TSTP Solution File: SWW267+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW267+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 : n001.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 00:13:24 EDT 2023
% Result : Theorem 13.24s 13.44s
% Output : CNFRefutation 13.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW267+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 20:12:33 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 13.24/13.37 %-------------------------------------------
% 13.24/13.37 % File :CSE---1.6
% 13.24/13.37 % Problem :theBenchmark
% 13.24/13.37 % Transform :cnf
% 13.24/13.37 % Format :tptp:raw
% 13.24/13.37 % Command :java -jar mcs_scs.jar %d %s
% 13.24/13.37
% 13.24/13.37 % Result :Theorem 12.220000s
% 13.24/13.37 % Output :CNFRefutation 12.220000s
% 13.24/13.37 %-------------------------------------------
% 13.24/13.37 %------------------------------------------------------------------------------
% 13.24/13.37 % File : SWW267+1 : TPTP v8.1.2. Released v5.2.0.
% 13.24/13.37 % Domain : Software Verification
% 13.24/13.37 % Problem : Fundamental Theorem of Algebra 438578, 1000 axioms selected
% 13.24/13.37 % Version : Especial.
% 13.24/13.37 % English :
% 13.24/13.37
% 13.24/13.37 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 13.24/13.37 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 13.24/13.37 % Source : [Bla11]
% 13.24/13.37 % Names : fta_438578.1000.p [Bla11]
% 13.24/13.37
% 13.24/13.37 % Status : Theorem
% 13.24/13.37 % Rating : 0.47 v8.1.0, 0.42 v7.5.0, 0.50 v7.3.0, 0.34 v7.1.0, 0.43 v7.0.0, 0.53 v6.4.0, 0.58 v6.3.0, 0.54 v6.2.0, 0.48 v6.1.0, 0.57 v6.0.0, 0.52 v5.5.0, 0.59 v5.4.0, 0.64 v5.3.0, 0.74 v5.2.0
% 13.24/13.37 % Syntax : Number of formulae : 1288 ( 392 unt; 0 def)
% 13.24/13.37 % Number of atoms : 2958 ( 763 equ)
% 13.24/13.37 % Maximal formula atoms : 8 ( 2 avg)
% 13.24/13.37 % Number of connectives : 1833 ( 163 ~; 53 |; 97 &)
% 13.24/13.37 % ( 224 <=>;1296 =>; 0 <=; 0 <~>)
% 13.24/13.37 % Maximal formula depth : 13 ( 4 avg)
% 13.24/13.37 % Maximal term depth : 12 ( 2 avg)
% 13.24/13.37 % Number of predicates : 83 ( 82 usr; 0 prp; 1-3 aty)
% 13.24/13.37 % Number of functors : 45 ( 45 usr; 16 con; 0-3 aty)
% 13.24/13.37 % Number of variables : 2673 (2649 !; 24 ?)
% 13.24/13.37 % SPC : FOF_THM_RFO_SEQ
% 13.24/13.38
% 13.24/13.38 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 13.24/13.38 % 2011-03-01 12:01:22
% 13.24/13.38 %------------------------------------------------------------------------------
% 13.24/13.38 %----Relevant facts (998)
% 13.24/13.38 fof(fact_ext,axiom,
% 13.24/13.38 ! [V_g_2,V_f_2] :
% 13.24/13.38 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 13.24/13.38 => V_f_2 = V_g_2 ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_t_I2_J,axiom,
% 13.24/13.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_assms,axiom,
% 13.24/13.38 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_kas_I2_J,axiom,
% 13.24/13.38 v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_kas_I1_J,axiom,
% 13.24/13.38 v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_t_I1_J,axiom,
% 13.24/13.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____) ).
% 13.24/13.38
% 13.24/13.38 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,
% 13.24/13.38 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____)))) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_w,axiom,
% 13.24/13.38 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) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_th120,axiom,
% 13.24/13.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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____)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_wm1,axiom,
% 13.24/13.38 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)) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_tw,axiom,
% 13.24/13.38 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____)) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_power__gt1__lemma,axiom,
% 13.24/13.38 ! [V_n,V_a,T_a] :
% 13.24/13.38 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.38 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 13.24/13.38 => 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))) ) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_power__less__power__Suc,axiom,
% 13.24/13.38 ! [V_n,V_a,T_a] :
% 13.24/13.38 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.38 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 13.24/13.38 => 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))) ) ) ).
% 13.24/13.38
% 13.24/13.38 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,
% 13.24/13.38 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____))))) ).
% 13.24/13.38
% 13.24/13.38 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,
% 13.24/13.38 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____)))) ).
% 13.24/13.38
% 13.24/13.38 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,
% 13.24/13.38 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____)))) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_of__real__1,axiom,
% 13.24/13.38 ! [T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.38 => c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_norm__one,axiom,
% 13.24/13.38 ! [T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 13.24/13.38 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_norm__add__less,axiom,
% 13.24/13.38 ! [V_s,V_y,V_r,V_x,T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.38 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 13.24/13.38 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 13.24/13.38 => 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)) ) ) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_norm__mult__less,axiom,
% 13.24/13.38 ! [V_s,V_y,V_r,V_x,T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.38 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 13.24/13.38 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 13.24/13.38 => 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)) ) ) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_w0,axiom,
% 13.24/13.38 v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_m_I1_J,axiom,
% 13.24/13.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ).
% 13.24/13.38
% 13.24/13.38 fof(fact__0960_A_060_At_A_094_Ak_096,axiom,
% 13.24/13.38 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____)) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_th121,axiom,
% 13.24/13.38 c_Orderings_Oord__class_Oless__eq(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)) ).
% 13.24/13.38
% 13.24/13.38 fof(fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096,axiom,
% 13.24/13.38 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____))) ).
% 13.24/13.38
% 13.24/13.38 fof(fact__096_091_124_A0_A_060_061_At_059_A0_A_060_Ak_A_124_093_A_061_061_062_At_A_094_Ak_A_060_A1_A_094_Ak_096,axiom,
% 13.24/13.38 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
% 13.24/13.38 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_k____)
% 13.24/13.38 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_k____)) ) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_m_I2_J,axiom,
% 13.24/13.38 ! [B_z] :
% 13.24/13.38 ( 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____))
% 13.24/13.38 => 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____) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact__096cmod_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_A_061t_A_094_Ak_A_K_A_It_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Acmod_A_Ipoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_J_J_096,axiom,
% 13.24/13.38 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____)))) = 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)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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____)))))) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_less_Oprems,axiom,
% 13.24/13.38 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_th12,axiom,
% 13.24/13.38 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),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____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 13.24/13.38
% 13.24/13.38 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,
% 13.24/13.38 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____)))))) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_th11,axiom,
% 13.24/13.38 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____)))))) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_norm__ge__zero,axiom,
% 13.24/13.38 ! [V_x,T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.38 => 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)) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_of__real__0,axiom,
% 13.24/13.38 ! [T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.38 => c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_of__real_Ozero,axiom,
% 13.24/13.38 ! [T_a] :
% 13.24/13.38 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.38 & class_RealVector_Oreal__normed__vector(T_a) )
% 13.24/13.38 => c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_norm__zero,axiom,
% 13.24/13.38 ! [T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.38 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_of__real__minus,axiom,
% 13.24/13.38 ! [V_x,T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.38 => 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)) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_of__real_Ominus,axiom,
% 13.24/13.38 ! [V_x,T_a] :
% 13.24/13.38 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.38 & class_RealVector_Oreal__normed__vector(T_a) )
% 13.24/13.38 => 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)) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_of__real__diff,axiom,
% 13.24/13.38 ! [V_y,V_x,T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.38 => 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)) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_of__real_Odiff,axiom,
% 13.24/13.38 ! [V_y,V_x,T_a] :
% 13.24/13.38 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.38 & class_RealVector_Oreal__normed__vector(T_a) )
% 13.24/13.38 => 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)) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_norm__triangle__ineq4,axiom,
% 13.24/13.38 ! [V_b,V_a,T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.38 => 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))) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_nat__zero__less__power__iff,axiom,
% 13.24/13.38 ! [V_n_2,V_x_2] :
% 13.24/13.38 ( 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))
% 13.24/13.38 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 13.24/13.38 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_of__real__eq__0__iff,axiom,
% 13.24/13.38 ! [V_x_2,T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.38 => ( c_RealVector_Oof__real(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.38 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_norm__eq__zero,axiom,
% 13.24/13.38 ! [V_x_2,T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.38 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 13.24/13.38 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_norm__le__zero__iff,axiom,
% 13.24/13.38 ! [V_x_2,T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.38 => ( 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))
% 13.24/13.38 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_norm__triangle__ineq2,axiom,
% 13.24/13.38 ! [V_b,V_a,T_a] :
% 13.24/13.38 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.38 => 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))) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_power__eq__0__iff,axiom,
% 13.24/13.38 ! [V_n_2,V_aa_2,T_a] :
% 13.24/13.38 ( ( class_Power_Opower(T_a)
% 13.24/13.38 & class_Rings_Omult__zero(T_a)
% 13.24/13.38 & class_Rings_Ono__zero__divisors(T_a)
% 13.24/13.38 & class_Rings_Ozero__neq__one(T_a) )
% 13.24/13.38 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.38 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.38 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_zero__le__power,axiom,
% 13.24/13.38 ! [V_n,V_a,T_a] :
% 13.24/13.38 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.38 => 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)) ) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_nat__power__less__imp__less,axiom,
% 13.24/13.38 ! [V_n,V_m,V_i] :
% 13.24/13.38 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 13.24/13.38 => ( 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))
% 13.24/13.38 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 13.24/13.38
% 13.24/13.38 fof(fact_power__mono,axiom,
% 13.24/13.38 ! [V_n,V_b,V_a,T_a] :
% 13.24/13.38 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.39 => 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)) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__eq__imp__eq__base,axiom,
% 13.24/13.39 ! [V_b,V_n,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( 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)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 13.24/13.39 => V_a = V_b ) ) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__decreasing,axiom,
% 13.24/13.39 ! [V_a,V_N,V_n,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 13.24/13.39 => 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)) ) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__strict__mono,axiom,
% 13.24/13.39 ! [V_n,V_b,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 13.24/13.39 => 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)) ) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult__left_Odiff,axiom,
% 13.24/13.39 ! [V_ya,V_y,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult_Odiff__left,axiom,
% 13.24/13.39 ! [V_b,V_a_H,V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult__right_Odiff,axiom,
% 13.24/13.39 ! [V_y,V_x,V_xa,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult_Odiff__right,axiom,
% 13.24/13.39 ! [V_b_H,V_b,V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult__left_Ominus,axiom,
% 13.24/13.39 ! [V_y,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult_Ominus__left,axiom,
% 13.24/13.39 ! [V_b,V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult__right_Ominus,axiom,
% 13.24/13.39 ! [V_x,V_xa,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult_Ominus__right,axiom,
% 13.24/13.39 ! [V_b,V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__minus__commute,axiom,
% 13.24/13.39 ! [V_b,V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__minus__cancel,axiom,
% 13.24/13.39 ! [V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__mult,axiom,
% 13.24/13.39 ! [V_n,V_m,V_a,T_a] :
% 13.24/13.39 ( class_Groups_Omonoid__mult(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult__right_Ozero,axiom,
% 13.24/13.39 ! [V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult_Ozero__right,axiom,
% 13.24/13.39 ! [V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult__left_Ozero,axiom,
% 13.24/13.39 ! [V_y,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult_Ozero__left,axiom,
% 13.24/13.39 ! [V_b,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__one__right,axiom,
% 13.24/13.39 ! [V_a,T_a] :
% 13.24/13.39 ( class_Groups_Omonoid__mult(T_a)
% 13.24/13.39 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_field__power__not__zero,axiom,
% 13.24/13.39 ! [V_n,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 13.24/13.39 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.39 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__diff__triangle__ineq,axiom,
% 13.24/13.39 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.39 => 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)))) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__diff__ineq,axiom,
% 13.24/13.39 ! [V_b,V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.39 => 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))) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__increasing,axiom,
% 13.24/13.39 ! [V_a,V_N,V_n,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 13.24/13.39 => 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)) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__less__imp__less__base,axiom,
% 13.24/13.39 ! [V_b,V_n,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( 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))
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.39 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__0__left,axiom,
% 13.24/13.39 ! [V_n,T_a] :
% 13.24/13.39 ( ( class_Power_Opower(T_a)
% 13.24/13.39 & class_Rings_Osemiring__0(T_a) )
% 13.24/13.39 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.39 => 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) )
% 13.24/13.39 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.39 => 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) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_zero__less__norm__iff,axiom,
% 13.24/13.39 ! [V_x_2,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.39 => ( 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))
% 13.24/13.39 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_constant__def,axiom,
% 13.24/13.39 ! [V_f_2,T_b,T_a] :
% 13.24/13.39 ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_a,T_b,V_f_2)
% 13.24/13.39 <=> ! [B_x,B_y] : hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__le__imp__le__exp,axiom,
% 13.24/13.39 ! [V_n,V_m,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 13.24/13.39 => ( 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))
% 13.24/13.39 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__increasing__iff,axiom,
% 13.24/13.39 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 13.24/13.39 => ( 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))
% 13.24/13.39 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_complex__mod__triangle__sub,axiom,
% 13.24/13.39 ! [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))) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult_Oprod__diff__prod,axiom,
% 13.24/13.39 ! [V_b,V_a,V_y,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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))) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__add,axiom,
% 13.24/13.39 ! [V_n,V_m,V_a,T_a] :
% 13.24/13.39 ( class_Groups_Omonoid__mult(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_one__le__power,axiom,
% 13.24/13.39 ! [V_n,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 13.24/13.39 => 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)) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__mult__ineq,axiom,
% 13.24/13.39 ! [V_y,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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))) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__triangle__ineq,axiom,
% 13.24/13.39 ! [V_y,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.39 => 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))) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_zero__less__power,axiom,
% 13.24/13.39 ! [V_n,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.39 => 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)) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__power__ineq,axiom,
% 13.24/13.39 ! [V_n,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__0,axiom,
% 13.24/13.39 ! [V_a,T_a] :
% 13.24/13.39 ( class_Power_Opower(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__not__less__zero,axiom,
% 13.24/13.39 ! [V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.39 => ~ 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__minus,axiom,
% 13.24/13.39 ! [V_n,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Oring__1(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__strict__decreasing,axiom,
% 13.24/13.39 ! [V_a,V_N,V_n,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 13.24/13.39 => 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)) ) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_one__less__power,axiom,
% 13.24/13.39 ! [V_n,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 13.24/13.39 => 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)) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_complex__of__real__power,axiom,
% 13.24/13.39 ! [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)) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__Suc__less,axiom,
% 13.24/13.39 ! [V_n,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 13.24/13.39 => 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)) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_of__real__eq__iff,axiom,
% 13.24/13.39 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.39 => ( c_RealVector_Oof__real(T_a,V_x_2) = c_RealVector_Oof__real(T_a,V_y_2)
% 13.24/13.39 <=> V_x_2 = V_y_2 ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult__left_Oadd,axiom,
% 13.24/13.39 ! [V_ya,V_y,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult_Oadd__left,axiom,
% 13.24/13.39 ! [V_b,V_a_H,V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult__right_Oadd,axiom,
% 13.24/13.39 ! [V_y,V_x,V_xa,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult_Oadd__right,axiom,
% 13.24/13.39 ! [V_b_H,V_b,V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__mult__distrib,axiom,
% 13.24/13.39 ! [V_n,V_b,V_a,T_a] :
% 13.24/13.39 ( class_Groups_Ocomm__monoid__mult(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__commutes,axiom,
% 13.24/13.39 ! [V_n,V_a,T_a] :
% 13.24/13.39 ( class_Groups_Omonoid__mult(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__one,axiom,
% 13.24/13.39 ! [V_n,T_a] :
% 13.24/13.39 ( class_Groups_Omonoid__mult(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__mult,axiom,
% 13.24/13.39 ! [V_y,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__power,axiom,
% 13.24/13.39 ! [V_n,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_of__real__mult,axiom,
% 13.24/13.39 ! [V_y,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_of__real_Oadd,axiom,
% 13.24/13.39 ! [V_y,V_x,T_a] :
% 13.24/13.39 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.39 & class_RealVector_Oreal__normed__vector(T_a) )
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_of__real__add,axiom,
% 13.24/13.39 ! [V_y,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_of__real__power,axiom,
% 13.24/13.39 ! [V_n,V_x,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__strict__increasing,axiom,
% 13.24/13.39 ! [V_a,V_N,V_n,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 13.24/13.39 => 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)) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__less__imp__less__exp,axiom,
% 13.24/13.39 ! [V_n,V_m,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 13.24/13.39 => ( 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))
% 13.24/13.39 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__strict__increasing__iff,axiom,
% 13.24/13.39 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 13.24/13.39 => ( 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))
% 13.24/13.39 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__inject__exp,axiom,
% 13.24/13.39 ! [V_n_2,V_ma_2,V_aa_2,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_aa_2)
% 13.24/13.39 => ( 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)
% 13.24/13.39 <=> V_ma_2 = V_n_2 ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact__096cmod_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_060_061_At_A_094_Ak_A_K_A_It_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_J_096,axiom,
% 13.24/13.39 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),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____)))),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____)))) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_th30,axiom,
% 13.24/13.39 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))) ).
% 13.24/13.39
% 13.24/13.39 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,
% 13.24/13.39 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)) ).
% 13.24/13.39
% 13.24/13.39 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,
% 13.24/13.39 ~ ! [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) ).
% 13.24/13.39
% 13.24/13.39 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,
% 13.24/13.39 ? [B_m] :
% 13.24/13.39 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)
% 13.24/13.39 & ! [B_z] :
% 13.24/13.39 ( 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____))
% 13.24/13.39 => 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) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact__0961_A_L_Aw_A_094_Ak_A_K_Aa_A_N_A1_A_061_A0_A_N_A1_096,axiom,
% 13.24/13.39 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)) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_convex__bound__lt,axiom,
% 13.24/13.39 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 13.24/13.39 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 13.24/13.39 => 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) ) ) ) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__ratiotest__lemma,axiom,
% 13.24/13.39 ! [V_y,V_x,V_c,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 13.24/13.39 => ( 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)))
% 13.24/13.39 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_convex__bound__le,axiom,
% 13.24/13.39 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__semiring__1(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 13.24/13.39 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 13.24/13.39 => 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) ) ) ) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_complex__mod__triangle__ineq2,axiom,
% 13.24/13.39 ! [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)) ).
% 13.24/13.39
% 13.24/13.39 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,
% 13.24/13.39 ! [V_d2] :
% 13.24/13.39 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2)
% 13.24/13.39 => ? [B_e] :
% 13.24/13.39 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
% 13.24/13.39 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 13.24/13.39 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,V_d2) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_pc0,axiom,
% 13.24/13.39 hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_c,axiom,
% 13.24/13.39 ! [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))) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_ath,axiom,
% 13.24/13.39 ! [V_t,V_x] :
% 13.24/13.39 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_t)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_t,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 13.24/13.39 => 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)) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_kn,axiom,
% 13.24/13.39 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)) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_t_I3_J,axiom,
% 13.24/13.39 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____))) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_real__norm__def,axiom,
% 13.24/13.39 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_le__Suc__ex__iff,axiom,
% 13.24/13.39 ! [V_l_2,V_ka_2] :
% 13.24/13.39 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_l_2)
% 13.24/13.39 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,B_n) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_abs__mult,axiom,
% 13.24/13.39 ! [V_b,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_abs__mult__self,axiom,
% 13.24/13.39 ! [V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_abs__one,axiom,
% 13.24/13.39 ! [T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.39 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_power__abs,axiom,
% 13.24/13.39 ! [V_n,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_abs__norm__cancel,axiom,
% 13.24/13.39 ! [V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_abs__mult__less,axiom,
% 13.24/13.39 ! [V_d,V_b,V_c,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
% 13.24/13.39 => 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)) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_abs__less__iff,axiom,
% 13.24/13.39 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)
% 13.24/13.39 <=> ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
% 13.24/13.39 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_complex__mod__minus__le__complex__mod,axiom,
% 13.24/13.39 ! [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)) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_complex__diff__def,axiom,
% 13.24/13.39 ! [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)) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_abs__eq__mult,axiom,
% 13.24/13.39 ! [V_b,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Oordered__ring__abs(T_a)
% 13.24/13.39 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.39 | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
% 13.24/13.39 & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.39 | c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 13.24/13.39 => 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)) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_abs__mult__pos,axiom,
% 13.24/13.39 ! [V_y,V_x,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 13.24/13.39 => 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)) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_abs__power__minus,axiom,
% 13.24/13.39 ! [V_n,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_rabs__ratiotest__lemma,axiom,
% 13.24/13.39 ! [V_y,V_x,V_c] :
% 13.24/13.39 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 13.24/13.39 => ( 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)))
% 13.24/13.39 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__of__real,axiom,
% 13.24/13.39 ! [V_r,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_zero__le__power__abs,axiom,
% 13.24/13.39 ! [V_n,V_a,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.39 => 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)) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_linorder__neqE__linordered__idom,axiom,
% 13.24/13.39 ! [V_y,V_x,T_a] :
% 13.24/13.39 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.39 => ( V_x != V_y
% 13.24/13.39 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.39 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_complex__of__real__minus__one,axiom,
% 13.24/13.39 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)) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_norm__triangle__ineq3,axiom,
% 13.24/13.39 ! [V_b,V_a,T_a] :
% 13.24/13.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.39 => 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))) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult__zero__left,axiom,
% 13.24/13.39 ! [V_a,T_a] :
% 13.24/13.39 ( class_Rings_Omult__zero(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult__zero__right,axiom,
% 13.24/13.39 ! [V_a,T_a] :
% 13.24/13.39 ( class_Rings_Omult__zero(T_a)
% 13.24/13.39 => 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) ) ).
% 13.24/13.39
% 13.24/13.39 fof(fact_mult__eq__0__iff,axiom,
% 13.24/13.39 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.39 ( class_Rings_Oring__no__zero__divisors(T_a)
% 13.24/13.39 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.39 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.39 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 13.24/13.39
% 13.24/13.40 fof(fact_no__zero__divisors,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Ono__zero__divisors(T_a)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_divisors__zero,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Ono__zero__divisors(T_a)
% 13.24/13.40 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_one__neq__zero,axiom,
% 13.24/13.40 ! [T_a] :
% 13.24/13.40 ( class_Rings_Ozero__neq__one(T_a)
% 13.24/13.40 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_zero__neq__one,axiom,
% 13.24/13.40 ! [T_a] :
% 13.24/13.40 ( class_Rings_Ozero__neq__one(T_a)
% 13.24/13.40 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_comm__semiring__class_Odistrib,axiom,
% 13.24/13.40 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Ocomm__semiring(T_a)
% 13.24/13.40 => 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)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_combine__common__factor,axiom,
% 13.24/13.40 ! [V_c,V_b,V_e,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Osemiring(T_a)
% 13.24/13.40 => 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) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_minus__mult__right,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oring(T_a)
% 13.24/13.40 => 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)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_minus__mult__left,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oring(T_a)
% 13.24/13.40 => 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) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_minus__mult__commute,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oring(T_a)
% 13.24/13.40 => 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)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_minus__mult__minus,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oring(T_a)
% 13.24/13.40 => 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) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_square__eq__iff,axiom,
% 13.24/13.40 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Oidom(T_a)
% 13.24/13.40 => ( 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)
% 13.24/13.40 <=> ( V_aa_2 = V_b_2
% 13.24/13.40 | V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_split__mult__neg__le,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__cancel__semiring(T_a)
% 13.24/13.40 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 13.24/13.40 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 13.24/13.40 => 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)) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_split__mult__pos__le,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__ring(T_a)
% 13.24/13.40 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 13.24/13.40 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 13.24/13.40 => 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)) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__mono,axiom,
% 13.24/13.40 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__semiring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__mono_H,axiom,
% 13.24/13.40 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__semiring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__left__mono__neg,axiom,
% 13.24/13.40 ! [V_c,V_a,V_b,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__ring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__right__mono__neg,axiom,
% 13.24/13.40 ! [V_c,V_a,V_b,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__ring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_comm__mult__left__mono,axiom,
% 13.24/13.40 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__comm__semiring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__left__mono,axiom,
% 13.24/13.40 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__semiring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__right__mono,axiom,
% 13.24/13.40 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__semiring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__nonpos__nonpos,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__ring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__nonpos__nonneg,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__cancel__semiring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__nonneg__nonpos2,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__cancel__semiring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__nonneg__nonpos,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__cancel__semiring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__nonneg__nonneg,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__cancel__semiring(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__le__0__iff,axiom,
% 13.24/13.40 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
% 13.24/13.40 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 13.24/13.40 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_zero__le__mult__iff,axiom,
% 13.24/13.40 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
% 13.24/13.40 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 13.24/13.40 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_zero__le__square,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring(T_a)
% 13.24/13.40 => 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)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_not__square__less__zero,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring(T_a)
% 13.24/13.40 => ~ 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)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__less__cancel__right__disj,axiom,
% 13.24/13.40 ! [V_b_2,V_ca_2,V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 13.24/13.40 & c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
% 13.24/13.40 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__less__cancel__left__disj,axiom,
% 13.24/13.40 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 13.24/13.40 & c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
% 13.24/13.40 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__less__cancel__left__pos,axiom,
% 13.24/13.40 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__pos__pos,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__pos__neg,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__pos__neg2,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_zero__less__mult__pos,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_zero__less__mult__pos2,axiom,
% 13.24/13.40 ! [V_a,V_b,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__less__cancel__left__neg,axiom,
% 13.24/13.40 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__neg__pos,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__neg__neg,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__strict__right__mono,axiom,
% 13.24/13.40 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__strict__left__mono,axiom,
% 13.24/13.40 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_comm__mult__strict__left__mono,axiom,
% 13.24/13.40 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__strict__right__mono__neg,axiom,
% 13.24/13.40 ! [V_c,V_a,V_b,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__strict__left__mono__neg,axiom,
% 13.24/13.40 ! [V_c,V_a,V_b,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_pos__add__strict,axiom,
% 13.24/13.40 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_zero__le__one,axiom,
% 13.24/13.40 ! [T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.40 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_not__one__le__zero,axiom,
% 13.24/13.40 ! [T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.40 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_not__one__less__zero,axiom,
% 13.24/13.40 ! [T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.40 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_zero__less__one,axiom,
% 13.24/13.40 ! [T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__1__mult,axiom,
% 13.24/13.40 ! [V_n,V_m,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__minus__self__iff,axiom,
% 13.24/13.40 ! [V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 13.24/13.40 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__add__one,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.40 => 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))) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_eq__add__iff2,axiom,
% 13.24/13.40 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Oring(T_a)
% 13.24/13.40 => ( 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)
% 13.24/13.40 <=> 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) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_eq__add__iff1,axiom,
% 13.24/13.40 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Oring(T_a)
% 13.24/13.40 => ( 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)
% 13.24/13.40 <=> 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 ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_square__eq__1__iff,axiom,
% 13.24/13.40 ! [V_x_2,T_a] :
% 13.24/13.40 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 13.24/13.40 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 13.24/13.40 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 13.24/13.40 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__le__cancel__left__pos,axiom,
% 13.24/13.40 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__le__cancel__left__neg,axiom,
% 13.24/13.40 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_aa_2) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__strict__mono,axiom,
% 13.24/13.40 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__strict__mono_H,axiom,
% 13.24/13.40 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__less__le__imp__less,axiom,
% 13.24/13.40 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__le__less__imp__less,axiom,
% 13.24/13.40 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => 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)) ) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__right__less__imp__less,axiom,
% 13.24/13.40 ! [V_b,V_c,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__less__imp__less__right,axiom,
% 13.24/13.40 ! [V_b,V_c,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__left__less__imp__less,axiom,
% 13.24/13.40 ! [V_b,V_a,V_c,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__less__imp__less__left,axiom,
% 13.24/13.40 ! [V_b,V_a,V_c,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__right__le__imp__le,axiom,
% 13.24/13.40 ! [V_b,V_c,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__left__le__imp__le,axiom,
% 13.24/13.40 ! [V_b,V_a,V_c,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.40 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__right__le__one__le,axiom,
% 13.24/13.40 ! [V_y,V_x,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 13.24/13.40 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__left__le__one__le,axiom,
% 13.24/13.40 ! [V_y,V_x,T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 13.24/13.40 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_zero__less__two,axiom,
% 13.24/13.40 ! [T_a] :
% 13.24/13.40 ( class_Rings_Olinordered__semidom(T_a)
% 13.24/13.40 => 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))) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_le__add__iff2,axiom,
% 13.24/13.40 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__ring(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> 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)) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_le__add__iff1,axiom,
% 13.24/13.40 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__ring(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> 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) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__add__iff2,axiom,
% 13.24/13.40 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__ring(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> 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)) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__add__iff1,axiom,
% 13.24/13.40 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Oordered__ring(T_a)
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> 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) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_k1n,axiom,
% 13.24/13.40 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____)) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_inv0,axiom,
% 13.24/13.40 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____))) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_abs__add__one__gt__zero,axiom,
% 13.24/13.40 ! [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))) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_le0,axiom,
% 13.24/13.40 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_realpow__minus__mult,axiom,
% 13.24/13.40 ! [V_x,V_n,T_a] :
% 13.24/13.40 ( class_Groups_Omonoid__mult(T_a)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 13.24/13.40 => 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) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__zeroE,axiom,
% 13.24/13.40 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_realpow__num__eq__if,axiom,
% 13.24/13.40 ! [V_m,V_n,T_a] :
% 13.24/13.40 ( class_Power_Opower(T_a)
% 13.24/13.40 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 13.24/13.40 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 => 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)))) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_power__eq__if,axiom,
% 13.24/13.40 ! [V_p,V_m] :
% 13.24/13.40 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 13.24/13.40 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 => 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)))) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_abs__sum__triangle__ineq,axiom,
% 13.24/13.40 ! [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))))) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__commute,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_inverse__eq__imp__eq,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 13.24/13.40 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b)
% 13.24/13.40 => V_a = V_b ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_inverse__eq__iff__eq,axiom,
% 13.24/13.40 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 13.24/13.40 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2) = c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)
% 13.24/13.40 <=> V_aa_2 = V_b_2 ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_inverse__inverse__eq,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 13.24/13.40 => c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_norm__inverse,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 13.24/13.40 & class_Rings_Odivision__ring__inverse__zero(T_a) )
% 13.24/13.40 => 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)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_of__real__inverse,axiom,
% 13.24/13.40 ! [V_x,T_a] :
% 13.24/13.40 ( ( class_RealVector_Oreal__div__algebra(T_a)
% 13.24/13.40 & class_Rings_Odivision__ring__inverse__zero(T_a) )
% 13.24/13.40 => 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)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_INVERSE__ZERO,axiom,
% 13.24/13.40 c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nonzero__norm__inverse,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => 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)) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nonzero__of__real__inverse,axiom,
% 13.24/13.40 ! [V_x,T_a] :
% 13.24/13.40 ( class_RealVector_Oreal__div__algebra(T_a)
% 13.24/13.40 => ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 13.24/13.40 => 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)) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_inverse__zero,axiom,
% 13.24/13.40 ! [T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 13.24/13.40 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_inverse__nonzero__iff__nonzero,axiom,
% 13.24/13.40 ! [V_aa_2,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 13.24/13.40 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nonzero__imp__inverse__nonzero,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nonzero__inverse__inverse__eq,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_inverse__zero__imp__zero,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nonzero__inverse__eq__imp__eq,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => V_a = V_b ) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_inverse__1,axiom,
% 13.24/13.40 ! [T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_power__inverse,axiom,
% 13.24/13.40 ! [V_n,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 13.24/13.40 => 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) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_inverse__minus__eq,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 13.24/13.40 => 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)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nonzero__inverse__mult__distrib,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_inverse__unique,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Oone__class_Oone(T_a)
% 13.24/13.40 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) = V_b ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nonzero__power__inverse,axiom,
% 13.24/13.40 ! [V_n,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => 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) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nonzero__inverse__minus__eq,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => 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)) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__mult__inverse__cancel2,axiom,
% 13.24/13.40 ! [V_u,V_y,V_x1,V_x] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)
% 13.24/13.40 => ( 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))
% 13.24/13.40 => 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))) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__mult__inverse__cancel,axiom,
% 13.24/13.40 ! [V_u,V_y,V_x1,V_x] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)
% 13.24/13.40 => ( 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))
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__mult__inverse__left,axiom,
% 13.24/13.40 ! [V_x] :
% 13.24/13.40 ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 13.24/13.40 => 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) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_psize__eq__0__iff,axiom,
% 13.24/13.40 ! [V_pb_2,T_a] :
% 13.24/13.40 ( class_Groups_Ozero(T_a)
% 13.24/13.40 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 <=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_division__ring__inverse__add,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_left__inverse,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => 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) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_right__inverse,axiom,
% 13.24/13.40 ! [V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => 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) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_division__ring__inverse__diff,axiom,
% 13.24/13.40 ! [V_b,V_a,T_a] :
% 13.24/13.40 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.40 => 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)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__0__eq__0,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_minus__nat_Odiff__0,axiom,
% 13.24/13.40 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__self__eq__0,axiom,
% 13.24/13.40 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diffs0__imp__equal,axiom,
% 13.24/13.40 ! [V_n,V_m] :
% 13.24/13.40 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 => V_m = V_n ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__le__refl,axiom,
% 13.24/13.40 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__le__linear,axiom,
% 13.24/13.40 ! [V_w,V_z] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 13.24/13.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__le__trans,axiom,
% 13.24/13.40 ! [V_k,V_j,V_i] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 13.24/13.40 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__le__antisym,axiom,
% 13.24/13.40 ! [V_w,V_z] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 13.24/13.40 => V_z = V_w ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nat__less__cases,axiom,
% 13.24/13.40 ! [V_P_2,V_n_2,V_ma_2] :
% 13.24/13.40 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 13.24/13.40 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 13.24/13.40 => ( ( V_ma_2 = V_n_2
% 13.24/13.40 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 13.24/13.40 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
% 13.24/13.40 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 13.24/13.40 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__less__mono2,axiom,
% 13.24/13.40 ! [V_l,V_n,V_m] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
% 13.24/13.40 => 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)) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__imp__diff__less,axiom,
% 13.24/13.40 ! [V_n,V_k,V_j] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__not__refl3,axiom,
% 13.24/13.40 ! [V_t,V_s] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 13.24/13.40 => V_s != V_t ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__not__refl2,axiom,
% 13.24/13.40 ! [V_m,V_n] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 13.24/13.40 => V_m != V_n ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__irrefl__nat,axiom,
% 13.24/13.40 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_linorder__neqE__nat,axiom,
% 13.24/13.40 ! [V_y,V_x] :
% 13.24/13.40 ( V_x != V_y
% 13.24/13.40 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nat__neq__iff,axiom,
% 13.24/13.40 ! [V_n_2,V_ma_2] :
% 13.24/13.40 ( V_ma_2 != V_n_2
% 13.24/13.40 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 13.24/13.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__not__refl,axiom,
% 13.24/13.40 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__cancel2,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__cancel,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nat__add__right__cancel,axiom,
% 13.24/13.40 ! [V_n_2,V_ka_2,V_ma_2] :
% 13.24/13.40 ( 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)
% 13.24/13.40 <=> V_ma_2 = V_n_2 ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nat__add__left__cancel,axiom,
% 13.24/13.40 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.40 ( 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)
% 13.24/13.40 <=> V_ma_2 = V_n_2 ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__diff__left,axiom,
% 13.24/13.40 ! [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)) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nat__add__assoc,axiom,
% 13.24/13.40 ! [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)) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__add__inverse,axiom,
% 13.24/13.40 ! [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 ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__add__inverse2,axiom,
% 13.24/13.40 ! [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 ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nat__add__left__commute,axiom,
% 13.24/13.40 ! [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)) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nat__add__commute,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_le__diff__iff,axiom,
% 13.24/13.40 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_ma_2)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_n_2)
% 13.24/13.40 => ( 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))
% 13.24/13.40 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_Nat_Odiff__diff__eq,axiom,
% 13.24/13.40 ! [V_n,V_m,V_k] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 13.24/13.40 => 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) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_eq__diff__iff,axiom,
% 13.24/13.40 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_ma_2)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_n_2)
% 13.24/13.40 => ( 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)
% 13.24/13.40 <=> V_ma_2 = V_n_2 ) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_le__antisym,axiom,
% 13.24/13.40 ! [V_n,V_m] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 13.24/13.40 => V_m = V_n ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_le__trans,axiom,
% 13.24/13.40 ! [V_k,V_j,V_i] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 13.24/13.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__diff__cancel,axiom,
% 13.24/13.40 ! [V_n,V_i] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
% 13.24/13.40 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__le__mono,axiom,
% 13.24/13.40 ! [V_l,V_n,V_m] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 13.24/13.40 => 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)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__le__mono2,axiom,
% 13.24/13.40 ! [V_l,V_n,V_m] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 13.24/13.40 => 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)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_eq__imp__le,axiom,
% 13.24/13.40 ! [V_n,V_m] :
% 13.24/13.40 ( V_m = V_n
% 13.24/13.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nat__le__linear,axiom,
% 13.24/13.40 ! [V_n,V_m] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 13.24/13.40 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__le__self,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_le__refl,axiom,
% 13.24/13.40 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__mult__commute,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__mult__assoc,axiom,
% 13.24/13.40 ! [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)) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__mult__distrib,axiom,
% 13.24/13.40 ! [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)) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nat__mult__assoc,axiom,
% 13.24/13.40 ! [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)) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__mult__distrib2,axiom,
% 13.24/13.40 ! [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)) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nat__mult__commute,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_not__less0,axiom,
% 13.24/13.40 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_neq0__conv,axiom,
% 13.24/13.40 ! [V_n_2] :
% 13.24/13.40 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__nat__zero__code,axiom,
% 13.24/13.40 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_gr__implies__not0,axiom,
% 13.24/13.40 ! [V_n,V_m] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 13.24/13.40 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_gr0I,axiom,
% 13.24/13.40 ! [V_n] :
% 13.24/13.40 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_zero__less__diff,axiom,
% 13.24/13.40 ! [V_ma_2,V_n_2] :
% 13.24/13.40 ( 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))
% 13.24/13.40 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__less,axiom,
% 13.24/13.40 ! [V_m,V_n] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__eq__real__def,axiom,
% 13.24/13.40 ! [V_y_2,V_x_2] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 13.24/13.40 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 13.24/13.40 | V_x_2 = V_y_2 ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__less__def,axiom,
% 13.24/13.40 ! [V_y_2,V_x_2] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 13.24/13.40 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 13.24/13.40 & V_x_2 != V_y_2 ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_plus__nat_Oadd__0,axiom,
% 13.24/13.40 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 13.24/13.40
% 13.24/13.40 fof(fact_Nat_Oadd__0__right,axiom,
% 13.24/13.40 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 13.24/13.40
% 13.24/13.40 fof(fact_add__is__0,axiom,
% 13.24/13.40 ! [V_n_2,V_ma_2] :
% 13.24/13.40 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_add__eq__self__zero,axiom,
% 13.24/13.40 ! [V_n,V_m] :
% 13.24/13.40 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 13.24/13.40 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__add__0,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 13.24/13.40 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_le__0__eq,axiom,
% 13.24/13.40 ! [V_n_2] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 13.24/13.40 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__is__0__eq_H,axiom,
% 13.24/13.40 ! [V_n,V_m] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 13.24/13.40 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_diff__is__0__eq,axiom,
% 13.24/13.40 ! [V_n_2,V_ma_2] :
% 13.24/13.40 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__0,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__0__right,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__is__0,axiom,
% 13.24/13.40 ! [V_n_2,V_ma_2] :
% 13.24/13.40 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.40 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__cancel1,axiom,
% 13.24/13.40 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.40 ( 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)
% 13.24/13.40 <=> ( V_ma_2 = V_n_2
% 13.24/13.40 | V_ka_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_mult__cancel2,axiom,
% 13.24/13.40 ! [V_n_2,V_ka_2,V_ma_2] :
% 13.24/13.40 ( 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)
% 13.24/13.40 <=> ( V_ma_2 = V_n_2
% 13.24/13.40 | V_ka_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_add__lessD1,axiom,
% 13.24/13.40 ! [V_k,V_j,V_i] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__add__eq__less,axiom,
% 13.24/13.40 ! [V_n,V_m,V_l,V_k] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 13.24/13.40 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_add__less__mono,axiom,
% 13.24/13.40 ! [V_l,V_k,V_j,V_i] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 13.24/13.40 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 13.24/13.40 => 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)) ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_add__less__mono1,axiom,
% 13.24/13.40 ! [V_k,V_j,V_i] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 13.24/13.40 => 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)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_trans__less__add2,axiom,
% 13.24/13.40 ! [V_m,V_j,V_i] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_trans__less__add1,axiom,
% 13.24/13.40 ! [V_m,V_j,V_i] :
% 13.24/13.40 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 13.24/13.40 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_add__diff__inverse,axiom,
% 13.24/13.40 ! [V_n,V_m] :
% 13.24/13.40 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 13.24/13.40 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_nat__add__left__cancel__less,axiom,
% 13.24/13.40 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.40 ( 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))
% 13.24/13.40 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__diff__conv,axiom,
% 13.24/13.40 ! [V_ka_2,V_j_2,V_i_2] :
% 13.24/13.40 ( 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))
% 13.24/13.40 <=> 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) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_not__add__less2,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_not__add__less1,axiom,
% 13.24/13.40 ! [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) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__mult__right__cancel,axiom,
% 13.24/13.40 ! [V_b_2,V_aa_2,V_ca_2] :
% 13.24/13.40 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 13.24/13.40 => ( 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)
% 13.24/13.40 <=> V_aa_2 = V_b_2 ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_real__mult__left__cancel,axiom,
% 13.24/13.40 ! [V_b_2,V_aa_2,V_ca_2] :
% 13.24/13.40 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 13.24/13.40 => ( 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)
% 13.24/13.40 <=> V_aa_2 = V_b_2 ) ) ).
% 13.24/13.40
% 13.24/13.40 fof(fact_less__or__eq__imp__le,axiom,
% 13.24/13.41 ! [V_n,V_m] :
% 13.24/13.41 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 13.24/13.41 | V_m = V_n )
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_less__diff__iff,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_ma_2)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_n_2)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_diff__less__mono,axiom,
% 13.24/13.41 ! [V_c,V_b,V_a] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__neq__implies__less,axiom,
% 13.24/13.41 ! [V_n,V_m] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 13.24/13.41 => ( V_m != V_n
% 13.24/13.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_less__imp__le__nat,axiom,
% 13.24/13.41 ! [V_n,V_m] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__eq__less__or__eq,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 13.24/13.41 | V_ma_2 = V_n_2 ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__less__le,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 13.24/13.41 & V_ma_2 != V_n_2 ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__leE,axiom,
% 13.24/13.41 ! [V_n,V_k,V_m] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 13.24/13.41 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 13.24/13.41 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__leD1,axiom,
% 13.24/13.41 ! [V_n,V_k,V_m] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__leD2,axiom,
% 13.24/13.41 ! [V_n,V_k,V_m] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__le__mono,axiom,
% 13.24/13.41 ! [V_l,V_k,V_j,V_i] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_diff__add__assoc2,axiom,
% 13.24/13.41 ! [V_i,V_j,V_k] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 13.24/13.41 => 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) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__diff__assoc2,axiom,
% 13.24/13.41 ! [V_i,V_j,V_k] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 13.24/13.41 => 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) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_diff__add__assoc,axiom,
% 13.24/13.41 ! [V_i,V_j,V_k] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__imp__diff__is__add,axiom,
% 13.24/13.41 ! [V_ka_2,V_j_2,V_i_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 13.24/13.41 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_ka_2
% 13.24/13.41 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_i_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__add__diff__inverse2,axiom,
% 13.24/13.41 ! [V_m,V_n] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 13.24/13.41 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__diff__conv2,axiom,
% 13.24/13.41 ! [V_i_2,V_j_2,V_ka_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ka_2,V_j_2)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> 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) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__diff__assoc,axiom,
% 13.24/13.41 ! [V_i,V_j,V_k] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 13.24/13.41 => 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) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__add__diff__inverse,axiom,
% 13.24/13.41 ! [V_m,V_n] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 13.24/13.41 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__le__mono1,axiom,
% 13.24/13.41 ! [V_k,V_j,V_i] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__add__diff,axiom,
% 13.24/13.41 ! [V_m,V_n,V_k] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_trans__le__add2,axiom,
% 13.24/13.41 ! [V_m,V_j,V_i] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_trans__le__add1,axiom,
% 13.24/13.41 ! [V_m,V_j,V_i] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__add__left__cancel__le,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__diff__conv,axiom,
% 13.24/13.41 ! [V_i_2,V_ka_2,V_j_2] :
% 13.24/13.41 ( 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)
% 13.24/13.41 <=> 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_diff__diff__right,axiom,
% 13.24/13.41 ! [V_i,V_j,V_k] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 13.24/13.41 => 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) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__iff__add,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 13.24/13.41 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__add1,axiom,
% 13.24/13.41 ! [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)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__add2,axiom,
% 13.24/13.41 ! [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)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__zero__not__eq__one,axiom,
% 13.24/13.41 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__mult__distrib,axiom,
% 13.24/13.41 ! [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)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__mult__distrib2,axiom,
% 13.24/13.41 ! [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)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__add__left__mono,axiom,
% 13.24/13.41 ! [V_z,V_y,V_x] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__le__mono,axiom,
% 13.24/13.41 ! [V_l,V_k,V_j,V_i] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__le__mono2,axiom,
% 13.24/13.41 ! [V_k,V_j,V_i] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__le__mono1,axiom,
% 13.24/13.41 ! [V_k,V_j,V_i] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__cube,axiom,
% 13.24/13.41 ! [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))) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__square,axiom,
% 13.24/13.41 ! [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)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__mult__1,axiom,
% 13.24/13.41 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__add__mult__distrib,axiom,
% 13.24/13.41 ! [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)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__mult__eq__1__iff,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2] :
% 13.24/13.41 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 13.24/13.41 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 13.24/13.41 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__mult__1__right,axiom,
% 13.24/13.41 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__1__eq__mult__iff,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2] :
% 13.24/13.41 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)
% 13.24/13.41 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 13.24/13.41 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__mult__1,axiom,
% 13.24/13.41 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 13.24/13.41
% 13.24/13.41 fof(fact_sum__squares__eq__zero__iff,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.41 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.41 => ( 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)
% 13.24/13.41 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__diff__mult,axiom,
% 13.24/13.41 ! [V_b,V_a,V_y,V_x,T_a] :
% 13.24/13.41 ( class_Rings_Oring(T_a)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__eq__0__iff,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__gr__0,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 13.24/13.41 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__diff__split__asm,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,V_P_2] :
% 13.24/13.41 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
% 13.24/13.41 <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)
% 13.24/13.41 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 13.24/13.41 | ? [B_d] :
% 13.24/13.41 ( V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 13.24/13.41 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__diff__split,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,V_P_2] :
% 13.24/13.41 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
% 13.24/13.41 <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)
% 13.24/13.41 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 13.24/13.41 & ! [B_d] :
% 13.24/13.41 ( V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 13.24/13.41 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__mult__less__iff1,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2,V_z_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__mult__order,axiom,
% 13.24/13.41 ! [V_y,V_x] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__mult__less__mono2,axiom,
% 13.24/13.41 ! [V_y,V_x,V_z] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__0__less__mult__iff,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 13.24/13.41 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__less__cancel1,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 13.24/13.41 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__less__cancel2,axiom,
% 13.24/13.41 ! [V_n_2,V_ka_2,V_ma_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 13.24/13.41 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__less__mono1,axiom,
% 13.24/13.41 ! [V_k,V_j,V_i] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__less__mono2,axiom,
% 13.24/13.41 ! [V_k,V_j,V_i] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__eq__self__implies__10,axiom,
% 13.24/13.41 ! [V_n,V_m] :
% 13.24/13.41 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 13.24/13.41 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 13.24/13.41 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__le__eq__diff,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 13.24/13.41 <=> 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__two__squares__add__zero__iff,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2] :
% 13.24/13.41 ( 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)
% 13.24/13.41 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 13.24/13.41 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__minus__mult__self__le,axiom,
% 13.24/13.41 ! [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)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__add__eq__0__iff,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2] :
% 13.24/13.41 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 13.24/13.41 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__add__minus__iff,axiom,
% 13.24/13.41 ! [V_aa_2,V_x_2] :
% 13.24/13.41 ( 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)
% 13.24/13.41 <=> V_x_2 = V_aa_2 ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_abs__le__interval__iff,axiom,
% 13.24/13.41 ! [V_r_2,V_x_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_r_2)
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r_2),V_x_2)
% 13.24/13.41 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_r_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__diff__def,axiom,
% 13.24/13.41 ! [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)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_minus__real__def,axiom,
% 13.24/13.41 ! [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)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_abs__minus__add__cancel,axiom,
% 13.24/13.41 ! [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))) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_sum__squares__le__zero__iff,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.41 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_sum__squares__ge__zero,axiom,
% 13.24/13.41 ! [V_y,V_x,T_a] :
% 13.24/13.41 ( class_Rings_Olinordered__ring(T_a)
% 13.24/13.41 => 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))) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_sum__squares__gt__zero__iff,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.41 ( class_Rings_Olinordered__ring__strict(T_a)
% 13.24/13.41 => ( 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)))
% 13.24/13.41 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_not__sum__squares__lt__zero,axiom,
% 13.24/13.41 ! [V_y,V_x,T_a] :
% 13.24/13.41 ( class_Rings_Olinordered__ring(T_a)
% 13.24/13.41 => ~ 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__squared__diff__one__factored,axiom,
% 13.24/13.41 ! [V_x,T_a] :
% 13.24/13.41 ( class_Rings_Oring__1(T_a)
% 13.24/13.41 => 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))) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__mult__le__cancel__iff1,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2,V_z_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__mult__le__cancel__iff2,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2,V_z_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__le__cancel1,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__le__cancel2,axiom,
% 13.24/13.41 ! [V_n_2,V_ka_2,V_ma_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__eq__if,axiom,
% 13.24/13.41 ! [V_n,V_m] :
% 13.24/13.41 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 13.24/13.41 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__0__le__add__iff,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__add__le__0__iff,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__0__less__add__iff,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__add__less__0__iff,axiom,
% 13.24/13.41 ! [V_y_2,V_x_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_abs__real__def,axiom,
% 13.24/13.41 ! [V_a] :
% 13.24/13.41 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 13.24/13.41 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a) )
% 13.24/13.41 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 13.24/13.41 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_real__abs__def,axiom,
% 13.24/13.41 ! [V_r] :
% 13.24/13.41 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 13.24/13.41 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r) )
% 13.24/13.41 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 13.24/13.41 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_abs__add__one__not__less__self,axiom,
% 13.24/13.41 ! [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) ).
% 13.24/13.41
% 13.24/13.41 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,
% 13.24/13.41 ~ ! [B_t] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 13.24/13.41 => ~ 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____))) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_q_I2_J,axiom,
% 13.24/13.41 ! [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)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_less_Ohyps,axiom,
% 13.24/13.41 ! [V_pb_2] :
% 13.24/13.41 ( 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____))
% 13.24/13.41 => ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2))
% 13.24/13.41 => ? [B_z] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2),B_z) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ).
% 13.24/13.41
% 13.24/13.41 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,
% 13.24/13.41 ? [B_q] :
% 13.24/13.41 ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
% 13.24/13.41 & ! [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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact__096poly_Ap_Ac_A_061_A0_A_061_061_062_AEX_Az_O_Apoly_Ap_Az_A_061_A0_096,axiom,
% 13.24/13.41 ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 13.24/13.41 => ? [B_z] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_z) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_q_I1_J,axiom,
% 13.24/13.41 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_Bseq__inverse__lemma,axiom,
% 13.24/13.41 ! [V_x,V_r,T_a] :
% 13.24/13.41 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_r,c_RealVector_Onorm__class_Onorm(T_a,V_x))
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 13.24/13.41 => 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)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_a00,axiom,
% 13.24/13.41 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) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_qnc,axiom,
% 13.24/13.41 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096,axiom,
% 13.24/13.41 ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_cq0,axiom,
% 13.24/13.41 ! [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))) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_pqc0,axiom,
% 13.24/13.41 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)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_kas_I3_J,axiom,
% 13.24/13.41 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____)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__less__add__iff2,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__less__add__iff1,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> 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) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_Deriv_Oinverse__diff__inverse,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Rings_Odivision__ring(T_a)
% 13.24/13.41 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 => 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))) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_one__le__inverse__iff,axiom,
% 13.24/13.41 ! [V_x_2,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 13.24/13.41 & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 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,
% 13.24/13.41 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))) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_qr,axiom,
% 13.24/13.41 ! [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))) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_r01,axiom,
% 13.24/13.41 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) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_lgqr,axiom,
% 13.24/13.41 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____)) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_rnc,axiom,
% 13.24/13.41 ~ 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____))) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mrmq__eq,axiom,
% 13.24/13.41 ! [V_wa_2] :
% 13.24/13.41 ( 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))
% 13.24/13.41 <=> 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)))) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_kas_I4_J,axiom,
% 13.24/13.41 ! [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))) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_Deriv_Oadd__diff__add,axiom,
% 13.24/13.41 ! [V_d,V_b,V_c,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_field__inverse__zero,axiom,
% 13.24/13.41 ! [T_a] :
% 13.24/13.41 ( class_Fields_Ofield__inverse__zero(T_a)
% 13.24/13.41 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__mult__distrib,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Fields_Ofield__inverse__zero(T_a)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.41 ( 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)
% 13.24/13.41 <=> ( V_ka_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.41 | V_ma_2 = V_n_2 ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__eq__1__iff,axiom,
% 13.24/13.41 ! [V_x_2,T_a] :
% 13.24/13.41 ( class_Fields_Ofield__inverse__zero(T_a)
% 13.24/13.41 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 13.24/13.41 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_left__add__mult__distrib,axiom,
% 13.24/13.41 ! [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) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_abs__inverse,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__nonnegative__iff__nonnegative,axiom,
% 13.24/13.41 ! [V_aa_2,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__nonpositive__iff__nonpositive,axiom,
% 13.24/13.41 ! [V_aa_2,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__positive__iff__positive,axiom,
% 13.24/13.41 ! [V_aa_2,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__negative__iff__negative,axiom,
% 13.24/13.41 ! [V_aa_2,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_positive__imp__inverse__positive,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__positive__imp__positive,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
% 13.24/13.41 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_negative__imp__inverse__negative,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.41 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_less__imp__inverse__less,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.41 => 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)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_less__imp__inverse__less__neg,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.41 => 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)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__negative__imp__negative,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.41 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__less__imp__less,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.41 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__less__imp__less__neg,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.41 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nonzero__abs__inverse,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__mult__eq__cancel1,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 13.24/13.41 => ( 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)
% 13.24/13.41 <=> V_ma_2 = V_n_2 ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__mult__less__cancel1,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__imp__inverse__le,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.41 => 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)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__imp__inverse__le__neg,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.41 => 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)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__le__imp__le,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__le__imp__le__neg,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__le__1__iff,axiom,
% 13.24/13.41 ! [V_x_2,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.41 | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__add,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Fields_Ofield(T_a)
% 13.24/13.41 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 => 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)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_one__less__inverse,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 13.24/13.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_one__less__inverse__iff,axiom,
% 13.24/13.41 ! [V_x_2,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 13.24/13.41 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_field__inverse,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Fields_Ofield(T_a)
% 13.24/13.41 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 => 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) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__mult__le__cancel1,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_ka_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__le__add__iff1,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> 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) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__diff__add__eq1,axiom,
% 13.24/13.41 ! [V_n,V_m,V_u,V_i,V_j] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
% 13.24/13.41 => 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) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__eq__add__iff1,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 13.24/13.41 => ( 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)
% 13.24/13.41 <=> 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 ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__le__add__iff2,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__diff__add__eq2,axiom,
% 13.24/13.41 ! [V_n,V_m,V_u,V_j,V_i] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_nat__eq__add__iff2,axiom,
% 13.24/13.41 ! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
% 13.24/13.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 13.24/13.41 => ( 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)
% 13.24/13.41 <=> 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) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_one__le__inverse,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_inverse__less__1__iff,axiom,
% 13.24/13.41 ! [V_x_2,T_a] :
% 13.24/13.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.41 | c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 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,
% 13.24/13.41 ( 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))
% 13.24/13.41 => ? [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)) ) ).
% 13.24/13.41
% 13.24/13.41 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,
% 13.24/13.41 ~ ! [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) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_abs__diff__less__iff,axiom,
% 13.24/13.41 ! [V_r_2,V_aa_2,V_x_2,T_a] :
% 13.24/13.41 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.41 => ( 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)
% 13.24/13.41 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_r_2),V_x_2)
% 13.24/13.41 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_r_2)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_abs__triangle__ineq4,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.41 => 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))) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_offset__poly__eq__0__lemma,axiom,
% 13.24/13.41 ! [V_a,V_p,V_c,T_a] :
% 13.24/13.41 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 => V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_zero__reorient,axiom,
% 13.24/13.41 ! [V_x_2,T_a] :
% 13.24/13.41 ( class_Groups_Ozero(T_a)
% 13.24/13.41 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 13.24/13.41 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 13.24/13.41 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oab__semigroup__mult(T_a)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 13.24/13.41 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oab__semigroup__add(T_a)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__left__cancel,axiom,
% 13.24/13.41 ! [V_ca_2,V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Ocancel__semigroup__add(T_a)
% 13.24/13.41 => ( 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)
% 13.24/13.41 <=> V_b_2 = V_ca_2 ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__right__cancel,axiom,
% 13.24/13.41 ! [V_ca_2,V_aa_2,V_b_2,T_a] :
% 13.24/13.41 ( class_Groups_Ocancel__semigroup__add(T_a)
% 13.24/13.41 => ( 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)
% 13.24/13.41 <=> V_b_2 = V_ca_2 ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__left__imp__eq,axiom,
% 13.24/13.41 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ocancel__semigroup__add(T_a)
% 13.24/13.41 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 13.24/13.41 => V_b = V_c ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__imp__eq,axiom,
% 13.24/13.41 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 13.24/13.41 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 13.24/13.41 => V_b = V_c ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__right__imp__eq,axiom,
% 13.24/13.41 ! [V_c,V_a,V_b,T_a] :
% 13.24/13.41 ( class_Groups_Ocancel__semigroup__add(T_a)
% 13.24/13.41 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 13.24/13.41 => V_b = V_c ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_one__reorient,axiom,
% 13.24/13.41 ! [V_x_2,T_a] :
% 13.24/13.41 ( class_Groups_Oone(T_a)
% 13.24/13.41 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 13.24/13.41 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_diff__eq__diff__eq,axiom,
% 13.24/13.41 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.41 => ( 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)
% 13.24/13.41 => ( V_aa_2 = V_b_2
% 13.24/13.41 <=> V_ca_2 = V_d_2 ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_neg__equal__iff__equal,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 13.24/13.41 <=> V_aa_2 = V_b_2 ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_minus__equation__iff,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_b_2
% 13.24/13.41 <=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_aa_2 ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_equation__minus__iff,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 13.24/13.41 <=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_minus__minus,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_abs__idempotent,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.41 => 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) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__0__left,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Omonoid__add(T_a)
% 13.24/13.41 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__0,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ocomm__monoid__add(T_a)
% 13.24/13.41 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_double__zero__sym,axiom,
% 13.24/13.41 ! [V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Olinordered__ab__group__add(T_a)
% 13.24/13.41 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)
% 13.24/13.41 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__0__right,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Omonoid__add(T_a)
% 13.24/13.41 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add_Ocomm__neutral,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ocomm__monoid__add(T_a)
% 13.24/13.41 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__le__cancel__right,axiom,
% 13.24/13.41 ! [V_b_2,V_ca_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__le__cancel__left,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__right__mono,axiom,
% 13.24/13.41 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__left__mono,axiom,
% 13.24/13.41 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__mono,axiom,
% 13.24/13.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 13.24/13.41 => 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)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__le__imp__le__right,axiom,
% 13.24/13.41 ! [V_b,V_c,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__le__imp__le__left,axiom,
% 13.24/13.41 ! [V_b,V_a,V_c,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__less__cancel__right,axiom,
% 13.24/13.41 ! [V_b_2,V_ca_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__less__cancel__left,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,V_ca_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__strict__right__mono,axiom,
% 13.24/13.41 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__strict__left__mono,axiom,
% 13.24/13.41 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__strict__mono,axiom,
% 13.24/13.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 13.24/13.41 => 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)) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__less__imp__less__right,axiom,
% 13.24/13.41 ! [V_b,V_c,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__less__imp__less__left,axiom,
% 13.24/13.41 ! [V_b,V_a,V_c,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_right__minus__eq,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 <=> V_aa_2 = V_b_2 ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_eq__iff__diff__eq__0,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.41 => ( V_aa_2 = V_b_2
% 13.24/13.41 <=> c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_diff__self,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_diff__0__right,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_diff__eq__diff__less__eq,axiom,
% 13.24/13.41 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.41 => ( 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)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_d_2) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_diff__eq__diff__less,axiom,
% 13.24/13.41 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.41 => ( 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)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2) ) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__1__left,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Omonoid__mult(T_a)
% 13.24/13.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__1,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ocomm__monoid__mult(T_a)
% 13.24/13.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult__1__right,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Omonoid__mult(T_a)
% 13.24/13.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_mult_Ocomm__neutral,axiom,
% 13.24/13.41 ! [V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ocomm__monoid__mult(T_a)
% 13.24/13.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_neg__equal__zero,axiom,
% 13.24/13.41 ! [V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Olinordered__ab__group__add(T_a)
% 13.24/13.41 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_aa_2
% 13.24/13.41 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_neg__equal__0__iff__equal,axiom,
% 13.24/13.41 ! [V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_equal__neg__zero,axiom,
% 13.24/13.41 ! [V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Olinordered__ab__group__add(T_a)
% 13.24/13.41 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
% 13.24/13.41 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_neg__0__equal__iff__equal,axiom,
% 13.24/13.41 ! [V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
% 13.24/13.41 <=> c_Groups_Ozero__class_Ozero(T_a) = V_aa_2 ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_minus__zero,axiom,
% 13.24/13.41 ! [T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__imp__neg__le,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.41 => 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)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_neg__le__iff__le,axiom,
% 13.24/13.41 ! [V_aa_2,V_b_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_minus__le__iff,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_le__minus__iff,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_diff__add__cancel,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__diff__cancel,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_less__minus__iff,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_minus__less__iff,axiom,
% 13.24/13.41 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_neg__less__iff__less,axiom,
% 13.24/13.41 ! [V_aa_2,V_b_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.41 => ( 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))
% 13.24/13.41 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_minus__add__distrib,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_minus__add,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => 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)) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_add__minus__cancel,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => 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 ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_minus__add__cancel,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.41 => 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 ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_minus__diff__eq,axiom,
% 13.24/13.41 ! [V_b,V_a,T_a] :
% 13.24/13.41 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.41 => 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) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_abs__eq__0,axiom,
% 13.24/13.41 ! [V_aa_2,T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.41 => ( c_Groups_Oabs__class_Oabs(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.41 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_abs__zero,axiom,
% 13.24/13.41 ! [T_a] :
% 13.24/13.41 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.41 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 13.24/13.41
% 13.24/13.41 fof(fact_abs__le__D1,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 13.24/13.42 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__ge__self,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__add__abs,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__minus__commute,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__minus__cancel,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__nonpos__nonpos,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => 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)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__increasing2,axiom,
% 13.24/13.42 ! [V_a,V_b,V_c,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 13.24/13.42 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__increasing,axiom,
% 13.24/13.42 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 13.24/13.42 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__nonneg__eq__0__iff,axiom,
% 13.24/13.42 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 13.24/13.42 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.42 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.42 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__nonneg__nonneg,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.42 => 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)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Olinordered__ab__group__add(T_a)
% 13.24/13.42 => ( 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))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Olinordered__ab__group__add(T_a)
% 13.24/13.42 => ( 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))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Olinordered__ab__group__add(T_a)
% 13.24/13.42 => ( 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))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Olinordered__ab__group__add(T_a)
% 13.24/13.42 => ( 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))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__pos__pos,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.42 => 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)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__neg__neg,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => 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)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__less__le__mono,axiom,
% 13.24/13.42 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 13.24/13.42 => 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)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__le__less__mono,axiom,
% 13.24/13.42 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 13.24/13.42 => 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)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_le__iff__diff__le__0,axiom,
% 13.24/13.42 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
% 13.24/13.42 <=> 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)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_less__iff__diff__less__0,axiom,
% 13.24/13.42 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
% 13.24/13.42 <=> 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)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_minus__le__self__iff,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Olinordered__ab__group__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_neg__le__0__iff__le,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.42 => ( 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))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_le__minus__self__iff,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Olinordered__ab__group__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_neg__0__le__iff__le,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.42 => ( 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))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_neg__less__nonneg,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Olinordered__ab__group__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_neg__less__0__iff__less,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_neg__0__less__iff__less,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_minus__unique,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.42 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.42 => c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_ab__left__minus,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_left__minus,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 13.24/13.42 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.42 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 13.24/13.42 <=> c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_right__minus,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_diff__0,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__of__nonneg,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.42 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__le__zero__iff,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => ( 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))
% 13.24/13.42 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__ge__zero,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__of__pos,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.42 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zero__less__abs__iff,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_aa_2))
% 13.24/13.42 <=> V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__not__less__zero,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_diff__minus__eq__add,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_ab__diff__minus,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_diff__def,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Ogroup__add(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__triangle__ineq,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__triangle__ineq2__sym,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__triangle__ineq2,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__triangle__ineq3,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__le__D2,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 13.24/13.42 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__leI,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
% 13.24/13.42 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__le__iff,axiom,
% 13.24/13.42 ! [V_b_2,V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)
% 13.24/13.42 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
% 13.24/13.42 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__ge__minus__self,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__pos__nonneg,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.42 => 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)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__nonneg__pos,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 13.24/13.42 => 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)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__strict__increasing,axiom,
% 13.24/13.42 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 13.24/13.42 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__strict__increasing2,axiom,
% 13.24/13.42 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 13.24/13.42 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__neg__nonpos,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => 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)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__nonpos__neg,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => 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)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__of__nonpos,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__minus__le__zero,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__of__neg,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__if,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oabs__if(T_a)
% 13.24/13.42 => ( ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) )
% 13.24/13.42 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.42 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__diff__triangle__ineq,axiom,
% 13.24/13.42 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 13.24/13.42 => 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)))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_th01,axiom,
% 13.24/13.42 ~ 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)))))) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_th02,axiom,
% 13.24/13.42 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))))) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__pCons,axiom,
% 13.24/13.42 ! [V_x,V_p,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_reduce__poly__simple,axiom,
% 13.24/13.42 ! [V_n,V_b] :
% 13.24/13.42 ( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 13.24/13.42 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.42 => ? [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)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_mult__poly__add__left,axiom,
% 13.24/13.42 ! [V_r,V_q,V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_monom__eq__iff,axiom,
% 13.24/13.42 ! [V_b_2,V_n_2,V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Ozero(T_a)
% 13.24/13.42 => ( c_Polynomial_Omonom(T_a,V_aa_2,V_n_2) = c_Polynomial_Omonom(T_a,V_b_2,V_n_2)
% 13.24/13.42 <=> V_aa_2 = V_b_2 ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_minus__monom,axiom,
% 13.24/13.42 ! [V_n,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_diff__monom,axiom,
% 13.24/13.42 ! [V_b,V_n,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__monom,axiom,
% 13.24/13.42 ! [V_b,V_n,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Ocomm__monoid__add(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_mult__monom,axiom,
% 13.24/13.42 ! [V_n,V_b,V_m,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_monom__eq__0__iff,axiom,
% 13.24/13.42 ! [V_n_2,V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Ozero(T_a)
% 13.24/13.42 => ( c_Polynomial_Omonom(T_a,V_aa_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 13.24/13.42 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_monom__eq__0,axiom,
% 13.24/13.42 ! [V_n,T_a] :
% 13.24/13.42 ( class_Groups_Ozero(T_a)
% 13.24/13.42 => c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__monom,axiom,
% 13.24/13.42 ! [V_n,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__monom,axiom,
% 13.24/13.42 ! [V_x,V_n,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_monom__0,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Groups_Ozero(T_a)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__eq__iff,axiom,
% 13.24/13.42 ! [V_qa_2,V_pb_2,T_a] :
% 13.24/13.42 ( ( class_Int_Oring__char__0(T_a)
% 13.24/13.42 & class_Rings_Oidom(T_a) )
% 13.24/13.42 => ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,V_qa_2)
% 13.24/13.42 <=> V_pb_2 = V_qa_2 ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_minus__poly__code_I1_J,axiom,
% 13.24/13.42 ! [T_a] :
% 13.24/13.42 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_mult__poly__0__left,axiom,
% 13.24/13.42 ! [V_q,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__poly__code_I1_J,axiom,
% 13.24/13.42 ! [V_q,T_a] :
% 13.24/13.42 ( class_Groups_Ocomm__monoid__add(T_a)
% 13.24/13.42 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_mult__poly__0__right,axiom,
% 13.24/13.42 ! [V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__poly__code_I2_J,axiom,
% 13.24/13.42 ! [V_p,T_a] :
% 13.24/13.42 ( class_Groups_Ocomm__monoid__add(T_a)
% 13.24/13.42 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_diff__poly__code_I2_J,axiom,
% 13.24/13.42 ! [V_p,T_a] :
% 13.24/13.42 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.42 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_diff__poly__code_I1_J,axiom,
% 13.24/13.42 ! [V_q,T_a] :
% 13.24/13.42 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__poly__def,axiom,
% 13.24/13.42 ! [V_x,T_a] :
% 13.24/13.42 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.42 => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 13.24/13.42 => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x) )
% 13.24/13.42 & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 13.24/13.42 => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = V_x ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_pCons__eq__iff,axiom,
% 13.24/13.42 ! [V_qa_2,V_b_2,V_pb_2,V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Ozero(T_a)
% 13.24/13.42 => ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Polynomial_OpCons(T_a,V_b_2,V_qa_2)
% 13.24/13.42 <=> ( V_aa_2 = V_b_2
% 13.24/13.42 & V_pb_2 = V_qa_2 ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__minus__right,axiom,
% 13.24/13.42 ! [V_p,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__ring(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_mult__smult__right,axiom,
% 13.24/13.42 ! [V_q,V_a,V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__add__right,axiom,
% 13.24/13.42 ! [V_q,V_p,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_mult__smult__left,axiom,
% 13.24/13.42 ! [V_q,V_p,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__diff__right,axiom,
% 13.24/13.42 ! [V_q,V_p,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__ring(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__replicate__append,axiom,
% 13.24/13.42 ! [V_x,V_p,V_n,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__ring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__mult,axiom,
% 13.24/13.42 ! [V_x,V_q,V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__add,axiom,
% 13.24/13.42 ! [V_x,V_q,V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__1,axiom,
% 13.24/13.42 ! [V_x,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__diff,axiom,
% 13.24/13.42 ! [V_x,V_q,V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__ring(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__pCons,axiom,
% 13.24/13.42 ! [V_q,V_b,V_p,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Ocomm__monoid__add(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__power,axiom,
% 13.24/13.42 ! [V_x,V_n,V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__minus,axiom,
% 13.24/13.42 ! [V_x,V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__ring(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_diff__pCons,axiom,
% 13.24/13.42 ! [V_q,V_b,V_p,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__smult,axiom,
% 13.24/13.42 ! [V_p,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__add__left,axiom,
% 13.24/13.42 ! [V_p,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__1__left,axiom,
% 13.24/13.42 ! [V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p) = V_p ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_minus__poly__code_I2_J,axiom,
% 13.24/13.42 ! [V_p,V_a,T_b] :
% 13.24/13.42 ( class_Groups_Oab__group__add(T_b)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_minus__pCons,axiom,
% 13.24/13.42 ! [V_p,V_a,T_a] :
% 13.24/13.42 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__diff__left,axiom,
% 13.24/13.42 ! [V_p,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__ring(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__minus__left,axiom,
% 13.24/13.42 ! [V_p,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__ring(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__zero,axiom,
% 13.24/13.42 ! [V_pb_2,T_a] :
% 13.24/13.42 ( ( class_Int_Oring__char__0(T_a)
% 13.24/13.42 & class_Rings_Oidom(T_a) )
% 13.24/13.42 => ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 13.24/13.42 <=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__0__right,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__0,axiom,
% 13.24/13.42 ! [V_x,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_pCons__0__0,axiom,
% 13.24/13.42 ! [T_a] :
% 13.24/13.42 ( class_Groups_Ozero(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_pCons__eq__0__iff,axiom,
% 13.24/13.42 ! [V_pb_2,V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Ozero(T_a)
% 13.24/13.42 => ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 13.24/13.42 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.42 & V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__eq__0__iff,axiom,
% 13.24/13.42 ! [V_pb_2,V_aa_2,T_a] :
% 13.24/13.42 ( class_Rings_Oidom(T_a)
% 13.24/13.42 => ( c_Polynomial_Osmult(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 13.24/13.42 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.42 | V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__0__left,axiom,
% 13.24/13.42 ! [V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_one__poly__def,axiom,
% 13.24/13.42 ! [T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__smult,axiom,
% 13.24/13.42 ! [V_x,V_p,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_mult__pCons__right,axiom,
% 13.24/13.42 ! [V_q,V_a,V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_mult__pCons__left,axiom,
% 13.24/13.42 ! [V_q,V_p,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_smult__pCons,axiom,
% 13.24/13.42 ! [V_p,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_synthetic__div__unique__lemma,axiom,
% 13.24/13.42 ! [V_a,V_p,V_c,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => ( c_Polynomial_Osmult(T_a,V_c,V_p) = c_Polynomial_OpCons(T_a,V_a,V_p)
% 13.24/13.42 => V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 13.24/13.42
% 13.24/13.42 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,
% 13.24/13.42 ? [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) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_synthetic__div__correct_H,axiom,
% 13.24/13.42 ! [V_p,V_c,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__ring__1(T_a)
% 13.24/13.42 => 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 ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zero__less__power__nat__eq,axiom,
% 13.24/13.42 ! [V_n_2,V_x_2] :
% 13.24/13.42 ( 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))
% 13.24/13.42 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_synthetic__div__0,axiom,
% 13.24/13.42 ! [V_c,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_synthetic__div__pCons,axiom,
% 13.24/13.42 ! [V_c,V_p,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_synthetic__div__correct,axiom,
% 13.24/13.42 ! [V_c,V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_synthetic__div__unique,axiom,
% 13.24/13.42 ! [V_r,V_q,V_c,V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => ( 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)
% 13.24/13.42 => ( V_r = hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)
% 13.24/13.42 & V_q = c_Polynomial_Osynthetic__div(T_a,V_p,V_c) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_not__real__square__gt__zero,axiom,
% 13.24/13.42 ! [V_x_2] :
% 13.24/13.42 ( ~ 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))
% 13.24/13.42 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 13.24/13.42 ! [V_q,V_p,V_x,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 13.24/13.42 ! [V_x,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 13.24/13.42 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 13.24/13.42 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 13.24/13.42 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 13.24/13.42 ! [V_rx,V_ly,V_lx,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 13.24/13.42 ! [V_rx,V_ly,V_lx,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 13.24/13.42 ! [V_ry,V_rx,V_lx,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 13.24/13.42 ! [V_ry,V_rx,V_lx,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 13.24/13.42 ! [V_b,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 13.24/13.42 ! [V_d,V_c,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 13.24/13.42 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 13.24/13.42 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 13.24/13.42 ! [V_d,V_c,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 13.24/13.42 ! [V_d,V_c,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 13.24/13.42 ! [V_c,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__0__iff,axiom,
% 13.24/13.42 ! [V_aa_2,V_b_2,T_a] :
% 13.24/13.42 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 13.24/13.42 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)
% 13.24/13.42 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_crossproduct__eq,axiom,
% 13.24/13.42 ! [V_z_2,V_x_2,V_y_2,V_wa_2,T_a] :
% 13.24/13.42 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 13.24/13.42 => ( 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))
% 13.24/13.42 <=> ( V_wa_2 = V_x_2
% 13.24/13.42 | V_y_2 = V_z_2 ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 13.24/13.42 ! [V_b,V_m,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 13.24/13.42 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_crossproduct__noteq,axiom,
% 13.24/13.42 ! [V_d_2,V_ca_2,V_b_2,V_aa_2,T_a] :
% 13.24/13.42 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 13.24/13.42 => ( ( V_aa_2 != V_b_2
% 13.24/13.42 & V_ca_2 != V_d_2 )
% 13.24/13.42 <=> 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)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 13.24/13.42 ! [V_z,V_y,V_x,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 13.24/13.42 ! [V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 13.24/13.42 ! [V_q,V_y,V_x,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 13.24/13.42 ! [V_q,V_p,V_x,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 13.24/13.42 ! [V_x,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add__scale__eq__noteq,axiom,
% 13.24/13.42 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 13.24/13.42 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 13.24/13.42 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.42 => ( ( V_a = V_b
% 13.24/13.42 & V_c != V_d )
% 13.24/13.42 => 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)) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 13.24/13.42 ! [V_m,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 13.24/13.42 ! [V_a,V_m,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 13.24/13.42 ! [V_m,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 13.24/13.42 ! [V_x,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__ring__1(T_a)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 13.24/13.42 ! [V_y,V_x,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__ring__1(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_pcompose__pCons,axiom,
% 13.24/13.42 ! [V_q,V_p,V_a,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_even__less__0__iff,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.42 => ( 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))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_of__real_Opos__bounded,axiom,
% 13.24/13.42 ! [T_a] :
% 13.24/13.42 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.42 & class_RealVector_Oreal__normed__vector(T_a) )
% 13.24/13.42 => ? [B_K] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 13.24/13.42 & ! [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)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_poly__pcompose,axiom,
% 13.24/13.42 ! [V_x,V_q,V_p,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_pcompose__0,axiom,
% 13.24/13.42 ! [V_q,T_a] :
% 13.24/13.42 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zero__less__zpower__abs__iff,axiom,
% 13.24/13.42 ! [V_n_2,V_x_2] :
% 13.24/13.42 ( 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))
% 13.24/13.42 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 13.24/13.42 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zpower__zadd__distrib,axiom,
% 13.24/13.42 ! [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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zpower__zpower,axiom,
% 13.24/13.42 ! [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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_double__eq__0__iff,axiom,
% 13.24/13.42 ! [V_aa_2,T_a] :
% 13.24/13.42 ( class_Groups_Olinordered__ab__group__add(T_a)
% 13.24/13.42 => ( c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.42 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_unimodular__reduce__norm,axiom,
% 13.24/13.42 ! [V_z] :
% 13.24/13.42 ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 13.24/13.42 => ( 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))
% 13.24/13.42 | 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))
% 13.24/13.42 | 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))
% 13.24/13.42 | 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)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_order__root,axiom,
% 13.24/13.42 ! [V_aa_2,V_pb_2,T_a] :
% 13.24/13.42 ( class_Rings_Oidom(T_a)
% 13.24/13.42 => ( hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.42 <=> ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 13.24/13.42 | c_Polynomial_Oorder(T_a,V_aa_2,V_pb_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zadd__0__right,axiom,
% 13.24/13.42 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zadd__0,axiom,
% 13.24/13.42 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zero__le__zpower__abs,axiom,
% 13.24/13.42 ! [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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zabs__def,axiom,
% 13.24/13.42 ! [V_i] :
% 13.24/13.42 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 13.24/13.42 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i) )
% 13.24/13.42 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 13.24/13.42 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = V_i ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_less__bin__lemma,axiom,
% 13.24/13.42 ! [V_l_2,V_ka_2] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_ka_2,V_l_2)
% 13.24/13.42 <=> 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zabs__less__one__iff,axiom,
% 13.24/13.42 ! [V_z_2] :
% 13.24/13.42 ( 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))
% 13.24/13.42 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zmult__zless__mono2,axiom,
% 13.24/13.42 ! [V_k,V_j,V_i] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 13.24/13.42 => 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)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_pos__zmult__eq__1__iff,axiom,
% 13.24/13.42 ! [V_n_2,V_ma_2] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)
% 13.24/13.42 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 13.24/13.42 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 13.24/13.42 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_int__one__le__iff__zero__less,axiom,
% 13.24/13.42 ! [V_z_2] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zminus__0,axiom,
% 13.24/13.42 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_int__0__less__1,axiom,
% 13.24/13.42 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_int__0__neq__1,axiom,
% 13.24/13.42 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zmult__1,axiom,
% 13.24/13.42 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zmult__1__right,axiom,
% 13.24/13.42 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zmult__commute,axiom,
% 13.24/13.42 ! [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) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zless__le,axiom,
% 13.24/13.42 ! [V_wa_2,V_z_2] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_wa_2)
% 13.24/13.42 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_wa_2)
% 13.24/13.42 & V_z_2 != V_wa_2 ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zless__linear,axiom,
% 13.24/13.42 ! [V_y,V_x] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 13.24/13.42 | V_x = V_y
% 13.24/13.42 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zmult__zminus,axiom,
% 13.24/13.42 ! [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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zmult__assoc,axiom,
% 13.24/13.42 ! [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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_abs__zmult__eq__1,axiom,
% 13.24/13.42 ! [V_n,V_m] :
% 13.24/13.42 ( 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)
% 13.24/13.42 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zdiff__zmult__distrib,axiom,
% 13.24/13.42 ! [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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zdiff__zmult__distrib2,axiom,
% 13.24/13.42 ! [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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zle__diff1__eq,axiom,
% 13.24/13.42 ! [V_z_2,V_wa_2] :
% 13.24/13.42 ( 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)))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zadd__zless__mono,axiom,
% 13.24/13.42 ! [V_z,V_z_H,V_w,V_w_H] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 13.24/13.42 => 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)) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zadd__strict__right__mono,axiom,
% 13.24/13.42 ! [V_k,V_j,V_i] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zless__imp__add1__zle,axiom,
% 13.24/13.42 ! [V_z,V_w] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zadd__zmult__distrib,axiom,
% 13.24/13.42 ! [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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_add1__zle__eq,axiom,
% 13.24/13.42 ! [V_z_2,V_wa_2] :
% 13.24/13.42 ( 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)
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zadd__zmult__distrib2,axiom,
% 13.24/13.42 ! [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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zless__add1__eq,axiom,
% 13.24/13.42 ! [V_z_2,V_wa_2] :
% 13.24/13.42 ( 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)))
% 13.24/13.42 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2)
% 13.24/13.42 | V_wa_2 = V_z_2 ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zle__add1__eq__le,axiom,
% 13.24/13.42 ! [V_z_2,V_wa_2] :
% 13.24/13.42 ( 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)))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_z_2) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_odd__nonzero,axiom,
% 13.24/13.42 ! [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) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zadd__zminus__inverse2,axiom,
% 13.24/13.42 ! [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) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_odd__less__0,axiom,
% 13.24/13.42 ! [V_z_2] :
% 13.24/13.42 ( 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))
% 13.24/13.42 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_le__imp__0__less,axiom,
% 13.24/13.42 ! [V_z] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 13.24/13.42 => 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)) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_complex__i__not__one,axiom,
% 13.24/13.42 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_complex__i__not__zero,axiom,
% 13.24/13.42 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_complex__i__mult__minus,axiom,
% 13.24/13.42 ! [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) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_inverse__i,axiom,
% 13.24/13.42 c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_i__mult__eq2,axiom,
% 13.24/13.42 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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_incr__lemma,axiom,
% 13.24/13.42 ! [V_x,V_z,V_d] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 13.24/13.42 => 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))) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_decr__lemma,axiom,
% 13.24/13.42 ! [V_z,V_x,V_d] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 13.24/13.42 => 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) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zminus__zadd__distrib,axiom,
% 13.24/13.42 ! [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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_diff__int__def__symmetric,axiom,
% 13.24/13.42 ! [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) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_diff__int__def,axiom,
% 13.24/13.42 ! [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)) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zminus__zminus,axiom,
% 13.24/13.42 ! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zle__refl,axiom,
% 13.24/13.42 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zle__linear,axiom,
% 13.24/13.42 ! [V_w,V_z] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 13.24/13.42 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zle__trans,axiom,
% 13.24/13.42 ! [V_k,V_j,V_i] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 13.24/13.42 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 13.24/13.42 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 13.24/13.42
% 13.24/13.42 fof(fact_zle__antisym,axiom,
% 13.24/13.42 ! [V_w,V_z] :
% 13.24/13.42 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 13.24/13.43 => V_z = V_w ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_zadd__left__mono,axiom,
% 13.24/13.43 ! [V_k,V_j,V_i] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_zadd__assoc,axiom,
% 13.24/13.43 ! [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)) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_zadd__left__commute,axiom,
% 13.24/13.43 ! [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)) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_zadd__commute,axiom,
% 13.24/13.43 ! [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) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_self__quotient__aux2,axiom,
% 13.24/13.43 ! [V_q,V_r,V_a] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 13.24/13.43 => ( 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))
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_self__quotient__aux1,axiom,
% 13.24/13.43 ! [V_q,V_r,V_a] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 13.24/13.43 => ( 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))
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 13.24/13.43 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 13.24/13.43 ( 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)
% 13.24/13.43 => ( 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))
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_unique__quotient__lemma__neg,axiom,
% 13.24/13.43 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 13.24/13.43 ( 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))
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_zdiv__mono2__lemma,axiom,
% 13.24/13.43 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 13.24/13.43 ( 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)
% 13.24/13.43 => ( 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))
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_unique__quotient__lemma,axiom,
% 13.24/13.43 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 13.24/13.43 ( 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))
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_q__neg__lemma,axiom,
% 13.24/13.43 ! [V_r_H,V_q_H,V_b_H] :
% 13.24/13.43 ( 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))
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_q__pos__lemma,axiom,
% 13.24/13.43 ! [V_r_H,V_q_H,V_b_H] :
% 13.24/13.43 ( 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))
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 13.24/13.43 ! [V_n,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 13.24/13.43 ! [V_y,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 13.24/13.43 => 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)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 13.24/13.43 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)) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 13.24/13.43 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)) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 13.24/13.43 ! [V_y,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 13.24/13.43 => 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)) ) ) ).
% 13.24/13.43
% 13.24/13.43 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,
% 13.24/13.43 ~ ! [B_m] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)
% 13.24/13.43 => ~ ! [B_z] :
% 13.24/13.43 ( 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____))
% 13.24/13.43 => 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) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__refl,axiom,
% 13.24/13.43 ! [V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_le__fun__def,axiom,
% 13.24/13.43 ! [V_g_2,V_f_2,T_a,T_b] :
% 13.24/13.43 ( class_Orderings_Oord(T_b)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 13.24/13.43 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__linear,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 13.24/13.43 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__eq__iff,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( V_x_2 = V_y_2
% 13.24/13.43 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 13.24/13.43 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__eq__refl,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ( V_x = V_y
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_le__funD,axiom,
% 13.24/13.43 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 13.24/13.43 ( class_Orderings_Oord(T_b)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__antisym__conv,axiom,
% 13.24/13.43 ! [V_x_2,V_y_2,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 13.24/13.43 <=> V_x_2 = V_y_2 ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_ord__eq__le__trans,axiom,
% 13.24/13.43 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.43 ( class_Orderings_Oord(T_a)
% 13.24/13.43 => ( V_a = V_b
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I3_J,axiom,
% 13.24/13.43 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( V_a = V_b
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_ord__le__eq__trans,axiom,
% 13.24/13.43 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.43 ( class_Orderings_Oord(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.43 => ( V_b = V_c
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I4_J,axiom,
% 13.24/13.43 ! [V_c,V_a,V_b,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 13.24/13.43 => ( V_b = V_c
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__antisym,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 13.24/13.43 => V_x = V_y ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__trans,axiom,
% 13.24/13.43 ! [V_z,V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I5_J,axiom,
% 13.24/13.43 ! [V_x,V_y,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 13.24/13.43 => V_x = V_y ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I6_J,axiom,
% 13.24/13.43 ! [V_z,V_x,V_y,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_le__funE,axiom,
% 13.24/13.43 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 13.24/13.43 ( class_Orderings_Oord(T_b)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__le__cases,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__cases,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => ( V_x != V_y
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__less__asym,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I10_J,axiom,
% 13.24/13.43 ! [V_z,V_x,V_y,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__less__trans,axiom,
% 13.24/13.43 ! [V_z,V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I2_J,axiom,
% 13.24/13.43 ! [V_c,V_a,V_b,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 13.24/13.43 => ( V_b = V_c
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_ord__less__eq__trans,axiom,
% 13.24/13.43 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.43 ( class_Orderings_Oord(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.43 => ( V_b = V_c
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I1_J,axiom,
% 13.24/13.43 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( V_a = V_b
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_ord__eq__less__trans,axiom,
% 13.24/13.43 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.43 ( class_Orderings_Oord(T_a)
% 13.24/13.43 => ( V_a = V_b
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I9_J,axiom,
% 13.24/13.43 ! [V_a,V_b,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 13.24/13.43 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__less__asym_H,axiom,
% 13.24/13.43 ! [V_b,V_a,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 13.24/13.43 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__less__imp__not__eq2,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => V_y != V_x ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__less__imp__not__eq,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => V_x != V_y ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__less__imp__not__less,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__less__not__sym,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_less__imp__neq,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => V_x != V_y ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__neqE,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( V_x != V_y
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__antisym__conv3,axiom,
% 13.24/13.43 ! [V_x_2,V_y_2,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 13.24/13.43 <=> V_x_2 = V_y_2 ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__less__linear,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 | V_x = V_y
% 13.24/13.43 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_not__less__iff__gr__or__eq,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 13.24/13.43 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 13.24/13.43 | V_x_2 = V_y_2 ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__neq__iff,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( V_x_2 != V_y_2
% 13.24/13.43 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 13.24/13.43 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__less__irrefl,axiom,
% 13.24/13.43 ! [V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I8_J,axiom,
% 13.24/13.43 ! [V_z,V_x,V_y,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__le__less__trans,axiom,
% 13.24/13.43 ! [V_z,V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I7_J,axiom,
% 13.24/13.43 ! [V_z,V_x,V_y,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__less__le__trans,axiom,
% 13.24/13.43 ! [V_z,V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I11_J,axiom,
% 13.24/13.43 ! [V_a,V_b,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 13.24/13.43 => ( V_a != V_b
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__le__neq__trans,axiom,
% 13.24/13.43 ! [V_b,V_a,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.43 => ( V_a != V_b
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__le__imp__less__or__eq,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 | V_x = V_y ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__antisym__conv2,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 13.24/13.43 <=> V_x_2 = V_y_2 ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__less__imp__le,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_leD,axiom,
% 13.24/13.43 ! [V_x,V_y,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 13.24/13.43 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_xt1_I12_J,axiom,
% 13.24/13.43 ! [V_b,V_a,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( V_a != V_b
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__neq__le__trans,axiom,
% 13.24/13.43 ! [V_b,V_a,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( V_a != V_b
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__antisym__conv1,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 13.24/13.43 <=> V_x_2 = V_y_2 ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_not__leE,axiom,
% 13.24/13.43 ! [V_x,V_y,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_leI,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__le__less,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 13.24/13.43 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 13.24/13.43 | V_x_2 = V_y_2 ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_less__le__not__le,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 13.24/13.43 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 13.24/13.43 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__less__le,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 13.24/13.43 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 13.24/13.43 & V_x_2 != V_y_2 ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__le__less__linear,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 13.24/13.43 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__not__le,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_linorder__not__less,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Orderings_Olinorder(T_a)
% 13.24/13.43 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 13.24/13.43
% 13.24/13.43 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,
% 13.24/13.43 ? [B_k,B_a] :
% 13.24/13.43 ( B_a != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 13.24/13.43 & B_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 13.24/13.43 & ? [B_q] :
% 13.24/13.43 ( 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____))
% 13.24/13.43 & ! [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))) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__add__one,axiom,
% 13.24/13.43 ! [V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_less__fun__def,axiom,
% 13.24/13.43 ! [V_g_2,V_f_2,T_a,T_b] :
% 13.24/13.43 ( class_Orderings_Oord(T_b)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 13.24/13.43 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 13.24/13.43 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__zero,axiom,
% 13.24/13.43 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_zero__le__natceiling,axiom,
% 13.24/13.43 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__mono,axiom,
% 13.24/13.43 ! [V_y,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__one,axiom,
% 13.24/13.43 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__neg,axiom,
% 13.24/13.43 ! [V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 13.24/13.43 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__le__eq__one,axiom,
% 13.24/13.43 ! [V_x_2] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_power__power__power,axiom,
% 13.24/13.43 ! [T_a] :
% 13.24/13.43 ( class_Power_Opower(T_a)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_of__real_Ononneg__bounded,axiom,
% 13.24/13.43 ! [T_a] :
% 13.24/13.43 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.43 & class_RealVector_Oreal__normed__vector(T_a) )
% 13.24/13.43 => ? [B_K] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 13.24/13.43 & ! [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)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_power_Opower_Opower__0,axiom,
% 13.24/13.43 ! [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 ).
% 13.24/13.43
% 13.24/13.43 fof(fact_lemmaCauchy,axiom,
% 13.24/13.43 ! [V_X_2,V_M_2,T_a,T_b] :
% 13.24/13.43 ( ( class_RealVector_Oreal__normed__vector(T_b)
% 13.24/13.43 & class_Orderings_Oord(T_a) )
% 13.24/13.43 => ( ! [B_n] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 13.24/13.43 => 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)) )
% 13.24/13.43 => ! [B_n] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 13.24/13.43 => 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)))) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_mult__left_Opos__bounded,axiom,
% 13.24/13.43 ! [V_y,T_a] :
% 13.24/13.43 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.43 => ? [B_K] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 13.24/13.43 & ! [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)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_mult_Opos__bounded,axiom,
% 13.24/13.43 ! [T_a] :
% 13.24/13.43 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.43 => ? [B_K] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 13.24/13.43 & ! [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)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_mult__right_Opos__bounded,axiom,
% 13.24/13.43 ! [V_x,T_a] :
% 13.24/13.43 ( class_RealVector_Oreal__normed__algebra(T_a)
% 13.24/13.43 => ? [B_K] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 13.24/13.43 & ! [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)) ) ) ).
% 13.24/13.43
% 13.24/13.43 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,
% 13.24/13.43 ~ ! [B_q] :
% 13.24/13.43 ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
% 13.24/13.43 => ~ ! [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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natfloor__add__one,axiom,
% 13.24/13.43 ! [V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natfloor__zero,axiom,
% 13.24/13.43 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natfloor__one,axiom,
% 13.24/13.43 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_zero__le__natfloor,axiom,
% 13.24/13.43 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natfloor__mono,axiom,
% 13.24/13.43 ! [V_y,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natfloor__neg,axiom,
% 13.24/13.43 ! [V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 13.24/13.43 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_le__natfloor__eq__one,axiom,
% 13.24/13.43 ! [V_x_2] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_le__mult__natfloor,axiom,
% 13.24/13.43 ! [V_b,V_a] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
% 13.24/13.43 => 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))) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_tsub__def,axiom,
% 13.24/13.43 ! [V_x,V_y] :
% 13.24/13.43 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 13.24/13.43 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) )
% 13.24/13.43 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 13.24/13.43 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_termination__basic__simps_I3_J,axiom,
% 13.24/13.43 ! [V_z,V_y,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 13.24/13.43 ! [V_y,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 13.24/13.43 => 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)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_tsub__eq,axiom,
% 13.24/13.43 ! [V_x,V_y] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 13.24/13.43 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_termination__basic__simps_I2_J,axiom,
% 13.24/13.43 ! [V_y,V_z,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_termination__basic__simps_I1_J,axiom,
% 13.24/13.43 ! [V_z,V_y,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_termination__basic__simps_I5_J,axiom,
% 13.24/13.43 ! [V_y,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_termination__basic__simps_I4_J,axiom,
% 13.24/13.43 ! [V_y,V_z,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__eq,axiom,
% 13.24/13.43 ! [V_x,V_n] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 13.24/13.43 => ( 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)))
% 13.24/13.43 => c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_pos__poly__pCons,axiom,
% 13.24/13.43 ! [V_pb_2,V_aa_2,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2))
% 13.24/13.43 <=> ( c_Polynomial_Opos__poly(T_a,V_pb_2)
% 13.24/13.43 | ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 13.24/13.43 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__ge__zero,axiom,
% 13.24/13.43 ! [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)) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__diff,axiom,
% 13.24/13.43 ! [V_m,V_n] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__less__iff,axiom,
% 13.24/13.43 ! [V_ma_2,V_n_2] :
% 13.24/13.43 ( 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))
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_not__real__of__nat__less__zero,axiom,
% 13.24/13.43 ! [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)) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_power__real__of__nat,axiom,
% 13.24/13.43 ! [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)) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__power,axiom,
% 13.24/13.43 ! [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) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_pos__poly__mult,axiom,
% 13.24/13.43 ! [V_q,V_p,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 13.24/13.43 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 13.24/13.43 => c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_abs__real__of__nat__cancel,axiom,
% 13.24/13.43 ! [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) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__zero__iff,axiom,
% 13.24/13.43 ! [V_n_2] :
% 13.24/13.43 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 13.24/13.43 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__zero,axiom,
% 13.24/13.43 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__mult,axiom,
% 13.24/13.43 ! [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)) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_not__pos__poly__0,axiom,
% 13.24/13.43 ! [T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__inject,axiom,
% 13.24/13.43 ! [V_ma_2,V_n_2] :
% 13.24/13.43 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)
% 13.24/13.43 <=> V_n_2 = V_ma_2 ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_pos__poly__add,axiom,
% 13.24/13.43 ! [V_q,V_p,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 13.24/13.43 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 13.24/13.43 => c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__add,axiom,
% 13.24/13.43 ! [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)) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__1,axiom,
% 13.24/13.43 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
% 13.24/13.43 ! [V_n_2] :
% 13.24/13.43 ( 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))
% 13.24/13.43 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__natceiling__ge,axiom,
% 13.24/13.43 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__le__iff,axiom,
% 13.24/13.43 ! [V_ma_2,V_n_2] :
% 13.24/13.43 ( 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))
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_less__eq__poly__def,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
% 13.24/13.43 <=> ( V_x_2 = V_y_2
% 13.24/13.43 | c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__real__of__nat,axiom,
% 13.24/13.43 ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natfloor__real__of__nat,axiom,
% 13.24/13.43 ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__natfloor__le,axiom,
% 13.24/13.43 ! [V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_le__natfloor,axiom,
% 13.24/13.43 ! [V_a,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__le,axiom,
% 13.24/13.43 ! [V_a,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natfloor__power,axiom,
% 13.24/13.43 ! [V_n,V_x] :
% 13.24/13.43 ( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))
% 13.24/13.43 => 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) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
% 13.24/13.43 ! [V_n_2] :
% 13.24/13.43 ( 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))
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_nat__less__real__le,axiom,
% 13.24/13.43 ! [V_ma_2,V_n_2] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
% 13.24/13.43 <=> 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_nat__le__real__less,axiom,
% 13.24/13.43 ! [V_ma_2,V_n_2] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
% 13.24/13.43 <=> 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))) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_le__natfloor__eq,axiom,
% 13.24/13.43 ! [V_aa_2,V_x_2] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_aa_2,c_RComplete_Onatfloor(V_x_2))
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2),V_x_2) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_pos__poly__total,axiom,
% 13.24/13.43 ! [V_p,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 13.24/13.43 | c_Polynomial_Opos__poly(T_a,V_p)
% 13.24/13.43 | c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__le__eq,axiom,
% 13.24/13.43 ! [V_aa_2,V_x_2] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_aa_2)
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__natfloor__add__one__gt,axiom,
% 13.24/13.43 ! [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))) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natfloor__subtract,axiom,
% 13.24/13.43 ! [V_x,V_a] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 13.24/13.43 => 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) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_real__natfloor__gt__diff__one,axiom,
% 13.24/13.43 ! [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))) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__subtract,axiom,
% 13.24/13.43 ! [V_x,V_a] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 13.24/13.43 => 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) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_less__natfloor,axiom,
% 13.24/13.43 ! [V_n,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
% 13.24/13.43 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natfloor__add,axiom,
% 13.24/13.43 ! [V_a,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 13.24/13.43 => 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) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
% 13.24/13.43 ! [V_n,V_z] :
% 13.24/13.43 ( 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)
% 13.24/13.43 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natfloor__eq,axiom,
% 13.24/13.43 ! [V_x,V_n] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 13.24/13.43 => ( 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)))
% 13.24/13.43 => c_RComplete_Onatfloor(V_x) = V_n ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_natceiling__add,axiom,
% 13.24/13.43 ! [V_a,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 13.24/13.43 => 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) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_less__poly__def,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
% 13.24/13.43 <=> c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
% 13.24/13.43 ! [V_n,V_x] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_reals__Archimedean6,axiom,
% 13.24/13.43 ! [V_r] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 13.24/13.43 => ? [B_n] :
% 13.24/13.43 ( 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)
% 13.24/13.43 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_Limits_Ominus__diff__minus,axiom,
% 13.24/13.43 ! [V_b,V_a,T_a] :
% 13.24/13.43 ( class_Groups_Oab__group__add(T_a)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_decseq__def,axiom,
% 13.24/13.43 ! [V_X_2,T_a] :
% 13.24/13.43 ( class_Orderings_Oorder(T_a)
% 13.24/13.43 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 13.24/13.43 <=> ! [B_m,B_n] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 13.24/13.43 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_poly__cont,axiom,
% 13.24/13.43 ! [V_p,V_z,V_e] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e)
% 13.24/13.43 => ? [B_d] :
% 13.24/13.43 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 13.24/13.43 & ! [B_w] :
% 13.24/13.43 ( ( 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)))
% 13.24/13.43 & 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) )
% 13.24/13.43 => 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) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_compl__mono,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_Lattices_Oboolean__algebra(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 13.24/13.43 => 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)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_compl__le__compl__iff,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Lattices_Oboolean__algebra(T_a)
% 13.24/13.43 => ( 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))
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_compl__eq__compl__iff,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Lattices_Oboolean__algebra(T_a)
% 13.24/13.43 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
% 13.24/13.43 <=> V_x_2 = V_y_2 ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_uminus__apply,axiom,
% 13.24/13.43 ! [V_x_2,V_A_2,T_b,T_a] :
% 13.24/13.43 ( class_Groups_Ouminus(T_a)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_double__compl,axiom,
% 13.24/13.43 ! [V_x,T_a] :
% 13.24/13.43 ( class_Lattices_Oboolean__algebra(T_a)
% 13.24/13.43 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_minus__apply,axiom,
% 13.24/13.43 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 13.24/13.43 ( class_Groups_Ominus(T_a)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_times_Oidem,axiom,
% 13.24/13.43 ! [V_a,T_a] :
% 13.24/13.43 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 13.24/13.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_mult__idem,axiom,
% 13.24/13.43 ! [V_x,T_a] :
% 13.24/13.43 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 13.24/13.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_mult__left__idem,axiom,
% 13.24/13.43 ! [V_b,V_a,T_a] :
% 13.24/13.43 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 13.24/13.43 => 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) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_of__real_Obounded,axiom,
% 13.24/13.43 ! [T_a] :
% 13.24/13.43 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 13.24/13.43 & class_RealVector_Oreal__normed__vector(T_a) )
% 13.24/13.43 => ? [B_K] :
% 13.24/13.43 ! [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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__poly__def,axiom,
% 13.24/13.43 ! [V_x,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 13.24/13.43 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 13.24/13.43 & ( V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 13.24/13.43 => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 13.24/13.43 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) )
% 13.24/13.43 & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 13.24/13.43 => 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))) ) ) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__less,axiom,
% 13.24/13.43 ! [V_aa_2,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__greater,axiom,
% 13.24/13.43 ! [V_aa_2,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_mult__sgn__abs,axiom,
% 13.24/13.43 ! [V_x,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => 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 ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_abs__sgn,axiom,
% 13.24/13.43 ! [V_k,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__mult,axiom,
% 13.24/13.43 ! [V_y,V_x,T_a] :
% 13.24/13.43 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__times,axiom,
% 13.24/13.43 ! [V_b,V_a,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn0,axiom,
% 13.24/13.43 ! [T_a] :
% 13.24/13.43 ( class_Groups_Osgn__if(T_a)
% 13.24/13.43 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__0__0,axiom,
% 13.24/13.43 ! [V_aa_2,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.43 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__zero__iff,axiom,
% 13.24/13.43 ! [V_x_2,T_a] :
% 13.24/13.43 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.43 => ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.43 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__zero,axiom,
% 13.24/13.43 ! [T_a] :
% 13.24/13.43 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.43 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__of__real,axiom,
% 13.24/13.43 ! [V_r,T_a] :
% 13.24/13.43 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__sgn,axiom,
% 13.24/13.43 ! [V_a,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => 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) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__minus,axiom,
% 13.24/13.43 ! [V_x,T_a] :
% 13.24/13.43 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.43 => 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)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__one,axiom,
% 13.24/13.43 ! [T_a] :
% 13.24/13.43 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 13.24/13.43 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__1__pos,axiom,
% 13.24/13.43 ! [V_aa_2,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Oone__class_Oone(T_a)
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__pos,axiom,
% 13.24/13.43 ! [V_a,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 13.24/13.43 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__if,axiom,
% 13.24/13.43 ! [V_x,T_a] :
% 13.24/13.43 ( class_Groups_Osgn__if(T_a)
% 13.24/13.43 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.43 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 13.24/13.43 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.43 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 13.24/13.43 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 13.24/13.43 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 13.24/13.43 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__1__neg,axiom,
% 13.24/13.43 ! [V_aa_2,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
% 13.24/13.43 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_sgn__neg,axiom,
% 13.24/13.43 ! [V_a,T_a] :
% 13.24/13.43 ( class_Rings_Olinordered__idom(T_a)
% 13.24/13.43 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 13.24/13.43 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_norm__sgn,axiom,
% 13.24/13.43 ! [V_x,T_a] :
% 13.24/13.43 ( class_RealVector_Oreal__normed__vector(T_a)
% 13.24/13.43 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.43 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 13.24/13.43 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 13.24/13.43 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_order__1,axiom,
% 13.24/13.43 ! [V_p,V_a,T_a] :
% 13.24/13.43 ( class_Rings_Oidom(T_a)
% 13.24/13.43 => 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) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_offset__poly__pCons,axiom,
% 13.24/13.43 ! [V_h,V_p,V_a,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.43 => 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))) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_dvd__0__right,axiom,
% 13.24/13.43 ! [V_a,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.43 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_dvd__minus__iff,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__ring__1(T_a)
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
% 13.24/13.43 <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_minus__dvd__iff,axiom,
% 13.24/13.43 ! [V_y_2,V_x_2,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__ring__1(T_a)
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)
% 13.24/13.43 <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_dvd__diff,axiom,
% 13.24/13.43 ! [V_z,V_y,V_x,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__ring__1(T_a)
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)
% 13.24/13.43 => c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_inf__period_I4_J,axiom,
% 13.24/13.43 ! [V_ta_2,V_D_2,V_d_2,T_a] :
% 13.24/13.43 ( ( class_Rings_Ocomm__ring(T_a)
% 13.24/13.43 & class_Rings_Odvd(T_a) )
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
% 13.24/13.43 => ! [B_x,B_k] :
% 13.24/13.43 ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))
% 13.24/13.43 <=> 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)) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_inf__period_I3_J,axiom,
% 13.24/13.43 ! [V_ta_2,V_D_2,V_d_2,T_a] :
% 13.24/13.43 ( ( class_Rings_Ocomm__ring(T_a)
% 13.24/13.43 & class_Rings_Odvd(T_a) )
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
% 13.24/13.43 => ! [B_x,B_k] :
% 13.24/13.43 ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))
% 13.24/13.43 <=> 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)) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_unity__coeff__ex,axiom,
% 13.24/13.43 ! [V_l_2,V_P_2,T_a] :
% 13.24/13.43 ( ( class_Rings_Odvd(T_a)
% 13.24/13.43 & class_Rings_Osemiring__0(T_a) )
% 13.24/13.43 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
% 13.24/13.43 <=> ? [B_x] :
% 13.24/13.43 ( 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)))
% 13.24/13.43 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_dvd__add,axiom,
% 13.24/13.43 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
% 13.24/13.43 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_one__dvd,axiom,
% 13.24/13.43 ! [V_a,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.43 => c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_offset__poly__eq__0__iff,axiom,
% 13.24/13.43 ! [V_h_2,V_pb_2,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.43 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pb_2,V_h_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 13.24/13.43 <=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_offset__poly__0,axiom,
% 13.24/13.43 ! [V_h,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__semiring__0(T_a)
% 13.24/13.43 => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_dvd__trans,axiom,
% 13.24/13.43 ! [V_c,V_b,V_a,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)
% 13.24/13.43 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_dvd__refl,axiom,
% 13.24/13.43 ! [V_a,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.43 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_a) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_dvd__smult,axiom,
% 13.24/13.43 ! [V_a,V_q,V_p,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
% 13.24/13.43 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q)) ) ) ).
% 13.24/13.43
% 13.24/13.43 fof(fact_smult__dvd__cancel,axiom,
% 13.24/13.43 ! [V_q,V_p,V_a,T_a] :
% 13.24/13.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 13.24/13.43 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)
% 13.24/13.43 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) ) ) ).
% 13.24/13.43
% 13.24/13.43 %----Arity declarations (289)
% 13.24/13.43 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 13.24/13.43 ! [T_1] :
% 13.24/13.43 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 13.24/13.43 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 13.24/13.43 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
% 13.24/13.43 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 13.24/13.43 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 13.24/13.43 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 13.24/13.43 ! [T_2,T_1] :
% 13.24/13.43 ( class_Lattices_Oboolean__algebra(T_1)
% 13.24/13.43 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_fun__Orderings_Opreorder,axiom,
% 13.24/13.43 ! [T_2,T_1] :
% 13.24/13.43 ( class_Orderings_Opreorder(T_1)
% 13.24/13.43 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_fun__Orderings_Oorder,axiom,
% 13.24/13.43 ! [T_2,T_1] :
% 13.24/13.43 ( class_Orderings_Oorder(T_1)
% 13.24/13.43 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_fun__Orderings_Oord,axiom,
% 13.24/13.43 ! [T_2,T_1] :
% 13.24/13.43 ( class_Orderings_Oord(T_1)
% 13.24/13.43 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_fun__Groups_Ouminus,axiom,
% 13.24/13.43 ! [T_2,T_1] :
% 13.24/13.43 ( class_Groups_Ouminus(T_1)
% 13.24/13.43 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_fun__Groups_Ominus,axiom,
% 13.24/13.43 ! [T_2,T_1] :
% 13.24/13.43 ( class_Groups_Ominus(T_1)
% 13.24/13.43 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 13.24/13.43 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 13.24/13.43 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 13.24/13.43 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 13.24/13.43 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 13.24/13.43 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 13.24/13.43 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 13.24/13.43 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 13.24/13.43 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 13.24/13.43 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 13.24/13.43 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 13.24/13.43 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 13.24/13.43 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 13.24/13.43 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 13.24/13.43 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 13.24/13.43 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 13.24/13.43 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 13.24/13.43 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 13.24/13.43 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 13.24/13.43 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 13.24/13.43 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 13.24/13.43 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 13.24/13.43 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 13.24/13.43 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 13.24/13.43 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 13.24/13.43 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 13.24/13.43 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 13.24/13.43 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 13.24/13.43 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 13.24/13.43 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 13.24/13.43 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 13.24/13.43 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 13.24/13.43 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 13.24/13.43 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 13.24/13.43 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 13.24/13.43 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 13.24/13.43 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 13.24/13.43 class_Orderings_Opreorder(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 13.24/13.43 class_Orderings_Olinorder(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 13.24/13.43 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 13.24/13.43 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 13.24/13.43 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 13.24/13.43 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 13.24/13.43 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 13.24/13.43 class_Rings_Omult__zero(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 13.24/13.43 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 13.24/13.43 class_Orderings_Oorder(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 13.24/13.43 class_Int_Oring__char__0(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 13.24/13.43 class_Rings_Osemiring(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 13.24/13.43 class_Orderings_Oord(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 13.24/13.43 class_Groups_Ouminus(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 13.24/13.43 class_Groups_Osgn__if(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 13.24/13.43 class_Groups_Oabs__if(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 13.24/13.43 class_Rings_Oring__1(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 13.24/13.43 class_Groups_Ominus(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Power_Opower,axiom,
% 13.24/13.43 class_Power_Opower(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 13.24/13.43 class_Groups_Ozero(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Oring,axiom,
% 13.24/13.43 class_Rings_Oring(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 13.24/13.43 class_Rings_Oidom(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Groups_Oone,axiom,
% 13.24/13.43 class_Groups_Oone(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 13.24/13.43 class_Rings_Odvd(tc_Int_Oint) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 13.24/13.43 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 13.24/13.43 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 13.24/13.43 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 13.24/13.43 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 13.24/13.43 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 13.24/13.43 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 13.24/13.43 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 13.24/13.43 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 13.24/13.43 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 13.24/13.43 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 13.24/13.43 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 13.24/13.43 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.43 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 13.24/13.43 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 13.24/13.43
% 13.24/13.44 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 13.24/13.44 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 13.24/13.44 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 13.24/13.44 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 13.24/13.44 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 13.24/13.44 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 13.24/13.44 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 13.24/13.44 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 13.24/13.44 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 13.24/13.44 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 13.24/13.44 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 13.24/13.44 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 13.24/13.44 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 13.24/13.44 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 13.24/13.44 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 13.24/13.44 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 13.24/13.44 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 13.24/13.44 class_Orderings_Oorder(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 13.24/13.44 class_Rings_Osemiring(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 13.24/13.44 class_Orderings_Oord(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 13.24/13.44 class_Groups_Ominus(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Power_Opower,axiom,
% 13.24/13.44 class_Power_Opower(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 13.24/13.44 class_Groups_Ozero(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 13.24/13.44 class_Groups_Oone(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 13.24/13.44 class_Rings_Odvd(tc_Nat_Onat) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 13.24/13.44 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 13.24/13.44 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 13.24/13.44 class_Orderings_Oorder(tc_HOL_Obool) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 13.24/13.44 class_Orderings_Oord(tc_HOL_Obool) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 13.24/13.44 class_Groups_Ouminus(tc_HOL_Obool) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 13.24/13.44 class_Groups_Ominus(tc_HOL_Obool) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 13.24/13.44 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 13.24/13.44 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 13.24/13.44 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 13.24/13.44 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
% 13.24/13.44 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 13.24/13.44 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 13.24/13.44 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 13.24/13.44 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
% 13.24/13.44 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 13.24/13.44 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 13.24/13.44 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 13.24/13.44 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 13.24/13.44 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 13.24/13.44 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 13.24/13.44 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 13.24/13.44 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 13.24/13.44 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 13.24/13.44 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 13.24/13.44 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 13.24/13.44 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 13.24/13.44 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 13.24/13.44 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 13.24/13.44 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__RealVector_Oreal__div__algebra,axiom,
% 13.24/13.44 class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 13.24/13.44 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 13.24/13.44 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 13.24/13.44 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
% 13.24/13.44 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
% 13.24/13.44 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 13.24/13.44 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 13.24/13.44 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 13.24/13.44 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 13.24/13.44 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
% 13.24/13.44 class_Fields_Olinordered__field(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 13.24/13.44 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
% 13.24/13.44 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 13.24/13.44 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 13.24/13.44 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 13.24/13.44 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 13.24/13.44 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 13.24/13.44 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
% 13.24/13.44 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
% 13.24/13.44 class_Rings_Odivision__ring(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 13.24/13.44 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 13.24/13.44 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 13.24/13.44 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 13.24/13.44 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 13.24/13.44 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 13.24/13.44 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 13.24/13.44 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 13.24/13.44 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 13.24/13.44 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 13.24/13.44 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 13.24/13.44 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 13.24/13.44 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 13.24/13.44 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 13.24/13.44 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 13.24/13.44 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 13.24/13.44 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 13.24/13.44 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
% 13.24/13.44 class_Groups_Ouminus(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom,
% 13.24/13.44 class_Groups_Osgn__if(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Oabs__if,axiom,
% 13.24/13.44 class_Groups_Oabs__if(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 13.24/13.44 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
% 13.24/13.44 class_Groups_Ominus(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 13.24/13.44 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 13.24/13.44 class_Power_Opower(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 13.24/13.44 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 13.24/13.44 class_Rings_Oring(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 13.24/13.44 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 13.24/13.44 class_Groups_Oone(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
% 13.24/13.44 class_Rings_Odvd(tc_RealDef_Oreal) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 13.24/13.44 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 13.24/13.44 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
% 13.24/13.44 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 13.24/13.44 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 13.24/13.44 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 13.24/13.44 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 13.24/13.44 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 13.24/13.44 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 13.24/13.44 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__RealVector_Oreal__div__algebra,axiom,
% 13.24/13.44 class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 13.24/13.44 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
% 13.24/13.44 class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
% 13.24/13.44 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 13.24/13.44 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 13.24/13.44 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 13.24/13.44 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 13.24/13.44 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 13.24/13.44 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 13.24/13.44 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 13.24/13.44 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
% 13.24/13.44 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 13.24/13.44 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 13.24/13.44 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 13.24/13.44 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 13.24/13.44 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 13.24/13.44 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 13.24/13.44 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 13.24/13.44 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 13.24/13.44 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 13.24/13.44 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 13.24/13.44 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 13.24/13.44 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 13.24/13.44 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
% 13.24/13.44 class_Groups_Ouminus(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 13.24/13.44 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
% 13.24/13.44 class_Groups_Ominus(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 13.24/13.44 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 13.24/13.44 class_Power_Opower(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 13.24/13.44 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 13.24/13.44 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 13.24/13.44 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 13.24/13.44 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
% 13.24/13.44 class_Rings_Odvd(tc_Complex_Ocomplex) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Oidom(T_1)
% 13.24/13.44 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 13.24/13.44 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Oidom(T_1)
% 13.24/13.44 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Oidom(T_1)
% 13.24/13.44 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 13.24/13.44 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__0(T_1)
% 13.24/13.44 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__1(T_1)
% 13.24/13.44 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Groups_Ocomm__monoid__add(T_1)
% 13.24/13.44 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Oidom(T_1)
% 13.24/13.44 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Groups_Ocomm__monoid__add(T_1)
% 13.24/13.44 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__1(T_1)
% 13.24/13.44 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__0(T_1)
% 13.24/13.44 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__0(T_1)
% 13.24/13.44 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Groups_Oab__group__add(T_1)
% 13.24/13.44 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__1(T_1)
% 13.24/13.44 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__1(T_1)
% 13.24/13.44 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__ring__1(T_1)
% 13.24/13.44 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Groups_Ocomm__monoid__add(T_1)
% 13.24/13.44 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__0(T_1)
% 13.24/13.44 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Groups_Oab__group__add(T_1)
% 13.24/13.44 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__0(T_1)
% 13.24/13.44 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__ring(T_1)
% 13.24/13.44 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__0(T_1)
% 13.24/13.44 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Groups_Oab__group__add(T_1)
% 13.24/13.44 => class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Olinordered__idom(T_1)
% 13.24/13.44 => class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__ring__1(T_1)
% 13.24/13.44 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Groups_Oab__group__add(T_1)
% 13.24/13.44 => class_Groups_Ominus(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Power_Opower,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__1(T_1)
% 13.24/13.44 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Groups_Ozero(T_1)
% 13.24/13.44 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__ring(T_1)
% 13.24/13.44 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Oidom(T_1)
% 13.24/13.44 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__1(T_1)
% 13.24/13.44 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
% 13.24/13.44 ! [T_1] :
% 13.24/13.44 ( class_Rings_Ocomm__semiring__1(T_1)
% 13.24/13.44 => class_Rings_Odvd(tc_Polynomial_Opoly(T_1)) ) ).
% 13.24/13.44
% 13.24/13.44 %----Conjectures (1)
% 13.24/13.44 fof(conj_0,conjecture,
% 13.24/13.44 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),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_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 13.24/13.44
% 13.24/13.44 %------------------------------------------------------------------------------
% 13.24/13.44 %-------------------------------------------
% 13.24/13.44 % Proof found
% 13.24/13.44 % SZS status Theorem for theBenchmark
% 13.24/13.44 % SZS output start Proof
% 13.24/13.44 %ClaNum:1803(EqnAxiom:204)
% 13.24/13.44 %VarNum:8654(SingletonVarNum:2965)
% 13.24/13.44 %MaxLitNum:7
% 13.24/13.44 %MaxfuncDepth:9
% 13.24/13.44 %SharedTerms:471
% 13.24/13.44 %goalClause: 609
% 13.24/13.44 %singleGoalClaCount:1
% 13.24/13.44 [205]P1(a1)
% 13.24/13.44 [206]P1(a2)
% 13.24/13.44 [207]P1(a3)
% 13.24/13.44 [208]P2(a1)
% 13.24/13.44 [209]P2(a4)
% 13.24/13.44 [210]P45(a1)
% 13.24/13.44 [211]P45(a4)
% 13.24/13.44 [212]P48(a1)
% 13.24/13.44 [213]P48(a4)
% 13.24/13.44 [214]P46(a1)
% 13.24/13.44 [215]P46(a4)
% 13.24/13.44 [216]P3(a1)
% 13.24/13.44 [217]P3(a4)
% 13.24/13.44 [218]P3(a2)
% 13.24/13.44 [219]P3(a3)
% 13.24/13.44 [220]P63(a1)
% 13.24/13.44 [221]P63(a4)
% 13.24/13.44 [222]P63(a2)
% 13.24/13.44 [223]P63(a3)
% 13.24/13.44 [224]P68(a1)
% 13.24/13.44 [225]P68(a4)
% 13.24/13.44 [226]P68(a2)
% 13.24/13.44 [227]P68(a3)
% 13.24/13.44 [228]P69(a1)
% 13.24/13.44 [229]P69(a4)
% 13.24/13.44 [230]P69(a2)
% 13.24/13.44 [231]P69(a3)
% 13.24/13.44 [232]P4(a1)
% 13.24/13.44 [233]P4(a4)
% 13.24/13.44 [234]P4(a2)
% 13.24/13.44 [235]P4(a3)
% 13.24/13.44 [236]P70(a1)
% 13.24/13.44 [237]P70(a4)
% 13.24/13.44 [238]P70(a3)
% 13.24/13.44 [239]P78(a1)
% 13.24/13.44 [240]P78(a4)
% 13.24/13.44 [241]P78(a2)
% 13.24/13.44 [242]P78(a3)
% 13.24/13.44 [243]P71(a1)
% 13.24/13.44 [244]P71(a4)
% 13.24/13.44 [245]P71(a3)
% 13.24/13.44 [246]P5(a1)
% 13.24/13.44 [247]P5(a4)
% 13.24/13.44 [248]P5(a2)
% 13.24/13.44 [249]P5(a3)
% 13.24/13.44 [250]P49(a1)
% 13.24/13.44 [251]P49(a4)
% 13.24/13.44 [252]P64(a1)
% 13.24/13.44 [253]P64(a3)
% 13.24/13.44 [254]P65(a1)
% 13.24/13.44 [255]P65(a3)
% 13.24/13.44 [256]P50(a1)
% 13.24/13.44 [257]P50(a3)
% 13.24/13.44 [258]P72(a1)
% 13.24/13.44 [259]P72(a3)
% 13.24/13.44 [260]P79(a1)
% 13.24/13.44 [261]P79(a4)
% 13.24/13.44 [262]P79(a3)
% 13.24/13.44 [263]P51(a1)
% 13.24/13.44 [264]P51(a4)
% 13.24/13.44 [265]P51(a2)
% 13.24/13.44 [266]P51(a3)
% 13.24/13.44 [267]P80(a1)
% 13.24/13.44 [268]P80(a4)
% 13.24/13.44 [269]P80(a2)
% 13.24/13.44 [270]P80(a3)
% 13.24/13.44 [271]P76(a1)
% 13.24/13.44 [272]P76(a4)
% 13.24/13.44 [273]P76(a3)
% 13.24/13.44 [274]P54(a1)
% 13.24/13.44 [275]P54(a4)
% 13.24/13.44 [276]P54(a3)
% 13.24/13.44 [277]P73(a1)
% 13.24/13.44 [278]P73(a2)
% 13.24/13.44 [279]P73(a3)
% 13.24/13.44 [280]P74(a1)
% 13.24/13.44 [281]P74(a3)
% 13.24/13.44 [282]P77(a1)
% 13.24/13.44 [283]P77(a2)
% 13.24/13.44 [284]P77(a3)
% 13.24/13.44 [285]P75(a1)
% 13.24/13.44 [286]P75(a2)
% 13.24/13.44 [287]P75(a3)
% 13.24/13.44 [288]P61(a1)
% 13.24/13.44 [289]P61(a3)
% 13.24/13.44 [290]P62(a1)
% 13.24/13.44 [291]P62(a3)
% 13.24/13.44 [292]P67(a1)
% 13.24/13.44 [293]P67(a2)
% 13.24/13.44 [294]P67(a3)
% 13.24/13.44 [295]P60(a1)
% 13.24/13.44 [296]P60(a2)
% 13.24/13.44 [297]P60(a3)
% 13.24/13.44 [298]P66(a1)
% 13.24/13.44 [299]P66(a2)
% 13.24/13.44 [300]P66(a3)
% 13.24/13.44 [301]P55(a1)
% 13.24/13.44 [302]P55(a4)
% 13.24/13.44 [303]P47(a1)
% 13.24/13.44 [304]P47(a4)
% 13.24/13.44 [305]P56(a1)
% 13.24/13.44 [306]P56(a4)
% 13.24/13.44 [307]P28(a1)
% 13.24/13.44 [308]P28(a4)
% 13.24/13.44 [309]P28(a2)
% 13.24/13.44 [310]P28(a3)
% 13.24/13.44 [311]P24(a1)
% 13.24/13.44 [312]P24(a4)
% 13.24/13.44 [313]P24(a3)
% 13.24/13.44 [314]P6(a1)
% 13.24/13.44 [315]P16(a1)
% 13.24/13.44 [316]P16(a4)
% 13.24/13.44 [317]P16(a3)
% 13.24/13.44 [318]P7(a1)
% 13.24/13.44 [319]P7(a4)
% 13.24/13.44 [320]P15(a1)
% 13.24/13.44 [321]P8(a1)
% 13.24/13.44 [322]P8(a4)
% 13.24/13.44 [323]P29(a1)
% 13.24/13.44 [324]P29(a3)
% 13.24/13.44 [325]P57(a1)
% 13.24/13.44 [326]P57(a4)
% 13.24/13.44 [327]P57(a2)
% 13.24/13.44 [328]P57(a3)
% 13.24/13.44 [329]P17(a1)
% 13.24/13.44 [330]P17(a4)
% 13.24/13.44 [331]P17(a2)
% 13.24/13.44 [332]P17(a3)
% 13.24/13.44 [333]P18(a1)
% 13.24/13.44 [334]P18(a4)
% 13.24/13.44 [335]P18(a2)
% 13.24/13.44 [336]P18(a3)
% 13.24/13.44 [337]P19(a1)
% 13.24/13.44 [338]P19(a4)
% 13.24/13.44 [339]P19(a2)
% 13.24/13.44 [340]P19(a3)
% 13.24/13.44 [341]P20(a1)
% 13.24/13.44 [342]P20(a4)
% 13.24/13.44 [343]P20(a2)
% 13.24/13.44 [344]P20(a3)
% 13.24/13.44 [345]P30(a1)
% 13.24/13.44 [346]P30(a4)
% 13.24/13.44 [347]P30(a2)
% 13.24/13.44 [348]P30(a3)
% 13.24/13.44 [349]P25(a1)
% 13.24/13.45 [350]P25(a4)
% 13.24/13.45 [351]P25(a2)
% 13.24/13.45 [352]P25(a3)
% 13.24/13.45 [353]P23(a1)
% 13.24/13.45 [354]P23(a4)
% 13.24/13.45 [355]P23(a2)
% 13.24/13.45 [356]P23(a3)
% 13.24/13.45 [357]P26(a1)
% 13.24/13.45 [358]P26(a3)
% 13.24/13.45 [359]P32(a1)
% 13.24/13.45 [360]P32(a2)
% 13.24/13.45 [361]P32(a3)
% 13.24/13.45 [362]P33(a1)
% 13.24/13.45 [363]P33(a2)
% 13.24/13.45 [364]P33(a3)
% 13.24/13.45 [365]P34(a1)
% 13.24/13.45 [366]P34(a2)
% 13.24/13.45 [367]P34(a3)
% 13.24/13.45 [368]P31(a1)
% 13.24/13.45 [369]P31(a3)
% 13.24/13.45 [370]P35(a1)
% 13.24/13.45 [371]P35(a2)
% 13.24/13.45 [372]P35(a3)
% 13.24/13.45 [373]P21(a1)
% 13.24/13.45 [374]P21(a3)
% 13.24/13.45 [375]P58(a1)
% 13.24/13.45 [376]P58(a4)
% 13.24/13.45 [377]P58(a2)
% 13.24/13.45 [378]P58(a3)
% 13.24/13.45 [379]P38(a1)
% 13.24/13.45 [380]P38(a4)
% 13.24/13.45 [381]P38(a3)
% 13.24/13.45 [382]P52(a1)
% 13.24/13.45 [383]P52(a4)
% 13.24/13.45 [384]P52(a3)
% 13.24/13.45 [385]P53(a1)
% 13.24/13.45 [386]P53(a4)
% 13.24/13.45 [387]P53(a3)
% 13.24/13.45 [388]P81(a1)
% 13.24/13.45 [389]P81(a4)
% 13.24/13.45 [390]P81(a2)
% 13.24/13.45 [391]P81(a3)
% 13.24/13.45 [392]P39(a1)
% 13.24/13.45 [393]P39(a2)
% 13.24/13.45 [394]P39(a3)
% 13.24/13.45 [395]P39(a71)
% 13.24/13.45 [396]P40(a1)
% 13.24/13.45 [397]P40(a2)
% 13.24/13.45 [398]P40(a3)
% 13.24/13.45 [399]P40(a71)
% 13.24/13.45 [400]P41(a1)
% 13.24/13.45 [401]P41(a2)
% 13.24/13.45 [402]P41(a3)
% 13.24/13.45 [403]P44(a1)
% 13.24/13.45 [404]P44(a2)
% 13.24/13.45 [405]P44(a3)
% 13.24/13.45 [406]P44(a71)
% 13.24/13.45 [407]P42(a71)
% 13.24/13.45 [408]P36(a1)
% 13.24/13.45 [409]P36(a4)
% 13.24/13.45 [410]P36(a3)
% 13.24/13.45 [411]P36(a71)
% 13.24/13.45 [412]P27(a1)
% 13.24/13.45 [413]P27(a4)
% 13.24/13.45 [414]P27(a2)
% 13.24/13.45 [415]P27(a3)
% 13.24/13.45 [416]P27(a71)
% 13.24/13.45 [417]P37(a1)
% 13.24/13.45 [418]P37(a3)
% 13.24/13.45 [419]P59(a1)
% 13.24/13.45 [420]P59(a4)
% 13.24/13.45 [421]P59(a2)
% 13.24/13.45 [422]P59(a3)
% 13.24/13.45 [423]P22(a1)
% 13.24/13.45 [424]P22(a4)
% 13.24/13.45 [425]P22(a2)
% 13.24/13.45 [426]P22(a3)
% 13.24/13.45 [435]E(f6(a4,a73),f6(a4,a80))
% 13.24/13.45 [436]E(f6(a4,a32),f6(a4,a73))
% 13.24/13.45 [437]E(f6(a4,a36),f6(a4,a73))
% 13.24/13.45 [438]E(f28(a4,a7),f13(a4,a7))
% 13.24/13.45 [453]P10(a1,a81,f5(a1))
% 13.24/13.45 [454]P10(a1,a33,f5(a1))
% 13.24/13.45 [455]P10(a1,f12(a1),a81)
% 13.24/13.45 [456]P10(a1,f12(a1),a74)
% 13.24/13.45 [457]P10(a1,f12(a1),a57)
% 13.24/13.45 [458]P10(a1,f12(a1),a33)
% 13.24/13.45 [459]P10(a1,f12(a1),a37)
% 13.24/13.45 [472]P10(a3,f12(a3),f5(a3))
% 13.24/13.45 [473]P9(a3,f12(a3),f5(a3))
% 13.24/13.45 [580]~E(f12(a2),a78)
% 13.24/13.45 [581]~E(f12(a4),a76)
% 13.24/13.45 [582]~E(f12(a4),a83)
% 13.24/13.45 [583]~E(f5(a4),a7)
% 13.24/13.45 [584]~E(f12(a4),a7)
% 13.24/13.45 [585]~E(f12(a2),a47)
% 13.24/13.45 [586]~E(f12(a4),a49)
% 13.24/13.45 [587]~E(f12(a1),f5(a1))
% 13.24/13.45 [588]~E(f12(a3),f5(a3))
% 13.24/13.45 [597]~P11(a4,a4,f17(a4,a79))
% 13.24/13.45 [598]~P11(a4,a4,f17(a4,a73))
% 13.24/13.45 [600]~P11(a4,a4,f17(a4,a80))
% 13.24/13.45 [427]E(f11(f5(a1)),f5(a2))
% 13.24/13.45 [428]E(f11(f12(a1)),f12(a2))
% 13.24/13.45 [429]E(f27(f5(a1)),f5(a2))
% 13.24/13.45 [430]E(f27(f12(a1)),f12(a2))
% 13.24/13.45 [431]E(f13(a3,f12(a3)),f12(a3))
% 13.24/13.45 [432]E(f28(a1,f12(a1)),f12(a1))
% 13.24/13.45 [433]E(f29(a2,f5(a2)),f5(a1))
% 13.24/13.45 [434]E(f29(a2,f12(a2)),f12(a1))
% 13.24/13.45 [477]E(f56(f17(a4,a80),f12(a4)),f56(f17(a4,a73),a75))
% 13.24/13.45 [505]P10(a2,f15(a2,a78,f5(a2)),f6(a4,a73))
% 13.24/13.45 [527]P9(a1,f56(f56(f14(a1),a81),f30(a4,a83)),f56(f56(f14(a1),f5(a1)),f30(a4,a83)))
% 13.24/13.45 [556]E(f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),f12(a4)),f5(a4))
% 13.24/13.45 [558]E(f10(a4,f15(a4,f5(a4),f56(f56(f14(a4),f56(f56(f23(a4),a83),a78)),a76)),f5(a4)),f10(a4,f12(a4),f5(a4)))
% 13.24/13.45 [589]~E(f56(f17(a4,a73),a75),f12(a4))
% 13.24/13.45 [590]~E(f56(f17(a4,a80),f12(a4)),f12(a4))
% 13.24/13.45 [596]~E(f15(a2,a78,f5(a2)),f6(a4,a73))
% 13.24/13.45 [469]E(f31(a4,f13(a1,f5(a1))),f13(a4,f5(a4)))
% 13.24/13.45 [470]E(f56(f56(f14(a4),a7),a7),f13(a4,f5(a4)))
% 13.24/13.45 [491]P10(a1,f12(a1),f56(f56(f23(a1),a81),a78))
% 13.24/13.45 [492]P9(a1,f56(f56(f23(a1),a81),a78),f5(a1))
% 13.24/13.45 [541]P9(a1,f30(a4,f56(f56(f14(a4),f31(a4,a81)),a83)),f30(a4,a83))
% 13.24/13.45 [515]E(f56(f56(f14(a4),f56(f56(f23(a4),a83),a78)),a76),f13(a4,f5(a4)))
% 13.24/13.45 [542]E(f6(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),f6(a4,a80))
% 13.24/13.45 [551]E(f6(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),f15(a2,f15(a2,f6(a4,a82),a78),f5(a2)))
% 13.24/13.45 [552]E(f6(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),f15(a2,f15(a2,f6(a4,a46),a47),f5(a2)))
% 13.24/13.45 [555]E(f6(a4,f20(a4,f5(a4),f18(a4,a76,f10(a2,a78,f5(a2))))),f15(a2,a78,f5(a2)))
% 13.24/13.45 [606]~P11(a4,a4,f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)))
% 13.24/13.45 [607]~P11(a4,a4,f17(a4,f20(a4,f5(a4),f18(a4,a76,f10(a2,a78,f5(a2))))))
% 13.24/13.45 [544]E(f15(a4,f5(a4),f56(f56(f14(a4),f56(f56(f23(a4),a83),a78)),a76)),f12(a4))
% 13.24/13.45 [545]E(f15(a4,f5(a4),f56(f56(f14(a4),f56(f56(f23(a4),a58),a78)),a76)),f12(a4))
% 13.24/13.45 [559]E(f56(f17(a4,f20(a4,f5(a4),f18(a4,a76,f10(a2,a78,f5(a2))))),a38),f12(a4))
% 13.24/13.45 [561]P10(a1,a81,f28(a1,f56(f56(f14(a1),f56(f56(f23(a1),f30(a4,a83)),f15(a2,a78,f5(a2)))),a74)))
% 13.24/13.45 [562]P10(a1,a33,f28(a1,f56(f56(f14(a1),f56(f56(f23(a1),f30(a4,a83)),f15(a2,a78,f5(a2)))),a74)))
% 13.24/13.45 [563]P10(a1,f12(a1),f28(a1,f56(f56(f14(a1),f56(f56(f23(a1),f30(a4,a83)),f15(a2,a78,f5(a2)))),a74)))
% 13.24/13.45 [564]P10(a1,f56(f56(f14(a1),a81),f56(f56(f14(a1),f56(f56(f23(a1),f30(a4,a83)),f15(a2,a78,f5(a2)))),a74)),f5(a1))
% 13.24/13.45 [573]P10(a1,f30(a4,f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83)))),f56(f56(f23(a1),a81),a78))
% 13.24/13.45 [574]E(f15(a4,f15(a4,f5(a4),f56(f56(f14(a4),f56(f56(f23(a4),f31(a4,a81)),a78)),f56(f56(f14(a4),f56(f56(f23(a4),a83),a78)),a76))),f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83)))),f15(a4,f31(a4,f10(a1,f5(a1),f56(f56(f23(a1),a81),a78))),f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83)))))
% 13.24/13.45 [608]~E(f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),a39),f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),a42))
% 13.24/13.45 [569]P10(a1,f56(f56(f14(a1),f56(f56(f23(a1),a81),a78)),f56(f56(f14(a1),a81),f56(f56(f14(a1),f56(f56(f23(a1),f30(a4,a83)),f15(a2,a78,f5(a2)))),a74))),f56(f56(f14(a1),f56(f56(f23(a1),a81),a78)),f5(a1)))
% 13.24/13.45 [575]P9(a1,f30(a4,f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83)))),f56(f56(f14(a1),f56(f56(f23(a1),a81),a78)),f56(f56(f14(a1),a81),f56(f56(f14(a1),f56(f56(f23(a1),f30(a4,a83)),f15(a2,a78,f5(a2)))),a74))))
% 13.24/13.45 [577]P10(a1,f15(a1,f9(a1,f10(a1,f5(a1),f56(f56(f23(a1),a81),a78))),f30(a4,f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83))))),f5(a1))
% 13.24/13.45 [579]P9(a1,f30(a4,f15(a4,f31(a4,f10(a1,f5(a1),f56(f56(f23(a1),a81),a78))),f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83))))),f15(a1,f30(a4,f31(a4,f10(a1,f5(a1),f56(f56(f23(a1),a81),a78)))),f30(a4,f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83))))))
% 13.24/13.45 [570]E(f56(f56(f14(a1),f56(f56(f23(a1),a81),a78)),f56(f56(f14(a1),a81),f56(f56(f14(a1),f56(f56(f23(a1),f30(a4,a83)),f15(a2,a78,f5(a2)))),f30(a4,f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83)))))),f30(a4,f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83)))))
% 13.24/13.45 [571]E(f15(a4,f31(a4,f10(a1,f5(a1),f56(f56(f23(a1),a81),a78))),f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83)))),f15(a4,f5(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f15(a4,a76,f56(f56(f14(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83)))))))
% 13.24/13.45 [572]E(f15(a4,f15(a4,f5(a4),f56(f56(f14(a4),f56(f56(f23(a4),f31(a4,a81)),a78)),f56(f56(f14(a4),f56(f56(f23(a4),a83),a78)),a76))),f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83)))),f15(a4,f5(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f15(a4,a76,f56(f56(f14(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83)))))))
% 13.24/13.45 [576]E(f30(a4,f15(a4,f31(a4,f10(a1,f5(a1),f56(f56(f23(a1),a81),a78))),f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83))))),f30(a4,f15(a4,f5(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f15(a4,a76,f56(f56(f14(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83))))))))
% 13.24/13.45 [578]P9(a1,f30(a4,f15(a4,f5(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f15(a4,a76,f56(f56(f14(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83))))))),f15(a1,f9(a1,f10(a1,f5(a1),f56(f56(f23(a1),a81),a78))),f30(a4,f56(f56(f14(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f56(f56(f14(a4),f31(a4,a81)),a83))),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83))))))
% 13.24/13.45 [609]~P10(a1,f30(a4,f15(a4,f5(a4),f56(f56(f14(a4),f56(f56(f23(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),a78)),f15(a4,a76,f56(f56(f14(a4),f56(f56(f14(a4),f31(a4,a81)),a83)),f56(f17(a4,a82),f56(f56(f14(a4),f31(a4,a81)),a83))))))),f5(a1))
% 13.24/13.45 [447]P9(a1,x4471,x4471)
% 13.24/13.45 [448]P9(a2,x4481,x4481)
% 13.24/13.45 [449]P9(a3,x4491,x4491)
% 13.24/13.45 [592]~P10(a2,x5921,x5921)
% 13.24/13.45 [439]E(f30(a1,x4391),f9(a1,x4391))
% 13.24/13.45 [461]E(f10(a2,x4611,x4611),f12(a2))
% 13.24/13.45 [463]P9(a2,f12(a2),x4631)
% 13.24/13.45 [479]P9(a1,f12(a1),f29(a2,x4791))
% 13.24/13.45 [595]~P10(a2,x5951,f12(a2))
% 13.24/13.45 [601]~P10(a1,f29(a2,x6011),f12(a1))
% 13.24/13.45 [440]E(f11(f29(a2,x4401)),x4401)
% 13.24/13.45 [441]E(f27(f29(a2,x4411)),x4411)
% 13.24/13.45 [442]E(f13(a3,f13(a3,x4421)),x4421)
% 13.24/13.45 [443]E(f9(a1,f29(a2,x4431)),f29(a2,x4431))
% 13.24/13.45 [444]E(f56(f56(f14(a2),x4441),f5(a2)),x4441)
% 13.24/13.45 [445]E(f56(f56(f14(a3),x4451),f5(a3)),x4451)
% 13.24/13.45 [446]E(f56(f56(f14(a2),x4461),f12(a2)),f12(a2))
% 13.24/13.45 [464]E(f15(a2,x4641,f12(a2)),x4641)
% 13.24/13.45 [465]E(f15(a3,x4651,f12(a3)),x4651)
% 13.24/13.45 [466]E(f10(a2,x4661,f12(a2)),x4661)
% 13.24/13.45 [467]E(f15(a2,f12(a2),x4671),x4671)
% 13.24/13.45 [468]E(f15(a3,f12(a3),x4681),x4681)
% 13.24/13.45 [471]E(f10(a2,f12(a2),x4711),f12(a2))
% 13.24/13.45 [478]E(f15(a3,f13(a3,x4781),x4781),f12(a3))
% 13.24/13.45 [480]P9(a1,x4801,f29(a2,f11(x4801)))
% 13.24/13.45 [495]P9(a1,f13(a1,f30(a4,x4951)),f30(a4,x4951))
% 13.24/13.45 [502]E(f56(f17(a4,a73),f15(a4,a75,x5021)),f56(f17(a4,a80),x5021))
% 13.24/13.45 [503]E(f56(f17(a4,a73),f15(a4,a75,x5031)),f56(f17(a4,a32),x5031))
% 13.24/13.45 [504]E(f56(f17(a4,a73),f15(a4,a75,x5041)),f56(f17(a4,a36),x5041))
% 13.24/13.45 [510]P10(a1,f10(a1,x5101,f5(a1)),f29(a2,f27(x5101)))
% 13.24/13.45 [511]P10(a1,f12(a1),f15(a1,f5(a1),f9(a1,x5111)))
% 13.24/13.45 [516]P10(a1,x5161,f15(a1,f29(a2,f27(x5161)),f5(a1)))
% 13.24/13.45 [605]~P10(a1,f15(a1,f9(a1,x6051),f5(a1)),x6051)
% 13.24/13.45 [450]E(f56(f56(f14(a1),f5(a1)),x4501),x4501)
% 13.24/13.45 [451]E(f56(f56(f14(a2),f5(a2)),x4511),x4511)
% 13.24/13.45 [452]E(f56(f56(f14(a3),f5(a3)),x4521),x4521)
% 13.24/13.45 [460]E(f56(f56(f14(a2),f12(a2)),x4601),f12(a2))
% 13.24/13.45 [494]P9(a2,x4941,f56(f56(f14(a2),x4941),x4941))
% 13.24/13.45 [531]P9(a1,f30(a4,f56(f17(a4,a73),a75)),f30(a4,f56(f17(a4,a73),x5311)))
% 13.24/13.45 [536]P9(a1,f30(a4,f56(f17(a4,a80),f12(a4))),f30(a4,f56(f17(a4,a73),x5361)))
% 13.24/13.45 [565]E(f56(f56(f14(a4),f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),x5651)),f56(f17(a4,a80),f12(a4))),f56(f17(a4,a80),x5651))
% 13.24/13.45 [604]~E(f15(a3,f15(a3,f5(a3),x6041),x6041),f12(a3))
% 13.24/13.45 [493]E(f56(f56(f14(a4),a7),f56(f56(f14(a4),a7),x4931)),f13(a4,x4931))
% 13.24/13.45 [528]P9(a2,x5281,f56(f56(f14(a2),x5281),f56(f56(f14(a2),x5281),x5281)))
% 13.24/13.45 [567]E(f15(a4,f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),f12(a4)),f56(f56(f14(a4),f56(f56(f23(a4),x5671),a78)),f56(f17(a4,f20(a4,a76,a82)),x5671))),f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),x5671))
% 13.24/13.45 [568]E(f15(a4,f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),f12(a4)),f56(f56(f14(a4),f56(f56(f23(a4),x5681),a47)),f56(f17(a4,f20(a4,a49,a46)),x5681))),f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),x5681))
% 13.24/13.45 [484]E(f15(a2,x4841,x4842),f15(a2,x4842,x4841))
% 13.24/13.45 [485]E(f15(a3,x4851,x4852),f15(a3,x4852,x4851))
% 13.24/13.45 [496]P9(a2,x4961,f15(a2,x4962,x4961))
% 13.24/13.45 [497]P9(a2,x4971,f15(a2,x4971,x4972))
% 13.24/13.45 [498]P9(a2,f10(a2,x4981,x4982),x4981)
% 13.24/13.45 [602]~P10(a2,f15(a2,x6021,x6022),x6022)
% 13.24/13.45 [603]~P10(a2,f15(a2,x6031,x6032),x6031)
% 13.24/13.45 [487]E(f15(a1,x4871,f13(a1,x4872)),f10(a1,x4871,x4872))
% 13.24/13.45 [488]E(f15(a4,x4881,f13(a4,x4882)),f10(a4,x4881,x4882))
% 13.24/13.45 [490]E(f15(a3,x4901,f13(a3,x4902)),f10(a3,x4901,x4902))
% 13.24/13.45 [499]E(f10(a2,f15(a2,x4991,x4992),x4992),x4991)
% 13.24/13.45 [500]E(f10(a2,f15(a2,x5001,x5002),x5001),x5002)
% 13.24/13.45 [501]E(f10(a2,x5011,f15(a2,x5011,x5012)),f12(a2))
% 13.24/13.45 [512]E(f15(a3,f13(a3,x5121),f13(a3,x5122)),f13(a3,f15(a3,x5121,x5122)))
% 13.24/13.45 [513]E(f15(a1,f29(a2,x5131),f29(a2,x5132)),f29(a2,f15(a2,x5131,x5132)))
% 13.24/13.45 [553]P9(a1,f30(a4,x5531),f15(a1,f30(a4,f15(a4,x5531,x5532)),f30(a4,x5532)))
% 13.24/13.45 [554]P9(a1,f10(a1,f30(a4,f15(a4,x5541,x5542)),f30(a4,x5541)),f30(a4,x5542))
% 13.24/13.45 [481]E(f56(f56(f14(a1),x4811),x4812),f56(f56(f14(a1),x4812),x4811))
% 13.24/13.45 [482]E(f56(f56(f14(a2),x4821),x4822),f56(f56(f14(a2),x4822),x4821))
% 13.24/13.45 [483]E(f56(f56(f14(a3),x4831),x4832),f56(f56(f14(a3),x4832),x4831))
% 13.24/13.45 [517]P9(a3,f12(a3),f56(f56(f23(a3),f9(a3,x5171)),x5172))
% 13.24/13.45 [529]E(f9(a1,f15(a1,x5291,f13(a1,x5292))),f9(a1,f15(a1,x5292,f13(a1,x5291))))
% 13.24/13.45 [507]E(f56(f56(f14(a3),f13(a3,x5071)),x5072),f13(a3,f56(f56(f14(a3),x5071),x5072)))
% 13.24/13.45 [508]E(f56(f56(f23(a1),f29(a2,x5081)),x5082),f29(a2,f56(f56(f23(a2),x5081),x5082)))
% 13.24/13.45 [509]E(f31(a4,f56(f56(f23(a1),x5091),x5092)),f56(f56(f23(a4),f31(a4,x5091)),x5092))
% 13.24/13.45 [514]E(f56(f56(f14(a1),f29(a2,x5141)),f29(a2,x5142)),f29(a2,f56(f56(f14(a2),x5141),x5142)))
% 13.24/13.45 [530]P9(a1,f13(a1,f56(f56(f14(a1),x5301),x5301)),f56(f56(f14(a1),x5302),x5302))
% 13.24/13.45 [519]E(f15(a2,x5191,f15(a2,x5192,x5193)),f15(a2,x5192,f15(a2,x5191,x5193)))
% 13.24/13.45 [520]E(f15(a3,x5201,f15(a3,x5202,x5203)),f15(a3,x5202,f15(a3,x5201,x5203)))
% 13.24/13.45 [521]E(f15(a2,f15(a2,x5211,x5212),x5213),f15(a2,x5211,f15(a2,x5212,x5213)))
% 13.24/13.45 [522]E(f15(a3,f15(a3,x5221,x5222),x5223),f15(a3,x5221,f15(a3,x5222,x5223)))
% 13.24/13.45 [523]E(f10(a2,f10(a2,x5231,x5232),x5233),f10(a2,x5231,f15(a2,x5232,x5233)))
% 13.24/13.45 [524]E(f10(a2,f10(a2,x5241,x5242),x5243),f10(a2,f10(a2,x5241,x5243),x5242))
% 13.24/13.45 [525]E(f10(a2,f15(a2,x5251,x5252),f15(a2,x5253,x5252)),f10(a2,x5251,x5253))
% 13.24/13.45 [526]E(f10(a2,f15(a2,x5261,x5262),f15(a2,x5261,x5263)),f10(a2,x5262,x5263))
% 13.24/13.45 [537]E(f15(a2,f56(f56(f14(a2),x5371),x5372),f56(f56(f14(a2),x5371),x5373)),f56(f56(f14(a2),x5371),f15(a2,x5372,x5373)))
% 13.24/13.45 [538]E(f10(a2,f56(f56(f14(a2),x5381),x5382),f56(f56(f14(a2),x5381),x5383)),f56(f56(f14(a2),x5381),f10(a2,x5382,x5383)))
% 13.24/13.45 [539]E(f15(a3,f56(f56(f14(a3),x5391),x5392),f56(f56(f14(a3),x5391),x5393)),f56(f56(f14(a3),x5391),f15(a3,x5392,x5393)))
% 13.24/13.45 [540]E(f10(a3,f56(f56(f14(a3),x5401),x5402),f56(f56(f14(a3),x5401),x5403)),f56(f56(f14(a3),x5401),f10(a3,x5402,x5403)))
% 13.24/13.45 [543]E(f56(f56(f14(a3),f56(f56(f23(a3),x5431),x5432)),f56(f56(f23(a3),x5431),x5433)),f56(f56(f23(a3),x5431),f15(a2,x5432,x5433)))
% 13.24/13.45 [546]E(f15(a1,f56(f56(f14(a1),x5461),x5462),f56(f56(f14(a1),x5463),x5462)),f56(f56(f14(a1),f15(a1,x5461,x5463)),x5462))
% 13.24/13.45 [547]E(f15(a2,f56(f56(f14(a2),x5471),x5472),f56(f56(f14(a2),x5473),x5472)),f56(f56(f14(a2),f15(a2,x5471,x5473)),x5472))
% 13.24/13.45 [548]E(f10(a2,f56(f56(f14(a2),x5481),x5482),f56(f56(f14(a2),x5483),x5482)),f56(f56(f14(a2),f10(a2,x5481,x5483)),x5482))
% 13.24/13.45 [549]E(f15(a3,f56(f56(f14(a3),x5491),x5492),f56(f56(f14(a3),x5493),x5492)),f56(f56(f14(a3),f15(a3,x5491,x5493)),x5492))
% 13.24/13.45 [550]E(f10(a3,f56(f56(f14(a3),x5501),x5502),f56(f56(f14(a3),x5503),x5502)),f56(f56(f14(a3),f10(a3,x5501,x5503)),x5502))
% 13.24/13.45 [532]E(f56(f56(f14(a1),f56(f56(f14(a1),x5321),x5322)),x5323),f56(f56(f14(a1),x5321),f56(f56(f14(a1),x5322),x5323)))
% 13.24/13.45 [533]E(f56(f56(f14(a2),f56(f56(f14(a2),x5331),x5332)),x5333),f56(f56(f14(a2),x5331),f56(f56(f14(a2),x5332),x5333)))
% 13.24/13.45 [534]E(f56(f56(f14(a3),f56(f56(f14(a3),x5341),x5342)),x5343),f56(f56(f14(a3),x5341),f56(f56(f14(a3),x5342),x5343)))
% 13.24/13.45 [535]E(f56(f56(f23(a3),f56(f56(f23(a3),x5351),x5352)),x5353),f56(f56(f23(a3),x5351),f56(f56(f14(a2),x5352),x5353)))
% 13.24/13.45 [518]E(f56(f56(f24(x5181,x5182,x5183),x5184),f12(a2)),x5182)
% 13.24/13.45 [560]P9(a1,f9(a1,f15(a1,f15(a1,x5601,x5602),f15(a1,f13(a1,x5603),f13(a1,x5604)))),f15(a1,f9(a1,f15(a1,x5601,f13(a1,x5603))),f9(a1,f15(a1,x5602,f13(a1,x5604)))))
% 13.24/13.45 [557]E(f15(a2,f56(f56(f14(a2),x5571),x5572),f15(a2,f56(f56(f14(a2),x5573),x5572),x5574)),f15(a2,f56(f56(f14(a2),f15(a2,x5571,x5573)),x5572),x5574))
% 13.24/13.45 [610]~P50(x6101)+P1(f72(x6101))
% 13.24/13.45 [611]~P58(x6111)+P3(f72(x6111))
% 13.24/13.45 [612]~P57(x6121)+P63(f72(x6121))
% 13.24/13.45 [613]~P54(x6131)+P68(f72(x6131))
% 13.24/13.45 [614]~P58(x6141)+P69(f72(x6141))
% 13.24/13.45 [615]~P58(x6151)+P4(f72(x6151))
% 13.24/13.45 [616]~P54(x6161)+P70(f72(x6161))
% 13.24/13.45 [617]~P57(x6171)+P78(f72(x6171))
% 13.24/13.45 [618]~P53(x6181)+P71(f72(x6181))
% 13.24/13.45 [619]~P58(x6191)+P5(f72(x6191))
% 13.24/13.45 [620]~P50(x6201)+P64(f72(x6201))
% 13.24/13.45 [621]~P50(x6211)+P65(f72(x6211))
% 13.24/13.45 [622]~P50(x6221)+P50(f72(x6221))
% 13.24/13.45 [623]~P50(x6231)+P72(f72(x6231))
% 13.24/13.45 [624]~P54(x6241)+P79(f72(x6241))
% 13.24/13.45 [625]~P57(x6251)+P51(f72(x6251))
% 13.24/13.45 [626]~P57(x6261)+P80(f72(x6261))
% 13.24/13.45 [627]~P52(x6271)+P76(f72(x6271))
% 13.24/13.45 [628]~P54(x6281)+P54(f72(x6281))
% 13.24/13.45 [629]~P50(x6291)+P73(f72(x6291))
% 13.24/13.45 [630]~P50(x6301)+P74(f72(x6301))
% 13.24/13.45 [631]~P50(x6311)+P77(f72(x6311))
% 13.24/13.45 [632]~P50(x6321)+P75(f72(x6321))
% 13.24/13.45 [633]~P50(x6331)+P61(f72(x6331))
% 13.24/13.45 [634]~P50(x6341)+P62(f72(x6341))
% 13.24/13.45 [635]~P50(x6351)+P67(f72(x6351))
% 13.24/13.45 [636]~P50(x6361)+P60(f72(x6361))
% 13.24/13.45 [637]~P50(x6371)+P66(f72(x6371))
% 13.24/13.45 [638]~P28(x6381)+P28(f72(x6381))
% 13.24/13.45 [639]~P16(x6391)+P24(f72(x6391))
% 13.24/13.45 [640]~P16(x6401)+P16(f72(x6401))
% 13.24/13.45 [641]~P50(x6411)+P29(f72(x6411))
% 13.24/13.45 [642]~P57(x6421)+P57(f72(x6421))
% 13.24/13.45 [643]~P57(x6431)+P17(f72(x6431))
% 13.24/13.45 [644]~P23(x6441)+P18(f72(x6441))
% 13.24/13.45 [645]~P22(x6451)+P19(f72(x6451))
% 13.24/13.45 [646]~P22(x6461)+P20(f72(x6461))
% 13.24/13.45 [647]~P58(x6471)+P30(f72(x6471))
% 13.24/13.45 [648]~P23(x6481)+P25(f72(x6481))
% 13.24/13.45 [649]~P23(x6491)+P23(f72(x6491))
% 13.24/13.45 [650]~P50(x6501)+P26(f72(x6501))
% 13.24/13.45 [651]~P50(x6511)+P32(f72(x6511))
% 13.24/13.45 [652]~P50(x6521)+P33(f72(x6521))
% 13.24/13.45 [653]~P50(x6531)+P34(f72(x6531))
% 13.24/13.45 [654]~P50(x6541)+P31(f72(x6541))
% 13.24/13.45 [655]~P50(x6551)+P35(f72(x6551))
% 13.24/13.45 [656]~P50(x6561)+P21(f72(x6561))
% 13.24/13.45 [657]~P58(x6571)+P58(f72(x6571))
% 13.24/13.45 [658]~P50(x6581)+P38(f72(x6581))
% 13.24/13.45 [659]~P52(x6591)+P52(f72(x6591))
% 13.24/13.45 [660]~P53(x6601)+P53(f72(x6601))
% 13.24/13.45 [661]~P54(x6611)+P81(f72(x6611))
% 13.24/13.45 [662]~P50(x6621)+P39(f72(x6621))
% 13.24/13.45 [663]~P50(x6631)+P40(f72(x6631))
% 13.24/13.45 [664]~P50(x6641)+P41(f72(x6641))
% 13.24/13.45 [665]~P50(x6651)+P44(f72(x6651))
% 13.24/13.45 [666]~P16(x6661)+P36(f72(x6661))
% 13.24/13.45 [667]~P16(x6671)+P27(f72(x6671))
% 13.24/13.45 [668]~P50(x6681)+P37(f72(x6681))
% 13.24/13.45 [669]~P58(x6691)+P59(f72(x6691))
% 13.24/13.45 [670]~P22(x6701)+P22(f72(x6701))
% 13.24/13.45 [672]~P69(x6721)+~E(f12(x6721),f5(x6721))
% 13.24/13.45 [673]~E(x6731,f12(a2))+E(f29(a2,x6731),f12(a1))
% 13.24/13.45 [674]E(x6741,f12(a2))+~E(f29(a2,x6741),f12(a1))
% 13.24/13.45 [752]E(x7521,f12(a2))+P10(a2,f12(a2),x7521)
% 13.24/13.45 [793]~P46(x7931)+P10(a1,f12(a1),f50(x7931))
% 13.24/13.45 [800]E(f9(a1,x8001),x8001)+P10(a1,x8001,f12(a1))
% 13.24/13.45 [801]E(f9(a3,x8011),x8011)+P10(a3,x8011,f12(a3))
% 13.24/13.45 [810]~P1(x8101)+P10(x8101,f12(x8101),f5(x8101))
% 13.24/13.45 [811]~P1(x8111)+P9(x8111,f12(x8111),f5(x8111))
% 13.24/13.45 [838]~E(x8381,f12(a3))+P10(a3,f9(a3,x8381),f5(a3))
% 13.24/13.45 [839]~E(x8391,f12(a2))+P9(a1,f29(a2,x8391),f12(a1))
% 13.24/13.45 [882]E(x8821,f12(a2))+~P9(a2,x8821,f12(a2))
% 13.24/13.45 [891]E(f11(x8911),f12(a2))+~P9(a1,x8911,f12(a1))
% 13.24/13.45 [892]E(f27(x8921),f12(a2))+~P9(a1,x8921,f12(a1))
% 13.24/13.45 [938]~P1(x9381)+~P10(x9381,f5(x9381),f12(x9381))
% 13.24/13.45 [939]~P1(x9391)+~P9(x9391,f5(x9391),f12(x9391))
% 13.24/13.45 [941]E(f13(a1,x9411),f9(a1,x9411))+~P10(a1,x9411,f12(a1))
% 13.24/13.45 [942]E(f13(a3,x9421),f9(a3,x9421))+~P10(a3,x9421,f12(a3))
% 13.24/13.45 [984]E(x9841,f12(a2))+~P9(a1,f29(a2,x9841),f12(a1))
% 13.24/13.45 [985]E(x9851,f12(a3))+~P10(a3,f9(a3,x9851),f5(a3))
% 13.24/13.45 [1023]~P9(a3,f5(a3),x10231)+P10(a3,f12(a3),x10231)
% 13.24/13.45 [1024]~P10(a3,f12(a3),x10241)+P9(a3,f5(a3),x10241)
% 13.24/13.45 [1026]P10(a1,f67(x10261),x10261)+~P10(a1,f12(a1),x10261)
% 13.24/13.45 [1053]~P9(a1,x10531,f5(a1))+P9(a2,f11(x10531),f5(a2))
% 13.24/13.45 [1054]~P10(a1,f12(a1),x10541)+P10(a1,f67(x10541),f5(a1))
% 13.24/13.45 [1055]~P10(a1,f12(a1),x10551)+P10(a1,f12(a1),f67(x10551))
% 13.24/13.45 [1056]~P9(a1,f5(a1),x10561)+P9(a2,f5(a2),f27(x10561))
% 13.24/13.45 [1061]~P9(a2,f11(x10611),f5(a2))+P9(a1,x10611,f5(a1))
% 13.24/13.45 [1062]~P9(a2,f5(a2),f27(x10621))+P9(a1,f5(a1),x10621)
% 13.24/13.45 [1067]~P10(a2,f12(a2),x10671)+P10(a1,f12(a1),f29(a2,x10671))
% 13.24/13.45 [1109]P10(a2,f12(a2),x11091)+~P10(a1,f12(a1),f29(a2,x11091))
% 13.24/13.45 [675]~P2(x6751)+E(f31(x6751,f5(a1)),f5(x6751))
% 13.24/13.45 [676]~P2(x6761)+E(f31(x6761,f12(a1)),f12(x6761))
% 13.24/13.45 [677]~P45(x6771)+E(f30(x6771,f5(x6771)),f5(a1))
% 13.24/13.45 [678]~P48(x6781)+E(f30(x6781,f12(x6781)),f12(a1))
% 13.24/13.45 [682]~P24(x6821)+E(f13(x6821,f12(x6821)),f12(x6821))
% 13.24/13.45 [683]~P50(x6831)+E(f9(x6831,f5(x6831)),f5(x6831))
% 13.24/13.45 [684]~P29(x6841)+E(f9(x6841,f12(x6841)),f12(x6841))
% 13.24/13.45 [685]~P56(x6851)+E(f28(x6851,f5(x6851)),f5(x6851))
% 13.24/13.45 [686]~P55(x6861)+E(f28(x6861,f12(x6861)),f12(x6861))
% 13.24/13.45 [687]~P7(x6871)+E(f28(x6871,f12(x6871)),f12(x6871))
% 13.24/13.45 [688]~P45(x6881)+E(f16(x6881,f5(x6881)),f5(x6881))
% 13.24/13.45 [689]~P48(x6891)+E(f16(x6891,f12(x6891)),f12(x6891))
% 13.24/13.45 [690]~P37(x6901)+E(f16(x6901,f12(x6901)),f12(x6901))
% 13.24/13.45 [748]~P50(x7481)+~P12(x7481,f12(f72(x7481)))
% 13.24/13.45 [822]~P3(x8221)+E(f24(x8221,f5(x8221),f14(x8221)),f23(x8221))
% 13.24/13.45 [1083]~P9(a1,f12(a1),x10831)+P10(a1,x10831,f29(a2,f61(x10831)))
% 13.24/13.45 [1084]~P9(a1,f12(a1),x10841)+P9(a1,f29(a2,f27(x10841)),x10841)
% 13.24/13.45 [1159]~P1(x11591)+P10(x11591,f12(x11591),f15(x11591,f5(x11591),f5(x11591)))
% 13.24/13.45 [1288]~P9(a3,f12(a3),x12881)+P10(a3,f12(a3),f15(a3,f5(a3),x12881))
% 13.24/13.45 [742]~P16(x7421)+E(f13(f72(x7421),f12(f72(x7421))),f12(f72(x7421)))
% 13.24/13.45 [893]~P58(x8931)+E(f20(x8931,f5(x8931),f12(f72(x8931))),f5(f72(x8931)))
% 13.24/13.45 [894]~P28(x8941)+E(f20(x8941,f12(x8941),f12(f72(x8941))),f12(f72(x8941)))
% 13.24/13.45 [909]E(x9091,f12(a1))+E(f56(f56(f14(a1),f28(a1,x9091)),x9091),f5(a1))
% 13.24/13.45 [1036]E(x10361,f12(a1))+P10(a1,f12(a1),f56(f56(f14(a1),x10361),x10361))
% 13.24/13.45 [1243]~E(x12431,f12(a1))+~P10(a1,f12(a1),f56(f56(f14(a1),x12431),x12431))
% 13.24/13.45 [1297]~P9(a1,f12(a1),x12971)+E(f11(f15(a1,x12971,f5(a1))),f15(a2,f11(x12971),f5(a2)))
% 13.24/13.45 [1298]~P9(a1,f12(a1),x12981)+E(f27(f15(a1,x12981,f5(a1))),f15(a2,f27(x12981),f5(a2)))
% 13.24/13.45 [1430]~P9(a1,f30(a4,x14301),f30(a4,a83))+P9(a1,f30(a4,f56(f17(a4,a82),x14301)),a74)
% 13.24/13.45 [1431]~P9(a1,f30(a4,x14311),f30(a4,a83))+P9(a1,f30(a4,f56(f17(a4,a82),x14311)),a57)
% 13.24/13.45 [1432]~P9(a1,f30(a4,x14321),f30(a4,a83))+P9(a1,f30(a4,f56(f17(a4,a82),x14321)),a37)
% 13.24/13.45 [1512]~P9(a1,f12(a1),x15121)+P9(a1,f29(a2,f10(a2,f61(x15121),f5(a2))),x15121)
% 13.24/13.45 [1596]~P10(a3,x15961,f12(a3))+P10(a3,f15(a3,f15(a3,f5(a3),x15961),x15961),f12(a3))
% 13.24/13.45 [1709]P10(a3,x17091,f12(a3))+~P10(a3,f15(a3,f15(a3,f5(a3),x17091),x17091),f12(a3))
% 13.24/13.45 [1799]~P10(a1,f30(a4,f56(f17(a4,a80),x17991)),f30(a4,f56(f17(a4,a80),f12(a4))))+P10(a1,f30(a4,f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),x17991)),f5(a1))
% 13.24/13.45 [1802]P10(a1,f30(a4,f56(f17(a4,a80),x18021)),f30(a4,f56(f17(a4,a80),f12(a4))))+~P10(a1,f30(a4,f56(f17(a4,f25(a4,f28(a4,f56(f17(a4,a80),f12(a4))),a80)),x18021)),f5(a1))
% 13.24/13.45 [743]~E(x7431,x7432)+P9(a1,x7431,x7432)
% 13.24/13.45 [746]~E(x7461,x7462)+P9(a2,x7461,x7462)
% 13.24/13.45 [762]~P39(x7621)+P9(x7621,x7622,x7622)
% 13.24/13.45 [763]~P58(x7631)+P13(x7631,x7632,x7632)
% 13.24/13.45 [848]~E(x8481,x8482)+~P10(a1,x8481,x8482)
% 13.24/13.45 [853]~E(x8531,x8532)+~P10(a2,x8531,x8532)
% 13.24/13.45 [854]~E(x8541,x8542)+~P10(a3,x8541,x8542)
% 13.24/13.45 [886]~P10(x8861,x8862,x8862)+~P39(x8861)
% 13.24/13.45 [926]P9(a1,x9262,x9261)+P9(a1,x9261,x9262)
% 13.24/13.45 [927]P9(a2,x9272,x9271)+P9(a2,x9271,x9272)
% 13.24/13.45 [928]P9(a3,x9282,x9281)+P9(a3,x9281,x9282)
% 13.24/13.45 [993]~P10(a1,x9931,x9932)+P9(a1,x9931,x9932)
% 13.24/13.45 [998]~P10(a2,x9981,x9982)+P9(a2,x9981,x9982)
% 13.24/13.45 [999]~P10(a3,x9991,x9992)+P9(a3,x9991,x9992)
% 13.24/13.45 [703]~P39(x7032)+P39(f77(x7031,x7032))
% 13.24/13.45 [704]~P40(x7042)+P40(f77(x7041,x7042))
% 13.24/13.45 [705]~P44(x7052)+P44(f77(x7051,x7052))
% 13.24/13.45 [706]~P42(x7062)+P42(f77(x7061,x7062))
% 13.24/13.45 [707]~P36(x7072)+P36(f77(x7071,x7072))
% 13.24/13.45 [708]~P27(x7082)+P27(f77(x7081,x7082))
% 13.24/13.45 [720]E(x7201,x7202)+~E(f29(a2,x7201),f29(a2,x7202))
% 13.24/13.45 [772]~P24(x7721)+E(f10(x7721,x7722,x7722),f12(x7721))
% 13.24/13.45 [779]~P58(x7791)+P13(x7791,x7792,f12(x7791))
% 13.24/13.45 [780]~P58(x7801)+P13(x7801,f5(x7801),x7802)
% 13.24/13.45 [798]P9(a3,x7982,x7981)+E(f19(x7981,x7982),f12(a3))
% 13.24/13.45 [821]~E(x8212,f13(a1,x8211))+E(f15(a1,x8211,x8212),f12(a1))
% 13.24/13.45 [855]~P29(x8551)+P9(x8551,x8552,f9(x8551,x8552))
% 13.24/13.45 [859]~E(f15(a2,x8592,x8591),x8592)+E(x8591,f12(a2))
% 13.24/13.45 [861]~P46(x8612)+P10(a1,f12(a1),f52(x8611,x8612))
% 13.24/13.45 [862]~P46(x8622)+P10(a1,f12(a1),f54(x8621,x8622))
% 13.24/13.45 [863]~P48(x8631)+P9(a1,f12(a1),f30(x8631,x8632))
% 13.24/13.45 [866]~P10(a2,x8662,x8661)+~E(x8661,f12(a2))
% 13.24/13.45 [875]E(x8751,f12(a2))+~E(f15(a2,x8752,x8751),f12(a2))
% 13.24/13.45 [876]E(x8761,f12(a2))+~E(f15(a2,x8761,x8762),f12(a2))
% 13.24/13.45 [887]~P29(x8871)+P9(x8871,f12(x8871),f9(x8871,x8872))
% 13.24/13.45 [915]E(x9151,f13(a1,x9152))+~E(f15(a1,x9152,x9151),f12(a1))
% 13.24/13.45 [943]~P29(x9431)+P9(x9431,f13(x9431,x9432),f9(x9431,x9432))
% 13.24/13.45 [991]~P48(x9911)+~P10(a1,f30(x9911,x9912),f12(a1))
% 13.24/13.45 [1008]~P9(a2,x10081,x10082)+E(f10(a2,x10081,x10082),f12(a2))
% 13.24/13.45 [1015]P9(a2,x10151,x10152)+~E(f10(a2,x10151,x10152),f12(a2))
% 13.24/13.45 [1021]~P29(x10211)+~P10(x10211,f9(x10211,x10212),f12(x10211))
% 13.24/13.45 [1032]~P9(a1,x10321,x10322)+P9(a2,f11(x10321),f11(x10322))
% 13.24/13.45 [1033]~P9(a1,x10331,x10332)+P9(a2,f27(x10331),f27(x10332))
% 13.24/13.45 [1047]~P9(a3,x10472,x10471)+E(f10(a3,x10471,x10472),f19(x10471,x10472))
% 13.24/13.45 [1079]P9(a1,x10791,x10792)+~P9(a1,f9(a1,x10791),x10792)
% 13.24/13.45 [1087]P9(a2,x10871,f27(x10872))+~P9(a1,f29(a2,x10871),x10872)
% 13.24/13.45 [1088]P9(a2,f11(x10881),x10882)+~P9(a1,x10881,f29(a2,x10882))
% 13.24/13.45 [1115]~P10(a2,x11151,x11152)+P10(a1,f29(a2,x11151),f29(a2,x11152))
% 13.24/13.45 [1116]~P9(a2,x11161,x11162)+P9(a1,f29(a2,x11161),f29(a2,x11162))
% 13.24/13.45 [1158]~P9(a1,f9(a1,x11582),x11581)+P9(a1,f13(a1,x11581),x11582)
% 13.24/13.45 [1183]P10(a2,x11831,x11832)+~P10(a1,f29(a2,x11831),f29(a2,x11832))
% 13.24/13.45 [1184]P9(a2,x11841,x11842)+~P9(a1,f29(a2,x11841),f29(a2,x11842))
% 13.24/13.45 [1267]~P10(a2,x12672,x12671)+P10(a2,f12(a2),f10(a2,x12671,x12672))
% 13.24/13.45 [1268]~P10(a3,x12681,x12682)+P10(a3,f10(a3,x12681,x12682),f12(a3))
% 13.24/13.45 [1269]~P9(a1,x12691,x12692)+P9(a1,f10(a1,x12691,x12692),f12(a1))
% 13.24/13.45 [1320]~P10(a1,f13(a1,x13201),x13202)+P10(a1,f12(a1),f15(a1,x13201,x13202))
% 13.24/13.45 [1321]~P9(a1,f13(a1,x13211),x13212)+P9(a1,f12(a1),f15(a1,x13211,x13212))
% 13.24/13.45 [1322]~P10(a1,x13222,f13(a1,x13221))+P10(a1,f15(a1,x13221,x13222),f12(a1))
% 13.24/13.45 [1323]~P9(a1,x13232,f13(a1,x13231))+P9(a1,f15(a1,x13231,x13232),f12(a1))
% 13.24/13.45 [1356]P10(a2,x13561,x13562)+~P10(a2,f12(a2),f10(a2,x13562,x13561))
% 13.24/13.45 [1357]P10(a3,x13571,x13572)+~P10(a3,f10(a3,x13571,x13572),f12(a3))
% 13.24/13.45 [1358]P9(a1,x13581,x13582)+~P9(a1,f10(a1,x13581,x13582),f12(a1))
% 13.24/13.45 [1386]P10(a1,x13861,f13(a1,x13862))+~P10(a1,f15(a1,x13862,x13861),f12(a1))
% 13.24/13.45 [1387]P9(a1,x13871,f13(a1,x13872))+~P9(a1,f15(a1,x13872,x13871),f12(a1))
% 13.24/13.45 [1388]P10(a1,f13(a1,x13881),x13882)+~P10(a1,f12(a1),f15(a1,x13881,x13882))
% 13.24/13.45 [1389]P9(a1,f13(a1,x13891),x13892)+~P9(a1,f12(a1),f15(a1,x13891,x13892))
% 13.24/13.45 [727]~P24(x7271)+E(f13(x7271,f13(x7271,x7272)),x7272)
% 13.24/13.45 [728]~P42(x7281)+E(f13(x7281,f13(x7281,x7282)),x7282)
% 13.24/13.45 [729]~P55(x7291)+E(f28(x7291,f28(x7291,x7292)),x7292)
% 13.24/13.45 [749]~P45(x7491)+E(f30(x7491,f31(x7491,x7492)),f9(a1,x7492))
% 13.24/13.45 [750]~P48(x7501)+E(f9(a1,f30(x7501,x7502)),f30(x7501,x7502))
% 13.24/13.45 [758]~P48(x7581)+E(f30(x7581,f13(x7581,x7582)),f30(x7581,x7582))
% 13.24/13.45 [759]~P29(x7591)+E(f9(x7591,f13(x7591,x7592)),f9(x7591,x7592))
% 13.24/13.45 [760]~P29(x7601)+E(f9(x7601,f9(x7601,x7602)),f9(x7601,x7602))
% 13.24/13.45 [761]~P50(x7611)+E(f16(x7611,f16(x7611,x7612)),f16(x7611,x7612))
% 13.24/13.45 [765]~P4(x7651)+E(f56(f56(f23(x7651),x7652),f5(a2)),x7652)
% 13.24/13.45 [766]~P58(x7661)+E(f56(f56(f23(x7661),x7662),f5(a2)),x7662)
% 13.24/13.45 [773]~P4(x7731)+E(f56(f56(f14(x7731),x7732),f5(x7731)),x7732)
% 13.24/13.45 [774]~P5(x7741)+E(f56(f56(f14(x7741),x7742),f5(x7741)),x7742)
% 13.24/13.45 [775]~P58(x7751)+E(f56(f56(f14(x7751),x7752),f5(x7751)),x7752)
% 13.24/13.45 [776]~P3(x7761)+E(f56(f56(f23(x7761),x7762),f12(a2)),f5(x7761))
% 13.24/13.45 [777]~P58(x7771)+E(f56(f56(f23(x7771),x7772),f12(a2)),f5(x7771))
% 13.24/13.45 [781]~P25(x7811)+E(f15(x7811,x7812,f12(x7811)),x7812)
% 13.24/13.45 [782]~P23(x7821)+E(f15(x7821,x7822,f12(x7821)),x7822)
% 13.24/13.45 [783]~P58(x7831)+E(f15(x7831,x7832,f12(x7831)),x7832)
% 13.24/13.45 [784]~P24(x7841)+E(f10(x7841,x7842,f12(x7841)),x7842)
% 13.24/13.45 [785]~P25(x7851)+E(f15(x7851,f12(x7851),x7852),x7852)
% 13.24/13.45 [786]~P23(x7861)+E(f15(x7861,f12(x7861),x7862),x7862)
% 13.24/13.45 [787]~P58(x7871)+E(f15(x7871,f12(x7871),x7872),x7872)
% 13.24/13.45 [788]~P58(x7881)+E(f25(x7881,f5(x7881),x7882),x7882)
% 13.24/13.45 [795]~P46(x7951)+E(f56(f56(f14(x7951),x7952),f12(x7951)),f12(x7951))
% 13.24/13.45 [796]~P63(x7961)+E(f56(f56(f14(x7961),x7962),f12(x7961)),f12(x7961))
% 13.24/13.45 [797]~P58(x7971)+E(f56(f56(f14(x7971),x7972),f12(x7971)),f12(x7971))
% 13.24/13.45 [823]~P57(x8231)+E(f25(x8231,f12(x8231),x8232),f12(f72(x8231)))
% 13.24/13.45 [824]~P28(x8241)+E(f18(x8241,f12(x8241),x8242),f12(f72(x8241)))
% 13.24/13.45 [831]~P24(x8311)+E(f10(x8311,f12(x8311),x8312),f13(x8311,x8312))
% 13.24/13.45 [833]~E(x8331,x8332)+E(f15(a1,x8331,f13(a1,x8332)),f12(a1))
% 13.24/13.45 [835]~P45(x8351)+E(f16(x8351,f31(x8351,x8352)),f31(x8351,f16(a1,x8352)))
% 13.24/13.45 [836]~P2(x8361)+E(f31(x8361,f13(a1,x8362)),f13(x8361,f31(x8361,x8362)))
% 13.24/13.45 [845]~P55(x8451)+E(f28(x8451,f13(x8451,x8452)),f13(x8451,f28(x8451,x8452)))
% 13.24/13.45 [846]~P6(x8461)+E(f28(x8461,f9(x8461,x8462)),f9(x8461,f28(x8461,x8462)))
% 13.24/13.45 [847]~P48(x8471)+E(f16(x8471,f13(x8471,x8472)),f13(x8471,f16(x8471,x8472)))
% 13.24/13.45 [879]~P24(x8791)+E(f15(x8791,x8792,f13(x8791,x8792)),f12(x8791))
% 13.24/13.45 [880]~P24(x8801)+E(f15(x8801,f13(x8801,x8802),x8802),f12(x8801))
% 13.24/13.45 [881]~P16(x8811)+E(f15(x8811,f13(x8811,x8812),x8812),f12(x8811))
% 13.24/13.45 [912]~P50(x9121)+E(f56(f56(f14(x9121),x9122),f16(x9121,x9122)),f9(x9121,x9122))
% 13.24/13.45 [979]E(x9791,x9792)+~E(f15(a1,x9791,f13(a1,x9792)),f12(a1))
% 13.24/13.45 [983]E(x9831,x9832)+~E(f56(x9831,f45(x9832,x9831)),f56(x9832,f45(x9832,x9831)))
% 13.24/13.45 [1003]~P50(x10031)+E(f56(f56(f14(x10031),f16(x10031,x10032)),f9(x10031,x10032)),x10032)
% 13.24/13.45 [1025]~P29(x10251)+P9(x10251,f13(x10251,f9(x10251,x10252)),f12(x10251))
% 13.24/13.45 [1064]~P9(a2,x10641,x10642)+E(f15(a2,x10641,f68(x10642,x10641)),x10642)
% 13.24/13.45 [1065]~P9(a2,x10651,x10652)+E(f15(a2,x10651,f69(x10652,x10651)),x10652)
% 13.24/13.45 [1066]~E(x10661,x10662)+P10(a3,x10661,f15(a3,x10662,f5(a3)))
% 13.24/13.45 [1108]~P1(x11081)+P10(x11081,x11082,f15(x11081,x11082,f5(x11081)))
% 13.24/13.45 [1187]P10(a2,x11872,x11871)+E(f15(a2,x11871,f10(a2,x11872,x11871)),x11872)
% 13.24/13.45 [1262]~P9(a2,x12621,x12622)+E(f15(a2,x12621,f10(a2,x12622,x12621)),x12622)
% 13.24/13.45 [1263]~P9(a2,x12632,x12631)+E(f10(a2,x12631,f10(a2,x12631,x12632)),x12632)
% 13.24/13.45 [1264]~P9(a2,x12642,x12641)+E(f15(a2,f10(a2,x12641,x12642),x12642),x12641)
% 13.24/13.45 [1270]~P10(a3,x12701,x12702)+P10(a3,x12701,f15(a3,x12702,f5(a3)))
% 13.24/13.45 [1271]~P9(a3,x12711,x12712)+P10(a3,x12711,f15(a3,x12712,f5(a3)))
% 13.24/13.45 [1272]~P10(a3,x12721,x12722)+P9(a3,x12721,f10(a3,x12722,f5(a3)))
% 13.24/13.45 [1274]~P10(a3,x12741,x12742)+P9(a3,f15(a3,x12741,f5(a3)),x12742)
% 13.24/13.45 [1344]~P9(a2,x13442,x13441)+E(f10(a1,f29(a2,x13441),f29(a2,x13442)),f29(a2,f10(a2,x13441,x13442)))
% 13.24/13.45 [1359]P10(a3,x13591,x13592)+~P9(a3,x13591,f10(a3,x13592,f5(a3)))
% 13.24/13.45 [1360]P9(a3,x13601,x13602)+~P10(a3,x13601,f15(a3,x13602,f5(a3)))
% 13.24/13.45 [1361]P10(a3,x13611,x13612)+~P9(a3,f15(a3,x13611,f5(a3)),x13612)
% 13.24/13.45 [1363]~P9(a2,x13631,x13632)+P10(a1,f29(a2,x13631),f15(a1,f29(a2,x13632),f5(a1)))
% 13.24/13.45 [1364]~P10(a2,x13641,x13642)+P9(a1,f15(a1,f29(a2,x13641),f5(a1)),f29(a2,x13642))
% 13.24/13.45 [1427]P10(a1,x14271,f29(a2,x14272))+~P9(a2,f15(a2,f27(x14271),f5(a2)),x14272)
% 13.24/13.45 [1515]P9(a2,x15151,x15152)+~P10(a1,f29(a2,x15151),f15(a1,f29(a2,x15152),f5(a1)))
% 13.24/13.45 [1516]P10(a2,x15161,x15162)+~P9(a1,f15(a1,f29(a2,x15161),f5(a1)),f29(a2,x15162))
% 13.24/13.45 [736]~E(x7362,f12(a2))+E(f56(f56(f14(a2),x7361),x7362),f12(a2))
% 13.24/13.45 [738]~E(x7381,f12(a2))+E(f56(f56(f14(a2),x7381),x7382),f12(a2))
% 13.24/13.45 [739]~E(x7392,f12(a2))+E(f56(f56(f23(a2),x7391),x7392),f5(a2))
% 13.24/13.45 [754]~P43(x7541)+E(f56(f56(f14(x7541),x7542),x7542),x7542)
% 13.24/13.45 [807]~P4(x8071)+E(f56(f56(f14(x8071),f5(x8071)),x8072),x8072)
% 13.24/13.45 [808]~P5(x8081)+E(f56(f56(f14(x8081),f5(x8081)),x8082),x8082)
% 13.24/13.45 [809]~P58(x8091)+E(f56(f56(f14(x8091),f5(x8091)),x8092),x8092)
% 13.24/13.45 [815]~P46(x8151)+E(f56(f56(f14(x8151),f12(x8151)),x8152),f12(x8151))
% 13.24/13.45 [816]~P63(x8161)+E(f56(f56(f14(x8161),f12(x8161)),x8162),f12(x8161))
% 13.24/13.45 [817]~P58(x8171)+E(f56(f56(f14(x8171),f12(x8171)),x8172),f12(x8171))
% 13.24/13.45 [818]~P4(x8181)+E(f56(f56(f23(x8181),f5(x8181)),x8182),f5(x8181))
% 13.24/13.45 [829]E(x8291,f5(a2))+~E(f56(f56(f14(a2),x8292),x8291),f5(a2))
% 13.24/13.45 [830]E(x8301,f5(a2))+~E(f56(f56(f14(a2),x8301),x8302),f5(a2))
% 13.24/13.45 [842]~P23(x8421)+E(f15(f72(x8421),x8422,f12(f72(x8421))),x8422)
% 13.24/13.45 [843]~P16(x8431)+E(f10(f72(x8431),x8432,f12(f72(x8431))),x8432)
% 13.24/13.45 [844]~P23(x8441)+E(f15(f72(x8441),f12(f72(x8441)),x8442),x8442)
% 13.24/13.45 [870]~P57(x8701)+E(f25(x8701,x8702,f12(f72(x8701))),f12(f72(x8701)))
% 13.24/13.45 [871]~P57(x8711)+E(f26(x8711,f12(f72(x8711)),x8712),f12(f72(x8711)))
% 13.24/13.45 [872]~P57(x8721)+E(f22(x8721,f12(f72(x8721)),x8722),f12(f72(x8721)))
% 13.24/13.45 [873]~P57(x8731)+E(f8(x8731,f12(f72(x8731)),x8732),f12(f72(x8731)))
% 13.24/13.45 [922]~P16(x9221)+E(f10(f72(x9221),f12(f72(x9221)),x9222),f13(f72(x9221),x9222))
% 13.24/13.45 [937]~P57(x9371)+E(f56(f56(f14(f72(x9371)),x9372),f12(f72(x9371))),f12(f72(x9371)))
% 13.24/13.45 [1002]~P28(x10021)+E(f20(x10021,x10022,f12(f72(x10021))),f18(x10021,x10022,f12(a2)))
% 13.24/13.45 [1060]~E(x10602,f12(a2))+P10(a2,f12(a2),f56(f56(f23(a2),x10601),x10602))
% 13.24/13.45 [1077]~P62(x10771)+P9(x10771,f12(x10771),f56(f56(f14(x10771),x10772),x10772))
% 13.24/13.45 [1134]~P50(x11341)+E(f56(f56(f14(x11341),f9(x11341,x11342)),f9(x11341,x11342)),f56(f56(f14(x11341),x11342),x11342))
% 13.24/13.45 [1240]~P10(a2,f12(a2),x12401)+P10(a2,f12(a2),f56(f56(f23(a2),x12401),x12402))
% 13.24/13.45 [1241]~P9(a3,f12(a3),x12411)+P9(a3,f12(a3),f56(f56(f23(a3),x12411),x12412))
% 13.24/13.45 [1261]E(x12611,f12(a3))+P10(a3,f12(a3),f56(f56(f23(a3),f9(a3,x12611)),x12612))
% 13.24/13.45 [1266]~E(x12662,f12(a2))+P10(a3,f12(a3),f56(f56(f23(a3),f9(a3,x12661)),x12662))
% 13.24/13.45 [1295]~P62(x12951)+~P10(x12951,f56(f56(f14(x12951),x12952),x12952),f12(x12951))
% 13.24/13.45 [1330]P10(a2,f12(a2),x13301)+~P10(a2,f12(a2),f56(f56(f14(a2),x13302),x13301))
% 13.24/13.45 [1331]P10(a2,f12(a2),x13311)+~P10(a2,f12(a2),f56(f56(f14(a2),x13311),x13312))
% 13.24/13.45 [1353]~P9(a1,f12(a1),x13531)+E(f11(f15(a1,x13531,f29(a2,x13532))),f15(a2,f11(x13531),x13532))
% 13.24/13.45 [1354]~P9(a1,f12(a1),x13541)+E(f27(f15(a1,x13541,f29(a2,x13542))),f15(a2,f27(x13541),x13542))
% 13.24/13.45 [1401]~P9(a1,f29(a2,x14012),x14011)+E(f11(f10(a1,x14011,f29(a2,x14012))),f10(a2,f11(x14011),x14012))
% 13.24/13.45 [1402]~P9(a1,f29(a2,x14022),x14021)+E(f27(f10(a1,x14021,f29(a2,x14022))),f10(a2,f27(x14021),x14022))
% 13.24/13.45 [1686]~P71(x16861)+E(f56(f56(f14(x16861),f15(x16861,x16862,f5(x16861))),f10(x16861,x16862,f5(x16861))),f10(x16861,f56(f56(f14(x16861),x16862),x16862),f5(x16861)))
% 13.24/13.45 [856]~P58(x8561)+E(f56(f17(x8561,f5(f72(x8561))),x8562),f5(x8561))
% 13.24/13.45 [857]~P57(x8571)+E(f56(f17(x8571,f12(f72(x8571))),x8572),f12(x8571))
% 13.24/13.45 [986]~P57(x9861)+E(f56(f56(f14(f72(x9861)),f12(f72(x9861))),x9862),f12(f72(x9861)))
% 13.24/13.45 [1035]~P53(x10351)+E(f56(f56(f14(x10351),f13(x10351,f5(x10351))),x10352),f13(x10351,x10352))
% 13.24/13.45 [1099]E(f9(a3,x10991),f5(a3))+~E(f9(a3,f56(f56(f14(a3),x10991),x10992)),f5(a3))
% 13.24/13.45 [1118]~E(f29(a2,f27(x11181)),x11181)+E(f27(f56(f56(f23(a1),x11181),x11182)),f56(f56(f23(a2),f27(x11181)),x11182))
% 13.24/13.45 [1469]E(x14691,f12(a1))+~E(f15(a1,f56(f56(f14(a1),x14692),x14692),f56(f56(f14(a1),x14691),x14691)),f12(a1))
% 13.24/13.45 [1470]E(x14701,f12(a1))+~E(f15(a1,f56(f56(f14(a1),x14701),x14701),f56(f56(f14(a1),x14702),x14702)),f12(a1))
% 13.24/13.45 [1472]~P58(x14721)+E(f15(x14721,x14722,x14722),f56(f56(f14(x14721),f15(x14721,f5(x14721),f5(x14721))),x14722))
% 13.24/13.45 [1496]E(x14961,f12(a2))+E(f56(f56(f14(a2),x14962),f56(f56(f23(a2),x14962),f10(a2,x14961,f5(a2)))),f56(f56(f23(a2),x14962),x14961))
% 13.24/13.45 [1755]~P9(a1,f12(a1),x17552)+P9(a1,f15(a1,f56(f56(f14(a1),f29(a2,x17551)),x17552),f5(a1)),f56(f56(f23(a1),f15(a1,x17552,f5(a1))),x17551))
% 13.24/13.45 [1706]E(x17061,f12(a2))+E(f15(a2,x17062,f56(f56(f14(a2),f10(a2,x17061,f5(a2))),x17062)),f56(f56(f14(a2),x17061),x17062))
% 13.24/13.45 [950]~P58(x9501)+E(f15(x9501,x9502,x9503),f15(x9501,x9503,x9502))
% 13.24/13.45 [1005]P9(a2,x10051,x10052)+~E(x10052,f15(a2,x10051,x10053))
% 13.24/13.45 [1068]E(x10681,x10682)+~E(f15(a2,x10683,x10681),f15(a2,x10683,x10682))
% 13.24/13.45 [1069]E(x10691,x10692)+~E(f15(a2,x10691,x10693),f15(a2,x10692,x10693))
% 13.24/13.45 [1249]~P10(a2,x12491,x12493)+P10(a2,x12491,f15(a2,x12492,x12493))
% 13.24/13.45 [1251]~P10(a2,x12511,x12512)+P10(a2,x12511,f15(a2,x12512,x12513))
% 13.24/13.45 [1253]~P9(a2,x12531,x12533)+P9(a2,x12531,f15(a2,x12532,x12533))
% 13.24/13.45 [1255]~P9(a2,x12551,x12552)+P9(a2,x12551,f15(a2,x12552,x12553))
% 13.24/13.45 [1256]~P10(a2,x12561,x12563)+P10(a2,f10(a2,x12561,x12562),x12563)
% 13.24/13.45 [1281]~P10(a1,f12(a1),x12813)+P10(a1,f12(a1),f63(x12811,x12812,x12813))
% 13.24/13.45 [1345]P10(a2,x13451,x13452)+~P10(a2,f15(a2,x13451,x13453),x13452)
% 13.24/13.45 [1348]P9(a2,x13481,x13482)+~P9(a2,f15(a2,x13483,x13481),x13482)
% 13.24/13.45 [1349]P9(a2,x13491,x13492)+~P9(a2,f15(a2,x13491,x13493),x13492)
% 13.24/13.45 [1413]~P10(a2,x14132,x14133)+P10(a2,f15(a2,x14131,x14132),f15(a2,x14131,x14133))
% 13.24/13.45 [1414]~P10(a2,x14141,x14143)+P10(a2,f15(a2,x14141,x14142),f15(a2,x14143,x14142))
% 13.24/13.45 [1415]~P10(a3,x14151,x14153)+P10(a3,f15(a3,x14151,x14152),f15(a3,x14153,x14152))
% 13.24/13.45 [1416]~P9(a1,x14162,x14163)+P9(a1,f15(a1,x14161,x14162),f15(a1,x14161,x14163))
% 13.24/13.45 [1417]~P9(a2,x14172,x14173)+P9(a2,f15(a2,x14171,x14172),f15(a2,x14171,x14173))
% 13.24/13.45 [1418]~P9(a2,x14181,x14183)+P9(a2,f15(a2,x14181,x14182),f15(a2,x14183,x14182))
% 13.24/13.45 [1419]~P9(a2,x14193,x14192)+P9(a2,f10(a2,x14191,x14192),f10(a2,x14191,x14193))
% 13.24/13.45 [1420]~P9(a2,x14201,x14203)+P9(a2,f10(a2,x14201,x14202),f10(a2,x14203,x14202))
% 13.24/13.45 [1421]~P9(a3,x14212,x14213)+P9(a3,f15(a3,x14211,x14212),f15(a3,x14211,x14213))
% 13.24/13.45 [1492]~P10(a2,f15(a2,x14921,x14923),x14922)+P10(a2,x14921,f10(a2,x14922,x14923))
% 13.24/13.45 [1493]~P9(a2,f10(a2,x14931,x14933),x14932)+P9(a2,x14931,f15(a2,x14932,x14933))
% 13.24/13.45 [1494]~P10(a2,x14941,f10(a2,x14943,x14942))+P10(a2,f15(a2,x14941,x14942),x14943)
% 13.24/13.45 [1495]~P9(a2,x14951,f15(a2,x14953,x14952))+P9(a2,f10(a2,x14951,x14952),x14953)
% 13.24/13.45 [1593]P10(a2,x15931,x15932)+~P10(a2,f15(a2,x15933,x15931),f15(a2,x15933,x15932))
% 13.24/13.45 [1594]P9(a2,x15941,x15942)+~P9(a2,f15(a2,x15943,x15941),f15(a2,x15943,x15942))
% 13.24/13.45 [960]P11(x9601,x9602,x9603)+~E(f56(x9603,f55(x9603)),f56(x9603,f59(x9603)))
% 13.24/13.45 [1017]~P24(x10171)+E(f15(x10171,x10172,f13(x10171,x10173)),f10(x10171,x10172,x10173))
% 13.24/13.45 [1018]~P16(x10181)+E(f15(x10181,x10182,f13(x10181,x10183)),f10(x10181,x10182,x10183))
% 13.24/13.45 [1019]~P53(x10191)+E(f15(x10191,x10192,f13(x10191,x10193)),f10(x10191,x10192,x10193))
% 13.24/13.45 [1020]~P24(x10201)+E(f10(x10201,x10202,f13(x10201,x10203)),f15(x10201,x10202,x10203))
% 13.24/13.45 [1072]~P24(x10721)+E(f15(x10721,f10(x10721,x10722,x10723),x10723),x10722)
% 13.24/13.45 [1073]~P24(x10731)+E(f10(x10731,f15(x10731,x10732,x10733),x10733),x10732)
% 13.24/13.45 [1114]~P16(x11141)+E(f13(x11141,f10(x11141,x11142,x11143)),f10(x11141,x11143,x11142))
% 13.24/13.45 [1157]~P24(x11571)+E(f15(x11571,f13(x11571,x11572),f15(x11571,x11572,x11573)),x11573)
% 13.24/13.45 [1189]~P52(x11891)+E(f13(f72(x11891),f25(x11891,x11892,x11893)),f25(x11891,f13(x11891,x11892),x11893))
% 13.24/13.45 [1190]~P16(x11901)+E(f13(f72(x11901),f18(x11901,x11902,x11903)),f18(x11901,f13(x11901,x11902),x11903))
% 13.24/13.45 [1224]~P2(x12241)+E(f15(x12241,f31(x12241,x12242),f31(x12241,x12243)),f31(x12241,f15(a1,x12242,x12243)))
% 13.24/13.45 [1225]~P2(x12251)+E(f10(x12251,f31(x12251,x12252),f31(x12251,x12253)),f31(x12251,f10(a1,x12252,x12253)))
% 13.24/13.45 [1227]~P24(x12271)+E(f15(x12271,f13(x12271,x12272),f13(x12271,x12273)),f13(x12271,f15(x12271,x12273,x12272)))
% 13.24/13.45 [1228]~P16(x12281)+E(f15(x12281,f13(x12281,x12282),f13(x12281,x12283)),f13(x12281,f15(x12281,x12282,x12283)))
% 13.24/13.45 [1229]~P16(x12291)+E(f10(x12291,f13(x12291,x12292),f13(x12291,x12293)),f13(x12291,f10(x12291,x12292,x12293)))
% 13.24/13.45 [1279]~P48(x12791)+E(f30(x12791,f10(x12791,x12792,x12793)),f30(x12791,f10(x12791,x12793,x12792)))
% 13.24/13.45 [1280]~P29(x12801)+E(f9(x12801,f10(x12801,x12802,x12803)),f9(x12801,f10(x12801,x12803,x12802)))
% 13.24/13.45 [1487]~P9(a2,x14872,x14873)+E(f10(a2,f15(a2,x14871,x14872),x14873),f10(a2,x14871,f10(a2,x14873,x14872)))
% 13.24/13.45 [1488]~P9(a2,x14883,x14882)+E(f15(a2,x14881,f10(a2,x14882,x14883)),f10(a2,f15(a2,x14881,x14882),x14883))
% 13.24/13.45 [1490]~P9(a2,x14902,x14901)+E(f15(a2,f10(a2,x14901,x14902),x14903),f10(a2,f15(a2,x14901,x14903),x14902))
% 13.24/13.45 [1558]~P9(a2,x15583,x15582)+P9(a2,x15581,f10(a2,f15(a2,x15582,x15581),x15583))
% 13.24/13.45 [1617]~P48(x16171)+P9(a1,f30(x16171,f15(x16171,x16172,x16173)),f15(a1,f30(x16171,x16172),f30(x16171,x16173)))
% 13.24/13.45 [1618]~P48(x16181)+P9(a1,f30(x16181,f10(x16181,x16182,x16183)),f15(a1,f30(x16181,x16182),f30(x16181,x16183)))
% 13.24/13.45 [1619]~P48(x16191)+P9(a1,f10(a1,f30(x16191,x16192),f30(x16191,x16193)),f30(x16191,f15(x16191,x16192,x16193)))
% 13.24/13.45 [1620]~P48(x16201)+P9(a1,f10(a1,f30(x16201,x16202),f30(x16201,x16203)),f30(x16201,f10(x16201,x16202,x16203)))
% 13.24/13.45 [1631]~P29(x16311)+P9(x16311,f9(x16311,f15(x16311,x16312,x16313)),f15(x16311,f9(x16311,x16312),f9(x16311,x16313)))
% 13.24/13.45 [1632]~P29(x16321)+P9(x16321,f9(x16321,f10(x16321,x16322,x16323)),f15(x16321,f9(x16321,x16322),f9(x16321,x16323)))
% 13.24/13.45 [1633]~P29(x16331)+P9(x16331,f10(x16331,f9(x16331,x16332),f9(x16331,x16333)),f9(x16331,f10(x16331,x16333,x16332)))
% 13.24/13.45 [1634]~P29(x16341)+P9(x16341,f10(x16341,f9(x16341,x16342),f9(x16341,x16343)),f9(x16341,f10(x16341,x16342,x16343)))
% 13.24/13.45 [1786]~P54(x17861)+P13(f72(x17861),f56(f56(f23(f72(x17861)),f20(x17861,f13(x17861,x17862),f20(x17861,f5(x17861),f12(f72(x17861))))),f21(x17861,x17862,x17863)),x17863)
% 13.24/13.45 [906]~E(x9062,f12(a2))+E(f56(f56(f14(a2),x9061),x9062),f56(f56(f14(a2),x9063),x9062))
% 13.24/13.45 [908]~E(x9081,f12(a2))+E(f56(f56(f14(a2),x9081),x9082),f56(f56(f14(a2),x9081),x9083))
% 13.24/13.45 [936]~P58(x9361)+E(f56(f56(f14(x9361),x9362),x9363),f56(f56(f14(x9361),x9363),x9362))
% 13.24/13.45 [1132]~P76(x11321)+E(f56(f56(f14(x11321),f13(x11321,x11322)),x11323),f56(f56(f14(x11321),x11322),f13(x11321,x11323)))
% 13.24/13.45 [1133]~P76(x11331)+E(f56(f56(f14(x11331),f13(x11331,x11332)),f13(x11331,x11333)),f56(f56(f14(x11331),x11332),x11333))
% 13.24/13.45 [1210]~P24(x12101)+E(f15(x12101,x12102,f15(x12101,f13(x12101,x12102),x12103)),x12103)
% 13.24/13.45 [1215]~P52(x12151)+E(f25(x12151,x12152,f13(f72(x12151),x12153)),f13(f72(x12151),f25(x12151,x12152,x12153)))
% 13.24/13.45 [1283]~P16(x12831)+E(f20(x12831,f13(x12831,x12832),f13(f72(x12831),x12833)),f13(f72(x12831),f20(x12831,x12832,x12833)))
% 13.24/13.45 [1316]~P50(x13161)+P9(x13161,f12(x13161),f56(f56(f23(x13161),f9(x13161,x13162)),x13163))
% 13.24/13.45 [1333]P10(a2,f12(a2),x13331)+P9(a2,f56(f56(f14(a2),x13332),x13331),f56(f56(f14(a2),x13333),x13331))
% 13.24/13.45 [1334]P10(a2,f12(a2),x13341)+P9(a2,f56(f56(f14(a2),x13341),x13342),f56(f56(f14(a2),x13341),x13343))
% 13.24/13.45 [1367]~P9(a2,x13672,x13673)+P9(a2,f56(f56(f14(a2),x13671),x13672),f56(f56(f14(a2),x13671),x13673))
% 13.24/13.45 [1369]~P9(a2,x13691,x13693)+P9(a2,f56(f56(f14(a2),x13691),x13692),f56(f56(f14(a2),x13693),x13692))
% 13.24/13.45 [1406]~P29(x14061)+E(f9(x14061,f15(x14061,f9(x14061,x14062),f9(x14061,x14063))),f15(x14061,f9(x14061,x14062),f9(x14061,x14063)))
% 13.24/13.45 [1521]P10(a2,x15211,x15212)+~P10(a2,f56(f56(f14(a2),x15213),x15211),f56(f56(f14(a2),x15213),x15212))
% 13.24/13.45 [1522]P10(a2,x15221,x15222)+~P10(a2,f56(f56(f14(a2),x15221),x15223),f56(f56(f14(a2),x15222),x15223))
% 13.24/13.45 [1525]P10(a2,f12(a2),x15251)+~P10(a2,f56(f56(f14(a2),x15252),x15251),f56(f56(f14(a2),x15253),x15251))
% 13.24/13.45 [1526]P10(a2,f12(a2),x15261)+~P10(a2,f56(f56(f14(a2),x15261),x15262),f56(f56(f14(a2),x15261),x15263))
% 13.24/13.45 [1693]~P57(x16931)+E(f20(x16931,f56(f17(x16931,x16932),x16933),f26(x16931,x16932,x16933)),f15(f72(x16931),x16932,f25(x16931,x16933,f26(x16931,x16932,x16933))))
% 13.24/13.45 [1721]~P48(x17211)+P9(a1,f9(a1,f10(a1,f30(x17211,x17212),f30(x17211,x17213))),f30(x17211,f10(x17211,x17212,x17213)))
% 13.24/13.45 [1722]~P29(x17221)+P9(x17221,f9(x17221,f10(x17221,f9(x17221,x17222),f9(x17221,x17223))),f9(x17221,f10(x17221,x17222,x17223)))
% 13.24/13.45 [1165]~P76(x11651)+E(f56(f56(f14(x11651),x11652),f13(x11651,x11653)),f13(x11651,f56(f56(f14(x11651),x11652),x11653)))
% 13.24/13.45 [1167]~P46(x11671)+E(f56(f56(f14(x11671),x11672),f13(x11671,x11673)),f13(x11671,f56(f56(f14(x11671),x11672),x11673)))
% 13.24/13.45 [1188]~P43(x11881)+E(f56(f56(f14(x11881),x11882),f56(f56(f14(x11881),x11882),x11883)),f56(f56(f14(x11881),x11882),x11883))
% 13.24/13.45 [1203]~P52(x12031)+E(f56(f17(x12031,f13(f72(x12031),x12032)),x12033),f13(x12031,f56(f17(x12031,x12032),x12033)))
% 13.24/13.45 [1204]~P2(x12041)+E(f31(x12041,f56(f56(f23(a1),x12042),x12043)),f56(f56(f23(x12041),f31(x12041,x12042)),x12043))
% 13.24/13.45 [1211]~P49(x12111)+E(f30(x12111,f56(f56(f23(x12111),x12112),x12113)),f56(f56(f23(a1),f30(x12111,x12112)),x12113))
% 13.24/13.45 [1216]~P76(x12161)+E(f56(f56(f14(x12161),f13(x12161,x12162)),x12163),f13(x12161,f56(f56(f14(x12161),x12162),x12163)))
% 13.24/13.45 [1217]~P50(x12171)+E(f56(f56(f23(x12171),f9(x12171,x12172)),x12173),f9(x12171,f56(f56(f23(x12171),x12172),x12173)))
% 13.24/13.45 [1218]~P55(x12181)+E(f56(f56(f23(x12181),f28(x12181,x12182)),x12183),f28(x12181,f56(f56(f23(x12181),x12182),x12183)))
% 13.24/13.45 [1220]~P46(x12201)+E(f56(f56(f14(x12201),f13(x12201,x12202)),x12203),f13(x12201,f56(f56(f14(x12201),x12202),x12203)))
% 13.24/13.45 [1260]~P2(x12601)+E(f56(f56(f14(x12601),f31(x12601,x12602)),f31(x12601,x12603)),f31(x12601,f56(f56(f14(a1),x12602),x12603)))
% 13.24/13.45 [1275]~P49(x12751)+E(f56(f56(f14(a1),f30(x12751,x12752)),f30(x12751,x12753)),f30(x12751,f56(f56(f14(x12751),x12752),x12753)))
% 13.24/13.45 [1284]~P50(x12841)+E(f56(f56(f14(x12841),f9(x12841,x12842)),f9(x12841,x12843)),f9(x12841,f56(f56(f14(x12841),x12842),x12843)))
% 13.24/13.45 [1285]~P7(x12851)+E(f56(f56(f14(x12851),f28(x12851,x12852)),f28(x12851,x12853)),f28(x12851,f56(f56(f14(x12851),x12852),x12853)))
% 13.24/13.45 [1286]~P49(x12861)+E(f56(f56(f14(x12861),f16(x12861,x12862)),f16(x12861,x12863)),f16(x12861,f56(f56(f14(x12861),x12862),x12863)))
% 13.24/13.45 [1287]~P50(x12871)+E(f56(f56(f14(x12871),f16(x12871,x12872)),f16(x12871,x12873)),f16(x12871,f56(f56(f14(x12871),x12872),x12873)))
% 13.24/13.45 [1412]~P50(x14121)+E(f9(x14121,f56(f56(f23(x14121),f13(x14121,x14122)),x14123)),f9(x14121,f56(f56(f23(x14121),x14122),x14123)))
% 13.24/13.45 [1584]~P58(x15841)+E(f15(x15841,x15842,f56(f56(f14(x15841),x15843),x15842)),f56(f56(f14(x15841),f15(x15841,x15843,f5(x15841))),x15842))
% 13.24/13.45 [1585]~P58(x15851)+E(f15(x15851,f56(f56(f14(x15851),x15852),x15853),x15853),f56(f56(f14(x15851),f15(x15851,x15852,f5(x15851))),x15853))
% 13.24/13.45 [1607]~P45(x16071)+P9(a1,f30(x16071,f56(f56(f23(x16071),x16072),x16073)),f56(f56(f23(a1),f30(x16071,x16072)),x16073))
% 13.24/13.45 [1655]~P46(x16551)+P9(a1,f30(x16551,f56(f56(f14(x16551),x16552),x16553)),f56(f56(f14(a1),f30(x16551,x16553)),f54(x16552,x16551)))
% 13.24/13.45 [1656]~P46(x16561)+P9(a1,f30(x16561,f56(f56(f14(x16561),x16562),x16563)),f56(f56(f14(a1),f30(x16561,x16562)),f30(x16561,x16563)))
% 13.24/13.45 [1657]~P46(x16571)+P9(a1,f30(x16571,f56(f56(f14(x16571),x16572),x16573)),f56(f56(f14(a1),f30(x16571,x16572)),f52(x16573,x16571)))
% 13.24/13.45 [1687]~P62(x16871)+P9(x16871,f12(x16871),f15(x16871,f56(f56(f14(x16871),x16872),x16872),f56(f56(f14(x16871),x16873),x16873)))
% 13.24/13.45 [1726]~P71(x17261)+E(f56(f56(f14(x17261),f56(f56(f23(x17261),f13(x17261,f5(x17261))),x17262)),f56(f56(f23(x17261),x17263),x17262)),f56(f56(f23(x17261),f13(x17261,x17263)),x17262))
% 13.24/13.45 [1736]~P62(x17361)+~P10(x17361,f15(x17361,f56(f56(f14(x17361),x17362),x17362),f56(f56(f14(x17361),x17363),x17363)),f12(x17361))
% 13.24/13.45 [1765]~P46(x17651)+P9(a1,f30(x17651,f56(f56(f14(x17651),x17652),x17653)),f56(f56(f14(a1),f56(f56(f14(a1),f30(x17651,x17652)),f30(x17651,x17653))),f50(x17651)))
% 13.24/13.45 [1795]~P53(x17951)+E(f15(f72(x17951),f56(f56(f14(f72(x17951)),f20(x17951,f13(x17951,x17952),f20(x17951,f5(x17951),f12(f72(x17951))))),f26(x17951,x17953,x17952)),f20(x17951,f56(f17(x17951,x17953),x17952),f12(f72(x17951)))),x17953)
% 13.24/13.45 [1520]~P4(x15201)+E(f56(f56(f14(x15201),f56(f56(f23(x15201),x15202),x15203)),x15202),f56(f56(f14(x15201),x15202),f56(f56(f23(x15201),x15202),x15203)))
% 13.24/13.45 [1800]~P10(a3,f12(a3),x18003)+P10(a3,x18001,f15(a3,x18002,f56(f56(f14(a3),f15(a3,f9(a3,f10(a3,x18002,x18001)),f5(a3))),x18003)))
% 13.24/13.45 [1801]~P10(a3,f12(a3),x18013)+P10(a3,f10(a3,x18011,f56(f56(f14(a3),f15(a3,f9(a3,f10(a3,x18011,x18012)),f5(a3))),x18013)),x18012)
% 13.24/13.45 [1390]~P58(x13901)+E(f15(x13901,x13902,f15(x13901,x13903,x13904)),f15(x13901,x13903,f15(x13901,x13902,x13904)))
% 13.24/13.45 [1392]~P18(x13921)+E(f15(x13921,f15(x13921,x13922,x13923),x13924),f15(x13921,x13922,f15(x13921,x13923,x13924)))
% 13.24/13.45 [1393]~P58(x13931)+E(f15(x13931,f15(x13931,x13932,x13933),x13934),f15(x13931,x13932,f15(x13931,x13933,x13934)))
% 13.24/13.45 [1394]~P58(x13941)+E(f15(x13941,f15(x13941,x13942,x13943),x13944),f15(x13941,f15(x13941,x13942,x13944),x13943))
% 13.24/13.45 [1511]~P57(x15111)+E(f26(x15111,f20(x15111,x15112,x15113),x15114),f20(x15111,f56(f17(x15111,x15113),x15114),f26(x15111,x15113,x15114)))
% 13.24/13.45 [1540]~P57(x15401)+E(f20(x15401,f56(f56(f14(x15401),x15402),x15403),f25(x15401,x15402,x15404)),f25(x15401,x15402,f20(x15401,x15403,x15404)))
% 13.24/13.45 [1542]~P57(x15421)+E(f15(f72(x15421),f25(x15421,x15422,x15423),f25(x15421,x15424,x15423)),f25(x15421,f15(x15421,x15422,x15424),x15423))
% 13.24/13.45 [1543]~P52(x15431)+E(f10(f72(x15431),f25(x15431,x15432,x15433),f25(x15431,x15434,x15433)),f25(x15431,f10(x15431,x15432,x15434),x15433))
% 13.24/13.45 [1544]~P23(x15441)+E(f15(f72(x15441),f18(x15441,x15442,x15443),f18(x15441,x15444,x15443)),f18(x15441,f15(x15441,x15442,x15444),x15443))
% 13.24/13.45 [1545]~P16(x15451)+E(f10(f72(x15451),f18(x15451,x15452,x15453),f18(x15451,x15454,x15453)),f18(x15451,f10(x15451,x15452,x15454),x15453))
% 13.24/13.45 [1006]~P36(x10062)+E(f56(f13(f77(x10061,x10062),x10063),x10064),f13(x10062,f56(x10063,x10064)))
% 13.24/13.45 [1473]~P57(x14731)+E(f56(f17(x14731,x14732),f56(f17(x14731,x14733),x14734)),f56(f17(x14731,f22(x14731,x14732,x14733)),x14734))
% 13.24/13.45 [1483]~P57(x14831)+E(f56(f56(f14(x14831),x14832),f56(f17(x14831,x14833),x14834)),f56(f17(x14831,f25(x14831,x14832,x14833)),x14834))
% 13.24/13.45 [1587]~P57(x15871)+E(f15(f72(x15871),f25(x15871,x15872,x15873),f25(x15871,x15872,x15874)),f25(x15871,x15872,f15(f72(x15871),x15873,x15874)))
% 13.24/13.45 [1588]~P52(x15881)+E(f10(f72(x15881),f25(x15881,x15882,x15883),f25(x15881,x15882,x15884)),f25(x15881,x15882,f10(f72(x15881),x15883,x15884)))
% 13.24/13.45 [1720]~P57(x17201)+E(f15(f72(x17201),f20(x17201,x17202,f12(f72(x17201))),f56(f56(f14(f72(x17201)),x17203),f22(x17201,x17204,x17203))),f22(x17201,f20(x17201,x17202,x17204),x17203))
% 13.24/13.45 [1733]~P57(x17331)+E(f15(f72(x17331),f25(x17331,x17332,f8(x17331,x17333,x17332)),f20(x17331,x17334,f8(x17331,x17333,x17332))),f8(x17331,f20(x17331,x17334,x17333),x17332))
% 13.24/13.45 [1365]~P58(x13651)+E(f56(f56(f14(x13651),x13652),f56(f56(f14(x13651),x13653),x13654)),f56(f56(f14(x13651),x13653),f56(f56(f14(x13651),x13652),x13654)))
% 13.24/13.45 [1378]~P57(x13781)+E(f25(x13781,f56(f56(f14(x13781),x13782),x13783),x13784),f25(x13781,x13782,f25(x13781,x13783,x13784)))
% 13.24/13.45 [1379]~P57(x13791)+E(f18(x13791,f56(f56(f14(x13791),x13792),x13793),x13794),f25(x13791,x13792,f18(x13791,x13793,x13794)))
% 13.24/13.45 [1514]~P58(x15141)+E(f56(f56(f14(x15141),x15142),f56(f56(f23(x15141),x15143),x15144)),f56(f17(x15141,f18(x15141,x15142,x15144)),x15143))
% 13.24/13.45 [1528]~P46(x15281)+E(f15(x15281,f56(f56(f14(x15281),x15282),x15283),f56(f56(f14(x15281),x15282),x15284)),f56(f56(f14(x15281),x15282),f15(x15281,x15283,x15284)))
% 13.24/13.45 [1529]~P58(x15291)+E(f15(x15291,f56(f56(f14(x15291),x15292),x15293),f56(f56(f14(x15291),x15292),x15294)),f56(f56(f14(x15291),x15292),f15(x15291,x15293,x15294)))
% 13.24/13.45 [1531]~P46(x15311)+E(f10(x15311,f56(f56(f14(x15311),x15312),x15313),f56(f56(f14(x15311),x15312),x15314)),f56(f56(f14(x15311),x15312),f10(x15311,x15313,x15314)))
% 13.24/13.45 [1614]~P57(x16141)+E(f15(x16141,f56(f17(x16141,x16142),x16143),f56(f17(x16141,x16144),x16143)),f56(f17(x16141,f15(f72(x16141),x16142,x16144)),x16143))
% 13.24/13.45 [1615]~P52(x16151)+E(f10(x16151,f56(f17(x16151,x16152),x16153),f56(f17(x16151,x16154),x16153)),f56(f17(x16151,f10(f72(x16151),x16152,x16154)),x16153))
% 13.24/13.45 [1638]~P4(x16381)+E(f56(f56(f14(x16381),f56(f56(f23(x16381),x16382),x16383)),f56(f56(f23(x16381),x16382),x16384)),f56(f56(f23(x16381),x16382),f15(a2,x16383,x16384)))
% 13.24/13.45 [1639]~P58(x16391)+E(f56(f56(f14(x16391),f56(f56(f23(x16391),x16392),x16393)),f56(f56(f23(x16391),x16392),x16394)),f56(f56(f23(x16391),x16392),f15(a2,x16393,x16394)))
% 13.24/13.45 [1649]~P46(x16491)+E(f15(x16491,f56(f56(f14(x16491),x16492),x16493),f56(f56(f14(x16491),x16494),x16493)),f56(f56(f14(x16491),f15(x16491,x16492,x16494)),x16493))
% 13.24/13.45 [1650]~P51(x16501)+E(f15(x16501,f56(f56(f14(x16501),x16502),x16503),f56(f56(f14(x16501),x16504),x16503)),f56(f56(f14(x16501),f15(x16501,x16502,x16504)),x16503))
% 13.24/13.45 [1653]~P46(x16531)+E(f10(x16531,f56(f56(f14(x16531),x16532),x16533),f56(f56(f14(x16531),x16534),x16533)),f56(f56(f14(x16531),f10(x16531,x16532,x16534)),x16533))
% 13.24/13.45 [1654]~P58(x16541)+E(f15(x16541,f56(f56(f14(x16541),x16542),x16543),f56(f56(f14(x16541),x16544),x16543)),f56(f56(f14(x16541),f15(x16541,x16542,x16544)),x16543))
% 13.24/13.45 [1685]~P57(x16851)+E(f15(x16851,x16852,f56(f56(f14(x16851),x16853),f56(f17(x16851,x16854),x16853))),f56(f17(x16851,f20(x16851,x16852,x16854)),x16853))
% 13.24/13.45 [1484]~P57(x14841)+E(f25(x14841,x14842,f56(f56(f14(f72(x14841)),x14843),x14844)),f56(f56(f14(f72(x14841)),x14843),f25(x14841,x14842,x14844)))
% 13.24/13.45 [1509]~P58(x15091)+E(f56(f56(f23(x15091),f56(f56(f23(x15091),x15092),x15093)),x15094),f56(f56(f23(x15091),x15092),f56(f56(f14(a2),x15093),x15094)))
% 13.24/13.45 [1510]~P4(x15101)+E(f56(f56(f23(x15101),f56(f56(f23(x15101),x15102),x15103)),x15104),f56(f56(f23(x15101),x15102),f56(f56(f14(a2),x15103),x15104)))
% 13.24/13.45 [1518]~P17(x15181)+E(f56(f56(f14(x15181),f56(f56(f14(x15181),x15182),x15183)),x15184),f56(f56(f14(x15181),x15182),f56(f56(f14(x15181),x15183),x15184)))
% 13.24/13.45 [1519]~P58(x15191)+E(f56(f56(f14(x15191),f56(f56(f14(x15191),x15192),x15193)),x15194),f56(f56(f14(x15191),x15192),f56(f56(f14(x15191),x15193),x15194)))
% 13.24/13.45 [1616]~P57(x16161)+E(f25(x16161,x16162,f56(f56(f14(f72(x16161)),x16163),x16164)),f56(f56(f14(f72(x16161)),f25(x16161,x16162,x16163)),x16164))
% 13.24/13.45 [1637]~P58(x16371)+E(f56(f56(f14(x16371),f56(f56(f14(x16371),x16372),x16373)),x16374),f56(f56(f14(x16371),f56(f56(f14(x16371),x16372),x16374)),x16373))
% 13.24/13.45 [1691]~P5(x16911)+E(f56(f56(f14(x16911),f56(f56(f23(x16911),x16912),x16913)),f56(f56(f23(x16911),x16914),x16913)),f56(f56(f23(x16911),f56(f56(f14(x16911),x16912),x16914)),x16913))
% 13.24/13.45 [1692]~P58(x16921)+E(f56(f56(f14(x16921),f56(f56(f23(x16921),x16922),x16923)),f56(f56(f23(x16921),x16924),x16923)),f56(f56(f23(x16921),f56(f56(f14(x16921),x16922),x16924)),x16923))
% 13.24/13.45 [1717]~P57(x17171)+E(f15(f72(x17171),f56(f56(f14(f72(x17171)),x17172),x17173),f56(f56(f14(f72(x17171)),x17174),x17173)),f56(f56(f14(f72(x17171)),f15(f72(x17171),x17172,x17174)),x17173))
% 13.24/13.45 [1666]~P58(x16661)+E(f56(f17(x16661,f56(f56(f23(f72(x16661)),x16662),x16663)),x16664),f56(f56(f23(x16661),f56(f17(x16661,x16662),x16664)),x16663))
% 13.24/13.45 [1707]~P57(x17071)+E(f56(f56(f14(x17071),f56(f17(x17071,x17072),x17073)),f56(f17(x17071,x17074),x17073)),f56(f17(x17071,f56(f56(f14(f72(x17071)),x17072),x17074)),x17073))
% 13.24/13.45 [1727]~P57(x17271)+E(f15(f72(x17271),f25(x17271,x17272,x17273),f20(x17271,f12(x17271),f56(f56(f14(f72(x17271)),x17273),x17274))),f56(f56(f14(f72(x17271)),x17273),f20(x17271,x17272,x17274)))
% 13.24/13.45 [1734]~P57(x17341)+E(f15(f72(x17341),f25(x17341,x17342,x17343),f20(x17341,f12(x17341),f56(f56(f14(f72(x17341)),x17344),x17343))),f56(f56(f14(f72(x17341)),f20(x17341,x17342,x17344)),x17343))
% 13.24/13.45 [1770]~P53(x17701)+E(f56(f17(x17701,f56(f56(f14(f72(x17701)),f18(x17701,f5(x17701),x17702)),x17703)),x17704),f56(f56(f14(x17701),f56(f56(f23(x17701),x17704),x17702)),f56(f17(x17701,x17703),x17704)))
% 13.24/13.45 [946]~P11(x9464,x9465,x9461)+E(f56(x9461,x9462),f56(x9461,x9463))
% 13.24/13.45 [1663]~P58(x16631)+E(f15(x16631,f15(x16631,x16632,x16633),f15(x16631,x16634,x16635)),f15(x16631,f15(x16631,x16632,x16634),f15(x16631,x16633,x16635)))
% 13.24/13.45 [1664]~P16(x16641)+E(f15(x16641,f10(x16641,x16642,x16643),f10(x16641,x16644,x16645)),f10(x16641,f15(x16641,x16642,x16644),f15(x16641,x16643,x16645)))
% 13.24/13.45 [1711]~P57(x17111)+E(f56(f56(f14(f72(x17111)),f18(x17111,x17112,x17113)),f18(x17111,x17114,x17115)),f18(x17111,f56(f56(f14(x17111),x17112),x17114),f15(a2,x17113,x17115)))
% 13.24/13.45 [1329]~P27(x13292)+E(f56(f10(f77(x13291,x13292),x13293,x13294),x13295),f10(x13292,f56(x13293,x13295),f56(x13294,x13295)))
% 13.24/13.45 [1667]~P23(x16671)+E(f20(x16671,f15(x16671,x16672,x16673),f15(f72(x16671),x16674,x16675)),f15(f72(x16671),f20(x16671,x16672,x16674),f20(x16671,x16673,x16675)))
% 13.24/13.45 [1668]~P16(x16681)+E(f20(x16681,f10(x16681,x16682,x16683),f10(f72(x16681),x16684,x16685)),f10(f72(x16681),f20(x16681,x16682,x16684),f20(x16681,x16683,x16685)))
% 13.24/13.45 [1775]~P48(x17751)+P9(a1,f30(x17751,f10(x17751,f15(x17751,x17752,x17753),f15(x17751,x17754,x17755))),f15(a1,f30(x17751,f10(x17751,x17752,x17754)),f30(x17751,f10(x17751,x17753,x17755))))
% 13.24/13.45 [1777]~P29(x17771)+P9(x17771,f9(x17771,f10(x17771,f15(x17771,x17772,x17773),f15(x17771,x17774,x17775))),f15(x17771,f9(x17771,f10(x17771,x17772,x17774)),f9(x17771,f10(x17771,x17773,x17775))))
% 13.24/13.45 [1719]~P58(x17191)+E(f56(f56(f14(x17191),f56(f56(f14(x17191),x17192),x17193)),f56(f56(f14(x17191),x17194),x17195)),f56(f56(f14(x17191),f56(f56(f14(x17191),x17192),x17194)),f56(f56(f14(x17191),x17193),x17195)))
% 13.24/13.45 [1756]~P76(x17561)+E(f15(x17561,f56(f56(f14(x17561),x17562),f10(x17561,x17563,x17564)),f56(f56(f14(x17561),f10(x17561,x17562,x17565)),x17564)),f10(x17561,f56(f56(f14(x17561),x17562),x17563),f56(f56(f14(x17561),x17565),x17564)))
% 13.24/13.45 [1796]~P46(x17961)+E(f15(x17961,f15(x17961,f56(f56(f14(x17961),f10(x17961,x17962,x17963)),f10(x17961,x17964,x17965)),f56(f56(f14(x17961),f10(x17961,x17962,x17963)),x17965)),f56(f56(f14(x17961),x17963),f10(x17961,x17964,x17965))),f10(x17961,f56(f56(f14(x17961),x17962),x17964),f56(f56(f14(x17961),x17963),x17965)))
% 13.24/13.45 [1748]~P80(x17481)+E(f15(x17481,f56(f56(f14(x17481),x17482),x17483),f15(x17481,f56(f56(f14(x17481),x17484),x17483),x17485)),f15(x17481,f56(f56(f14(x17481),f15(x17481,x17482,x17484)),x17483),x17485))
% 13.24/13.45 [1771]~P9(a2,x17711,x17714)+E(f10(a2,f15(a2,f56(f56(f14(a2),x17711),x17712),x17713),f15(a2,f56(f56(f14(a2),x17714),x17712),x17715)),f10(a2,x17713,f15(a2,f56(f56(f14(a2),f10(a2,x17714,x17711)),x17712),x17715)))
% 13.24/13.45 [1772]~P9(a2,x17724,x17721)+E(f10(a2,f15(a2,f56(f56(f14(a2),x17721),x17722),x17723),f15(a2,f56(f56(f14(a2),x17724),x17722),x17725)),f10(a2,f15(a2,f56(f56(f14(a2),f10(a2,x17721,x17724)),x17722),x17723),x17725))
% 13.24/13.45 [1508]~P10(a2,f12(a2),a78)+~P9(a1,f12(a1),a81)+P10(a1,f56(f56(f23(a1),a81),a78),f56(f56(f23(a1),f5(a1)),a78))
% 13.24/13.45 [819]~P2(x8191)+~P48(x8191)+P10(a1,f12(a1),f44(x8191))
% 13.24/13.45 [820]~P2(x8201)+~P48(x8201)+P9(a1,f12(a1),f51(x8201))
% 13.24/13.45 [1314]~P10(a2,f6(a4,x13141),f6(a4,a73))+P11(a4,a4,f17(a4,x13141))+E(f56(f17(a4,x13141),f35(x13141)),f12(a4))
% 13.24/13.45 [933]E(x9331,x9332)+P10(a2,x9332,x9331)+P10(a2,x9331,x9332)
% 13.24/13.45 [934]E(x9341,x9342)+P10(a3,x9342,x9341)+P10(a3,x9341,x9342)
% 13.24/13.45 [1010]E(x10101,x10102)+P10(a1,x10101,x10102)+~P9(a1,x10101,x10102)
% 13.24/13.45 [1013]E(x10131,x10132)+P10(a2,x10131,x10132)+~P9(a2,x10131,x10132)
% 13.24/13.45 [1014]E(x10141,x10142)+P10(a3,x10141,x10142)+~P9(a3,x10141,x10142)
% 13.24/13.45 [1074]E(x10741,x10742)+~P9(a1,x10742,x10741)+~P9(a1,x10741,x10742)
% 13.24/13.45 [1075]E(x10751,x10752)+~P9(a2,x10752,x10751)+~P9(a2,x10751,x10752)
% 13.24/13.45 [1076]E(x10761,x10762)+~P9(a3,x10762,x10761)+~P9(a3,x10761,x10762)
% 13.24/13.45 [680]~P26(x6801)+~E(x6802,f12(x6801))+E(f13(x6801,x6802),x6802)
% 13.24/13.45 [681]~P2(x6811)+E(f31(x6811,x6812),f12(x6811))+~E(x6812,f12(a1))
% 13.24/13.45 [691]~P48(x6911)+~E(x6912,f12(x6911))+E(f30(x6911,x6912),f12(a1))
% 13.24/13.45 [692]~P24(x6921)+~E(f12(x6921),x6922)+E(f13(x6921,x6922),f12(x6921))
% 13.24/13.45 [693]~P24(x6931)+~E(x6932,f12(x6931))+E(f13(x6931,x6932),f12(x6931))
% 13.24/13.45 [694]~P29(x6941)+~E(x6942,f12(x6941))+E(f9(x6941,x6942),f12(x6941))
% 13.24/13.45 [695]~P7(x6951)+~E(x6952,f5(x6951))+E(f28(x6951,x6952),f5(x6951))
% 13.24/13.45 [696]~P55(x6961)+~E(x6962,f12(x6961))+E(f28(x6961,x6962),f12(x6961))
% 13.24/13.45 [697]~P48(x6971)+~E(x6972,f12(x6971))+E(f16(x6971,x6972),f12(x6971))
% 13.24/13.45 [698]~P50(x6981)+~E(x6982,f12(x6981))+E(f16(x6981,x6982),f12(x6981))
% 13.24/13.45 [699]~P37(x6991)+~E(x6992,f12(x6991))+E(f16(x6991,x6992),f12(x6991))
% 13.24/13.45 [702]~P26(x7022)+~E(f13(x7022,x7021),x7021)+E(x7021,f12(x7022))
% 13.24/13.45 [709]~P48(x7092)+E(x7091,f12(x7092))+~E(f30(x7092,x7091),f12(a1))
% 13.24/13.45 [710]~P2(x7102)+~E(f31(x7102,x7101),f12(x7102))+E(x7101,f12(a1))
% 13.24/13.45 [711]~P7(x7112)+~E(f28(x7112,x7111),f5(x7112))+E(x7111,f5(x7112))
% 13.24/13.45 [712]~P24(x7122)+~E(f13(x7122,x7121),f12(x7122))+E(x7121,f12(x7122))
% 13.24/13.45 [713]~P29(x7132)+~E(f9(x7132,x7131),f12(x7132))+E(x7131,f12(x7132))
% 13.24/13.45 [714]~P55(x7142)+~E(f28(x7142,x7141),f12(x7142))+E(x7141,f12(x7142))
% 13.24/13.45 [716]~P56(x7162)+~E(f28(x7162,x7161),f12(x7162))+E(x7161,f12(x7162))
% 13.24/13.45 [717]~P48(x7172)+~E(f16(x7172,x7171),f12(x7172))+E(x7171,f12(x7172))
% 13.24/13.45 [718]~P50(x7182)+~E(f16(x7182,x7181),f12(x7182))+E(x7181,f12(x7182))
% 13.24/13.45 [719]~P24(x7191)+~E(f13(x7191,x7192),f12(x7191))+E(f12(x7191),x7192)
% 13.24/13.45 [778]~E(x7782,f12(a2))+~E(x7781,f12(a2))+E(f15(a2,x7781,x7782),f12(a2))
% 13.24/13.45 [813]~P26(x8131)+~E(x8132,f12(x8131))+E(f15(x8131,x8132,x8132),f12(x8131))
% 13.24/13.45 [834]~P21(x8341)+P10(x8341,x8342,f12(x8341))+E(f9(x8341,x8342),x8342)
% 13.24/13.45 [889]~P48(x8892)+E(x8891,f12(x8892))+P10(a1,f12(a1),f30(x8892,x8891))
% 13.24/13.45 [895]~P50(x8951)+P10(x8951,f12(x8951),x8952)+~E(f16(x8951,x8952),f5(x8951))
% 13.24/13.45 [905]~P48(x9051)+~E(x9052,f12(x9051))+P9(a1,f30(x9051,x9052),f12(a1))
% 13.24/13.45 [913]~P29(x9132)+P10(x9132,f12(x9132),f9(x9132,x9131))+E(x9131,f12(x9132))
% 13.24/13.45 [919]~P29(x9191)+P9(x9191,f9(x9191,x9192),f12(x9191))+~E(x9192,f12(x9191))
% 13.24/13.45 [921]~P26(x9212)+~E(f15(x9212,x9211,x9211),f12(x9212))+E(x9211,f12(x9212))
% 13.24/13.45 [958]~P29(x9581)+~P10(x9581,f12(x9581),x9582)+E(f9(x9581,x9582),x9582)
% 13.24/13.45 [959]~P29(x9591)+~P9(x9591,f12(x9591),x9592)+E(f9(x9591,x9592),x9592)
% 13.24/13.45 [974]~P50(x9741)+~P10(x9741,f12(x9741),x9742)+E(f16(x9741,x9742),f5(x9741))
% 13.24/13.45 [982]~P44(x9821)+P14(x9821,x9822)+P9(a2,f60(x9822,x9821),f62(x9822,x9821))
% 13.24/13.45 [987]~P29(x9871)+~P10(x9871,x9872,f12(x9871))+E(f13(x9871,x9872),f9(x9871,x9872))
% 13.24/13.45 [988]~P29(x9881)+~P9(x9881,x9882,f12(x9881))+E(f13(x9881,x9882),f9(x9881,x9882))
% 13.24/13.45 [989]~P21(x9891)+~P10(x9891,x9892,f12(x9891))+E(f13(x9891,x9892),f9(x9891,x9892))
% 13.24/13.45 [1016]~P48(x10162)+E(x10161,f12(x10162))+~P9(a1,f30(x10162,x10161),f12(a1))
% 13.24/13.45 [1022]~P48(x10222)+~E(x10221,f12(x10222))+~P10(a1,f12(a1),f30(x10222,x10221))
% 13.24/13.45 [1031]~P29(x10312)+~P9(x10312,f9(x10312,x10311),f12(x10312))+E(x10311,f12(x10312))
% 13.24/13.45 [1058]~P29(x10582)+~P10(x10582,f12(x10582),f9(x10582,x10581))+~E(x10581,f12(x10582))
% 13.24/13.45 [1085]E(x10851,x10852)+~E(f10(a2,x10852,x10851),f12(a2))+~E(f10(a2,x10851,x10852),f12(a2))
% 13.24/13.45 [1119]~P50(x11191)+~P10(x11191,x11192,f12(x11191))+P10(x11191,x11192,f13(x11191,x11192))
% 13.24/13.45 [1120]~P26(x11201)+~P9(x11201,x11202,f12(x11201))+P9(x11201,x11202,f13(x11201,x11202))
% 13.24/13.45 [1121]~P26(x11211)+~P10(x11211,f12(x11211),x11212)+P10(x11211,f13(x11211,x11212),x11212)
% 13.24/13.45 [1122]~P26(x11221)+~P9(x11221,f12(x11221),x11222)+P9(x11221,f13(x11221,x11222),x11222)
% 13.24/13.45 [1136]~P31(x11361)+~P10(x11361,x11362,f12(x11361))+P10(x11361,f12(x11361),f13(x11361,x11362))
% 13.24/13.45 [1137]~P31(x11371)+~P9(x11371,x11372,f12(x11371))+P9(x11371,f12(x11371),f13(x11371,x11372))
% 13.24/13.45 [1138]~P6(x11381)+~P10(x11381,f12(x11381),x11382)+P10(x11381,f12(x11381),f28(x11381,x11382))
% 13.24/13.45 [1139]~P15(x11391)+~P10(x11391,f12(x11391),x11392)+P10(x11391,f12(x11391),f28(x11391,x11392))
% 13.24/13.45 [1140]~P50(x11401)+~P10(x11401,f12(x11401),x11402)+P10(x11401,f12(x11401),f16(x11401,x11402))
% 13.24/13.45 [1141]~P6(x11411)+~P9(x11411,f12(x11411),x11412)+P9(x11411,f12(x11411),f28(x11411,x11412))
% 13.24/13.45 [1142]~P6(x11421)+~P9(x11421,x11422,f12(x11421))+P10(x11421,f28(x11421,x11422),f5(x11421))
% 13.24/13.45 [1143]~P6(x11431)+~P10(x11431,x11432,f12(x11431))+P10(x11431,f28(x11431,x11432),f12(x11431))
% 13.24/13.45 [1144]~P15(x11441)+~P10(x11441,x11442,f12(x11441))+P10(x11441,f28(x11441,x11442),f12(x11441))
% 13.24/13.45 [1145]~P50(x11451)+~P10(x11451,x11452,f12(x11451))+P10(x11451,f16(x11451,x11452),f12(x11451))
% 13.24/13.45 [1146]~P6(x11461)+~P9(x11461,x11462,f12(x11461))+P9(x11461,f28(x11461,x11462),f5(x11461))
% 13.24/13.45 [1147]~P6(x11471)+~P9(x11471,x11472,f12(x11471))+P9(x11471,f28(x11471,x11472),f12(x11471))
% 13.24/13.45 [1148]~P31(x11481)+~P10(x11481,f12(x11481),x11482)+P10(x11481,f13(x11481,x11482),f12(x11481))
% 13.24/13.45 [1149]~P6(x11491)+~P10(x11491,f5(x11491),x11492)+P10(x11491,f28(x11491,x11492),f5(x11491))
% 13.24/13.45 [1150]~P31(x11501)+~P9(x11501,f12(x11501),x11502)+P9(x11501,f13(x11501,x11502),f12(x11501))
% 13.24/13.45 [1151]~P6(x11511)+~P9(x11511,f5(x11511),x11512)+P9(x11511,f28(x11511,x11512),f5(x11511))
% 13.24/13.45 [1153]~P50(x11531)+~P10(x11531,x11532,f13(x11531,x11532))+P10(x11531,x11532,f12(x11531))
% 13.24/13.45 [1154]~P26(x11541)+~P9(x11541,x11542,f13(x11541,x11542))+P9(x11541,x11542,f12(x11541))
% 13.24/13.45 [1155]~P26(x11551)+~P10(x11551,f13(x11551,x11552),x11552)+P10(x11551,f12(x11551),x11552)
% 13.24/13.45 [1156]~P26(x11561)+~P9(x11561,f13(x11561,x11562),x11562)+P9(x11561,f12(x11561),x11562)
% 13.24/13.45 [1169]~P6(x11691)+~P10(x11691,f5(x11691),f28(x11691,x11692))+P10(x11691,x11692,f5(x11691))
% 13.24/13.45 [1170]~P31(x11701)+~P10(x11701,f12(x11701),f13(x11701,x11702))+P10(x11701,x11702,f12(x11701))
% 13.24/13.45 [1171]~P6(x11711)+~P9(x11711,f5(x11711),f28(x11711,x11712))+P9(x11711,x11712,f5(x11711))
% 13.24/13.45 [1172]~P31(x11721)+~P9(x11721,f12(x11721),f13(x11721,x11722))+P9(x11721,x11722,f12(x11721))
% 13.24/13.45 [1173]~P50(x11731)+~P10(x11731,f16(x11731,x11732),f12(x11731))+P10(x11731,x11732,f12(x11731))
% 13.24/13.45 [1174]~P6(x11741)+~P10(x11741,f28(x11741,x11742),f12(x11741))+P10(x11741,x11742,f12(x11741))
% 13.24/13.45 [1175]~P6(x11751)+~P9(x11751,f28(x11751,x11752),f12(x11751))+P9(x11751,x11752,f12(x11751))
% 13.24/13.45 [1176]~P50(x11761)+~P10(x11761,f12(x11761),f16(x11761,x11762))+P10(x11761,f12(x11761),x11762)
% 13.24/13.45 [1177]~P6(x11771)+~P10(x11771,f5(x11771),f28(x11771,x11772))+P10(x11771,f12(x11771),x11772)
% 13.24/13.45 [1178]~P6(x11781)+~P10(x11781,f12(x11781),f28(x11781,x11782))+P10(x11781,f12(x11781),x11782)
% 13.24/13.45 [1179]~P6(x11791)+~P9(x11791,f5(x11791),f28(x11791,x11792))+P10(x11791,f12(x11791),x11792)
% 13.24/13.45 [1180]~P6(x11801)+~P9(x11801,f12(x11801),f28(x11801,x11802))+P9(x11801,f12(x11801),x11802)
% 13.24/13.45 [1181]~P31(x11811)+~P10(x11811,f13(x11811,x11812),f12(x11811))+P10(x11811,f12(x11811),x11812)
% 13.24/13.45 [1182]~P31(x11821)+~P9(x11821,f13(x11821,x11822),f12(x11821))+P9(x11821,f12(x11821),x11822)
% 13.24/13.45 [1289]~P9(a2,f11(x12891),x12892)+P9(a1,x12891,f29(a2,x12892))+~P9(a1,f12(a1),x12891)
% 13.24/13.45 [1290]~P9(a2,x12901,f27(x12902))+P9(a1,f29(a2,x12901),x12902)+~P9(a1,f12(a1),x12902)
% 13.24/13.45 [1291]~P9(a3,f12(a3),x12912)+~P9(a3,f12(a3),x12911)+P9(a3,f12(a3),f19(x12911,x12912))
% 13.24/13.45 [1305]P10(a2,f27(x13051),x13052)+~P10(a1,x13051,f29(a2,x13052))+~P9(a1,f12(a1),x13051)
% 13.24/13.45 [1308]~P26(x13081)+~P10(x13081,f12(x13081),x13082)+P10(x13081,f12(x13081),f15(x13081,x13082,x13082))
% 13.24/13.45 [1309]~P26(x13091)+~P9(x13091,f12(x13091),x13092)+P9(x13091,f12(x13091),f15(x13091,x13092,x13092))
% 13.24/13.45 [1310]~P50(x13101)+~P10(x13101,x13102,f12(x13101))+P10(x13101,f15(x13101,x13102,x13102),f12(x13101))
% 13.24/13.45 [1311]~P26(x13111)+~P10(x13111,x13112,f12(x13111))+P10(x13111,f15(x13111,x13112,x13112),f12(x13111))
% 13.24/13.45 [1312]~P26(x13121)+~P9(x13121,x13122,f12(x13121))+P9(x13121,f15(x13121,x13122,x13122),f12(x13121))
% 13.24/13.45 [1324]~P9(a1,x13241,x13242)+~P9(a1,f13(a1,x13242),x13241)+P9(a1,f9(a1,x13241),x13242)
% 13.24/13.45 [1395]~P50(x13951)+~P10(x13951,f15(x13951,x13952,x13952),f12(x13951))+P10(x13951,x13952,f12(x13951))
% 13.24/13.45 [1396]~P26(x13961)+~P10(x13961,f15(x13961,x13962,x13962),f12(x13961))+P10(x13961,x13962,f12(x13961))
% 13.24/13.45 [1397]~P26(x13971)+~P9(x13971,f15(x13971,x13972,x13972),f12(x13971))+P9(x13971,x13972,f12(x13971))
% 13.24/13.45 [1398]~P26(x13981)+~P10(x13981,f12(x13981),f15(x13981,x13982,x13982))+P10(x13981,f12(x13981),x13982)
% 13.24/13.45 [1399]~P26(x13991)+~P9(x13991,f12(x13991),f15(x13991,x13992,x13992))+P9(x13991,f12(x13991),x13992)
% 13.24/13.45 [1403]P10(a2,f10(a2,x14031,x14032),x14031)+~P10(a2,f12(a2),x14031)+~P10(a2,f12(a2),x14032)
% 13.24/13.45 [1405]~P9(a3,f12(a3),x14052)+~P9(a3,f12(a3),x14051)+P9(a3,f12(a3),f15(a3,x14051,x14052))
% 13.24/13.45 [1460]P10(a2,f12(a2),x14601)+P10(a2,f12(a2),x14602)+~P10(a2,f12(a2),f15(a2,x14602,x14601))
% 13.24/13.45 [721]~P28(x7211)+E(f6(x7211,x7212),f12(a2))+~E(x7212,f12(f72(x7211)))
% 13.24/13.45 [722]~P28(x7222)+~E(f6(x7222,x7221),f12(a2))+E(x7221,f12(f72(x7222)))
% 13.24/13.45 [730]~P56(x7302)+E(x7301,f12(x7302))+E(f28(x7302,f28(x7302,x7301)),x7301)
% 13.24/13.45 [740]~P48(x7402)+E(x7401,f12(x7402))+E(f30(x7402,f16(x7402,x7401)),f5(a1))
% 13.24/13.45 [741]~P50(x7411)+~E(x7412,f12(f72(x7411)))+E(f16(f72(x7411),x7412),f12(f72(x7411)))
% 13.24/13.45 [747]~P48(x7471)+~E(x7472,f12(x7471))+E(f30(x7471,f16(x7471,x7472)),f12(a1))
% 13.24/13.45 [858]~P47(x8582)+E(x8581,f12(a1))+E(f31(x8582,f28(a1,x8581)),f28(x8582,f31(x8582,x8581)))
% 13.24/13.45 [874]~P49(x8742)+E(x8741,f12(x8742))+E(f30(x8742,f28(x8742,x8741)),f28(a1,f30(x8742,x8741)))
% 13.24/13.45 [878]~P55(x8781)+~P47(x8781)+E(f31(x8781,f28(a1,x8782)),f28(x8781,f31(x8781,x8782)))
% 13.24/13.45 [883]~P56(x8832)+E(x8831,f12(x8832))+E(f28(x8832,f13(x8832,x8831)),f13(x8832,f28(x8832,x8831)))
% 13.24/13.45 [884]~P15(x8842)+E(x8841,f12(x8842))+E(f28(x8842,f9(x8842,x8841)),f9(x8842,f28(x8842,x8841)))
% 13.24/13.45 [885]~P49(x8851)+~P55(x8851)+E(f30(x8851,f28(x8851,x8852)),f28(a1,f30(x8851,x8852)))
% 13.24/13.45 [890]~P56(x8902)+E(x8901,f12(x8902))+E(f56(f56(f14(x8902),x8901),f28(x8902,x8901)),f5(x8902))
% 13.24/13.45 [929]~P50(x9291)+P10(f72(x9291),x9292,f12(f72(x9291)))+E(f9(f72(x9291),x9292),x9292)
% 13.24/13.45 [975]~P50(x9751)+P10(x9751,x9752,f12(x9751))+~E(f16(x9751,x9752),f13(x9751,f5(x9751)))
% 13.24/13.45 [1001]~P50(x10011)+~P10(x10011,x10012,f12(x10011))+E(f16(x10011,x10012),f13(x10011,f5(x10011)))
% 13.24/13.45 [1078]~P50(x10781)+~P10(f72(x10781),x10782,f12(f72(x10781)))+E(f13(f72(x10781),x10782),f9(f72(x10781),x10782))
% 13.24/13.45 [1362]E(x13621,x13622)+P10(a3,x13621,x13622)+~P10(a3,x13621,f15(a3,x13622,f5(a3)))
% 13.24/13.45 [1407]~P2(x14071)+~P48(x14071)+P9(a1,f30(x14071,f31(x14071,x14072)),f56(f56(f14(a1),f30(a1,x14072)),f44(x14071)))
% 13.24/13.45 [1408]~P2(x14081)+~P48(x14081)+P9(a1,f30(x14081,f31(x14081,x14082)),f56(f56(f14(a1),f30(a1,x14082)),f51(x14081)))
% 13.24/13.45 [1409]~P2(x14091)+~P48(x14091)+P9(a1,f30(x14091,f31(x14091,x14092)),f56(f56(f14(a1),f30(a1,x14092)),f64(x14091)))
% 13.24/13.45 [1428]~P44(x14281)+P14(x14281,x14282)+~P9(x14281,f56(x14282,f62(x14282,x14281)),f56(x14282,f60(x14282,x14281)))
% 13.24/13.45 [1583]E(f27(x15831),x15832)+~P9(a1,f29(a2,x15832),x15831)+~P10(a1,x15831,f15(a1,f29(a2,x15832),f5(a1)))
% 13.24/13.45 [1621]~P10(a1,f29(a2,x16212),x16211)+~P9(a1,x16211,f15(a1,f29(a2,x16212),f5(a1)))+E(f11(x16211),f15(a2,x16212,f5(a2)))
% 13.24/13.45 [756]~E(x7562,f5(a2))+~E(x7561,f5(a2))+E(f56(f56(f14(a2),x7561),x7562),f5(a2))
% 13.24/13.45 [806]~P70(x8061)+~E(x8062,f5(x8061))+E(f56(f56(f14(x8061),x8062),x8062),f5(x8061))
% 13.24/13.45 [832]E(x8321,f5(a2))+E(x8322,f12(a2))+~E(f56(f56(f14(a2),x8322),x8321),x8322)
% 13.24/13.45 [837]E(x8371,f12(a2))+E(x8372,f12(a2))+~E(f56(f56(f14(a2),x8372),x8371),f12(a2))
% 13.24/13.45 [903]~P70(x9031)+~E(x9032,f13(x9031,f5(x9031)))+E(f56(f56(f14(x9031),x9032),x9032),f5(x9031))
% 13.24/13.45 [971]~P56(x9712)+E(x9711,f12(x9712))+E(f56(f56(f14(x9712),f28(x9712,x9711)),x9711),f5(x9712))
% 13.24/13.45 [972]~P8(x9722)+E(x9721,f12(x9722))+E(f56(f56(f14(x9722),f28(x9722,x9721)),x9721),f5(x9722))
% 13.24/13.45 [1070]E(x10701,f5(a3))+~P10(a3,f12(a3),x10702)+~E(f56(f56(f14(a3),x10702),x10701),f5(a3))
% 13.24/13.45 [1071]E(x10711,f5(a3))+~P10(a3,f12(a3),x10711)+~E(f56(f56(f14(a3),x10711),x10712),f5(a3))
% 13.24/13.45 [1336]E(x13361,f12(a2))+P10(a2,f12(a2),x13362)+~P10(a2,f12(a2),f56(f56(f23(a2),x13362),x13361))
% 13.24/13.45 [1375]~P10(a1,f12(a1),x13752)+~P10(a1,f12(a1),x13751)+P10(a1,f12(a1),f56(f56(f14(a1),x13751),x13752))
% 13.24/13.45 [1376]~P10(a2,f12(a2),x13762)+~P10(a2,f12(a2),x13761)+P10(a2,f12(a2),f56(f56(f14(a2),x13761),x13762))
% 13.24/13.45 [1377]~P9(a3,f12(a3),x13772)+~P9(a3,f12(a3),x13771)+P9(a3,f12(a3),f56(f56(f14(a3),x13771),x13772))
% 13.24/13.45 [1474]E(x14741,f12(a2))+~E(x14742,f12(a3))+~P10(a3,f12(a3),f56(f56(f23(a3),f9(a3,x14742)),x14741))
% 13.24/13.45 [1276]~E(x12762,f12(a1))+~E(x12761,f12(a1))+E(f15(a1,f56(f56(f14(a1),x12761),x12761),f56(f56(f14(a1),x12762),x12762)),f12(a1))
% 13.24/13.45 [1665]~P9(a1,f12(a1),x16652)+~P9(a1,f12(a1),x16651)+P9(a2,f56(f56(f14(a2),f27(x16651)),f27(x16652)),f27(f56(f56(f14(a1),x16651),x16652)))
% 13.24/13.45 [1776]E(x17761,f12(a2))+E(x17762,f12(a4))+P10(a1,f30(a4,f15(a4,f5(a4),f56(f56(f14(a4),x17762),f56(f56(f23(a4),f43(x17761,x17762)),x17761)))),f5(a1))
% 13.24/13.45 [769]~E(x7692,x7693)+~P39(x7691)+P9(x7691,x7692,x7693)
% 13.24/13.45 [771]~E(x7712,x7713)+~P44(x7711)+P9(x7711,x7712,x7713)
% 13.24/13.45 [901]~P10(x9013,x9011,x9012)+~E(x9011,x9012)+~P41(x9013)
% 13.24/13.45 [902]~P10(x9023,x9021,x9022)+~E(x9021,x9022)+~P44(x9023)
% 13.24/13.45 [955]P9(x9551,x9553,x9552)+~P41(x9551)+P10(x9551,x9552,x9553)
% 13.24/13.45 [957]P9(x9571,x9573,x9572)+~P41(x9571)+P9(x9571,x9572,x9573)
% 13.24/13.45 [1028]~P39(x10281)+~P10(x10281,x10282,x10283)+P9(x10281,x10282,x10283)
% 13.24/13.45 [1030]~P44(x10301)+~P10(x10301,x10302,x10303)+P9(x10301,x10302,x10303)
% 13.24/13.45 [1092]~P10(x10921,x10923,x10922)+~P39(x10921)+~P10(x10921,x10922,x10923)
% 13.24/13.45 [1093]~P9(x10931,x10933,x10932)+~P39(x10931)+~P10(x10931,x10932,x10933)
% 13.24/13.45 [1094]~P10(x10941,x10943,x10942)+~P41(x10941)+~P10(x10941,x10942,x10943)
% 13.24/13.45 [1097]~P9(x10971,x10973,x10972)+~P41(x10971)+~P10(x10971,x10972,x10973)
% 13.24/13.45 [1098]~P10(x10981,x10983,x10982)+~P44(x10981)+~P10(x10981,x10982,x10983)
% 13.24/13.45 [1207]~P9(a1,x12071,x12073)+P9(a1,x12071,x12072)+~P9(a1,x12073,x12072)
% 13.24/13.45 [1208]~P9(a2,x12081,x12083)+P9(a2,x12081,x12082)+~P9(a2,x12083,x12082)
% 13.24/13.45 [1209]~P9(a3,x12091,x12093)+P9(a3,x12091,x12092)+~P9(a3,x12093,x12092)
% 13.24/13.45 [724]~P24(x7242)+~E(x7243,f13(x7242,x7241))+E(x7241,f13(x7242,x7243))
% 13.24/13.45 [726]~P24(x7261)+~E(f13(x7261,x7263),x7262)+E(f13(x7261,x7262),x7263)
% 13.24/13.45 [731]~P2(x7313)+E(x7311,x7312)+~E(f31(x7313,x7311),f31(x7313,x7312))
% 13.24/13.45 [732]~P24(x7323)+E(x7321,x7322)+~E(f13(x7323,x7321),f13(x7323,x7322))
% 13.24/13.45 [733]~P42(x7333)+E(x7331,x7332)+~E(f13(x7333,x7331),f13(x7333,x7332))
% 13.24/13.45 [735]~P55(x7353)+E(x7351,x7352)+~E(f28(x7353,x7351),f28(x7353,x7352))
% 13.24/13.45 [790]~E(x7902,x7903)+~P24(x7901)+E(f10(x7901,x7902,x7903),f12(x7901))
% 13.24/13.45 [791]~E(x7912,x7913)+~P16(x7911)+E(f10(x7911,x7912,x7913),f12(x7911))
% 13.24/13.45 [802]~P81(x8021)+~E(x8023,f12(x8021))+E(f15(x8021,x8022,x8023),x8022)
% 13.24/13.45 [803]~E(x8032,x8033)+~P50(x8031)+P9(f72(x8031),x8032,x8033)
% 13.24/13.45 [864]~P24(x8641)+~E(x8643,f13(x8641,x8642))+E(f15(x8641,x8642,x8643),f12(x8641))
% 13.24/13.45 [865]~P24(x8651)+~E(x8652,f13(x8651,x8653))+E(f15(x8651,x8652,x8653),f12(x8651))
% 13.24/13.45 [914]~P81(x9142)+~E(f15(x9142,x9143,x9141),x9143)+E(x9141,f12(x9142))
% 13.24/13.45 [917]~P24(x9173)+E(x9171,x9172)+~E(f10(x9173,x9171,x9172),f12(x9173))
% 13.24/13.45 [918]~P16(x9183)+E(x9181,x9182)+~E(f10(x9183,x9181,x9182),f12(x9183))
% 13.24/13.45 [947]~P24(x9472)+~E(f15(x9472,x9473,x9471),f12(x9472))+E(x9471,f13(x9472,x9473))
% 13.24/13.45 [948]~P24(x9482)+~E(f15(x9482,x9481,x9483),f12(x9482))+E(x9481,f13(x9482,x9483))
% 13.24/13.45 [949]~P24(x9491)+~E(f15(x9491,x9492,x9493),f12(x9491))+E(f13(x9491,x9492),x9493)
% 13.24/13.45 [1057]~P50(x10571)+~P12(x10571,x10573)+P12(x10571,f20(x10571,x10572,x10573))
% 13.24/13.45 [1081]~P53(x10811)+~P13(x10811,x10812,x10813)+P13(x10811,x10812,f13(x10811,x10813))
% 13.24/13.45 [1082]~P53(x10821)+~P13(x10821,x10822,x10823)+P13(x10821,f13(x10821,x10822),x10823)
% 13.24/13.45 [1127]~P53(x11271)+P13(x11271,x11272,x11273)+~P13(x11271,x11272,f13(x11271,x11273))
% 13.24/13.45 [1128]~P50(x11281)+P10(x11281,x11282,x11283)+~P10(x11281,f9(x11281,x11282),x11283)
% 13.24/13.45 [1130]~P29(x11301)+P9(x11301,x11302,x11303)+~P9(x11301,f9(x11301,x11302),x11303)
% 13.24/13.45 [1131]~P53(x11311)+P13(x11311,x11312,x11313)+~P13(x11311,f13(x11311,x11312),x11313)
% 13.24/13.45 [1160]~P31(x11601)+~P10(x11601,x11603,x11602)+P10(x11601,f13(x11601,x11602),f13(x11601,x11603))
% 13.24/13.45 [1162]~P31(x11621)+~P9(x11621,x11623,x11622)+P9(x11621,f13(x11621,x11622),f13(x11621,x11623))
% 13.24/13.45 [1164]~P42(x11641)+~P9(x11641,x11643,x11642)+P9(x11641,f13(x11641,x11642),f13(x11641,x11643))
% 13.24/13.45 [1192]~P31(x11921)+~P10(x11921,x11923,f13(x11921,x11922))+P10(x11921,x11922,f13(x11921,x11923))
% 13.24/13.45 [1194]~P31(x11941)+~P9(x11941,x11943,f13(x11941,x11942))+P9(x11941,x11942,f13(x11941,x11943))
% 13.24/13.45 [1196]~P31(x11961)+~P10(x11961,f13(x11961,x11963),x11962)+P10(x11961,f13(x11961,x11962),x11963)
% 13.24/13.45 [1197]~P50(x11971)+~P10(x11971,f9(x11971,x11972),x11973)+P10(x11971,f13(x11971,x11972),x11973)
% 13.24/13.45 [1199]~P31(x11991)+~P9(x11991,f13(x11991,x11993),x11992)+P9(x11991,f13(x11991,x11992),x11993)
% 13.24/13.45 [1201]~P29(x12011)+~P9(x12011,f9(x12011,x12012),x12013)+P9(x12011,f13(x12011,x12012),x12013)
% 13.24/13.45 [1212]~P9(a2,x12123,x12121)+~E(f10(a2,x12121,x12123),x12122)+E(x12121,f15(a2,x12122,x12123))
% 13.24/13.45 [1213]~P9(a2,x12132,x12131)+~E(x12131,f15(a2,x12133,x12132))+E(f10(a2,x12131,x12132),x12133)
% 13.24/13.45 [1221]~P31(x12211)+P10(x12211,x12212,x12213)+~P10(x12211,f13(x12211,x12213),f13(x12211,x12212))
% 13.24/13.45 [1222]~P31(x12221)+P9(x12221,x12222,x12223)+~P9(x12221,f13(x12221,x12223),f13(x12221,x12222))
% 13.24/13.45 [1223]~P42(x12231)+P9(x12231,x12232,x12233)+~P9(x12231,f13(x12231,x12233),f13(x12231,x12232))
% 13.24/13.45 [1292]~P31(x12921)+~P10(x12921,x12922,x12923)+P10(x12921,f10(x12921,x12922,x12923),f12(x12921))
% 13.24/13.45 [1293]~P31(x12931)+~P9(x12931,x12932,x12933)+P9(x12931,f10(x12931,x12932,x12933),f12(x12931))
% 13.24/13.45 [1380]~P31(x13801)+P10(x13801,x13802,x13803)+~P10(x13801,f10(x13801,x13802,x13803),f12(x13801))
% 13.24/13.45 [1381]~P31(x13811)+P9(x13811,x13812,x13813)+~P9(x13811,f10(x13811,x13812,x13813),f12(x13811))
% 13.24/13.45 [1536]~P10(a2,x15363,x15361)+~P10(a2,x15363,x15362)+P10(a2,f10(a2,x15361,x15362),f10(a2,x15361,x15363))
% 13.24/13.45 [1537]~P10(a2,x15371,x15373)+~P9(a2,x15372,x15371)+P10(a2,f10(a2,x15371,x15372),f10(a2,x15373,x15372))
% 13.24/13.45 [1608]~P9(a2,x16083,x16082)+~P9(a2,f15(a2,x16081,x16083),x16082)+P9(a2,x16081,f10(a2,x16082,x16083))
% 13.24/13.45 [1609]~P9(a2,x16092,x16093)+~P9(a2,x16091,f10(a2,x16093,x16092))+P9(a2,f15(a2,x16091,x16092),x16093)
% 13.24/13.45 [789]~P54(x7891)+~E(x7892,f12(f72(x7891)))+E(f56(f17(x7891,x7892),x7893),f12(x7891))
% 13.24/13.45 [825]~P54(x8251)+~E(x8252,f12(x8251))+E(f25(x8251,x8252,x8253),f12(f72(x8251)))
% 13.24/13.45 [826]~P28(x8261)+~E(x8262,f12(x8261))+E(f18(x8261,x8262,x8263),f12(f72(x8261)))
% 13.24/13.45 [867]~P54(x8671)+~E(x8673,f12(f72(x8671)))+E(f25(x8671,x8672,x8673),f12(f72(x8671)))
% 13.24/13.45 [868]~P57(x8681)+~E(x8682,f12(f72(x8681)))+E(f8(x8681,x8682,x8683),f12(f72(x8681)))
% 13.24/13.45 [931]~P54(x9311)+E(f21(x9311,x9312,x9313),f12(a2))+E(f56(f17(x9311,x9313),x9312),f12(x9311))
% 13.24/13.45 [944]~P28(x9442)+E(x9441,f12(x9442))+~E(f18(x9442,x9441,x9443),f12(f72(x9442)))
% 13.24/13.45 [945]~P28(x9452)+E(x9451,f12(x9452))+~E(f20(x9452,x9451,x9453),f12(f72(x9452)))
% 13.24/13.45 [968]~P57(x9682)+~E(f8(x9682,x9681,x9683),f12(f72(x9682)))+E(x9681,f12(f72(x9682)))
% 13.24/13.45 [969]~P28(x9692)+~E(f20(x9692,x9693,x9691),f12(f72(x9692)))+E(x9691,f12(f72(x9692)))
% 13.24/13.45 [1244]~P50(x12441)+~P10(f72(x12441),x12443,x12442)+P12(x12441,f10(f72(x12441),x12442,x12443))
% 13.24/13.45 [1318]~P50(x13181)+P10(f72(x13181),x13182,x13183)+~P12(x13181,f10(f72(x13181),x13183,x13182))
% 13.24/13.45 [1319]~P50(x13191)+P9(f72(x13191),x13192,x13193)+~P12(x13191,f10(f72(x13191),x13193,x13192))
% 13.24/13.45 [1532]E(x15321,f12(a1))+~P9(a1,x15322,f12(a1))+~P9(a1,f9(a1,x15321),f56(f56(f14(a1),x15322),f9(a1,x15323)))
% 13.24/13.45 [1581]P10(a2,x15812,x15811)+E(f15(a2,x15811,f70(x15811,x15812,x15813)),x15812)+P82(f56(x15813,f10(a2,x15812,x15811)))
% 13.24/13.45 [1582]P10(a2,x15822,x15821)+E(f15(a2,x15821,f34(x15821,x15822,x15823)),x15822)+P82(f56(x15823,f10(a2,x15822,x15821)))
% 13.24/13.45 [1590]E(f15(a2,x15901,f70(x15901,x15902,x15903)),x15902)+P82(f56(x15903,f10(a2,x15902,x15901)))+~P82(f56(x15903,f12(a2)))
% 13.24/13.45 [1591]E(f15(a2,x15911,f34(x15911,x15912,x15913)),x15912)+P82(f56(x15913,f10(a2,x15912,x15911)))+~P82(f56(x15913,f12(a2)))
% 13.24/13.45 [1598]~P9(a2,x15982,x15983)+~P9(a2,x15982,x15981)+E(f10(a2,f10(a2,x15981,x15982),f10(a2,x15983,x15982)),f10(a2,x15981,x15983))
% 13.24/13.45 [1613]~P10(a2,x16132,x16133)+~P82(f56(x16131,f10(a2,x16132,x16133)))+P82(f56(x16131,f12(a2)))
% 13.24/13.45 [1712]P10(a2,x17121,x17122)+~P82(f56(x17123,f70(x17122,x17121,x17123)))+P82(f56(x17123,f10(a2,x17121,x17122)))
% 13.24/13.45 [1713]P10(a2,x17131,x17132)+~P82(f56(x17133,f34(x17132,x17131,x17133)))+P82(f56(x17133,f10(a2,x17131,x17132)))
% 13.24/13.45 [1715]~P82(f56(x17151,f70(x17153,x17152,x17151)))+P82(f56(x17151,f10(a2,x17152,x17153)))+~P82(f56(x17151,f12(a2)))
% 13.24/13.45 [1716]~P82(f56(x17161,f34(x17163,x17162,x17161)))+P82(f56(x17161,f10(a2,x17162,x17163)))+~P82(f56(x17161,f12(a2)))
% 13.24/13.45 [792]~P3(x7921)+~E(x7923,f12(a2))+E(f56(f56(f23(x7921),x7922),x7923),f5(x7921))
% 13.24/13.45 [804]~P79(x8041)+~E(x8043,f12(x8041))+E(f56(f56(f14(x8041),x8042),x8043),f12(x8041))
% 13.24/13.45 [805]~P79(x8051)+~E(x8052,f12(x8051))+E(f56(f56(f14(x8051),x8052),x8053),f12(x8051))
% 13.24/13.45 [916]~P70(x9162)+E(x9161,f12(x9162))+~E(f56(f56(f23(x9162),x9161),x9163),f12(x9162))
% 13.24/13.45 [935]~P56(x9351)+E(f28(x9351,x9352),x9353)+~E(f56(f56(f14(x9351),x9352),x9353),f5(x9351))
% 13.24/13.45 [990]~P54(x9901)+~E(x9902,f13(x9901,x9903))+E(f56(f56(f14(x9901),x9902),x9902),f56(f56(f14(x9901),x9903),x9903))
% 13.24/13.45 [1048]E(x10481,x10482)+E(x10483,f12(a1))+~E(f56(f56(f14(a1),x10483),x10481),f56(f56(f14(a1),x10483),x10482))
% 13.24/13.45 [1050]E(x10501,x10502)+E(x10503,f12(a2))+~E(f56(f56(f14(a2),x10503),x10501),f56(f56(f14(a2),x10503),x10502))
% 13.24/13.45 [1051]E(x10511,x10512)+E(x10513,f12(a1))+~E(f56(f56(f14(a1),x10511),x10513),f56(f56(f14(a1),x10512),x10513))
% 13.24/13.45 [1052]E(x10521,x10522)+E(x10523,f12(a2))+~E(f56(f56(f14(a2),x10521),x10523),f56(f56(f14(a2),x10522),x10523))
% 13.24/13.45 [1242]E(x12421,x12422)+~P10(a2,f12(a2),x12423)+~E(f56(f56(f14(a2),x12423),x12421),f56(f56(f14(a2),x12423),x12422))
% 13.24/13.45 [1301]~P1(x13011)+~P10(x13011,f12(x13011),x13012)+P10(x13011,f12(x13011),f56(f56(f23(x13011),x13012),x13013))
% 13.24/13.45 [1302]~P1(x13021)+~P9(x13021,f5(x13021),x13022)+P9(x13021,f5(x13021),f56(f56(f23(x13021),x13022),x13023))
% 13.24/13.45 [1303]~P1(x13031)+~P9(x13031,f12(x13031),x13032)+P9(x13031,f12(x13031),f56(f56(f23(x13031),x13032),x13033))
% 13.24/13.45 [1497]~P10(a1,x14971,x14973)+~P10(a1,f12(a1),x14972)+P10(a1,f56(f56(f14(a1),x14971),x14972),f56(f56(f14(a1),x14973),x14972))
% 13.24/13.45 [1498]~P10(a1,x14982,x14983)+~P10(a1,f12(a1),x14981)+P10(a1,f56(f56(f14(a1),x14981),x14982),f56(f56(f14(a1),x14981),x14983))
% 13.24/13.45 [1502]~P10(a2,x15021,x15023)+~P10(a2,f12(a2),x15022)+P10(a2,f56(f56(f14(a2),x15021),x15022),f56(f56(f14(a2),x15023),x15022))
% 13.24/13.45 [1503]~P10(a2,x15032,x15033)+~P10(a2,f12(a2),x15031)+P10(a2,f56(f56(f14(a2),x15031),x15032),f56(f56(f14(a2),x15031),x15033))
% 13.24/13.45 [1504]~P10(a3,x15042,x15043)+~P10(a3,f12(a3),x15041)+P10(a3,f56(f56(f14(a3),x15041),x15042),f56(f56(f14(a3),x15041),x15043))
% 13.24/13.45 [1505]~P9(a1,x15052,x15053)+~P10(a1,f12(a1),x15051)+P9(a1,f56(f56(f14(a1),x15051),x15052),f56(f56(f14(a1),x15051),x15053))
% 13.24/13.45 [1506]~P9(a1,x15061,x15063)+~P10(a1,f12(a1),x15062)+P9(a1,f56(f56(f14(a1),x15061),x15062),f56(f56(f14(a1),x15063),x15062))
% 13.24/13.45 [1622]P10(a1,x16221,x16222)+~P10(a1,f12(a1),x16223)+~P10(a1,f56(f56(f14(a1),x16221),x16223),f56(f56(f14(a1),x16222),x16223))
% 13.24/13.45 [1624]P10(a2,x16241,x16242)+~P10(a2,f12(a2),x16243)+~P10(a2,f56(f56(f23(a2),x16243),x16241),f56(f56(f23(a2),x16243),x16242))
% 13.24/13.45 [1625]P9(a1,x16251,x16252)+~P10(a1,f12(a1),x16253)+~P9(a1,f56(f56(f14(a1),x16253),x16251),f56(f56(f14(a1),x16253),x16252))
% 13.24/13.45 [1626]P9(a1,x16261,x16262)+~P10(a1,f12(a1),x16263)+~P9(a1,f56(f56(f14(a1),x16261),x16263),f56(f56(f14(a1),x16262),x16263))
% 13.24/13.45 [1628]P9(a2,x16281,x16282)+~P10(a2,f12(a2),x16283)+~P9(a2,f56(f56(f14(a2),x16283),x16281),f56(f56(f14(a2),x16283),x16282))
% 13.24/13.45 [1629]P9(a2,x16291,x16292)+~P10(a2,f12(a2),x16293)+~P9(a2,f56(f56(f14(a2),x16291),x16293),f56(f56(f14(a2),x16292),x16293))
% 13.24/13.45 [1226]~P56(x12262)+E(x12261,f12(x12262))+E(f56(f56(f23(x12262),f28(x12262,x12261)),x12263),f28(x12262,f56(f56(f23(x12262),x12261),x12263)))
% 13.24/13.45 [1374]~P50(x13741)+~P9(x13741,f12(x13741),x13743)+E(f56(f56(f14(x13741),f9(x13741,x13742)),x13743),f9(x13741,f56(f56(f14(x13741),x13742),x13743)))
% 13.24/13.45 [1533]~P61(x15332)+E(x15331,f12(x15332))+~E(f15(x15332,f56(f56(f14(x15332),x15333),x15333),f56(f56(f14(x15332),x15331),x15331)),f12(x15332))
% 13.24/13.45 [1534]~P61(x15342)+E(x15341,f12(x15342))+~E(f15(x15342,f56(f56(f14(x15342),x15341),x15341),f56(f56(f14(x15342),x15343),x15343)),f12(x15342))
% 13.24/13.45 [1541]~P3(x15412)+E(x15411,f12(a2))+E(f56(f56(f14(x15412),x15413),f56(f56(f23(x15412),x15413),f10(a2,x15411,f5(a2)))),f56(f56(f23(x15412),x15413),x15411))
% 13.24/13.45 [1597]~P1(x15971)+~P10(x15971,f5(x15971),x15972)+P10(x15971,f5(x15971),f56(f56(f14(x15971),x15972),f56(f56(f23(x15971),x15972),x15973)))
% 13.24/13.45 [1684]~P1(x16841)+~P10(x16841,f5(x16841),x16842)+P10(x16841,f56(f56(f23(x16841),x16842),x16843),f56(f56(f14(x16841),x16842),f56(f56(f23(x16841),x16842),x16843)))
% 13.24/13.45 [1688]~P61(x16882)+E(x16881,f12(x16882))+P10(x16882,f12(x16882),f15(x16882,f56(f56(f14(x16882),x16883),x16883),f56(f56(f14(x16882),x16881),x16881)))
% 13.24/13.45 [1689]~P61(x16892)+E(x16891,f12(x16892))+P10(x16892,f12(x16892),f15(x16892,f56(f56(f14(x16892),x16891),x16891),f56(f56(f14(x16892),x16893),x16893)))
% 13.24/13.45 [1737]~P61(x17372)+E(x17371,f12(x17372))+~P9(x17372,f15(x17372,f56(f56(f14(x17372),x17373),x17373),f56(f56(f14(x17372),x17371),x17371)),f12(x17372))
% 13.24/13.45 [1738]~P61(x17382)+E(x17381,f12(x17382))+~P9(x17382,f15(x17382,f56(f56(f14(x17382),x17381),x17381),f56(f56(f14(x17382),x17383),x17383)),f12(x17382))
% 13.24/13.45 [1731]~P4(x17311)+~P10(a2,f12(a2),x17313)+E(f56(f56(f14(x17311),f56(f56(f23(x17311),x17312),f10(a2,x17313,f5(a2)))),x17312),f56(f56(f23(x17311),x17312),x17313))
% 13.24/13.45 [1101]~P19(x11013)+E(x11011,x11012)+~E(f15(x11013,x11014,x11011),f15(x11013,x11014,x11012))
% 13.24/13.45 [1102]~P20(x11023)+E(x11021,x11022)+~E(f15(x11023,x11024,x11021),f15(x11023,x11024,x11022))
% 13.24/13.45 [1104]~P19(x11043)+E(x11041,x11042)+~E(f15(x11043,x11041,x11044),f15(x11043,x11042,x11044))
% 13.24/13.45 [1105]~P28(x11053)+E(x11051,x11052)+~E(f18(x11053,x11051,x11054),f18(x11053,x11052,x11054))
% 13.24/13.45 [1202]~P40(x12022)+~P10(f77(x12021,x12022),x12023,x12024)+P9(f77(x12021,x12022),x12023,x12024)
% 13.24/13.45 [1294]~P40(x12941)+~P9(f77(x12942,x12941),x12944,x12943)+~P10(f77(x12942,x12941),x12943,x12944)
% 13.24/13.45 [1313]~P58(x13131)+~P13(f72(x13131),x13132,x13134)+P13(f72(x13131),x13132,f25(x13131,x13133,x13134))
% 13.24/13.45 [1355]~P10(a2,x13553,x13554)+P10(a2,x13551,x13552)+~E(f15(a2,x13553,x13552),f15(a2,x13551,x13554))
% 13.24/13.45 [1400]~P58(x14001)+~P13(f72(x14001),f25(x14001,x14004,x14002),x14003)+P13(f72(x14001),x14002,x14003)
% 13.24/13.45 [1433]~P32(x14331)+~P10(x14331,x14333,x14334)+P10(x14331,f15(x14331,x14332,x14333),f15(x14331,x14332,x14334))
% 13.24/13.45 [1434]~P34(x14341)+~P10(x14341,x14343,x14344)+P10(x14341,f15(x14341,x14342,x14343),f15(x14341,x14342,x14344))
% 13.24/13.45 [1435]~P32(x14351)+~P10(x14351,x14352,x14354)+P10(x14351,f15(x14351,x14352,x14353),f15(x14351,x14354,x14353))
% 13.24/13.45 [1436]~P34(x14361)+~P10(x14361,x14362,x14364)+P10(x14361,f15(x14361,x14362,x14363),f15(x14361,x14364,x14363))
% 13.24/13.45 [1437]~P32(x14371)+~P9(x14371,x14373,x14374)+P9(x14371,f15(x14371,x14372,x14373),f15(x14371,x14372,x14374))
% 13.24/13.45 [1438]~P33(x14381)+~P9(x14381,x14383,x14384)+P9(x14381,f15(x14381,x14382,x14383),f15(x14381,x14382,x14384))
% 13.24/13.45 [1439]~P32(x14391)+~P9(x14391,x14392,x14394)+P9(x14391,f15(x14391,x14392,x14393),f15(x14391,x14394,x14393))
% 13.24/13.45 [1440]~P33(x14401)+~P9(x14401,x14402,x14404)+P9(x14401,f15(x14401,x14402,x14403),f15(x14401,x14404,x14403))
% 13.24/13.45 [1535]~P10(a2,x15352,x15354)+~P10(a2,x15351,x15353)+P10(a2,f15(a2,x15351,x15352),f15(a2,x15353,x15354))
% 13.24/13.45 [1538]~P10(a3,x15381,x15383)+~P9(a3,x15382,x15384)+P10(a3,f15(a3,x15381,x15382),f15(a3,x15383,x15384))
% 13.24/13.45 [1539]~P9(a2,x15392,x15394)+~P9(a2,x15391,x15393)+P9(a2,f15(a2,x15391,x15392),f15(a2,x15393,x15394))
% 13.24/13.45 [1600]~P32(x16001)+P10(x16001,x16002,x16003)+~P10(x16001,f15(x16001,x16004,x16002),f15(x16001,x16004,x16003))
% 13.24/13.45 [1602]~P32(x16021)+P10(x16021,x16022,x16023)+~P10(x16021,f15(x16021,x16022,x16024),f15(x16021,x16023,x16024))
% 13.24/13.45 [1604]~P32(x16041)+P9(x16041,x16042,x16043)+~P9(x16041,f15(x16041,x16044,x16042),f15(x16041,x16044,x16043))
% 13.24/13.45 [1606]~P32(x16061)+P9(x16061,x16062,x16063)+~P9(x16061,f15(x16061,x16062,x16064),f15(x16061,x16063,x16064))
% 13.24/13.45 [1135]~P57(x11352)+~E(f20(x11352,x11353,x11351),f25(x11352,x11354,x11351))+E(x11351,f12(f72(x11352)))
% 13.24/13.45 [1595]~P57(x15952)+~E(f15(f72(x15952),f25(x15952,x15953,x15951),f20(x15952,x15954,x15951)),f12(f72(x15952)))+E(x15951,f12(f72(x15952)))
% 13.24/13.45 [1611]~E(x16113,f15(a2,x16114,x16112))+P82(f56(x16111,x16112))+~P82(f56(x16111,f10(a2,x16113,x16114)))
% 13.24/13.45 [1704]~P50(x17041)+P10(x17041,x17042,f15(x17041,x17043,x17044))+~P10(x17041,f9(x17041,f10(x17041,x17042,x17043)),x17044)
% 13.24/13.45 [1705]~P50(x17051)+P10(x17051,f10(x17051,x17052,x17053),x17054)+~P10(x17051,f9(x17051,f10(x17051,x17054,x17052)),x17053)
% 13.24/13.45 [1797]~P40(x17972)+P9(f77(x17971,x17972),x17973,x17974)+~P9(x17972,f56(x17973,f48(x17974,x17973,x17971,x17972)),f56(x17974,f48(x17974,x17973,x17971,x17972)))
% 13.24/13.45 [1491]~P9(a2,x14912,x14914)+~P9(a2,x14911,x14913)+P9(a2,f56(f56(f14(a2),x14911),x14912),f56(f56(f14(a2),x14913),x14914))
% 13.24/13.45 [1106]~P28(x11063)+E(x11061,x11062)+~E(f20(x11063,x11064,x11061),f20(x11063,x11065,x11062))
% 13.24/13.45 [1107]~P28(x11073)+E(x11071,x11072)+~E(f20(x11073,x11071,x11074),f20(x11073,x11072,x11075))
% 13.24/13.45 [1259]~P40(x12591)+P9(x12591,f56(x12592,x12593),f56(x12594,x12593))+~P9(f77(x12595,x12591),x12592,x12594)
% 13.24/13.45 [1485]~P57(x14852)+~E(f15(f72(x14852),x14853,f25(x14852,x14854,x14855)),f20(x14852,x14851,x14855))+E(x14851,f56(f17(x14852,x14853),x14854))
% 13.24/13.45 [1513]~P57(x15132)+E(x15131,f26(x15132,x15133,x15134))+~E(f15(f72(x15132),x15133,f25(x15132,x15134,x15131)),f20(x15132,x15135,x15131))
% 13.24/13.45 [1643]~E(x16432,x16434)+~P81(x16431)+E(f15(x16431,f56(f56(f14(x16431),x16432),x16433),f56(f56(f14(x16431),x16434),x16435)),f15(x16431,f56(f56(f14(x16431),x16432),x16435),f56(f56(f14(x16431),x16434),x16433)))
% 13.24/13.45 [1751]~P9(a2,x17513,x17512)+E(x17511,f15(a2,f56(f56(f14(a2),f10(a2,x17512,x17513)),x17514),x17515))+~E(f15(a2,f56(f56(f14(a2),x17513),x17514),x17511),f15(a2,f56(f56(f14(a2),x17512),x17514),x17515))
% 13.24/13.45 [1752]~P9(a2,x17522,x17521)+E(f15(a2,f56(f56(f14(a2),f10(a2,x17521,x17522)),x17523),x17524),x17525)+~E(f15(a2,f56(f56(f14(a2),x17521),x17523),x17524),f15(a2,f56(f56(f14(a2),x17522),x17523),x17525))
% 13.24/13.45 [1760]~P9(a2,x17604,x17601)+~E(x17605,f15(a2,f56(f56(f14(a2),f10(a2,x17601,x17604)),x17602),x17603))+E(f15(a2,f56(f56(f14(a2),x17601),x17602),x17603),f15(a2,f56(f56(f14(a2),x17604),x17602),x17605))
% 13.24/13.45 [1761]~P9(a2,x17614,x17611)+~E(f15(a2,f56(f56(f14(a2),f10(a2,x17611,x17614)),x17612),x17613),x17615)+E(f15(a2,f56(f56(f14(a2),x17611),x17612),x17613),f15(a2,f56(f56(f14(a2),x17614),x17612),x17615))
% 13.24/13.45 [1778]~P9(a2,x17783,x17782)+P10(a2,x17781,f15(a2,f56(f56(f14(a2),f10(a2,x17782,x17783)),x17784),x17785))+~P10(a2,f15(a2,f56(f56(f14(a2),x17783),x17784),x17781),f15(a2,f56(f56(f14(a2),x17782),x17784),x17785))
% 13.24/13.45 [1779]~P9(a2,x17793,x17792)+P9(a2,x17791,f15(a2,f56(f56(f14(a2),f10(a2,x17792,x17793)),x17794),x17795))+~P9(a2,f15(a2,f56(f56(f14(a2),x17793),x17794),x17791),f15(a2,f56(f56(f14(a2),x17792),x17794),x17795))
% 13.24/13.45 [1780]~P9(a2,x17802,x17801)+P10(a2,f15(a2,f56(f56(f14(a2),f10(a2,x17801,x17802)),x17803),x17804),x17805)+~P10(a2,f15(a2,f56(f56(f14(a2),x17801),x17803),x17804),f15(a2,f56(f56(f14(a2),x17802),x17803),x17805))
% 13.24/13.45 [1781]~P9(a2,x17812,x17811)+P9(a2,f15(a2,f56(f56(f14(a2),f10(a2,x17811,x17812)),x17813),x17814),x17815)+~P9(a2,f15(a2,f56(f56(f14(a2),x17811),x17813),x17814),f15(a2,f56(f56(f14(a2),x17812),x17813),x17815))
% 13.24/13.45 [1787]~P9(a2,x17871,x17874)+~P10(a2,x17873,f15(a2,f56(f56(f14(a2),f10(a2,x17874,x17871)),x17872),x17875))+P10(a2,f15(a2,f56(f56(f14(a2),x17871),x17872),x17873),f15(a2,f56(f56(f14(a2),x17874),x17872),x17875))
% 13.24/13.45 [1788]~P9(a2,x17881,x17884)+~P9(a2,x17883,f15(a2,f56(f56(f14(a2),f10(a2,x17884,x17881)),x17882),x17885))+P9(a2,f15(a2,f56(f56(f14(a2),x17881),x17882),x17883),f15(a2,f56(f56(f14(a2),x17884),x17882),x17885))
% 13.24/13.45 [1789]~P9(a2,x17894,x17891)+~P10(a2,f15(a2,f56(f56(f14(a2),f10(a2,x17891,x17894)),x17892),x17893),x17895)+P10(a2,f15(a2,f56(f56(f14(a2),x17891),x17892),x17893),f15(a2,f56(f56(f14(a2),x17894),x17892),x17895))
% 13.24/13.45 [1790]~P9(a2,x17904,x17901)+~P9(a2,f15(a2,f56(f56(f14(a2),f10(a2,x17901,x17904)),x17902),x17903),x17905)+P9(a2,f15(a2,f56(f56(f14(a2),x17901),x17902),x17903),f15(a2,f56(f56(f14(a2),x17904),x17902),x17905))
% 13.24/13.45 [1749]~P76(x17492)+~E(f15(x17492,f56(f56(f14(x17492),x17494),x17495),x17491),f15(x17492,f56(f56(f14(x17492),x17493),x17495),x17496))+E(x17491,f15(x17492,f56(f56(f14(x17492),f10(x17492,x17493,x17494)),x17495),x17496))
% 13.24/13.45 [1750]~P76(x17501)+~E(f15(x17501,f56(f56(f14(x17501),x17502),x17504),x17505),f15(x17501,f56(f56(f14(x17501),x17503),x17504),x17506))+E(f15(x17501,f56(f56(f14(x17501),f10(x17501,x17502,x17503)),x17504),x17505),x17506)
% 13.24/13.45 [1758]~P76(x17581)+~E(x17586,f15(x17581,f56(f56(f14(x17581),f10(x17581,x17582,x17585)),x17583),x17584))+E(f15(x17581,f56(f56(f14(x17581),x17582),x17583),x17584),f15(x17581,f56(f56(f14(x17581),x17585),x17583),x17586))
% 13.24/13.45 [1759]~P76(x17591)+~E(f15(x17591,f56(f56(f14(x17591),f10(x17591,x17592,x17595)),x17593),x17594),x17596)+E(f15(x17591,f56(f56(f14(x17591),x17592),x17593),x17594),f15(x17591,f56(f56(f14(x17591),x17595),x17593),x17596))
% 13.24/13.45 [1782]~P74(x17821)+~P10(x17821,f15(x17821,f56(f56(f14(x17821),x17824),x17825),x17822),f15(x17821,f56(f56(f14(x17821),x17823),x17825),x17826))+P10(x17821,x17822,f15(x17821,f56(f56(f14(x17821),f10(x17821,x17823,x17824)),x17825),x17826))
% 13.24/13.45 [1783]~P74(x17831)+~P9(x17831,f15(x17831,f56(f56(f14(x17831),x17834),x17835),x17832),f15(x17831,f56(f56(f14(x17831),x17833),x17835),x17836))+P9(x17831,x17832,f15(x17831,f56(f56(f14(x17831),f10(x17831,x17833,x17834)),x17835),x17836))
% 13.24/13.45 [1784]~P74(x17841)+~P10(x17841,f15(x17841,f56(f56(f14(x17841),x17842),x17844),x17845),f15(x17841,f56(f56(f14(x17841),x17843),x17844),x17846))+P10(x17841,f15(x17841,f56(f56(f14(x17841),f10(x17841,x17842,x17843)),x17844),x17845),x17846)
% 13.24/13.45 [1785]~P74(x17851)+~P9(x17851,f15(x17851,f56(f56(f14(x17851),x17852),x17854),x17855),f15(x17851,f56(f56(f14(x17851),x17853),x17854),x17856))+P9(x17851,f15(x17851,f56(f56(f14(x17851),f10(x17851,x17852,x17853)),x17854),x17855),x17856)
% 13.24/13.45 [1791]~P74(x17911)+~P10(x17911,x17914,f15(x17911,f56(f56(f14(x17911),f10(x17911,x17915,x17912)),x17913),x17916))+P10(x17911,f15(x17911,f56(f56(f14(x17911),x17912),x17913),x17914),f15(x17911,f56(f56(f14(x17911),x17915),x17913),x17916))
% 13.24/13.45 [1792]~P74(x17921)+~P9(x17921,x17924,f15(x17921,f56(f56(f14(x17921),f10(x17921,x17925,x17922)),x17923),x17926))+P9(x17921,f15(x17921,f56(f56(f14(x17921),x17922),x17923),x17924),f15(x17921,f56(f56(f14(x17921),x17925),x17923),x17926))
% 13.24/13.45 [1793]~P74(x17931)+~P10(x17931,f15(x17931,f56(f56(f14(x17931),f10(x17931,x17932,x17935)),x17933),x17934),x17936)+P10(x17931,f15(x17931,f56(f56(f14(x17931),x17932),x17933),x17934),f15(x17931,f56(f56(f14(x17931),x17935),x17933),x17936))
% 13.24/13.45 [1794]~P74(x17941)+~P9(x17941,f15(x17941,f56(f56(f14(x17941),f10(x17941,x17942,x17945)),x17943),x17944),x17946)+P9(x17941,f15(x17941,f56(f56(f14(x17941),x17942),x17943),x17944),f15(x17941,f56(f56(f14(x17941),x17945),x17943),x17946))
% 13.24/13.45 [981]~P37(x9812)+~P10(x9812,f12(x9812),x9811)+E(f16(x9812,x9811),f5(x9812))+E(x9811,f12(x9812))
% 13.24/13.45 [1185]~P15(x11852)+~P10(x11852,f28(x11852,x11851),f12(x11852))+P10(x11852,x11851,f12(x11852))+E(x11851,f12(x11852))
% 13.24/13.45 [1186]~P15(x11862)+~P10(x11862,f12(x11862),f28(x11862,x11861))+P10(x11862,f12(x11862),x11861)+E(x11861,f12(x11862))
% 13.24/13.45 [1299]~P6(x12991)+P10(x12991,f5(x12991),x12992)+~P10(x12991,f28(x12991,x12992),f5(x12991))+P9(x12991,x12992,f12(x12991))
% 13.24/13.45 [1300]~P6(x13001)+P9(x13001,f5(x13001),x13002)+~P9(x13001,f28(x13001,x13002),f5(x13001))+P9(x13001,x13002,f12(x13001))
% 13.24/13.45 [1325]~P6(x13251)+~P10(x13251,x13252,f5(x13251))+~P10(x13251,f12(x13251),x13252)+P10(x13251,f5(x13251),f28(x13251,x13252))
% 13.24/13.45 [1326]~P15(x13261)+~P10(x13261,x13262,f5(x13261))+~P10(x13261,f12(x13261),x13262)+P10(x13261,f5(x13261),f28(x13261,x13262))
% 13.24/13.45 [1327]~P6(x13271)+~P9(x13271,x13272,f5(x13271))+~P10(x13271,f12(x13271),x13272)+P9(x13271,f5(x13271),f28(x13271,x13272))
% 13.24/13.45 [1328]~P15(x13281)+~P9(x13281,x13282,f5(x13281))+~P10(x13281,f12(x13281),x13282)+P9(x13281,f5(x13281),f28(x13281,x13282))
% 13.24/13.45 [840]P12(x8402,x8401)+~P50(x8402)+P12(x8402,f13(f72(x8402),x8401))+E(x8401,f12(f72(x8402)))
% 13.24/13.45 [930]~P37(x9302)+P10(x9302,f12(x9302),x9301)+E(x9301,f12(x9302))+E(f16(x9302,x9301),f13(x9302,f5(x9302)))
% 13.24/13.45 [1080]~P50(x10802)+~P10(f72(x10802),f12(f72(x10802)),x10801)+E(f16(f72(x10802),x10801),f5(f72(x10802)))+E(x10801,f12(f72(x10802)))
% 13.24/13.45 [841]~P3(x8412)+~P78(x8412)+E(x8411,f12(a2))+E(f56(f56(f23(x8412),f12(x8412)),x8411),f12(x8412))
% 13.24/13.45 [976]~P70(x9762)+E(x9761,f5(x9762))+E(x9761,f13(x9762,f5(x9762)))+~E(f56(f56(f14(x9762),x9761),x9761),f5(x9762))
% 13.24/13.45 [1034]~E(x10342,f5(a3))+~E(x10341,f5(a3))+~P10(a3,f12(a3),x10341)+E(f56(f56(f14(a3),x10341),x10342),f5(a3))
% 13.24/13.45 [1063]~P50(x10632)+P10(f72(x10632),f12(f72(x10632)),x10631)+E(x10631,f12(f72(x10632)))+E(f16(f72(x10632),x10631),f13(f72(x10632),f5(f72(x10632))))
% 13.24/13.45 [1735]~P10(a1,x17352,x17351)+~P9(a1,x17351,f5(a1))+~P9(a1,f12(a1),x17352)+P10(a1,f15(a1,f9(a1,f10(a1,f5(a1),x17351)),x17352),f5(a1))
% 13.24/13.45 [961]P10(x9613,x9611,x9612)+~P50(x9613)+E(x9611,x9612)+P10(x9613,x9612,x9611)
% 13.24/13.45 [967]P10(x9673,x9671,x9672)+~P41(x9673)+E(x9671,x9672)+P10(x9673,x9672,x9671)
% 13.24/13.45 [970]P9(x9701,x9702,x9703)+~E(x9702,x9703)+~P41(x9701)+P10(x9701,x9702,x9703)
% 13.24/13.45 [1037]~P44(x10373)+~P9(x10373,x10372,x10371)+E(x10371,x10372)+P10(x10373,x10372,x10371)
% 13.24/13.45 [1039]~P41(x10393)+~P9(x10393,x10391,x10392)+E(x10391,x10392)+P10(x10393,x10391,x10392)
% 13.24/13.45 [1045]~P44(x10453)+~P9(x10453,x10451,x10452)+E(x10451,x10452)+P10(x10453,x10451,x10452)
% 13.24/13.45 [1113]~P9(x11133,x11132,x11131)+~P9(x11133,x11131,x11132)+E(x11131,x11132)+~P44(x11133)
% 13.24/13.45 [1168]P9(x11681,x11683,x11682)+~P39(x11681)+~P9(x11681,x11682,x11683)+P10(x11681,x11682,x11683)
% 13.24/13.45 [757]~P54(x7573)+~P38(x7573)+E(x7571,x7572)+~E(f17(x7573,x7571),f17(x7573,x7572))
% 13.24/13.45 [1315]~P50(x13151)+P12(x13151,x13152)+P10(x13151,f12(x13151),x13153)+~P12(x13151,f20(x13151,x13153,x13152))
% 13.24/13.46 [1338]~P15(x13381)+~P10(x13381,x13383,x13382)+~P10(x13381,x13382,f12(x13381))+P10(x13381,f28(x13381,x13382),f28(x13381,x13383))
% 13.24/13.46 [1339]~P15(x13391)+~P9(x13391,x13393,x13392)+~P10(x13391,x13392,f12(x13391))+P9(x13391,f28(x13391,x13392),f28(x13391,x13393))
% 13.24/13.46 [1340]~P15(x13401)+~P10(x13401,x13403,x13402)+~P10(x13401,f12(x13401),x13403)+P10(x13401,f28(x13401,x13402),f28(x13401,x13403))
% 13.24/13.46 [1341]~P15(x13411)+~P9(x13411,x13413,x13412)+~P10(x13411,f12(x13411),x13413)+P9(x13411,f28(x13411,x13412),f28(x13411,x13413))
% 13.24/13.46 [1350]~P50(x13501)+~P10(x13501,x13502,x13503)+~P10(x13501,f13(x13501,x13502),x13503)+P10(x13501,f9(x13501,x13502),x13503)
% 13.24/13.46 [1352]~P29(x13521)+~P9(x13521,x13522,x13523)+~P9(x13521,f13(x13521,x13522),x13523)+P9(x13521,f9(x13521,x13522),x13523)
% 13.24/13.46 [1382]~P15(x13821)+P10(x13821,x13822,x13823)+~P10(x13821,x13822,f12(x13821))+~P10(x13821,f28(x13821,x13823),f28(x13821,x13822))
% 13.24/13.46 [1383]~P15(x13831)+P9(x13831,x13832,x13833)+~P10(x13831,x13832,f12(x13831))+~P9(x13831,f28(x13831,x13833),f28(x13831,x13832))
% 13.24/13.46 [1384]~P15(x13841)+P10(x13841,x13842,x13843)+~P10(x13841,f12(x13841),x13843)+~P10(x13841,f28(x13841,x13843),f28(x13841,x13842))
% 13.24/13.46 [1385]~P15(x13851)+P9(x13851,x13852,x13853)+~P10(x13851,f12(x13851),x13853)+~P9(x13851,f28(x13851,x13853),f28(x13851,x13852))
% 13.24/13.46 [1404]E(x14041,x14042)+~P9(a2,x14043,x14042)+~P9(a2,x14043,x14041)+~E(f10(a2,x14041,x14043),f10(a2,x14042,x14043))
% 13.24/13.46 [1461]~P35(x14611)+~P10(x14611,f12(x14611),x14613)+~P10(x14611,f12(x14611),x14612)+P10(x14611,f12(x14611),f15(x14611,x14612,x14613))
% 13.24/13.46 [1465]~P35(x14651)+~P10(x14651,x14653,f12(x14651))+~P10(x14651,x14652,f12(x14651))+P10(x14651,f15(x14651,x14652,x14653),f12(x14651))
% 13.24/13.46 [1466]~P35(x14661)+~P10(x14661,x14663,f12(x14661))+~P9(x14661,x14662,f12(x14661))+P10(x14661,f15(x14661,x14662,x14663),f12(x14661))
% 13.24/13.46 [1467]~P35(x14671)+~P10(x14671,x14672,f12(x14671))+~P9(x14671,x14673,f12(x14671))+P10(x14671,f15(x14671,x14672,x14673),f12(x14671))
% 13.24/13.46 [1468]~P35(x14681)+~P9(x14681,x14683,f12(x14681))+~P9(x14681,x14682,f12(x14681))+P9(x14681,f15(x14681,x14682,x14683),f12(x14681))
% 13.24/13.46 [1702]~P9(a2,x17023,x17021)+P10(a2,x17021,x17022)+~P9(a2,x17023,x17022)+~P10(a2,f10(a2,x17021,x17023),f10(a2,x17022,x17023))
% 13.24/13.46 [1703]~P9(a2,x17033,x17031)+P9(a2,x17031,x17032)+~P9(a2,x17033,x17032)+~P9(a2,f10(a2,x17031,x17033),f10(a2,x17032,x17033))
% 13.24/13.46 [910]~P28(x9101)+~E(x9102,f12(x9101))+~E(x9103,f12(f72(x9101)))+E(f20(x9101,x9102,x9103),f12(f72(x9101)))
% 13.24/13.46 [980]~P54(x9802)+E(x9801,f12(x9802))+~E(f25(x9802,x9801,x9803),f12(f72(x9802)))+E(x9803,f12(f72(x9802)))
% 13.24/13.46 [1086]~P54(x10862)+~E(f21(x10862,x10863,x10861),f12(a2))+~E(f56(f17(x10862,x10861),x10863),f12(x10862))+E(x10861,f12(f72(x10862)))
% 13.24/13.46 [1125]~P50(x11251)+~P12(x11251,x11253)+~P12(x11251,x11252)+P12(x11251,f15(f72(x11251),x11252,x11253))
% 13.24/13.46 [1214]P12(x12142,x12141)+~P50(x12142)+~P12(x12142,f20(x12142,x12143,x12141))+E(x12141,f12(f72(x12142)))
% 13.24/13.46 [1247]~P50(x12473)+E(x12471,x12472)+~P9(f72(x12473),x12471,x12472)+P12(x12473,f10(f72(x12473),x12472,x12471))
% 13.24/13.46 [1265]~P50(x12651)+~P10(x12651,f12(x12651),x12652)+P12(x12651,f20(x12651,x12652,x12653))+~E(x12653,f12(f72(x12651)))
% 13.24/13.46 [1471]~P49(x14711)+~P9(a1,x14713,f30(x14711,x14712))+~P10(a1,f12(a1),x14713)+P9(a1,f30(x14711,f28(x14711,x14712)),f28(a1,x14713))
% 13.24/13.46 [1745]~P56(x17452)+E(x17451,f12(x17452))+E(x17453,f12(x17452))+E(f56(f56(f14(x17452),f56(f56(f14(x17452),f28(x17452,x17453)),f15(x17452,x17453,x17451))),f28(x17452,x17451)),f15(x17452,f28(x17452,x17453),f28(x17452,x17451)))
% 13.24/13.46 [1746]~P56(x17462)+E(x17461,f12(x17462))+E(x17463,f12(x17462))+E(f56(f56(f14(x17462),f56(f56(f14(x17462),f28(x17462,x17463)),f10(x17462,x17461,x17463))),f28(x17462,x17461)),f10(x17462,f28(x17462,x17463),f28(x17462,x17461)))
% 13.24/13.46 [1764]~P8(x17642)+E(x17641,f12(x17642))+E(x17643,f12(x17642))+E(f56(f56(f14(x17642),f56(f56(f14(x17642),f15(x17642,x17643,x17641)),f28(x17642,x17643))),f28(x17642,x17641)),f15(x17642,f28(x17642,x17643),f28(x17642,x17641)))
% 13.24/13.46 [924]~P68(x9242)+E(x9241,f12(x9242))+E(x9243,f12(x9242))+~E(f56(f56(f14(x9242),x9243),x9241),f12(x9242))
% 13.24/13.46 [925]~P79(x9252)+E(x9251,f12(x9252))+E(x9253,f12(x9252))+~E(f56(f56(f14(x9252),x9253),x9251),f12(x9252))
% 13.24/13.46 [1126]~P54(x11263)+E(x11261,x11262)+E(x11261,f13(x11263,x11262))+~E(f56(f56(f14(x11263),x11261),x11261),f56(f56(f14(x11263),x11262),x11262))
% 13.24/13.46 [1429]~P1(x14291)+~P10(x14291,f5(x14291),x14292)+~P10(a2,f12(a2),x14293)+P10(x14291,f5(x14291),f56(f56(f23(x14291),x14292),x14293))
% 13.24/13.46 [1441]~P61(x14411)+~P10(x14411,x14413,f12(x14411))+~P10(x14411,x14412,f12(x14411))+P10(x14411,f12(x14411),f56(f56(f14(x14411),x14412),x14413))
% 13.24/13.46 [1443]~P74(x14431)+~P9(x14431,x14433,f12(x14431))+~P9(x14431,x14432,f12(x14431))+P9(x14431,f12(x14431),f56(f56(f14(x14431),x14432),x14433))
% 13.24/13.46 [1444]~P61(x14441)+~P9(x14441,x14443,f12(x14441))+~P9(x14441,x14442,f12(x14441))+P9(x14441,f12(x14441),f56(f56(f14(x14441),x14442),x14443))
% 13.24/13.46 [1445]~P1(x14451)+~P10(x14451,f5(x14451),x14453)+~P10(x14451,f5(x14451),x14452)+P10(x14451,f5(x14451),f56(f56(f14(x14451),x14452),x14453))
% 13.24/13.46 [1446]~P67(x14461)+~P10(x14461,f12(x14461),x14463)+~P10(x14461,f12(x14461),x14462)+P10(x14461,f12(x14461),f56(f56(f14(x14461),x14462),x14463))
% 13.24/13.46 [1447]~P73(x14471)+~P9(x14471,f12(x14471),x14473)+~P9(x14471,f12(x14471),x14472)+P9(x14471,f12(x14471),f56(f56(f14(x14471),x14472),x14473))
% 13.24/13.46 [1448]~P74(x14481)+~P9(x14481,f12(x14481),x14483)+~P9(x14481,f12(x14481),x14482)+P9(x14481,f12(x14481),f56(f56(f14(x14481),x14482),x14483))
% 13.24/13.46 [1449]~P61(x14491)+~P9(x14491,f12(x14491),x14493)+~P9(x14491,f12(x14491),x14492)+P9(x14491,f12(x14491),f56(f56(f14(x14491),x14492),x14493))
% 13.24/13.46 [1451]~P67(x14511)+~P10(x14511,x14513,f12(x14511))+~P10(x14511,f12(x14511),x14512)+P10(x14511,f56(f56(f14(x14511),x14512),x14513),f12(x14511))
% 13.24/13.46 [1452]~P67(x14521)+~P10(x14521,x14522,f12(x14521))+~P10(x14521,f12(x14521),x14523)+P10(x14521,f56(f56(f14(x14521),x14522),x14523),f12(x14521))
% 13.24/13.46 [1455]~P73(x14551)+~P9(x14551,x14553,f12(x14551))+~P9(x14551,f12(x14551),x14552)+P9(x14551,f56(f56(f14(x14551),x14552),x14553),f12(x14551))
% 13.24/13.46 [1457]~P73(x14571)+~P9(x14571,x14572,f12(x14571))+~P9(x14571,f12(x14571),x14573)+P9(x14571,f56(f56(f14(x14571),x14572),x14573),f12(x14571))
% 13.24/13.46 [1458]~P61(x14581)+~P9(x14581,x14583,f12(x14581))+~P9(x14581,f12(x14581),x14582)+P9(x14581,f56(f56(f14(x14581),x14582),x14583),f12(x14581))
% 13.24/13.46 [1459]~P61(x14591)+~P9(x14591,x14592,f12(x14591))+~P9(x14591,f12(x14591),x14593)+P9(x14591,f56(f56(f14(x14591),x14592),x14593),f12(x14591))
% 13.24/13.46 [1475]~P61(x14751)+P9(x14751,x14752,f12(x14751))+P9(x14751,x14753,f12(x14751))+~P9(x14751,f56(f56(f14(x14751),x14753),x14752),f12(x14751))
% 13.24/13.46 [1476]~P61(x14761)+P9(x14761,x14762,f12(x14761))+P9(x14761,f12(x14761),x14763)+~P9(x14761,f12(x14761),f56(f56(f14(x14761),x14763),x14762))
% 13.24/13.46 [1477]~P61(x14771)+P9(x14771,x14772,f12(x14771))+P9(x14771,f12(x14771),x14773)+~P9(x14771,f12(x14771),f56(f56(f14(x14771),x14772),x14773))
% 13.24/13.46 [1478]~P61(x14781)+P9(x14781,f12(x14781),x14782)+P9(x14781,x14782,f12(x14781))+~P9(x14781,f12(x14781),f56(f56(f14(x14781),x14783),x14782))
% 13.24/13.46 [1479]~P61(x14791)+P9(x14791,f12(x14791),x14792)+P9(x14791,x14792,f12(x14791))+~P9(x14791,f12(x14791),f56(f56(f14(x14791),x14792),x14793))
% 13.24/13.46 [1480]~P61(x14801)+P9(x14801,f12(x14801),x14802)+P9(x14801,x14802,f12(x14801))+~P9(x14801,f56(f56(f14(x14801),x14803),x14802),f12(x14801))
% 13.24/13.46 [1481]~P61(x14811)+P9(x14811,f12(x14811),x14812)+P9(x14811,x14812,f12(x14811))+~P9(x14811,f56(f56(f14(x14811),x14812),x14813),f12(x14811))
% 13.24/13.46 [1482]~P61(x14821)+P9(x14821,f12(x14821),x14822)+P9(x14821,f12(x14821),x14823)+~P9(x14821,f56(f56(f14(x14821),x14822),x14823),f12(x14821))
% 13.24/13.46 [1523]~P67(x15231)+P10(x15231,f12(x15231),x15232)+~P10(x15231,f12(x15231),x15233)+~P10(x15231,f12(x15231),f56(f56(f14(x15231),x15233),x15232))
% 13.24/13.46 [1524]~P67(x15241)+P10(x15241,f12(x15241),x15242)+~P10(x15241,f12(x15241),x15243)+~P10(x15241,f12(x15241),f56(f56(f14(x15241),x15242),x15243))
% 13.24/13.46 [1773]~P56(x17732)+E(x17731,f12(x17732))+E(x17733,f12(x17732))+E(f13(x17732,f56(f56(f14(x17732),f56(f56(f14(x17732),f28(x17732,x17733)),f10(x17732,x17733,x17731))),f28(x17732,x17731))),f10(x17732,f28(x17732,x17733),f28(x17732,x17731)))
% 13.24/13.46 [1205]~P50(x12051)+~P12(x12051,x12053)+~P12(x12051,x12052)+P12(x12051,f56(f56(f14(f72(x12051)),x12052),x12053))
% 13.24/13.46 [1296]~P56(x12962)+E(x12961,f12(x12962))+E(x12963,f12(x12962))+E(f56(f56(f14(x12962),f28(x12962,x12961)),f28(x12962,x12963)),f28(x12962,f56(f56(f14(x12962),x12963),x12961)))
% 13.24/13.46 [1332]~P61(x13321)+~E(x13323,f12(x13321))+~E(x13322,f12(x13321))+E(f15(x13321,f56(f56(f14(x13321),x13322),x13322),f56(f56(f14(x13321),x13323),x13323)),f12(x13321))
% 13.24/13.46 [1546]~P72(x15461)+~P9(x15461,x15462,f12(x15461))+~P9(x15461,x15463,f12(x15461))+E(f56(f56(f14(x15461),f9(x15461,x15462)),f9(x15461,x15463)),f9(x15461,f56(f56(f14(x15461),x15462),x15463)))
% 13.24/13.46 [1547]~P72(x15471)+~P9(x15471,x15472,f12(x15471))+~P9(x15471,f12(x15471),x15473)+E(f56(f56(f14(x15471),f9(x15471,x15472)),f9(x15471,x15473)),f9(x15471,f56(f56(f14(x15471),x15472),x15473)))
% 13.24/13.46 [1548]~P72(x15481)+~P9(x15481,x15483,f12(x15481))+~P9(x15481,f12(x15481),x15482)+E(f56(f56(f14(x15481),f9(x15481,x15482)),f9(x15481,x15483)),f9(x15481,f56(f56(f14(x15481),x15482),x15483)))
% 13.24/13.46 [1549]~P72(x15491)+~P9(x15491,f12(x15491),x15492)+~P9(x15491,f12(x15491),x15493)+E(f56(f56(f14(x15491),f9(x15491,x15492)),f9(x15491,x15493)),f9(x15491,f56(f56(f14(x15491),x15492),x15493)))
% 13.24/13.46 [1589]~P10(a3,x15892,x15893)+~P10(a3,f12(a3),x15893)+P9(a3,f5(a3),x15891)+~E(f15(a3,x15892,f56(f56(f14(a3),x15893),x15891)),x15893)
% 13.24/13.46 [1592]~P10(a3,f12(a3),x15923)+~P9(a3,f12(a3),x15922)+P9(a3,x15921,f5(a3))+~E(f15(a3,x15922,f56(f56(f14(a3),x15923),x15921)),x15923)
% 13.24/13.46 [1690]~P61(x16901)+~E(x16903,f12(x16901))+~E(x16902,f12(x16901))+P9(x16901,f15(x16901,f56(f56(f14(x16901),x16902),x16902),f56(f56(f14(x16901),x16903),x16903)),f12(x16901))
% 13.24/13.46 [1710]~P1(x17101)+~P10(x17101,x17102,f5(x17101))+~P10(x17101,f12(x17101),x17102)+P10(x17101,f56(f56(f14(x17101),x17102),f56(f56(f23(x17101),x17102),x17103)),f56(f56(f23(x17101),x17102),x17103))
% 13.24/13.46 [1723]~P10(a3,x17232,x17233)+~P10(a3,f12(a3),x17233)+P9(a3,f12(a3),x17231)+~P9(a3,f12(a3),f15(a3,f56(f56(f14(a3),x17233),x17231),x17232))
% 13.24/13.46 [1724]P9(a3,x17241,f12(a3))+~P10(a3,f12(a3),x17242)+~P9(a3,f12(a3),x17243)+~P10(a3,f15(a3,f56(f56(f14(a3),x17242),x17241),x17243),f12(a3))
% 13.24/13.46 [1740]~P61(x17402)+~E(x17401,f12(x17402))+~E(x17403,f12(x17402))+~P10(x17402,f12(x17402),f15(x17402,f56(f56(f14(x17402),x17403),x17403),f56(f56(f14(x17402),x17401),x17401)))
% 13.24/13.46 [1230]~P44(x12301)+~P10(x12301,x12304,x12303)+P10(x12301,x12302,x12303)+~P10(x12301,x12302,x12304)
% 13.24/13.46 [1231]~P44(x12311)+~P9(x12311,x12314,x12313)+P10(x12311,x12312,x12313)+~P10(x12311,x12312,x12314)
% 13.24/13.46 [1232]~P44(x12321)+~P9(x12321,x12322,x12324)+P10(x12321,x12322,x12323)+~P10(x12321,x12324,x12323)
% 13.24/13.46 [1233]~P39(x12331)+~P10(x12331,x12332,x12334)+P10(x12331,x12332,x12333)+~P10(x12331,x12334,x12333)
% 13.24/13.46 [1234]~P39(x12341)+~P9(x12341,x12342,x12344)+P10(x12341,x12342,x12343)+~P10(x12341,x12344,x12343)
% 13.24/13.46 [1235]~P39(x12351)+~P9(x12351,x12354,x12353)+P10(x12351,x12352,x12353)+~P10(x12351,x12352,x12354)
% 13.24/13.46 [1236]~P44(x12361)+~P9(x12361,x12364,x12363)+P9(x12361,x12362,x12363)+~P9(x12361,x12362,x12364)
% 13.24/13.46 [1237]~P39(x12371)+~P9(x12371,x12372,x12374)+P9(x12371,x12372,x12373)+~P9(x12371,x12374,x12373)
% 13.24/13.46 [1238]~P58(x12381)+~P13(x12381,x12382,x12384)+P13(x12381,x12382,x12383)+~P13(x12381,x12384,x12383)
% 13.24/13.46 [1206]~P44(x12061)+~P14(x12061,x12062)+~P9(a2,x12064,x12063)+P9(x12061,f56(x12062,x12063),f56(x12062,x12064))
% 13.24/13.46 [1337]~P40(x13372)+P9(f77(x13371,x13372),x13374,x13373)+~P9(f77(x13371,x13372),x13373,x13374)+P10(f77(x13371,x13372),x13373,x13374)
% 13.24/13.46 [1410]~P58(x14101)+~P13(x14101,x14102,x14104)+~P13(x14101,x14102,x14103)+P13(x14101,x14102,f15(x14101,x14103,x14104))
% 13.24/13.46 [1411]~P53(x14111)+~P13(x14111,x14112,x14114)+~P13(x14111,x14112,x14113)+P13(x14111,x14112,f10(x14111,x14113,x14114))
% 13.24/13.46 [1422]~P1(x14221)+~P10(x14221,x14222,x14224)+~P10(x14221,f12(x14221),x14223)+P10(x14221,x14222,f15(x14221,x14223,x14224))
% 13.24/13.46 [1423]~P35(x14231)+~P10(x14231,x14232,x14234)+~P9(x14231,f12(x14231),x14233)+P10(x14231,x14232,f15(x14231,x14233,x14234))
% 13.24/13.46 [1424]~P35(x14241)+~P9(x14241,x14242,x14244)+~P10(x14241,f12(x14241),x14243)+P10(x14241,x14242,f15(x14241,x14243,x14244))
% 13.24/13.46 [1425]~P35(x14251)+~P9(x14251,x14252,x14253)+~P9(x14251,f12(x14251),x14254)+P9(x14251,x14252,f15(x14251,x14253,x14254))
% 13.24/13.46 [1426]~P35(x14261)+~P9(x14261,x14262,x14264)+~P9(x14261,f12(x14261),x14263)+P9(x14261,x14262,f15(x14261,x14263,x14264))
% 13.24/13.46 [1578]~P48(x15782)+E(x15781,f12(x15782))+~P9(a1,x15783,f12(a1))+~P9(a1,f30(x15782,x15781),f56(f56(f14(a1),x15783),f30(x15782,x15784)))
% 13.24/13.46 [1728]~P50(x17281)+~P10(x17281,x17282,f15(x17281,x17283,x17284))+~P10(x17281,f10(x17281,x17283,x17284),x17282)+P10(x17281,f9(x17281,f10(x17281,x17282,x17283)),x17284)
% 13.24/13.46 [1307]~P1(x13073)+E(x13071,x13072)+~P10(x13073,f5(x13073),x13074)+~E(f56(f56(f23(x13073),x13074),x13071),f56(f56(f23(x13073),x13074),x13072))
% 13.24/13.46 [1551]~P1(x15511)+~P10(a2,x15513,x15514)+~P10(x15511,f5(x15511),x15512)+P10(x15511,f56(f56(f23(x15511),x15512),x15513),f56(f56(f23(x15511),x15512),x15514))
% 13.24/13.46 [1552]~P1(x15521)+~P9(a2,x15523,x15524)+~P10(x15521,f5(x15521),x15522)+P9(x15521,f56(f56(f23(x15521),x15522),x15523),f56(f56(f23(x15521),x15522),x15524))
% 13.24/13.46 [1553]~P1(x15531)+~P9(a2,x15533,x15534)+~P9(x15531,f5(x15531),x15532)+P9(x15531,f56(f56(f23(x15531),x15532),x15533),f56(f56(f23(x15531),x15532),x15534))
% 13.24/13.46 [1562]~P61(x15621)+~P10(x15621,x15624,x15622)+~P10(x15621,x15623,f12(x15621))+P10(x15621,f56(f56(f14(x15621),x15622),x15623),f56(f56(f14(x15621),x15624),x15623))
% 13.24/13.46 [1563]~P61(x15631)+~P10(x15631,x15634,x15633)+~P10(x15631,x15632,f12(x15631))+P10(x15631,f56(f56(f14(x15631),x15632),x15633),f56(f56(f14(x15631),x15632),x15634))
% 13.24/13.46 [1564]~P74(x15641)+~P9(x15641,x15644,x15643)+~P9(x15641,x15642,f12(x15641))+P9(x15641,f56(f56(f14(x15641),x15642),x15643),f56(f56(f14(x15641),x15642),x15644))
% 13.24/13.46 [1565]~P61(x15651)+~P9(x15651,x15654,x15653)+~P10(x15651,x15652,f12(x15651))+P9(x15651,f56(f56(f14(x15651),x15652),x15653),f56(f56(f14(x15651),x15652),x15654))
% 13.24/13.46 [1566]~P74(x15661)+~P9(x15661,x15664,x15662)+~P9(x15661,x15663,f12(x15661))+P9(x15661,f56(f56(f14(x15661),x15662),x15663),f56(f56(f14(x15661),x15664),x15663))
% 13.24/13.46 [1568]~P67(x15681)+~P10(x15681,x15683,x15684)+~P10(x15681,f12(x15681),x15682)+P10(x15681,f56(f56(f14(x15681),x15682),x15683),f56(f56(f14(x15681),x15682),x15684))
% 13.24/13.46 [1569]~P60(x15691)+~P10(x15691,x15693,x15694)+~P10(x15691,f12(x15691),x15692)+P10(x15691,f56(f56(f14(x15691),x15692),x15693),f56(f56(f14(x15691),x15692),x15694))
% 13.24/13.46 [1570]~P61(x15701)+~P10(x15701,x15702,x15704)+~P10(x15701,f12(x15701),x15703)+P10(x15701,f56(f56(f14(x15701),x15702),x15703),f56(f56(f14(x15701),x15704),x15703))
% 13.24/13.46 [1571]~P67(x15711)+~P10(x15711,x15712,x15714)+~P10(x15711,f12(x15711),x15713)+P10(x15711,f56(f56(f14(x15711),x15712),x15713),f56(f56(f14(x15711),x15714),x15713))
% 13.24/13.46 [1572]~P61(x15721)+~P10(x15721,x15723,x15724)+~P10(x15721,f12(x15721),x15722)+P10(x15721,f56(f56(f14(x15721),x15722),x15723),f56(f56(f14(x15721),x15722),x15724))
% 13.24/13.46 [1573]~P77(x15731)+~P9(x15731,x15733,x15734)+~P9(x15731,f12(x15731),x15732)+P9(x15731,f56(f56(f14(x15731),x15732),x15733),f56(f56(f14(x15731),x15732),x15734))
% 13.24/13.46 [1574]~P75(x15741)+~P9(x15741,x15743,x15744)+~P9(x15741,f12(x15741),x15742)+P9(x15741,f56(f56(f14(x15741),x15742),x15743),f56(f56(f14(x15741),x15742),x15744))
% 13.24/13.46 [1575]~P61(x15751)+~P9(x15751,x15753,x15754)+~P10(x15751,f12(x15751),x15752)+P9(x15751,f56(f56(f14(x15751),x15752),x15753),f56(f56(f14(x15751),x15752),x15754))
% 13.24/13.46 [1576]~P77(x15761)+~P9(x15761,x15762,x15764)+~P9(x15761,f12(x15761),x15763)+P9(x15761,f56(f56(f14(x15761),x15762),x15763),f56(f56(f14(x15761),x15764),x15763))
% 13.24/13.46 [1577]~P1(x15771)+~P9(x15771,x15772,x15774)+~P9(x15771,f12(x15771),x15772)+P9(x15771,f56(f56(f23(x15771),x15772),x15773),f56(f56(f23(x15771),x15774),x15773))
% 13.24/13.46 [1640]P10(x16401,x16403,x16402)+~P61(x16401)+P10(x16401,x16402,x16403)+~P10(x16401,f56(f56(f14(x16401),x16404),x16402),f56(f56(f14(x16401),x16404),x16403))
% 13.24/13.46 [1641]P10(x16411,x16413,x16412)+~P61(x16411)+P10(x16411,x16412,x16413)+~P10(x16411,f56(f56(f14(x16411),x16412),x16414),f56(f56(f14(x16411),x16413),x16414))
% 13.24/13.46 [1644]~P61(x16441)+P10(x16441,x16442,x16443)+P10(x16441,x16444,f12(x16441))+~P10(x16441,f56(f56(f14(x16441),x16442),x16444),f56(f56(f14(x16441),x16443),x16444))
% 13.24/13.46 [1645]~P61(x16451)+P10(x16451,x16452,x16453)+P10(x16451,x16454,f12(x16451))+~P10(x16451,f56(f56(f14(x16451),x16454),x16452),f56(f56(f14(x16451),x16454),x16453))
% 13.24/13.46 [1646]~P61(x16461)+P10(x16461,x16462,x16463)+P10(x16461,f12(x16461),x16464)+~P10(x16461,f56(f56(f14(x16461),x16464),x16463),f56(f56(f14(x16461),x16464),x16462))
% 13.24/13.46 [1647]~P61(x16471)+P10(x16471,x16472,x16473)+P10(x16471,f12(x16471),x16474)+~P10(x16471,f56(f56(f14(x16471),x16473),x16474),f56(f56(f14(x16471),x16472),x16474))
% 13.24/13.46 [1658]~P61(x16581)+P10(x16581,f12(x16581),x16582)+P10(x16581,x16582,f12(x16581))+~P10(x16581,f56(f56(f14(x16581),x16583),x16582),f56(f56(f14(x16581),x16584),x16582))
% 13.24/13.46 [1659]~P61(x16591)+P10(x16591,f12(x16591),x16592)+P10(x16591,x16592,f12(x16591))+~P10(x16591,f56(f56(f14(x16591),x16592),x16593),f56(f56(f14(x16591),x16592),x16594))
% 13.24/13.46 [1670]~P1(x16703)+P10(a2,x16701,x16702)+~P10(x16703,f5(x16703),x16704)+~P10(x16703,f56(f56(f23(x16703),x16704),x16701),f56(f56(f23(x16703),x16704),x16702))
% 13.24/13.46 [1672]~P1(x16723)+P9(a2,x16721,x16722)+~P10(x16723,f5(x16723),x16724)+~P9(x16723,f56(f56(f23(x16723),x16724),x16721),f56(f56(f23(x16723),x16724),x16722))
% 13.24/13.46 [1673]~P61(x16731)+P10(x16731,x16732,x16733)+~P10(x16731,x16734,f12(x16731))+~P10(x16731,f56(f56(f14(x16731),x16734),x16733),f56(f56(f14(x16731),x16734),x16732))
% 13.24/13.46 [1674]~P61(x16741)+P9(x16741,x16742,x16743)+~P10(x16741,x16744,f12(x16741))+~P9(x16741,f56(f56(f14(x16741),x16744),x16743),f56(f56(f14(x16741),x16744),x16742))
% 13.24/13.46 [1675]~P61(x16751)+P10(x16751,x16752,x16753)+~P10(x16751,f12(x16751),x16754)+~P10(x16751,f56(f56(f14(x16751),x16754),x16752),f56(f56(f14(x16751),x16754),x16753))
% 13.24/13.46 [1676]~P67(x16761)+P10(x16761,x16762,x16763)+~P9(x16761,f12(x16761),x16764)+~P10(x16761,f56(f56(f14(x16761),x16764),x16762),f56(f56(f14(x16761),x16764),x16763))
% 13.24/13.46 [1677]~P66(x16771)+P10(x16771,x16772,x16773)+~P9(x16771,f12(x16771),x16774)+~P10(x16771,f56(f56(f14(x16771),x16774),x16772),f56(f56(f14(x16771),x16774),x16773))
% 13.24/13.46 [1678]~P1(x16781)+P10(x16781,x16782,x16783)+~P9(x16781,f12(x16781),x16783)+~P10(x16781,f56(f56(f23(x16781),x16782),x16784),f56(f56(f23(x16781),x16783),x16784))
% 13.24/13.46 [1679]~P67(x16791)+P10(x16791,x16792,x16793)+~P9(x16791,f12(x16791),x16794)+~P10(x16791,f56(f56(f14(x16791),x16792),x16794),f56(f56(f14(x16791),x16793),x16794))
% 13.24/13.46 [1680]~P66(x16801)+P10(x16801,x16802,x16803)+~P9(x16801,f12(x16801),x16804)+~P10(x16801,f56(f56(f14(x16801),x16802),x16804),f56(f56(f14(x16801),x16803),x16804))
% 13.24/13.46 [1681]~P61(x16811)+P9(x16811,x16812,x16813)+~P10(x16811,f12(x16811),x16814)+~P9(x16811,f56(f56(f14(x16811),x16814),x16812),f56(f56(f14(x16811),x16814),x16813))
% 13.24/13.46 [1682]~P67(x16821)+P9(x16821,x16822,x16823)+~P10(x16821,f12(x16821),x16824)+~P9(x16821,f56(f56(f14(x16821),x16824),x16822),f56(f56(f14(x16821),x16824),x16823))
% 13.24/13.46 [1683]~P67(x16831)+P9(x16831,x16832,x16833)+~P10(x16831,f12(x16831),x16834)+~P9(x16831,f56(f56(f14(x16831),x16832),x16834),f56(f56(f14(x16831),x16833),x16834))
% 13.24/13.46 [1732]~P10(a1,f12(a1),x17324)+~P10(a1,f12(a1),x17322)+P10(a1,f56(f56(f14(a1),x17321),f28(a1,x17322)),f56(f56(f14(a1),x17323),f28(a1,x17324)))+~P10(a1,f56(f56(f14(a1),x17324),x17321),f56(f56(f14(a1),x17322),x17323))
% 13.24/13.46 [1741]~P10(a1,f12(a1),x17413)+~P10(a1,f12(a1),x17411)+~P10(a1,f56(f56(f14(a1),x17413),x17412),f56(f56(f14(a1),x17411),x17414))+P10(a1,f56(f56(f14(a1),f28(a1,x17411)),x17412),f56(f56(f14(a1),f28(a1,x17413)),x17414))
% 13.24/13.46 [1694]~P78(x16943)+~P59(x16943)+P82(f56(x16941,f65(x16942,x16941,x16943)))+~P82(f56(x16941,f56(f56(f14(x16943),x16942),x16944)))
% 13.24/13.46 [1725]~P78(x17251)+~P59(x17251)+P13(x17251,x17252,f15(x17251,f65(x17252,x17253,x17251),f12(x17251)))+~P82(f56(x17253,f56(f56(f14(x17251),x17252),x17254)))
% 13.24/13.46 [1774]~P10(a1,f12(a1),x17744)+~P10(a1,f30(a4,f10(a4,x17742,x17743)),f63(x17741,x17743,x17744))+~P10(a1,f12(a1),f30(a4,f10(a4,x17742,x17743)))+P10(a1,f30(a4,f10(a4,f56(f17(a4,x17741),x17742),f56(f17(a4,x17741),x17743))),x17744)
% 13.24/13.46 [1124]~P16(x11245)+E(x11241,x11242)+~E(x11243,x11244)+~E(f10(x11245,x11243,x11244),f10(x11245,x11241,x11242))
% 13.24/13.46 [1371]~P31(x13711)+~P10(x13711,x13714,x13715)+P10(x13711,x13712,x13713)+~E(f10(x13711,x13714,x13715),f10(x13711,x13712,x13713))
% 13.24/13.46 [1373]~P31(x13731)+~P9(x13731,x13734,x13735)+P9(x13731,x13732,x13733)+~E(f10(x13731,x13734,x13735),f10(x13731,x13732,x13733))
% 13.24/13.46 [1554]~P34(x15541)+~P10(x15541,x15543,x15545)+~P10(x15541,x15542,x15544)+P10(x15541,f15(x15541,x15542,x15543),f15(x15541,x15544,x15545))
% 13.24/13.46 [1555]~P34(x15551)+~P10(x15551,x15553,x15555)+~P9(x15551,x15552,x15554)+P10(x15551,f15(x15551,x15552,x15553),f15(x15551,x15554,x15555))
% 13.24/13.46 [1556]~P34(x15561)+~P10(x15561,x15562,x15564)+~P9(x15561,x15563,x15565)+P10(x15561,f15(x15561,x15562,x15563),f15(x15561,x15564,x15565))
% 13.24/13.46 [1557]~P33(x15571)+~P9(x15571,x15573,x15575)+~P9(x15571,x15572,x15574)+P9(x15571,f15(x15571,x15572,x15573),f15(x15571,x15574,x15575))
% 13.24/13.46 [1708]~P48(x17081)+~P10(a1,f30(x17081,x17083),x17085)+~P10(a1,f30(x17081,x17082),x17084)+P10(a1,f30(x17081,f15(x17081,x17082,x17083)),f15(a1,x17084,x17085))
% 13.24/13.46 [1714]~P50(x17141)+~P10(x17141,f9(x17141,x17142),x17144)+~P10(x17141,f9(x17141,x17143),x17145)+P10(x17141,f56(f56(f14(x17141),f9(x17141,x17142)),f9(x17141,x17143)),f56(f56(f14(x17141),x17144),x17145))
% 13.24/13.46 [1695]~P46(x16951)+~P10(a1,f30(x16951,x16953),x16955)+~P10(a1,f30(x16951,x16952),x16954)+P10(a1,f30(x16951,f56(f56(f14(x16951),x16952),x16953)),f56(f56(f14(a1),x16954),x16955))
% 13.24/13.46 [1730]~P81(x17305)+E(x17301,x17302)+E(x17303,x17304)+~E(f15(x17305,f56(f56(f14(x17305),x17303),x17301),f56(f56(f14(x17305),x17304),x17302)),f15(x17305,f56(f56(f14(x17305),x17303),x17302),f56(f56(f14(x17305),x17304),x17301)))
% 13.24/13.46 [1757]~E(f30(a4,x17571),f5(a1))+P10(a1,f30(a4,f10(a4,x17571,a7)),f5(a1))+P10(a1,f30(a4,f15(a4,x17571,a7)),f5(a1))+P10(a1,f30(a4,f15(a4,x17571,f5(a4))),f5(a1))+P10(a1,f30(a4,f10(a4,x17571,f5(a4))),f5(a1))
% 13.24/13.46 [767]~P56(x7673)+E(x7671,x7672)+~E(f28(x7673,x7671),f28(x7673,x7672))+E(x7672,f12(x7673))+E(x7671,f12(x7673))
% 13.24/13.46 [1342]~P35(x13422)+~P9(x13422,f12(x13422),x13423)+~P9(x13422,f12(x13422),x13421)+~E(f15(x13422,x13423,x13421),f12(x13422))+E(x13421,f12(x13422))
% 13.24/13.46 [1343]~P35(x13432)+~P9(x13432,f12(x13432),x13433)+~P9(x13432,f12(x13432),x13431)+~E(f15(x13432,x13431,x13433),f12(x13432))+E(x13431,f12(x13432))
% 13.24/13.46 [1579]~P50(x15791)+~P9(x15791,x15792,f5(x15791))+~P9(x15791,f12(x15791),x15792)+~P9(x15791,f12(x15791),x15793)+P9(x15791,f56(f56(f14(x15791),x15792),x15793),x15793)
% 13.24/13.46 [1580]~P50(x15801)+~P9(x15801,x15803,f5(x15801))+~P9(x15801,f12(x15801),x15803)+~P9(x15801,f12(x15801),x15802)+P9(x15801,f56(f56(f14(x15801),x15802),x15803),x15802)
% 13.24/13.46 [1660]~P1(x16601)+~P10(x16601,x16602,x16604)+~P9(x16601,f12(x16601),x16602)+~P10(a2,f12(a2),x16603)+P10(x16601,f56(f56(f23(x16601),x16602),x16603),f56(f56(f23(x16601),x16604),x16603))
% 13.24/13.46 [1661]~P1(x16611)+~P10(a2,x16614,x16613)+~P10(x16611,x16612,f5(x16611))+~P10(x16611,f12(x16611),x16612)+P10(x16611,f56(f56(f23(x16611),x16612),x16613),f56(f56(f23(x16611),x16612),x16614))
% 13.24/13.46 [1662]~P1(x16621)+~P9(a2,x16624,x16623)+~P9(x16621,x16622,f5(x16621))+~P9(x16621,f12(x16621),x16622)+P9(x16621,f56(f56(f23(x16621),x16622),x16623),f56(f56(f23(x16621),x16622),x16624))
% 13.24/13.46 [1742]~P78(x17422)+~P59(x17422)+~P13(x17422,x17423,f15(x17422,x17424,f12(x17422)))+~P82(f56(x17421,x17424))+P82(f56(x17421,f56(f56(f14(x17422),x17423),f66(x17423,x17421,x17422))))
% 13.24/13.46 [1747]~P48(x17474)+~P40(x17471)+~P9(x17471,x17472,x17475)+P9(x17471,x17472,f53(x17473,x17472,x17471,x17474))+P10(a1,f30(x17474,f56(x17473,x17475)),f15(a1,f5(a1),f30(x17474,f56(x17473,x17472))))
% 13.24/13.46 [1762]P9(a3,x17621,x17622)+~P10(a3,x17623,x17624)+~P10(a3,x17623,x17625)+~P9(a3,x17624,f12(a3))+~P9(a3,f15(a3,f56(f56(f14(a3),x17623),x17622),x17625),f15(a3,f56(f56(f14(a3),x17623),x17621),x17624))
% 13.24/13.46 [1763]P9(a3,x17631,x17632)+~P10(a3,x17633,x17634)+~P10(a3,x17635,x17634)+~P9(a3,f12(a3),x17635)+~P9(a3,f15(a3,f56(f56(f14(a3),x17634),x17631),x17635),f15(a3,f56(f56(f14(a3),x17634),x17632),x17633))
% 13.24/13.46 [1803]~P48(x18031)+~P9(x18035,x18034,x18033)+~P40(x18035)+P10(a1,f30(x18031,f56(x18032,x18033)),f15(a1,f5(a1),f30(x18031,f56(x18032,x18034))))+~P10(a1,f30(x18031,f10(x18031,f56(x18032,x18034),f56(x18032,f53(x18032,x18034,x18035,x18031)))),f5(a1))
% 13.24/13.46 [1630]~P81(x16304)+E(x16301,x16302)+~E(x16305,x16306)+E(x16303,f12(x16304))+~E(f15(x16304,x16305,f56(f56(f14(x16304),x16303),x16301)),f15(x16304,x16306,f56(f56(f14(x16304),x16303),x16302)))
% 13.24/13.46 [1754]~P52(x17541)+~P59(x17541)+~P13(x17541,x17542,x17545)+~P13(x17541,x17542,f15(x17541,x17543,x17546))+P13(x17541,x17542,f15(x17541,f10(x17541,x17543,f56(f56(f14(x17541),x17544),x17545)),x17546))
% 13.24/13.46 [1769]~P52(x17691)+~P59(x17691)+~P13(x17691,x17692,x17695)+P13(x17691,x17692,f15(x17691,x17693,x17694))+~P13(x17691,x17692,f15(x17691,f10(x17691,x17693,f56(f56(f14(x17691),x17696),x17695)),x17694))
% 13.24/13.46 [1317]~P35(x13171)+~P9(x13171,f12(x13171),x13173)+~P9(x13171,f12(x13171),x13172)+~E(x13173,f12(x13171))+~E(x13172,f12(x13171))+E(f15(x13171,x13172,x13173),f12(x13171))
% 13.24/13.46 [977]~P3(x9772)+~P63(x9772)+~P68(x9772)+~P69(x9772)+E(x9771,f12(x9772))+~E(f56(f56(f23(x9772),x9771),x9773),f12(x9772))
% 13.24/13.46 [978]~P3(x9782)+~P63(x9782)+~P68(x9782)+~P69(x9782)+~E(x9781,f12(a2))+~E(f56(f56(f23(x9782),x9783),x9781),f12(x9782))
% 13.24/13.46 [1586]~P1(x15863)+E(x15861,x15862)+~P9(x15863,f12(x15863),x15862)+~P9(x15863,f12(x15863),x15861)+~P10(a2,f12(a2),x15864)+~E(f56(f56(f23(x15863),x15861),x15864),f56(f56(f23(x15863),x15862),x15864))
% 13.24/13.46 [1696]~P67(x16961)+~P10(x16961,x16963,x16965)+~P10(x16961,x16962,x16964)+~P10(x16961,f12(x16961),x16964)+~P9(x16961,f12(x16961),x16963)+P10(x16961,f56(f56(f14(x16961),x16962),x16963),f56(f56(f14(x16961),x16964),x16965))
% 13.24/13.46 [1697]~P67(x16971)+~P10(x16971,x16973,x16975)+~P10(x16971,x16972,x16974)+~P9(x16971,f12(x16971),x16973)+~P9(x16971,f12(x16971),x16972)+P10(x16971,f56(f56(f14(x16971),x16972),x16973),f56(f56(f14(x16971),x16974),x16975))
% 13.24/13.46 [1698]~P67(x16981)+~P10(x16981,x16983,x16985)+~P9(x16981,x16982,x16984)+~P10(x16981,f12(x16981),x16982)+~P9(x16981,f12(x16981),x16983)+P10(x16981,f56(f56(f14(x16981),x16982),x16983),f56(f56(f14(x16981),x16984),x16985))
% 13.24/13.46 [1699]~P67(x16991)+~P10(x16991,x16992,x16994)+~P9(x16991,x16993,x16995)+~P10(x16991,f12(x16991),x16993)+~P9(x16991,f12(x16991),x16992)+P10(x16991,f56(f56(f14(x16991),x16992),x16993),f56(f56(f14(x16991),x16994),x16995))
% 13.24/13.46 [1700]~P77(x17001)+~P9(x17001,x17003,x17005)+~P9(x17001,x17002,x17004)+~P9(x17001,f12(x17001),x17003)+~P9(x17001,f12(x17001),x17004)+P9(x17001,f56(f56(f14(x17001),x17002),x17003),f56(f56(f14(x17001),x17004),x17005))
% 13.24/13.46 [1701]~P77(x17011)+~P9(x17011,x17013,x17015)+~P9(x17011,x17012,x17014)+~P9(x17011,f12(x17011),x17013)+~P9(x17011,f12(x17011),x17012)+P9(x17011,f56(f56(f14(x17011),x17012),x17013),f56(f56(f14(x17011),x17014),x17015))
% 13.24/13.46 [904]~P3(x9042)+~P63(x9042)+~P68(x9042)+~P69(x9042)+~E(x9043,f12(x9042))+E(x9041,f12(a2))+E(f56(f56(f23(x9042),x9043),x9041),f12(x9042))
% 13.24/13.46 [1743]~P64(x17431)+~P10(x17431,x17435,x17436)+~P10(x17431,x17433,x17436)+~P9(x17431,f12(x17431),x17434)+~P9(x17431,f12(x17431),x17432)+~E(f15(x17431,x17432,x17434),f5(x17431))+P10(x17431,f15(x17431,f56(f56(f14(x17431),x17432),x17433),f56(f56(f14(x17431),x17434),x17435)),x17436)
% 13.24/13.46 [1744]~P65(x17441)+~P9(x17441,x17445,x17446)+~P9(x17441,x17443,x17446)+~P9(x17441,f12(x17441),x17444)+~P9(x17441,f12(x17441),x17442)+~E(f15(x17441,x17442,x17444),f5(x17441))+P9(x17441,f15(x17441,f56(f56(f14(x17441),x17442),x17443),f56(f56(f14(x17441),x17444),x17445)),x17446)
% 13.24/13.46 [1766]~P10(a3,x17666,x17665)+~P9(a3,x17665,x17663)+P9(a3,x17661,x17662)+~P10(a3,f12(a3),x17665)+~P9(a3,f12(a3),x17664)+~P9(a3,f12(a3),f15(a3,f56(f56(f14(a3),x17665),x17662),x17666))+~E(f15(a3,f56(f56(f14(a3),x17663),x17661),x17664),f15(a3,f56(f56(f14(a3),x17665),x17662),x17666))
% 13.24/13.46 [1767]~P10(a3,x17674,x17673)+~P9(a3,x17675,x17673)+P9(a3,x17671,x17672)+~P10(a3,f12(a3),x17675)+~P9(a3,f12(a3),x17676)+~P10(a3,f15(a3,f56(f56(f14(a3),x17675),x17671),x17676),f12(a3))+~E(f15(a3,f56(f56(f14(a3),x17673),x17672),x17674),f15(a3,f56(f56(f14(a3),x17675),x17671),x17676))
% 13.24/13.46 %EqnAxiom
% 13.24/13.46 [1]E(x11,x11)
% 13.24/13.46 [2]E(x22,x21)+~E(x21,x22)
% 13.24/13.46 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 13.24/13.46 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 13.24/13.46 [5]~E(x51,x52)+E(f11(x51),f11(x52))
% 13.24/13.46 [6]~E(x61,x62)+E(f30(x61,x63),f30(x62,x63))
% 13.24/13.46 [7]~E(x71,x72)+E(f30(x73,x71),f30(x73,x72))
% 13.24/13.46 [8]~E(x81,x82)+E(f12(x81),f12(x82))
% 13.24/13.46 [9]~E(x91,x92)+E(f56(x91,x93),f56(x92,x93))
% 13.24/13.46 [10]~E(x101,x102)+E(f56(x103,x101),f56(x103,x102))
% 13.24/13.46 [11]~E(x111,x112)+E(f72(x111),f72(x112))
% 13.24/13.46 [12]~E(x121,x122)+E(f10(x121,x123,x124),f10(x122,x123,x124))
% 13.24/13.46 [13]~E(x131,x132)+E(f10(x133,x131,x134),f10(x133,x132,x134))
% 13.24/13.46 [14]~E(x141,x142)+E(f10(x143,x144,x141),f10(x143,x144,x142))
% 13.24/13.46 [15]~E(x151,x152)+E(f27(x151),f27(x152))
% 13.24/13.46 [16]~E(x161,x162)+E(f14(x161),f14(x162))
% 13.24/13.46 [17]~E(x171,x172)+E(f15(x171,x173,x174),f15(x172,x173,x174))
% 13.24/13.46 [18]~E(x181,x182)+E(f15(x183,x181,x184),f15(x183,x182,x184))
% 13.24/13.46 [19]~E(x191,x192)+E(f15(x193,x194,x191),f15(x193,x194,x192))
% 13.24/13.46 [20]~E(x201,x202)+E(f13(x201,x203),f13(x202,x203))
% 13.24/13.46 [21]~E(x211,x212)+E(f13(x213,x211),f13(x213,x212))
% 13.24/13.46 [22]~E(x221,x222)+E(f9(x221,x223),f9(x222,x223))
% 13.24/13.46 [23]~E(x231,x232)+E(f9(x233,x231),f9(x233,x232))
% 13.24/13.46 [24]~E(x241,x242)+E(f17(x241,x243),f17(x242,x243))
% 13.24/13.46 [25]~E(x251,x252)+E(f17(x253,x251),f17(x253,x252))
% 13.24/13.46 [26]~E(x261,x262)+E(f23(x261),f23(x262))
% 13.24/13.46 [27]~E(x271,x272)+E(f28(x271,x273),f28(x272,x273))
% 13.24/13.46 [28]~E(x281,x282)+E(f28(x283,x281),f28(x283,x282))
% 13.24/13.46 [29]~E(x291,x292)+E(f20(x291,x293,x294),f20(x292,x293,x294))
% 13.24/13.46 [30]~E(x301,x302)+E(f20(x303,x301,x304),f20(x303,x302,x304))
% 13.24/13.46 [31]~E(x311,x312)+E(f20(x313,x314,x311),f20(x313,x314,x312))
% 13.24/13.46 [32]~E(x321,x322)+E(f6(x321,x323),f6(x322,x323))
% 13.24/13.46 [33]~E(x331,x332)+E(f6(x333,x331),f6(x333,x332))
% 13.24/13.46 [34]~E(x341,x342)+E(f25(x341,x343,x344),f25(x342,x343,x344))
% 13.24/13.46 [35]~E(x351,x352)+E(f25(x353,x351,x354),f25(x353,x352,x354))
% 13.24/13.46 [36]~E(x361,x362)+E(f25(x363,x364,x361),f25(x363,x364,x362))
% 13.24/13.46 [37]~E(x371,x372)+E(f53(x371,x373,x374,x375),f53(x372,x373,x374,x375))
% 13.24/13.46 [38]~E(x381,x382)+E(f53(x383,x381,x384,x385),f53(x383,x382,x384,x385))
% 13.24/13.46 [39]~E(x391,x392)+E(f53(x393,x394,x391,x395),f53(x393,x394,x392,x395))
% 13.24/13.46 [40]~E(x401,x402)+E(f53(x403,x404,x405,x401),f53(x403,x404,x405,x402))
% 13.24/13.46 [41]~E(x411,x412)+E(f29(x411,x413),f29(x412,x413))
% 13.24/13.46 [42]~E(x421,x422)+E(f29(x423,x421),f29(x423,x422))
% 13.24/13.46 [43]~E(x431,x432)+E(f77(x431,x433),f77(x432,x433))
% 13.24/13.46 [44]~E(x441,x442)+E(f77(x443,x441),f77(x443,x442))
% 13.24/13.46 [45]~E(x451,x452)+E(f54(x451,x453),f54(x452,x453))
% 13.24/13.46 [46]~E(x461,x462)+E(f54(x463,x461),f54(x463,x462))
% 13.24/13.46 [47]~E(x471,x472)+E(f18(x471,x473,x474),f18(x472,x473,x474))
% 13.24/13.46 [48]~E(x481,x482)+E(f18(x483,x481,x484),f18(x483,x482,x484))
% 13.24/13.46 [49]~E(x491,x492)+E(f18(x493,x494,x491),f18(x493,x494,x492))
% 13.24/13.46 [50]~E(x501,x502)+E(f43(x501,x503),f43(x502,x503))
% 13.24/13.46 [51]~E(x511,x512)+E(f43(x513,x511),f43(x513,x512))
% 13.24/13.46 [52]~E(x521,x522)+E(f16(x521,x523),f16(x522,x523))
% 13.24/13.46 [53]~E(x531,x532)+E(f16(x533,x531),f16(x533,x532))
% 13.24/13.46 [54]~E(x541,x542)+E(f22(x541,x543,x544),f22(x542,x543,x544))
% 13.24/13.46 [55]~E(x551,x552)+E(f22(x553,x551,x554),f22(x553,x552,x554))
% 13.24/13.46 [56]~E(x561,x562)+E(f22(x563,x564,x561),f22(x563,x564,x562))
% 13.24/13.46 [57]~E(x571,x572)+E(f31(x571,x573),f31(x572,x573))
% 13.24/13.46 [58]~E(x581,x582)+E(f31(x583,x581),f31(x583,x582))
% 13.24/13.46 [59]~E(x591,x592)+E(f8(x591,x593,x594),f8(x592,x593,x594))
% 13.24/13.46 [60]~E(x601,x602)+E(f8(x603,x601,x604),f8(x603,x602,x604))
% 13.24/13.46 [61]~E(x611,x612)+E(f8(x613,x614,x611),f8(x613,x614,x612))
% 13.24/13.46 [62]~E(x621,x622)+E(f19(x621,x623),f19(x622,x623))
% 13.24/13.46 [63]~E(x631,x632)+E(f19(x633,x631),f19(x633,x632))
% 13.24/13.46 [64]~E(x641,x642)+E(f61(x641),f61(x642))
% 13.24/13.46 [65]~E(x651,x652)+E(f34(x651,x653,x654),f34(x652,x653,x654))
% 13.24/13.46 [66]~E(x661,x662)+E(f34(x663,x661,x664),f34(x663,x662,x664))
% 13.24/13.46 [67]~E(x671,x672)+E(f34(x673,x674,x671),f34(x673,x674,x672))
% 13.24/13.46 [68]~E(x681,x682)+E(f65(x681,x683,x684),f65(x682,x683,x684))
% 13.24/13.46 [69]~E(x691,x692)+E(f65(x693,x691,x694),f65(x693,x692,x694))
% 13.24/13.46 [70]~E(x701,x702)+E(f65(x703,x704,x701),f65(x703,x704,x702))
% 13.24/13.46 [71]~E(x711,x712)+E(f26(x711,x713,x714),f26(x712,x713,x714))
% 13.24/13.46 [72]~E(x721,x722)+E(f26(x723,x721,x724),f26(x723,x722,x724))
% 13.24/13.46 [73]~E(x731,x732)+E(f26(x733,x734,x731),f26(x733,x734,x732))
% 13.24/13.46 [74]~E(x741,x742)+E(f44(x741),f44(x742))
% 13.24/13.46 [75]~E(x751,x752)+E(f45(x751,x753),f45(x752,x753))
% 13.24/13.46 [76]~E(x761,x762)+E(f45(x763,x761),f45(x763,x762))
% 13.24/13.46 [77]~E(x771,x772)+E(f64(x771),f64(x772))
% 13.24/13.46 [78]~E(x781,x782)+E(f50(x781),f50(x782))
% 13.24/13.46 [79]~E(x791,x792)+E(f67(x791),f67(x792))
% 13.24/13.46 [80]~E(x801,x802)+E(f63(x801,x803,x804),f63(x802,x803,x804))
% 13.24/13.46 [81]~E(x811,x812)+E(f63(x813,x811,x814),f63(x813,x812,x814))
% 13.24/13.46 [82]~E(x821,x822)+E(f63(x823,x824,x821),f63(x823,x824,x822))
% 13.24/13.46 [83]~E(x831,x832)+E(f62(x831,x833),f62(x832,x833))
% 13.24/13.46 [84]~E(x841,x842)+E(f62(x843,x841),f62(x843,x842))
% 13.24/13.46 [85]~E(x851,x852)+E(f48(x851,x853,x854,x855),f48(x852,x853,x854,x855))
% 13.24/13.46 [86]~E(x861,x862)+E(f48(x863,x861,x864,x865),f48(x863,x862,x864,x865))
% 13.24/13.46 [87]~E(x871,x872)+E(f48(x873,x874,x871,x875),f48(x873,x874,x872,x875))
% 13.24/13.46 [88]~E(x881,x882)+E(f48(x883,x884,x885,x881),f48(x883,x884,x885,x882))
% 13.24/13.46 [89]~E(x891,x892)+E(f59(x891),f59(x892))
% 13.24/13.46 [90]~E(x901,x902)+E(f66(x901,x903,x904),f66(x902,x903,x904))
% 13.24/13.46 [91]~E(x911,x912)+E(f66(x913,x911,x914),f66(x913,x912,x914))
% 13.24/13.46 [92]~E(x921,x922)+E(f66(x923,x924,x921),f66(x923,x924,x922))
% 13.24/13.46 [93]~E(x931,x932)+E(f68(x931,x933),f68(x932,x933))
% 13.24/13.46 [94]~E(x941,x942)+E(f68(x943,x941),f68(x943,x942))
% 13.24/13.46 [95]~E(x951,x952)+E(f60(x951,x953),f60(x952,x953))
% 13.24/13.46 [96]~E(x961,x962)+E(f60(x963,x961),f60(x963,x962))
% 13.24/13.46 [97]~E(x971,x972)+E(f70(x971,x973,x974),f70(x972,x973,x974))
% 13.24/13.46 [98]~E(x981,x982)+E(f70(x983,x981,x984),f70(x983,x982,x984))
% 13.24/13.46 [99]~E(x991,x992)+E(f70(x993,x994,x991),f70(x993,x994,x992))
% 13.24/13.46 [100]~E(x1001,x1002)+E(f24(x1001,x1003,x1004),f24(x1002,x1003,x1004))
% 13.24/13.46 [101]~E(x1011,x1012)+E(f24(x1013,x1011,x1014),f24(x1013,x1012,x1014))
% 13.24/13.46 [102]~E(x1021,x1022)+E(f24(x1023,x1024,x1021),f24(x1023,x1024,x1022))
% 13.24/13.46 [103]~E(x1031,x1032)+E(f51(x1031),f51(x1032))
% 13.24/13.46 [104]~E(x1041,x1042)+E(f52(x1041,x1043),f52(x1042,x1043))
% 13.24/13.46 [105]~E(x1051,x1052)+E(f52(x1053,x1051),f52(x1053,x1052))
% 13.24/13.46 [106]~E(x1061,x1062)+E(f21(x1061,x1063,x1064),f21(x1062,x1063,x1064))
% 13.24/13.46 [107]~E(x1071,x1072)+E(f21(x1073,x1071,x1074),f21(x1073,x1072,x1074))
% 13.24/13.46 [108]~E(x1081,x1082)+E(f21(x1083,x1084,x1081),f21(x1083,x1084,x1082))
% 13.24/13.46 [109]~E(x1091,x1092)+E(f55(x1091),f55(x1092))
% 13.24/13.46 [110]~E(x1101,x1102)+E(f69(x1101,x1103),f69(x1102,x1103))
% 13.24/13.46 [111]~E(x1111,x1112)+E(f69(x1113,x1111),f69(x1113,x1112))
% 13.24/13.46 [112]~E(x1121,x1122)+E(f35(x1121),f35(x1122))
% 13.24/13.46 [113]~P1(x1131)+P1(x1132)+~E(x1131,x1132)
% 13.24/13.46 [114]P10(x1142,x1143,x1144)+~E(x1141,x1142)+~P10(x1141,x1143,x1144)
% 13.24/13.46 [115]P10(x1153,x1152,x1154)+~E(x1151,x1152)+~P10(x1153,x1151,x1154)
% 13.24/13.46 [116]P10(x1163,x1164,x1162)+~E(x1161,x1162)+~P10(x1163,x1164,x1161)
% 13.24/13.46 [117]P9(x1172,x1173,x1174)+~E(x1171,x1172)+~P9(x1171,x1173,x1174)
% 13.24/13.46 [118]P9(x1183,x1182,x1184)+~E(x1181,x1182)+~P9(x1183,x1181,x1184)
% 13.24/13.46 [119]P9(x1193,x1194,x1192)+~E(x1191,x1192)+~P9(x1193,x1194,x1191)
% 13.24/13.46 [120]~P2(x1201)+P2(x1202)+~E(x1201,x1202)
% 13.24/13.46 [121]~P31(x1211)+P31(x1212)+~E(x1211,x1212)
% 13.24/13.46 [122]~P45(x1221)+P45(x1222)+~E(x1221,x1222)
% 13.24/13.46 [123]~P24(x1231)+P24(x1232)+~E(x1231,x1232)
% 13.24/13.46 [124]~P48(x1241)+P48(x1242)+~E(x1241,x1242)
% 13.24/13.46 [125]~P16(x1251)+P16(x1252)+~E(x1251,x1252)
% 13.24/13.46 [126]~P46(x1261)+P46(x1262)+~E(x1261,x1262)
% 13.24/13.46 [127]~P67(x1271)+P67(x1272)+~E(x1271,x1272)
% 13.24/13.46 [128]~P3(x1281)+P3(x1282)+~E(x1281,x1282)
% 13.24/13.46 [129]P12(x1292,x1293)+~E(x1291,x1292)+~P12(x1291,x1293)
% 13.24/13.46 [130]P12(x1303,x1302)+~E(x1301,x1302)+~P12(x1303,x1301)
% 13.24/13.46 [131]~P15(x1311)+P15(x1312)+~E(x1311,x1312)
% 13.24/13.46 [132]~P44(x1321)+P44(x1322)+~E(x1321,x1322)
% 13.24/13.46 [133]~P63(x1331)+P63(x1332)+~E(x1331,x1332)
% 13.24/13.46 [134]P13(x1342,x1343,x1344)+~E(x1341,x1342)+~P13(x1341,x1343,x1344)
% 13.24/13.46 [135]P13(x1353,x1352,x1354)+~E(x1351,x1352)+~P13(x1353,x1351,x1354)
% 13.24/13.46 [136]P13(x1363,x1364,x1362)+~E(x1361,x1362)+~P13(x1363,x1364,x1361)
% 13.24/13.46 [137]~P58(x1371)+P58(x1372)+~E(x1371,x1372)
% 13.24/13.46 [138]~P82(x1381)+P82(x1382)+~E(x1381,x1382)
% 13.24/13.46 [139]~P68(x1391)+P68(x1392)+~E(x1391,x1392)
% 13.24/13.46 [140]~P4(x1401)+P4(x1402)+~E(x1401,x1402)
% 13.24/13.46 [141]~P52(x1411)+P52(x1412)+~E(x1411,x1412)
% 13.24/13.46 [142]~P57(x1421)+P57(x1422)+~E(x1421,x1422)
% 13.24/13.46 [143]~P69(x1431)+P69(x1432)+~E(x1431,x1432)
% 13.24/13.46 [144]~P26(x1441)+P26(x1442)+~E(x1441,x1442)
% 13.24/13.46 [145]~P41(x1451)+P41(x1452)+~E(x1451,x1452)
% 13.24/13.46 [146]~P62(x1461)+P62(x1462)+~E(x1461,x1462)
% 13.24/13.46 [147]~P78(x1471)+P78(x1472)+~E(x1471,x1472)
% 13.24/13.46 [148]~P50(x1481)+P50(x1482)+~E(x1481,x1482)
% 13.24/13.46 [149]~P61(x1491)+P61(x1492)+~E(x1491,x1492)
% 13.24/13.46 [150]~P28(x1501)+P28(x1502)+~E(x1501,x1502)
% 13.24/13.46 [151]~P70(x1511)+P70(x1512)+~E(x1511,x1512)
% 13.24/13.46 [152]~P32(x1521)+P32(x1522)+~E(x1521,x1522)
% 13.24/13.46 [153]~P36(x1531)+P36(x1532)+~E(x1531,x1532)
% 13.24/13.46 [154]~P81(x1541)+P81(x1542)+~E(x1541,x1542)
% 13.24/13.46 [155]~P29(x1551)+P29(x1552)+~E(x1551,x1552)
% 13.24/13.46 [156]~P76(x1561)+P76(x1562)+~E(x1561,x1562)
% 13.24/13.46 [157]~P53(x1571)+P53(x1572)+~E(x1571,x1572)
% 13.24/13.46 [158]~P71(x1581)+P71(x1582)+~E(x1581,x1582)
% 13.24/13.46 [159]~P55(x1591)+P55(x1592)+~E(x1591,x1592)
% 13.24/13.46 [160]~P56(x1601)+P56(x1602)+~E(x1601,x1602)
% 13.24/13.46 [161]~P5(x1611)+P5(x1612)+~E(x1611,x1612)
% 13.24/13.46 [162]~P39(x1621)+P39(x1622)+~E(x1621,x1622)
% 13.24/13.46 [163]~P54(x1631)+P54(x1632)+~E(x1631,x1632)
% 13.24/13.46 [164]~P74(x1641)+P74(x1642)+~E(x1641,x1642)
% 13.24/13.46 [165]~P49(x1651)+P49(x1652)+~E(x1651,x1652)
% 13.24/13.46 [166]~P77(x1661)+P77(x1662)+~E(x1661,x1662)
% 13.24/13.46 [167]~P64(x1671)+P64(x1672)+~E(x1671,x1672)
% 13.24/13.46 [168]~P79(x1681)+P79(x1682)+~E(x1681,x1682)
% 13.24/13.46 [169]~P65(x1691)+P65(x1692)+~E(x1691,x1692)
% 13.24/13.46 [170]P11(x1702,x1703,x1704)+~E(x1701,x1702)+~P11(x1701,x1703,x1704)
% 13.24/13.46 [171]P11(x1713,x1712,x1714)+~E(x1711,x1712)+~P11(x1713,x1711,x1714)
% 13.24/13.46 [172]P11(x1723,x1724,x1722)+~E(x1721,x1722)+~P11(x1723,x1724,x1721)
% 13.24/13.46 [173]~P40(x1731)+P40(x1732)+~E(x1731,x1732)
% 13.24/13.46 [174]~P25(x1741)+P25(x1742)+~E(x1741,x1742)
% 13.24/13.46 [175]~P72(x1751)+P72(x1752)+~E(x1751,x1752)
% 13.24/13.46 [176]~P18(x1761)+P18(x1762)+~E(x1761,x1762)
% 13.24/13.46 [177]~P23(x1771)+P23(x1772)+~E(x1771,x1772)
% 13.24/13.46 [178]~P51(x1781)+P51(x1782)+~E(x1781,x1782)
% 13.24/13.46 [179]~P35(x1791)+P35(x1792)+~E(x1791,x1792)
% 13.24/13.46 [180]~P27(x1801)+P27(x1802)+~E(x1801,x1802)
% 13.24/13.46 [181]~P59(x1811)+P59(x1812)+~E(x1811,x1812)
% 13.24/13.46 [182]~P34(x1821)+P34(x1822)+~E(x1821,x1822)
% 13.24/13.46 [183]~P8(x1831)+P8(x1832)+~E(x1831,x1832)
% 13.24/13.46 [184]~P80(x1841)+P80(x1842)+~E(x1841,x1842)
% 13.24/13.46 [185]~P6(x1851)+P6(x1852)+~E(x1851,x1852)
% 13.24/13.46 [186]~P20(x1861)+P20(x1862)+~E(x1861,x1862)
% 13.24/13.46 [187]~P42(x1871)+P42(x1872)+~E(x1871,x1872)
% 13.24/13.46 [188]~P38(x1881)+P38(x1882)+~E(x1881,x1882)
% 13.24/13.46 [189]~P33(x1891)+P33(x1892)+~E(x1891,x1892)
% 13.24/13.46 [190]~P75(x1901)+P75(x1902)+~E(x1901,x1902)
% 13.24/13.46 [191]~P22(x1911)+P22(x1912)+~E(x1911,x1912)
% 13.24/13.46 [192]~P30(x1921)+P30(x1922)+~E(x1921,x1922)
% 13.24/13.46 [193]~P21(x1931)+P21(x1932)+~E(x1931,x1932)
% 13.24/13.46 [194]~P73(x1941)+P73(x1942)+~E(x1941,x1942)
% 13.24/13.46 [195]P14(x1952,x1953)+~E(x1951,x1952)+~P14(x1951,x1953)
% 13.24/13.46 [196]P14(x1963,x1962)+~E(x1961,x1962)+~P14(x1963,x1961)
% 13.24/13.46 [197]~P17(x1971)+P17(x1972)+~E(x1971,x1972)
% 13.24/13.46 [198]~P37(x1981)+P37(x1982)+~E(x1981,x1982)
% 13.24/13.46 [199]~P66(x1991)+P66(x1992)+~E(x1991,x1992)
% 13.24/13.46 [200]~P7(x2001)+P7(x2002)+~E(x2001,x2002)
% 13.24/13.46 [201]~P19(x2011)+P19(x2012)+~E(x2011,x2012)
% 13.24/13.46 [202]~P47(x2021)+P47(x2022)+~E(x2021,x2022)
% 13.24/13.46 [203]~P60(x2031)+P60(x2032)+~E(x2031,x2032)
% 13.24/13.46 [204]~P43(x2041)+P43(x2042)+~E(x2041,x2042)
% 13.24/13.46
% 13.24/13.46 %-------------------------------------------
% 13.24/13.48 cnf(1805,plain,
% 13.24/13.48 (~P10(a1,x18051,x18051)),
% 13.24/13.48 inference(scs_inference,[],[392,437,2,886])).
% 13.24/13.48 cnf(1812,plain,
% 13.24/13.48 (P9(a3,x18121,x18121)),
% 13.24/13.48 inference(rename_variables,[],[449])).
% 13.24/13.48 cnf(1815,plain,
% 13.24/13.48 (P9(a3,x18151,x18151)),
% 13.24/13.48 inference(rename_variables,[],[449])).
% 13.24/13.48 cnf(1818,plain,
% 13.24/13.48 (P9(a2,x18181,f15(a2,x18182,x18181))),
% 13.24/13.48 inference(rename_variables,[],[496])).
% 13.24/13.48 cnf(1821,plain,
% 13.24/13.48 (P9(a2,x18211,f15(a2,x18212,x18211))),
% 13.24/13.48 inference(rename_variables,[],[496])).
% 13.24/13.48 cnf(1826,plain,
% 13.24/13.48 (~P10(a2,x18261,x18261)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(1829,plain,
% 13.24/13.48 (~P10(a2,f15(a2,x18291,x18292),x18292)),
% 13.24/13.48 inference(rename_variables,[],[602])).
% 13.24/13.48 cnf(1832,plain,
% 13.24/13.48 (~P10(a2,f15(a2,x18321,x18322),x18322)),
% 13.24/13.48 inference(rename_variables,[],[602])).
% 13.24/13.48 cnf(1835,plain,
% 13.24/13.48 (P9(a1,x18351,x18351)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(1842,plain,
% 13.24/13.48 (~P10(a1,f15(a1,f9(a1,x18421),f5(a1)),x18421)),
% 13.24/13.48 inference(rename_variables,[],[605])).
% 13.24/13.48 cnf(1850,plain,
% 13.24/13.48 (P9(a1,x18501,f29(a2,f11(x18501)))),
% 13.24/13.48 inference(rename_variables,[],[480])).
% 13.24/13.48 cnf(1853,plain,
% 13.24/13.48 (P10(a1,x18531,f15(a1,f29(a2,f27(x18531)),f5(a1)))),
% 13.24/13.48 inference(rename_variables,[],[516])).
% 13.24/13.48 cnf(1856,plain,
% 13.24/13.48 (P9(a2,x18561,x18561)),
% 13.24/13.48 inference(rename_variables,[],[448])).
% 13.24/13.48 cnf(1861,plain,
% 13.24/13.48 (P9(a1,x18611,f29(a2,f11(x18611)))),
% 13.24/13.48 inference(rename_variables,[],[480])).
% 13.24/13.48 cnf(1866,plain,
% 13.24/13.48 (P9(a1,x18661,x18661)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(1869,plain,
% 13.24/13.48 (P9(a1,x18691,f29(a2,f11(x18691)))),
% 13.24/13.48 inference(rename_variables,[],[480])).
% 13.24/13.48 cnf(1872,plain,
% 13.24/13.48 (E(f10(a2,f15(a2,x18721,x18722),x18722),x18721)),
% 13.24/13.48 inference(rename_variables,[],[499])).
% 13.24/13.48 cnf(1879,plain,
% 13.24/13.48 (~P10(a1,f15(a1,f9(a1,x18791),f5(a1)),x18791)),
% 13.24/13.48 inference(rename_variables,[],[605])).
% 13.24/13.48 cnf(1882,plain,
% 13.24/13.48 (P10(a1,x18821,f15(a1,f29(a2,f27(x18821)),f5(a1)))),
% 13.24/13.48 inference(rename_variables,[],[516])).
% 13.24/13.48 cnf(1885,plain,
% 13.24/13.48 (~P10(a2,x18851,x18851)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(1888,plain,
% 13.24/13.48 (~P10(a2,x18881,x18881)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(1891,plain,
% 13.24/13.48 (P9(a1,x18911,x18911)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(1893,plain,
% 13.24/13.48 (P9(a1,x18931,x18931)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(1908,plain,
% 13.24/13.48 (P9(a2,f10(a2,x19081,x19082),x19081)),
% 13.24/13.48 inference(rename_variables,[],[498])).
% 13.24/13.48 cnf(1909,plain,
% 13.24/13.48 (P9(a2,f12(a2),x19091)),
% 13.24/13.48 inference(rename_variables,[],[463])).
% 13.24/13.48 cnf(1912,plain,
% 13.24/13.48 (P9(a2,f12(a2),x19121)),
% 13.24/13.48 inference(rename_variables,[],[463])).
% 13.24/13.48 cnf(1927,plain,
% 13.24/13.48 (P9(a3,x19271,x19271)),
% 13.24/13.48 inference(rename_variables,[],[449])).
% 13.24/13.48 cnf(1930,plain,
% 13.24/13.48 (P10(a1,x19301,f15(a1,f29(a2,f27(x19301)),f5(a1)))),
% 13.24/13.48 inference(rename_variables,[],[516])).
% 13.24/13.48 cnf(1933,plain,
% 13.24/13.48 (P9(a1,x19331,x19331)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(1934,plain,
% 13.24/13.48 (~P10(a2,x19341,x19341)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(1937,plain,
% 13.24/13.48 (P9(a1,x19371,x19371)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(1938,plain,
% 13.24/13.48 (P9(a2,x19381,x19381)),
% 13.24/13.48 inference(rename_variables,[],[448])).
% 13.24/13.48 cnf(1945,plain,
% 13.24/13.48 (E(f15(a2,f12(a2),x19451),x19451)),
% 13.24/13.48 inference(rename_variables,[],[467])).
% 13.24/13.48 cnf(1948,plain,
% 13.24/13.48 (P9(a1,x19481,x19481)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(1953,plain,
% 13.24/13.48 (E(f10(a2,f12(a2),x19531),f12(a2))),
% 13.24/13.48 inference(rename_variables,[],[471])).
% 13.24/13.48 cnf(1962,plain,
% 13.24/13.48 (~E(f15(a4,x19621,f56(f17(a4,a73),a75)),x19621)),
% 13.24/13.48 inference(scs_inference,[],[609,447,1835,1866,1891,1893,1933,1937,448,1856,449,1812,1815,592,1826,1885,1888,208,256,324,338,357,389,392,393,394,400,401,403,404,463,1909,453,455,580,437,436,472,596,505,589,428,432,555,608,574,496,1818,498,602,1829,601,480,1850,1861,499,467,605,1842,495,471,1953,516,1853,1882,2,886,848,866,1361,1359,1349,1348,1345,1256,1251,1249,1079,1005,1026,800,1281,10,1594,1516,1515,1427,1413,1184,1183,1088,1087,1015,946,942,1322,1388,1494,1492,119,118,116,115,3,1098,1097,1094,1093,1092,1075,1013,957,955,902,901,771,1403,1130,1128,1305,1290,681,1535,1355,1324,1104,918,917,1155,1153,914])).
% 13.24/13.48 cnf(1967,plain,
% 13.24/13.48 (E(f11(f29(a2,x19671)),x19671)),
% 13.24/13.48 inference(rename_variables,[],[440])).
% 13.24/13.48 cnf(1972,plain,
% 13.24/13.48 (P10(a1,x19721,f15(a1,f29(a2,f27(x19721)),f5(a1)))),
% 13.24/13.48 inference(rename_variables,[],[516])).
% 13.24/13.48 cnf(1975,plain,
% 13.24/13.48 (~P10(a1,f15(a1,f9(a1,x19751),f5(a1)),x19751)),
% 13.24/13.48 inference(rename_variables,[],[605])).
% 13.24/13.48 cnf(1978,plain,
% 13.24/13.48 (~P10(a2,x19781,f12(a2))),
% 13.24/13.48 inference(rename_variables,[],[595])).
% 13.24/13.48 cnf(1983,plain,
% 13.24/13.48 (~P10(a1,f15(a1,f9(a1,x19831),f5(a1)),x19831)),
% 13.24/13.48 inference(rename_variables,[],[605])).
% 13.24/13.48 cnf(2046,plain,
% 13.24/13.48 (~P10(a1,f15(a1,f9(a1,x20461),f5(a1)),x20461)),
% 13.24/13.48 inference(rename_variables,[],[605])).
% 13.24/13.48 cnf(2051,plain,
% 13.24/13.48 (E(f10(a2,f15(a2,x20511,x20512),x20512),x20511)),
% 13.24/13.48 inference(rename_variables,[],[499])).
% 13.24/13.48 cnf(2066,plain,
% 13.24/13.48 (P10(a1,x20661,f15(a1,f29(a2,f27(x20661)),f5(a1)))),
% 13.24/13.48 inference(rename_variables,[],[516])).
% 13.24/13.48 cnf(2069,plain,
% 13.24/13.48 (P10(a1,x20691,f15(a1,f29(a2,f27(x20691)),f5(a1)))),
% 13.24/13.48 inference(rename_variables,[],[516])).
% 13.24/13.48 cnf(2080,plain,
% 13.24/13.48 (~P10(a2,x20801,x20801)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(2083,plain,
% 13.24/13.48 (P9(a2,x20831,x20831)),
% 13.24/13.48 inference(rename_variables,[],[448])).
% 13.24/13.48 cnf(2084,plain,
% 13.24/13.48 (P9(a2,f12(a2),x20841)),
% 13.24/13.48 inference(rename_variables,[],[463])).
% 13.24/13.48 cnf(2089,plain,
% 13.24/13.48 (E(f15(a2,x20891,x20892),f15(a2,x20892,x20891))),
% 13.24/13.48 inference(rename_variables,[],[484])).
% 13.24/13.48 cnf(2092,plain,
% 13.24/13.48 (E(f15(a2,x20921,x20922),f15(a2,x20922,x20921))),
% 13.24/13.48 inference(rename_variables,[],[484])).
% 13.24/13.48 cnf(2095,plain,
% 13.24/13.48 (P9(a1,x20951,x20951)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2098,plain,
% 13.24/13.48 (~P10(a1,f15(a1,f9(a1,x20981),f5(a1)),x20981)),
% 13.24/13.48 inference(rename_variables,[],[605])).
% 13.24/13.48 cnf(2105,plain,
% 13.24/13.48 (P9(a2,x21051,f15(a2,x21052,x21051))),
% 13.24/13.48 inference(rename_variables,[],[496])).
% 13.24/13.48 cnf(2110,plain,
% 13.24/13.48 (P10(a1,x21101,f15(a1,f29(a2,f27(x21101)),f5(a1)))),
% 13.24/13.48 inference(rename_variables,[],[516])).
% 13.24/13.48 cnf(2113,plain,
% 13.24/13.48 (P9(a2,f12(a2),x21131)),
% 13.24/13.48 inference(rename_variables,[],[463])).
% 13.24/13.48 cnf(2116,plain,
% 13.24/13.48 (~P10(a2,x21161,f12(a2))),
% 13.24/13.48 inference(rename_variables,[],[595])).
% 13.24/13.48 cnf(2119,plain,
% 13.24/13.48 (~P10(a2,x21191,f12(a2))),
% 13.24/13.48 inference(rename_variables,[],[595])).
% 13.24/13.48 cnf(2126,plain,
% 13.24/13.48 (E(f10(a2,f15(a2,x21261,x21262),x21262),x21261)),
% 13.24/13.48 inference(rename_variables,[],[499])).
% 13.24/13.48 cnf(2127,plain,
% 13.24/13.48 (P9(a2,f12(a2),x21271)),
% 13.24/13.48 inference(rename_variables,[],[463])).
% 13.24/13.48 cnf(2128,plain,
% 13.24/13.48 (P9(a2,x21281,x21281)),
% 13.24/13.48 inference(rename_variables,[],[448])).
% 13.24/13.48 cnf(2131,plain,
% 13.24/13.48 (P9(a2,f12(a2),x21311)),
% 13.24/13.48 inference(rename_variables,[],[463])).
% 13.24/13.48 cnf(2134,plain,
% 13.24/13.48 (P9(a2,f12(a2),x21341)),
% 13.24/13.48 inference(rename_variables,[],[463])).
% 13.24/13.48 cnf(2137,plain,
% 13.24/13.48 (~P10(a2,x21371,x21371)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(2140,plain,
% 13.24/13.48 (~P10(a1,f15(a1,f9(a1,x21401),f5(a1)),x21401)),
% 13.24/13.48 inference(rename_variables,[],[605])).
% 13.24/13.48 cnf(2141,plain,
% 13.24/13.48 (P9(a1,x21411,x21411)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2144,plain,
% 13.24/13.48 (~P10(a1,f15(a1,f9(a1,x21441),f5(a1)),x21441)),
% 13.24/13.48 inference(rename_variables,[],[605])).
% 13.24/13.48 cnf(2149,plain,
% 13.24/13.48 (~P10(a2,f15(a2,x21491,x21492),x21492)),
% 13.24/13.48 inference(rename_variables,[],[602])).
% 13.24/13.48 cnf(2152,plain,
% 13.24/13.48 (~P10(a2,f15(a2,x21521,x21522),x21521)),
% 13.24/13.48 inference(rename_variables,[],[603])).
% 13.24/13.48 cnf(2155,plain,
% 13.24/13.48 (~P10(a1,f15(a1,f9(a1,x21551),f5(a1)),x21551)),
% 13.24/13.48 inference(rename_variables,[],[605])).
% 13.24/13.48 cnf(2156,plain,
% 13.24/13.48 (P10(a1,x21561,f15(a1,f29(a2,f27(x21561)),f5(a1)))),
% 13.24/13.48 inference(rename_variables,[],[516])).
% 13.24/13.48 cnf(2159,plain,
% 13.24/13.48 (P9(a1,x21591,f29(a2,f11(x21591)))),
% 13.24/13.48 inference(rename_variables,[],[480])).
% 13.24/13.48 cnf(2160,plain,
% 13.24/13.48 (P9(a1,f12(a1),f29(a2,x21601))),
% 13.24/13.48 inference(rename_variables,[],[479])).
% 13.24/13.48 cnf(2165,plain,
% 13.24/13.48 (E(f11(f29(a2,x21651)),x21651)),
% 13.24/13.48 inference(rename_variables,[],[440])).
% 13.24/13.48 cnf(2168,plain,
% 13.24/13.48 (~P10(a1,f15(a1,f9(a1,x21681),f5(a1)),x21681)),
% 13.24/13.48 inference(rename_variables,[],[605])).
% 13.24/13.48 cnf(2173,plain,
% 13.24/13.48 (P9(a2,x21731,x21731)),
% 13.24/13.48 inference(rename_variables,[],[448])).
% 13.24/13.48 cnf(2186,plain,
% 13.24/13.48 (E(f15(a2,x21861,x21862),f15(a2,x21862,x21861))),
% 13.24/13.48 inference(rename_variables,[],[484])).
% 13.24/13.48 cnf(2189,plain,
% 13.24/13.48 (P9(a2,f12(a2),x21891)),
% 13.24/13.48 inference(rename_variables,[],[463])).
% 13.24/13.48 cnf(2287,plain,
% 13.24/13.48 (P58(f72(a1))),
% 13.24/13.48 inference(scs_inference,[],[609,447,1835,1866,1891,1893,1933,1937,1948,2095,448,1856,1938,2083,2128,449,1812,1815,592,1826,1885,1888,1934,2080,205,208,212,213,233,256,257,271,274,275,280,302,305,306,307,312,313,314,315,318,320,323,324,325,326,338,357,358,359,363,365,366,368,370,371,375,382,385,389,390,392,393,394,395,396,400,401,403,404,407,408,412,423,463,1909,1912,2084,2113,2127,2131,2134,595,1978,2116,2119,453,454,455,458,580,581,585,437,436,435,472,473,587,596,505,589,428,431,432,590,492,491,555,608,569,574,496,1818,1821,497,498,1908,602,1829,1832,603,484,2089,2092,479,601,440,1967,480,1850,1861,1869,499,1872,2051,467,605,1842,1879,1975,1983,2046,2098,2140,2144,2155,495,501,471,1953,516,1853,1882,1930,1972,2066,2069,2110,450,604,2,886,848,866,1361,1359,1349,1348,1345,1256,1251,1249,1079,1005,1026,800,1281,10,1594,1516,1515,1427,1413,1184,1183,1088,1087,1015,946,942,1322,1388,1494,1492,119,118,116,115,3,1098,1097,1094,1093,1092,1075,1013,957,955,902,901,771,1403,1130,1128,1305,1290,681,1535,1355,1324,1104,918,917,1155,1153,914,722,721,702,1602,1436,1292,1197,1192,1160,1181,1179,1178,1177,1176,1174,1173,1170,1169,1058,1031,969,968,919,913,789,719,718,717,716,714,713,712,711,693,692,1398,1397,1396,1395,1135,1085,921,949,935,865,864,1705,1704,931,1595,1485,1789,1787,1781,1779,1752,1751,1797,1782,1750,1749,1236,1233,1230,1113,1045,1037,970,967,1404,1426,1425,1424,1423,1422,1557,1556,1555,1554,1352,1732,1265,1384,1340,1468,1328,1327,1326,1325,980,1630,1317,999,998,993,928,927,926,854,853,763,762,746,743,1024,1023,752,1360,1274,1272,1271,1270,1255,1253,1066,991,780,779,766,765,748,708,707,706,705,704,703,670,669,668,667,666,665,664,663,662,661,660,659,658,657])).
% 13.24/13.48 cnf(2388,plain,
% 13.24/13.48 (P9(a1,x23881,x23881)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2393,plain,
% 13.24/13.48 (P9(a1,x23931,x23931)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2400,plain,
% 13.24/13.48 (P9(a1,x24001,x24001)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2403,plain,
% 13.24/13.48 (~E(f15(a3,f15(a3,f5(a3),x24031),x24031),f12(a3))),
% 13.24/13.48 inference(rename_variables,[],[604])).
% 13.24/13.48 cnf(2434,plain,
% 13.24/13.48 (~P10(a2,x24341,x24341)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(2437,plain,
% 13.24/13.48 (~P10(a2,x24371,x24371)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(2440,plain,
% 13.24/13.48 (P9(a3,x24401,x24401)),
% 13.24/13.48 inference(rename_variables,[],[449])).
% 13.24/13.48 cnf(2447,plain,
% 13.24/13.48 (P9(a3,x24471,x24471)),
% 13.24/13.48 inference(rename_variables,[],[449])).
% 13.24/13.48 cnf(2452,plain,
% 13.24/13.48 (~P10(a2,x24521,x24521)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(2461,plain,
% 13.24/13.48 (P9(a1,x24611,x24611)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2574,plain,
% 13.24/13.48 (~P10(a2,x25741,f12(a2))),
% 13.24/13.48 inference(rename_variables,[],[595])).
% 13.24/13.48 cnf(2583,plain,
% 13.24/13.48 (P9(a1,x25831,x25831)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2586,plain,
% 13.24/13.48 (P9(a1,x25861,x25861)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2589,plain,
% 13.24/13.48 (P9(a1,x25891,x25891)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2615,plain,
% 13.24/13.48 (~P9(a1,f10(a1,f5(a1),a81),f12(a1))),
% 13.24/13.48 inference(scs_inference,[],[609,447,1835,1866,1891,1893,1933,1937,1948,2095,2141,2388,2393,2400,2461,2583,2586,448,1856,1938,2083,2128,2173,449,1812,1815,1927,2440,592,1826,1885,1888,1934,2080,2137,2434,2437,205,208,212,213,214,233,256,257,271,274,275,280,302,305,306,307,312,313,314,315,318,320,323,324,325,326,338,353,357,358,359,363,365,366,368,370,371,375,382,385,389,390,392,393,394,395,396,400,401,403,404,407,408,412,423,463,1909,1912,2084,2113,2127,2131,2134,2189,595,1978,2116,2119,2574,453,454,455,458,580,581,585,437,436,435,472,473,587,596,505,589,428,431,432,590,492,491,555,608,569,574,496,1818,1821,497,498,1908,602,1829,1832,603,484,2089,2092,479,2160,601,440,1967,480,1850,1861,1869,499,1872,2051,467,605,1842,1879,1975,1983,2046,2098,2140,2144,2155,495,501,471,1953,516,1853,1882,1930,1972,2066,2069,2110,450,604,2403,2,886,848,866,1361,1359,1349,1348,1345,1256,1251,1249,1079,1005,1026,800,1281,10,1594,1516,1515,1427,1413,1184,1183,1088,1087,1015,946,942,1322,1388,1494,1492,119,118,116,115,3,1098,1097,1094,1093,1092,1075,1013,957,955,902,901,771,1403,1130,1128,1305,1290,681,1535,1355,1324,1104,918,917,1155,1153,914,722,721,702,1602,1436,1292,1197,1192,1160,1181,1179,1178,1177,1176,1174,1173,1170,1169,1058,1031,969,968,919,913,789,719,718,717,716,714,713,712,711,693,692,1398,1397,1396,1395,1135,1085,921,949,935,865,864,1705,1704,931,1595,1485,1789,1787,1781,1779,1752,1751,1797,1782,1750,1749,1236,1233,1230,1113,1045,1037,970,967,1404,1426,1425,1424,1423,1422,1557,1556,1555,1554,1352,1732,1265,1384,1340,1468,1328,1327,1326,1325,980,1630,1317,999,998,993,928,927,926,854,853,763,762,746,743,1024,1023,752,1360,1274,1272,1271,1270,1255,1253,1066,991,780,779,766,765,748,708,707,706,705,704,703,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,1801,1800,1512,1084,1083,1061,1054,1053,985,984,876,875,863,862,861,839,838,793,739,738,736,674,673,1331,1330,1288,1266,1261,1241,1240,1109,1067,1062,1060,1056,1055,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,9,8,7,6,5,4,1593,1558,1522,1521,1432,1431,1430,1421,1420,1419,1418,1417,1416,1415,1414,1369,1367,1364,1363,1358])).
% 13.24/13.48 cnf(2628,plain,
% 13.24/13.48 (P9(a1,x26281,x26281)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2634,plain,
% 13.24/13.48 (P10(a1,x26341,f15(a1,x26341,f5(a1)))),
% 13.24/13.48 inference(scs_inference,[],[609,447,1835,1866,1891,1893,1933,1937,1948,2095,2141,2388,2393,2400,2461,2583,2586,2589,448,1856,1938,2083,2128,2173,449,1812,1815,1927,2440,592,1826,1885,1888,1934,2080,2137,2434,2437,205,208,212,213,214,233,256,257,271,274,275,280,290,302,305,306,307,312,313,314,315,318,320,323,324,325,326,338,353,357,358,359,363,365,366,368,370,371,375,382,385,389,390,392,393,394,395,396,400,401,403,404,407,408,412,423,463,1909,1912,2084,2113,2127,2131,2134,2189,595,1978,2116,2119,2574,453,454,455,458,580,581,585,437,436,435,472,473,587,596,505,589,428,431,432,590,492,491,555,608,569,574,496,1818,1821,497,498,1908,602,1829,1832,603,484,2089,2092,479,2160,601,440,1967,480,1850,1861,1869,499,1872,2051,467,605,1842,1879,1975,1983,2046,2098,2140,2144,2155,495,501,471,1953,516,1853,1882,1930,1972,2066,2069,2110,450,604,2403,2,886,848,866,1361,1359,1349,1348,1345,1256,1251,1249,1079,1005,1026,800,1281,10,1594,1516,1515,1427,1413,1184,1183,1088,1087,1015,946,942,1322,1388,1494,1492,119,118,116,115,3,1098,1097,1094,1093,1092,1075,1013,957,955,902,901,771,1403,1130,1128,1305,1290,681,1535,1355,1324,1104,918,917,1155,1153,914,722,721,702,1602,1436,1292,1197,1192,1160,1181,1179,1178,1177,1176,1174,1173,1170,1169,1058,1031,969,968,919,913,789,719,718,717,716,714,713,712,711,693,692,1398,1397,1396,1395,1135,1085,921,949,935,865,864,1705,1704,931,1595,1485,1789,1787,1781,1779,1752,1751,1797,1782,1750,1749,1236,1233,1230,1113,1045,1037,970,967,1404,1426,1425,1424,1423,1422,1557,1556,1555,1554,1352,1732,1265,1384,1340,1468,1328,1327,1326,1325,980,1630,1317,999,998,993,928,927,926,854,853,763,762,746,743,1024,1023,752,1360,1274,1272,1271,1270,1255,1253,1066,991,780,779,766,765,748,708,707,706,705,704,703,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,1801,1800,1512,1084,1083,1061,1054,1053,985,984,876,875,863,862,861,839,838,793,739,738,736,674,673,1331,1330,1288,1266,1261,1241,1240,1109,1067,1062,1060,1056,1055,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,9,8,7,6,5,4,1593,1558,1522,1521,1432,1431,1430,1421,1420,1419,1418,1417,1416,1415,1414,1369,1367,1364,1363,1358,1357,1329,1295,1269,1268,1158,1116,1115,1108])).
% 13.24/13.48 cnf(2735,plain,
% 13.24/13.48 (P9(a1,x27351,x27351)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2744,plain,
% 13.24/13.48 (~P10(a2,x27441,x27441)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(2747,plain,
% 13.24/13.48 (~P10(a2,x27471,x27471)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(2758,plain,
% 13.24/13.48 (P9(a1,x27581,x27581)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2761,plain,
% 13.24/13.48 (P9(a1,x27611,x27611)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2764,plain,
% 13.24/13.48 (~P10(a2,x27641,x27641)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(2767,plain,
% 13.24/13.48 (~P10(a2,x27671,x27671)),
% 13.24/13.48 inference(rename_variables,[],[592])).
% 13.24/13.48 cnf(2770,plain,
% 13.24/13.48 (P9(a1,x27701,x27701)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2773,plain,
% 13.24/13.48 (P9(a1,x27731,x27731)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2796,plain,
% 13.24/13.48 (P9(a1,x27961,x27961)),
% 13.24/13.48 inference(rename_variables,[],[447])).
% 13.24/13.48 cnf(2869,plain,
% 13.24/13.48 (E(f11(f29(a2,x28691)),x28691)),
% 13.24/13.48 inference(rename_variables,[],[440])).
% 13.24/13.48 cnf(2910,plain,
% 13.24/13.48 (P10(a1,x29101,f15(a1,f29(a2,f27(x29101)),f5(a1)))),
% 13.24/13.48 inference(rename_variables,[],[516])).
% 13.24/13.48 cnf(3156,plain,
% 13.24/13.48 (P13(f72(a1),f56(f56(f23(f72(a1)),f20(a1,f13(a1,x31561),f20(a1,f5(a1),f12(f72(a1))))),f21(a1,x31561,x31562)),x31562)),
% 13.24/13.48 inference(scs_inference,[],[609,447,1835,1866,1891,1893,1933,1937,1948,2095,2141,2388,2393,2400,2461,2583,2586,2589,2628,2735,2758,2761,2770,2773,2796,448,1856,1938,2083,2128,2173,449,1812,1815,1927,2440,2447,592,1826,1885,1888,1934,2080,2137,2434,2437,2452,2744,2747,2764,205,206,208,210,212,213,214,215,216,217,221,229,232,233,243,247,250,251,256,257,267,271,272,274,275,280,290,301,302,305,306,307,311,312,313,314,315,318,319,320,323,324,325,326,334,338,353,354,357,358,359,363,365,366,368,370,371,375,376,382,385,389,390,392,393,394,395,396,400,401,403,404,407,408,412,417,423,463,1909,1912,2084,2113,2127,2131,2134,2189,595,1978,2116,2119,2574,453,454,455,458,597,580,581,585,437,436,435,472,473,587,596,505,589,428,431,432,590,492,491,555,608,569,574,496,1818,1821,2105,497,498,1908,602,1829,1832,603,484,2089,2092,479,2160,601,440,1967,2165,480,1850,1861,1869,2159,499,1872,2051,467,605,1842,1879,1975,1983,2046,2098,2140,2144,2155,2168,495,501,471,1953,516,1853,1882,1930,1972,2066,2069,2110,2156,450,604,2403,2,886,848,866,1361,1359,1349,1348,1345,1256,1251,1249,1079,1005,1026,800,1281,10,1594,1516,1515,1427,1413,1184,1183,1088,1087,1015,946,942,1322,1388,1494,1492,119,118,116,115,3,1098,1097,1094,1093,1092,1075,1013,957,955,902,901,771,1403,1130,1128,1305,1290,681,1535,1355,1324,1104,918,917,1155,1153,914,722,721,702,1602,1436,1292,1197,1192,1160,1181,1179,1178,1177,1176,1174,1173,1170,1169,1058,1031,969,968,919,913,789,719,718,717,716,714,713,712,711,693,692,1398,1397,1396,1395,1135,1085,921,949,935,865,864,1705,1704,931,1595,1485,1789,1787,1781,1779,1752,1751,1797,1782,1750,1749,1236,1233,1230,1113,1045,1037,970,967,1404,1426,1425,1424,1423,1422,1557,1556,1555,1554,1352,1732,1265,1384,1340,1468,1328,1327,1326,1325,980,1630,1317,999,998,993,928,927,926,854,853,763,762,746,743,1024,1023,752,1360,1274,1272,1271,1270,1255,1253,1066,991,780,779,766,765,748,708,707,706,705,704,703,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,1801,1800,1512,1084,1083,1061,1054,1053,985,984,876,875,863,862,861,839,838,793,739,738,736,674,673,1331,1330,1288,1266,1261,1241,1240,1109,1067,1062,1060,1056,1055,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,9,8,7,6,5,4,1593,1558,1522,1521,1432,1431,1430,1421,1420,1419,1418,1417,1416,1415,1414,1369,1367,1364,1363,1358,1357,1329,1295,1269,1268,1158,1116,1115,1108,1077,1073,1072,1069,1068,1033,1032,1021,1008,1006,979,950,943,939,938,936,887,844,843,842,833,811,810,809,808,798,788,787,786,784,783,782,777,776,775,774,773,772,750,749,729,728,727,720,678,677,676,675,672,1755,1709,1706,1596,1526,1525,1496,1470,1469,1356,1354,1353,1334,1333,1298,1297,1267,909,908,906,1243,1036,1607,1510,1509,1386,1323,1316,1264,1263,1262,1211,1210,1204,1187,1157,1114,1065,1064,1025,1020,1019,1003,1002,986,937,922,912,881,880,879,873,872,871,870,857,856,836,835,831,824,823,821,818,817,816,797,796,761,760,759,758,742,690,689,688,687,685,684,683,682,1321,1320,1772,1771,1736,1721,1687,1666,1657,1656,1655,1639,1638,1637,1620,1619,1618,1617,1616,1520,1519,1518,1514,1495,1493,1490,1488,1487,1484,1483,1473,1394,1393,1392,1390,1379,1378,1365,1344,1280,1279,1275,1260,1225,1224,1220,1218,1217,1216,1215,1203,1190,1189,1167,1165,1159,1134,1133,1132,1047,1035,960,894,893,847,846,845,822,1765,1717,1711,1707,1692,1691,1685,1654,1653,1634,1633,1632,1631,1615,1614,1588,1587,1585,1584,1545,1544,1543,1542,1540,1531,1529,1528,1511,1472,1412,1402,1401,1287,1286,1285,1284,1283,1229,1228,1227,1722,1719,1693,1668,1667,1664,1663,983,1770,1748,1734,1733,1727,1726,1720,1406,1786])).
% 13.24/13.48 cnf(3170,plain,
% 13.24/13.48 (~E(a1,x31701)+P60(x31701)),
% 13.24/13.48 inference(scs_inference,[],[609,447,1835,1866,1891,1893,1933,1937,1948,2095,2141,2388,2393,2400,2461,2583,2586,2589,2628,2735,2758,2761,2770,2773,2796,448,1856,1938,2083,2128,2173,449,1812,1815,1927,2440,2447,592,1826,1885,1888,1934,2080,2137,2434,2437,2452,2744,2747,2764,205,206,208,210,212,213,214,215,216,217,221,229,232,233,243,247,250,251,256,257,267,271,272,274,275,280,290,295,301,302,305,306,307,311,312,313,314,315,318,319,320,323,324,325,326,334,338,353,354,357,358,359,363,365,366,368,370,371,375,376,382,385,389,390,392,393,394,395,396,400,401,403,404,407,408,412,417,423,463,1909,1912,2084,2113,2127,2131,2134,2189,595,1978,2116,2119,2574,453,454,455,458,597,580,581,585,437,436,435,472,473,587,596,505,589,428,431,432,590,492,491,555,608,569,574,496,1818,1821,2105,497,498,1908,602,1829,1832,603,484,2089,2092,479,2160,601,440,1967,2165,480,1850,1861,1869,2159,499,1872,2051,467,605,1842,1879,1975,1983,2046,2098,2140,2144,2155,2168,495,501,471,1953,516,1853,1882,1930,1972,2066,2069,2110,2156,450,604,2403,2,886,848,866,1361,1359,1349,1348,1345,1256,1251,1249,1079,1005,1026,800,1281,10,1594,1516,1515,1427,1413,1184,1183,1088,1087,1015,946,942,1322,1388,1494,1492,119,118,116,115,3,1098,1097,1094,1093,1092,1075,1013,957,955,902,901,771,1403,1130,1128,1305,1290,681,1535,1355,1324,1104,918,917,1155,1153,914,722,721,702,1602,1436,1292,1197,1192,1160,1181,1179,1178,1177,1176,1174,1173,1170,1169,1058,1031,969,968,919,913,789,719,718,717,716,714,713,712,711,693,692,1398,1397,1396,1395,1135,1085,921,949,935,865,864,1705,1704,931,1595,1485,1789,1787,1781,1779,1752,1751,1797,1782,1750,1749,1236,1233,1230,1113,1045,1037,970,967,1404,1426,1425,1424,1423,1422,1557,1556,1555,1554,1352,1732,1265,1384,1340,1468,1328,1327,1326,1325,980,1630,1317,999,998,993,928,927,926,854,853,763,762,746,743,1024,1023,752,1360,1274,1272,1271,1270,1255,1253,1066,991,780,779,766,765,748,708,707,706,705,704,703,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,1801,1800,1512,1084,1083,1061,1054,1053,985,984,876,875,863,862,861,839,838,793,739,738,736,674,673,1331,1330,1288,1266,1261,1241,1240,1109,1067,1062,1060,1056,1055,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,9,8,7,6,5,4,1593,1558,1522,1521,1432,1431,1430,1421,1420,1419,1418,1417,1416,1415,1414,1369,1367,1364,1363,1358,1357,1329,1295,1269,1268,1158,1116,1115,1108,1077,1073,1072,1069,1068,1033,1032,1021,1008,1006,979,950,943,939,938,936,887,844,843,842,833,811,810,809,808,798,788,787,786,784,783,782,777,776,775,774,773,772,750,749,729,728,727,720,678,677,676,675,672,1755,1709,1706,1596,1526,1525,1496,1470,1469,1356,1354,1353,1334,1333,1298,1297,1267,909,908,906,1243,1036,1607,1510,1509,1386,1323,1316,1264,1263,1262,1211,1210,1204,1187,1157,1114,1065,1064,1025,1020,1019,1003,1002,986,937,922,912,881,880,879,873,872,871,870,857,856,836,835,831,824,823,821,818,817,816,797,796,761,760,759,758,742,690,689,688,687,685,684,683,682,1321,1320,1772,1771,1736,1721,1687,1666,1657,1656,1655,1639,1638,1637,1620,1619,1618,1617,1616,1520,1519,1518,1514,1495,1493,1490,1488,1487,1484,1483,1473,1394,1393,1392,1390,1379,1378,1365,1344,1280,1279,1275,1260,1225,1224,1220,1218,1217,1216,1215,1203,1190,1189,1167,1165,1159,1134,1133,1132,1047,1035,960,894,893,847,846,845,822,1765,1717,1711,1707,1692,1691,1685,1654,1653,1634,1633,1632,1631,1615,1614,1588,1587,1585,1584,1545,1544,1543,1542,1540,1531,1529,1528,1511,1472,1412,1402,1401,1287,1286,1285,1284,1283,1229,1228,1227,1722,1719,1693,1668,1667,1664,1663,983,1770,1748,1734,1733,1727,1726,1720,1406,1786,1775,1756,1686,1777,1795,1796,203])).
% 13.24/13.48 cnf(3189,plain,
% 13.24/13.48 (E(f29(a2,f27(f12(a1))),f12(a1))),
% 13.24/13.48 inference(scs_inference,[],[609,447,1835,1866,1891,1893,1933,1937,1948,2095,2141,2388,2393,2400,2461,2583,2586,2589,2628,2735,2758,2761,2770,2773,2796,448,1856,1938,2083,2128,2173,449,1812,1815,1927,2440,2447,592,1826,1885,1888,1934,2080,2137,2434,2437,2452,2744,2747,2764,205,206,208,210,212,213,214,215,216,217,221,229,232,233,243,247,250,251,256,257,267,271,272,274,275,280,290,295,301,302,305,306,307,311,312,313,314,315,318,319,320,323,324,325,326,334,338,353,354,357,358,359,363,365,366,368,369,370,371,375,376,382,385,389,390,392,393,394,395,396,400,401,403,404,407,408,412,417,423,463,1909,1912,2084,2113,2127,2131,2134,2189,595,1978,2116,2119,2574,453,454,455,458,597,580,581,585,437,436,435,472,473,587,588,596,505,589,428,431,432,590,492,491,555,608,569,574,496,1818,1821,2105,497,498,1908,602,1829,1832,603,484,2089,2092,479,2160,601,440,1967,2165,2869,441,480,1850,1861,1869,2159,499,1872,2051,2126,500,467,605,1842,1879,1975,1983,2046,2098,2140,2144,2155,2168,495,501,471,1953,516,1853,1882,1930,1972,2066,2069,2110,2156,450,604,2403,2,886,848,866,1361,1359,1349,1348,1345,1256,1251,1249,1079,1005,1026,800,1281,10,1594,1516,1515,1427,1413,1184,1183,1088,1087,1015,946,942,1322,1388,1494,1492,119,118,116,115,3,1098,1097,1094,1093,1092,1075,1013,957,955,902,901,771,1403,1130,1128,1305,1290,681,1535,1355,1324,1104,918,917,1155,1153,914,722,721,702,1602,1436,1292,1197,1192,1160,1181,1179,1178,1177,1176,1174,1173,1170,1169,1058,1031,969,968,919,913,789,719,718,717,716,714,713,712,711,693,692,1398,1397,1396,1395,1135,1085,921,949,935,865,864,1705,1704,931,1595,1485,1789,1787,1781,1779,1752,1751,1797,1782,1750,1749,1236,1233,1230,1113,1045,1037,970,967,1404,1426,1425,1424,1423,1422,1557,1556,1555,1554,1352,1732,1265,1384,1340,1468,1328,1327,1326,1325,980,1630,1317,999,998,993,928,927,926,854,853,763,762,746,743,1024,1023,752,1360,1274,1272,1271,1270,1255,1253,1066,991,780,779,766,765,748,708,707,706,705,704,703,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,1801,1800,1512,1084,1083,1061,1054,1053,985,984,876,875,863,862,861,839,838,793,739,738,736,674,673,1331,1330,1288,1266,1261,1241,1240,1109,1067,1062,1060,1056,1055,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,9,8,7,6,5,4,1593,1558,1522,1521,1432,1431,1430,1421,1420,1419,1418,1417,1416,1415,1414,1369,1367,1364,1363,1358,1357,1329,1295,1269,1268,1158,1116,1115,1108,1077,1073,1072,1069,1068,1033,1032,1021,1008,1006,979,950,943,939,938,936,887,844,843,842,833,811,810,809,808,798,788,787,786,784,783,782,777,776,775,774,773,772,750,749,729,728,727,720,678,677,676,675,672,1755,1709,1706,1596,1526,1525,1496,1470,1469,1356,1354,1353,1334,1333,1298,1297,1267,909,908,906,1243,1036,1607,1510,1509,1386,1323,1316,1264,1263,1262,1211,1210,1204,1187,1157,1114,1065,1064,1025,1020,1019,1003,1002,986,937,922,912,881,880,879,873,872,871,870,857,856,836,835,831,824,823,821,818,817,816,797,796,761,760,759,758,742,690,689,688,687,685,684,683,682,1321,1320,1772,1771,1736,1721,1687,1666,1657,1656,1655,1639,1638,1637,1620,1619,1618,1617,1616,1520,1519,1518,1514,1495,1493,1490,1488,1487,1484,1483,1473,1394,1393,1392,1390,1379,1378,1365,1344,1280,1279,1275,1260,1225,1224,1220,1218,1217,1216,1215,1203,1190,1189,1167,1165,1159,1134,1133,1132,1047,1035,960,894,893,847,846,845,822,1765,1717,1711,1707,1692,1691,1685,1654,1653,1634,1633,1632,1631,1615,1614,1588,1587,1585,1584,1545,1544,1543,1542,1540,1531,1529,1528,1511,1472,1412,1402,1401,1287,1286,1285,1284,1283,1229,1228,1227,1722,1719,1693,1668,1667,1664,1663,983,1770,1748,1734,1733,1727,1726,1720,1406,1786,1775,1756,1686,1777,1795,1796,203,172,171,170,130,129,125,123,121,117,114,1208,1207,1076,1074,1010])).
% 13.24/13.48 cnf(3235,plain,
% 13.24/13.48 (P13(f72(a1),f13(f72(a1),f56(f56(f23(f72(a1)),f20(a1,f13(a1,x32351),f20(a1,f5(a1),f12(f72(a1))))),f21(a1,x32351,x32352))),x32352)),
% 13.24/13.48 inference(scs_inference,[],[609,447,1835,1866,1891,1893,1933,1937,1948,2095,2141,2388,2393,2400,2461,2583,2586,2589,2628,2735,2758,2761,2770,2773,2796,448,1856,1938,2083,2128,2173,449,1812,1815,1927,2440,2447,592,1826,1885,1888,1934,2080,2137,2434,2437,2452,2744,2747,2764,2767,205,206,208,210,212,213,214,215,216,217,221,229,232,233,243,247,250,251,256,257,267,271,272,274,275,280,290,295,301,302,305,306,307,311,312,313,314,315,318,319,320,323,324,325,326,334,338,353,354,357,358,359,363,365,366,368,369,370,371,375,376,382,385,389,390,392,393,394,395,396,400,401,403,404,407,408,412,417,423,463,1909,1912,2084,2113,2127,2131,2134,2189,595,1978,2116,2119,2574,453,454,455,458,597,580,581,585,437,436,435,438,472,473,587,588,596,505,589,427,428,430,431,432,590,492,491,555,608,569,574,496,1818,1821,2105,497,498,1908,602,1829,1832,2149,603,484,2089,2092,479,2160,601,440,1967,2165,2869,441,480,1850,1861,1869,2159,499,1872,2051,2126,500,467,605,1842,1879,1975,1983,2046,2098,2140,2144,2155,2168,495,501,471,1953,516,1853,1882,1930,1972,2066,2069,2110,2156,450,604,2403,2,886,848,866,1361,1359,1349,1348,1345,1256,1251,1249,1079,1005,1026,800,1281,10,1594,1516,1515,1427,1413,1184,1183,1088,1087,1015,946,942,1322,1388,1494,1492,119,118,116,115,3,1098,1097,1094,1093,1092,1075,1013,957,955,902,901,771,1403,1130,1128,1305,1290,681,1535,1355,1324,1104,918,917,1155,1153,914,722,721,702,1602,1436,1292,1197,1192,1160,1181,1179,1178,1177,1176,1174,1173,1170,1169,1058,1031,969,968,919,913,789,719,718,717,716,714,713,712,711,693,692,1398,1397,1396,1395,1135,1085,921,949,935,865,864,1705,1704,931,1595,1485,1789,1787,1781,1779,1752,1751,1797,1782,1750,1749,1236,1233,1230,1113,1045,1037,970,967,1404,1426,1425,1424,1423,1422,1557,1556,1555,1554,1352,1732,1265,1384,1340,1468,1328,1327,1326,1325,980,1630,1317,999,998,993,928,927,926,854,853,763,762,746,743,1024,1023,752,1360,1274,1272,1271,1270,1255,1253,1066,991,780,779,766,765,748,708,707,706,705,704,703,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,1801,1800,1512,1084,1083,1061,1054,1053,985,984,876,875,863,862,861,839,838,793,739,738,736,674,673,1331,1330,1288,1266,1261,1241,1240,1109,1067,1062,1060,1056,1055,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,9,8,7,6,5,4,1593,1558,1522,1521,1432,1431,1430,1421,1420,1419,1418,1417,1416,1415,1414,1369,1367,1364,1363,1358,1357,1329,1295,1269,1268,1158,1116,1115,1108,1077,1073,1072,1069,1068,1033,1032,1021,1008,1006,979,950,943,939,938,936,887,844,843,842,833,811,810,809,808,798,788,787,786,784,783,782,777,776,775,774,773,772,750,749,729,728,727,720,678,677,676,675,672,1755,1709,1706,1596,1526,1525,1496,1470,1469,1356,1354,1353,1334,1333,1298,1297,1267,909,908,906,1243,1036,1607,1510,1509,1386,1323,1316,1264,1263,1262,1211,1210,1204,1187,1157,1114,1065,1064,1025,1020,1019,1003,1002,986,937,922,912,881,880,879,873,872,871,870,857,856,836,835,831,824,823,821,818,817,816,797,796,761,760,759,758,742,690,689,688,687,685,684,683,682,1321,1320,1772,1771,1736,1721,1687,1666,1657,1656,1655,1639,1638,1637,1620,1619,1618,1617,1616,1520,1519,1518,1514,1495,1493,1490,1488,1487,1484,1483,1473,1394,1393,1392,1390,1379,1378,1365,1344,1280,1279,1275,1260,1225,1224,1220,1218,1217,1216,1215,1203,1190,1189,1167,1165,1159,1134,1133,1132,1047,1035,960,894,893,847,846,845,822,1765,1717,1711,1707,1692,1691,1685,1654,1653,1634,1633,1632,1631,1615,1614,1588,1587,1585,1584,1545,1544,1543,1542,1540,1531,1529,1528,1511,1472,1412,1402,1401,1287,1286,1285,1284,1283,1229,1228,1227,1722,1719,1693,1668,1667,1664,1663,983,1770,1748,1734,1733,1727,1726,1720,1406,1786,1775,1756,1686,1777,1795,1796,203,172,171,170,130,129,125,123,121,117,114,1208,1207,1076,1074,1010,934,933,769,803,1362,820,819,1532,1070,837,778,756,1474,1460,1405,1377,1376,1375,1336,1291,1131,1127,1082])).
% 13.24/13.48 cnf(3379,plain,
% 13.24/13.48 (~P9(a1,f13(a1,a81),f13(a1,f5(a1)))),
% 13.24/13.48 inference(scs_inference,[],[609,447,1835,1866,1891,1893,1933,1937,1948,2095,2141,2388,2393,2400,2461,2583,2586,2589,2628,2735,2758,2761,2770,2773,2796,448,1856,1938,2083,2128,2173,449,1812,1815,1927,2440,2447,592,1826,1885,1888,1934,2080,2137,2434,2437,2452,2744,2747,2764,2767,205,206,208,210,212,213,214,215,216,217,221,229,232,233,243,247,250,251,256,257,267,271,272,274,275,280,290,295,301,302,303,305,306,307,311,312,313,314,315,318,319,320,323,324,325,326,334,338,341,353,354,357,358,359,360,363,365,366,368,369,370,371,374,375,376,382,385,389,390,392,393,394,395,396,400,401,403,404,407,408,412,417,423,463,1909,1912,2084,2113,2127,2131,2134,2189,595,1978,2116,2119,2574,453,454,455,458,597,580,581,585,437,436,435,438,472,473,587,588,596,505,589,427,428,430,431,432,590,492,491,555,608,569,574,496,1818,1821,2105,497,498,1908,602,1829,1832,2149,603,484,2089,2092,479,2160,601,440,1967,2165,2869,441,480,1850,1861,1869,2159,499,1872,2051,2126,500,467,605,1842,1879,1975,1983,2046,2098,2140,2144,2155,2168,495,501,471,1953,516,1853,1882,1930,1972,2066,2069,2110,2156,450,604,2403,2,886,848,866,1361,1359,1349,1348,1345,1256,1251,1249,1079,1005,1026,800,1281,10,1594,1516,1515,1427,1413,1184,1183,1088,1087,1015,946,942,1322,1388,1494,1492,119,118,116,115,3,1098,1097,1094,1093,1092,1075,1013,957,955,902,901,771,1403,1130,1128,1305,1290,681,1535,1355,1324,1104,918,917,1155,1153,914,722,721,702,1602,1436,1292,1197,1192,1160,1181,1179,1178,1177,1176,1174,1173,1170,1169,1058,1031,969,968,919,913,789,719,718,717,716,714,713,712,711,693,692,1398,1397,1396,1395,1135,1085,921,949,935,865,864,1705,1704,931,1595,1485,1789,1787,1781,1779,1752,1751,1797,1782,1750,1749,1236,1233,1230,1113,1045,1037,970,967,1404,1426,1425,1424,1423,1422,1557,1556,1555,1554,1352,1732,1265,1384,1340,1468,1328,1327,1326,1325,980,1630,1317,999,998,993,928,927,926,854,853,763,762,746,743,1024,1023,752,1360,1274,1272,1271,1270,1255,1253,1066,991,780,779,766,765,748,708,707,706,705,704,703,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,1801,1800,1512,1084,1083,1061,1054,1053,985,984,876,875,863,862,861,839,838,793,739,738,736,674,673,1331,1330,1288,1266,1261,1241,1240,1109,1067,1062,1060,1056,1055,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,9,8,7,6,5,4,1593,1558,1522,1521,1432,1431,1430,1421,1420,1419,1418,1417,1416,1415,1414,1369,1367,1364,1363,1358,1357,1329,1295,1269,1268,1158,1116,1115,1108,1077,1073,1072,1069,1068,1033,1032,1021,1008,1006,979,950,943,939,938,936,887,844,843,842,833,811,810,809,808,798,788,787,786,784,783,782,777,776,775,774,773,772,750,749,729,728,727,720,678,677,676,675,672,1755,1709,1706,1596,1526,1525,1496,1470,1469,1356,1354,1353,1334,1333,1298,1297,1267,909,908,906,1243,1036,1607,1510,1509,1386,1323,1316,1264,1263,1262,1211,1210,1204,1187,1157,1114,1065,1064,1025,1020,1019,1003,1002,986,937,922,912,881,880,879,873,872,871,870,857,856,836,835,831,824,823,821,818,817,816,797,796,761,760,759,758,742,690,689,688,687,685,684,683,682,1321,1320,1772,1771,1736,1721,1687,1666,1657,1656,1655,1639,1638,1637,1620,1619,1618,1617,1616,1520,1519,1518,1514,1495,1493,1490,1488,1487,1484,1483,1473,1394,1393,1392,1390,1379,1378,1365,1344,1280,1279,1275,1260,1225,1224,1220,1218,1217,1216,1215,1203,1190,1189,1167,1165,1159,1134,1133,1132,1047,1035,960,894,893,847,846,845,822,1765,1717,1711,1707,1692,1691,1685,1654,1653,1634,1633,1632,1631,1615,1614,1588,1587,1585,1584,1545,1544,1543,1542,1540,1531,1529,1528,1511,1472,1412,1402,1401,1287,1286,1285,1284,1283,1229,1228,1227,1722,1719,1693,1668,1667,1664,1663,983,1770,1748,1734,1733,1727,1726,1720,1406,1786,1775,1756,1686,1777,1795,1796,203,172,171,170,130,129,125,123,121,117,114,1208,1207,1076,1074,1010,934,933,769,803,1362,820,819,1532,1070,837,778,756,1474,1460,1405,1377,1376,1375,1336,1291,1131,1127,1082,1081,1057,792,1539,1538,1491,1107,1106,1105,1102,1101,791,790,735,733,732,731,1629,1628,1626,1625,1622,1504,1503,1502,1498,1497,1242,1052,1051,1050,1048,1776,1665,1276,1537,1536,1156,1122,1121,1120,1119,1016,959,958,905,834,802,709,691,680,1731,1541,1022,889,858,1606,1604,1600,1440,1438,1435,1434,1433,1409,1408,1407,1381,1380,1294,1293,1222])).
% 13.24/13.48 cnf(3546,plain,
% 13.24/13.48 (~E(f15(a3,f15(a3,f5(a3),x35461),x35461),f12(a3))),
% 13.24/13.48 inference(rename_variables,[],[604])).
% 13.24/13.48 cnf(3816,plain,
% 13.24/13.48 (P9(a3,x38161,x38161)),
% 13.24/13.48 inference(rename_variables,[],[449])).
% 13.24/13.48 cnf(3819,plain,
% 13.24/13.48 (P9(a3,x38191,x38191)),
% 13.24/13.48 inference(rename_variables,[],[449])).
% 13.24/13.48 cnf(3849,plain,
% 13.24/13.48 (~E(f15(a2,x38491,f6(a1,f15(a4,f12(f72(a1)),f56(f17(a4,a73),a75)))),x38491)),
% 13.24/13.48 inference(scs_inference,[],[609,447,1835,1866,1891,1893,1933,1937,1948,2095,2141,2388,2393,2400,2461,2583,2586,2589,2628,2735,2758,2761,2770,2773,2796,448,1856,1938,2083,2128,2173,449,1812,1815,1927,2440,2447,3816,3819,592,1826,1885,1888,1934,2080,2137,2434,2437,2452,2744,2747,2764,2767,205,206,207,208,210,212,213,214,215,216,217,218,220,221,222,224,225,226,228,229,230,232,233,236,237,239,243,247,250,251,253,255,256,257,259,261,262,267,271,272,273,274,275,276,278,279,280,281,282,283,284,287,288,289,290,292,293,294,295,300,301,302,303,305,306,307,308,309,311,312,313,314,315,318,319,320,322,323,324,325,326,334,338,341,353,354,357,358,359,360,363,365,366,368,369,370,371,372,373,374,375,376,379,382,385,388,389,390,392,393,394,395,396,400,401,403,404,407,408,412,417,418,423,463,1909,1912,2084,2113,2127,2131,2134,2189,595,1978,2116,2119,2574,453,454,455,456,457,458,597,580,581,585,437,436,435,438,472,473,587,588,596,505,589,427,428,430,431,432,433,434,590,492,491,470,555,544,545,608,569,573,574,496,1818,1821,2105,497,498,1908,602,1829,1832,2149,603,2152,484,2089,2092,2186,485,461,479,2160,601,440,1967,2165,2869,441,480,1850,1861,1869,2159,499,1872,2051,2126,500,464,465,466,467,1945,468,605,1842,1879,1975,1983,2046,2098,2140,2144,2155,2168,495,494,501,471,1953,516,1853,1882,1930,1972,2066,2069,2110,2156,2910,450,604,2403,3546,517,528,560,2,886,848,866,1361,1359,1349,1348,1345,1256,1251,1249,1079,1005,1026,800,1281,10,1594,1516,1515,1427,1413,1184,1183,1088,1087,1015,946,942,1322,1388,1494,1492,119,118,116,115,3,1098,1097,1094,1093,1092,1075,1013,957,955,902,901,771,1403,1130,1128,1305,1290,681,1535,1355,1324,1104,918,917,1155,1153,914,722,721,702,1602,1436,1292,1197,1192,1160,1181,1179,1178,1177,1176,1174,1173,1170,1169,1058,1031,969,968,919,913,789,719,718,717,716,714,713,712,711,693,692,1398,1397,1396,1395,1135,1085,921,949,935,865,864,1705,1704,931,1595,1485,1789,1787,1781,1779,1752,1751,1797,1782,1750,1749,1236,1233,1230,1113,1045,1037,970,967,1404,1426,1425,1424,1423,1422,1557,1556,1555,1554,1352,1732,1265,1384,1340,1468,1328,1327,1326,1325,980,1630,1317,999,998,993,928,927,926,854,853,763,762,746,743,1024,1023,752,1360,1274,1272,1271,1270,1255,1253,1066,991,780,779,766,765,748,708,707,706,705,704,703,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,1801,1800,1512,1084,1083,1061,1054,1053,985,984,876,875,863,862,861,839,838,793,739,738,736,674,673,1331,1330,1288,1266,1261,1241,1240,1109,1067,1062,1060,1056,1055,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,9,8,7,6,5,4,1593,1558,1522,1521,1432,1431,1430,1421,1420,1419,1418,1417,1416,1415,1414,1369,1367,1364,1363,1358,1357,1329,1295,1269,1268,1158,1116,1115,1108,1077,1073,1072,1069,1068,1033,1032,1021,1008,1006,979,950,943,939,938,936,887,844,843,842,833,811,810,809,808,798,788,787,786,784,783,782,777,776,775,774,773,772,750,749,729,728,727,720,678,677,676,675,672,1755,1709,1706,1596,1526,1525,1496,1470,1469,1356,1354,1353,1334,1333,1298,1297,1267,909,908,906,1243,1036,1607,1510,1509,1386,1323,1316,1264,1263,1262,1211,1210,1204,1187,1157,1114,1065,1064,1025,1020,1019,1003,1002,986,937,922,912,881,880,879,873,872,871,870,857,856,836,835,831,824,823,821,818,817,816,797,796,761,760,759,758,742,690,689,688,687,685,684,683,682,1321,1320,1772,1771,1736,1721,1687,1666,1657,1656,1655,1639,1638,1637,1620,1619,1618,1617,1616,1520,1519,1518,1514,1495,1493,1490,1488,1487,1484,1483,1473,1394,1393,1392,1390,1379,1378,1365,1344,1280,1279,1275,1260,1225,1224,1220,1218,1217,1216,1215,1203,1190,1189,1167,1165,1159,1134,1133,1132,1047,1035,960,894,893,847,846,845,822,1765,1717,1711,1707,1692,1691,1685,1654,1653,1634,1633,1632,1631,1615,1614,1588,1587,1585,1584,1545,1544,1543,1542,1540,1531,1529,1528,1511,1472,1412,1402,1401,1287,1286,1285,1284,1283,1229,1228,1227,1722,1719,1693,1668,1667,1664,1663,983,1770,1748,1734,1733,1727,1726,1720,1406,1786,1775,1756,1686,1777,1795,1796,203,172,171,170,130,129,125,123,121,117,114,1208,1207,1076,1074,1010,934,933,769,803,1362,820,819,1532,1070,837,778,756,1474,1460,1405,1377,1376,1375,1336,1291,1131,1127,1082,1081,1057,792,1539,1538,1491,1107,1106,1105,1102,1101,791,790,735,733,732,731,1629,1628,1626,1625,1622,1504,1503,1502,1498,1497,1242,1052,1051,1050,1048,1776,1665,1276,1537,1536,1156,1122,1121,1120,1119,1016,959,958,905,834,802,709,691,680,1731,1541,1022,889,858,1606,1604,1600,1440,1438,1435,1434,1433,1409,1408,1407,1381,1380,1294,1293,1222,1221,1201,1199,1196,1194,1162,885,878,726,724,1609,1608,1313,1303,1302,1301,1213,1212,1182,1172,1151,1150,1149,1148,1147,1146,1145,1144,1143,1142,1141,1140,1139,1138,1137,1136,974,945,944,916,895,868,867,826,825,805,804,747,741,740,730,699,698,697,696,695,694,1598,1428,1312,1311,1310,1309,1308,989,988,987,813,806,1001,975,948,947,1643,1597,972,971,903,890,874,1684,990,1738,1737,1689,1688,1534,1533,1374,1226,883,1790,1788,1780,1778,1761,1760,1794,1793,1792,1791,1785,1784,1783,1759,1758,1168,1039,961,1724,1034,1589,1411,1410,1205,1125,1124,757,841,1578,1429,1672,1670,1553,1551,1315,1307,1471,1373,1371,1350,1741,1730,1678,1577,1683,1682,1681,1680,1679,1677,1676,1675,1674,1673,1647,1646,1645,1644,1576,1574,1573,1572,1571,1570,1569,1568,1566,1564,1563,1562,1126,1524,1523,1479,1475,1467,1466,1465,1461,1459,1458,1457,1455,1452,1451,1449,1448,1447,1446,1445,1444,1443,1441,1185,981,925,924,910,1659,1658,1708,1695,976,1710,1740,1728,1690,1332,1714,1549,1548,1547,1546,1296,1764,1746,1745,1773,1763,1762,1660,1661,1580,1579,1754,1343,1342,978,977,1701,1700,1699,1698,1697,1696,904,1744,1743,882,892,891,859])).
% 13.24/13.48 cnf(3855,plain,
% 13.24/13.48 (E(x38551,f13(a1,f10(a1,f12(a1),x38551)))),
% 13.24/13.48 inference(scs_inference,[],[609,447,1835,1866,1891,1893,1933,1937,1948,2095,2141,2388,2393,2400,2461,2583,2586,2589,2628,2735,2758,2761,2770,2773,2796,448,1856,1938,2083,2128,2173,449,1812,1815,1927,2440,2447,3816,3819,592,1826,1885,1888,1934,2080,2137,2434,2437,2452,2744,2747,2764,2767,205,206,207,208,210,212,213,214,215,216,217,218,220,221,222,224,225,226,228,229,230,232,233,236,237,239,243,247,250,251,253,255,256,257,259,261,262,267,271,272,273,274,275,276,278,279,280,281,282,283,284,287,288,289,290,292,293,294,295,300,301,302,303,305,306,307,308,309,311,312,313,314,315,318,319,320,322,323,324,325,326,334,338,341,353,354,357,358,359,360,363,365,366,368,369,370,371,372,373,374,375,376,379,382,385,388,389,390,392,393,394,395,396,400,401,403,404,407,408,412,417,418,423,463,1909,1912,2084,2113,2127,2131,2134,2189,595,1978,2116,2119,2574,453,454,455,456,457,458,597,580,581,585,437,436,435,438,472,473,587,588,596,505,589,427,428,430,431,432,433,434,590,492,491,470,555,544,545,608,569,573,574,496,1818,1821,2105,497,498,1908,602,1829,1832,2149,603,2152,484,2089,2092,2186,485,461,479,2160,601,440,1967,2165,2869,441,480,1850,1861,1869,2159,499,1872,2051,2126,500,464,465,466,467,1945,468,605,1842,1879,1975,1983,2046,2098,2140,2144,2155,2168,495,494,501,471,1953,516,1853,1882,1930,1972,2066,2069,2110,2156,2910,450,604,2403,3546,517,528,560,2,886,848,866,1361,1359,1349,1348,1345,1256,1251,1249,1079,1005,1026,800,1281,10,1594,1516,1515,1427,1413,1184,1183,1088,1087,1015,946,942,1322,1388,1494,1492,119,118,116,115,3,1098,1097,1094,1093,1092,1075,1013,957,955,902,901,771,1403,1130,1128,1305,1290,681,1535,1355,1324,1104,918,917,1155,1153,914,722,721,702,1602,1436,1292,1197,1192,1160,1181,1179,1178,1177,1176,1174,1173,1170,1169,1058,1031,969,968,919,913,789,719,718,717,716,714,713,712,711,693,692,1398,1397,1396,1395,1135,1085,921,949,935,865,864,1705,1704,931,1595,1485,1789,1787,1781,1779,1752,1751,1797,1782,1750,1749,1236,1233,1230,1113,1045,1037,970,967,1404,1426,1425,1424,1423,1422,1557,1556,1555,1554,1352,1732,1265,1384,1340,1468,1328,1327,1326,1325,980,1630,1317,999,998,993,928,927,926,854,853,763,762,746,743,1024,1023,752,1360,1274,1272,1271,1270,1255,1253,1066,991,780,779,766,765,748,708,707,706,705,704,703,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,1801,1800,1512,1084,1083,1061,1054,1053,985,984,876,875,863,862,861,839,838,793,739,738,736,674,673,1331,1330,1288,1266,1261,1241,1240,1109,1067,1062,1060,1056,1055,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,9,8,7,6,5,4,1593,1558,1522,1521,1432,1431,1430,1421,1420,1419,1418,1417,1416,1415,1414,1369,1367,1364,1363,1358,1357,1329,1295,1269,1268,1158,1116,1115,1108,1077,1073,1072,1069,1068,1033,1032,1021,1008,1006,979,950,943,939,938,936,887,844,843,842,833,811,810,809,808,798,788,787,786,784,783,782,777,776,775,774,773,772,750,749,729,728,727,720,678,677,676,675,672,1755,1709,1706,1596,1526,1525,1496,1470,1469,1356,1354,1353,1334,1333,1298,1297,1267,909,908,906,1243,1036,1607,1510,1509,1386,1323,1316,1264,1263,1262,1211,1210,1204,1187,1157,1114,1065,1064,1025,1020,1019,1003,1002,986,937,922,912,881,880,879,873,872,871,870,857,856,836,835,831,824,823,821,818,817,816,797,796,761,760,759,758,742,690,689,688,687,685,684,683,682,1321,1320,1772,1771,1736,1721,1687,1666,1657,1656,1655,1639,1638,1637,1620,1619,1618,1617,1616,1520,1519,1518,1514,1495,1493,1490,1488,1487,1484,1483,1473,1394,1393,1392,1390,1379,1378,1365,1344,1280,1279,1275,1260,1225,1224,1220,1218,1217,1216,1215,1203,1190,1189,1167,1165,1159,1134,1133,1132,1047,1035,960,894,893,847,846,845,822,1765,1717,1711,1707,1692,1691,1685,1654,1653,1634,1633,1632,1631,1615,1614,1588,1587,1585,1584,1545,1544,1543,1542,1540,1531,1529,1528,1511,1472,1412,1402,1401,1287,1286,1285,1284,1283,1229,1228,1227,1722,1719,1693,1668,1667,1664,1663,983,1770,1748,1734,1733,1727,1726,1720,1406,1786,1775,1756,1686,1777,1795,1796,203,172,171,170,130,129,125,123,121,117,114,1208,1207,1076,1074,1010,934,933,769,803,1362,820,819,1532,1070,837,778,756,1474,1460,1405,1377,1376,1375,1336,1291,1131,1127,1082,1081,1057,792,1539,1538,1491,1107,1106,1105,1102,1101,791,790,735,733,732,731,1629,1628,1626,1625,1622,1504,1503,1502,1498,1497,1242,1052,1051,1050,1048,1776,1665,1276,1537,1536,1156,1122,1121,1120,1119,1016,959,958,905,834,802,709,691,680,1731,1541,1022,889,858,1606,1604,1600,1440,1438,1435,1434,1433,1409,1408,1407,1381,1380,1294,1293,1222,1221,1201,1199,1196,1194,1162,885,878,726,724,1609,1608,1313,1303,1302,1301,1213,1212,1182,1172,1151,1150,1149,1148,1147,1146,1145,1144,1143,1142,1141,1140,1139,1138,1137,1136,974,945,944,916,895,868,867,826,825,805,804,747,741,740,730,699,698,697,696,695,694,1598,1428,1312,1311,1310,1309,1308,989,988,987,813,806,1001,975,948,947,1643,1597,972,971,903,890,874,1684,990,1738,1737,1689,1688,1534,1533,1374,1226,883,1790,1788,1780,1778,1761,1760,1794,1793,1792,1791,1785,1784,1783,1759,1758,1168,1039,961,1724,1034,1589,1411,1410,1205,1125,1124,757,841,1578,1429,1672,1670,1553,1551,1315,1307,1471,1373,1371,1350,1741,1730,1678,1577,1683,1682,1681,1680,1679,1677,1676,1675,1674,1673,1647,1646,1645,1644,1576,1574,1573,1572,1571,1570,1569,1568,1566,1564,1563,1562,1126,1524,1523,1479,1475,1467,1466,1465,1461,1459,1458,1457,1455,1452,1451,1449,1448,1447,1446,1445,1444,1443,1441,1185,981,925,924,910,1659,1658,1708,1695,976,1710,1740,1728,1690,1332,1714,1549,1548,1547,1546,1296,1764,1746,1745,1773,1763,1762,1660,1661,1580,1579,1754,1343,1342,978,977,1701,1700,1699,1698,1697,1696,904,1744,1743,882,892,891,859,801,941,915])).
% 13.24/13.48 cnf(3905,plain,
% 13.24/13.48 (E(x39051,f13(a1,f10(a1,f12(a1),x39051)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3907,plain,
% 13.24/13.48 (~E(f15(a2,x39071,f6(a1,f15(a4,f12(f72(a1)),f56(f17(a4,a73),a75)))),x39071)),
% 13.24/13.48 inference(rename_variables,[],[3849])).
% 13.24/13.48 cnf(3910,plain,
% 13.24/13.48 (~E(f15(a2,x39101,f6(a1,f15(a4,f12(f72(a1)),f56(f17(a4,a73),a75)))),x39101)),
% 13.24/13.48 inference(rename_variables,[],[3849])).
% 13.24/13.48 cnf(3913,plain,
% 13.24/13.48 (~P10(a1,x39131,x39131)),
% 13.24/13.48 inference(rename_variables,[],[1805])).
% 13.24/13.48 cnf(3922,plain,
% 13.24/13.48 (E(x39221,f13(a1,f10(a1,f12(a1),x39221)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3924,plain,
% 13.24/13.48 (E(x39241,f13(a1,f10(a1,f12(a1),x39241)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3926,plain,
% 13.24/13.48 (E(x39261,f13(a1,f10(a1,f12(a1),x39261)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3928,plain,
% 13.24/13.48 (E(x39281,f13(a1,f10(a1,f12(a1),x39281)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3930,plain,
% 13.24/13.48 (E(x39301,f13(a1,f10(a1,f12(a1),x39301)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3932,plain,
% 13.24/13.48 (E(x39321,f13(a1,f10(a1,f12(a1),x39321)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3934,plain,
% 13.24/13.48 (E(x39341,f13(a1,f10(a1,f12(a1),x39341)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3936,plain,
% 13.24/13.48 (E(x39361,f13(a1,f10(a1,f12(a1),x39361)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3938,plain,
% 13.24/13.48 (E(x39381,f13(a1,f10(a1,f12(a1),x39381)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3940,plain,
% 13.24/13.48 (E(x39401,f13(a1,f10(a1,f12(a1),x39401)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3942,plain,
% 13.24/13.48 (E(x39421,f13(a1,f10(a1,f12(a1),x39421)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3944,plain,
% 13.24/13.48 (E(x39441,f13(a1,f10(a1,f12(a1),x39441)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3946,plain,
% 13.24/13.48 (E(x39461,f13(a1,f10(a1,f12(a1),x39461)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3948,plain,
% 13.24/13.48 (E(x39481,f13(a1,f10(a1,f12(a1),x39481)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3950,plain,
% 13.24/13.48 (E(x39501,f13(a1,f10(a1,f12(a1),x39501)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3952,plain,
% 13.24/13.48 (E(x39521,f13(a1,f10(a1,f12(a1),x39521)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3954,plain,
% 13.24/13.48 (E(x39541,f13(a1,f10(a1,f12(a1),x39541)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3956,plain,
% 13.24/13.48 (E(x39561,f13(a1,f10(a1,f12(a1),x39561)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3958,plain,
% 13.24/13.48 (E(x39581,f13(a1,f10(a1,f12(a1),x39581)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3960,plain,
% 13.24/13.48 (E(x39601,f13(a1,f10(a1,f12(a1),x39601)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3962,plain,
% 13.24/13.48 (E(x39621,f13(a1,f10(a1,f12(a1),x39621)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3964,plain,
% 13.24/13.48 (E(x39641,f13(a1,f10(a1,f12(a1),x39641)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3966,plain,
% 13.24/13.48 (E(x39661,f13(a1,f10(a1,f12(a1),x39661)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3968,plain,
% 13.24/13.48 (E(x39681,f13(a1,f10(a1,f12(a1),x39681)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3970,plain,
% 13.24/13.48 (E(x39701,f13(a1,f10(a1,f12(a1),x39701)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3972,plain,
% 13.24/13.48 (E(x39721,f13(a1,f10(a1,f12(a1),x39721)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3974,plain,
% 13.24/13.48 (E(x39741,f13(a1,f10(a1,f12(a1),x39741)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3976,plain,
% 13.24/13.48 (E(x39761,f13(a1,f10(a1,f12(a1),x39761)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3978,plain,
% 13.24/13.48 (E(x39781,f13(a1,f10(a1,f12(a1),x39781)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3980,plain,
% 13.24/13.48 (E(x39801,f13(a1,f10(a1,f12(a1),x39801)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3982,plain,
% 13.24/13.48 (E(x39821,f13(a1,f10(a1,f12(a1),x39821)))),
% 13.24/13.48 inference(rename_variables,[],[3855])).
% 13.24/13.48 cnf(3984,plain,
% 13.24/13.49 (E(x39841,f13(a1,f10(a1,f12(a1),x39841)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(3986,plain,
% 13.24/13.49 (E(x39861,f13(a1,f10(a1,f12(a1),x39861)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(3988,plain,
% 13.24/13.49 (E(x39881,f13(a1,f10(a1,f12(a1),x39881)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(3990,plain,
% 13.24/13.49 (E(x39901,f13(a1,f10(a1,f12(a1),x39901)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(3992,plain,
% 13.24/13.49 (E(x39921,f13(a1,f10(a1,f12(a1),x39921)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(3994,plain,
% 13.24/13.49 (E(x39941,f13(a1,f10(a1,f12(a1),x39941)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(3996,plain,
% 13.24/13.49 (E(x39961,f13(a1,f10(a1,f12(a1),x39961)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(3998,plain,
% 13.24/13.49 (E(x39981,f13(a1,f10(a1,f12(a1),x39981)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4000,plain,
% 13.24/13.49 (E(x40001,f13(a1,f10(a1,f12(a1),x40001)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4002,plain,
% 13.24/13.49 (E(x40021,f13(a1,f10(a1,f12(a1),x40021)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4004,plain,
% 13.24/13.49 (E(x40041,f13(a1,f10(a1,f12(a1),x40041)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4006,plain,
% 13.24/13.49 (E(x40061,f13(a1,f10(a1,f12(a1),x40061)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4008,plain,
% 13.24/13.49 (E(x40081,f13(a1,f10(a1,f12(a1),x40081)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4010,plain,
% 13.24/13.49 (E(x40101,f13(a1,f10(a1,f12(a1),x40101)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4012,plain,
% 13.24/13.49 (E(x40121,f13(a1,f10(a1,f12(a1),x40121)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4014,plain,
% 13.24/13.49 (E(x40141,f13(a1,f10(a1,f12(a1),x40141)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4016,plain,
% 13.24/13.49 (E(x40161,f13(a1,f10(a1,f12(a1),x40161)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4018,plain,
% 13.24/13.49 (E(x40181,f13(a1,f10(a1,f12(a1),x40181)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4020,plain,
% 13.24/13.49 (E(x40201,f13(a1,f10(a1,f12(a1),x40201)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4022,plain,
% 13.24/13.49 (E(x40221,f13(a1,f10(a1,f12(a1),x40221)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4024,plain,
% 13.24/13.49 (E(x40241,f13(a1,f10(a1,f12(a1),x40241)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4026,plain,
% 13.24/13.49 (E(x40261,f13(a1,f10(a1,f12(a1),x40261)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4028,plain,
% 13.24/13.49 (E(x40281,f13(a1,f10(a1,f12(a1),x40281)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4030,plain,
% 13.24/13.49 (E(x40301,f13(a1,f10(a1,f12(a1),x40301)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4032,plain,
% 13.24/13.49 (E(x40321,f13(a1,f10(a1,f12(a1),x40321)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4034,plain,
% 13.24/13.49 (E(x40341,f13(a1,f10(a1,f12(a1),x40341)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4036,plain,
% 13.24/13.49 (E(x40361,f13(a1,f10(a1,f12(a1),x40361)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4038,plain,
% 13.24/13.49 (E(x40381,f13(a1,f10(a1,f12(a1),x40381)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4040,plain,
% 13.24/13.49 (E(x40401,f13(a1,f10(a1,f12(a1),x40401)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4042,plain,
% 13.24/13.49 (E(x40421,f13(a1,f10(a1,f12(a1),x40421)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4044,plain,
% 13.24/13.49 (E(x40441,f13(a1,f10(a1,f12(a1),x40441)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4046,plain,
% 13.24/13.49 (E(x40461,f13(a1,f10(a1,f12(a1),x40461)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4048,plain,
% 13.24/13.49 (E(x40481,f13(a1,f10(a1,f12(a1),x40481)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4050,plain,
% 13.24/13.49 (E(x40501,f13(a1,f10(a1,f12(a1),x40501)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4052,plain,
% 13.24/13.49 (E(x40521,f13(a1,f10(a1,f12(a1),x40521)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4054,plain,
% 13.24/13.49 (E(x40541,f13(a1,f10(a1,f12(a1),x40541)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4056,plain,
% 13.24/13.49 (E(x40561,f13(a1,f10(a1,f12(a1),x40561)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4058,plain,
% 13.24/13.49 (E(x40581,f13(a1,f10(a1,f12(a1),x40581)))),
% 13.24/13.49 inference(rename_variables,[],[3855])).
% 13.24/13.49 cnf(4078,plain,
% 13.24/13.49 (~P10(a1,x40781,x40781)),
% 13.24/13.49 inference(rename_variables,[],[1805])).
% 13.24/13.49 cnf(4083,plain,
% 13.24/13.49 ($false),
% 13.24/13.49 inference(scs_inference,[],[609,1805,3913,4078,209,211,219,223,227,231,234,238,240,244,246,252,254,258,260,263,268,277,285,291,298,304,310,321,327,329,333,339,342,345,349,355,367,377,380,383,386,391,397,402,406,409,413,419,424,527,577,575,578,362,447,273,276,282,302,305,319,373,417,395,360,215,293,370,250,407,207,280,403,392,320,357,213,257,324,288,314,3849,3907,3910,1962,3379,3855,3905,3922,3924,3926,3928,3930,3932,3934,3936,3938,3940,3942,3944,3946,3948,3950,3952,3954,3956,3958,3960,3962,3964,3966,3968,3970,3972,3974,3976,3978,3980,3982,3984,3986,3988,3990,3992,3994,3996,3998,4000,4002,4004,4006,4008,4010,4012,4014,4016,4018,4020,4022,4024,4026,4028,4030,4032,4034,4036,4038,4040,4042,4044,4046,4048,4050,4052,4054,4056,4058,3156,2615,3235,3189,2634,2287,3170,830,829,1802,1387,1118,1389,202,201,200,199,198,197,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,137,133,132,131,128,127,126,124,122,120,113,1180,1175,1621,1399,884,1513,1238,1235,1234,1232]),
% 13.24/13.49 ['proof']).
% 13.24/13.49 % SZS output end Proof
% 13.24/13.49 % Total time :12.220000s
%------------------------------------------------------------------------------