)+E(x15381,f10(x15382))+~E(f13(x15382,f54(f54(f12(x15382),x15381),x15381),f54(f54(f12(x15382),x15383),x15383)),f10(x15382))
% 1.96/1.91 [1545]~P26(x15452)+E(x15451,f10(a69))+E(f54(f54(f12(x15452),x15453),f54(f54(f21(x15452),x15453),f8(a69,x15451,f3(a69)))),f54(f54(f21(x15452),x15453),x15451))
% 1.96/1.91 [1602]~P46(x16021)+~P8(x16021,f3(x16021),x16022)+P8(x16021,f3(x16021),f54(f54(f12(x16021),x16022),f54(f54(f21(x16021),x16022),x16023)))
% 1.96/1.91 [1690]~P46(x16901)+~P8(x16901,f3(x16901),x16902)+P8(x16901,f54(f54(f21(x16901),x16902),x16903),f54(f54(f12(x16901),x16902),f54(f54(f21(x16901),x16902),x16903)))
% 1.96/1.91 [1694]~P61(x16942)+E(x16941,f10(x16942))+P8(x16942,f10(x16942),f13(x16942,f54(f54(f12(x16942),x16943),x16943),f54(f54(f12(x16942),x16941),x16941)))
% 1.96/1.91 [1695]~P61(x16952)+E(x16951,f10(x16952))+P8(x16952,f10(x16952),f13(x16952,f54(f54(f12(x16952),x16951),x16951),f54(f54(f12(x16952),x16953),x16953)))
% 1.96/1.91 [1743]~P61(x17432)+E(x17431,f10(x17432))+~P7(x17432,f13(x17432,f54(f54(f12(x17432),x17433),x17433),f54(f54(f12(x17432),x17431),x17431)),f10(x17432))
% 1.96/1.91 [1744]~P61(x17442)+E(x17441,f10(x17442))+~P7(x17442,f13(x17442,f54(f54(f12(x17442),x17441),x17441),f54(f54(f12(x17442),x17443),x17443)),f10(x17442))
% 1.96/1.91 [1737]~P2(x17371)+~P8(a69,f10(a69),x17373)+E(f54(f54(f12(x17371),f54(f54(f21(x17371),x17372),f8(a69,x17373,f3(a69)))),x17372),f54(f54(f21(x17371),x17372),x17373))
% 1.96/1.91 [1093]~P17(x10933)+E(x10931,x10932)+~E(f13(x10933,x10934,x10931),f13(x10933,x10934,x10932))
% 1.96/1.91 [1094]~P18(x10943)+E(x10941,x10942)+~E(f13(x10943,x10944,x10941),f13(x10943,x10944,x10942))
% 1.96/1.91 [1096]~P17(x10963)+E(x10961,x10962)+~E(f13(x10963,x10961,x10964),f13(x10963,x10962,x10964))
% 1.96/1.91 [1097]~P34(x10973)+E(x10971,x10972)+~E(f16(x10973,x10971,x10974),f16(x10973,x10972,x10974))
% 1.96/1.91 [1195]~P39(x11952)+~P8(f77(x11951,x11952),x11953,x11954)+P7(f77(x11951,x11952),x11953,x11954)
% 1.96/1.91 [1288]~P39(x12881)+~P7(f77(x12882,x12881),x12884,x12883)+~P8(f77(x12882,x12881),x12883,x12884)
% 1.96/1.91 [1307]~P50(x13071)+~P11(f72(x13071),x13072,x13074)+P11(f72(x13071),x13072,f23(x13071,x13073,x13074))
% 1.96/1.91 [1355]~P8(a69,x13553,x13554)+P8(a69,x13551,x13552)+~E(f13(a69,x13553,x13552),f13(a69,x13551,x13554))
% 1.96/1.91 [1402]~P50(x14021)+~P11(f72(x14021),f23(x14021,x14024,x14022),x14023)+P11(f72(x14021),x14022,x14023)
% 1.96/1.91 [1438]~P29(x14381)+~P8(x14381,x14383,x14384)+P8(x14381,f13(x14381,x14382,x14383),f13(x14381,x14382,x14384))
% 1.96/1.91 [1439]~P33(x14391)+~P8(x14391,x14393,x14394)+P8(x14391,f13(x14391,x14392,x14393),f13(x14391,x14392,x14394))
% 1.96/1.91 [1440]~P29(x14401)+~P8(x14401,x14402,x14404)+P8(x14401,f13(x14401,x14402,x14403),f13(x14401,x14404,x14403))
% 1.96/1.91 [1441]~P33(x14411)+~P8(x14411,x14412,x14414)+P8(x14411,f13(x14411,x14412,x14413),f13(x14411,x14414,x14413))
% 1.96/1.91 [1442]~P29(x14421)+~P7(x14421,x14423,x14424)+P7(x14421,f13(x14421,x14422,x14423),f13(x14421,x14422,x14424))
% 1.96/1.91 [1443]~P30(x14431)+~P7(x14431,x14433,x14434)+P7(x14431,f13(x14431,x14432,x14433),f13(x14431,x14432,x14434))
% 1.96/1.91 [1444]~P29(x14441)+~P7(x14441,x14442,x14444)+P7(x14441,f13(x14441,x14442,x14443),f13(x14441,x14444,x14443))
% 1.96/1.91 [1445]~P30(x14451)+~P7(x14451,x14452,x14454)+P7(x14451,f13(x14451,x14452,x14453),f13(x14451,x14454,x14453))
% 1.96/1.91 [1539]~P8(a69,x15392,x15394)+~P8(a69,x15391,x15393)+P8(a69,f13(a69,x15391,x15392),f13(a69,x15393,x15394))
% 1.96/1.91 [1542]~P8(a70,x15421,x15423)+~P7(a70,x15422,x15424)+P8(a70,f13(a70,x15421,x15422),f13(a70,x15423,x15424))
% 1.96/1.91 [1543]~P7(a69,x15432,x15434)+~P7(a69,x15431,x15433)+P7(a69,f13(a69,x15431,x15432),f13(a69,x15433,x15434))
% 1.96/1.91 [1606]~P29(x16061)+P8(x16061,x16062,x16063)+~P8(x16061,f13(x16061,x16064,x16062),f13(x16061,x16064,x16063))
% 1.96/1.91 [1608]~P29(x16081)+P8(x16081,x16082,x16083)+~P8(x16081,f13(x16081,x16082,x16084),f13(x16081,x16083,x16084))
% 1.96/1.91 [1610]~P29(x16101)+P7(x16101,x16102,x16103)+~P7(x16101,f13(x16101,x16104,x16102),f13(x16101,x16104,x16103))
% 1.96/1.91 [1612]~P29(x16121)+P7(x16121,x16122,x16123)+~P7(x16121,f13(x16121,x16122,x16124),f13(x16121,x16123,x16124))
% 1.96/1.91 [1127]~P54(x11272)+~E(f18(x11272,x11273,x11271),f23(x11272,x11274,x11271))+E(x11271,f10(f72(x11272)))
% 1.96/1.91 [1600]~P54(x16002)+~E(f13(f72(x16002),f23(x16002,x16003,x16001),f18(x16002,x16004,x16001)),f10(f72(x16002)))+E(x16001,f10(f72(x16002)))
% 1.96/1.91 [1617]~E(x16173,f13(a69,x16174,x16172))+P82(f54(x16171,x16172))+~P82(f54(x16171,f8(a69,x16173,x16174)))
% 1.96/1.91 [1710]~P57(x17101)+P8(x17101,x17102,f13(x17101,x17103,x17104))+~P8(x17101,f7(x17101,f8(x17101,x17102,x17103)),x17104)
% 1.96/1.91 [1711]~P57(x17111)+P8(x17111,f8(x17111,x17112,x17113),x17114)+~P8(x17111,f7(x17111,f8(x17111,x17114,x17112)),x17113)
% 1.96/1.91 [1803]~P39(x18032)+P7(f77(x18031,x18032),x18033,x18034)+~P7(x18032,f54(x18033,f49(x18034,x18033,x18031,x18032)),f54(x18034,f49(x18034,x18033,x18031,x18032)))
% 1.96/1.91 [1015]~P60(x10151)+P11(x10151,x10152,x10153)+~E(x10153,f54(f54(f12(x10151),x10152),x10154))
% 1.96/1.91 [1273]~P50(x12731)+~P11(x12731,x12732,x12734)+P11(x12731,x12732,f54(f54(f12(x12731),x12733),x12734))
% 1.96/1.91 [1274]~P50(x12741)+~P11(x12741,x12742,x12743)+P11(x12741,x12742,f54(f54(f12(x12741),x12743),x12744))
% 1.96/1.91 [1312]~P59(x13121)+~E(x13122,f10(x13121))+P11(x13121,f54(f54(f12(x13121),x13122),x13123),f54(f54(f12(x13121),x13122),x13124))
% 1.96/1.91 [1359]~P50(x13591)+P11(x13591,x13592,x13593)+~P11(x13591,f54(f54(f12(x13591),x13594),x13592),x13593)
% 1.96/1.91 [1360]~P50(x13601)+P11(x13601,x13602,x13603)+~P11(x13601,f54(f54(f12(x13601),x13602),x13604),x13603)
% 1.96/1.91 [1433]~P59(x14331)+~P11(x14331,x14333,x14334)+P11(x14331,f54(f54(f12(x14331),x14332),x14333),f54(f54(f12(x14331),x14332),x14334))
% 1.96/1.91 [1496]~P7(a69,x14962,x14964)+~P7(a69,x14961,x14963)+P7(a69,f54(f54(f12(a69),x14961),x14962),f54(f54(f12(a69),x14963),x14964))
% 1.96/1.91 [1098]~P34(x10983)+E(x10981,x10982)+~E(f18(x10983,x10984,x10981),f18(x10983,x10985,x10982))
% 1.96/1.91 [1099]~P34(x10993)+E(x10991,x10992)+~E(f18(x10993,x10991,x10994),f18(x10993,x10992,x10995))
% 1.96/1.91 [1251]~P39(x12511)+P7(x12511,f54(x12512,x12513),f54(x12514,x12513))+~P7(f77(x12515,x12511),x12512,x12514)
% 1.96/1.91 [1490]~P54(x14902)+~E(f13(f72(x14902),x14903,f23(x14902,x14904,x14905)),f18(x14902,x14901,x14905))+E(x14901,f54(f15(x14902,x14903),x14904))
% 1.96/1.91 [1517]~P54(x15172)+E(x15171,f24(x15172,x15173,x15174))+~E(f13(f72(x15172),x15173,f23(x15172,x15174,x15171)),f18(x15172,x15175,x15171))
% 1.96/1.91 [1649]~E(x16492,x16494)+~P81(x16491)+E(f13(x16491,f54(f54(f12(x16491),x16492),x16493),f54(f54(f12(x16491),x16494),x16495)),f13(x16491,f54(f54(f12(x16491),x16492),x16495),f54(f54(f12(x16491),x16494),x16493)))
% 1.96/1.91 [1757]~P7(a69,x17573,x17572)+E(x17571,f13(a69,f54(f54(f12(a69),f8(a69,x17572,x17573)),x17574),x17575))+~E(f13(a69,f54(f54(f12(a69),x17573),x17574),x17571),f13(a69,f54(f54(f12(a69),x17572),x17574),x17575))
% 1.96/1.91 [1758]~P7(a69,x17582,x17581)+E(f13(a69,f54(f54(f12(a69),f8(a69,x17581,x17582)),x17583),x17584),x17585)+~E(f13(a69,f54(f54(f12(a69),x17581),x17583),x17584),f13(a69,f54(f54(f12(a69),x17582),x17583),x17585))
% 1.96/1.91 [1766]~P7(a69,x17664,x17661)+~E(x17665,f13(a69,f54(f54(f12(a69),f8(a69,x17661,x17664)),x17662),x17663))+E(f13(a69,f54(f54(f12(a69),x17661),x17662),x17663),f13(a69,f54(f54(f12(a69),x17664),x17662),x17665))
% 1.96/1.91 [1767]~P7(a69,x17674,x17671)+~E(f13(a69,f54(f54(f12(a69),f8(a69,x17671,x17674)),x17672),x17673),x17675)+E(f13(a69,f54(f54(f12(a69),x17671),x17672),x17673),f13(a69,f54(f54(f12(a69),x17674),x17672),x17675))
% 1.96/1.91 [1784]~P7(a69,x17843,x17842)+P8(a69,x17841,f13(a69,f54(f54(f12(a69),f8(a69,x17842,x17843)),x17844),x17845))+~P8(a69,f13(a69,f54(f54(f12(a69),x17843),x17844),x17841),f13(a69,f54(f54(f12(a69),x17842),x17844),x17845))
% 1.96/1.91 [1785]~P7(a69,x17853,x17852)+P7(a69,x17851,f13(a69,f54(f54(f12(a69),f8(a69,x17852,x17853)),x17854),x17855))+~P7(a69,f13(a69,f54(f54(f12(a69),x17853),x17854),x17851),f13(a69,f54(f54(f12(a69),x17852),x17854),x17855))
% 1.96/1.91 [1786]~P7(a69,x17862,x17861)+P8(a69,f13(a69,f54(f54(f12(a69),f8(a69,x17861,x17862)),x17863),x17864),x17865)+~P8(a69,f13(a69,f54(f54(f12(a69),x17861),x17863),x17864),f13(a69,f54(f54(f12(a69),x17862),x17863),x17865))
% 1.96/1.91 [1787]~P7(a69,x17872,x17871)+P7(a69,f13(a69,f54(f54(f12(a69),f8(a69,x17871,x17872)),x17873),x17874),x17875)+~P7(a69,f13(a69,f54(f54(f12(a69),x17871),x17873),x17874),f13(a69,f54(f54(f12(a69),x17872),x17873),x17875))
% 1.96/1.91 [1793]~P7(a69,x17931,x17934)+~P8(a69,x17933,f13(a69,f54(f54(f12(a69),f8(a69,x17934,x17931)),x17932),x17935))+P8(a69,f13(a69,f54(f54(f12(a69),x17931),x17932),x17933),f13(a69,f54(f54(f12(a69),x17934),x17932),x17935))
% 1.96/1.91 [1794]~P7(a69,x17941,x17944)+~P7(a69,x17943,f13(a69,f54(f54(f12(a69),f8(a69,x17944,x17941)),x17942),x17945))+P7(a69,f13(a69,f54(f54(f12(a69),x17941),x17942),x17943),f13(a69,f54(f54(f12(a69),x17944),x17942),x17945))
% 1.96/1.91 [1795]~P7(a69,x17954,x17951)+~P8(a69,f13(a69,f54(f54(f12(a69),f8(a69,x17951,x17954)),x17952),x17953),x17955)+P8(a69,f13(a69,f54(f54(f12(a69),x17951),x17952),x17953),f13(a69,f54(f54(f12(a69),x17954),x17952),x17955))
% 1.96/1.91 [1796]~P7(a69,x17964,x17961)+~P7(a69,f13(a69,f54(f54(f12(a69),f8(a69,x17961,x17964)),x17962),x17963),x17965)+P7(a69,f13(a69,f54(f54(f12(a69),x17961),x17962),x17963),f13(a69,f54(f54(f12(a69),x17964),x17962),x17965))
% 1.96/1.91 [1755]~P76(x17552)+~E(f13(x17552,f54(f54(f12(x17552),x17554),x17555),x17551),f13(x17552,f54(f54(f12(x17552),x17553),x17555),x17556))+E(x17551,f13(x17552,f54(f54(f12(x17552),f8(x17552,x17553,x17554)),x17555),x17556))
% 1.96/1.91 [1756]~P76(x17561)+~E(f13(x17561,f54(f54(f12(x17561),x17562),x17564),x17565),f13(x17561,f54(f54(f12(x17561),x17563),x17564),x17566))+E(f13(x17561,f54(f54(f12(x17561),f8(x17561,x17562,x17563)),x17564),x17565),x17566)
% 1.96/1.91 [1764]~P76(x17641)+~E(x17646,f13(x17641,f54(f54(f12(x17641),f8(x17641,x17642,x17645)),x17643),x17644))+E(f13(x17641,f54(f54(f12(x17641),x17642),x17643),x17644),f13(x17641,f54(f54(f12(x17641),x17645),x17643),x17646))
% 1.96/1.91 [1765]~P76(x17651)+~E(f13(x17651,f54(f54(f12(x17651),f8(x17651,x17652,x17655)),x17653),x17654),x17656)+E(f13(x17651,f54(f54(f12(x17651),x17652),x17653),x17654),f13(x17651,f54(f54(f12(x17651),x17655),x17653),x17656))
% 1.96/1.91 [1788]~P72(x17881)+~P8(x17881,f13(x17881,f54(f54(f12(x17881),x17884),x17885),x17882),f13(x17881,f54(f54(f12(x17881),x17883),x17885),x17886))+P8(x17881,x17882,f13(x17881,f54(f54(f12(x17881),f8(x17881,x17883,x17884)),x17885),x17886))
% 1.96/1.91 [1789]~P72(x17891)+~P7(x17891,f13(x17891,f54(f54(f12(x17891),x17894),x17895),x17892),f13(x17891,f54(f54(f12(x17891),x17893),x17895),x17896))+P7(x17891,x17892,f13(x17891,f54(f54(f12(x17891),f8(x17891,x17893,x17894)),x17895),x17896))
% 1.96/1.91 [1790]~P72(x17901)+~P8(x17901,f13(x17901,f54(f54(f12(x17901),x17902),x17904),x17905),f13(x17901,f54(f54(f12(x17901),x17903),x17904),x17906))+P8(x17901,f13(x17901,f54(f54(f12(x17901),f8(x17901,x17902,x17903)),x17904),x17905),x17906)
% 1.96/1.91 [1791]~P72(x17911)+~P7(x17911,f13(x17911,f54(f54(f12(x17911),x17912),x17914),x17915),f13(x17911,f54(f54(f12(x17911),x17913),x17914),x17916))+P7(x17911,f13(x17911,f54(f54(f12(x17911),f8(x17911,x17912,x17913)),x17914),x17915),x17916)
% 1.96/1.91 [1797]~P72(x17971)+~P8(x17971,x17974,f13(x17971,f54(f54(f12(x17971),f8(x17971,x17975,x17972)),x17973),x17976))+P8(x17971,f13(x17971,f54(f54(f12(x17971),x17972),x17973),x17974),f13(x17971,f54(f54(f12(x17971),x17975),x17973),x17976))
% 1.96/1.91 [1798]~P72(x17981)+~P7(x17981,x17984,f13(x17981,f54(f54(f12(x17981),f8(x17981,x17985,x17982)),x17983),x17986))+P7(x17981,f13(x17981,f54(f54(f12(x17981),x17982),x17983),x17984),f13(x17981,f54(f54(f12(x17981),x17985),x17983),x17986))
% 1.96/1.91 [1799]~P72(x17991)+~P8(x17991,f13(x17991,f54(f54(f12(x17991),f8(x17991,x17992,x17995)),x17993),x17994),x17996)+P8(x17991,f13(x17991,f54(f54(f12(x17991),x17992),x17993),x17994),f13(x17991,f54(f54(f12(x17991),x17995),x17993),x17996))
% 1.96/1.91 [1800]~P72(x18001)+~P7(x18001,f13(x18001,f54(f54(f12(x18001),f8(x18001,x18002,x18005)),x18003),x18004),x18006)+P7(x18001,f13(x18001,f54(f54(f12(x18001),x18002),x18003),x18004),f13(x18001,f54(f54(f12(x18001),x18005),x18003),x18006))
% 1.96/1.91 [970]~P36(x9702)+~P8(x9702,f10(x9702),x9701)+E(f14(x9702,x9701),f3(x9702))+E(x9701,f10(x9702))
% 1.96/1.91 [1178]~P4(x11782)+~P8(x11782,f26(x11782,x11781),f10(x11782))+P8(x11782,x11781,f10(x11782))+E(x11781,f10(x11782))
% 1.96/1.91 [1179]~P4(x11792)+~P8(x11792,f10(x11792),f26(x11792,x11791))+P8(x11792,f10(x11792),x11791)+E(x11791,f10(x11792))
% 1.96/1.91 [1293]~P13(x12931)+P8(x12931,f3(x12931),x12932)+~P8(x12931,f26(x12931,x12932),f3(x12931))+P7(x12931,x12932,f10(x12931))
% 1.96/1.91 [1294]~P13(x12941)+P7(x12941,f3(x12941),x12942)+~P7(x12941,f26(x12941,x12942),f3(x12941))+P7(x12941,x12942,f10(x12941))
% 1.96/1.91 [1323]~P4(x13231)+~P8(x13231,x13232,f3(x13231))+~P8(x13231,f10(x13231),x13232)+P8(x13231,f3(x13231),f26(x13231,x13232))
% 1.96/1.91 [1324]~P13(x13241)+~P8(x13241,x13242,f3(x13241))+~P8(x13241,f10(x13241),x13242)+P8(x13241,f3(x13241),f26(x13241,x13242))
% 1.96/1.91 [1325]~P4(x13251)+~P7(x13251,x13252,f3(x13251))+~P8(x13251,f10(x13251),x13252)+P7(x13251,f3(x13251),f26(x13251,x13252))
% 1.96/1.91 [1326]~P13(x13261)+~P7(x13261,x13262,f3(x13261))+~P8(x13261,f10(x13261),x13262)+P7(x13261,f3(x13261),f26(x13261,x13262))
% 1.96/1.91 [832]P10(x8322,x8321)+~P57(x8322)+P10(x8322,f11(f72(x8322),x8321))+E(x8321,f10(f72(x8322)))
% 1.96/1.91 [920]~P36(x9202)+P8(x9202,f10(x9202),x9201)+E(x9201,f10(x9202))+E(f14(x9202,x9201),f11(x9202,f3(x9202)))
% 1.96/1.91 [1072]~P57(x10722)+~P8(f72(x10722),f10(f72(x10722)),x10721)+E(f14(f72(x10722),x10721),f3(f72(x10722)))+E(x10721,f10(f72(x10722)))
% 1.96/1.91 [833]~P26(x8332)+~P78(x8332)+E(x8331,f10(a69))+E(f54(f54(f21(x8332),f10(x8332)),x8331),f10(x8332))
% 1.96/1.91 [965]~P70(x9652)+E(x9651,f3(x9652))+E(x9651,f11(x9652,f3(x9652)))+~E(f54(f54(f12(x9652),x9651),x9651),f3(x9652))
% 1.96/1.91 [1024]~E(x10242,f3(a70))+~E(x10241,f3(a70))+~P8(a70,f10(a70),x10241)+E(f54(f54(f12(a70),x10241),x10242),f3(a70))
% 1.96/1.91 [1053]~P57(x10532)+P8(f72(x10532),f10(f72(x10532)),x10531)+E(x10531,f10(f72(x10532)))+E(f14(f72(x10532),x10531),f11(f72(x10532),f3(f72(x10532))))
% 1.96/1.91 [1741]~P8(a1,x17412,x17411)+~P7(a1,x17411,f3(a1))+~P7(a1,f10(a1),x17412)+P8(a1,f13(a1,f7(a1,f8(a1,f3(a1),x17411)),x17412),f3(a1))
% 1.96/1.91 [951]P8(x9513,x9511,x9512)+~P57(x9513)+E(x9511,x9512)+P8(x9513,x9512,x9511)
% 1.96/1.91 [957]P8(x9573,x9571,x9572)+~P40(x9573)+E(x9571,x9572)+P8(x9573,x9572,x9571)
% 1.96/1.91 [959]P7(x9591,x9592,x9593)+~E(x9592,x9593)+~P40(x9591)+P8(x9591,x9592,x9593)
% 1.96/1.91 [1027]~P43(x10273)+~P7(x10273,x10272,x10271)+E(x10271,x10272)+P8(x10273,x10272,x10271)
% 1.96/1.91 [1029]~P40(x10293)+~P7(x10293,x10291,x10292)+E(x10291,x10292)+P8(x10293,x10291,x10292)
% 1.96/1.91 [1035]~P43(x10353)+~P7(x10353,x10351,x10352)+E(x10351,x10352)+P8(x10353,x10351,x10352)
% 1.96/1.91 [1105]~P7(x11053,x11052,x11051)+~P7(x11053,x11051,x11052)+E(x11051,x11052)+~P43(x11053)
% 1.96/1.91 [1161]P7(x11611,x11613,x11612)+~P38(x11611)+~P7(x11611,x11612,x11613)+P8(x11611,x11612,x11613)
% 1.96/1.91 [751]~P59(x7513)+~P37(x7513)+E(x7511,x7512)+~E(f15(x7513,x7511),f15(x7513,x7512))
% 1.96/1.91 [1309]~P57(x13091)+P10(x13091,x13092)+P8(x13091,f10(x13091),x13093)+~P10(x13091,f18(x13091,x13093,x13092))
% 1.96/1.91 [1338]~P4(x13381)+~P8(x13381,x13383,x13382)+~P8(x13381,x13382,f10(x13381))+P8(x13381,f26(x13381,x13382),f26(x13381,x13383))
% 1.96/1.91 [1339]~P4(x13391)+~P7(x13391,x13393,x13392)+~P8(x13391,x13392,f10(x13391))+P7(x13391,f26(x13391,x13392),f26(x13391,x13393))
% 1.96/1.91 [1340]~P4(x13401)+~P8(x13401,x13403,x13402)+~P8(x13401,f10(x13401),x13403)+P8(x13401,f26(x13401,x13402),f26(x13401,x13403))
% 1.96/1.91 [1341]~P4(x13411)+~P7(x13411,x13413,x13412)+~P8(x13411,f10(x13411),x13413)+P7(x13411,f26(x13411,x13412),f26(x13411,x13413))
% 1.96/1.91 [1350]~P57(x13501)+~P8(x13501,x13502,x13503)+~P8(x13501,f11(x13501,x13502),x13503)+P8(x13501,f7(x13501,x13502),x13503)
% 1.96/1.91 [1352]~P32(x13521)+~P7(x13521,x13522,x13523)+~P7(x13521,f11(x13521,x13522),x13523)+P7(x13521,f7(x13521,x13522),x13523)
% 1.96/1.91 [1384]~P4(x13841)+P8(x13841,x13842,x13843)+~P8(x13841,x13842,f10(x13841))+~P8(x13841,f26(x13841,x13843),f26(x13841,x13842))
% 1.96/1.91 [1385]~P4(x13851)+P7(x13851,x13852,x13853)+~P8(x13851,x13852,f10(x13851))+~P7(x13851,f26(x13851,x13853),f26(x13851,x13852))
% 1.96/1.91 [1386]~P4(x13861)+P8(x13861,x13862,x13863)+~P8(x13861,f10(x13861),x13863)+~P8(x13861,f26(x13861,x13863),f26(x13861,x13862))
% 1.96/1.91 [1387]~P4(x13871)+P7(x13871,x13872,x13873)+~P8(x13871,f10(x13871),x13873)+~P7(x13871,f26(x13871,x13873),f26(x13871,x13872))
% 1.96/1.91 [1406]E(x14061,x14062)+~P7(a69,x14063,x14062)+~P7(a69,x14063,x14061)+~E(f8(a69,x14061,x14063),f8(a69,x14062,x14063))
% 1.96/1.91 [1466]~P27(x14661)+~P8(x14661,f10(x14661),x14663)+~P8(x14661,f10(x14661),x14662)+P8(x14661,f10(x14661),f13(x14661,x14662,x14663))
% 1.96/1.91 [1470]~P27(x14701)+~P8(x14701,x14703,f10(x14701))+~P8(x14701,x14702,f10(x14701))+P8(x14701,f13(x14701,x14702,x14703),f10(x14701))
% 1.96/1.91 [1471]~P27(x14711)+~P8(x14711,x14713,f10(x14711))+~P7(x14711,x14712,f10(x14711))+P8(x14711,f13(x14711,x14712,x14713),f10(x14711))
% 1.96/1.91 [1472]~P27(x14721)+~P8(x14721,x14722,f10(x14721))+~P7(x14721,x14723,f10(x14721))+P8(x14721,f13(x14721,x14722,x14723),f10(x14721))
% 1.96/1.91 [1473]~P27(x14731)+~P7(x14731,x14733,f10(x14731))+~P7(x14731,x14732,f10(x14731))+P7(x14731,f13(x14731,x14732,x14733),f10(x14731))
% 1.96/1.91 [1708]~P7(a69,x17083,x17081)+P8(a69,x17081,x17082)+~P7(a69,x17083,x17082)+~P8(a69,f8(a69,x17081,x17083),f8(a69,x17082,x17083))
% 1.96/1.91 [1709]~P7(a69,x17093,x17091)+P7(a69,x17091,x17092)+~P7(a69,x17093,x17092)+~P7(a69,f8(a69,x17091,x17093),f8(a69,x17092,x17093))
% 1.96/1.91 [900]~P34(x9001)+~E(x9002,f10(x9001))+~E(x9003,f10(f72(x9001)))+E(f18(x9001,x9002,x9003),f10(f72(x9001)))
% 1.96/1.91 [969]~P59(x9692)+E(x9691,f10(x9692))+~E(f23(x9692,x9691,x9693),f10(f72(x9692)))+E(x9693,f10(f72(x9692)))
% 1.96/1.91 [1078]~P59(x10782)+~E(f19(x10782,x10783,x10781),f10(a69))+~E(f54(f15(x10782,x10781),x10783),f10(x10782))+E(x10781,f10(f72(x10782)))
% 1.96/1.91 [1117]~P57(x11171)+~P10(x11171,x11173)+~P10(x11171,x11172)+P10(x11171,f13(f72(x11171),x11172,x11173))
% 1.96/1.91 [1207]P10(x12072,x12071)+~P57(x12072)+~P10(x12072,f18(x12072,x12073,x12071))+E(x12071,f10(f72(x12072)))
% 1.96/1.91 [1239]~P57(x12393)+E(x12391,x12392)+~P7(f72(x12393),x12391,x12392)+P10(x12393,f8(f72(x12393),x12392,x12391))
% 1.96/1.91 [1257]~P57(x12571)+~P8(x12571,f10(x12571),x12572)+P10(x12571,f18(x12571,x12572,x12573))+~E(x12573,f10(f72(x12571)))
% 1.96/1.91 [1476]~P47(x14761)+~P7(a1,x14763,f28(x14761,x14762))+~P8(a1,f10(a1),x14763)+P7(a1,f28(x14761,f26(x14761,x14762)),f26(a1,x14763))
% 1.96/1.91 [1751]~P56(x17512)+E(x17511,f10(x17512))+E(x17513,f10(x17512))+E(f54(f54(f12(x17512),f54(f54(f12(x17512),f26(x17512,x17513)),f13(x17512,x17513,x17511))),f26(x17512,x17511)),f13(x17512,f26(x17512,x17513),f26(x17512,x17511)))
% 1.96/1.91 [1752]~P56(x17522)+E(x17521,f10(x17522))+E(x17523,f10(x17522))+E(f54(f54(f12(x17522),f54(f54(f12(x17522),f26(x17522,x17523)),f8(x17522,x17521,x17523))),f26(x17522,x17521)),f8(x17522,f26(x17522,x17523),f26(x17522,x17521)))
% 1.96/1.91 [1770]~P6(x17702)+E(x17701,f10(x17702))+E(x17703,f10(x17702))+E(f54(f54(f12(x17702),f54(f54(f12(x17702),f13(x17702,x17703,x17701)),f26(x17702,x17703))),f26(x17702,x17701)),f13(x17702,f26(x17702,x17703),f26(x17702,x17701)))
% 1.96/1.91 [914]~P68(x9142)+E(x9141,f10(x9142))+E(x9143,f10(x9142))+~E(f54(f54(f12(x9142),x9143),x9141),f10(x9142))
% 1.96/1.91 [915]~P79(x9152)+E(x9151,f10(x9152))+E(x9153,f10(x9152))+~E(f54(f54(f12(x9152),x9153),x9151),f10(x9152))
% 1.96/1.91 [1118]~P59(x11183)+E(x11181,x11182)+E(x11181,f11(x11183,x11182))+~E(f54(f54(f12(x11183),x11181),x11181),f54(f54(f12(x11183),x11182),x11182))
% 1.96/1.91 [1434]~P46(x14341)+~P8(x14341,f3(x14341),x14342)+~P8(a69,f10(a69),x14343)+P8(x14341,f3(x14341),f54(f54(f21(x14341),x14342),x14343))
% 1.96/1.91 [1446]~P61(x14461)+~P8(x14461,x14463,f10(x14461))+~P8(x14461,x14462,f10(x14461))+P8(x14461,f10(x14461),f54(f54(f12(x14461),x14462),x14463))
% 1.96/1.91 [1448]~P72(x14481)+~P7(x14481,x14483,f10(x14481))+~P7(x14481,x14482,f10(x14481))+P7(x14481,f10(x14481),f54(f54(f12(x14481),x14482),x14483))
% 1.96/1.91 [1449]~P61(x14491)+~P7(x14491,x14493,f10(x14491))+~P7(x14491,x14492,f10(x14491))+P7(x14491,f10(x14491),f54(f54(f12(x14491),x14492),x14493))
% 1.96/1.91 [1450]~P46(x14501)+~P8(x14501,f3(x14501),x14503)+~P8(x14501,f3(x14501),x14502)+P8(x14501,f3(x14501),f54(f54(f12(x14501),x14502),x14503))
% 1.96/1.91 [1451]~P67(x14511)+~P8(x14511,f10(x14511),x14513)+~P8(x14511,f10(x14511),x14512)+P8(x14511,f10(x14511),f54(f54(f12(x14511),x14512),x14513))
% 1.96/1.91 [1452]~P71(x14521)+~P7(x14521,f10(x14521),x14523)+~P7(x14521,f10(x14521),x14522)+P7(x14521,f10(x14521),f54(f54(f12(x14521),x14522),x14523))
% 1.96/1.91 [1453]~P72(x14531)+~P7(x14531,f10(x14531),x14533)+~P7(x14531,f10(x14531),x14532)+P7(x14531,f10(x14531),f54(f54(f12(x14531),x14532),x14533))
% 1.96/1.91 [1454]~P61(x14541)+~P7(x14541,f10(x14541),x14543)+~P7(x14541,f10(x14541),x14542)+P7(x14541,f10(x14541),f54(f54(f12(x14541),x14542),x14543))
% 1.96/1.91 [1456]~P67(x14561)+~P8(x14561,x14563,f10(x14561))+~P8(x14561,f10(x14561),x14562)+P8(x14561,f54(f54(f12(x14561),x14562),x14563),f10(x14561))
% 1.96/1.91 [1457]~P67(x14571)+~P8(x14571,x14572,f10(x14571))+~P8(x14571,f10(x14571),x14573)+P8(x14571,f54(f54(f12(x14571),x14572),x14573),f10(x14571))
% 1.96/1.91 [1460]~P71(x14601)+~P7(x14601,x14603,f10(x14601))+~P7(x14601,f10(x14601),x14602)+P7(x14601,f54(f54(f12(x14601),x14602),x14603),f10(x14601))
% 1.96/1.91 [1462]~P71(x14621)+~P7(x14621,x14622,f10(x14621))+~P7(x14621,f10(x14621),x14623)+P7(x14621,f54(f54(f12(x14621),x14622),x14623),f10(x14621))
% 1.96/1.91 [1463]~P61(x14631)+~P7(x14631,x14633,f10(x14631))+~P7(x14631,f10(x14631),x14632)+P7(x14631,f54(f54(f12(x14631),x14632),x14633),f10(x14631))
% 1.96/1.91 [1464]~P61(x14641)+~P7(x14641,x14642,f10(x14641))+~P7(x14641,f10(x14641),x14643)+P7(x14641,f54(f54(f12(x14641),x14642),x14643),f10(x14641))
% 1.96/1.91 [1480]~P61(x14801)+P7(x14801,x14802,f10(x14801))+P7(x14801,x14803,f10(x14801))+~P7(x14801,f54(f54(f12(x14801),x14803),x14802),f10(x14801))
% 1.96/1.91 [1481]~P61(x14811)+P7(x14811,x14812,f10(x14811))+P7(x14811,f10(x14811),x14813)+~P7(x14811,f10(x14811),f54(f54(f12(x14811),x14813),x14812))
% 1.96/1.91 [1482]~P61(x14821)+P7(x14821,x14822,f10(x14821))+P7(x14821,f10(x14821),x14823)+~P7(x14821,f10(x14821),f54(f54(f12(x14821),x14822),x14823))
% 1.96/1.91 [1483]~P61(x14831)+P7(x14831,f10(x14831),x14832)+P7(x14831,x14832,f10(x14831))+~P7(x14831,f10(x14831),f54(f54(f12(x14831),x14833),x14832))
% 1.96/1.91 [1484]~P61(x14841)+P7(x14841,f10(x14841),x14842)+P7(x14841,x14842,f10(x14841))+~P7(x14841,f10(x14841),f54(f54(f12(x14841),x14842),x14843))
% 1.96/1.91 [1485]~P61(x14851)+P7(x14851,f10(x14851),x14852)+P7(x14851,x14852,f10(x14851))+~P7(x14851,f54(f54(f12(x14851),x14853),x14852),f10(x14851))
% 1.96/1.91 [1486]~P61(x14861)+P7(x14861,f10(x14861),x14862)+P7(x14861,x14862,f10(x14861))+~P7(x14861,f54(f54(f12(x14861),x14862),x14863),f10(x14861))
% 1.96/1.91 [1487]~P61(x14871)+P7(x14871,f10(x14871),x14872)+P7(x14871,f10(x14871),x14873)+~P7(x14871,f54(f54(f12(x14871),x14872),x14873),f10(x14871))
% 1.96/1.91 [1527]~P67(x15271)+P8(x15271,f10(x15271),x15272)+~P8(x15271,f10(x15271),x15273)+~P8(x15271,f10(x15271),f54(f54(f12(x15271),x15273),x15272))
% 1.96/1.91 [1528]~P67(x15281)+P8(x15281,f10(x15281),x15282)+~P8(x15281,f10(x15281),x15283)+~P8(x15281,f10(x15281),f54(f54(f12(x15281),x15282),x15283))
% 1.96/1.91 [1779]~P56(x17792)+E(x17791,f10(x17792))+E(x17793,f10(x17792))+E(f11(x17792,f54(f54(f12(x17792),f54(f54(f12(x17792),f26(x17792,x17793)),f8(x17792,x17793,x17791))),f26(x17792,x17791))),f8(x17792,f26(x17792,x17793),f26(x17792,x17791)))
% 1.96/1.91 [1198]~P57(x11981)+~P10(x11981,x11983)+~P10(x11981,x11982)+P10(x11981,f54(f54(f12(f72(x11981)),x11982),x11983))
% 1.96/1.91 [1290]~P56(x12902)+E(x12901,f10(x12902))+E(x12903,f10(x12902))+E(f54(f54(f12(x12902),f26(x12902,x12901)),f26(x12902,x12903)),f26(x12902,f54(f54(f12(x12902),x12903),x12901)))
% 1.96/1.91 [1330]~P61(x13301)+~E(x13303,f10(x13301))+~E(x13302,f10(x13301))+E(f13(x13301,f54(f54(f12(x13301),x13302),x13302),f54(f54(f12(x13301),x13303),x13303)),f10(x13301))
% 1.96/1.91 [1551]~P75(x15511)+~P7(x15511,x15512,f10(x15511))+~P7(x15511,x15513,f10(x15511))+E(f54(f54(f12(x15511),f7(x15511,x15512)),f7(x15511,x15513)),f7(x15511,f54(f54(f12(x15511),x15512),x15513)))
% 1.96/1.91 [1552]~P75(x15521)+~P7(x15521,x15522,f10(x15521))+~P7(x15521,f10(x15521),x15523)+E(f54(f54(f12(x15521),f7(x15521,x15522)),f7(x15521,x15523)),f7(x15521,f54(f54(f12(x15521),x15522),x15523)))
% 1.96/1.91 [1553]~P75(x15531)+~P7(x15531,x15533,f10(x15531))+~P7(x15531,f10(x15531),x15532)+E(f54(f54(f12(x15531),f7(x15531,x15532)),f7(x15531,x15533)),f7(x15531,f54(f54(f12(x15531),x15532),x15533)))
% 1.96/1.91 [1554]~P75(x15541)+~P7(x15541,f10(x15541),x15542)+~P7(x15541,f10(x15541),x15543)+E(f54(f54(f12(x15541),f7(x15541,x15542)),f7(x15541,x15543)),f7(x15541,f54(f54(f12(x15541),x15542),x15543)))
% 1.96/1.91 [1594]~P8(a70,x15942,x15943)+~P8(a70,f10(a70),x15943)+P7(a70,f3(a70),x15941)+~E(f13(a70,x15942,f54(f54(f12(a70),x15943),x15941)),x15943)
% 1.96/1.91 [1597]~P8(a70,f10(a70),x15973)+~P7(a70,f10(a70),x15972)+P7(a70,x15971,f3(a70))+~E(f13(a70,x15972,f54(f54(f12(a70),x15973),x15971)),x15973)
% 1.96/1.91 [1696]~P61(x16961)+~E(x16963,f10(x16961))+~E(x16962,f10(x16961))+P7(x16961,f13(x16961,f54(f54(f12(x16961),x16962),x16962),f54(f54(f12(x16961),x16963),x16963)),f10(x16961))
% 1.96/1.91 [1716]~P46(x17161)+~P8(x17161,x17162,f3(x17161))+~P8(x17161,f10(x17161),x17162)+P8(x17161,f54(f54(f12(x17161),x17162),f54(f54(f21(x17161),x17162),x17163)),f54(f54(f21(x17161),x17162),x17163))
% 1.96/1.91 [1729]~P8(a70,x17292,x17293)+~P8(a70,f10(a70),x17293)+P7(a70,f10(a70),x17291)+~P7(a70,f10(a70),f13(a70,f54(f54(f12(a70),x17293),x17291),x17292))
% 1.96/1.91 [1730]P7(a70,x17301,f10(a70))+~P8(a70,f10(a70),x17302)+~P7(a70,f10(a70),x17303)+~P8(a70,f13(a70,f54(f54(f12(a70),x17302),x17301),x17303),f10(a70))
% 1.96/1.91 [1746]~P61(x17462)+~E(x17461,f10(x17462))+~E(x17463,f10(x17462))+~P8(x17462,f10(x17462),f13(x17462,f54(f54(f12(x17462),x17463),x17463),f54(f54(f12(x17462),x17461),x17461)))
% 1.96/1.91 [1223]~P43(x12231)+~P8(x12231,x12234,x12233)+P8(x12231,x12232,x12233)+~P8(x12231,x12232,x12234)
% 1.96/1.91 [1224]~P43(x12241)+~P7(x12241,x12244,x12243)+P8(x12241,x12242,x12243)+~P8(x12241,x12242,x12244)
% 1.96/1.91 [1225]~P43(x12251)+~P7(x12251,x12252,x12254)+P8(x12251,x12252,x12253)+~P8(x12251,x12254,x12253)
% 1.96/1.91 [1226]~P38(x12261)+~P8(x12261,x12262,x12264)+P8(x12261,x12262,x12263)+~P8(x12261,x12264,x12263)
% 1.96/1.91 [1227]~P38(x12271)+~P7(x12271,x12272,x12274)+P8(x12271,x12272,x12273)+~P8(x12271,x12274,x12273)
% 1.96/1.91 [1228]~P38(x12281)+~P7(x12281,x12284,x12283)+P8(x12281,x12282,x12283)+~P8(x12281,x12282,x12284)
% 1.96/1.91 [1229]~P43(x12291)+~P7(x12291,x12294,x12293)+P7(x12291,x12292,x12293)+~P7(x12291,x12292,x12294)
% 1.96/1.91 [1230]~P38(x12301)+~P7(x12301,x12302,x12304)+P7(x12301,x12302,x12303)+~P7(x12301,x12304,x12303)
% 1.96/1.91 [1199]~P43(x11991)+~P12(x11991,x11992)+~P7(a69,x11994,x11993)+P7(x11991,f54(x11992,x11993),f54(x11992,x11994))
% 1.96/1.91 [1313]~P6(x13132)+~P11(f72(x13132),x13133,x13134)+P11(f72(x13132),x13133,f23(x13132,x13131,x13134))+E(x13131,f10(x13132))
% 1.96/1.91 [1315]~P6(x13152)+~P11(f72(x13152),x13153,x13154)+P11(f72(x13152),f23(x13152,x13151,x13153),x13154)+E(x13151,f10(x13152))
% 1.96/1.91 [1337]~P39(x13372)+P7(f77(x13371,x13372),x13374,x13373)+~P7(f77(x13371,x13372),x13373,x13374)+P8(f77(x13371,x13372),x13373,x13374)
% 1.96/1.91 [1408]~P6(x14082)+~P11(f72(x14082),x14083,f23(x14082,x14081,x14084))+P11(f72(x14082),x14083,x14084)+E(x14081,f10(x14082))
% 1.96/1.91 [1409]~P6(x14092)+~P11(f72(x14092),f23(x14092,x14091,x14093),x14094)+P11(f72(x14092),x14093,x14094)+E(x14091,f10(x14092))
% 1.96/1.91 [1415]~P52(x14151)+~P11(x14151,x14152,x14154)+~P11(x14151,x14152,x14153)+P11(x14151,x14152,f8(x14151,x14153,x14154))
% 1.96/1.91 [1426]~P46(x14261)+~P8(x14261,x14262,x14264)+~P8(x14261,f10(x14261),x14263)+P8(x14261,x14262,f13(x14261,x14263,x14264))
% 1.96/1.91 [1427]~P27(x14271)+~P8(x14271,x14272,x14274)+~P7(x14271,f10(x14271),x14273)+P8(x14271,x14272,f13(x14271,x14273,x14274))
% 1.96/1.91 [1428]~P27(x14281)+~P7(x14281,x14282,x14284)+~P8(x14281,f10(x14281),x14283)+P8(x14281,x14282,f13(x14281,x14283,x14284))
% 1.96/1.91 [1429]~P27(x14291)+~P7(x14291,x14292,x14293)+~P7(x14291,f10(x14291),x14294)+P7(x14291,x14292,f13(x14291,x14293,x14294))
% 1.96/1.91 [1430]~P27(x14301)+~P7(x14301,x14302,x14304)+~P7(x14301,f10(x14301),x14303)+P7(x14301,x14302,f13(x14301,x14303,x14304))
% 1.96/1.91 [1157]~P6(x11571)+P11(f72(x11571),f23(x11571,x11572,x11573),x11574)+~E(x11572,f10(x11571))+~E(x11574,f10(f72(x11571)))
% 1.96/1.91 [1331]~P6(x13311)+~P11(f72(x13311),x13313,x13314)+P11(f72(x13311),f23(x13311,x13312,x13313),x13314)+~E(x13314,f10(f72(x13311)))
% 1.96/1.91 [1336]~P6(x13362)+~P11(f72(x13362),f23(x13362,x13363,x13364),x13361)+~E(x13363,f10(x13362))+E(x13361,f10(f72(x13362)))
% 1.96/1.91 [1583]~P49(x15832)+E(x15831,f10(x15832))+~P7(a1,x15833,f10(a1))+~P7(a1,f28(x15832,x15831),f54(f54(f12(a1),x15833),f28(x15832,x15834)))
% 1.96/1.91 [1734]~P57(x17341)+~P8(x17341,x17342,f13(x17341,x17343,x17344))+~P8(x17341,f8(x17341,x17343,x17344),x17342)+P8(x17341,f7(x17341,f8(x17341,x17342,x17343)),x17344)
% 1.96/1.91 [1301]~P46(x13013)+E(x13011,x13012)+~P8(x13013,f3(x13013),x13014)+~E(f54(f54(f21(x13013),x13014),x13011),f54(f54(f21(x13013),x13014),x13012))
% 1.96/1.91 [1556]~P46(x15561)+~P8(a69,x15563,x15564)+~P8(x15561,f3(x15561),x15562)+P8(x15561,f54(f54(f21(x15561),x15562),x15563),f54(f54(f21(x15561),x15562),x15564))
% 1.96/1.91 [1557]~P46(x15571)+~P7(a69,x15573,x15574)+~P8(x15571,f3(x15571),x15572)+P7(x15571,f54(f54(f21(x15571),x15572),x15573),f54(f54(f21(x15571),x15572),x15574))
% 1.96/1.91 [1558]~P46(x15581)+~P7(a69,x15583,x15584)+~P7(x15581,f3(x15581),x15582)+P7(x15581,f54(f54(f21(x15581),x15582),x15583),f54(f54(f21(x15581),x15582),x15584))
% 1.96/1.91 [1567]~P61(x15671)+~P8(x15671,x15674,x15672)+~P8(x15671,x15673,f10(x15671))+P8(x15671,f54(f54(f12(x15671),x15672),x15673),f54(f54(f12(x15671),x15674),x15673))
% 1.96/1.91 [1568]~P61(x15681)+~P8(x15681,x15684,x15683)+~P8(x15681,x15682,f10(x15681))+P8(x15681,f54(f54(f12(x15681),x15682),x15683),f54(f54(f12(x15681),x15682),x15684))
% 1.96/1.91 [1569]~P72(x15691)+~P7(x15691,x15694,x15693)+~P7(x15691,x15692,f10(x15691))+P7(x15691,f54(f54(f12(x15691),x15692),x15693),f54(f54(f12(x15691),x15692),x15694))
% 1.96/1.91 [1570]~P61(x15701)+~P7(x15701,x15704,x15703)+~P8(x15701,x15702,f10(x15701))+P7(x15701,f54(f54(f12(x15701),x15702),x15703),f54(f54(f12(x15701),x15702),x15704))
% 1.96/1.91 [1571]~P72(x15711)+~P7(x15711,x15714,x15712)+~P7(x15711,x15713,f10(x15711))+P7(x15711,f54(f54(f12(x15711),x15712),x15713),f54(f54(f12(x15711),x15714),x15713))
% 1.96/1.91 [1573]~P67(x15731)+~P8(x15731,x15733,x15734)+~P8(x15731,f10(x15731),x15732)+P8(x15731,f54(f54(f12(x15731),x15732),x15733),f54(f54(f12(x15731),x15732),x15734))
% 1.96/1.91 [1574]~P58(x15741)+~P8(x15741,x15743,x15744)+~P8(x15741,f10(x15741),x15742)+P8(x15741,f54(f54(f12(x15741),x15742),x15743),f54(f54(f12(x15741),x15742),x15744))
% 1.96/1.91 [1575]~P61(x15751)+~P8(x15751,x15752,x15754)+~P8(x15751,f10(x15751),x15753)+P8(x15751,f54(f54(f12(x15751),x15752),x15753),f54(f54(f12(x15751),x15754),x15753))
% 1.96/1.91 [1576]~P67(x15761)+~P8(x15761,x15762,x15764)+~P8(x15761,f10(x15761),x15763)+P8(x15761,f54(f54(f12(x15761),x15762),x15763),f54(f54(f12(x15761),x15764),x15763))
% 1.96/1.91 [1577]~P61(x15771)+~P8(x15771,x15773,x15774)+~P8(x15771,f10(x15771),x15772)+P8(x15771,f54(f54(f12(x15771),x15772),x15773),f54(f54(f12(x15771),x15772),x15774))
% 1.96/1.91 [1578]~P46(x15781)+~P7(x15781,x15782,x15784)+~P7(x15781,f10(x15781),x15782)+P7(x15781,f54(f54(f21(x15781),x15782),x15783),f54(f54(f21(x15781),x15784),x15783))
% 1.96/1.91 [1579]~P74(x15791)+~P7(x15791,x15793,x15794)+~P7(x15791,f10(x15791),x15792)+P7(x15791,f54(f54(f12(x15791),x15792),x15793),f54(f54(f12(x15791),x15792),x15794))
% 1.96/1.91 [1580]~P73(x15801)+~P7(x15801,x15803,x15804)+~P7(x15801,f10(x15801),x15802)+P7(x15801,f54(f54(f12(x15801),x15802),x15803),f54(f54(f12(x15801),x15802),x15804))
% 1.96/1.91 [1581]~P61(x15811)+~P7(x15811,x15813,x15814)+~P8(x15811,f10(x15811),x15812)+P7(x15811,f54(f54(f12(x15811),x15812),x15813),f54(f54(f12(x15811),x15812),x15814))
% 1.96/1.91 [1582]~P74(x15821)+~P7(x15821,x15822,x15824)+~P7(x15821,f10(x15821),x15823)+P7(x15821,f54(f54(f12(x15821),x15822),x15823),f54(f54(f12(x15821),x15824),x15823))
% 1.96/1.91 [1603]~P59(x16032)+P11(x16032,x16033,x16034)+E(x16031,f10(x16032))+~P11(x16032,f54(f54(f12(x16032),x16031),x16033),f54(f54(f12(x16032),x16031),x16034))
% 1.96/1.91 [1646]P8(x16461,x16463,x16462)+~P61(x16461)+P8(x16461,x16462,x16463)+~P8(x16461,f54(f54(f12(x16461),x16464),x16462),f54(f54(f12(x16461),x16464),x16463))
% 1.96/1.91 [1647]P8(x16471,x16473,x16472)+~P61(x16471)+P8(x16471,x16472,x16473)+~P8(x16471,f54(f54(f12(x16471),x16472),x16474),f54(f54(f12(x16471),x16473),x16474))
% 1.96/1.91 [1650]~P61(x16501)+P8(x16501,x16502,x16503)+P8(x16501,x16504,f10(x16501))+~P8(x16501,f54(f54(f12(x16501),x16502),x16504),f54(f54(f12(x16501),x16503),x16504))
% 1.96/1.91 [1651]~P61(x16511)+P8(x16511,x16512,x16513)+P8(x16511,x16514,f10(x16511))+~P8(x16511,f54(f54(f12(x16511),x16514),x16512),f54(f54(f12(x16511),x16514),x16513))
% 1.96/1.91 [1652]~P61(x16521)+P8(x16521,x16522,x16523)+P8(x16521,f10(x16521),x16524)+~P8(x16521,f54(f54(f12(x16521),x16524),x16523),f54(f54(f12(x16521),x16524),x16522))
% 1.96/1.91 [1653]~P61(x16531)+P8(x16531,x16532,x16533)+P8(x16531,f10(x16531),x16534)+~P8(x16531,f54(f54(f12(x16531),x16533),x16534),f54(f54(f12(x16531),x16532),x16534))
% 1.96/1.91 [1664]~P61(x16641)+P8(x16641,f10(x16641),x16642)+P8(x16641,x16642,f10(x16641))+~P8(x16641,f54(f54(f12(x16641),x16643),x16642),f54(f54(f12(x16641),x16644),x16642))
% 1.96/1.91 [1665]~P61(x16651)+P8(x16651,f10(x16651),x16652)+P8(x16651,x16652,f10(x16651))+~P8(x16651,f54(f54(f12(x16651),x16652),x16653),f54(f54(f12(x16651),x16652),x16654))
% 1.96/1.91 [1676]~P46(x16763)+P8(a69,x16761,x16762)+~P8(x16763,f3(x16763),x16764)+~P8(x16763,f54(f54(f21(x16763),x16764),x16761),f54(f54(f21(x16763),x16764),x16762))
% 1.96/1.91 [1678]~P46(x16783)+P7(a69,x16781,x16782)+~P8(x16783,f3(x16783),x16784)+~P7(x16783,f54(f54(f21(x16783),x16784),x16781),f54(f54(f21(x16783),x16784),x16782))
% 1.96/1.91 [1679]~P61(x16791)+P8(x16791,x16792,x16793)+~P8(x16791,x16794,f10(x16791))+~P8(x16791,f54(f54(f12(x16791),x16794),x16793),f54(f54(f12(x16791),x16794),x16792))
% 1.96/1.91 [1680]~P61(x16801)+P7(x16801,x16802,x16803)+~P8(x16801,x16804,f10(x16801))+~P7(x16801,f54(f54(f12(x16801),x16804),x16803),f54(f54(f12(x16801),x16804),x16802))
% 1.96/1.91 [1681]~P61(x16811)+P8(x16811,x16812,x16813)+~P8(x16811,f10(x16811),x16814)+~P8(x16811,f54(f54(f12(x16811),x16814),x16812),f54(f54(f12(x16811),x16814),x16813))
% 1.96/1.91 [1682]~P67(x16821)+P8(x16821,x16822,x16823)+~P7(x16821,f10(x16821),x16824)+~P8(x16821,f54(f54(f12(x16821),x16824),x16822),f54(f54(f12(x16821),x16824),x16823))
% 1.96/1.91 [1683]~P66(x16831)+P8(x16831,x16832,x16833)+~P7(x16831,f10(x16831),x16834)+~P8(x16831,f54(f54(f12(x16831),x16834),x16832),f54(f54(f12(x16831),x16834),x16833))
% 1.96/1.91 [1684]~P46(x16841)+P8(x16841,x16842,x16843)+~P7(x16841,f10(x16841),x16843)+~P8(x16841,f54(f54(f21(x16841),x16842),x16844),f54(f54(f21(x16841),x16843),x16844))
% 1.96/1.91 [1685]~P67(x16851)+P8(x16851,x16852,x16853)+~P7(x16851,f10(x16851),x16854)+~P8(x16851,f54(f54(f12(x16851),x16852),x16854),f54(f54(f12(x16851),x16853),x16854))
% 1.96/1.91 [1686]~P66(x16861)+P8(x16861,x16862,x16863)+~P7(x16861,f10(x16861),x16864)+~P8(x16861,f54(f54(f12(x16861),x16862),x16864),f54(f54(f12(x16861),x16863),x16864))
% 1.96/1.91 [1687]~P61(x16871)+P7(x16871,x16872,x16873)+~P8(x16871,f10(x16871),x16874)+~P7(x16871,f54(f54(f12(x16871),x16874),x16872),f54(f54(f12(x16871),x16874),x16873))
% 1.96/1.91 [1688]~P67(x16881)+P7(x16881,x16882,x16883)+~P8(x16881,f10(x16881),x16884)+~P7(x16881,f54(f54(f12(x16881),x16884),x16882),f54(f54(f12(x16881),x16884),x16883))
% 1.96/1.91 [1689]~P67(x16891)+P7(x16891,x16892,x16893)+~P8(x16891,f10(x16891),x16894)+~P7(x16891,f54(f54(f12(x16891),x16892),x16894),f54(f54(f12(x16891),x16893),x16894))
% 1.96/1.91 [1738]~P8(a1,f10(a1),x17384)+~P8(a1,f10(a1),x17382)+P8(a1,f54(f54(f12(a1),x17381),f26(a1,x17382)),f54(f54(f12(a1),x17383),f26(a1,x17384)))+~P8(a1,f54(f54(f12(a1),x17384),x17381),f54(f54(f12(a1),x17382),x17383))
% 1.96/1.91 [1747]~P8(a1,f10(a1),x17473)+~P8(a1,f10(a1),x17471)+~P8(a1,f54(f54(f12(a1),x17473),x17472),f54(f54(f12(a1),x17471),x17474))+P8(a1,f54(f54(f12(a1),f26(a1,x17471)),x17472),f54(f54(f12(a1),f26(a1,x17473)),x17474))
% 1.96/1.91 [1700]~P78(x17003)+~P60(x17003)+P82(f54(x17001,f62(x17002,x17001,x17003)))+~P82(f54(x17001,f54(f54(f12(x17003),x17002),x17004)))
% 1.96/1.91 [1731]~P78(x17311)+~P60(x17311)+P11(x17311,x17312,f13(x17311,f62(x17312,x17313,x17311),f10(x17311)))+~P82(f54(x17313,f54(f54(f12(x17311),x17312),x17314)))
% 1.96/1.91 [1780]~P8(a1,f10(a1),x17804)+~P8(a1,f28(a2,f8(a2,x17802,x17803)),f58(x17801,x17803,x17804))+~P8(a1,f10(a1),f28(a2,f8(a2,x17802,x17803)))+P8(a1,f28(a2,f8(a2,f54(f15(a2,x17801),x17802),f54(f15(a2,x17801),x17803))),x17804)
% 1.96/1.91 [1116]~P16(x11165)+E(x11161,x11162)+~E(x11163,x11164)+~E(f8(x11165,x11163,x11164),f8(x11165,x11161,x11162))
% 1.96/1.91 [1373]~P31(x13731)+~P8(x13731,x13734,x13735)+P8(x13731,x13732,x13733)+~E(f8(x13731,x13734,x13735),f8(x13731,x13732,x13733))
% 1.96/1.91 [1375]~P31(x13751)+~P7(x13751,x13754,x13755)+P7(x13751,x13752,x13753)+~E(f8(x13751,x13754,x13755),f8(x13751,x13752,x13753))
% 1.96/1.91 [1559]~P33(x15591)+~P8(x15591,x15593,x15595)+~P8(x15591,x15592,x15594)+P8(x15591,f13(x15591,x15592,x15593),f13(x15591,x15594,x15595))
% 1.96/1.91 [1560]~P33(x15601)+~P8(x15601,x15603,x15605)+~P7(x15601,x15602,x15604)+P8(x15601,f13(x15601,x15602,x15603),f13(x15601,x15604,x15605))
% 1.96/1.91 [1561]~P33(x15611)+~P8(x15611,x15612,x15614)+~P7(x15611,x15613,x15615)+P8(x15611,f13(x15611,x15612,x15613),f13(x15611,x15614,x15615))
% 1.96/1.91 [1562]~P30(x15621)+~P7(x15621,x15623,x15625)+~P7(x15621,x15622,x15624)+P7(x15621,f13(x15621,x15622,x15623),f13(x15621,x15624,x15625))
% 1.96/1.91 [1714]~P49(x17141)+~P8(a1,f28(x17141,x17143),x17145)+~P8(a1,f28(x17141,x17142),x17144)+P8(a1,f28(x17141,f13(x17141,x17142,x17143)),f13(a1,x17144,x17145))
% 1.96/1.91 [1546]~P50(x15461)+~P11(x15461,x15463,x15465)+~P11(x15461,x15462,x15464)+P11(x15461,f54(f54(f12(x15461),x15462),x15463),f54(f54(f12(x15461),x15464),x15465))
% 1.96/1.91 [1720]~P57(x17201)+~P8(x17201,f7(x17201,x17202),x17204)+~P8(x17201,f7(x17201,x17203),x17205)+P8(x17201,f54(f54(f12(x17201),f7(x17201,x17202)),f7(x17201,x17203)),f54(f54(f12(x17201),x17204),x17205))
% 1.96/1.91 [1701]~P1(x17011)+~P8(a1,f28(x17011,x17013),x17015)+~P8(a1,f28(x17011,x17012),x17014)+P8(a1,f28(x17011,f54(f54(f12(x17011),x17012),x17013)),f54(f54(f12(a1),x17014),x17015))
% 1.96/1.91 [1736]~P81(x17365)+E(x17361,x17362)+E(x17363,x17364)+~E(f13(x17365,f54(f54(f12(x17365),x17363),x17361),f54(f54(f12(x17365),x17364),x17362)),f13(x17365,f54(f54(f12(x17365),x17363),x17362),f54(f54(f12(x17365),x17364),x17361)))
% 1.96/1.91 [1763]~E(f28(a2,x17631),f3(a1))+P8(a1,f28(a2,f8(a2,x17631,a4)),f3(a1))+P8(a1,f28(a2,f13(a2,x17631,a4)),f3(a1))+P8(a1,f28(a2,f13(a2,x17631,f3(a2))),f3(a1))+P8(a1,f28(a2,f8(a2,x17631,f3(a2))),f3(a1))
% 1.96/1.91 [760]~P56(x7603)+E(x7601,x7602)+~E(f26(x7603,x7601),f26(x7603,x7602))+E(x7602,f10(x7603))+E(x7601,f10(x7603))
% 1.96/1.91 [1342]~P27(x13422)+~P7(x13422,f10(x13422),x13423)+~P7(x13422,f10(x13422),x13421)+~E(f13(x13422,x13423,x13421),f10(x13422))+E(x13421,f10(x13422))
% 1.96/1.91 [1343]~P27(x13432)+~P7(x13432,f10(x13432),x13433)+~P7(x13432,f10(x13432),x13431)+~E(f13(x13432,x13431,x13433),f10(x13432))+E(x13431,f10(x13432))
% 1.96/1.91 [1584]~P57(x15841)+~P7(x15841,x15842,f3(x15841))+~P7(x15841,f10(x15841),x15842)+~P7(x15841,f10(x15841),x15843)+P7(x15841,f54(f54(f12(x15841),x15842),x15843),x15843)
% 1.96/1.91 [1585]~P57(x15851)+~P7(x15851,x15853,f3(x15851))+~P7(x15851,f10(x15851),x15853)+~P7(x15851,f10(x15851),x15852)+P7(x15851,f54(f54(f12(x15851),x15852),x15853),x15852)
% 1.96/1.91 [1666]~P46(x16661)+~P8(x16661,x16662,x16664)+~P7(x16661,f10(x16661),x16662)+~P8(a69,f10(a69),x16663)+P8(x16661,f54(f54(f21(x16661),x16662),x16663),f54(f54(f21(x16661),x16664),x16663))
% 1.96/1.91 [1667]~P46(x16671)+~P8(a69,x16674,x16673)+~P8(x16671,x16672,f3(x16671))+~P8(x16671,f10(x16671),x16672)+P8(x16671,f54(f54(f21(x16671),x16672),x16673),f54(f54(f21(x16671),x16672),x16674))
% 1.96/1.91 [1668]~P46(x16681)+~P7(a69,x16684,x16683)+~P7(x16681,x16682,f3(x16681))+~P7(x16681,f10(x16681),x16682)+P7(x16681,f54(f54(f21(x16681),x16682),x16683),f54(f54(f21(x16681),x16682),x16684))
% 1.96/1.91 [1748]~P78(x17482)+~P60(x17482)+~P11(x17482,x17483,f13(x17482,x17484,f10(x17482)))+~P82(f54(x17481,x17484))+P82(f54(x17481,f54(f54(f12(x17482),x17483),f63(x17483,x17481,x17482))))
% 1.96/1.91 [1753]~P49(x17534)+~P39(x17531)+~P7(x17531,x17532,x17535)+P7(x17531,x17532,f51(x17533,x17532,x17531,x17534))+P8(a1,f28(x17534,f54(x17533,x17535)),f13(a1,f3(a1),f28(x17534,f54(x17533,x17532))))
% 1.96/1.91 [1768]P7(a70,x17681,x17682)+~P8(a70,x17683,x17684)+~P8(a70,x17683,x17685)+~P7(a70,x17684,f10(a70))+~P7(a70,f13(a70,f54(f54(f12(a70),x17683),x17682),x17685),f13(a70,f54(f54(f12(a70),x17683),x17681),x17684))
% 1.96/1.91 [1769]P7(a70,x17691,x17692)+~P8(a70,x17693,x17694)+~P8(a70,x17695,x17694)+~P7(a70,f10(a70),x17695)+~P7(a70,f13(a70,f54(f54(f12(a70),x17694),x17691),x17695),f13(a70,f54(f54(f12(a70),x17694),x17692),x17693))
% 1.96/1.91 [1809]~P49(x18091)+~P7(x18095,x18094,x18093)+~P39(x18095)+P8(a1,f28(x18091,f54(x18092,x18093)),f13(a1,f3(a1),f28(x18091,f54(x18092,x18094))))+~P8(a1,f28(x18091,f8(x18091,f54(x18092,x18094),f54(x18092,f51(x18092,x18094,x18095,x18091)))),f3(a1))
% 1.96/1.91 [1636]~P81(x16364)+E(x16361,x16362)+~E(x16365,x16366)+E(x16363,f10(x16364))+~E(f13(x16364,x16365,f54(f54(f12(x16364),x16363),x16361)),f13(x16364,x16366,f54(f54(f12(x16364),x16363),x16362)))
% 1.96/1.91 [1760]~P53(x17601)+~P60(x17601)+~P11(x17601,x17602,x17605)+~P11(x17601,x17602,f13(x17601,x17603,x17606))+P11(x17601,x17602,f13(x17601,f8(x17601,x17603,f54(f54(f12(x17601),x17604),x17605)),x17606))
% 1.96/1.91 [1775]~P53(x17751)+~P60(x17751)+~P11(x17751,x17752,x17755)+P11(x17751,x17752,f13(x17751,x17753,x17754))+~P11(x17751,x17752,f13(x17751,f8(x17751,x17753,f54(f54(f12(x17751),x17756),x17755)),x17754))
% 1.96/1.91 [1311]~P27(x13111)+~P7(x13111,f10(x13111),x13113)+~P7(x13111,f10(x13111),x13112)+~E(x13113,f10(x13111))+~E(x13112,f10(x13111))+E(f13(x13111,x13112,x13113),f10(x13111))
% 1.96/1.91 [966]~P26(x9662)+~P63(x9662)+~P68(x9662)+~P69(x9662)+E(x9661,f10(x9662))+~E(f54(f54(f21(x9662),x9661),x9663),f10(x9662))
% 1.96/1.91 [967]~P26(x9672)+~P63(x9672)+~P68(x9672)+~P69(x9672)+~E(x9671,f10(a69))+~E(f54(f54(f21(x9672),x9673),x9671),f10(x9672))
% 1.96/1.91 [1591]~P46(x15913)+E(x15911,x15912)+~P7(x15913,f10(x15913),x15912)+~P7(x15913,f10(x15913),x15911)+~P8(a69,f10(a69),x15914)+~E(f54(f54(f21(x15913),x15911),x15914),f54(f54(f21(x15913),x15912),x15914))
% 1.96/1.91 [1702]~P67(x17021)+~P8(x17021,x17023,x17025)+~P8(x17021,x17022,x17024)+~P8(x17021,f10(x17021),x17024)+~P7(x17021,f10(x17021),x17023)+P8(x17021,f54(f54(f12(x17021),x17022),x17023),f54(f54(f12(x17021),x17024),x17025))
% 1.96/1.91 [1703]~P67(x17031)+~P8(x17031,x17033,x17035)+~P8(x17031,x17032,x17034)+~P7(x17031,f10(x17031),x17033)+~P7(x17031,f10(x17031),x17032)+P8(x17031,f54(f54(f12(x17031),x17032),x17033),f54(f54(f12(x17031),x17034),x17035))
% 1.96/1.91 [1704]~P67(x17041)+~P8(x17041,x17043,x17045)+~P7(x17041,x17042,x17044)+~P8(x17041,f10(x17041),x17042)+~P7(x17041,f10(x17041),x17043)+P8(x17041,f54(f54(f12(x17041),x17042),x17043),f54(f54(f12(x17041),x17044),x17045))
% 1.96/1.91 [1705]~P67(x17051)+~P8(x17051,x17052,x17054)+~P7(x17051,x17053,x17055)+~P8(x17051,f10(x17051),x17053)+~P7(x17051,f10(x17051),x17052)+P8(x17051,f54(f54(f12(x17051),x17052),x17053),f54(f54(f12(x17051),x17054),x17055))
% 1.96/1.91 [1706]~P74(x17061)+~P7(x17061,x17063,x17065)+~P7(x17061,x17062,x17064)+~P7(x17061,f10(x17061),x17063)+~P7(x17061,f10(x17061),x17064)+P7(x17061,f54(f54(f12(x17061),x17062),x17063),f54(f54(f12(x17061),x17064),x17065))
% 1.96/1.91 [1707]~P74(x17071)+~P7(x17071,x17073,x17075)+~P7(x17071,x17072,x17074)+~P7(x17071,f10(x17071),x17073)+~P7(x17071,f10(x17071),x17072)+P7(x17071,f54(f54(f12(x17071),x17072),x17073),f54(f54(f12(x17071),x17074),x17075))
% 1.96/1.91 [894]~P26(x8942)+~P63(x8942)+~P68(x8942)+~P69(x8942)+~E(x8943,f10(x8942))+E(x8941,f10(a69))+E(f54(f54(f21(x8942),x8943),x8941),f10(x8942))
% 1.96/1.91 [1749]~P64(x17491)+~P8(x17491,x17495,x17496)+~P8(x17491,x17493,x17496)+~P7(x17491,f10(x17491),x17494)+~P7(x17491,f10(x17491),x17492)+~E(f13(x17491,x17492,x17494),f3(x17491))+P8(x17491,f13(x17491,f54(f54(f12(x17491),x17492),x17493),f54(f54(f12(x17491),x17494),x17495)),x17496)
% 1.96/1.91 [1750]~P65(x17501)+~P7(x17501,x17505,x17506)+~P7(x17501,x17503,x17506)+~P7(x17501,f10(x17501),x17504)+~P7(x17501,f10(x17501),x17502)+~E(f13(x17501,x17502,x17504),f3(x17501))+P7(x17501,f13(x17501,f54(f54(f12(x17501),x17502),x17503),f54(f54(f12(x17501),x17504),x17505)),x17506)
% 1.96/1.91 [1772]~P8(a70,x17726,x17725)+~P7(a70,x17725,x17723)+P7(a70,x17721,x17722)+~P8(a70,f10(a70),x17725)+~P7(a70,f10(a70),x17724)+~P7(a70,f10(a70),f13(a70,f54(f54(f12(a70),x17725),x17722),x17726))+~E(f13(a70,f54(f54(f12(a70),x17723),x17721),x17724),f13(a70,f54(f54(f12(a70),x17725),x17722),x17726))
% 1.96/1.91 [1773]~P8(a70,x17734,x17733)+~P7(a70,x17735,x17733)+P7(a70,x17731,x17732)+~P8(a70,f10(a70),x17735)+~P7(a70,f10(a70),x17736)+~P8(a70,f13(a70,f54(f54(f12(a70),x17735),x17731),x17736),f10(a70))+~E(f13(a70,f54(f54(f12(a70),x17733),x17732),x17734),f13(a70,f54(f54(f12(a70),x17735),x17731),x17736))
% 1.96/1.91 %EqnAxiom
% 1.96/1.91 [1]E(x11,x11)
% 1.96/1.91 [2]E(x22,x21)+~E(x21,x22)
% 1.96/1.91 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.96/1.91 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 1.96/1.91 [5]~E(x51,x52)+E(f9(x51),f9(x52))
% 1.96/1.91 [6]~E(x61,x62)+E(f28(x61,x63),f28(x62,x63))
% 1.96/1.91 [7]~E(x71,x72)+E(f28(x73,x71),f28(x73,x72))
% 1.96/1.91 [8]~E(x81,x82)+E(f10(x81),f10(x82))
% 1.96/1.91 [9]~E(x91,x92)+E(f54(x91,x93),f54(x92,x93))
% 1.96/1.91 [10]~E(x101,x102)+E(f54(x103,x101),f54(x103,x102))
% 1.96/1.91 [11]~E(x111,x112)+E(f12(x111),f12(x112))
% 1.96/1.91 [12]~E(x121,x122)+E(f8(x121,x123,x124),f8(x122,x123,x124))
% 1.96/1.91 [13]~E(x131,x132)+E(f8(x133,x131,x134),f8(x133,x132,x134))
% 1.96/1.91 [14]~E(x141,x142)+E(f8(x143,x144,x141),f8(x143,x144,x142))
% 1.96/1.91 [15]~E(x151,x152)+E(f25(x151),f25(x152))
% 1.96/1.91 [16]~E(x161,x162)+E(f21(x161),f21(x162))
% 1.96/1.91 [17]~E(x171,x172)+E(f72(x171),f72(x172))
% 1.96/1.91 [18]~E(x181,x182)+E(f13(x181,x183,x184),f13(x182,x183,x184))
% 1.96/1.91 [19]~E(x191,x192)+E(f13(x193,x191,x194),f13(x193,x192,x194))
% 1.96/1.91 [20]~E(x201,x202)+E(f13(x203,x204,x201),f13(x203,x204,x202))
% 1.96/1.91 [21]~E(x211,x212)+E(f15(x211,x213),f15(x212,x213))
% 1.96/1.91 [22]~E(x221,x222)+E(f15(x223,x221),f15(x223,x222))
% 1.96/1.91 [23]~E(x231,x232)+E(f60(x231),f60(x232))
% 1.96/1.91 [24]~E(x241,x242)+E(f26(x241,x243),f26(x242,x243))
% 1.96/1.91 [25]~E(x251,x252)+E(f26(x253,x251),f26(x253,x252))
% 1.96/1.91 [26]~E(x261,x262)+E(f18(x261,x263,x264),f18(x262,x263,x264))
% 1.96/1.91 [27]~E(x271,x272)+E(f18(x273,x271,x274),f18(x273,x272,x274))
% 1.96/1.91 [28]~E(x281,x282)+E(f18(x283,x284,x281),f18(x283,x284,x282))
% 1.96/1.91 [29]~E(x291,x292)+E(f16(x291,x293,x294),f16(x292,x293,x294))
% 1.96/1.91 [30]~E(x301,x302)+E(f16(x303,x301,x304),f16(x303,x302,x304))
% 1.96/1.91 [31]~E(x311,x312)+E(f16(x313,x314,x311),f16(x313,x314,x312))
% 1.96/1.91 [32]~E(x321,x322)+E(f11(x321,x323),f11(x322,x323))
% 1.96/1.91 [33]~E(x331,x332)+E(f11(x333,x331),f11(x333,x332))
% 1.96/1.91 [34]~E(x341,x342)+E(f7(x341,x343),f7(x342,x343))
% 1.96/1.91 [35]~E(x351,x352)+E(f7(x353,x351),f7(x353,x352))
% 1.96/1.91 [36]~E(x361,x362)+E(f51(x361,x363,x364,x365),f51(x362,x363,x364,x365))
% 1.96/1.91 [37]~E(x371,x372)+E(f51(x373,x371,x374,x375),f51(x373,x372,x374,x375))
% 1.96/1.91 [38]~E(x381,x382)+E(f51(x383,x384,x381,x385),f51(x383,x384,x382,x385))
% 1.96/1.91 [39]~E(x391,x392)+E(f51(x393,x394,x395,x391),f51(x393,x394,x395,x392))
% 1.96/1.91 [40]~E(x401,x402)+E(f27(x401,x403),f27(x402,x403))
% 1.96/1.91 [41]~E(x411,x412)+E(f27(x413,x411),f27(x413,x412))
% 1.96/1.91 [42]~E(x421,x422)+E(f29(x421,x423),f29(x422,x423))
% 1.96/1.91 [43]~E(x431,x432)+E(f29(x433,x431),f29(x433,x432))
% 1.96/1.91 [44]~E(x441,x442)+E(f20(x441,x443,x444),f20(x442,x443,x444))
% 1.96/1.91 [45]~E(x451,x452)+E(f20(x453,x451,x454),f20(x453,x452,x454))
% 1.96/1.91 [46]~E(x461,x462)+E(f20(x463,x464,x461),f20(x463,x464,x462))
% 1.96/1.91 [47]~E(x471,x472)+E(f23(x471,x473,x474),f23(x472,x473,x474))
% 1.96/1.91 [48]~E(x481,x482)+E(f23(x483,x481,x484),f23(x483,x482,x484))
% 1.96/1.91 [49]~E(x491,x492)+E(f23(x493,x494,x491),f23(x493,x494,x492))
% 1.96/1.91 [50]~E(x501,x502)+E(f5(x501,x503),f5(x502,x503))
% 1.96/1.91 [51]~E(x511,x512)+E(f5(x513,x511),f5(x513,x512))
% 1.96/1.91 [52]~E(x521,x522)+E(f24(x521,x523,x524),f24(x522,x523,x524))
% 1.96/1.91 [53]~E(x531,x532)+E(f24(x533,x531,x534),f24(x533,x532,x534))
% 1.96/1.91 [54]~E(x541,x542)+E(f24(x543,x544,x541),f24(x543,x544,x542))
% 1.96/1.91 [55]~E(x551,x552)+E(f77(x551,x553),f77(x552,x553))
% 1.96/1.91 [56]~E(x561,x562)+E(f77(x563,x561),f77(x563,x562))
% 1.96/1.91 [57]~E(x571,x572)+E(f52(x571,x573),f52(x572,x573))
% 1.96/1.91 [58]~E(x581,x582)+E(f52(x583,x581),f52(x583,x582))
% 1.96/1.91 [59]~E(x591,x592)+E(f14(x591,x593),f14(x592,x593))
% 1.96/1.91 [60]~E(x601,x602)+E(f14(x603,x601),f14(x603,x602))
% 1.96/1.91 [61]~E(x611,x612)+E(f46(x611),f46(x612))
% 1.96/1.91 [62]~E(x621,x622)+E(f57(x621),f57(x622))
% 1.96/1.91 [63]~E(x631,x632)+E(f48(x631),f48(x632))
% 1.96/1.91 [64]~E(x641,x642)+E(f66(x641,x643,x644),f66(x642,x643,x644))
% 1.96/1.91 [65]~E(x651,x652)+E(f66(x653,x651,x654),f66(x653,x652,x654))
% 1.96/1.91 [66]~E(x661,x662)+E(f66(x663,x664,x661),f66(x663,x664,x662))
% 1.96/1.91 [67]~E(x671,x672)+E(f33(x671),f33(x672))
% 1.96/1.91 [68]~E(x681,x682)+E(f68(x681,x683,x684),f68(x682,x683,x684))
% 1.96/1.91 [69]~E(x691,x692)+E(f68(x693,x691,x694),f68(x693,x692,x694))
% 1.96/1.91 [70]~E(x701,x702)+E(f68(x703,x704,x701),f68(x703,x704,x702))
% 1.96/1.91 [71]~E(x711,x712)+E(f58(x711,x713,x714),f58(x712,x713,x714))
% 1.96/1.91 [72]~E(x721,x722)+E(f58(x723,x721,x724),f58(x723,x722,x724))
% 1.96/1.91 [73]~E(x731,x732)+E(f58(x733,x734,x731),f58(x733,x734,x732))
% 1.96/1.91 [74]~E(x741,x742)+E(f56(x741,x743),f56(x742,x743))
% 1.96/1.91 [75]~E(x751,x752)+E(f56(x753,x751),f56(x753,x752))
% 1.96/1.91 [76]~E(x761,x762)+E(f19(x761,x763,x764),f19(x762,x763,x764))
% 1.96/1.91 [77]~E(x771,x772)+E(f19(x773,x771,x774),f19(x773,x772,x774))
% 1.96/1.91 [78]~E(x781,x782)+E(f19(x783,x784,x781),f19(x783,x784,x782))
% 1.96/1.91 [79]~E(x791,x792)+E(f34(x791),f34(x792))
% 1.96/1.91 [80]~E(x801,x802)+E(f6(x801,x803,x804),f6(x802,x803,x804))
% 1.96/1.91 [81]~E(x811,x812)+E(f6(x813,x811,x814),f6(x813,x812,x814))
% 1.96/1.91 [82]~E(x821,x822)+E(f6(x823,x824,x821),f6(x823,x824,x822))
% 1.96/1.91 [83]~E(x831,x832)+E(f64(x831,x833),f64(x832,x833))
% 1.96/1.91 [84]~E(x841,x842)+E(f64(x843,x841),f64(x843,x842))
% 1.96/1.91 [85]~E(x851,x852)+E(f50(x851,x853),f50(x852,x853))
% 1.96/1.91 [86]~E(x861,x862)+E(f50(x863,x861),f50(x863,x862))
% 1.96/1.91 [87]~E(x871,x872)+E(f62(x871,x873,x874),f62(x872,x873,x874))
% 1.96/1.91 [88]~E(x881,x882)+E(f62(x883,x881,x884),f62(x883,x882,x884))
% 1.96/1.91 [89]~E(x891,x892)+E(f62(x893,x894,x891),f62(x893,x894,x892))
% 1.96/1.91 [90]~E(x901,x902)+E(f17(x901,x903),f17(x902,x903))
% 1.96/1.91 [91]~E(x911,x912)+E(f17(x913,x911),f17(x913,x912))
% 1.96/1.91 [92]~E(x921,x922)+E(f45(x921,x923),f45(x922,x923))
% 1.96/1.91 [93]~E(x931,x932)+E(f45(x933,x931),f45(x933,x932))
% 1.96/1.91 [94]~E(x941,x942)+E(f59(x941,x943),f59(x942,x943))
% 1.96/1.91 [95]~E(x951,x952)+E(f59(x953,x951),f59(x953,x952))
% 1.96/1.91 [96]~E(x961,x962)+E(f67(x961,x963),f67(x962,x963))
% 1.96/1.91 [97]~E(x971,x972)+E(f67(x973,x971),f67(x973,x972))
% 1.96/1.91 [98]~E(x981,x982)+E(f53(x981),f53(x982))
% 1.96/1.91 [99]~E(x991,x992)+E(f49(x991,x993,x994,x995),f49(x992,x993,x994,x995))
% 1.96/1.91 [100]~E(x1001,x1002)+E(f49(x1003,x1001,x1004,x1005),f49(x1003,x1002,x1004,x1005))
% 1.96/1.91 [101]~E(x1011,x1012)+E(f49(x1013,x1014,x1011,x1015),f49(x1013,x1014,x1012,x1015))
% 1.96/1.91 [102]~E(x1021,x1022)+E(f49(x1023,x1024,x1025,x1021),f49(x1023,x1024,x1025,x1022))
% 1.96/1.91 [103]~E(x1031,x1032)+E(f22(x1031,x1033,x1034),f22(x1032,x1033,x1034))
% 1.96/1.91 [104]~E(x1041,x1042)+E(f22(x1043,x1041,x1044),f22(x1043,x1042,x1044))
% 1.96/1.91 [105]~E(x1051,x1052)+E(f22(x1053,x1054,x1051),f22(x1053,x1054,x1052))
% 1.96/1.91 [106]~E(x1061,x1062)+E(f35(x1061),f35(x1062))
% 1.96/1.91 [107]~E(x1071,x1072)+E(f63(x1071,x1073,x1074),f63(x1072,x1073,x1074))
% 1.96/1.91 [108]~E(x1081,x1082)+E(f63(x1083,x1081,x1084),f63(x1083,x1082,x1084))
% 1.96/1.91 [109]~E(x1091,x1092)+E(f63(x1093,x1094,x1091),f63(x1093,x1094,x1092))
% 1.96/1.91 [110]~E(x1101,x1102)+E(f61(x1101),f61(x1102))
% 1.96/1.91 [111]~E(x1111,x1112)+E(f65(x1111,x1113),f65(x1112,x1113))
% 1.96/1.91 [112]~E(x1121,x1122)+E(f65(x1123,x1121),f65(x1123,x1122))
% 1.96/1.91 [113]~P1(x1131)+P1(x1132)+~E(x1131,x1132)
% 1.96/1.91 [114]P8(x1142,x1143,x1144)+~E(x1141,x1142)+~P8(x1141,x1143,x1144)
% 1.96/1.91 [115]P8(x1153,x1152,x1154)+~E(x1151,x1152)+~P8(x1153,x1151,x1154)
% 1.96/1.91 [116]P8(x1163,x1164,x1162)+~E(x1161,x1162)+~P8(x1163,x1164,x1161)
% 1.96/1.91 [117]~P46(x1171)+P46(x1172)+~E(x1171,x1172)
% 1.96/1.91 [118]P7(x1182,x1183,x1184)+~E(x1181,x1182)+~P7(x1181,x1183,x1184)
% 1.96/1.91 [119]P7(x1193,x1192,x1194)+~E(x1191,x1192)+~P7(x1193,x1191,x1194)
% 1.96/1.91 [120]P7(x1203,x1204,x1202)+~E(x1201,x1202)+~P7(x1203,x1204,x1201)
% 1.96/1.91 [121]~P54(x1211)+P54(x1212)+~E(x1211,x1212)
% 1.96/1.91 [122]~P47(x1221)+P47(x1222)+~E(x1221,x1222)
% 1.96/1.91 [123]~P31(x1231)+P31(x1232)+~E(x1231,x1232)
% 1.96/1.91 [124]~P48(x1241)+P48(x1242)+~E(x1241,x1242)
% 1.96/1.91 [125]~P52(x1251)+P52(x1252)+~E(x1251,x1252)
% 1.96/1.91 [126]~P49(x1261)+P49(x1262)+~E(x1261,x1262)
% 1.96/1.91 [127]~P38(x1271)+P38(x1272)+~E(x1271,x1272)
% 1.96/1.91 [128]~P2(x1281)+P2(x1282)+~E(x1281,x1282)
% 1.96/1.91 [129]~P39(x1291)+P39(x1292)+~E(x1291,x1292)
% 1.96/1.91 [130]~P32(x1301)+P32(x1302)+~E(x1301,x1302)
% 1.96/1.91 [131]~P57(x1311)+P57(x1312)+~E(x1311,x1312)
% 1.96/1.91 [132]~P50(x1321)+P50(x1322)+~E(x1321,x1322)
% 1.96/1.91 [133]~P24(x1331)+P24(x1332)+~E(x1331,x1332)
% 1.96/1.91 [134]~P40(x1341)+P40(x1342)+~E(x1341,x1342)
% 1.96/1.91 [135]~P51(x1351)+P51(x1352)+~E(x1351,x1352)
% 1.96/1.91 [136]~P55(x1361)+P55(x1362)+~E(x1361,x1362)
% 1.96/1.91 [137]~P34(x1371)+P34(x1372)+~E(x1371,x1372)
% 1.96/1.91 [138]~P26(x1381)+P26(x1382)+~E(x1381,x1382)
% 1.96/1.91 [139]~P5(x1391)+P5(x1392)+~E(x1391,x1392)
% 1.96/1.91 [140]P10(x1402,x1403)+~E(x1401,x1402)+~P10(x1401,x1403)
% 1.96/1.91 [141]P10(x1413,x1412)+~E(x1411,x1412)+~P10(x1413,x1411)
% 1.96/1.91 [142]P11(x1422,x1423,x1424)+~E(x1421,x1422)+~P11(x1421,x1423,x1424)
% 1.96/1.91 [143]P11(x1433,x1432,x1434)+~E(x1431,x1432)+~P11(x1433,x1431,x1434)
% 1.96/1.91 [144]P11(x1443,x1444,x1442)+~E(x1441,x1442)+~P11(x1443,x1444,x1441)
% 1.96/1.91 [145]~P63(x1451)+P63(x1452)+~E(x1451,x1452)
% 1.96/1.91 [146]~P76(x1461)+P76(x1462)+~E(x1461,x1462)
% 1.96/1.91 [147]~P59(x1471)+P59(x1472)+~E(x1471,x1472)
% 1.96/1.91 [148]~P36(x1481)+P36(x1482)+~E(x1481,x1482)
% 1.96/1.91 [149]~P68(x1491)+P68(x1492)+~E(x1491,x1492)
% 1.96/1.91 [150]~P60(x1501)+P60(x1502)+~E(x1501,x1502)
% 1.96/1.91 [151]~P61(x1511)+P61(x1512)+~E(x1511,x1512)
% 1.96/1.91 [152]~P13(x1521)+P13(x1522)+~E(x1521,x1522)
% 1.96/1.91 [153]~P69(x1531)+P69(x1532)+~E(x1531,x1532)
% 1.96/1.91 [154]~P43(x1541)+P43(x1542)+~E(x1541,x1542)
% 1.96/1.91 [155]~P4(x1551)+P4(x1552)+~E(x1551,x1552)
% 1.96/1.91 [156]~P23(x1561)+P23(x1562)+~E(x1561,x1562)
% 1.96/1.91 [157]~P56(x1571)+P56(x1572)+~E(x1571,x1572)
% 1.96/1.91 [158]~P66(x1581)+P66(x1582)+~E(x1581,x1582)
% 1.96/1.91 [159]~P81(x1591)+P81(x1592)+~E(x1591,x1592)
% 1.96/1.91 [160]~P29(x1601)+P29(x1602)+~E(x1601,x1602)
% 1.96/1.91 [161]~P82(x1611)+P82(x1612)+~E(x1611,x1612)
% 1.96/1.91 [162]~P58(x1621)+P58(x1622)+~E(x1621,x1622)
% 1.96/1.91 [163]~P70(x1631)+P70(x1632)+~E(x1631,x1632)
% 1.96/1.91 [164]~P25(x1641)+P25(x1642)+~E(x1641,x1642)
% 1.96/1.91 [165]~P44(x1651)+P44(x1652)+~E(x1651,x1652)
% 1.96/1.91 [166]~P78(x1661)+P78(x1662)+~E(x1661,x1662)
% 1.96/1.91 [167]P9(x1672,x1673,x1674)+~E(x1671,x1672)+~P9(x1671,x1673,x1674)
% 1.96/1.91 [168]P9(x1683,x1682,x1684)+~E(x1681,x1682)+~P9(x1683,x1681,x1684)
% 1.96/1.91 [169]P9(x1693,x1694,x1692)+~E(x1691,x1692)+~P9(x1693,x1694,x1691)
% 1.96/1.91 [170]~P33(x1701)+P33(x1702)+~E(x1701,x1702)
% 1.96/1.91 [171]~P17(x1711)+P17(x1712)+~E(x1711,x1712)
% 1.96/1.91 [172]~P3(x1721)+P3(x1722)+~E(x1721,x1722)
% 1.96/1.91 [173]~P62(x1731)+P62(x1732)+~E(x1731,x1732)
% 1.96/1.91 [174]~P67(x1741)+P67(x1742)+~E(x1741,x1742)
% 1.96/1.91 [175]~P53(x1751)+P53(x1752)+~E(x1751,x1752)
% 1.96/1.91 [176]~P64(x1761)+P64(x1762)+~E(x1761,x1762)
% 1.96/1.91 [177]~P21(x1771)+P21(x1772)+~E(x1771,x1772)
% 1.96/1.91 [178]~P16(x1781)+P16(x1782)+~E(x1781,x1782)
% 1.96/1.91 [179]P12(x1792,x1793)+~E(x1791,x1792)+~P12(x1791,x1793)
% 1.96/1.91 [180]P12(x1803,x1802)+~E(x1801,x1802)+~P12(x1803,x1801)
% 1.96/1.91 [181]~P65(x1811)+P65(x1812)+~E(x1811,x1812)
% 1.96/1.91 [182]~P27(x1821)+P27(x1822)+~E(x1821,x1822)
% 1.96/1.91 [183]~P72(x1831)+P72(x1832)+~E(x1831,x1832)
% 1.96/1.91 [184]~P71(x1841)+P71(x1842)+~E(x1841,x1842)
% 1.96/1.91 [185]~P79(x1851)+P79(x1852)+~E(x1851,x1852)
% 1.96/1.91 [186]~P6(x1861)+P6(x1862)+~E(x1861,x1862)
% 1.96/1.91 [187]~P41(x1871)+P41(x1872)+~E(x1871,x1872)
% 1.96/1.91 [188]~P75(x1881)+P75(x1882)+~E(x1881,x1882)
% 1.96/1.91 [189]~P35(x1891)+P35(x1892)+~E(x1891,x1892)
% 1.96/1.91 [190]~P20(x1901)+P20(x1902)+~E(x1901,x1902)
% 1.96/1.91 [191]~P45(x1911)+P45(x1912)+~E(x1911,x1912)
% 1.96/1.91 [192]~P80(x1921)+P80(x1922)+~E(x1921,x1922)
% 1.96/1.91 [193]~P18(x1931)+P18(x1932)+~E(x1931,x1932)
% 1.96/1.91 [194]~P30(x1941)+P30(x1942)+~E(x1941,x1942)
% 1.96/1.91 [195]~P22(x1951)+P22(x1952)+~E(x1951,x1952)
% 1.96/1.91 [196]~P37(x1961)+P37(x1962)+~E(x1961,x1962)
% 1.96/1.91 [197]~P28(x1971)+P28(x1972)+~E(x1971,x1972)
% 1.96/1.91 [198]~P14(x1981)+P14(x1982)+~E(x1981,x1982)
% 1.96/1.91 [199]~P77(x1991)+P77(x1992)+~E(x1991,x1992)
% 1.96/1.91 [200]~P73(x2001)+P73(x2002)+~E(x2001,x2002)
% 1.96/1.91 [201]~P42(x2011)+P42(x2012)+~E(x2011,x2012)
% 1.96/1.91 [202]~P19(x2021)+P19(x2022)+~E(x2021,x2022)
% 1.96/1.91 [203]~P74(x2031)+P74(x2032)+~E(x2031,x2032)
% 1.96/1.91 [204]~P15(x2041)+P15(x2042)+~E(x2041,x2042)
% 1.96/1.91
% 1.96/1.91 %-------------------------------------------
% 2.08/1.92 cnf(1818,plain,
% 2.08/1.92 (P7(a70,x18181,x18181)),
% 2.08/1.92 inference(rename_variables,[],[449])).
% 2.08/1.92 cnf(1821,plain,
% 2.08/1.92 (P7(a70,x18211,x18211)),
% 2.08/1.92 inference(rename_variables,[],[449])).
% 2.08/1.92 cnf(1824,plain,
% 2.08/1.92 (P7(a69,x18241,f13(a69,x18242,x18241))),
% 2.08/1.92 inference(rename_variables,[],[495])).
% 2.08/1.92 cnf(1832,plain,
% 2.08/1.92 (~P8(a69,x18321,x18321)),
% 2.08/1.92 inference(rename_variables,[],[586])).
% 2.08/1.92 cnf(1835,plain,
% 2.08/1.92 (~P8(a69,f13(a69,x18351,x18352),x18352)),
% 2.08/1.92 inference(rename_variables,[],[596])).
% 2.08/1.92 cnf(1841,plain,
% 2.08/1.92 (P7(a1,x18411,x18411)),
% 2.08/1.92 inference(rename_variables,[],[447])).
% 2.08/1.92 cnf(1848,plain,
% 2.08/1.92 (~P8(a1,f13(a1,f7(a1,x18481),f3(a1)),x18481)),
% 2.08/1.92 inference(rename_variables,[],[599])).
% 2.08/1.92 cnf(1856,plain,
% 2.08/1.92 (P7(a1,x18561,f27(a69,f9(x18561)))),
% 2.08/1.92 inference(rename_variables,[],[480])).
% 2.08/1.92 cnf(1859,plain,
% 2.08/1.92 (P8(a1,x18591,f13(a1,f27(a69,f25(x18591)),f3(a1)))),
% 2.08/1.92 inference(rename_variables,[],[515])).
% 2.08/1.92 cnf(1862,plain,
% 2.08/1.92 (P7(a69,x18621,x18621)),
% 2.08/1.92 inference(rename_variables,[],[448])).
% 2.08/1.92 cnf(1867,plain,
% 2.08/1.92 (P7(a1,x18671,f27(a69,f9(x18671)))),
% 2.08/1.92 inference(rename_variables,[],[480])).
% 2.08/1.92 cnf(1872,plain,
% 2.08/1.92 (P7(a1,x18721,x18721)),
% 2.08/1.92 inference(rename_variables,[],[447])).
% 2.08/1.92 cnf(1885,plain,
% 2.08/1.92 (~P8(a1,f13(a1,f7(a1,x18851),f3(a1)),x18851)),
% 2.08/1.92 inference(rename_variables,[],[599])).
% 2.08/1.92 cnf(1888,plain,
% 2.08/1.92 (P8(a1,x18881,f13(a1,f27(a69,f25(x18881)),f3(a1)))),
% 2.08/1.92 inference(rename_variables,[],[515])).
% 2.08/1.92 cnf(1891,plain,
% 2.08/1.92 (~P8(a69,x18911,x18911)),
% 2.08/1.92 inference(rename_variables,[],[586])).
% 2.08/1.92 cnf(1894,plain,
% 2.08/1.92 (~P8(a69,x18941,x18941)),
% 2.08/1.92 inference(rename_variables,[],[586])).
% 2.08/1.92 cnf(1897,plain,
% 2.08/1.92 (P7(a1,x18971,x18971)),
% 2.08/1.92 inference(rename_variables,[],[447])).
% 2.08/1.92 cnf(1899,plain,
% 2.08/1.92 (P7(a1,x18991,x18991)),
% 2.08/1.92 inference(rename_variables,[],[447])).
% 2.08/1.92 cnf(1916,plain,
% 2.08/1.92 (P7(a69,f10(a69),x19161)),
% 2.08/1.92 inference(rename_variables,[],[463])).
% 2.08/1.92 cnf(1943,plain,
% 2.08/1.92 (P7(a1,x19431,x19431)),
% 2.08/1.92 inference(rename_variables,[],[447])).
% 2.08/1.92 cnf(1947,plain,
% 2.08/1.92 (P7(a1,x19471,x19471)),
% 2.08/1.92 inference(rename_variables,[],[447])).
% 2.08/1.92 cnf(1963,plain,
% 2.08/1.92 (E(f8(a69,f10(a69),x19631),f10(a69))),
% 2.08/1.92 inference(rename_variables,[],[471])).
% 2.08/1.92 cnf(1970,plain,
% 2.08/1.92 ($false),
% 2.08/1.92 inference(scs_inference,[],[603,447,1841,1872,1897,1899,1943,1947,448,1862,449,1818,1821,586,1832,1891,1894,265,318,358,377,392,393,394,400,401,403,404,419,463,1916,453,455,574,438,437,472,590,504,428,431,491,554,563,602,570,495,1824,497,596,1835,440,480,1856,1867,498,467,599,1848,1885,494,471,1963,515,1859,1888,2,876,840,858,1363,1361,1349,1348,1345,1248,1243,1241,1071,994,1016,792,1275,10,1599,1520,1519,1431,1417,1177,1176,1080,1079,1004,936,932,1320,1390,1499,1497,120,119,116,115,3,1090,1089,1086,1085,1084,1067,1002,947,945,892,891,764,1405,1122,1120,1015,1299,1284,675,1539,1355,1322,1096,908,907,1631,1503]),
% 2.08/1.92 ['proof']).
% 2.08/1.92 % SZS output end Proof
% 2.08/1.92 % Total time :0.680000s
%------------------------------------------------------------------------------