%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW377+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n022.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 : Mon Jun 24 18:08:48 EDT 2024 % Result : Theorem 167.45s 167.48s % Output : CNFRefutation 167.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SWW377+1 : TPTP v8.2.0. Released v5.2.0. % 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n022.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 : Wed Jun 19 04:25:54 EDT 2024 % 0.13/0.34 % CPUTime : % 0.59/0.64 start to proof:theBenchmark % 167.16/167.31 %------------------------------------------- % 167.16/167.31 % File :CSE---1.7 % 167.16/167.31 % Problem :theBenchmark % 167.16/167.31 % Transform :cnf % 167.16/167.31 % Format :tptp:raw % 167.16/167.31 % Command :java -jar mcs_scs.jar %d %s % 167.16/167.31 % 167.16/167.31 % Result :Theorem 147.750000s % 167.16/167.31 % Output :CNFRefutation 147.750000s % 167.16/167.31 %------------------------------------------- % 167.16/167.32 %------------------------------------------------------------------------------ % 167.16/167.32 % File : SWW377+1 : TPTP v8.2.0. Released v5.2.0. % 167.16/167.32 % Domain : Software Verification % 167.16/167.32 % Problem : Hoare's Logic with Procedures 435564, 5000 axioms selected % 167.16/167.32 % Version : Especial. % 167.16/167.32 % English : % 167.16/167.32 % 167.16/167.32 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 167.16/167.32 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 167.16/167.32 % Source : [Bla11] % 167.16/167.32 % Names : hoare_435564.5000.p [Bla11] % 167.16/167.32 % 167.16/167.32 % Status : ContradictoryAxioms % 167.16/167.32 % Rating : 0.83 v8.2.0, 0.81 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.87 v7.0.0, 0.93 v6.4.0, 0.88 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.96 v5.3.0, 1.00 v5.2.0 % 167.16/167.32 % Syntax : Number of formulae : 5240 (1727 unt; 0 def) % 167.16/167.32 % Number of atoms : 12607 (4520 equ) % 167.16/167.32 % Maximal formula atoms : 13 ( 2 avg) % 167.16/167.32 % Number of connectives : 8376 (1009 ~; 155 |; 718 &) % 167.16/167.32 % ( 898 <=>;5596 =>; 0 <=; 0 <~>) % 167.16/167.32 % Maximal formula depth : 22 ( 6 avg) % 167.16/167.32 % Maximal term depth : 19 ( 2 avg) % 167.16/167.32 % Number of predicates : 145 ( 144 usr; 2 prp; 0-6 aty) % 167.16/167.32 % Number of functors : 383 ( 383 usr; 55 con; 0-7 aty) % 167.16/167.32 % Number of variables : 16655 (16511 !; 144 ?) % 167.16/167.32 % SPC : FOF_CAX_RFO_SEQ % 167.16/167.32 % 167.16/167.32 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 167.16/167.32 % 2011-03-01 12:50:57 % 167.16/167.32 %------------------------------------------------------------------------------ % 167.16/167.32 %----Relevant facts (4986) % 167.16/167.32 fof(fact_ext,axiom, % 167.16/167.32 ! [V_g_2,V_f_2] : % 167.16/167.32 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 167.16/167.32 => V_f_2 = V_g_2 ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_triple_Oinject,axiom, % 167.16/167.32 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] : % 167.16/167.32 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H_2),V_com_H_2),V_fun2_H_2) % 167.16/167.32 <=> ( V_fun1_2 = V_fun1_H_2 % 167.16/167.32 & V_com_2 = V_com_H_2 % 167.16/167.32 & V_fun2_2 = V_fun2_H_2 ) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_cut,axiom, % 167.16/167.32 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 167.16/167.32 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 167.16/167.32 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_G_H_2) % 167.16/167.32 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_hoare__derivs_OBody,axiom, % 167.16/167.32 ! [V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 167.16/167.32 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2)) % 167.16/167.32 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_evalc__elim__cases_I6_J,axiom, % 167.16/167.32 ! [V_s1,V_s,V_P] : % 167.16/167.32 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) % 167.16/167.32 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_evalc_OBody,axiom, % 167.16/167.32 ! [V_s1,V_s0,V_pn] : % 167.16/167.32 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) % 167.16/167.32 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_Body__sound__lemma,axiom, % 167.16/167.32 ! [V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 167.16/167.32 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2)) % 167.16/167.32 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_finite__imageI,axiom, % 167.16/167.32 ! [V_h_2,T_b,V_F_2,T_a] : % 167.16/167.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 167.16/167.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_evalc_Oequations_I9_J,axiom, % 167.16/167.32 ! [V_a3_2,V_a2_2,V_a1_2] : % 167.16/167.32 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) % 167.16/167.32 <=> hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup1E,axiom, % 167.16/167.32 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.16/167.32 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 167.16/167.32 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 167.16/167.32 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup1CI,axiom, % 167.16/167.32 ! [T_a,V_A_2,V_x_2,V_B_2] : % 167.16/167.32 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 167.16/167.32 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 167.16/167.32 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup__fun__def,axiom, % 167.16/167.32 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 167.16/167.32 ( class_Lattices_Olattice(T_a) % 167.16/167.32 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_triple_Orecs,axiom, % 167.16/167.32 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 167.16/167.32 % 167.16/167.32 fof(fact_triple_Osimps_I2_J,axiom, % 167.16/167.32 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 167.16/167.32 % 167.16/167.32 fof(fact_image__Un,axiom, % 167.16/167.32 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup__apply,axiom, % 167.16/167.32 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 167.16/167.32 ( class_Lattices_Olattice(T_a) % 167.16/167.32 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_hoare__sound,axiom, % 167.16/167.32 ! [V_ts_2,V_Ga_2,T_a] : % 167.16/167.32 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 167.16/167.32 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_finite__code,axiom, % 167.16/167.32 ! [V_A_2,T_a] : % 167.16/167.32 ( class_Finite__Set_Ofinite(T_a) % 167.16/167.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_finite,axiom, % 167.16/167.32 ! [V_A_2,T_a] : % 167.16/167.32 ( class_Finite__Set_Ofinite(T_a) % 167.16/167.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup__assoc,axiom, % 167.16/167.32 ! [V_z,V_y,V_x,T_a] : % 167.16/167.32 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_inf__sup__aci_I6_J,axiom, % 167.16/167.32 ! [V_z,V_y,V_x,T_a] : % 167.16/167.32 ( class_Lattices_Olattice(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup_Oassoc,axiom, % 167.16/167.32 ! [V_c,V_b,V_a,T_a] : % 167.16/167.32 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup__left__commute,axiom, % 167.16/167.32 ! [V_z,V_y,V_x,T_a] : % 167.16/167.32 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_inf__sup__aci_I7_J,axiom, % 167.16/167.32 ! [V_z,V_y,V_x,T_a] : % 167.16/167.32 ( class_Lattices_Olattice(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup_Oleft__commute,axiom, % 167.16/167.32 ! [V_c,V_a,V_b,T_a] : % 167.16/167.32 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup__left__idem,axiom, % 167.16/167.32 ! [V_y,V_x,T_a] : % 167.16/167.32 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_inf__sup__aci_I8_J,axiom, % 167.16/167.32 ! [V_y,V_x,T_a] : % 167.16/167.32 ( class_Lattices_Olattice(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup_Oleft__idem,axiom, % 167.16/167.32 ! [V_b,V_a,T_a] : % 167.16/167.32 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup__commute,axiom, % 167.16/167.32 ! [V_y,V_x,T_a] : % 167.16/167.32 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_inf__sup__aci_I5_J,axiom, % 167.16/167.32 ! [V_y,V_x,T_a] : % 167.16/167.32 ( class_Lattices_Olattice(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup_Ocommute,axiom, % 167.16/167.32 ! [V_b,V_a,T_a] : % 167.16/167.32 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup__idem,axiom, % 167.16/167.32 ! [V_x,T_a] : % 167.16/167.32 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup_Oidem,axiom, % 167.16/167.32 ! [V_a,T_a] : % 167.16/167.32 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 167.16/167.32 % 167.16/167.32 fof(fact_sup1I2,axiom, % 167.16/167.33 ! [V_A_2,T_a,V_x_2,V_B_2] : % 167.16/167.33 ( hBOOL(hAPP(V_B_2,V_x_2)) % 167.16/167.33 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_sup1I1,axiom, % 167.16/167.33 ! [V_B_2,T_a,V_x_2,V_A_2] : % 167.16/167.33 ( hBOOL(hAPP(V_A_2,V_x_2)) % 167.16/167.33 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_ball__Un,axiom, % 167.16/167.33 ! [V_P_2,V_B_2,V_A_2,T_a] : % 167.16/167.33 ( ! [B_x] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.33 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.16/167.33 <=> ( ! [B_x] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.33 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.16/167.33 & ! [B_x] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 167.16/167.33 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_bex__Un,axiom, % 167.16/167.33 ! [V_P_2,V_B_2,V_A_2,T_a] : % 167.16/167.33 ( ? [B_x] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.33 & hBOOL(hAPP(V_P_2,B_x)) ) % 167.16/167.33 <=> ( ? [B_x] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.33 & hBOOL(hAPP(V_P_2,B_x)) ) % 167.16/167.33 | ? [B_x] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 167.16/167.33 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_Un__assoc,axiom, % 167.16/167.33 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.16/167.33 % 167.16/167.33 fof(fact_Un__left__commute,axiom, % 167.16/167.33 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.16/167.33 % 167.16/167.33 fof(fact_Un__left__absorb,axiom, % 167.16/167.33 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.16/167.33 % 167.16/167.33 fof(fact_Un__commute,axiom, % 167.16/167.33 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 167.16/167.33 % 167.16/167.33 fof(fact_Un__absorb,axiom, % 167.16/167.33 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 167.16/167.33 % 167.16/167.33 fof(fact_com__det,axiom, % 167.16/167.33 ! [V_u,V_t,V_s,V_c] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_t)) % 167.16/167.33 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_u)) % 167.16/167.33 => V_u = V_t ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_image__image,axiom, % 167.16/167.33 ! [V_A_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_c,T_a,hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_f_2),V_g_2)),V_A_2) ). % 167.16/167.33 % 167.16/167.33 fof(fact_finite__UnI,axiom, % 167.16/167.33 ! [V_Ga_2,V_F_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 167.16/167.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) % 167.16/167.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_finite__Un,axiom, % 167.16/167.33 ! [V_Ga_2,V_F_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) % 167.16/167.33 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 167.16/167.33 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_MGT__def,axiom, % 167.16/167.33 ! [V_c_2] : c_Hoare__Mirabelle_OMGT(V_c_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_c_2),hAPP(c_Natural_Oevalc,V_c_2)) ). % 167.16/167.33 % 167.16/167.33 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 167.16/167.33 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.33 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 167.16/167.33 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_image__ident,axiom, % 167.16/167.33 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 167.16/167.33 % 167.16/167.33 fof(fact_com_Osimps_I6_J,axiom, % 167.16/167.33 ! [V_pname_H_2,V_pname_2] : % 167.16/167.33 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 167.16/167.33 <=> V_pname_2 = V_pname_H_2 ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_Sup__fin_Oidem,axiom, % 167.16/167.33 ! [V_x,T_a] : % 167.16/167.33 ( class_Lattices_Olattice(T_a) % 167.16/167.33 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_Body1,axiom, % 167.16/167.33 ! [V_pn_2,V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 167.16/167.33 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2)) % 167.16/167.33 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procsa_2)) % 167.16/167.33 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_Body__triple__valid__Suc,axiom, % 167.16/167.33 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] : % 167.16/167.33 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)) % 167.16/167.33 <=> c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_BodyN,axiom, % 167.16/167.33 ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_a] : % 167.16/167.33 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.16/167.33 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_weak__Body,axiom, % 167.16/167.33 ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_a] : % 167.16/167.33 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.16/167.33 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_folding__image_Odistrib,axiom, % 167.16/167.33 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.33 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 167.16/167.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.33 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_finite__range__imageI,axiom, % 167.16/167.33 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 167.16/167.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 167.16/167.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(c_COMBB(T_a,T_c,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_inv__imagep__def,axiom, % 167.16/167.33 ! [V_y_2,V_x_2,V_f_2,V_r_2,T_b,T_a] : % 167.16/167.33 ( c_Predicate_Oinv__imagep(T_a,T_b,V_r_2,V_f_2,V_x_2,V_y_2) % 167.16/167.33 <=> hBOOL(hAPP(hAPP(V_r_2,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_equalityCE,axiom, % 167.16/167.33 ! [V_c_2,T_a,V_B_2,V_A_2] : % 167.16/167.33 ( V_A_2 = V_B_2 % 167.16/167.33 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.33 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) % 167.16/167.33 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_top1I,axiom, % 167.16/167.33 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 167.16/167.33 % 167.16/167.33 fof(fact_emptyE,axiom, % 167.16/167.33 ! [V_a_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insertE,axiom, % 167.16/167.33 ! [V_A_2,V_b_2,V_a_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 167.16/167.33 => ( V_a_2 != V_b_2 % 167.16/167.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insertCI,axiom, % 167.16/167.33 ! [V_b_2,V_B_2,V_a_2,T_a] : % 167.16/167.33 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 167.16/167.33 => V_a_2 = V_b_2 ) % 167.16/167.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_UNIV__I,axiom, % 167.16/167.33 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.16/167.33 % 167.16/167.33 fof(fact_image__eqI,axiom, % 167.16/167.33 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] : % 167.16/167.33 ( V_b_2 = hAPP(V_f_2,V_x_2) % 167.16/167.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 167.16/167.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_finite_OemptyI,axiom, % 167.16/167.33 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.16/167.33 % 167.16/167.33 fof(fact_UnE,axiom, % 167.16/167.33 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_UnCI,axiom, % 167.16/167.33 ! [V_A_2,V_B_2,V_c_2,T_a] : % 167.16/167.33 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 167.16/167.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) % 167.16/167.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_finite_OinsertI,axiom, % 167.16/167.33 ! [V_a_2,V_A_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_UNIV__not__empty,axiom, % 167.16/167.33 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.33 % 167.16/167.33 fof(fact_empty__not__insert,axiom, % 167.16/167.33 ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insert__not__empty,axiom, % 167.16/167.33 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.33 % 167.16/167.33 fof(fact_bot__empty__eq,axiom, % 167.16/167.33 ! [V_x_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 167.16/167.33 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insertI1,axiom, % 167.16/167.33 ! [V_B_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ). % 167.16/167.33 % 167.16/167.33 fof(fact_all__not__in__conv,axiom, % 167.16/167.33 ! [V_A_2,T_a] : % 167.16/167.33 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.33 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_ex__in__conv,axiom, % 167.16/167.33 ! [V_A_2,T_a] : % 167.16/167.33 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.33 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_empty__iff,axiom, % 167.16/167.33 ! [V_c_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.16/167.33 % 167.16/167.33 fof(fact_mem__def,axiom, % 167.16/167.33 ! [V_A_2,V_x_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.33 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_eq__mem,axiom, % 167.16/167.33 ! [V_y_2,V_x_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 167.16/167.33 <=> V_x_2 = V_y_2 ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_singleton__iff,axiom, % 167.16/167.33 ! [V_a_2,V_b_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 167.16/167.33 <=> V_b_2 = V_a_2 ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insert__absorb2,axiom, % 167.16/167.33 ! [V_A_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insert__commute,axiom, % 167.16/167.33 ! [V_A_2,V_y_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insert__iff,axiom, % 167.16/167.33 ! [V_A_2,V_b_2,V_a_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 167.16/167.33 <=> ( V_a_2 = V_b_2 % 167.16/167.33 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_doubleton__eq__iff,axiom, % 167.16/167.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.16/167.33 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 167.16/167.33 <=> ( ( V_a_2 = V_c_2 % 167.16/167.33 & V_b_2 = V_d_2 ) % 167.16/167.33 | ( V_a_2 = V_d_2 % 167.16/167.33 & V_b_2 = V_c_2 ) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insert__code,axiom, % 167.16/167.33 ! [V_x_2,V_A_2,V_y_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2)) % 167.16/167.33 <=> ( V_y_2 = V_x_2 % 167.16/167.33 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insert__ident,axiom, % 167.16/167.33 ! [V_B_2,V_A_2,V_x_2,T_a] : % 167.16/167.33 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.16/167.33 => ( hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2) % 167.16/167.33 <=> V_A_2 = V_B_2 ) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_equals0D,axiom, % 167.16/167.33 ! [V_a_2,T_a,V_A_2] : % 167.16/167.33 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.33 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insertI2,axiom, % 167.16/167.33 ! [V_b_2,V_B_2,V_a_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 167.16/167.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insert__absorb,axiom, % 167.16/167.33 ! [V_A_2,V_a_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.33 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_eqset__imp__iff,axiom, % 167.16/167.33 ! [V_x_2,T_a,V_B_2,V_A_2] : % 167.16/167.33 ( V_A_2 = V_B_2 % 167.16/167.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.33 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_eqelem__imp__iff,axiom, % 167.16/167.33 ! [V_A_2,T_a,V_y_2,V_x_2] : % 167.16/167.33 ( V_x_2 = V_y_2 % 167.16/167.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.33 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_eq__mem__trans,axiom, % 167.16/167.33 ! [V_A_2,T_a,V_b_2,V_a_2] : % 167.16/167.33 ( V_a_2 = V_b_2 % 167.16/167.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 167.16/167.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_singletonE,axiom, % 167.16/167.33 ! [V_a_2,V_b_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 167.16/167.33 => V_b_2 = V_a_2 ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_singleton__inject,axiom, % 167.16/167.33 ! [V_b_2,V_a_2,T_a] : % 167.16/167.33 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 167.16/167.33 => V_a_2 = V_b_2 ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_triple__valid__Suc,axiom, % 167.16/167.33 ! [V_t,V_n,T_a] : % 167.16/167.33 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 167.16/167.33 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_image__constant,axiom, % 167.16/167.33 ! [V_c_2,T_b,V_A_2,V_x_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.33 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_finite__fun__UNIVD2,axiom, % 167.16/167.33 ! [T_b,T_a] : % 167.16/167.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))) % 167.16/167.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_insert__image,axiom, % 167.16/167.33 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 167.16/167.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.33 => hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_finite__Plus__UNIV__iff,axiom, % 167.16/167.33 ! [T_b,T_a] : % 167.16/167.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)))) % 167.16/167.33 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 167.16/167.33 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_finite__option__UNIV,axiom, % 167.16/167.33 ! [T_a] : % 167.16/167.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)))) % 167.16/167.33 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_finite__Prod__UNIV,axiom, % 167.16/167.33 ! [T_b,T_a] : % 167.16/167.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 167.16/167.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 167.16/167.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ) ). % 167.16/167.33 % 167.16/167.33 fof(fact_range__eqI,axiom, % 167.16/167.33 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] : % 167.16/167.34 ( V_b_2 = hAPP(V_f_2,V_x_2) % 167.16/167.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_rangeI,axiom, % 167.16/167.34 ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ). % 167.16/167.34 % 167.16/167.34 fof(fact_insert__is__Un,axiom, % 167.16/167.34 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_A_2) ). % 167.16/167.34 % 167.16/167.34 fof(fact_hoare__derivs_Oinsert,axiom, % 167.16/167.34 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 167.16/167.34 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.16/167.34 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_derivs__insertD,axiom, % 167.16/167.34 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 167.16/167.34 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) % 167.16/167.34 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.16/167.34 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_pred__equals__eq,axiom, % 167.16/167.34 ! [V_S_2,V_R_2,T_a] : % 167.16/167.34 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2) % 167.16/167.34 <=> V_R_2 = V_S_2 ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__image__simple__idem_Oidem,axiom, % 167.16/167.34 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.34 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_image__constant__conv,axiom, % 167.16/167.34 ! [V_c_2,T_b,T_a,V_A_2] : % 167.16/167.34 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 167.16/167.34 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 167.16/167.34 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.34 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 167.16/167.34 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 167.16/167.34 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_MGF__complete,axiom, % 167.16/167.34 ! [V_Q_2,V_P_2,V_c_2] : % 167.16/167.34 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 167.16/167.34 => ( c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_finite__insert,axiom, % 167.16/167.34 ! [V_A_2,V_a_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) % 167.16/167.34 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_image__insert,axiom, % 167.16/167.34 ! [V_B_2,V_a_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Un__insert__right,axiom, % 167.16/167.34 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Un__insert__left,axiom, % 167.16/167.34 ! [V_C_2,V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.16/167.34 % 167.16/167.34 fof(fact_in__inv__imagep,axiom, % 167.16/167.34 ! [V_y_2,V_x_2,V_f_2,V_r_2,T_b,T_a] : % 167.16/167.34 ( c_Predicate_Oinv__imagep(T_a,T_b,V_r_2,V_f_2,V_x_2,V_y_2) % 167.16/167.34 <=> hBOOL(hAPP(hAPP(V_r_2,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_finite__UNIV,axiom, % 167.16/167.34 ! [T_a] : % 167.16/167.34 ( class_Finite__Set_Ofinite(T_a) % 167.16/167.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_image__iff,axiom, % 167.16/167.34 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 167.16/167.34 <=> ? [B_x] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.34 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_imageI,axiom, % 167.16/167.34 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.34 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_rev__image__eqI,axiom, % 167.16/167.34 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.34 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 167.16/167.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Un__iff,axiom, % 167.16/167.34 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.34 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.34 | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_UnI1,axiom, % 167.16/167.34 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_UnI2,axiom, % 167.16/167.34 ! [V_A_2,V_B_2,V_c_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 167.16/167.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Un__UNIV__left,axiom, % 167.16/167.34 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Un__UNIV__right,axiom, % 167.16/167.34 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.34 % 167.16/167.34 fof(fact_finite_Oequations_I1_J,axiom, % 167.16/167.34 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.16/167.34 % 167.16/167.34 fof(fact_empty__is__image,axiom, % 167.16/167.34 ! [V_A_2,V_f_2,T_b,T_a] : % 167.16/167.34 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) % 167.16/167.34 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_image__empty,axiom, % 167.16/167.34 ! [V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.34 % 167.16/167.34 fof(fact_image__is__empty,axiom, % 167.16/167.34 ! [V_A_2,V_f_2,T_a,T_b] : % 167.16/167.34 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Un__empty__left,axiom, % 167.16/167.34 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 167.16/167.34 % 167.16/167.34 fof(fact_Un__empty__right,axiom, % 167.16/167.34 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 167.16/167.34 % 167.16/167.34 fof(fact_Un__empty,axiom, % 167.16/167.34 ! [V_B_2,V_A_2,T_a] : % 167.16/167.34 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_empty,axiom, % 167.16/167.34 ! [V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 167.16/167.34 % 167.16/167.34 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 167.16/167.34 ! [V_a_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 167.16/167.34 % 167.16/167.34 fof(fact_sup__Un__eq,axiom, % 167.16/167.34 ! [V_x_2,V_S_2,V_R_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) % 167.16/167.34 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_range__composition,axiom, % 167.16/167.34 ! [V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBB(T_c,T_a,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 167.16/167.34 % 167.16/167.34 fof(fact_sup__bot__left,axiom, % 167.16/167.34 ! [V_x,T_a] : % 167.16/167.34 ( class_Lattices_Obounded__lattice__bot(T_a) % 167.16/167.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_sup__bot__right,axiom, % 167.16/167.34 ! [V_x,T_a] : % 167.16/167.34 ( class_Lattices_Obounded__lattice__bot(T_a) % 167.16/167.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_sup__eq__bot__iff,axiom, % 167.16/167.34 ! [V_y_2,V_x_2,T_a] : % 167.16/167.34 ( class_Lattices_Obounded__lattice__bot(T_a) % 167.16/167.34 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) % 167.16/167.34 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a) % 167.16/167.34 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_sup__top__left,axiom, % 167.16/167.34 ! [V_x,T_a] : % 167.16/167.34 ( class_Lattices_Obounded__lattice__top(T_a) % 167.16/167.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_sup__top__right,axiom, % 167.16/167.34 ! [V_x,T_a] : % 167.16/167.34 ( class_Lattices_Obounded__lattice__top(T_a) % 167.16/167.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_MGT__BodyN,axiom, % 167.16/167.34 ! [V_Ga_2,V_pn_2] : % 167.16/167.34 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_finite__pointwise,axiom, % 167.16/167.34 ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_b,V_U_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) % 167.16/167.34 => ( ! [B_p] : % 167.16/167.34 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) % 167.16/167.34 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2)) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_the__elem__eq,axiom, % 167.16/167.34 ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ). % 167.16/167.34 % 167.16/167.34 fof(fact_bot__fun__def,axiom, % 167.16/167.34 ! [V_x_2,T_b,T_a] : % 167.16/167.34 ( class_Orderings_Obot(T_a) % 167.16/167.34 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__one_Oinsert,axiom, % 167.16/167.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_top__apply,axiom, % 167.16/167.34 ! [V_x_2,T_b,T_a] : % 167.16/167.34 ( class_Orderings_Otop(T_a) % 167.16/167.34 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_iso__tuple__UNIV__I,axiom, % 167.16/167.34 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.16/167.34 % 167.16/167.34 fof(fact_bot__apply,axiom, % 167.16/167.34 ! [V_x_2,T_b,T_a] : % 167.16/167.34 ( class_Orderings_Obot(T_a) % 167.16/167.34 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__one__idem_Ounion__idem,axiom, % 167.16/167.34 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 167.16/167.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_escape,axiom, % 167.16/167.34 ! [V_Q_2,V_c_2,V_Ga_2,T_a,V_P_2] : % 167.16/167.34 ( ! [B_Z,B_s] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_c_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_MGT__alternI,axiom, % 167.16/167.34 ! [V_c_2,V_Ga_2] : % 167.16/167.34 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__one__idem_Oidem,axiom, % 167.16/167.34 ! [V_x_2,V_F_2,V_f_2,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 167.16/167.34 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__one_Osingleton,axiom, % 167.16/167.34 ! [V_x_2,V_F_2,V_f_2,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 167.16/167.34 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__one__idem_Oin__idem,axiom, % 167.16/167.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.34 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_MGT__alternD,axiom, % 167.16/167.34 ! [V_c_2,V_Ga_2] : % 167.16/167.34 ( c_Hoare__Mirabelle_Ostate__not__singleton % 167.16/167.34 => ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__one_Oclosed,axiom, % 167.16/167.34 ! [V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 167.16/167.34 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 167.16/167.34 ! [V_a2_2,V_a1_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 167.16/167.34 % 167.16/167.34 fof(fact_hoare__derivs_OSkip,axiom, % 167.16/167.34 ! [V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 167.16/167.34 % 167.16/167.34 fof(fact_image__eq__fold__image,axiom, % 167.16/167.34 ! [V_f_2,T_b,V_A_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_b,tc_HOL_Obool),T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Sup__fin_Oinsert,axiom, % 167.16/167.34 ! [V_x_2,V_A_2,T_a] : % 167.16/167.34 ( class_Lattices_Olattice(T_a) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_the__elem__def,axiom, % 167.16/167.34 ! [V_X_2,T_a] : c_Set_Othe__elem(T_a,V_X_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 167.16/167.34 % 167.16/167.34 fof(fact_conseq1,axiom, % 167.16/167.34 ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_Ga_2,T_a] : % 167.16/167.34 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.16/167.34 => ( ! [B_Z,B_s] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 167.16/167.34 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_conseq2,axiom, % 167.16/167.34 ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_Ga_2,T_a] : % 167.16/167.34 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.16/167.34 => ( ! [B_Z,B_s] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 167.16/167.34 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__one__idem_Ohom__commute,axiom, % 167.16/167.34 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 167.16/167.34 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.16/167.34 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evaln_OBody,axiom, % 167.16/167.34 ! [V_s1,V_n,V_s0,V_pn] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_n),V_s1)) % 167.16/167.34 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),hAPP(c_Nat_OSuc,V_n)),V_s1)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evaln_OSkip,axiom, % 167.16/167.34 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evaln__elim__cases_I1_J,axiom, % 167.16/167.34 ! [V_t,V_n,V_s] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t)) % 167.16/167.34 => V_t = V_s ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evalc_OSkip,axiom, % 167.16/167.34 ! [V_s] : hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),V_s),V_s)) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evalc__elim__cases_I1_J,axiom, % 167.16/167.34 ! [V_t,V_s] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),V_s),V_t)) % 167.16/167.34 => V_t = V_s ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evaln_Oequations_I1_J,axiom, % 167.16/167.34 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evaln__Suc,axiom, % 167.16/167.34 ! [V_s_H,V_n,V_s,V_c] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H)) % 167.16/167.34 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_eval__eq,axiom, % 167.16/167.34 ! [V_t_2,V_s_2,V_c_2] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c_2),V_s_2),V_t_2)) % 167.16/167.34 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s_2),B_n),V_t_2)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evaln__evalc,axiom, % 167.16/167.34 ! [V_t,V_n,V_s,V_c] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 167.16/167.34 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_t)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_fold__image__empty,axiom, % 167.16/167.34 ! [V_z_2,V_g_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ). % 167.16/167.34 % 167.16/167.34 fof(fact_evalc_Oequations_I1_J,axiom, % 167.16/167.34 ! [V_a] : hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),V_a),V_a)) ). % 167.16/167.34 % 167.16/167.34 fof(fact_com_Osimps_I18_J,axiom, % 167.16/167.34 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 167.16/167.34 % 167.16/167.34 fof(fact_com_Osimps_I19_J,axiom, % 167.16/167.34 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 167.16/167.34 % 167.16/167.34 fof(fact_Sup__fin_Osingleton,axiom, % 167.16/167.34 ! [V_x_2,T_a] : % 167.16/167.34 ( class_Lattices_Olattice(T_a) % 167.16/167.34 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_triple__valid__def2,axiom, % 167.16/167.34 ! [V_Q_2,V_c_2,V_P_2,V_n_2,T_a] : % 167.16/167.34 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)) % 167.16/167.34 <=> ! [B_Z,B_s] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 167.16/167.34 => ! [B_s_H] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),B_s),V_n_2),B_s_H)) % 167.16/167.34 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__image_Oeq__fold,axiom, % 167.16/167.34 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.34 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Sup__fin_Oin__idem,axiom, % 167.16/167.34 ! [V_x_2,V_A_2,T_a] : % 167.16/167.34 ( class_Lattices_Olattice(T_a) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_triple__valid__def,axiom, % 167.16/167.34 ! [V_t_2,V_n_2,T_a] : % 167.16/167.34 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2) % 167.16/167.34 <=> hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(T_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),V_n_2))))))))),V_t_2)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evaln_Oequations_I9_J,axiom, % 167.16/167.34 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),hAPP(c_Nat_OSuc,V_a3_2)),V_a4_2)) % 167.16/167.34 <=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2),V_a4_2)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Sup__fin_Oinsert__idem,axiom, % 167.16/167.34 ! [V_x_2,V_A_2,T_a] : % 167.16/167.34 ( class_Lattices_Olattice(T_a) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Sup__fin_Ounion__idem,axiom, % 167.16/167.34 ! [V_B_2,V_A_2,T_a] : % 167.16/167.34 ( class_Lattices_Olattice(T_a) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evaln__elim__cases_I6_J,axiom, % 167.16/167.34 ! [V_s1,V_n,V_s,V_P] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1)) % 167.16/167.34 => ~ ! [B_n] : % 167.16/167.34 ( V_n = hAPP(c_Nat_OSuc,B_n) % 167.16/167.34 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),B_n),V_s1)) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_comm__monoid__big_OF__eq,axiom, % 167.16/167.34 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.34 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 167.16/167.34 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.34 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) % 167.16/167.34 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.34 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Sup__fin_Oclosed,axiom, % 167.16/167.34 ! [V_A_2,T_a] : % 167.16/167.34 ( class_Lattices_Olattice(T_a) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 167.16/167.34 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Sup__fin_Ohom__commute,axiom, % 167.16/167.34 ! [V_N_2,V_h_2,T_a] : % 167.16/167.34 ( class_Lattices_Olattice(T_a) % 167.16/167.34 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.16/167.34 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Sup__fin_Oremove,axiom, % 167.16/167.34 ! [V_x_2,V_A_2,T_a] : % 167.16/167.34 ( class_Lattices_Olattice(T_a) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.34 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) % 167.16/167.34 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.34 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_MGF,axiom, % 167.16/167.34 ! [V_c_2] : % 167.16/167.34 ( c_Hoare__Mirabelle_Ostate__not__singleton % 167.16/167.34 => ( c_Com_OWT__bodies % 167.16/167.34 => ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_Comp,axiom, % 167.16/167.34 ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_a] : % 167.16/167.34 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.16/167.34 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.16/167.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_folding__image__simple_Oinsert,axiom, % 167.16/167.34 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.34 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 167.16/167.34 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_the__eq__trivial,axiom, % 167.16/167.34 ! [V_a_2,T_a] : c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ). % 167.16/167.34 % 167.16/167.34 fof(fact_the__sym__eq__trivial,axiom, % 167.16/167.34 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 167.16/167.34 % 167.16/167.34 fof(fact_LoopF,axiom, % 167.16/167.34 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 167.16/167.34 % 167.16/167.34 fof(fact_DiffE,axiom, % 167.16/167.34 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.34 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_DiffI,axiom, % 167.16/167.34 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 167.16/167.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_finite__Diff,axiom, % 167.16/167.34 ! [V_B_2,V_A_2,T_a] : % 167.16/167.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evaln_OWhileTrue,axiom, % 167.16/167.34 ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] : % 167.16/167.34 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 167.16/167.34 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s0_2),V_n_2),V_s1_2)) % 167.16/167.34 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_n_2),V_s2_2)) % 167.16/167.34 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_n_2),V_s2_2)) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evaln_OWhileFalse,axiom, % 167.16/167.34 ! [V_n_2,V_c_2,V_s_2,V_b_2] : % 167.16/167.34 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.16/167.34 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_n_2),V_s_2)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evalc_OWhileTrue,axiom, % 167.16/167.34 ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] : % 167.16/167.34 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 167.16/167.34 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c_2),V_s0_2),V_s1_2)) % 167.16/167.34 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2)) % 167.16/167.34 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evalc_OWhileFalse,axiom, % 167.16/167.34 ! [V_c_2,V_s_2,V_b_2] : % 167.16/167.34 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.16/167.34 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_WTs__elim__cases_I6_J,axiom, % 167.16/167.34 ! [V_c_2,V_b_2] : % 167.16/167.34 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) % 167.16/167.34 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ). % 167.16/167.34 % 167.16/167.34 fof(fact_evaln_OSemi,axiom, % 167.16/167.35 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2)) % 167.16/167.35 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_evalc_OSemi,axiom, % 167.16/167.35 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c0),V_s0),V_s1)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1),V_s1),V_s2)) % 167.16/167.35 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_WTs__elim__cases_I4_J,axiom, % 167.16/167.35 ! [V_c2,V_c1] : % 167.16/167.35 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) % 167.16/167.35 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 167.16/167.35 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_WT_OSemi,axiom, % 167.16/167.35 ! [V_c1,V_c0] : % 167.16/167.35 ( hBOOL(hAPP(c_Com_OWT,V_c0)) % 167.16/167.35 => ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 167.16/167.35 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_While,axiom, % 167.16/167.35 ! [V_b_2,V_c_2] : % 167.16/167.35 ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 167.16/167.35 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I5_J,axiom, % 167.16/167.35 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 167.16/167.35 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 167.16/167.35 <=> ( V_fun_2 = V_fun_H_2 % 167.16/167.35 & V_com_2 = V_com_H_2 ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I3_J,axiom, % 167.16/167.35 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 167.16/167.35 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 167.16/167.35 <=> ( V_com1_2 = V_com1_H_2 % 167.16/167.35 & V_com2_2 = V_com2_H_2 ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_WT_Oequations_I4_J,axiom, % 167.16/167.35 ! [V_a2_2,V_a1_2] : % 167.16/167.35 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) % 167.16/167.35 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 167.16/167.35 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_WT_Oequations_I6_J,axiom, % 167.16/167.35 ! [V_a1_2,V_a2_2] : % 167.16/167.35 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) % 167.16/167.35 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I47_J,axiom, % 167.16/167.35 ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I46_J,axiom, % 167.16/167.35 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_minus__apply,axiom, % 167.16/167.35 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 167.16/167.35 ( class_Groups_Ominus(T_a) % 167.16/167.35 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__idemp,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__diff__def,axiom, % 167.16/167.35 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 167.16/167.35 ( class_Groups_Ominus(T_a) % 167.16/167.35 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_DiffD2,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.35 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_DiffD1,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.35 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__iff,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.35 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.35 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__cancel,axiom, % 167.16/167.35 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__empty,axiom, % 167.16/167.35 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 167.16/167.35 % 167.16/167.35 fof(fact_empty__Diff,axiom, % 167.16/167.35 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_finite__Diff2,axiom, % 167.16/167.35 ! [V_A_2,V_B_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.35 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Un__Diff,axiom, % 167.16/167.35 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Un__Diff__cancel2,axiom, % 167.16/167.35 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Un__Diff__cancel,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_evaln_Oequations_I8_J,axiom, % 167.16/167.35 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a6_2)) % 167.16/167.35 <=> ( ( V_a6_2 = V_a2_2 % 167.16/167.35 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 167.16/167.35 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.16/167.35 & ? [B_s1] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 167.16/167.35 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a6_2)) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_evaln_Oequations_I7_J,axiom, % 167.16/167.35 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a2_2)) % 167.16/167.35 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.16/167.35 => ? [B_s1] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 167.16/167.35 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a2_2)) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_evalc_Oequations_I8_J,axiom, % 167.16/167.35 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 167.16/167.35 <=> ( ( V_a5_2 = V_a2_2 % 167.16/167.35 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 167.16/167.35 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.16/167.35 & ? [B_s1] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),B_s1)) % 167.16/167.35 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_evalc_Oequations_I7_J,axiom, % 167.16/167.35 ! [V_a2_2,V_a3_2,V_a1_2] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 167.16/167.35 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.16/167.35 => ? [B_s1] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),B_s1)) % 167.16/167.35 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I58_J,axiom, % 167.16/167.35 ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I59_J,axiom, % 167.16/167.35 ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_WT_Oequations_I1_J,axiom, % 167.16/167.35 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_WT_OSkip,axiom, % 167.16/167.35 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I17_J,axiom, % 167.16/167.35 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I16_J,axiom, % 167.16/167.35 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_evaln_Oequations_I4_J,axiom, % 167.16/167.35 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_a1_2,V_a5_2)),V_a2_2),V_a3_2),V_a6_2)) % 167.16/167.35 <=> ? [B_s1] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1)) % 167.16/167.35 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_evalc_Oequations_I4_J,axiom, % 167.16/167.35 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 167.16/167.35 <=> ? [B_s1] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a1_2),V_a2_2),B_s1)) % 167.16/167.35 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a4_2),B_s1),V_a5_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I48_J,axiom, % 167.16/167.35 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I49_J,axiom, % 167.16/167.35 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I13_J,axiom, % 167.16/167.35 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 167.16/167.35 % 167.16/167.35 fof(fact_com_Osimps_I12_J,axiom, % 167.16/167.35 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.35 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_insert__Diff1,axiom, % 167.16/167.35 ! [V_A_2,V_B_2,V_x_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.16/167.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_insert__Diff__if,axiom, % 167.16/167.35 ! [V_A_2,V_B_2,V_x_2,T_a] : % 167.16/167.35 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.16/167.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) % 167.16/167.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.16/167.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_insert__Diff__single,axiom, % 167.16/167.35 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__insert2,axiom, % 167.16/167.35 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__insert,axiom, % 167.16/167.35 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.16/167.35 % 167.16/167.35 fof(fact_finite__Diff__insert,axiom, % 167.16/167.35 ! [V_B_2,V_a_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)))) % 167.16/167.35 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__UNIV,axiom, % 167.16/167.35 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__image__simple_Oempty,axiom, % 167.16/167.35 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.35 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__image__simple_Oremove,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_insert__Diff,axiom, % 167.16/167.35 ! [V_A_2,V_a_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2 ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__insert__absorb,axiom, % 167.16/167.35 ! [V_A_2,V_x_2,T_a] : % 167.16/167.35 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 167.16/167.35 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.35 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__one_Oinsert__remove,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 167.16/167.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_comm__monoid__big_Oinfinite,axiom, % 167.16/167.35 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 167.16/167.35 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.35 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Sup__fin_Oinsert__remove,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 167.16/167.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__one_Oremove,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 167.16/167.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__upd__image,axiom, % 167.16/167.35 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 167.16/167.35 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) % 167.16/167.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_finite__empty__induct,axiom, % 167.16/167.35 ! [V_P_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(V_P_2,V_A_2)) % 167.16/167.35 => ( ! [B_a,B_A] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) % 167.16/167.35 => ( hBOOL(hAPP(V_P_2,B_A)) % 167.16/167.35 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_a),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) % 167.16/167.35 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_MGF__lemma1,axiom, % 167.16/167.35 ! [V_c_2,V_Ga_2] : % 167.16/167.35 ( c_Hoare__Mirabelle_Ostate__not__singleton % 167.16/167.35 => ( ! [B_x] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) % 167.16/167.35 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) % 167.16/167.35 => ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 167.16/167.35 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_card__Suc__Diff1,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm__idem__remove,axiom, % 167.16/167.35 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 167.16/167.35 % 167.16/167.35 fof(fact_setsum__diff1__ring,axiom, % 167.16/167.35 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 167.16/167.35 ( class_Rings_Oring(T_b) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_setsum__diff1,axiom, % 167.16/167.35 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 167.16/167.35 ( class_Groups_Oab__group__add(T_b) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 167.16/167.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Sup__fin_Ounion__inter,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.35 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_x_2),V_A_2) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_finite__induct,axiom, % 167.16/167.35 ! [V_P_2,V_F_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 167.16/167.35 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 167.16/167.35 => ( ! [B_x,B_F] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 167.16/167.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F)) % 167.16/167.35 => ( hBOOL(hAPP(V_P_2,B_F)) % 167.16/167.35 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) ) % 167.16/167.35 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf1I,axiom, % 167.16/167.35 ! [T_a,V_B_2,V_x_2,V_A_2] : % 167.16/167.35 ( hBOOL(hAPP(V_A_2,V_x_2)) % 167.16/167.35 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 167.16/167.35 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf1E,axiom, % 167.16/167.35 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 167.16/167.35 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 167.16/167.35 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__upd__triv,axiom, % 167.16/167.35 ! [V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ). % 167.16/167.35 % 167.16/167.35 fof(fact_IntI,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 167.16/167.35 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_IntE,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.35 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.35 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_finite__Int,axiom, % 167.16/167.35 ! [V_Ga_2,V_F_2,T_a] : % 167.16/167.35 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 167.16/167.35 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) % 167.16/167.35 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__fun__def,axiom, % 167.16/167.35 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm__idem__inf,axiom, % 167.16/167.35 ! [T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__absorb,axiom, % 167.16/167.35 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf_Oidem,axiom, % 167.16/167.35 ! [V_a,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__idem,axiom, % 167.16/167.35 ! [V_x,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__commute,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf_Ocommute,axiom, % 167.16/167.35 ! [V_b,V_a,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__sup__aci_I1_J,axiom, % 167.16/167.35 ! [V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__commute,axiom, % 167.16/167.35 ! [V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__left__absorb,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf_Oleft__idem,axiom, % 167.16/167.35 ! [V_b,V_a,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__sup__aci_I4_J,axiom, % 167.16/167.35 ! [V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__left__idem,axiom, % 167.16/167.35 ! [V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__left__commute,axiom, % 167.16/167.35 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf_Oleft__commute,axiom, % 167.16/167.35 ! [V_c,V_a,V_b,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__sup__aci_I3_J,axiom, % 167.16/167.35 ! [V_z,V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__left__commute,axiom, % 167.16/167.35 ! [V_z,V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__assoc,axiom, % 167.16/167.35 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf_Oassoc,axiom, % 167.16/167.35 ! [V_c,V_b,V_a,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__sup__aci_I2_J,axiom, % 167.16/167.35 ! [V_z,V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__assoc,axiom, % 167.16/167.35 ! [V_z,V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__apply,axiom, % 167.16/167.35 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf1D1,axiom, % 167.16/167.35 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 167.16/167.35 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf1D2,axiom, % 167.16/167.35 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 167.16/167.35 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Inf__fin_Oidem,axiom, % 167.16/167.35 ! [V_x,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__upd__idem__iff,axiom, % 167.16/167.35 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 % 167.16/167.35 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__upd__upd,axiom, % 167.16/167.35 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_z_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__upd__same,axiom, % 167.16/167.35 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__upd__apply,axiom, % 167.16/167.35 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 167.16/167.35 ( ( V_z_2 = V_x_2 % 167.16/167.35 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 ) % 167.16/167.35 & ( V_z_2 != V_x_2 % 167.16/167.35 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__upd__twist,axiom, % 167.16/167.35 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_c_2,V_a_2] : % 167.16/167.35 ( V_a_2 != V_c_2 % 167.16/167.35 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__upd__other,axiom, % 167.16/167.35 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 167.16/167.35 ( V_z_2 != V_x_2 % 167.16/167.35 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__upd__idem,axiom, % 167.16/167.35 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] : % 167.16/167.35 ( hAPP(V_f_2,V_x_2) = V_y_2 % 167.16/167.35 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 167.16/167.35 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 167.16/167.35 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_setsum__commute,axiom, % 167.16/167.35 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 167.16/167.35 ( class_Groups_Ocomm__monoid__add(T_a) % 167.16/167.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_a),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))),V_A_2)),V_B_2) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_card__Diff__subset__Int,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.35 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__upd__def,axiom, % 167.16/167.35 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] : % 167.16/167.35 ( ( V_x_2 = V_a_2 % 167.16/167.35 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 ) % 167.16/167.35 & ( V_x_2 != V_a_2 % 167.16/167.35 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fold__inf__insert,axiom, % 167.16/167.35 ! [V_a_2,V_b_2,V_A_2,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 167.16/167.35 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 167.16/167.35 => c_Finite__Set_Ofun__left__comm__idem(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__bot__left,axiom, % 167.16/167.35 ! [V_x,T_a] : % 167.16/167.35 ( class_Lattices_Obounded__lattice__bot(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__bot__right,axiom, % 167.16/167.35 ! [V_x,T_a] : % 167.16/167.35 ( class_Lattices_Obounded__lattice__bot(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__sup__absorb,axiom, % 167.16/167.35 ! [V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_sup__inf__absorb,axiom, % 167.16/167.35 ! [V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__sup__distrib1,axiom, % 167.16/167.35 ! [V_z,V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Odistrib__lattice(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_sup__inf__distrib1,axiom, % 167.16/167.35 ! [V_z,V_y,V_x,T_a] : % 167.16/167.35 ( class_Lattices_Odistrib__lattice(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__sup__distrib2,axiom, % 167.16/167.35 ! [V_x,V_z,V_y,T_a] : % 167.16/167.35 ( class_Lattices_Odistrib__lattice(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_sup__inf__distrib2,axiom, % 167.16/167.35 ! [V_x,V_z,V_y,T_a] : % 167.16/167.35 ( class_Lattices_Odistrib__lattice(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__top__left,axiom, % 167.16/167.35 ! [V_x,T_a] : % 167.16/167.35 ( class_Lattices_Obounded__lattice__top(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__top__right,axiom, % 167.16/167.35 ! [V_x,T_a] : % 167.16/167.35 ( class_Lattices_Obounded__lattice__top(T_a) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__eq__top__iff,axiom, % 167.16/167.35 ! [V_y_2,V_x_2,T_a] : % 167.16/167.35 ( class_Lattices_Obounded__lattice__top(T_a) % 167.16/167.35 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a) % 167.16/167.35 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a) % 167.16/167.35 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__iff,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.35 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.35 & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_IntD1,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.35 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_IntD2,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_c_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.35 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fold__empty,axiom, % 167.16/167.35 ! [V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__empty__left,axiom, % 167.16/167.35 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__empty__right,axiom, % 167.16/167.35 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_disjoint__iff__not__equal,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : % 167.16/167.35 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 <=> ! [B_x] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.35 => ! [B_xa] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) % 167.16/167.35 => B_x != B_xa ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_insert__inter__insert,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__UNIV__left,axiom, % 167.16/167.35 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__UNIV__right,axiom, % 167.16/167.35 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__Un__distrib,axiom, % 167.16/167.35 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Un__Int__distrib,axiom, % 167.16/167.35 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__Un__distrib2,axiom, % 167.16/167.35 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Un__Int__distrib2,axiom, % 167.16/167.35 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Un__Int__crazy,axiom, % 167.16/167.35 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__Int__distrib,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_C_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__Diff,axiom, % 167.16/167.35 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__Int__distrib2,axiom, % 167.16/167.35 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__Int2,axiom, % 167.16/167.35 ! [V_B_2,V_C_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 167.16/167.35 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 167.16/167.35 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_setsum__subtractf,axiom, % 167.16/167.35 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( class_Groups_Oab__group__add(T_a) % 167.16/167.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__Int__eq,axiom, % 167.16/167.35 ! [V_x_2,V_S_2,V_R_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) % 167.16/167.35 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fold__image__def,axiom, % 167.16/167.35 ! [V_g_2,V_f_2,T_b,T_a] : hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_b,T_a,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_setsum__diff1__nat,axiom, % 167.16/167.35 ! [V_f_2,V_A_2,V_a_2,T_a] : % 167.16/167.35 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 167.16/167.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm__idem__insert,axiom, % 167.16/167.35 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 167.16/167.35 ! [V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 167.16/167.35 => ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.16/167.35 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm__idem__sup,axiom, % 167.16/167.35 ! [T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.35 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__insert__right,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_a_2,T_a] : % 167.16/167.35 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 167.16/167.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__insert__left,axiom, % 167.16/167.35 ! [V_B_2,V_C_2,V_a_2,T_a] : % 167.16/167.35 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) % 167.16/167.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__insert__right__if0,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_a_2,T_a] : % 167.16/167.35 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__insert__left__if0,axiom, % 167.16/167.35 ! [V_B_2,V_C_2,V_a_2,T_a] : % 167.16/167.35 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__insert__right__if1,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_a_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Int__insert__left__if1,axiom, % 167.16/167.35 ! [V_B_2,V_C_2,V_a_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__disjoint,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__triv,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : % 167.16/167.35 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Un__Diff__Int,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__Un,axiom, % 167.16/167.35 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Diff__Int,axiom, % 167.16/167.35 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.16/167.35 % 167.16/167.35 fof(fact_union__fold__insert,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)),V_B_2),V_A_2) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fold__sup__insert,axiom, % 167.16/167.35 ! [V_a_2,V_b_2,V_A_2,T_a] : % 167.16/167.35 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_inf__Sup__absorb,axiom, % 167.16/167.35 ! [V_a_2,V_A_2,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = V_a_2 ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 167.16/167.35 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_a_2),V_A_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__image__simple_Ounion__inter,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 167.16/167.35 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_finite__dom__body,axiom, % 167.16/167.35 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 167.16/167.35 % 167.16/167.35 fof(fact_card__insert__if,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) % 167.16/167.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_card__insert__disjoint,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 167.16/167.35 ! [V_a_2,V_A_2,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_a_2),V_A_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_minus__fold__remove,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2),V_A_2) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__one_Oeq__fold_H,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_x_2),V_A_2) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__one_Ounion__inter,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.35 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__one_Ounion__disjoint,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 167.16/167.35 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 167.16/167.35 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 167.16/167.35 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_card__insert,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm_Ofold__rec,axiom, % 167.16/167.35 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 167.16/167.35 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_Inf__fin_Oremove,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,T_a] : % 167.16/167.35 ( class_Lattices_Olattice(T_a) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) % 167.16/167.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.35 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_INFI__fold__inf,axiom, % 167.16/167.35 ! [V_f_2,V_A_2,T_a,T_b] : % 167.16/167.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_SUPR__fold__sup,axiom, % 167.16/167.35 ! [V_f_2,V_A_2,T_a,T_b] : % 167.16/167.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm_Ofold__insert,axiom, % 167.16/167.35 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 167.16/167.35 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.16/167.35 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_card__Diff__singleton__if,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 167.16/167.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_card__Diff__singleton,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ). % 167.16/167.35 % 167.16/167.35 fof(fact_card__Diff1__less,axiom, % 167.16/167.35 ! [V_x_2,V_A_2,T_a] : % 167.16/167.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ). % 167.16/167.35 % 167.16/167.36 fof(fact_card__Diff2__less,axiom, % 167.16/167.36 ! [V_y_2,V_x_2,V_A_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INF1__E,axiom, % 167.16/167.36 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 167.16/167.36 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INF1__D,axiom, % 167.16/167.36 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_SUP1__I,axiom, % 167.16/167.36 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INF2__E,axiom, % 167.16/167.36 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 167.16/167.36 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INF2__D,axiom, % 167.16/167.36 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_SUP2__I,axiom, % 167.16/167.36 ! [T_c,T_b,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_finite__INT,axiom, % 167.16/167.36 ! [V_A_2,T_b,V_I_2,T_a] : % 167.16/167.36 ( ? [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) % 167.16/167.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) ) % 167.16/167.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_card__UNIV__unit,axiom, % 167.16/167.36 hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 167.16/167.36 % 167.16/167.36 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 167.16/167.36 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : % 167.16/167.36 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.36 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_linorder__cases,axiom, % 167.16/167.36 ! [V_y,V_x,T_a] : % 167.16/167.36 ( class_Orderings_Olinorder(T_a) % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.36 => ( V_x != V_y % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_order__less__asym,axiom, % 167.16/167.36 ! [V_y,V_x,T_a] : % 167.16/167.36 ( class_Orderings_Opreorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_xt1_I10_J,axiom, % 167.16/167.36 ! [V_z,V_x,V_y,T_a] : % 167.16/167.36 ( class_Orderings_Oorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_order__less__trans,axiom, % 167.16/167.36 ! [V_z,V_y,V_x,T_a] : % 167.16/167.36 ( class_Orderings_Opreorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_xt1_I2_J,axiom, % 167.16/167.36 ! [V_c,V_a,V_b,T_a] : % 167.16/167.36 ( class_Orderings_Oorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 167.16/167.36 => ( V_b = V_c % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_ord__less__eq__trans,axiom, % 167.16/167.36 ! [V_c,V_b,V_a,T_a] : % 167.16/167.36 ( class_Orderings_Oord(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.36 => ( V_b = V_c % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_xt1_I1_J,axiom, % 167.16/167.36 ! [V_c,V_b,V_a,T_a] : % 167.16/167.36 ( class_Orderings_Oorder(T_a) % 167.16/167.36 => ( V_a = V_b % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_ord__eq__less__trans,axiom, % 167.16/167.36 ! [V_c,V_b,V_a,T_a] : % 167.16/167.36 ( class_Orderings_Oord(T_a) % 167.16/167.36 => ( V_a = V_b % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_xt1_I9_J,axiom, % 167.16/167.36 ! [V_a,V_b,T_a] : % 167.16/167.36 ( class_Orderings_Oorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 167.16/167.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_order__less__asym_H,axiom, % 167.16/167.36 ! [V_b,V_a,T_a] : % 167.16/167.36 ( class_Orderings_Opreorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_order__less__imp__not__eq2,axiom, % 167.16/167.36 ! [V_y,V_x,T_a] : % 167.16/167.36 ( class_Orderings_Oorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.36 => V_y != V_x ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_order__less__imp__not__eq,axiom, % 167.16/167.36 ! [V_y,V_x,T_a] : % 167.16/167.36 ( class_Orderings_Oorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.36 => V_x != V_y ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_order__less__imp__not__less,axiom, % 167.16/167.36 ! [V_y,V_x,T_a] : % 167.16/167.36 ( class_Orderings_Opreorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_order__less__not__sym,axiom, % 167.16/167.36 ! [V_y,V_x,T_a] : % 167.16/167.36 ( class_Orderings_Opreorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__imp__neq,axiom, % 167.16/167.36 ! [V_y,V_x,T_a] : % 167.16/167.36 ( class_Orderings_Oorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.36 => V_x != V_y ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_linorder__neqE,axiom, % 167.16/167.36 ! [V_y,V_x,T_a] : % 167.16/167.36 ( class_Orderings_Olinorder(T_a) % 167.16/167.36 => ( V_x != V_y % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_linorder__antisym__conv3,axiom, % 167.16/167.36 ! [V_x_2,V_y_2,T_a] : % 167.16/167.36 ( class_Orderings_Olinorder(T_a) % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.16/167.36 <=> V_x_2 = V_y_2 ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_linorder__less__linear,axiom, % 167.16/167.36 ! [V_y,V_x,T_a] : % 167.16/167.36 ( class_Orderings_Olinorder(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.36 | V_x = V_y % 167.16/167.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_not__less__iff__gr__or__eq,axiom, % 167.16/167.36 ! [V_y_2,V_x_2,T_a] : % 167.16/167.36 ( class_Orderings_Olinorder(T_a) % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.16/167.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 167.16/167.36 | V_x_2 = V_y_2 ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_linorder__neq__iff,axiom, % 167.16/167.36 ! [V_y_2,V_x_2,T_a] : % 167.16/167.36 ( class_Orderings_Olinorder(T_a) % 167.16/167.36 => ( V_x_2 != V_y_2 % 167.16/167.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.16/167.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_order__less__irrefl,axiom, % 167.16/167.36 ! [V_x,T_a] : % 167.16/167.36 ( class_Orderings_Opreorder(T_a) % 167.16/167.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 167.16/167.36 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 167.16/167.36 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.36 => c_Finite__Set_Ofun__left__comm(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_finite__UN,axiom, % 167.16/167.36 ! [V_B_2,T_b,V_A_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.36 <=> ! [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__supI2,axiom, % 167.16/167.36 ! [V_a,V_b,V_x,T_a] : % 167.16/167.36 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__supI1,axiom, % 167.16/167.36 ! [V_b,V_a,V_x,T_a] : % 167.16/167.36 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__infI2,axiom, % 167.16/167.36 ! [V_a,V_x,V_b,T_a] : % 167.16/167.36 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__infI1,axiom, % 167.16/167.36 ! [V_b,V_x,V_a,T_a] : % 167.16/167.36 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__Suc__eq__diff__pred,axiom, % 167.16/167.36 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n) ). % 167.16/167.36 % 167.16/167.36 fof(fact_card__eq__setsum,axiom, % 167.16/167.36 ! [V_A_2,T_a] : hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INF__INT__eq,axiom, % 167.16/167.36 ! [V_x_2,V_r_2,T_b,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2)) % 167.16/167.36 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_SUP__UN__eq,axiom, % 167.16/167.36 ! [V_x_2,V_r_2,T_b,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2)) % 167.16/167.36 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Osingleton,axiom, % 167.16/167.36 ! [V_x_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 167.16/167.36 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.16/167.36 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_sup__Inf__absorb,axiom, % 167.16/167.36 ! [V_a_2,V_A_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = V_a_2 ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Oin__idem,axiom, % 167.16/167.36 ! [V_x_2,V_A_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Oinsert__idem,axiom, % 167.16/167.36 ! [V_x_2,V_A_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Ounion__idem,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 167.16/167.36 ! [V_a_2,V_A_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_a_2),V_A_2) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_sup__SUPR__fold__sup,axiom, % 167.16/167.36 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_inf__INFI__fold__inf,axiom, % 167.16/167.36 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_card__Diff__insert,axiom, % 167.16/167.36 ! [V_B_2,V_a_2,V_A_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 167.16/167.36 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Oinsert,axiom, % 167.16/167.36 ! [V_x_2,V_A_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Oinsert__remove,axiom, % 167.16/167.36 ! [V_x_2,V_A_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 167.16/167.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Ounion__inter,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 167.16/167.36 ! [V_x_2,V_A_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.36 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_x_2),V_A_2) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_lessI,axiom, % 167.16/167.36 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__mono,axiom, % 167.16/167.36 ! [V_n,V_m] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__simps_I4_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__simps_I3_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__extend__simps_I3_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__simps_I2_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__simps_I1_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_image__eq__UN,axiom, % 167.16/167.36 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__D,axiom, % 167.16/167.36 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__E,axiom, % 167.16/167.36 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) % 167.16/167.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__I,axiom, % 167.16/167.36 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_ball__UN,axiom, % 167.16/167.36 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] : % 167.16/167.36 ( ! [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.36 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.16/167.36 <=> ! [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.36 => ! [B_xa] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) % 167.16/167.36 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__UN__flatten,axiom, % 167.16/167.36 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__simps_I9_J,axiom, % 167.16/167.36 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__simps_I9_J,axiom, % 167.16/167.36 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__extend__simps_I9_J,axiom, % 167.16/167.36 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__extend__simps_I9_J,axiom, % 167.16/167.36 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INF1__iff,axiom, % 167.16/167.36 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 167.16/167.36 <=> ! [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_SUP1__iff,axiom, % 167.16/167.36 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 167.16/167.36 <=> ? [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.36 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INF2__iff,axiom, % 167.16/167.36 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 167.16/167.36 <=> ! [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_SUP2__iff,axiom, % 167.16/167.36 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 167.16/167.36 <=> ? [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.36 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_psubsetD,axiom, % 167.16/167.36 ! [V_c_2,V_B_2,V_A_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_not__psubset__empty,axiom, % 167.16/167.36 ! [V_A_2,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.16/167.36 % 167.16/167.36 fof(fact_psubset__card__mono,axiom, % 167.16/167.36 ! [V_A_2,V_B_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__inject,axiom, % 167.16/167.36 ! [V_y,V_x] : % 167.16/167.36 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 167.16/167.36 => V_x = V_y ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat_Oinject,axiom, % 167.16/167.36 ! [V_nat_H_2,V_nat_2] : % 167.16/167.36 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 167.16/167.36 <=> V_nat_2 = V_nat_H_2 ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__n__not__n,axiom, % 167.16/167.36 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 167.16/167.36 % 167.16/167.36 fof(fact_n__not__Suc__n,axiom, % 167.16/167.36 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__less__cases,axiom, % 167.16/167.36 ! [V_P_2,V_n_2,V_m_2] : % 167.16/167.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 167.16/167.36 => ( ( V_m_2 = V_n_2 % 167.16/167.36 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 167.16/167.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 167.16/167.36 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__not__refl3,axiom, % 167.16/167.36 ! [V_t,V_s] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 167.16/167.36 => V_s != V_t ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__not__refl2,axiom, % 167.16/167.36 ! [V_m,V_n] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 167.16/167.36 => V_m != V_n ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__irrefl__nat,axiom, % 167.16/167.36 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_linorder__neqE__nat,axiom, % 167.16/167.36 ! [V_y,V_x] : % 167.16/167.36 ( V_x != V_y % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__neq__iff,axiom, % 167.16/167.36 ! [V_n_2,V_m_2] : % 167.16/167.36 ( V_m_2 != V_n_2 % 167.16/167.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__not__refl,axiom, % 167.16/167.36 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__commute,axiom, % 167.16/167.36 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__iff,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.36 <=> ? [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.36 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__iff,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.36 <=> ! [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UNION__empty__conv_I2_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_a,T_b] : % 167.16/167.36 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 <=> ! [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.36 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__constant,axiom, % 167.16/167.36 ! [V_c_2,T_b,T_a,V_A_2] : % 167.16/167.36 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 167.16/167.36 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2 ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__empty2,axiom, % 167.16/167.36 ! [V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UNION__empty__conv_I1_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a] : % 167.16/167.36 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) % 167.16/167.36 <=> ! [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.36 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__extend__simps_I5_J,axiom, % 167.16/167.36 ! [V_B_2,V_C_2,T_b,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__simps_I5_J,axiom, % 167.16/167.36 ! [V_B_2,V_a_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__extend__simps_I10_J,axiom, % 167.16/167.36 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ). % 167.16/167.36 % 167.16/167.36 fof(fact_image__UN,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Oimage(T_b,T_a,V_f_2)),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__simps_I10_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_a,T_b] : % 167.16/167.36 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 <=> ! [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.36 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a] : % 167.16/167.36 ( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) % 167.16/167.36 <=> ! [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.36 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__extend__simps_I10_J,axiom, % 167.16/167.36 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__simps_I10_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__Un__distrib,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__Un,axiom, % 167.16/167.36 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__simps_I7_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__simps_I6_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__extend__simps_I7_J,axiom, % 167.16/167.36 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Un__INT__distrib,axiom, % 167.16/167.36 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__extend__simps_I6_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Un__INT__distrib2,axiom, % 167.16/167.36 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__simps_I5_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__simps_I4_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__extend__simps_I5_J,axiom, % 167.16/167.36 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Int__UN__distrib,axiom, % 167.16/167.36 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__extend__simps_I4_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Int__UN__distrib2,axiom, % 167.16/167.36 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__Int__distrib,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_SUP__commute,axiom, % 167.16/167.36 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_SUPR__apply,axiom, % 167.16/167.36 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__extend__simps_I6_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__simps_I6_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__extend__simps_I7_J,axiom, % 167.16/167.36 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__simps_I7_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INF__commute,axiom, % 167.16/167.36 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INFI__apply,axiom, % 167.16/167.36 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__less__SucD,axiom, % 167.16/167.36 ! [V_n,V_m] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__lessD,axiom, % 167.16/167.36 ! [V_n,V_m] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__SucE,axiom, % 167.16/167.36 ! [V_n,V_m] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 167.16/167.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.16/167.36 => V_m = V_n ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__trans__Suc,axiom, % 167.16/167.36 ! [V_k,V_j,V_i] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__lessI,axiom, % 167.16/167.36 ! [V_n,V_m] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.16/167.36 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__SucI,axiom, % 167.16/167.36 ! [V_n,V_m] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__antisym,axiom, % 167.16/167.36 ! [V_m,V_n] : % 167.16/167.36 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 167.16/167.36 => V_m = V_n ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_not__less__less__Suc__eq,axiom, % 167.16/167.36 ! [V_m_2,V_n_2] : % 167.16/167.36 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 167.16/167.36 <=> V_n_2 = V_m_2 ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__less__eq,axiom, % 167.16/167.36 ! [V_n_2,V_m_2] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) % 167.16/167.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__Suc__eq,axiom, % 167.16/167.36 ! [V_n_2,V_m_2] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 167.16/167.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.36 | V_m_2 = V_n_2 ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_not__less__eq,axiom, % 167.16/167.36 ! [V_n_2,V_m_2] : % 167.16/167.36 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__diff__diff,axiom, % 167.16/167.36 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__Suc__Suc,axiom, % 167.16/167.36 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__less__mono2,axiom, % 167.16/167.36 ! [V_l,V_n,V_m] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__imp__diff__less,axiom, % 167.16/167.36 ! [V_n,V_k,V_j] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__insert__distrib,axiom, % 167.16/167.36 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__insert__distrib,axiom, % 167.16/167.36 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__absorb,axiom, % 167.16/167.36 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__absorb,axiom, % 167.16/167.36 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__extend__simps_I1_J,axiom, % 167.16/167.36 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__singleton,axiom, % 167.16/167.36 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__simps_I1_J,axiom, % 167.16/167.36 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__constant,axiom, % 167.16/167.36 ! [V_c_2,T_b,T_a,V_A_2] : % 167.16/167.36 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 167.16/167.36 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2 ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__empty,axiom, % 167.16/167.36 ! [V_B_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__SUP__iff,axiom, % 167.16/167.36 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] : % 167.16/167.36 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 & class_Orderings_Olinorder(T_a) ) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_f_2))) % 167.16/167.36 <=> ? [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__simps_I3_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__simps_I2_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__extend__simps_I3_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__extend__simps_I2_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__extend__simps_I2_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__extend__simps_I1_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_UN__insert,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__insert,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_SUP__const,axiom, % 167.16/167.36 ! [V_M_2,T_a,V_A_2,T_b] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 167.16/167.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__extend__simps_I4_J,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 167.16/167.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 167.16/167.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INF__less__iff,axiom, % 167.16/167.36 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] : % 167.16/167.36 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 & class_Orderings_Olinorder(T_a) ) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_f_2)),V_a_2)) % 167.16/167.36 <=> ? [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INT__Un,axiom, % 167.16/167.36 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INF__const,axiom, % 167.16/167.36 ! [V_M_2,T_a,V_A_2,T_b] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 167.16/167.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__less__Suc,axiom, % 167.16/167.36 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__Suc__1,axiom, % 167.16/167.36 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Oclosed,axiom, % 167.16/167.36 ! [V_A_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_card_Oremove,axiom, % 167.16/167.36 ! [V_x_2,V_A_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.36 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__eq__diff__less,axiom, % 167.16/167.36 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.16/167.36 ( class_Groups_Oordered__ab__group__add(T_a) % 167.16/167.36 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 167.16/167.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fin_Ohom__commute,axiom, % 167.16/167.36 ! [V_N_2,V_h_2,T_a] : % 167.16/167.36 ( class_Lattices_Olattice(T_a) % 167.16/167.36 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.16/167.36 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_card_Oinsert__remove,axiom, % 167.16/167.36 ! [V_x_2,V_A_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_fold__Un__disjoint,axiom, % 167.16/167.36 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) ) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_setsum__strict__mono,axiom, % 167.16/167.36 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 167.16/167.36 ( ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.36 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) ) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.36 => ( ! [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2))) ) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_setsum__diff1_H,axiom, % 167.16/167.36 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 167.16/167.36 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_setsum_Oremove,axiom, % 167.16/167.36 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 167.16/167.36 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__fold__inf,axiom, % 167.16/167.36 ! [V_A_2,T_a] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),c_Orderings_Otop__class_Otop(T_a)),V_A_2) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_InterD,axiom, % 167.16/167.36 ! [V_X_2,V_C_2,V_A_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_InterE,axiom, % 167.16/167.36 ! [V_X_2,V_C_2,V_A_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_finite__Inter,axiom, % 167.16/167.36 ! [V_M_2,T_a] : % 167.16/167.36 ( ? [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) % 167.16/167.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 167.16/167.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_psubset__trans,axiom, % 167.16/167.36 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__add__right__cancel,axiom, % 167.16/167.36 ! [V_n_2,V_k_2,V_m_2] : % 167.16/167.36 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) % 167.16/167.36 <=> V_m_2 = V_n_2 ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__add__left__cancel,axiom, % 167.16/167.36 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.36 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) % 167.16/167.36 <=> V_m_2 = V_n_2 ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__mult__distrib,axiom, % 167.16/167.36 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(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)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__add__assoc,axiom, % 167.16/167.36 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__mult__distrib2,axiom, % 167.16/167.36 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(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)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__add__left__commute,axiom, % 167.16/167.36 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__add__commute,axiom, % 167.16/167.36 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m) ). % 167.16/167.36 % 167.16/167.36 fof(fact_mult__Suc__right,axiom, % 167.16/167.36 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_mult__Suc,axiom, % 167.16/167.36 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 167.16/167.36 ! [V_c,V_b,V_a,T_a] : % 167.16/167.36 ( class_Groups_Oab__semigroup__add(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 167.16/167.36 ! [V_c,V_b,V_a,T_a] : % 167.16/167.36 ( class_Groups_Oab__semigroup__mult(T_a) % 167.16/167.36 => 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)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__left__cancel,axiom, % 167.16/167.36 ! [V_c_2,V_b_2,V_a_2,T_a] : % 167.16/167.36 ( class_Groups_Ocancel__semigroup__add(T_a) % 167.16/167.36 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2) % 167.16/167.36 <=> V_b_2 = V_c_2 ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__right__cancel,axiom, % 167.16/167.36 ! [V_c_2,V_a_2,V_b_2,T_a] : % 167.16/167.36 ( class_Groups_Ocancel__semigroup__add(T_a) % 167.16/167.36 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2) % 167.16/167.36 <=> V_b_2 = V_c_2 ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__left__imp__eq,axiom, % 167.16/167.36 ! [V_c,V_b,V_a,T_a] : % 167.16/167.36 ( class_Groups_Ocancel__semigroup__add(T_a) % 167.16/167.36 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 167.16/167.36 => V_b = V_c ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__imp__eq,axiom, % 167.16/167.36 ! [V_c,V_b,V_a,T_a] : % 167.16/167.36 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 167.16/167.36 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 167.16/167.36 => V_b = V_c ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__right__imp__eq,axiom, % 167.16/167.36 ! [V_c,V_a,V_b,T_a] : % 167.16/167.36 ( class_Groups_Ocancel__semigroup__add(T_a) % 167.16/167.36 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) % 167.16/167.36 => V_b = V_c ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_mult__left__idem,axiom, % 167.16/167.36 ! [V_b,V_a,T_a] : % 167.16/167.36 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.16/167.36 => 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) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_mult__idem,axiom, % 167.16/167.36 ! [V_x,T_a] : % 167.16/167.36 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_times_Oidem,axiom, % 167.16/167.36 ! [V_a,T_a] : % 167.16/167.36 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__less__cancel__right,axiom, % 167.16/167.36 ! [V_b_2,V_c_2,V_a_2,T_a] : % 167.16/167.36 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) % 167.16/167.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__less__cancel__left,axiom, % 167.16/167.36 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.16/167.36 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) % 167.16/167.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__strict__right__mono,axiom, % 167.16/167.36 ! [V_c,V_b,V_a,T_a] : % 167.16/167.36 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__strict__left__mono,axiom, % 167.16/167.36 ! [V_c,V_b,V_a,T_a] : % 167.16/167.36 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__strict__mono,axiom, % 167.16/167.36 ! [V_d,V_c,V_b,V_a,T_a] : % 167.16/167.36 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__less__imp__less__right,axiom, % 167.16/167.36 ! [V_b,V_c,V_a,T_a] : % 167.16/167.36 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__less__imp__less__left,axiom, % 167.16/167.36 ! [V_b,V_a,V_c,T_a] : % 167.16/167.36 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__add__cancel,axiom, % 167.16/167.36 ! [V_b,V_a,T_a] : % 167.16/167.36 ( class_Groups_Ogroup__add(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__diff__cancel,axiom, % 167.16/167.36 ! [V_b,V_a,T_a] : % 167.16/167.36 ( class_Groups_Ogroup__add(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_mult__1__left,axiom, % 167.16/167.36 ! [V_a,T_a] : % 167.16/167.36 ( class_Groups_Omonoid__mult(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_mult__1,axiom, % 167.16/167.36 ! [V_a,T_a] : % 167.16/167.36 ( class_Groups_Ocomm__monoid__mult(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_mult__1__right,axiom, % 167.16/167.36 ! [V_a,T_a] : % 167.16/167.36 ( class_Groups_Omonoid__mult(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_mult_Ocomm__neutral,axiom, % 167.16/167.36 ! [V_a,T_a] : % 167.16/167.36 ( class_Groups_Ocomm__monoid__mult(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__Suc__right,axiom, % 167.16/167.36 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__Suc,axiom, % 167.16/167.36 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__Suc__shift,axiom, % 167.16/167.36 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_not__add__less1,axiom, % 167.16/167.36 ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_not__add__less2,axiom, % 167.16/167.36 ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__add__left__cancel__less,axiom, % 167.16/167.36 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 167.16/167.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_trans__less__add1,axiom, % 167.16/167.36 ! [V_m,V_j,V_i] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_trans__less__add2,axiom, % 167.16/167.36 ! [V_m,V_j,V_i] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__less__mono1,axiom, % 167.16/167.36 ! [V_k,V_j,V_i] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__less__mono,axiom, % 167.16/167.36 ! [V_l,V_k,V_j,V_i] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__add__eq__less,axiom, % 167.16/167.36 ! [V_n,V_m,V_l,V_k] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 167.16/167.36 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__lessD1,axiom, % 167.16/167.36 ! [V_k,V_j,V_i] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) % 167.16/167.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__mult__cancel1,axiom, % 167.16/167.36 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.36 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2) % 167.16/167.36 <=> V_m_2 = V_n_2 ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__add__inverse2,axiom, % 167.16/167.36 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__add__inverse,axiom, % 167.16/167.36 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__diff__left,axiom, % 167.16/167.36 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__cancel,axiom, % 167.16/167.36 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__cancel2,axiom, % 167.16/167.36 ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__mult__distrib2,axiom, % 167.16/167.36 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(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)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__mult__distrib,axiom, % 167.16/167.36 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(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)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inter__UNIV,axiom, % 167.16/167.36 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__mult__1,axiom, % 167.16/167.36 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__1__eq__mult__iff,axiom, % 167.16/167.36 ! [V_n_2,V_m_2] : % 167.16/167.36 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 167.16/167.36 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 167.16/167.36 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__mult__1__right,axiom, % 167.16/167.36 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 167.16/167.36 % 167.16/167.36 fof(fact_nat__mult__eq__1__iff,axiom, % 167.16/167.36 ! [V_n_2,V_m_2] : % 167.16/167.36 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 167.16/167.36 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 167.16/167.36 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inter__empty,axiom, % 167.16/167.36 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inter__Un__distrib,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inter__insert,axiom, % 167.16/167.36 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Int__eq__Inter,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ). % 167.16/167.36 % 167.16/167.36 fof(fact_fun__left__comm,axiom, % 167.16/167.36 ! [T_a] : % 167.16/167.36 ( class_Groups_Oab__semigroup__mult(T_a) % 167.16/167.36 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_fun__left__comm__idem,axiom, % 167.16/167.36 ! [T_a] : % 167.16/167.36 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.16/167.36 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_setsum__addf,axiom, % 167.16/167.36 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 167.16/167.36 ( class_Groups_Ocomm__monoid__add(T_a) % 167.16/167.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_setsum__right__distrib,axiom, % 167.16/167.36 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] : % 167.16/167.36 ( class_Rings_Osemiring__0(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2)),V_f_2)),V_A_2) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_setsum__left__distrib,axiom, % 167.16/167.36 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 167.16/167.36 ( class_Rings_Osemiring__0(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_r_2)),V_A_2) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_setsum__product,axiom, % 167.16/167.36 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 167.16/167.36 ( class_Rings_Osemiring__0(T_a) % 167.16/167.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_a),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_a),tc_fun(tc_fun(T_c,T_a),tc_fun(T_c,T_a)),T_b),c_COMBB(T_a,T_a,T_c)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__less__iff,axiom, % 167.16/167.36 ! [V_a_2,V_S_2,T_a] : % 167.16/167.36 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 & class_Orderings_Olinorder(T_a) ) % 167.16/167.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) % 167.16/167.36 <=> ? [B_x] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 167.16/167.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Un__Inter,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inter__image__eq,axiom, % 167.16/167.36 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.16/167.36 % 167.16/167.36 fof(fact_INTER__eq__Inter__image,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__iff__Suc__add,axiom, % 167.16/167.36 ! [V_n_2,V_m_2] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.36 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__add__Suc2,axiom, % 167.16/167.36 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__add__Suc1,axiom, % 167.16/167.36 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__mult__less__cancel1,axiom, % 167.16/167.36 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) % 167.16/167.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_less__diff__conv,axiom, % 167.16/167.36 ! [V_k_2,V_j_2,V_i_2] : % 167.16/167.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 167.16/167.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_add__diff__inverse,axiom, % 167.16/167.36 ! [V_n,V_m] : % 167.16/167.36 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.16/167.36 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__eq__plus1,axiom, % 167.16/167.36 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Suc__eq__plus1__left,axiom, % 167.16/167.36 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ). % 167.16/167.36 % 167.16/167.36 fof(fact_setsum_Odistrib,axiom, % 167.16/167.36 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 167.16/167.36 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Oplus__class_Oplus(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_h_2),V_A_2)) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Int__Inter__image,axiom, % 167.16/167.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__singleton,axiom, % 167.16/167.36 ! [V_a_2,T_a] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__empty,axiom, % 167.16/167.36 ! [T_a] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__UNIV,axiom, % 167.16/167.36 ! [T_a] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_Inf__insert,axiom, % 167.16/167.36 ! [V_A_2,V_a_2,T_a] : % 167.16/167.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.36 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_diff__eq__diff__eq,axiom, % 167.16/167.36 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.16/167.36 ( class_Groups_Oab__group__add(T_a) % 167.16/167.36 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) % 167.16/167.36 => ( V_a_2 = V_b_2 % 167.16/167.36 <=> V_c_2 = V_d_2 ) ) ) ). % 167.16/167.36 % 167.16/167.36 fof(fact_one__reorient,axiom, % 167.16/167.36 ! [V_x_2,T_a] : % 167.16/167.36 ( class_Groups_Oone(T_a) % 167.16/167.36 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 167.16/167.36 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 167.16/167.36 % 167.16/167.37 fof(fact_fold__image__distrib,axiom, % 167.16/167.37 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_b)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__insert,axiom, % 167.16/167.37 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 167.16/167.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_F_2)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum_Oinsert,axiom, % 167.16/167.37 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__Un__Int,axiom, % 167.16/167.37 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold__image__insert,axiom, % 167.16/167.37 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Oab__semigroup__mult(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.37 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card_Ounion__inter,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card__Un__Int,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Inf__binary,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,T_a] : % 167.16/167.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_inf__Inf__fold__inf,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a] : % 167.16/167.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_B_2),V_A_2) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Inf__fin__Inf,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum_Oinsert__remove,axiom, % 167.16/167.37 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__Un__disjoint,axiom, % 167.16/167.37 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__Un,axiom, % 167.16/167.37 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Oab__group__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card__Un__disjoint,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card_Oinsert,axiom, % 167.16/167.37 ! [V_x_2,V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold__image__Un__Int,axiom, % 167.16/167.37 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__Un__nat,axiom, % 167.16/167.37 ! [V_f_2,V_B_2,V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_less__add__iff2,axiom, % 167.16/167.37 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 167.16/167.37 ( class_Rings_Oordered__ring(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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))) % 167.16/167.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_less__add__iff1,axiom, % 167.16/167.37 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 167.16/167.37 ( class_Rings_Oordered__ring(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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))) % 167.16/167.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 167.16/167.37 ! [V_m,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 167.16/167.37 ! [V_a,V_m,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 167.16/167.37 ! [V_m,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_eq__add__iff1,axiom, % 167.16/167.37 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 167.16/167.37 ( class_Rings_Oring(T_a) % 167.16/167.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(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) % 167.16/167.37 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_eq__add__iff2,axiom, % 167.16/167.37 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 167.16/167.37 ( class_Rings_Oring(T_a) % 167.16/167.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(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) % 167.16/167.37 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_less__1__mult,axiom, % 167.16/167.37 ! [V_n,V_m,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semidom(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_less__add__one,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semidom(T_a) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_nat__mult__assoc,axiom, % 167.16/167.37 ! [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)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_nat__mult__commute,axiom, % 167.16/167.37 ! [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) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Inter__def,axiom, % 167.16/167.37 ! [V_S_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ). % 167.16/167.37 % 167.16/167.37 fof(fact_linorder__neqE__linordered__idom,axiom, % 167.16/167.37 ! [V_y,V_x,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__idom(T_a) % 167.16/167.37 => ( V_x != V_y % 167.16/167.37 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 167.16/167.37 ! [V_d,V_c,V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 167.16/167.37 ! [V_c,V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 167.16/167.37 ! [V_c,V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 167.16/167.37 ! [V_d,V_c,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 167.16/167.37 ! [V_d,V_c,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 167.16/167.37 ! [V_c,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 167.16/167.37 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => 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)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 167.16/167.37 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => 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)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 167.16/167.37 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => 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))) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 167.16/167.37 ! [V_rx,V_ly,V_lx,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => 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) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 167.16/167.37 ! [V_rx,V_ly,V_lx,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => 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)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 167.16/167.37 ! [V_ry,V_rx,V_lx,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => 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) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 167.16/167.37 ! [V_ry,V_rx,V_lx,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => 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)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 167.16/167.37 ! [V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => 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) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_crossproduct__eq,axiom, % 167.16/167.37 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 167.16/167.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 167.16/167.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) % 167.16/167.37 <=> ( V_w_2 = V_x_2 % 167.16/167.37 | V_y_2 = V_z_2 ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_combine__common__factor,axiom, % 167.16/167.37 ! [V_c,V_b,V_e,V_a,T_a] : % 167.16/167.37 ( class_Rings_Osemiring(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 167.16/167.37 ! [V_b,V_m,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 167.16/167.37 ! [V_c,V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(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)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__class_Odistrib,axiom, % 167.16/167.37 ! [V_c,V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(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)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_crossproduct__noteq,axiom, % 167.16/167.37 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.16/167.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 167.16/167.37 => ( ( V_a_2 != V_b_2 % 167.16/167.37 & V_c_2 != V_d_2 ) % 167.16/167.37 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 167.16/167.37 ! [V_z,V_y,V_x,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(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)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold__image__Un__one,axiom, % 167.16/167.37 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 167.16/167.37 => ( ! [B_x] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 167.16/167.37 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 167.16/167.37 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_T_2)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_left__add__mult__distrib,axiom, % 167.16/167.37 ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k) ). % 167.16/167.37 % 167.16/167.37 fof(fact_termination__basic__simps_I2_J,axiom, % 167.16/167.37 ! [V_y,V_z,V_x] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_termination__basic__simps_I1_J,axiom, % 167.16/167.37 ! [V_z,V_y,V_x] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold__graph__permute__diff,axiom, % 167.16/167.37 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] : % 167.16/167.37 ( class_Groups_Oab__semigroup__mult(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_x_2)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Sup__fold__sup,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),c_Orderings_Obot__class_Obot(T_a)),V_A_2) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1__eq__fold,axiom, % 167.16/167.37 ! [V_a_2,V_A_2,T_a] : % 167.16/167.37 ( class_Groups_Oab__semigroup__mult(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.37 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1__Un,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a] : % 167.16/167.37 ( class_Groups_Oab__semigroup__mult(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.37 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 167.16/167.37 => ( ! [B_x] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.37 => hAPP(V_g_2,B_x) = V_z_2 ) % 167.16/167.37 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_UnionI,axiom, % 167.16/167.37 ! [V_A_2,V_C_2,V_X_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_finite__UnionD,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_empty__fold__graphE,axiom, % 167.16/167.37 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) % 167.16/167.37 => V_x_2 = V_z_2 ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold__graph_OemptyI,axiom, % 167.16/167.37 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold__graph_Oequations_I1_J,axiom, % 167.16/167.37 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold__graph__imp__finite,axiom, % 167.16/167.37 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_image__Union,axiom, % 167.16/167.37 ! [V_S_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_b,T_a,V_f_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Int__Union,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Int__Union2,axiom, % 167.16/167.37 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_UN__extend__simps_I8_J,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ). % 167.16/167.37 % 167.16/167.37 fof(fact_UN__simps_I8_J,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_less__Sup__iff,axiom, % 167.16/167.37 ! [V_S_2,V_a_2,T_a] : % 167.16/167.37 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 & class_Orderings_Olinorder(T_a) ) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) % 167.16/167.37 <=> ? [B_x] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 167.16/167.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 167.16/167.37 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.37 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 167.16/167.37 => V_y_2 = V_x_2 ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Union__disjoint,axiom, % 167.16/167.37 ! [V_A_2,V_C_2,T_a] : % 167.16/167.37 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 <=> ! [B_x] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) % 167.16/167.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Union__empty,axiom, % 167.16/167.37 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1__singleton__def,axiom, % 167.16/167.37 ! [V_a_2,V_f_2,T_a,V_g_2] : % 167.16/167.37 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2) % 167.16/167.37 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1__singleton,axiom, % 167.16/167.37 ! [V_a_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ). % 167.16/167.37 % 167.16/167.37 fof(fact_Union__insert,axiom, % 167.16/167.37 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold__graph_OinsertI,axiom, % 167.16/167.37 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 167.16/167.37 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Union__UNIV,axiom, % 167.16/167.37 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Union__Un__distrib,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Union__image__eq,axiom, % 167.16/167.37 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.16/167.37 % 167.16/167.37 fof(fact_UNION__eq__Union__image,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_folding__one_Oeq__fold,axiom, % 167.16/167.37 ! [V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.37 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Sup__empty,axiom, % 167.16/167.37 ! [T_a] : % 167.16/167.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Sup__singleton,axiom, % 167.16/167.37 ! [V_a_2,T_a] : % 167.16/167.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Sup__insert,axiom, % 167.16/167.37 ! [V_A_2,V_a_2,T_a] : % 167.16/167.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fun__left__comm_Ofold__equality,axiom, % 167.16/167.37 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.37 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 167.16/167.37 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Sup__UNIV,axiom, % 167.16/167.37 ! [T_a] : % 167.16/167.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_INT__extend__simps_I8_J,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ). % 167.16/167.37 % 167.16/167.37 fof(fact_INT__simps_I8_J,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold__def,axiom, % 167.16/167.37 ! [V_A_2,V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold__graph(T_b,T_a,V_f_2,V_z_2,V_A_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold__graph__insert__swap,axiom, % 167.16/167.37 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] : % 167.16/167.37 ( class_Groups_Oab__semigroup__mult(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_y_2)) % 167.16/167.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2),V_y_2))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Sup__fin_OF__eq,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( class_Lattices_Olattice(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_A_2) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Inf__fin_OF__eq,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( class_Lattices_Olattice(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Un__eq__Union,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Un__Union__image,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 167.16/167.37 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] : % 167.16/167.37 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Sup__binary,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,T_a] : % 167.16/167.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_sup__Sup__fold__sup,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a] : % 167.16/167.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_B_2),V_A_2) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Sup__fin__Sup,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1__insert__idem,axiom, % 167.16/167.37 ! [V_x_2,V_A_2,T_a] : % 167.16/167.37 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.16/167.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1__Un2,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a] : % 167.16/167.37 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1__eq__fold__idem,axiom, % 167.16/167.37 ! [V_a_2,V_A_2,T_a] : % 167.16/167.37 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Diff1__fold__graph,axiom, % 167.16/167.37 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_y_2)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1__insert,axiom, % 167.16/167.37 ! [V_x_2,V_A_2,T_a] : % 167.16/167.37 ( class_Groups_Oab__semigroup__mult(T_a) % 167.16/167.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.37 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_semilattice__big_OF__eq,axiom, % 167.16/167.37 ! [V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.37 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1Set_Ointros,axiom, % 167.16/167.37 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) % 167.16/167.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),V_x_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 167.16/167.37 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.37 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.37 => ? [B_y_H] : % 167.16/167.37 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 167.16/167.37 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1__in,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( class_Groups_Oab__semigroup__mult(T_a) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),V_A_2)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_hom__fold1__commute,axiom, % 167.16/167.37 ! [V_N_2,V_h_2,T_a] : % 167.16/167.37 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.16/167.37 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.16/167.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 167.16/167.37 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.37 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_v_2)) % 167.16/167.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.37 => ~ ! [B_y] : % 167.16/167.37 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 167.16/167.37 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_insert__partition,axiom, % 167.16/167.37 ! [V_F_2,V_x_2,T_a] : % 167.16/167.37 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) % 167.16/167.37 => ( ! [B_x] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))) % 167.16/167.37 => ! [B_xa] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))) % 167.16/167.37 => ( B_x != B_xa % 167.16/167.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 167.16/167.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_finite__fun__UNIVD1,axiom, % 167.16/167.37 ! [T_b,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))) % 167.16/167.37 => ( hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_finite__UN__I,axiom, % 167.16/167.37 ! [V_B_2,T_b,V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( ! [B_a] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_less__zeroE,axiom, % 167.16/167.37 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.16/167.37 % 167.16/167.37 fof(fact_zero__less__Suc,axiom, % 167.16/167.37 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Union__def,axiom, % 167.16/167.37 ! [V_S_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ). % 167.16/167.37 % 167.16/167.37 fof(fact_zero__reorient,axiom, % 167.16/167.37 ! [V_x_2,T_a] : % 167.16/167.37 ( class_Groups_Ozero(T_a) % 167.16/167.37 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 167.16/167.37 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_bot__nat__def,axiom, % 167.16/167.37 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__0__iff,axiom, % 167.16/167.37 ! [V_a_2,V_b_2,T_a] : % 167.16/167.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 167.16/167.37 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 167.16/167.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add_Ocomm__neutral,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__0__right,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Groups_Omonoid__add(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_double__zero__sym,axiom, % 167.16/167.37 ! [V_a_2,T_a] : % 167.16/167.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.16/167.37 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 167.16/167.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__0,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__0__left,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Groups_Omonoid__add(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_divisors__zero,axiom, % 167.16/167.37 ! [V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ono__zero__divisors(T_a) % 167.16/167.37 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.37 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.37 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_no__zero__divisors,axiom, % 167.16/167.37 ! [V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Ono__zero__divisors(T_a) % 167.16/167.37 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.37 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__eq__0__iff,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,T_a] : % 167.16/167.37 ( class_Rings_Oring__no__zero__divisors(T_a) % 167.16/167.37 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.37 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.37 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => 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) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__zero__right,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Rings_Omult__zero(T_a) % 167.16/167.37 => 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) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.37 => 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) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__zero__left,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Rings_Omult__zero(T_a) % 167.16/167.37 => 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) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_right__minus__eq,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,T_a] : % 167.16/167.37 ( class_Groups_Ogroup__add(T_a) % 167.16/167.37 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.37 <=> V_a_2 = V_b_2 ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_eq__iff__diff__eq__0,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,T_a] : % 167.16/167.37 ( class_Groups_Oab__group__add(T_a) % 167.16/167.37 => ( V_a_2 = V_b_2 % 167.16/167.37 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_diff__self,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Groups_Ogroup__add(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_diff__0__right,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Groups_Ogroup__add(T_a) % 167.16/167.37 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_zero__neq__one,axiom, % 167.16/167.37 ! [T_a] : % 167.16/167.37 ( class_Rings_Ozero__neq__one(T_a) % 167.16/167.37 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_one__neq__zero,axiom, % 167.16/167.37 ! [T_a] : % 167.16/167.37 ( class_Rings_Ozero__neq__one(T_a) % 167.16/167.37 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Suc__neq__Zero,axiom, % 167.16/167.37 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Zero__neq__Suc,axiom, % 167.16/167.37 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 167.16/167.37 % 167.16/167.37 fof(fact_nat_Osimps_I3_J,axiom, % 167.16/167.37 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Suc__not__Zero,axiom, % 167.16/167.37 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.37 % 167.16/167.37 fof(fact_nat_Osimps_I2_J,axiom, % 167.16/167.37 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Zero__not__Suc,axiom, % 167.16/167.37 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 167.16/167.37 % 167.16/167.37 fof(fact_gr0I,axiom, % 167.16/167.37 ! [V_n] : % 167.16/167.37 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_gr__implies__not0,axiom, % 167.16/167.37 ! [V_n,V_m] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.16/167.37 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_less__nat__zero__code,axiom, % 167.16/167.37 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.16/167.37 % 167.16/167.37 fof(fact_neq0__conv,axiom, % 167.16/167.37 ! [V_n_2] : % 167.16/167.37 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_not__less0,axiom, % 167.16/167.37 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.16/167.37 % 167.16/167.37 fof(fact_plus__nat_Oadd__0,axiom, % 167.16/167.37 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 167.16/167.37 % 167.16/167.37 fof(fact_Nat_Oadd__0__right,axiom, % 167.16/167.37 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__is__0,axiom, % 167.16/167.37 ! [V_n_2,V_m_2] : % 167.16/167.37 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__eq__self__zero,axiom, % 167.16/167.37 ! [V_n,V_m] : % 167.16/167.37 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 167.16/167.37 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_diffs0__imp__equal,axiom, % 167.16/167.37 ! [V_n,V_m] : % 167.16/167.37 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 => V_m = V_n ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_diff__self__eq__0,axiom, % 167.16/167.37 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.37 % 167.16/167.37 fof(fact_minus__nat_Odiff__0,axiom, % 167.16/167.37 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 167.16/167.37 % 167.16/167.37 fof(fact_diff__0__eq__0,axiom, % 167.16/167.37 ! [V_n] : hAPP(hAPP(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) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__cancel2,axiom, % 167.16/167.37 ! [V_n_2,V_k_2,V_m_2] : % 167.16/167.37 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) % 167.16/167.37 <=> ( V_m_2 = V_n_2 % 167.16/167.37 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__cancel1,axiom, % 167.16/167.37 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.37 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 167.16/167.37 <=> ( V_m_2 = V_n_2 % 167.16/167.37 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__is__0,axiom, % 167.16/167.37 ! [V_n_2,V_m_2] : % 167.16/167.37 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__0__right,axiom, % 167.16/167.37 ! [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) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__0,axiom, % 167.16/167.37 ! [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) ). % 167.16/167.37 % 167.16/167.37 fof(fact_nat__mult__eq__cancel__disj,axiom, % 167.16/167.37 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.37 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 167.16/167.37 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 | V_m_2 = V_n_2 ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__0,axiom, % 167.16/167.37 ! [V_A_2,T_b,T_a] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_a) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_A_2) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_empty__fold1SetE,axiom, % 167.16/167.37 ! [V_x_2,V_f_2,T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1Set__nonempty,axiom, % 167.16/167.37 ! [V_x_2,V_A_2,V_f_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) % 167.16/167.37 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_pos__add__strict,axiom, % 167.16/167.37 ! [V_c,V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semidom(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__neg__neg,axiom, % 167.16/167.37 ! [V_b,V_a,T_a] : % 167.16/167.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__pos__pos,axiom, % 167.16/167.37 ! [V_b,V_a,T_a] : % 167.16/167.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 167.16/167.37 ! [V_a_2,T_a] : % 167.16/167.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 167.16/167.37 ! [V_a_2,T_a] : % 167.16/167.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 167.16/167.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__strict__left__mono__neg,axiom, % 167.16/167.37 ! [V_c,V_a,V_b,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__strict__right__mono__neg,axiom, % 167.16/167.37 ! [V_c,V_a,V_b,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_comm__mult__strict__left__mono,axiom, % 167.16/167.37 ! [V_c,V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__strict__left__mono,axiom, % 167.16/167.37 ! [V_c,V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__strict__right__mono,axiom, % 167.16/167.37 ! [V_c,V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__neg__neg,axiom, % 167.16/167.37 ! [V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__neg__pos,axiom, % 167.16/167.37 ! [V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__less__cancel__left__neg,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 167.16/167.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_zero__less__mult__pos2,axiom, % 167.16/167.37 ! [V_a,V_b,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(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))) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_zero__less__mult__pos,axiom, % 167.16/167.37 ! [V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(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))) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__pos__neg2,axiom, % 167.16/167.37 ! [V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__pos__neg,axiom, % 167.16/167.37 ! [V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__pos__pos,axiom, % 167.16/167.37 ! [V_b,V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__less__cancel__left__pos,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 167.16/167.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__less__cancel__left__disj,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 167.16/167.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.16/167.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 167.16/167.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__less__cancel__right__disj,axiom, % 167.16/167.37 ! [V_b_2,V_c_2,V_a_2,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))) % 167.16/167.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.16/167.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 167.16/167.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_not__square__less__zero,axiom, % 167.16/167.37 ! [V_a,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__ring(T_a) % 167.16/167.37 => ~ hBOOL(hAPP(hAPP(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))) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_less__iff__diff__less__0,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,T_a] : % 167.16/167.37 ( class_Groups_Oordered__ab__group__add(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 167.16/167.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__scale__eq__noteq,axiom, % 167.16/167.37 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 167.16/167.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 167.16/167.37 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.37 => ( ( V_a = V_b % 167.16/167.37 & V_c != V_d ) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_sum__squares__eq__zero__iff,axiom, % 167.16/167.37 ! [V_y_2,V_x_2,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.37 => ( hAPP(hAPP(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) % 167.16/167.37 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.37 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_zero__less__one,axiom, % 167.16/167.37 ! [T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semidom(T_a) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_not__one__less__zero,axiom, % 167.16/167.37 ! [T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semidom(T_a) % 167.16/167.37 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum_Oempty,axiom, % 167.16/167.37 ! [V_g_2,T_b,T_a] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_a) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__empty,axiom, % 167.16/167.37 ! [V_f_2,T_b,T_a] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_a) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__infinite,axiom, % 167.16/167.37 ! [V_f_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum_Oinfinite,axiom, % 167.16/167.37 ! [V_g_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_gr0__conv__Suc,axiom, % 167.16/167.37 ! [V_n_2] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 167.16/167.37 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_less__Suc0,axiom, % 167.16/167.37 ! [V_n_2] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) % 167.16/167.37 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_less__Suc__eq__0__disj,axiom, % 167.16/167.37 ! [V_n_2,V_m_2] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 167.16/167.37 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 | ? [B_j] : % 167.16/167.37 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 167.16/167.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__is__1,axiom, % 167.16/167.37 ! [V_n_2,V_m_2] : % 167.16/167.37 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.16/167.37 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.16/167.37 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.16/167.37 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_one__is__add,axiom, % 167.16/167.37 ! [V_n_2,V_m_2] : % 167.16/167.37 ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) % 167.16/167.37 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.16/167.37 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.16/167.37 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__gr__0,axiom, % 167.16/167.37 ! [V_n_2,V_m_2] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))) % 167.16/167.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 167.16/167.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card_Oempty,axiom, % 167.16/167.37 ! [T_a] : hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card__infinite,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__eq__1__iff,axiom, % 167.16/167.37 ! [V_n_2,V_m_2] : % 167.16/167.37 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.16/167.37 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.16/167.37 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_diff__less,axiom, % 167.16/167.37 ! [V_m,V_n] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_zero__less__diff,axiom, % 167.16/167.37 ! [V_m_2,V_n_2] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) % 167.16/167.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__less__mono2,axiom, % 167.16/167.37 ! [V_k,V_j,V_i] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__less__mono1,axiom, % 167.16/167.37 ! [V_k,V_j,V_i] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 167.16/167.37 => hBOOL(hAPP(hAPP(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))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__less__cancel2,axiom, % 167.16/167.37 ! [V_n_2,V_k_2,V_m_2] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 167.16/167.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.16/167.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__less__cancel1,axiom, % 167.16/167.37 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 167.16/167.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.16/167.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_nat__0__less__mult__iff,axiom, % 167.16/167.37 ! [V_n_2,V_m_2] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(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_m_2),V_n_2))) % 167.16/167.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 167.16/167.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_nat__mult__less__cancel1,axiom, % 167.16/167.37 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 167.16/167.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_nat__mult__eq__cancel1,axiom, % 167.16/167.37 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.16/167.37 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 167.16/167.37 <=> V_m_2 = V_n_2 ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_diff__add__0,axiom, % 167.16/167.37 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.37 % 167.16/167.37 fof(fact_One__nat__def,axiom, % 167.16/167.37 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__eq__self__implies__10,axiom, % 167.16/167.37 ! [V_n,V_m] : % 167.16/167.37 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 167.16/167.37 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 167.16/167.37 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__eq__0__iff,axiom, % 167.16/167.37 ! [V_f_2,V_F_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 167.16/167.37 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 <=> ! [B_x] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 167.16/167.37 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_not__sum__squares__lt__zero,axiom, % 167.16/167.37 ! [V_y,V_x,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__ring(T_a) % 167.16/167.37 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(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))) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_sum__squares__gt__zero__iff,axiom, % 167.16/167.37 ! [V_y_2,V_x_2,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(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)))) % 167.16/167.37 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.37 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_zero__less__two,axiom, % 167.16/167.37 ! [T_a] : % 167.16/167.37 ( class_Rings_Olinordered__semidom(T_a) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card__eq__0__iff,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card__ge__0__finite,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 167.16/167.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Suc__pred,axiom, % 167.16/167.37 ! [V_n] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.16/167.37 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_diff__Suc__less,axiom, % 167.16/167.37 ! [V_i,V_n] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_n__less__m__mult__n,axiom, % 167.16/167.37 ! [V_m,V_n] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_n__less__n__mult__m,axiom, % 167.16/167.37 ! [V_m,V_n] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_one__less__mult,axiom, % 167.16/167.37 ! [V_m,V_n] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_nat__diff__split,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,V_P_2] : % 167.16/167.37 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 167.16/167.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 167.16/167.37 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 167.16/167.37 & ! [B_d] : % 167.16/167.37 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 167.16/167.37 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_nat__diff__split__asm,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,V_P_2] : % 167.16/167.37 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 167.16/167.37 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 167.16/167.37 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 167.16/167.37 | ? [B_d] : % 167.16/167.37 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 167.16/167.37 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__eq__Suc0__iff,axiom, % 167.16/167.37 ! [V_f_2,V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.16/167.37 <=> ? [B_x] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.37 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.16/167.37 & ! [B_xa] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 167.16/167.37 => ( B_x != B_xa % 167.16/167.37 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__eq__1__iff,axiom, % 167.16/167.37 ! [V_f_2,V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 167.16/167.37 <=> ? [B_x] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.37 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 167.16/167.37 & ! [B_xa] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 167.16/167.37 => ( B_x != B_xa % 167.16/167.37 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__delta_H,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.16/167.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 167.16/167.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__delta,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.16/167.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 167.16/167.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1Set__sing,axiom, % 167.16/167.37 ! [V_b_2,V_a_2,V_f_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_b_2)) % 167.16/167.37 <=> V_a_2 = V_b_2 ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Body__triple__valid__0,axiom, % 167.16/167.37 ! [V_Q_2,V_pn_2,V_P_2,T_a] : c_Hoare__Mirabelle_Otriple__valid(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card__gt__0__iff,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 167.16/167.37 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_finite__UNIV__card__ge__0,axiom, % 167.16/167.37 ! [T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 167.16/167.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum_OF__eq,axiom, % 167.16/167.37 ! [V_g_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) % 167.16/167.37 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum_Oeq__fold,axiom, % 167.16/167.37 ! [V_g_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Suc__diff__1,axiom, % 167.16/167.37 ! [V_n] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.16/167.37 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_Suc__pred_H,axiom, % 167.16/167.37 ! [V_n] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.16/167.37 => V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_add__eq__if,axiom, % 167.16/167.37 ! [V_n,V_m] : % 167.16/167.37 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 167.16/167.37 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_mult__eq__if,axiom, % 167.16/167.37 ! [V_n,V_m] : % 167.16/167.37 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.16/167.37 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__restrict__set,axiom, % 167.16/167.37 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card_Oeq__fold__g,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card__def,axiom, % 167.16/167.37 ! [V_A_2,T_a] : % 167.16/167.37 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) % 167.16/167.37 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_fold1__def,axiom, % 167.16/167.37 ! [V_A_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2)) ). % 167.16/167.37 % 167.16/167.37 fof(fact_triple_Osize_I1_J,axiom, % 167.16/167.37 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_a] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_a,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.37 % 167.16/167.37 fof(fact_even__less__0__iff,axiom, % 167.16/167.37 ! [V_a_2,T_a] : % 167.16/167.37 ( class_Rings_Olinordered__idom(T_a) % 167.16/167.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_triple_Osize_I2_J,axiom, % 167.16/167.37 ! [V_fun2_2,V_com_2,V_fun1_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.37 % 167.16/167.37 fof(fact_card_Ounion__inter__neutral,axiom, % 167.16/167.37 ! [V_B_2,V_A_2,T_a] : % 167.16/167.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.37 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.16/167.37 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum_Ounion__inter__neutral,axiom, % 167.16/167.37 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.37 => ( ! [B_x] : % 167.16/167.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.37 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 167.16/167.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 167.16/167.37 % 167.16/167.37 fof(fact_setsum__Un__zero,axiom, % 167.16/167.37 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 167.16/167.37 ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.16/167.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 167.16/167.38 => ( ! [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 167.16/167.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 167.16/167.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_card__Suc__eq,axiom, % 167.16/167.38 ! [V_k_2,V_A_2,T_a] : % 167.16/167.38 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 167.16/167.38 <=> ? [B_b,B_B] : % 167.16/167.38 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) % 167.16/167.38 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B)) % 167.16/167.38 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2 % 167.16/167.38 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.38 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_finite__Union,axiom, % 167.16/167.38 ! [V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) % 167.16/167.38 => ( ! [B_M] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) ) % 167.16/167.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_double__eq__0__iff,axiom, % 167.16/167.38 ! [V_a_2,T_a] : % 167.16/167.38 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.16/167.38 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Ints__odd__less__0,axiom, % 167.16/167.38 ! [V_a_2,T_a] : % 167.16/167.38 ( class_Rings_Olinordered__idom(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_com_Osize_I4_J,axiom, % 167.16/167.38 ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_card__Plus__conv__if,axiom, % 167.16/167.38 ! [V_B_2,T_b,V_A_2,T_a] : % 167.16/167.38 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.38 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 167.16/167.38 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) % 167.16/167.38 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.38 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 167.16/167.38 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_com_Osize_I6_J,axiom, % 167.16/167.38 ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_com_Osize_I12_J,axiom, % 167.16/167.38 ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_com_Osize_I14_J,axiom, % 167.16/167.38 ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_diff__Suc,axiom, % 167.16/167.38 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_insert__fold1SetE,axiom, % 167.16/167.38 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2)),V_x_2)) % 167.16/167.38 => ~ ! [B_a,B_A] : % 167.16/167.38 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 167.16/167.38 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_nat__case__0,axiom, % 167.16/167.38 ! [V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 167.16/167.38 % 167.16/167.38 fof(fact_nat__case__Suc,axiom, % 167.16/167.38 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Ints__0,axiom, % 167.16/167.38 ! [T_a] : % 167.16/167.38 ( class_Rings_Oring__1(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Ints__add,axiom, % 167.16/167.38 ! [V_b_2,V_a_2,T_a] : % 167.16/167.38 ( class_Rings_Oring__1(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Ints__mult,axiom, % 167.16/167.38 ! [V_b_2,V_a_2,T_a] : % 167.16/167.38 ( class_Rings_Oring__1(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Ints__diff,axiom, % 167.16/167.38 ! [V_b_2,V_a_2,T_a] : % 167.16/167.38 ( class_Rings_Oring__1(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Ints__1,axiom, % 167.16/167.38 ! [T_a] : % 167.16/167.38 ( class_Rings_Oring__1(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_com_Osize_I15_J,axiom, % 167.16/167.38 ! [V_pname] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.38 % 167.16/167.38 fof(fact_com_Osize_I7_J,axiom, % 167.16/167.38 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.38 % 167.16/167.38 fof(fact_com_Osize_I9_J,axiom, % 167.16/167.38 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.38 % 167.16/167.38 fof(fact_com_Osize_I1_J,axiom, % 167.16/167.38 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Ints__double__eq__0__iff,axiom, % 167.16/167.38 ! [V_a_2,T_a] : % 167.16/167.38 ( class_Int_Oring__char__0(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.16/167.38 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_finite__Plus__iff,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_b,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 167.16/167.38 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.38 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_finite__Plus,axiom, % 167.16/167.38 ! [V_B_2,T_b,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_finite__PlusD_I1_J,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_b,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 167.16/167.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_finite__PlusD_I2_J,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_b,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 167.16/167.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_card__Plus,axiom, % 167.16/167.38 ! [V_B_2,T_b,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 167.16/167.38 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Ints__odd__nonzero,axiom, % 167.16/167.38 ! [V_a_2,T_a] : % 167.16/167.38 ( class_Int_Oring__char__0(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.16/167.38 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_UNIV__Plus__UNIV,axiom, % 167.16/167.38 ! [T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Plus__eq__empty__conv,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_b,T_a] : % 167.16/167.38 ( c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) % 167.16/167.38 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.38 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_fold1Set_Oequations,axiom, % 167.16/167.38 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2)),V_a3_2)) % 167.16/167.38 <=> ? [B_a,B_A] : % 167.16/167.38 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 167.16/167.38 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2)) % 167.16/167.38 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_arith__series__nat,axiom, % 167.16/167.38 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_psubset__insert__iff,axiom, % 167.16/167.38 ! [V_B_2,V_x_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 167.16/167.38 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 167.16/167.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.16/167.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) % 167.16/167.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setsum__SucD,axiom, % 167.16/167.38 ! [V_n_2,V_A_2,V_f_2,T_a] : % 167.16/167.38 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2) % 167.16/167.38 => ? [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setprod_Oremove,axiom, % 167.16/167.38 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 167.16/167.38 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_card__Diff1__le,axiom, % 167.16/167.38 ! [V_x_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__refl,axiom, % 167.16/167.38 ! [V_x,T_a] : % 167.16/167.38 ( class_Orderings_Opreorder(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_equalityI,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.38 => V_A_2 = V_B_2 ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_finite__lessThan,axiom, % 167.16/167.38 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_subsetD,axiom, % 167.16/167.38 ! [V_c_2,V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_empty__subsetI,axiom, % 167.16/167.38 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le0,axiom, % 167.16/167.38 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_card__lessThan,axiom, % 167.16/167.38 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2 ). % 167.16/167.38 % 167.16/167.38 fof(fact_Union__mono,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_SUP__subset,axiom, % 167.16/167.38 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_B_2),V_f_2))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 167.16/167.38 ! [V_N_2] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 167.16/167.38 <=> ? [B_m] : % 167.16/167.38 ! [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_UN__lessThan__UNIV,axiom, % 167.16/167.38 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Inter__anti__mono,axiom, % 167.16/167.38 ! [V_A_2,V_B_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_INF__subset,axiom, % 167.16/167.38 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__antisym,axiom, % 167.16/167.38 ! [V_n,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.16/167.38 => V_m = V_n ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__trans,axiom, % 167.16/167.38 ! [V_k,V_j,V_i] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_eq__imp__le,axiom, % 167.16/167.38 ! [V_n,V_m] : % 167.16/167.38 ( V_m = V_n % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_nat__le__linear,axiom, % 167.16/167.38 ! [V_n,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.16/167.38 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__refl,axiom, % 167.16/167.38 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_lessThan__eq__iff,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) % 167.16/167.38 <=> V_x_2 = V_y_2 ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_lessThan__subset__iff,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_equalityE,axiom, % 167.16/167.38 ! [T_a,V_B_2,V_A_2] : % 167.16/167.38 ( V_A_2 = V_B_2 % 167.16/167.38 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_subset__trans,axiom, % 167.16/167.38 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_predicate1D,axiom, % 167.16/167.38 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 167.16/167.38 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.16/167.38 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_equalityD2,axiom, % 167.16/167.38 ! [T_a,V_B_2,V_A_2] : % 167.16/167.38 ( V_A_2 = V_B_2 % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_equalityD1,axiom, % 167.16/167.38 ! [T_a,V_B_2,V_A_2] : % 167.16/167.38 ( V_A_2 = V_B_2 % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_rev__predicate1D,axiom, % 167.16/167.38 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 167.16/167.38 ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 167.16/167.38 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_set__eq__subset,axiom, % 167.16/167.38 ! [T_a,V_B_2,V_A_2] : % 167.16/167.38 ( V_A_2 = V_B_2 % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_subset__refl,axiom, % 167.16/167.38 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_linorder__le__cases,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__funE,axiom, % 167.16/167.38 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 167.16/167.38 ( class_Orderings_Oord(T_b) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_xt1_I6_J,axiom, % 167.16/167.38 ! [V_z,V_x,V_y,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_xt1_I5_J,axiom, % 167.16/167.38 ! [V_x,V_y,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.16/167.38 => V_x = V_y ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__trans,axiom, % 167.16/167.38 ! [V_z,V_y,V_x,T_a] : % 167.16/167.38 ( class_Orderings_Opreorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__antisym,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.16/167.38 => V_x = V_y ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_xt1_I4_J,axiom, % 167.16/167.38 ! [V_c,V_a,V_b,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.16/167.38 => ( V_b = V_c % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_ord__le__eq__trans,axiom, % 167.16/167.38 ! [V_c,V_b,V_a,T_a] : % 167.16/167.38 ( class_Orderings_Oord(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.38 => ( V_b = V_c % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_xt1_I3_J,axiom, % 167.16/167.38 ! [V_c,V_b,V_a,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( V_a = V_b % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_ord__eq__le__trans,axiom, % 167.16/167.38 ! [V_c,V_b,V_a,T_a] : % 167.16/167.38 ( class_Orderings_Oord(T_a) % 167.16/167.38 => ( V_a = V_b % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__antisym__conv,axiom, % 167.16/167.38 ! [V_x_2,V_y_2,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.16/167.38 <=> V_x_2 = V_y_2 ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__funD,axiom, % 167.16/167.38 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 167.16/167.38 ( class_Orderings_Oord(T_b) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__eq__refl,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Orderings_Opreorder(T_a) % 167.16/167.38 => ( V_x = V_y % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__eq__iff,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( V_x_2 = V_y_2 % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.16/167.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_linorder__linear,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.16/167.38 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__fun__def,axiom, % 167.16/167.38 ! [V_g_2,V_f_2,T_a,T_b] : % 167.16/167.38 ( class_Orderings_Oord(T_b) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.16/167.38 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_lessThan__Suc,axiom, % 167.16/167.38 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_lessThan__0,axiom, % 167.16/167.38 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 167.16/167.38 ! [V_n_2,V_m_2] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 167.16/167.38 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_card__mono,axiom, % 167.16/167.38 ! [V_A_2,V_B_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_card__seteq,axiom, % 167.16/167.38 ! [V_A_2,V_B_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 167.16/167.38 => V_A_2 = V_B_2 ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_xt1_I8_J,axiom, % 167.16/167.38 ! [V_z,V_x,V_y,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__le__less__trans,axiom, % 167.16/167.38 ! [V_z,V_y,V_x,T_a] : % 167.16/167.38 ( class_Orderings_Opreorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_xt1_I7_J,axiom, % 167.16/167.38 ! [V_z,V_x,V_y,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__less__le__trans,axiom, % 167.16/167.38 ! [V_z,V_y,V_x,T_a] : % 167.16/167.38 ( class_Orderings_Opreorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_xt1_I11_J,axiom, % 167.16/167.38 ! [V_a,V_b,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.16/167.38 => ( V_a != V_b % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__le__neq__trans,axiom, % 167.16/167.38 ! [V_b,V_a,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.38 => ( V_a != V_b % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__le__imp__less__or__eq,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.38 | V_x = V_y ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_linorder__antisym__conv2,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.16/167.38 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.16/167.38 <=> V_x_2 = V_y_2 ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__less__imp__le,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Orderings_Opreorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_leD,axiom, % 167.16/167.38 ! [V_x,V_y,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.16/167.38 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_xt1_I12_J,axiom, % 167.16/167.38 ! [V_b,V_a,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( V_a != V_b % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__neq__le__trans,axiom, % 167.16/167.38 ! [V_b,V_a,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( V_a != V_b % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_linorder__antisym__conv1,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.16/167.38 <=> V_x_2 = V_y_2 ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_not__leE,axiom, % 167.16/167.38 ! [V_x,V_y,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_leI,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__le__less,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.16/167.38 | V_x_2 = V_y_2 ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_less__le__not__le,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Orderings_Opreorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.16/167.38 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_order__less__le,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Orderings_Oorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.16/167.38 & V_x_2 != V_y_2 ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_linorder__le__less__linear,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.16/167.38 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_linorder__not__le,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_linorder__not__less,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_set__mp,axiom, % 167.16/167.38 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_set__rev__mp,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,V_x_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_in__mono,axiom, % 167.16/167.38 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__le__cancel__right,axiom, % 167.16/167.38 ! [V_b_2,V_c_2,V_a_2,T_a] : % 167.16/167.38 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__le__cancel__left,axiom, % 167.16/167.38 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.16/167.38 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__right__mono,axiom, % 167.16/167.38 ! [V_c,V_b,V_a,T_a] : % 167.16/167.38 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__left__mono,axiom, % 167.16/167.38 ! [V_c,V_b,V_a,T_a] : % 167.16/167.38 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__mono,axiom, % 167.16/167.38 ! [V_d,V_c,V_b,V_a,T_a] : % 167.16/167.38 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__le__imp__le__right,axiom, % 167.16/167.38 ! [V_b,V_c,V_a,T_a] : % 167.16/167.38 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__le__imp__le__left,axiom, % 167.16/167.38 ! [V_b,V_a,V_c,T_a] : % 167.16/167.38 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_bot__least,axiom, % 167.16/167.38 ! [V_x,T_a] : % 167.16/167.38 ( class_Orderings_Obot(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_diff__eq__diff__less__eq,axiom, % 167.16/167.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.16/167.38 ( class_Groups_Oordered__ab__group__add(T_a) % 167.16/167.38 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_subset__empty,axiom, % 167.16/167.38 ! [V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 167.16/167.38 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__supE,axiom, % 167.16/167.38 ! [V_x,V_b,V_a,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) % 167.16/167.38 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.16/167.38 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_sup__mono,axiom, % 167.16/167.38 ! [V_d,V_b,V_c,V_a,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_sup__least,axiom, % 167.16/167.38 ! [V_z,V_x,V_y,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__supI,axiom, % 167.16/167.38 ! [V_b,V_x,V_a,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_sup__absorb1,axiom, % 167.16/167.38 ! [V_x,V_y,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.16/167.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_sup__absorb2,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.16/167.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__supI2,axiom, % 167.16/167.38 ! [V_a,V_b,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__supI1,axiom, % 167.16/167.38 ! [V_b,V_a,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__sup__iff,axiom, % 167.16/167.38 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2)),V_z_2)) % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 167.16/167.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__iff__sup,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.16/167.38 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_sup__ge2,axiom, % 167.16/167.38 ! [V_x,V_y,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_inf__sup__ord_I4_J,axiom, % 167.16/167.38 ! [V_x,V_y,T_a] : % 167.16/167.38 ( class_Lattices_Olattice(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_sup__ge1,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_inf__sup__ord_I3_J,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Olattice(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_finite__subset,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_rev__finite__subset,axiom, % 167.16/167.38 ! [V_A_2,V_B_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__infE,axiom, % 167.16/167.38 ! [V_b,V_a,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) % 167.16/167.38 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.16/167.38 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_inf__mono,axiom, % 167.16/167.38 ! [V_d,V_b,V_c,V_a,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_inf__greatest,axiom, % 167.16/167.38 ! [V_z,V_y,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__infI,axiom, % 167.16/167.38 ! [V_b,V_a,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_inf__absorb2,axiom, % 167.16/167.38 ! [V_x,V_y,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.16/167.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_inf__absorb1,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.16/167.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__infI2,axiom, % 167.16/167.38 ! [V_a,V_x,V_b,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__infI1,axiom, % 167.16/167.38 ! [V_b,V_x,V_a,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__inf__iff,axiom, % 167.16/167.38 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2))) % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.16/167.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__iff__inf,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.16/167.38 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_inf__le2,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_inf__sup__ord_I2_J,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Olattice(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_inf__le1,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_inf__sup__ord_I1_J,axiom, % 167.16/167.38 ! [V_y,V_x,T_a] : % 167.16/167.38 ( class_Lattices_Olattice(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__0__eq,axiom, % 167.16/167.38 ! [V_n_2] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 167.16/167.38 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 167.16/167.38 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_top__greatest,axiom, % 167.16/167.38 ! [V_x,T_a] : % 167.16/167.38 ( class_Orderings_Otop(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_insert__mono,axiom, % 167.16/167.38 ! [V_a_2,V_D_2,V_C_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_D_2))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_subset__insertI2,axiom, % 167.16/167.38 ! [V_b_2,V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_subset__insertI,axiom, % 167.16/167.38 ! [V_a_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Suc__n__not__le__n,axiom, % 167.16/167.38 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_not__less__eq__eq,axiom, % 167.16/167.38 ! [V_n_2,V_m_2] : % 167.16/167.38 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__Suc__eq,axiom, % 167.16/167.38 ! [V_n_2,V_m_2] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.38 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Suc__le__mono,axiom, % 167.16/167.38 ! [V_m_2,V_n_2] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__SucI,axiom, % 167.16/167.38 ! [V_n,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__SucE,axiom, % 167.16/167.38 ! [V_n,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 167.16/167.38 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.16/167.38 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Suc__leD,axiom, % 167.16/167.38 ! [V_n,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_termination__basic__simps_I5_J,axiom, % 167.16/167.38 ! [V_y,V_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_nat__less__le,axiom, % 167.16/167.38 ! [V_n_2,V_m_2] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.38 & V_m_2 != V_n_2 ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__eq__less__or__eq,axiom, % 167.16/167.38 ! [V_n_2,V_m_2] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.38 | V_m_2 = V_n_2 ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_less__imp__le__nat,axiom, % 167.16/167.38 ! [V_n,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__neq__implies__less,axiom, % 167.16/167.38 ! [V_n,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.16/167.38 => ( V_m != V_n % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_less__or__eq__imp__le,axiom, % 167.16/167.38 ! [V_n,V_m] : % 167.16/167.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.16/167.38 | V_m = V_n ) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_image__mono,axiom, % 167.16/167.38 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_subset__image__iff,axiom, % 167.16/167.38 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 167.16/167.38 <=> ? [B_AA] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) % 167.16/167.38 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_subset__UNIV,axiom, % 167.16/167.38 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_termination__basic__simps_I4_J,axiom, % 167.16/167.38 ! [V_y,V_z,V_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_termination__basic__simps_I3_J,axiom, % 167.16/167.38 ! [V_z,V_y,V_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__leE,axiom, % 167.16/167.38 ! [V_n,V_k,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 167.16/167.38 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.16/167.38 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__leD1,axiom, % 167.16/167.38 ! [V_n,V_k,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__leD2,axiom, % 167.16/167.38 ! [V_n,V_k,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__le__mono,axiom, % 167.16/167.38 ! [V_l,V_k,V_j,V_i] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__le__mono1,axiom, % 167.16/167.38 ! [V_k,V_j,V_i] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_trans__le__add2,axiom, % 167.16/167.38 ! [V_m,V_j,V_i] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_trans__le__add1,axiom, % 167.16/167.38 ! [V_m,V_j,V_i] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_nat__add__left__cancel__le,axiom, % 167.16/167.38 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__iff__add,axiom, % 167.16/167.38 ! [V_n_2,V_m_2] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.38 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__add1,axiom, % 167.16/167.38 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__add2,axiom, % 167.16/167.38 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Un__mono,axiom, % 167.16/167.38 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Un__least,axiom, % 167.16/167.38 ! [V_B_2,V_C_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Un__absorb2,axiom, % 167.16/167.38 ! [V_A_2,V_B_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Un__absorb1,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_subset__Un__eq,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Un__upper2,axiom, % 167.16/167.38 ! [V_A_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Un__upper1,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Int__mono,axiom, % 167.16/167.38 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Int__greatest,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,V_C_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Int__absorb1,axiom, % 167.16/167.38 ! [V_A_2,V_B_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Int__absorb2,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Int__lower2,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Int__lower1,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_double__diff,axiom, % 167.16/167.38 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.16/167.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Diff__mono,axiom, % 167.16/167.38 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Diff__subset,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_diff__le__self,axiom, % 167.16/167.38 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ). % 167.16/167.38 % 167.16/167.38 fof(fact_diff__le__mono2,axiom, % 167.16/167.38 ! [V_l,V_n,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_diff__le__mono,axiom, % 167.16/167.38 ! [V_l,V_n,V_m] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_diff__diff__cancel,axiom, % 167.16/167.38 ! [V_n,V_i] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 167.16/167.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_eq__diff__iff,axiom, % 167.16/167.38 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 167.16/167.38 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2) % 167.16/167.38 <=> V_m_2 = V_n_2 ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Nat_Odiff__diff__eq,axiom, % 167.16/167.38 ! [V_n,V_m,V_k] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 167.16/167.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__diff__iff,axiom, % 167.16/167.38 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__square,axiom, % 167.16/167.38 ! [V_m] : hBOOL(hAPP(hAPP(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))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__cube,axiom, % 167.16/167.38 ! [V_m] : hBOOL(hAPP(hAPP(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)))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_mult__le__mono1,axiom, % 167.16/167.38 ! [V_k,V_j,V_i] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.16/167.38 => hBOOL(hAPP(hAPP(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))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_mult__le__mono2,axiom, % 167.16/167.38 ! [V_k,V_j,V_i] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.16/167.38 => hBOOL(hAPP(hAPP(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))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_mult__le__mono,axiom, % 167.16/167.38 ! [V_l,V_k,V_j,V_i] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 167.16/167.38 => hBOOL(hAPP(hAPP(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))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_Sup__le__iff,axiom, % 167.16/167.38 ! [V_b_2,V_A_2,T_a] : % 167.16/167.38 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)),V_b_2)) % 167.16/167.38 <=> ! [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_less__fun__def,axiom, % 167.16/167.38 ! [V_g_2,V_f_2,T_a,T_b] : % 167.16/167.38 ( class_Orderings_Oord(T_b) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.16/167.38 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_evaln__nonstrict,axiom, % 167.16/167.38 ! [V_m,V_t,V_n,V_s,V_c] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.16/167.38 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setprod__timesf,axiom, % 167.16/167.38 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 167.16/167.38 ( class_Groups_Ocomm__monoid__mult(T_a) % 167.16/167.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),V_A_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_thin,axiom, % 167.16/167.38 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 167.16/167.38 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) % 167.16/167.38 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_weaken,axiom, % 167.16/167.38 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_a] : % 167.16/167.38 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_H_2) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_ts_H_2)) % 167.16/167.38 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_asm,axiom, % 167.16/167.38 ! [V_Ga_2,V_ts_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_Ga_2)) % 167.16/167.38 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__Inf__iff,axiom, % 167.16/167.38 ! [V_A_2,V_b_2,T_a] : % 167.16/167.38 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2))) % 167.16/167.38 <=> ! [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setprod__1,axiom, % 167.16/167.38 ! [V_A_2,T_b,T_a] : % 167.16/167.38 ( class_Groups_Ocomm__monoid__mult(T_a) % 167.16/167.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Oone__class_Oone(T_a))),V_A_2) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_subset__psubset__trans,axiom, % 167.16/167.38 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_psubset__subset__trans,axiom, % 167.16/167.38 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_psubset__imp__subset,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_subset__iff__psubset__eq,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 | V_A_2 = V_B_2 ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_psubset__eq,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.38 & V_A_2 != V_B_2 ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 167.16/167.38 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) ). % 167.16/167.38 % 167.16/167.38 fof(fact_pred__subset__eq,axiom, % 167.16/167.38 ! [V_S_2,V_R_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_SUP__le__iff,axiom, % 167.16/167.38 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] : % 167.16/167.38 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_M_2)),V_u_2)) % 167.16/167.38 <=> ! [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_UN__subset__iff,axiom, % 167.16/167.38 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) % 167.16/167.38 <=> ! [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_le__INF__iff,axiom, % 167.16/167.38 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] : % 167.16/167.38 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_M_2))) % 167.16/167.38 <=> ! [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_INT__subset__iff,axiom, % 167.16/167.38 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))) % 167.16/167.38 <=> ! [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_lessThan__iff,axiom, % 167.16/167.38 ! [V_k_2,V_i_2,T_a] : % 167.16/167.38 ( class_Orderings_Oord(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setsum__lessThan__Suc,axiom, % 167.16/167.38 ! [V_n_2,V_f_2,T_a] : % 167.16/167.38 ( class_Groups_Ocomm__monoid__add(T_a) % 167.16/167.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setprod__zero__iff,axiom, % 167.16/167.38 ! [V_f_2,V_A_2,T_a,T_b] : % 167.16/167.38 ( ( class_Rings_Ocomm__semiring__1(T_b) % 167.16/167.38 & class_Rings_Ono__zero__divisors(T_b) ) % 167.16/167.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.38 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) % 167.16/167.38 <=> ? [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.38 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setprod__zero,axiom, % 167.16/167.38 ! [V_f_2,V_A_2,T_a,T_b] : % 167.16/167.38 ( class_Rings_Ocomm__semiring__1(T_b) % 167.16/167.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.38 => ( ? [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.38 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 167.16/167.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setprod_Oempty,axiom, % 167.16/167.38 ! [V_g_2,T_b,T_a] : % 167.16/167.38 ( class_Groups_Ocomm__monoid__mult(T_a) % 167.16/167.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setprod__empty,axiom, % 167.16/167.38 ! [V_f_2,T_b,T_a] : % 167.16/167.38 ( class_Groups_Ocomm__monoid__mult(T_a) % 167.16/167.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setprod__infinite,axiom, % 167.16/167.38 ! [V_f_2,V_A_2,T_a,T_b] : % 167.16/167.38 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.38 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setprod_Oinfinite,axiom, % 167.16/167.38 ! [V_g_2,V_A_2,T_a,T_b] : % 167.16/167.38 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.38 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_setprod__eq__1__iff,axiom, % 167.16/167.38 ! [V_f_2,V_F_2,T_a] : % 167.16/167.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 167.16/167.38 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 167.16/167.38 <=> ! [B_x] : % 167.16/167.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 167.16/167.38 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_lessThan__strict__subset__iff,axiom, % 167.16/167.38 ! [V_n_2,V_m_2,T_a] : % 167.16/167.38 ( class_Orderings_Olinorder(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_n_2))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__nonpos__nonpos,axiom, % 167.16/167.38 ! [V_b,V_a,T_a] : % 167.16/167.38 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__increasing2,axiom, % 167.16/167.38 ! [V_a,V_b,V_c,T_a] : % 167.16/167.38 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__increasing,axiom, % 167.16/167.38 ! [V_c,V_b,V_a,T_a] : % 167.16/167.38 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__nonneg__eq__0__iff,axiom, % 167.16/167.38 ! [V_y_2,V_x_2,T_a] : % 167.16/167.38 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 167.16/167.38 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.38 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.38 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_add__nonneg__nonneg,axiom, % 167.16/167.38 ! [V_b,V_a,T_a] : % 167.16/167.38 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.16/167.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 167.16/167.38 ! [V_a_2,T_a] : % 167.16/167.38 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 167.16/167.38 ! [V_a_2,T_a] : % 167.16/167.38 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 167.16/167.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_zero__le__square,axiom, % 167.16/167.38 ! [V_a,T_a] : % 167.16/167.38 ( class_Rings_Olinordered__ring(T_a) % 167.16/167.38 => hBOOL(hAPP(hAPP(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))) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_zero__le__mult__iff,axiom, % 167.16/167.38 ! [V_b_2,V_a_2,T_a] : % 167.16/167.38 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(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_2),V_b_2))) % 167.16/167.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 167.16/167.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 167.16/167.38 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 167.16/167.38 % 167.16/167.38 fof(fact_mult__le__0__iff,axiom, % 167.16/167.38 ! [V_b_2,V_a_2,T_a] : % 167.16/167.38 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 167.16/167.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 167.16/167.38 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 167.16/167.38 % 167.16/167.39 fof(fact_mult__nonneg__nonneg,axiom, % 167.16/167.39 ! [V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__cancel__semiring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__nonneg__nonpos,axiom, % 167.16/167.39 ! [V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__cancel__semiring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__nonneg__nonpos2,axiom, % 167.16/167.39 ! [V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__cancel__semiring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__nonpos__nonneg,axiom, % 167.16/167.39 ! [V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__cancel__semiring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__nonpos__nonpos,axiom, % 167.16/167.39 ! [V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__ring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__right__mono,axiom, % 167.16/167.39 ! [V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__semiring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__left__mono,axiom, % 167.16/167.39 ! [V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__semiring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_comm__mult__left__mono,axiom, % 167.16/167.39 ! [V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__comm__semiring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__right__mono__neg,axiom, % 167.16/167.39 ! [V_c,V_a,V_b,T_a] : % 167.16/167.39 ( class_Rings_Oordered__ring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__left__mono__neg,axiom, % 167.16/167.39 ! [V_c,V_a,V_b,T_a] : % 167.16/167.39 ( class_Rings_Oordered__ring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__mono_H,axiom, % 167.16/167.39 ! [V_d,V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__semiring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__mono,axiom, % 167.16/167.39 ! [V_d,V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__semiring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_split__mult__pos__le,axiom, % 167.16/167.39 ! [V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__ring(T_a) % 167.16/167.39 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 167.16/167.39 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_split__mult__neg__le,axiom, % 167.16/167.39 ! [V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Oordered__cancel__semiring(T_a) % 167.16/167.39 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 167.16/167.39 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_add__less__le__mono,axiom, % 167.16/167.39 ! [V_d,V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_add__le__less__mono,axiom, % 167.16/167.39 ! [V_d,V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__iff__diff__le__0,axiom, % 167.16/167.39 ! [V_b_2,V_a_2,T_a] : % 167.16/167.39 ( class_Groups_Oordered__ab__group__add(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_zero__le__one,axiom, % 167.16/167.39 ! [T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semidom(T_a) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_not__one__le__zero,axiom, % 167.16/167.39 ! [T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semidom(T_a) % 167.16/167.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_subset__insert,axiom, % 167.16/167.39 ! [V_B_2,V_A_2,V_x_2,T_a] : % 167.16/167.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_insert__subset,axiom, % 167.16/167.39 ! [V_B_2,V_A_2,V_x_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2)) % 167.16/167.39 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.16/167.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod_Odistrib,axiom, % 167.16/167.39 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_h_2),V_A_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_distrib__sup__le,axiom, % 167.16/167.39 ! [V_z,V_y,V_x,T_a] : % 167.16/167.39 ( class_Lattices_Olattice(T_a) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_distrib__inf__le,axiom, % 167.16/167.39 ! [V_z,V_y,V_x,T_a] : % 167.16/167.39 ( class_Lattices_Olattice(T_a) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_subset__singletonD,axiom, % 167.16/167.39 ! [V_x_2,V_A_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 167.16/167.39 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.39 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_finite__surj,axiom, % 167.16/167.39 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.16/167.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Suc__le__lessD,axiom, % 167.16/167.39 ! [V_n,V_m] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__less__Suc__eq,axiom, % 167.16/167.39 ! [V_n_2,V_m_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 167.16/167.39 <=> V_n_2 = V_m_2 ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Suc__leI,axiom, % 167.16/167.39 ! [V_n,V_m] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__imp__less__Suc,axiom, % 167.16/167.39 ! [V_n,V_m] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Suc__le__eq,axiom, % 167.16/167.39 ! [V_n_2,V_m_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_less__Suc__eq__le,axiom, % 167.16/167.39 ! [V_n_2,V_m_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_less__eq__Suc__le,axiom, % 167.16/167.39 ! [V_m_2,V_n_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_image__Int__subset,axiom, % 167.16/167.39 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)))) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Sup__upper,axiom, % 167.16/167.39 ! [V_A_2,V_x_2,T_a] : % 167.16/167.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_diff__is__0__eq,axiom, % 167.16/167.39 ! [V_n_2,V_m_2] : % 167.16/167.39 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_diff__is__0__eq_H,axiom, % 167.16/167.39 ! [V_n,V_m] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Un__Int__assoc__eq,axiom, % 167.16/167.39 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.16/167.39 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Suc__diff__le,axiom, % 167.16/167.39 ! [V_m,V_n] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Suc__mult__le__cancel1,axiom, % 167.16/167.39 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_diff__less__mono,axiom, % 167.16/167.39 ! [V_c,V_b,V_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_less__diff__iff,axiom, % 167.16/167.39 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_image__diff__subset,axiom, % 167.16/167.39 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 167.16/167.39 % 167.16/167.39 fof(fact_diff__diff__right,axiom, % 167.16/167.39 ! [V_i,V_j,V_k] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__diff__conv,axiom, % 167.16/167.39 ! [V_i_2,V_k_2,V_j_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2)) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__add__diff,axiom, % 167.16/167.39 ! [V_m,V_n,V_k] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__add__diff__inverse,axiom, % 167.16/167.39 ! [V_m,V_n] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_add__diff__assoc,axiom, % 167.16/167.39 ! [V_i,V_j,V_k] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__diff__conv2,axiom, % 167.16/167.39 ! [V_i_2,V_j_2,V_k_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__add__diff__inverse2,axiom, % 167.16/167.39 ! [V_m,V_n] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__imp__diff__is__add,axiom, % 167.16/167.39 ! [V_k_2,V_j_2,V_i_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 167.16/167.39 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 167.16/167.39 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_diff__add__assoc,axiom, % 167.16/167.39 ! [V_i,V_j,V_k] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_add__diff__assoc2,axiom, % 167.16/167.39 ! [V_i,V_j,V_k] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_diff__add__assoc2,axiom, % 167.16/167.39 ! [V_i,V_j,V_k] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Diff__subset__conv,axiom, % 167.16/167.39 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Diff__partition,axiom, % 167.16/167.39 ! [V_B_2,V_A_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Inf__lower,axiom, % 167.16/167.39 ! [V_A_2,V_x_2,T_a] : % 167.16/167.39 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)),V_x_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Union__Int__subset,axiom, % 167.16/167.39 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)))) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Union__upper,axiom, % 167.16/167.39 ! [V_A_2,V_B_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Inter__Un__subset,axiom, % 167.16/167.39 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Inter__lower,axiom, % 167.16/167.39 ! [V_A_2,V_B_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__SUPI,axiom, % 167.16/167.39 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 167.16/167.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_M_2))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_INF__leI,axiom, % 167.16/167.39 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 167.16/167.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_UN__upper,axiom, % 167.16/167.39 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_less__eq__Suc__le__raw,axiom, % 167.16/167.39 ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) ). % 167.16/167.39 % 167.16/167.39 fof(fact_INT__lower,axiom, % 167.16/167.39 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod__pos__nat__iff,axiom, % 167.16/167.39 ! [V_f_2,V_S_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_S_2))) % 167.16/167.39 <=> ! [B_x] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 167.16/167.39 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 167.16/167.39 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.39 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_single__Diff__lessThan,axiom, % 167.16/167.39 ! [V_k_2,T_a] : % 167.16/167.39 ( class_Orderings_Oorder(T_a) % 167.16/167.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod__delta,axiom, % 167.16/167.39 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.16/167.39 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 167.16/167.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod__delta_H,axiom, % 167.16/167.39 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.16/167.39 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 167.16/167.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_add__pos__nonneg,axiom, % 167.16/167.39 ! [V_b,V_a,T_a] : % 167.16/167.39 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_add__nonneg__pos,axiom, % 167.16/167.39 ! [V_b,V_a,T_a] : % 167.16/167.39 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_add__strict__increasing,axiom, % 167.16/167.39 ! [V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_add__strict__increasing2,axiom, % 167.16/167.39 ! [V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_add__neg__nonpos,axiom, % 167.16/167.39 ! [V_b,V_a,T_a] : % 167.16/167.39 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_add__nonpos__neg,axiom, % 167.16/167.39 ! [V_b,V_a,T_a] : % 167.16/167.39 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__le__cancel__left__pos,axiom, % 167.16/167.39 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__le__cancel__left__neg,axiom, % 167.16/167.39 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__strict__mono,axiom, % 167.16/167.39 ! [V_d,V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__strict__mono_H,axiom, % 167.16/167.39 ! [V_d,V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__less__le__imp__less,axiom, % 167.16/167.39 ! [V_d,V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__le__less__imp__less,axiom, % 167.16/167.39 ! [V_d,V_c,V_b,V_a,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__right__less__imp__less,axiom, % 167.16/167.39 ! [V_b,V_c,V_a,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(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))) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__less__imp__less__right,axiom, % 167.16/167.39 ! [V_b,V_c,V_a,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(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))) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__left__less__imp__less,axiom, % 167.16/167.39 ! [V_b,V_a,V_c,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(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))) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__less__imp__less__left,axiom, % 167.16/167.39 ! [V_b,V_a,V_c,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(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))) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__right__le__imp__le,axiom, % 167.16/167.39 ! [V_b,V_c,V_a,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(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))) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__left__le__imp__le,axiom, % 167.16/167.39 ! [V_b,V_a,V_c,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(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))) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_sum__squares__le__zero__iff,axiom, % 167.16/167.39 ! [V_y_2,V_x_2,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__ring__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(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))) % 167.16/167.39 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.16/167.39 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_sum__squares__ge__zero,axiom, % 167.16/167.39 ! [V_y,V_x,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__ring(T_a) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(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)))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__left__le__one__le,axiom, % 167.16/167.39 ! [V_y,V_x,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__idom(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__right__le__one__le,axiom, % 167.16/167.39 ! [V_y,V_x,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__idom(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__add__iff1,axiom, % 167.16/167.39 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 167.16/167.39 ( class_Rings_Oordered__ring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_le__add__iff2,axiom, % 167.16/167.39 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 167.16/167.39 ( class_Rings_Oordered__ring(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_card__insert__le,axiom, % 167.16/167.39 ! [V_x_2,V_A_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_one__le__mult__iff,axiom, % 167.16/167.39 ! [V_n_2,V_m_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 167.16/167.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) % 167.16/167.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_nat__mult__le__cancel1,axiom, % 167.16/167.39 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__le__cancel2,axiom, % 167.16/167.39 ! [V_n_2,V_k_2,V_m_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 167.16/167.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_mult__le__cancel1,axiom, % 167.16/167.39 ! [V_n_2,V_m_2,V_k_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 167.16/167.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_card__image__le,axiom, % 167.16/167.39 ! [V_f_2,T_b,V_A_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_diff__Suc__diff__eq2,axiom, % 167.16/167.39 ! [V_m,V_j,V_k] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_diff__Suc__diff__eq1,axiom, % 167.16/167.39 ! [V_m,V_j,V_k] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_nat__le__add__iff1,axiom, % 167.16/167.39 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(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_m_2)),hAPP(hAPP(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))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_nat__diff__add__eq1,axiom, % 167.16/167.39 ! [V_n,V_m,V_u,V_i,V_j] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_nat__eq__add__iff1,axiom, % 167.16/167.39 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 167.16/167.39 => ( hAPP(hAPP(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_m_2) = hAPP(hAPP(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) % 167.16/167.39 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_nat__le__add__iff2,axiom, % 167.16/167.39 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(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_m_2)),hAPP(hAPP(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))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_nat__diff__add__eq2,axiom, % 167.16/167.39 ! [V_n,V_m,V_u,V_j,V_i] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_nat__eq__add__iff2,axiom, % 167.16/167.39 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 167.16/167.39 => ( hAPP(hAPP(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_m_2) = hAPP(hAPP(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) % 167.16/167.39 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_finite__nat__set__iff__bounded,axiom, % 167.16/167.39 ! [V_N_2] : % 167.16/167.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 167.16/167.39 <=> ? [B_m] : % 167.16/167.39 ! [B_x] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod_Oinsert,axiom, % 167.16/167.39 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod__insert,axiom, % 167.16/167.39 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod_Ounion__inter,axiom, % 167.16/167.39 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod__Un__Int,axiom, % 167.16/167.39 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_folding__one__idem_Osubset__idem,axiom, % 167.16/167.39 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 167.16/167.39 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.39 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod_Oeq__fold,axiom, % 167.16/167.39 ! [V_g_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod_OF__eq,axiom, % 167.16/167.39 ! [V_g_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) % 167.16/167.39 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_convex__bound__le,axiom, % 167.16/167.39 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring__1(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 167.16/167.39 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(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)) ) ) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_diff__single__insert,axiom, % 167.16/167.39 ! [V_B_2,V_x_2,V_A_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_subset__insert__iff,axiom, % 167.16/167.39 ! [V_B_2,V_x_2,V_A_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 167.16/167.39 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) % 167.16/167.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_sup__le__fold__sup,axiom, % 167.16/167.39 ! [V_b_2,V_a_2,V_A_2,T_a] : % 167.16/167.39 ( class_Lattices_Osemilattice__sup(T_a) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_fold__inf__le__inf,axiom, % 167.16/167.39 ! [V_b_2,V_a_2,V_A_2,T_a] : % 167.16/167.39 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setsum__diff,axiom, % 167.16/167.39 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Oab__group__add(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_fold1__belowI,axiom, % 167.16/167.39 ! [V_a_2,V_A_2,T_a] : % 167.16/167.39 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)),V_a_2)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_nat__less__add__iff2,axiom, % 167.16/167.39 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(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_m_2)),hAPP(hAPP(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))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_nat__less__add__iff1,axiom, % 167.16/167.39 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(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_m_2)),hAPP(hAPP(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))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_below__fold1__iff,axiom, % 167.16/167.39 ! [V_x_2,V_A_2,T_a] : % 167.16/167.39 ( class_Lattices_Osemilattice__inf(T_a) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2))) % 167.16/167.39 <=> ! [B_x] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_card__Diff__subset,axiom, % 167.16/167.39 ! [V_A_2,V_B_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.39 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_diff__card__le__card__Diff,axiom, % 167.16/167.39 ! [V_A_2,V_B_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Sup__fin_Osubset__idem,axiom, % 167.16/167.39 ! [V_B_2,V_A_2,T_a] : % 167.16/167.39 ( class_Lattices_Olattice(T_a) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Inf__fin_Osubset__idem,axiom, % 167.16/167.39 ! [V_B_2,V_A_2,T_a] : % 167.16/167.39 ( class_Lattices_Olattice(T_a) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.39 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_card__psubset,axiom, % 167.16/167.39 ! [V_A_2,V_B_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod_Oinsert__remove,axiom, % 167.16/167.39 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod_Ounion__disjoint,axiom, % 167.16/167.39 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.39 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod__Un__disjoint,axiom, % 167.16/167.39 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.39 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setsum__diff__nat,axiom, % 167.16/167.39 ! [V_f_2,V_A_2,V_B_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_Inf__le__Sup,axiom, % 167.16/167.39 ! [V_A_2,T_a] : % 167.16/167.39 ( class_Lattices_Olattice(T_a) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2))) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_convex__bound__lt,axiom, % 167.16/167.39 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 167.16/167.39 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 167.16/167.39 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(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)) ) ) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setsum__mono2,axiom, % 167.16/167.39 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Oordered__comm__monoid__add(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.39 => ( ! [B_b] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) ) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_flat__lub__def,axiom, % 167.16/167.39 ! [V_b_2,V_A_2,T_a] : % 167.16/167.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 167.16/167.39 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) % 167.16/167.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 167.16/167.39 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_arith__series__general,axiom, % 167.16/167.39 ! [V_n_2,V_d_2,V_a_2,T_a] : % 167.16/167.39 ( class_Rings_Ocomm__semiring__1(T_a) % 167.16/167.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod__Un__one,axiom, % 167.16/167.39 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 167.16/167.39 => ( ! [B_x] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 167.16/167.39 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setprod_Ounion__inter__neutral,axiom, % 167.16/167.39 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 167.16/167.39 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.39 => ( ! [B_x] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.16/167.39 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 167.16/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_setsum__mono3,axiom, % 167.16/167.39 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 167.16/167.39 ( ( class_Groups_Ocomm__monoid__add(T_b) % 167.16/167.39 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 167.16/167.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.16/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.16/167.39 => ( ! [B_x] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 167.16/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_ord_OatMost__iff,axiom, % 167.16/167.39 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_ord_OatLeast__iff,axiom, % 167.16/167.39 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 167.16/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 167.16/167.39 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 167.16/167.39 % 167.16/167.39 fof(fact_int__setprod,axiom, % 167.16/167.39 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zle__int,axiom, % 167.45/167.39 ! [V_n_2,V_m_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__le__0__conv,axiom, % 167.45/167.39 ! [V_n_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.39 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__eq__iff,axiom, % 167.45/167.39 ! [V_n_2,V_m_2,T_a] : % 167.45/167.39 ( class_Nat_Osemiring__char__0(T_a) % 167.45/167.39 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) % 167.45/167.39 <=> V_m_2 = V_n_2 ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_infinite__UNIV__nat,axiom, % 167.45/167.39 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__0,axiom, % 167.45/167.39 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__eq__0__conv,axiom, % 167.45/167.39 ! [V_n_2] : % 167.45/167.39 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.39 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zless__iff__Suc__zadd,axiom, % 167.45/167.39 ! [V_z_2,V_w_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 167.45/167.39 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__Suc,axiom, % 167.45/167.39 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zless__int,axiom, % 167.45/167.39 ! [V_n_2,V_m_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__int,axiom, % 167.45/167.39 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__int__left,axiom, % 167.45/167.39 ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zmult__int,axiom, % 167.45/167.39 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__mult,axiom, % 167.45/167.39 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__1,axiom, % 167.45/167.39 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__setprod,axiom, % 167.45/167.39 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.39 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 167.45/167.39 & class_Rings_Osemiring__1(T_a) ) % 167.45/167.39 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__setsum,axiom, % 167.45/167.39 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__Suc0__eq__1,axiom, % 167.45/167.39 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zmult__zless__mono2__lemma,axiom, % 167.45/167.39 ! [V_k,V_j,V_i] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zero__less__int__conv,axiom, % 167.45/167.39 ! [V_n_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zero__le__imp__of__nat,axiom, % 167.45/167.39 ! [V_m,T_a] : % 167.45/167.39 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__0__le__iff,axiom, % 167.45/167.39 ! [V_n,T_a] : % 167.45/167.39 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zdiff__int,axiom, % 167.45/167.39 ! [V_m,V_n] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.45/167.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__less__0__iff,axiom, % 167.45/167.39 ! [V_m,T_a] : % 167.45/167.39 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__0,axiom, % 167.45/167.39 ! [T_a] : % 167.45/167.39 ( class_Rings_Osemiring__1(T_a) % 167.45/167.39 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__less__imp__less,axiom, % 167.45/167.39 ! [V_n,V_m,T_a] : % 167.45/167.39 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_less__imp__of__nat__less,axiom, % 167.45/167.39 ! [V_n,V_m,T_a] : % 167.45/167.39 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__less__iff,axiom, % 167.45/167.39 ! [V_n_2,V_m_2,T_a] : % 167.45/167.39 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__le__iff,axiom, % 167.45/167.39 ! [V_n_2,V_m_2,T_a] : % 167.45/167.39 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__add,axiom, % 167.45/167.39 ! [V_n,V_m,T_a] : % 167.45/167.39 ( class_Rings_Osemiring__1(T_a) % 167.45/167.39 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__mult,axiom, % 167.45/167.39 ! [V_n,V_m,T_a] : % 167.45/167.39 ( class_Rings_Osemiring__1(T_a) % 167.45/167.39 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__1,axiom, % 167.45/167.39 ! [T_a] : % 167.45/167.39 ( class_Rings_Osemiring__1(T_a) % 167.45/167.39 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_Ints__of__nat,axiom, % 167.45/167.39 ! [V_n_2,T_a] : % 167.45/167.39 ( class_Rings_Oring__1(T_a) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__setsum,axiom, % 167.45/167.39 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.39 ( class_Rings_Osemiring__1(T_a) % 167.45/167.39 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__Suc,axiom, % 167.45/167.39 ! [V_m,T_a] : % 167.45/167.39 ( class_Rings_Osemiring__1(T_a) % 167.45/167.39 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__diff,axiom, % 167.45/167.39 ! [V_m,V_n,T_a] : % 167.45/167.39 ( class_Rings_Oring__1(T_a) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.45/167.39 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_setsum__constant,axiom, % 167.45/167.39 ! [V_A_2,V_y_2,T_b,T_a] : % 167.45/167.39 ( class_Rings_Osemiring__1(T_a) % 167.45/167.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_y_2) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__0__less__iff,axiom, % 167.45/167.39 ! [V_n_2,T_a] : % 167.45/167.39 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 167.45/167.39 ! [V_n_2,T_a] : % 167.45/167.39 ( class_Rings_Osemiring__1(T_a) % 167.45/167.39 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_Groups_Oone__class_Oone(T_a)),V_n_2,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zdiff__int__split,axiom, % 167.45/167.39 ! [V_y_2,V_x_2,V_P_2] : % 167.45/167.39 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)))) % 167.45/167.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 167.45/167.39 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) ) % 167.45/167.39 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 167.45/167.39 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_setsum__bounded,axiom, % 167.45/167.39 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] : % 167.45/167.39 ( ( class_Groups_Oordered__ab__semigroup__add(T_b) % 167.45/167.39 & class_Rings_Osemiring__1(T_b) ) % 167.45/167.39 => ( ! [B_i] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) ) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))),V_K_2))) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 167.45/167.39 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 167.45/167.39 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 167.45/167.39 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_ord_OatLeastLessThan__iff,axiom, % 167.45/167.39 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 167.45/167.39 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 167.45/167.39 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 167.45/167.39 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))) % 167.45/167.39 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 167.45/167.39 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zle__diff1__eq,axiom, % 167.45/167.39 ! [V_z_2,V_w_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zless__le,axiom, % 167.45/167.39 ! [V_w_2,V_z_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 167.45/167.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 167.45/167.39 & V_z_2 != V_w_2 ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zle__add1__eq__le,axiom, % 167.45/167.39 ! [V_z_2,V_w_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_add1__zle__eq,axiom, % 167.45/167.39 ! [V_z_2,V_w_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zless__imp__add1__zle,axiom, % 167.45/167.39 ! [V_z,V_w] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__zless__mono,axiom, % 167.45/167.39 ! [V_z,V_z_H,V_w,V_w_H] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zle__iff__zadd,axiom, % 167.45/167.39 ! [V_z_2,V_w_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 167.45/167.39 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__left__mono,axiom, % 167.45/167.39 ! [V_k,V_j,V_i] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zle__antisym,axiom, % 167.45/167.39 ! [V_w,V_z] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 167.45/167.39 => V_z = V_w ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zle__trans,axiom, % 167.45/167.39 ! [V_k,V_j,V_i] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zle__linear,axiom, % 167.45/167.39 ! [V_w,V_z] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 167.45/167.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zle__refl,axiom, % 167.45/167.39 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zero__zle__int,axiom, % 167.45/167.39 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 167.45/167.39 % 167.45/167.39 fof(fact_le__imp__0__less,axiom, % 167.45/167.39 ! [V_z] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__one__le__iff__zero__less,axiom, % 167.45/167.39 ! [V_z_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_less__bin__lemma,axiom, % 167.45/167.39 ! [V_l_2,V_k_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__less__0__conv,axiom, % 167.45/167.39 ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__0__less__1,axiom, % 167.45/167.39 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 167.45/167.39 % 167.45/167.39 fof(fact_odd__less__0,axiom, % 167.45/167.39 ! [V_z_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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))) % 167.45/167.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zmult__zless__mono2,axiom, % 167.45/167.39 ! [V_k,V_j,V_i] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 167.45/167.39 => hBOOL(hAPP(hAPP(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))) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_pos__zmult__eq__1__iff,axiom, % 167.45/167.39 ! [V_n_2,V_m_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 167.45/167.39 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 167.45/167.39 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 167.45/167.39 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__int__eq,axiom, % 167.45/167.39 ! [V_n_2,V_m_2] : % 167.45/167.39 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) % 167.45/167.39 <=> V_m_2 = V_n_2 ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__strict__right__mono,axiom, % 167.45/167.39 ! [V_k,V_j,V_i] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zless__add1__eq,axiom, % 167.45/167.39 ! [V_z_2,V_w_2] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 167.45/167.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 167.45/167.39 | V_w_2 = V_z_2 ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zless__linear,axiom, % 167.45/167.39 ! [V_y,V_x] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 167.45/167.39 | V_x = V_y % 167.45/167.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__commute,axiom, % 167.45/167.39 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__left__commute,axiom, % 167.45/167.39 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__assoc,axiom, % 167.45/167.39 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zdiff__zmult__distrib2,axiom, % 167.45/167.39 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(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)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zdiff__zmult__distrib,axiom, % 167.45/167.39 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(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)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zmult__1,axiom, % 167.45/167.39 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 167.45/167.39 % 167.45/167.39 fof(fact_zmult__1__right,axiom, % 167.45/167.39 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__zmult__distrib,axiom, % 167.45/167.39 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(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)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zmult__assoc,axiom, % 167.45/167.39 ! [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)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__zmult__distrib2,axiom, % 167.45/167.39 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(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)) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zmult__commute,axiom, % 167.45/167.39 ! [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) ). % 167.45/167.39 % 167.45/167.39 fof(fact_int__0__neq__1,axiom, % 167.45/167.39 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 167.45/167.39 % 167.45/167.39 fof(fact_odd__nonzero,axiom, % 167.45/167.39 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__0__right,axiom, % 167.45/167.39 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 167.45/167.39 % 167.45/167.39 fof(fact_zadd__0,axiom, % 167.45/167.39 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 167.45/167.39 ! [V_i_2,V_inc_2,T_a] : % 167.45/167.39 ( class_Rings_Osemiring__1(T_a) % 167.45/167.39 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 167.45/167.39 ! [V_i_2,V_n_2,V_inc_2,T_a] : % 167.45/167.39 ( class_Rings_Osemiring__1(T_a) % 167.45/167.39 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_self__quotient__aux2,axiom, % 167.45/167.39 ! [V_q,V_r,V_a] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.39 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_self__quotient__aux1,axiom, % 167.45/167.39 ! [V_q,V_r,V_a] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.39 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_q__pos__lemma,axiom, % 167.45/167.39 ! [V_r_H,V_q_H,V_b_H] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(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))) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_q__neg__lemma,axiom, % 167.45/167.39 ! [V_r_H,V_q_H,V_b_H] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(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))) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_unique__quotient__lemma,axiom, % 167.45/167.39 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zdiv__mono2__lemma,axiom, % 167.45/167.39 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 167.45/167.39 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(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) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(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))) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_zdiv__mono2__neg__lemma,axiom, % 167.45/167.39 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 167.45/167.39 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(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) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(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))) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 167.45/167.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 167.45/167.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 167.45/167.39 % 167.45/167.39 fof(fact_unique__quotient__lemma__neg,axiom, % 167.45/167.39 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 167.45/167.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 167.45/167.40 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 167.45/167.40 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 167.45/167.40 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 167.45/167.40 ! [V_y_2,V_x_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 167.45/167.40 ! [V_y_2,V_x_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 167.45/167.40 ! [V_y,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 167.45/167.40 ! [V_B_2,V_A_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 167.45/167.40 ! [V_y_2,V_x_2] : % 167.45/167.40 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2) % 167.45/167.40 <=> V_x_2 = V_y_2 ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 167.45/167.40 ! [V_B_2,V_A_2] : % 167.45/167.40 ( V_A_2 = V_B_2 % 167.45/167.40 <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 167.45/167.40 ! [V_A_2,V_x_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 167.45/167.40 ! [V_B_2,V_A_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 167.45/167.40 hBOOL(hAPP(hAPP(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))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 167.45/167.40 c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 167.45/167.40 ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 167.45/167.40 ! [V_A_2] : % 167.45/167.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 167.45/167.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 167.45/167.40 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 167.45/167.40 ! [V_y,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 167.45/167.40 ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 167.45/167.40 ! [V_P_2] : % 167.45/167.40 ( ? [B_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 167.45/167.40 & hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.40 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 167.45/167.40 ! [V_P_2] : % 167.45/167.40 ( ! [B_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 167.45/167.40 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.40 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 167.45/167.40 hBOOL(hAPP(hAPP(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))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ord_OlessThan__iff,axiom, % 167.45/167.40 ! [V_k_2,V_less_2,V_i_2,T_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ord_OgreaterThan__iff,axiom, % 167.45/167.40 ! [V_k_2,V_less_2,V_i_2,T_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ord_OatLeastAtMost__iff,axiom, % 167.45/167.40 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2))) % 167.45/167.40 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 167.45/167.40 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setprod__gen__delta,axiom, % 167.45/167.40 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_a,T_b] : % 167.45/167.40 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.45/167.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.45/167.40 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_c_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_tsub__def,axiom, % 167.45/167.40 ! [V_x,V_y] : % 167.45/167.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 167.45/167.40 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 167.45/167.40 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 167.45/167.40 ! [V_x_2,V_y_2,V_c_2] : % 167.45/167.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 167.45/167.40 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 167.45/167.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 167.45/167.40 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 167.45/167.40 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_finite__atLeastLessThan,axiom, % 167.45/167.40 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 167.45/167.40 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_int__power,axiom, % 167.45/167.40 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zpower__int,axiom, % 167.45/167.40 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_infinite__UNIV__int,axiom, % 167.45/167.40 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 167.45/167.40 ! [V_q,V_y,V_x,T_a] : % 167.45/167.40 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.40 => 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)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 167.45/167.40 ! [V_q,V_p,V_x,T_a] : % 167.45/167.40 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.40 => 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)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zpower__zpower,axiom, % 167.45/167.40 ! [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)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 167.45/167.40 ! [V_x,T_a] : % 167.45/167.40 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastLessThan__eq__iff,axiom, % 167.45/167.40 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.40 ( class_Orderings_Olinorder(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 167.45/167.40 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2) % 167.45/167.40 <=> ( V_a_2 = V_c_2 % 167.45/167.40 & V_b_2 = V_d_2 ) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 167.45/167.40 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.40 ( class_Orderings_Olinorder(T_a) % 167.45/167.40 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 167.45/167.40 => V_a_2 = V_c_2 ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 167.45/167.40 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.40 ( class_Orderings_Olinorder(T_a) % 167.45/167.40 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 167.45/167.40 => V_b_2 = V_d_2 ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 167.45/167.40 ! [V_q,V_x,T_a] : % 167.45/167.40 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 167.45/167.40 ! [V_q,V_x,T_a] : % 167.45/167.40 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 167.45/167.40 ! [V_q,V_x,T_a] : % 167.45/167.40 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 167.45/167.40 ! [V_x,T_a] : % 167.45/167.40 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.40 => 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) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 167.45/167.40 ! [V_q,V_p,V_x,T_a] : % 167.45/167.40 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.40 => 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastLessThan__add__Un,axiom, % 167.45/167.40 ! [V_k_2,V_j_2,V_i_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 167.45/167.40 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 167.45/167.40 ! [V_n,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zpower__zadd__distrib,axiom, % 167.45/167.40 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(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)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastLessThan0,axiom, % 167.45/167.40 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Ints__power,axiom, % 167.45/167.40 ! [V_n_2,V_a_2,T_a] : % 167.45/167.40 ( class_Rings_Oring__1(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeast0LessThan,axiom, % 167.45/167.40 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) ). % 167.45/167.40 % 167.45/167.40 fof(fact_subset__card__intvl__is__intvl,axiom, % 167.45/167.40 ! [V_k_2,V_A_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))))) % 167.45/167.40 => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_card__atLeastLessThan,axiom, % 167.45/167.40 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ). % 167.45/167.40 % 167.45/167.40 fof(fact_image__Suc__atLeastLessThan,axiom, % 167.45/167.40 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastLessThan__empty,axiom, % 167.45/167.40 ! [V_a_2,V_b_2,T_a] : % 167.45/167.40 ( class_Orderings_Oorder(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 167.45/167.40 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastLessThan__empty__iff,axiom, % 167.45/167.40 ! [V_b_2,V_a_2,T_a] : % 167.45/167.40 ( class_Orderings_Oorder(T_a) % 167.45/167.40 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.40 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastLessThan__empty__iff2,axiom, % 167.45/167.40 ! [V_b_2,V_a_2,T_a] : % 167.45/167.40 ( class_Orderings_Oorder(T_a) % 167.45/167.40 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) % 167.45/167.40 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastLessThan__subset__iff,axiom, % 167.45/167.40 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.40 ( class_Orderings_Olinorder(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 167.45/167.40 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 167.45/167.40 ! [V_n_2,V_m_2,V_f_2,T_a] : % 167.45/167.40 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ivl__disj__un_I17_J,axiom, % 167.45/167.40 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.40 ( class_Orderings_Olinorder(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 167.45/167.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 167.45/167.40 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 167.45/167.40 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ivl__diff,axiom, % 167.45/167.40 ! [V_m_2,V_n_2,V_i_2,T_a] : % 167.45/167.40 ( class_Orderings_Olinorder(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2)) % 167.45/167.40 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_n_2),V_m_2) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ivl__disj__int_I11_J,axiom, % 167.45/167.40 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.40 ( class_Orderings_Oorder(T_a) % 167.45/167.40 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_image__add__atLeastLessThan,axiom, % 167.45/167.40 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setsum__add__nat__ivl,axiom, % 167.45/167.40 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 167.45/167.40 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 167.45/167.40 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setsum__diff__nat__ivl,axiom, % 167.45/167.40 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 167.45/167.40 ( class_Groups_Oab__group__add(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 167.45/167.40 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastLessThan__singleton,axiom, % 167.45/167.40 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setprod__constant,axiom, % 167.45/167.40 ! [V_y_2,V_A_2,T_a,T_b] : % 167.45/167.40 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.45/167.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_COMBK(T_b,T_a),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_UN__UN__finite__eq,axiom, % 167.45/167.40 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ivl__disj__un_I8_J,axiom, % 167.45/167.40 ! [V_u_2,V_l_2,T_a] : % 167.45/167.40 ( class_Orderings_Olinorder(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 167.45/167.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ivl__disj__int_I2_J,axiom, % 167.45/167.40 ! [V_u_2,V_l_2,T_a] : % 167.45/167.40 ( class_Orderings_Oorder(T_a) % 167.45/167.40 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 167.45/167.40 ! [V_k_2,V_f_2,T_a] : % 167.45/167.40 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.40 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setsum__head__upt__Suc,axiom, % 167.45/167.40 ! [V_f_2,V_n_2,V_m_2,T_a] : % 167.45/167.40 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__eq__if,axiom, % 167.45/167.40 ! [V_p,V_m] : % 167.45/167.40 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 167.45/167.40 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.40 => 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastLessThanSuc,axiom, % 167.45/167.40 ! [V_n_2,V_m_2] : % 167.45/167.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.40 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.40 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setsum__op__ivl__Suc,axiom, % 167.45/167.40 ! [V_f_2,V_m_2,V_n_2,T_a] : % 167.45/167.40 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_a) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 167.45/167.40 ! [V_y,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_tsub__eq,axiom, % 167.45/167.40 ! [V_x,V_y] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 167.45/167.40 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 167.45/167.40 ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__strict__mono,axiom, % 167.45/167.40 ! [V_n,V_b,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_one__less__power,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__increasing__iff,axiom, % 167.45/167.40 ! [V_y_2,V_x_2,V_b_2,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(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))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__le__imp__le__exp,axiom, % 167.45/167.40 ! [V_n,V_m,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(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))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__decreasing,axiom, % 167.45/167.40 ! [V_a,V_N,V_n,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__strict__decreasing,axiom, % 167.45/167.40 ! [V_a,V_N,V_n,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_finite__atLeastLessThan__int,axiom, % 167.45/167.40 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 167.45/167.40 ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_image__add__int__atLeastLessThan,axiom, % 167.45/167.40 ! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2) ). % 167.45/167.40 % 167.45/167.40 fof(fact_field__power__not__zero,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 167.45/167.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 167.45/167.40 ! [V_m_2,V_x_2] : % 167.45/167.40 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.45/167.40 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.40 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__Suc__0,axiom, % 167.45/167.40 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__power__less__imp__less,axiom, % 167.45/167.40 ! [V_n,V_m,V_i] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(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))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__zero__less__power__iff,axiom, % 167.45/167.40 ! [V_n_2,V_x_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(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))) % 167.45/167.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 167.45/167.40 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__mult__distrib,axiom, % 167.45/167.40 ! [V_n,V_b,V_a,T_a] : % 167.45/167.40 ( class_Groups_Ocomm__monoid__mult(T_a) % 167.45/167.40 => 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)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__commutes,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Groups_Omonoid__mult(T_a) % 167.45/167.40 => 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)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__one,axiom, % 167.45/167.40 ! [V_n,T_a] : % 167.45/167.40 ( class_Groups_Omonoid__mult(T_a) % 167.45/167.40 => 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) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_of__nat__power,axiom, % 167.45/167.40 ! [V_n,V_m,T_a] : % 167.45/167.40 ( class_Rings_Osemiring__1(T_a) % 167.45/167.40 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__mult,axiom, % 167.45/167.40 ! [V_n,V_m,V_a,T_a] : % 167.45/167.40 ( class_Groups_Omonoid__mult(T_a) % 167.45/167.40 => 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) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__one__right,axiom, % 167.45/167.40 ! [V_a,T_a] : % 167.45/167.40 ( class_Groups_Omonoid__mult(T_a) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zero__le__power,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__mono,axiom, % 167.45/167.40 ! [V_n,V_b,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zero__less__power,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__eq__0__iff,axiom, % 167.45/167.40 ! [V_n_2,V_a_2,T_a] : % 167.45/167.40 ( ( class_Power_Opower(T_a) % 167.45/167.40 & class_Rings_Omult__zero(T_a) % 167.45/167.40 & class_Rings_Ono__zero__divisors(T_a) % 167.45/167.40 & class_Rings_Ozero__neq__one(T_a) ) % 167.45/167.40 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_one__le__power,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__0__Suc,axiom, % 167.45/167.40 ! [V_n,T_a] : % 167.45/167.40 ( ( class_Power_Opower(T_a) % 167.45/167.40 & class_Rings_Osemiring__0(T_a) ) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__inject__exp,axiom, % 167.45/167.40 ! [V_n_2,V_m_2,V_a_2,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 167.45/167.40 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) % 167.45/167.40 <=> V_m_2 = V_n_2 ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__Suc2,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Groups_Omonoid__mult(T_a) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__Suc,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Power_Opower(T_a) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,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)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__one__le__power,axiom, % 167.45/167.40 ! [V_n,V_i] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__0,axiom, % 167.45/167.40 ! [V_a,T_a] : % 167.45/167.40 ( class_Power_Opower(T_a) % 167.45/167.40 => 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) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__add,axiom, % 167.45/167.40 ! [V_n,V_m,V_a,T_a] : % 167.45/167.40 ( class_Groups_Omonoid__mult(T_a) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(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)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__less__imp__less__base,axiom, % 167.45/167.40 ! [V_b,V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(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))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__inject__base,axiom, % 167.45/167.40 ! [V_b,V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.45/167.40 => V_a = V_b ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__le__imp__le__base,axiom, % 167.45/167.40 ! [V_b,V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__gt1__lemma,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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)))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__less__power__Suc,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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)))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__0__left,axiom, % 167.45/167.40 ! [V_n,T_a] : % 167.45/167.40 ( ( class_Power_Opower(T_a) % 167.45/167.40 & class_Rings_Osemiring__0(T_a) ) % 167.45/167.40 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.40 => 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) ) % 167.45/167.40 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.40 => 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) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__gt1,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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),hAPP(c_Nat_OSuc,V_n)))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__strict__increasing__iff,axiom, % 167.45/167.40 ! [V_y_2,V_x_2,V_b_2,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(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))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__less__imp__less__exp,axiom, % 167.45/167.40 ! [V_n,V_m,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(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))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__strict__increasing,axiom, % 167.45/167.40 ! [V_a,V_N,V_n,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__increasing,axiom, % 167.45/167.40 ! [V_a,V_N,V_n,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__Suc__less,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__eq__imp__eq__base,axiom, % 167.45/167.40 ! [V_b,V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( 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) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.40 => V_a = V_b ) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__Suc__less__one,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_all__nat__less__eq,axiom, % 167.45/167.40 ! [V_P_2,V_n_2] : % 167.45/167.40 ( ! [B_m] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 167.45/167.40 => hBOOL(hAPP(V_P_2,B_m)) ) % 167.45/167.40 <=> ! [B_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) % 167.45/167.40 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ex__nat__less__eq,axiom, % 167.45/167.40 ! [V_P_2,V_n_2] : % 167.45/167.40 ( ? [B_m] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 167.45/167.40 & hBOOL(hAPP(V_P_2,B_m)) ) % 167.45/167.40 <=> ? [B_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) % 167.45/167.40 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_UN__finite2__subset,axiom, % 167.45/167.40 ! [V_B_2,V_k_2,V_A_2,T_a] : % 167.45/167.40 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__power__power,axiom, % 167.45/167.40 ! [T_a] : % 167.45/167.40 ( class_Power_Opower(T_a) % 167.45/167.40 => 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)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_UN__finite2__eq,axiom, % 167.45/167.40 ! [V_B_2,V_k_2,V_A_2,T_a] : % 167.45/167.40 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2) % 167.45/167.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_UN__finite__subset,axiom, % 167.45/167.40 ! [V_C_2,V_A_2,T_a] : % 167.45/167.40 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power_Opower_Opower__0,axiom, % 167.45/167.40 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ). % 167.45/167.40 % 167.45/167.40 fof(fact_power_Opower_Opower__Suc,axiom, % 167.45/167.40 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ivl__disj__un_I3_J,axiom, % 167.45/167.40 ! [V_u_2,V_l_2,T_a] : % 167.45/167.40 ( class_Orderings_Olinorder(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 167.45/167.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_int__power__div__base,axiom, % 167.45/167.40 ! [V_k,V_m] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Powp__mono,axiom, % 167.45/167.40 ! [V_B_2,V_A_2,T_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_a,V_A_2)),c_Predicate_OPowp(T_a,V_B_2))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setprod__diff1,axiom, % 167.45/167.40 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] : % 167.45/167.40 ( class_Fields_Ofield(T_b) % 167.45/167.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.40 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) % 167.45/167.40 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_image__atLeastZeroLessThan__int,axiom, % 167.45/167.40 ! [V_u_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 167.45/167.40 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setsum__nonneg__0,axiom, % 167.45/167.40 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] : % 167.45/167.40 ( class_Groups_Oordered__ab__group__add(T_b) % 167.45/167.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 167.45/167.40 => ( ! [B_i] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 167.45/167.40 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_b) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 167.45/167.40 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_finite__greaterThanLessThan,axiom, % 167.45/167.40 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_finite__greaterThanLessThan__int,axiom, % 167.45/167.40 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__zero,axiom, % 167.45/167.40 ! [V_a,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__zero__left,axiom, % 167.45/167.40 ! [V_a,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring(T_a) % 167.45/167.40 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_add__divide__distrib,axiom, % 167.45/167.40 ! [V_c,V_b,V_a,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring(T_a) % 167.45/167.40 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_times__divide__eq__right,axiom, % 167.45/167.40 ! [V_c,V_b,V_a,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring(T_a) % 167.45/167.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_diff__divide__distrib,axiom, % 167.45/167.40 ! [V_c,V_b,V_a,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring(T_a) % 167.45/167.40 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__1,axiom, % 167.45/167.40 ! [V_a,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring(T_a) % 167.45/167.40 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zdiv__zero,axiom, % 167.45/167.40 ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__divide,axiom, % 167.45/167.40 ! [V_n,V_b,V_a,T_a] : % 167.45/167.40 ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__int,axiom, % 167.45/167.40 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__by__0,axiom, % 167.45/167.40 ! [V_a,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__0,axiom, % 167.45/167.40 ! [V_a,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__by__1,axiom, % 167.45/167.40 ! [V_a,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_setsum__divide__distrib,axiom, % 167.45/167.40 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.40 ( class_Fields_Ofield(T_a) % 167.45/167.40 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Rings_Oinverse__class_Odivide(T_a)),V_f_2)),V_r_2)),V_A_2) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nonzero__eq__divide__eq,axiom, % 167.45/167.40 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring(T_a) % 167.45/167.40 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) % 167.45/167.40 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nonzero__divide__eq__eq,axiom, % 167.45/167.40 ! [V_a_2,V_b_2,V_c_2,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring(T_a) % 167.45/167.40 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2 % 167.45/167.40 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__eq__imp,axiom, % 167.45/167.40 ! [V_a,V_b,V_c,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring(T_a) % 167.45/167.40 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 167.45/167.40 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_eq__divide__imp,axiom, % 167.45/167.40 ! [V_b,V_a,V_c,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring(T_a) % 167.45/167.40 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 167.45/167.40 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_right__inverse__eq,axiom, % 167.45/167.40 ! [V_a_2,V_b_2,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring(T_a) % 167.45/167.40 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 167.45/167.40 <=> V_a_2 = V_b_2 ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__self,axiom, % 167.45/167.40 ! [V_a,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring(T_a) % 167.45/167.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__self__if,axiom, % 167.45/167.40 ! [V_a,T_a] : % 167.45/167.40 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 167.45/167.40 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 167.45/167.40 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nonzero__power__divide,axiom, % 167.45/167.40 ! [V_n,V_a,V_b,T_a] : % 167.45/167.40 ( class_Fields_Ofield(T_a) % 167.45/167.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 167.45/167.40 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__0,axiom, % 167.45/167.40 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 167.45/167.40 ! [V_y,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 167.45/167.40 ! [V_a_2,V_b_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 167.45/167.40 ! [V_a_2,V_b_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__neg__pos__less0,axiom, % 167.45/167.40 ! [V_b,V_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ex__nat,axiom, % 167.45/167.40 ! [V_P_2] : % 167.45/167.40 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 167.45/167.40 <=> ? [B_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 167.45/167.40 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_all__nat,axiom, % 167.45/167.40 ! [V_P_2] : % 167.45/167.40 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 167.45/167.40 <=> ! [B_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 167.45/167.40 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 167.45/167.40 ! [V_y_2,V_x_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 167.45/167.40 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 167.45/167.40 <=> V_x_2 = V_y_2 ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_eq__nat__nat__iff,axiom, % 167.45/167.40 ! [V_z_H_2,V_z_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 167.45/167.40 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 167.45/167.40 <=> V_z_2 = V_z_H_2 ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__one__over,axiom, % 167.45/167.40 ! [V_n,V_a,T_a] : % 167.45/167.40 ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zdiv__self,axiom, % 167.45/167.40 ! [V_a] : % 167.45/167.40 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 167.45/167.40 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__mult__mult1__if,axiom, % 167.45/167.40 ! [V_b,V_a,V_c,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(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)) = c_Groups_Ozero__class_Ozero(T_a) ) % 167.45/167.40 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(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)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__mult__self2__is__id,axiom, % 167.45/167.40 ! [V_a,V_b,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__mult__self1__is__id,axiom, % 167.45/167.40 ! [V_a,V_b,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__mult__mult2,axiom, % 167.45/167.40 ! [V_b,V_a,V_c,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(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)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__mult__mult1,axiom, % 167.45/167.40 ! [V_b,V_a,V_c,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(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)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__self,axiom, % 167.45/167.40 ! [V_a,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 167.45/167.40 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__int__nat__set__return__embed,axiom, % 167.45/167.40 ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2 ). % 167.45/167.40 % 167.45/167.40 fof(fact_setprod__dividef,axiom, % 167.45/167.40 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 167.45/167.40 ( class_Fields_Ofield__inverse__zero(T_b) % 167.45/167.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_card__greaterThanLessThan__int,axiom, % 167.45/167.40 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 167.45/167.40 ! [V_A_2,V_f_2,T_a] : % 167.45/167.40 ( ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.40 & class_Groups_Ocomm__monoid__mult(T_a) ) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 167.45/167.40 c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_greaterThanLessThan__empty,axiom, % 167.45/167.40 ! [V_k_2,V_l_2,T_a] : % 167.45/167.40 ( class_Orderings_Oorder(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 167.45/167.40 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__le__0,axiom, % 167.45/167.40 ! [V_z] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__0__iff,axiom, % 167.45/167.40 ! [V_i_2] : % 167.45/167.40 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zdiv__mono1__neg,axiom, % 167.45/167.40 ! [V_b,V_a_H,V_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zdiv__mono1,axiom, % 167.45/167.40 ! [V_b,V_a_H,V_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__neg__neg__trivial,axiom, % 167.45/167.40 ! [V_b,V_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zdiv__mono2__neg,axiom, % 167.45/167.40 ! [V_b,V_b_H,V_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__nonpos__pos__le0,axiom, % 167.45/167.40 ! [V_b,V_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 167.45/167.40 ! [V_a_2,V_b_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__pos__pos__trivial,axiom, % 167.45/167.40 ! [V_b,V_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__nonneg__neg__le0,axiom, % 167.45/167.40 ! [V_b,V_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zdiv__mono2,axiom, % 167.45/167.40 ! [V_b,V_b_H,V_a] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 167.45/167.40 ! [V_b_2,V_a_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 167.45/167.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 167.45/167.40 ! [V_i_2,V_k_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 167.45/167.40 ! [V_a_2,V_b_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zdiv__eq__0__iff,axiom, % 167.45/167.40 ! [V_k_2,V_i_2] : % 167.45/167.40 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.40 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.40 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 167.45/167.40 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 167.45/167.40 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zless__nat__conj,axiom, % 167.45/167.40 ! [V_z_2,V_w_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 167.45/167.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__mono__iff,axiom, % 167.45/167.40 ! [V_w_2,V_z_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 167.45/167.40 ! [V_y_2,V_x_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__1,axiom, % 167.45/167.40 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_int__div__less__self,axiom, % 167.45/167.40 ! [V_k,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zdiv__zmult2__eq,axiom, % 167.45/167.40 ! [V_b,V_a,V_c] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_int__nat__eq,axiom, % 167.45/167.40 ! [V_z] : % 167.45/167.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.45/167.40 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.45/167.40 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_int__eq__iff,axiom, % 167.45/167.40 ! [V_z_2,V_m_2] : % 167.45/167.40 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 167.45/167.40 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__0__le,axiom, % 167.45/167.40 ! [V_z] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.45/167.40 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zless__nat__eq__int__zless,axiom, % 167.45/167.40 ! [V_z_2,V_m_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__mult__self2,axiom, % 167.45/167.40 ! [V_c,V_a,V_b,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__mult__self1,axiom, % 167.45/167.40 ! [V_c,V_a,V_b,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__add__self1,axiom, % 167.45/167.40 ! [V_a,V_b,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__add__self2,axiom, % 167.45/167.40 ! [V_a,V_b,T_a] : % 167.45/167.40 ( class_Divides_Osemiring__div(T_a) % 167.45/167.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 167.45/167.40 ! [V_A_2,V_f_2,T_a] : % 167.45/167.40 ( ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.40 & class_Groups_Ocomm__monoid__mult(T_a) ) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_card__atLeastZeroLessThan__int,axiom, % 167.45/167.40 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2) ). % 167.45/167.40 % 167.45/167.40 fof(fact_card__atLeastLessThan__int,axiom, % 167.45/167.40 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zero__less__nat__eq,axiom, % 167.45/167.40 ! [V_z_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_power__diff,axiom, % 167.45/167.40 ! [V_m,V_n,V_a,T_a] : % 167.45/167.40 ( class_Fields_Ofield(T_a) % 167.45/167.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 167.45/167.40 ! [V_y_2,V_x_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__less__eq__zless,axiom, % 167.45/167.40 ! [V_z_2,V_w_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__eq__iff,axiom, % 167.45/167.40 ! [V_m_2,V_w_2] : % 167.45/167.40 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 167.45/167.40 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.45/167.40 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.45/167.40 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__eq__iff2,axiom, % 167.45/167.40 ! [V_w_2,V_m_2] : % 167.45/167.40 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 167.45/167.40 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.45/167.40 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.45/167.40 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__le__eq__zle,axiom, % 167.45/167.40 ! [V_z_2,V_w_2] : % 167.45/167.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.45/167.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_split__nat,axiom, % 167.45/167.40 ! [V_i_2,V_P_2] : % 167.45/167.40 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) % 167.45/167.40 <=> ( ! [B_n] : % 167.45/167.40 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 167.45/167.40 => hBOOL(hAPP(V_P_2,B_n)) ) % 167.45/167.40 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 167.45/167.40 ! [V_y,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.40 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__add__distrib,axiom, % 167.45/167.40 ! [V_z_H,V_z] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 167.45/167.40 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 167.45/167.40 ! [V_y,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__mult__distrib,axiom, % 167.45/167.40 ! [V_z_H,V_z] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.45/167.40 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 167.45/167.40 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__diff__distrib,axiom, % 167.45/167.40 ! [V_z,V_z_H] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 167.45/167.40 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 167.45/167.40 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 167.45/167.40 ! [V_n,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__power__eq,axiom, % 167.45/167.40 ! [V_n,V_z] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.45/167.40 => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 167.45/167.40 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ivl__disj__int_I9_J,axiom, % 167.45/167.40 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.40 ( class_Orderings_Oorder(T_a) % 167.45/167.40 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 167.45/167.40 ! [V_y,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.40 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_card__greaterThanLessThan,axiom, % 167.45/167.40 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 167.45/167.40 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2) ). % 167.45/167.40 % 167.45/167.40 fof(fact_one__less__nat__eq,axiom, % 167.45/167.40 ! [V_z_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_split__zdiv,axiom, % 167.45/167.40 ! [V_k_2,V_n_2,V_P_2] : % 167.45/167.40 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 167.45/167.40 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.40 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.40 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 167.45/167.40 => ! [B_i] : % 167.45/167.40 ( ? [B_j] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 167.45/167.40 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 167.45/167.40 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 167.45/167.40 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 => ! [B_i] : % 167.45/167.40 ( ? [B_j] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.40 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 167.45/167.40 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divmod__int__rel__div__eq,axiom, % 167.45/167.40 ! [V_r_1,V_y,V_b_1,V_a_1] : % 167.45/167.40 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) % 167.45/167.40 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 167.45/167.40 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__less__iff,axiom, % 167.45/167.40 ! [V_m_2,V_w_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 167.45/167.40 ! [V_z] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.45/167.40 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_ivl__disj__un_I15_J,axiom, % 167.45/167.40 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.40 ( class_Orderings_Olinorder(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 167.45/167.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_geometric__sum,axiom, % 167.45/167.40 ! [V_n_2,V_x_2,T_a] : % 167.45/167.40 ( class_Fields_Ofield(T_a) % 167.45/167.40 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a) % 167.45/167.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_Power_Opower__class_Opower(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x_2),c_Groups_Oone__class_Oone(T_a))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_le__divide__eq,axiom, % 167.45/167.40 ! [V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 167.45/167.40 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__le__eq,axiom, % 167.45/167.40 ! [V_a_2,V_c_2,V_b_2,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 167.45/167.40 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_pos__le__divide__eq,axiom, % 167.45/167.40 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_pos__divide__le__eq,axiom, % 167.45/167.40 ! [V_a_2,V_b_2,V_c_2,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 167.45/167.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_mult__imp__div__pos__le,axiom, % 167.45/167.40 ! [V_z,V_x,V_y,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_mult__imp__le__div__pos,axiom, % 167.45/167.40 ! [V_x,V_z,V_y,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__le__dividend,axiom, % 167.45/167.40 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__le__mono,axiom, % 167.45/167.40 ! [V_k,V_n,V_m] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__mult2__eq,axiom, % 167.45/167.40 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__1,axiom, % 167.45/167.40 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__less,axiom, % 167.45/167.40 ! [V_n,V_m] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__mult__div__cancel__disj,axiom, % 167.45/167.40 ! [V_n,V_m,V_k] : % 167.45/167.40 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(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)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.40 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(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)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zdiv__int,axiom, % 167.45/167.40 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 167.45/167.40 ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__le__mono2,axiom, % 167.45/167.40 ! [V_k,V_n,V_m] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__mult__self__is__m,axiom, % 167.45/167.40 ! [V_m,V_n] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__mult__self1__is__m,axiom, % 167.45/167.40 ! [V_m,V_n] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__mult__div__cancel1,axiom, % 167.45/167.40 ! [V_n,V_m,V_k] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(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)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__less__dividend,axiom, % 167.45/167.40 ! [V_m,V_n] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__if,axiom, % 167.45/167.40 ! [V_m,V_n] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_div__geq,axiom, % 167.45/167.40 ! [V_m,V_n] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.40 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_split__div,axiom, % 167.45/167.40 ! [V_k_2,V_n_2,V_P_2] : % 167.45/167.40 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 167.45/167.40 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.40 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 167.45/167.40 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.40 => ! [B_i,B_j] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 167.45/167.40 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) % 167.45/167.40 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_nat__div__distrib,axiom, % 167.45/167.40 ! [V_y,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 167.45/167.40 ! [V_y,V_x] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_le__div__geq,axiom, % 167.45/167.40 ! [V_m,V_n] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.45/167.40 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_split__div__lemma,axiom, % 167.45/167.40 ! [V_m_2,V_q_2,V_n_2] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 167.45/167.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2)))) ) % 167.45/167.40 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_split__div_H,axiom, % 167.45/167.40 ! [V_n_2,V_m_2,V_P_2] : % 167.45/167.40 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 167.45/167.40 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.40 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 167.45/167.40 | ? [B_q] : % 167.45/167.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q)))) % 167.45/167.40 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_times__divide__times__eq,axiom, % 167.45/167.40 ! [V_w,V_z,V_y,V_x,T_a] : % 167.45/167.40 ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__right__mono__neg,axiom, % 167.45/167.40 ! [V_c,V_b,V_a,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__right__mono,axiom, % 167.45/167.40 ! [V_c,V_b,V_a,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__le__0__iff,axiom, % 167.45/167.40 ! [V_b_2,V_a_2,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 167.45/167.40 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zero__le__divide__iff,axiom, % 167.45/167.40 ! [V_b_2,V_a_2,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2))) % 167.45/167.40 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 167.45/167.40 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_zero__less__divide__iff,axiom, % 167.45/167.40 ! [V_b_2,V_a_2,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2))) % 167.45/167.40 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 167.45/167.40 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__less__0__iff,axiom, % 167.45/167.40 ! [V_b_2,V_a_2,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 167.45/167.40 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__pos__pos,axiom, % 167.45/167.40 ! [V_y,V_x,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__pos__neg,axiom, % 167.45/167.40 ! [V_y,V_x,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__neg__pos,axiom, % 167.45/167.40 ! [V_y,V_x,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__neg__neg,axiom, % 167.45/167.40 ! [V_y,V_x,T_a] : % 167.45/167.40 ( class_Fields_Olinordered__field(T_a) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 167.45/167.40 % 167.45/167.40 fof(fact_divide__strict__right__mono,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__strict__right__mono__neg,axiom, % 167.45/167.41 ! [V_c,V_a,V_b,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_frac__eq__eq,axiom, % 167.45/167.41 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] : % 167.45/167.41 ( class_Fields_Ofield(T_a) % 167.45/167.41 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w_2),V_z_2) % 167.45/167.41 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mult__divide__mult__cancel__left,axiom, % 167.45/167.41 ! [V_b,V_a,V_c,T_a] : % 167.45/167.41 ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.41 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mult__divide__mult__cancel__right,axiom, % 167.45/167.41 ! [V_b,V_a,V_c,T_a] : % 167.45/167.41 ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.41 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__eq__eq,axiom, % 167.45/167.41 ! [V_a_2,V_c_2,V_b_2,T_a] : % 167.45/167.41 ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.41 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2 % 167.45/167.41 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) % 167.45/167.41 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_eq__divide__eq,axiom, % 167.45/167.41 ! [V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.41 ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.41 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) % 167.45/167.41 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) % 167.45/167.41 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__nonneg__pos,axiom, % 167.45/167.41 ! [V_y,V_x,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__nonneg__neg,axiom, % 167.45/167.41 ! [V_y,V_x,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_frac__less2,axiom, % 167.45/167.41 ! [V_z,V_w,V_y,V_x,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_frac__less,axiom, % 167.45/167.41 ! [V_z,V_w,V_y,V_x,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_frac__le,axiom, % 167.45/167.41 ! [V_z,V_w,V_y,V_x,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__nonpos__pos,axiom, % 167.45/167.41 ! [V_y,V_x,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__nonpos__neg,axiom, % 167.45/167.41 ! [V_y,V_x,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__strict__left__mono__neg,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(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))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__strict__left__mono,axiom, % 167.45/167.41 ! [V_c,V_a,V_b,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(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))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_neg__divide__less__eq,axiom, % 167.45/167.41 ! [V_a_2,V_b_2,V_c_2,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_neg__less__divide__eq,axiom, % 167.45/167.41 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mult__imp__less__div__pos,axiom, % 167.45/167.41 ! [V_x,V_z,V_y,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mult__imp__div__pos__less,axiom, % 167.45/167.41 ! [V_z,V_x,V_y,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_pos__divide__less__eq,axiom, % 167.45/167.41 ! [V_a_2,V_b_2,V_c_2,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_pos__less__divide__eq,axiom, % 167.45/167.41 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__less__eq,axiom, % 167.45/167.41 ! [V_a_2,V_c_2,V_b_2,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 167.45/167.41 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 167.45/167.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.41 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 167.45/167.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_less__divide__eq,axiom, % 167.45/167.41 ! [V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 167.45/167.41 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 167.45/167.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.41 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 167.45/167.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_add__frac__eq,axiom, % 167.45/167.41 ! [V_w,V_x,V_z,V_y,T_a] : % 167.45/167.41 ( class_Fields_Ofield(T_a) % 167.45/167.41 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__add__eq__iff,axiom, % 167.45/167.41 ! [V_y,V_x,V_z,T_a] : % 167.45/167.41 ( class_Fields_Ofield(T_a) % 167.45/167.41 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_add__frac__num,axiom, % 167.45/167.41 ! [V_z,V_x,V_y,T_a] : % 167.45/167.41 ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.41 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_add__divide__eq__iff,axiom, % 167.45/167.41 ! [V_y,V_x,V_z,T_a] : % 167.45/167.41 ( class_Fields_Ofield(T_a) % 167.45/167.41 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_add__num__frac,axiom, % 167.45/167.41 ! [V_x,V_z,V_y,T_a] : % 167.45/167.41 ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.41 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_diff__divide__eq__iff,axiom, % 167.45/167.41 ! [V_y,V_x,V_z,T_a] : % 167.45/167.41 ( class_Fields_Ofield(T_a) % 167.45/167.41 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__diff__eq__iff,axiom, % 167.45/167.41 ! [V_y,V_x,V_z,T_a] : % 167.45/167.41 ( class_Fields_Ofield(T_a) % 167.45/167.41 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_diff__frac__eq,axiom, % 167.45/167.41 ! [V_w,V_x,V_z,V_y,T_a] : % 167.45/167.41 ( class_Fields_Ofield(T_a) % 167.45/167.41 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_gt__half__sum,axiom, % 167.45/167.41 ! [V_b,V_a,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_less__half__sum,axiom, % 167.45/167.41 ! [V_b,V_a,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__left__mono__neg,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(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))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_divide__left__mono,axiom, % 167.45/167.41 ! [V_c,V_a,V_b,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(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))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_neg__divide__le__eq,axiom, % 167.45/167.41 ! [V_a_2,V_b_2,V_c_2,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_neg__le__divide__eq,axiom, % 167.45/167.41 ! [V_b_2,V_a_2,V_c_2,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_nat__aux__def,axiom, % 167.45/167.41 ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 167.45/167.41 ! [V_B_2,V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 167.45/167.41 ! [V_B_2,V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__morphism__nat__int,axiom, % 167.45/167.41 c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 167.45/167.41 ! [V_f_2,V_A_2,T_a] : % 167.45/167.41 ( ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.41 & class_Groups_Ocomm__monoid__mult(T_a) ) % 167.45/167.41 => ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setprod__Un,axiom, % 167.45/167.41 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 167.45/167.41 ( class_Fields_Ofield(T_b) % 167.45/167.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.41 => ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.45/167.41 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) ) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 167.45/167.41 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 167.45/167.41 ! [V_B_2,V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.45/167.41 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 167.45/167.41 ! [V_B_2,V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.45/167.41 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_nat__set__def,axiom, % 167.45/167.41 ! [V_S_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_S_2) % 167.45/167.41 <=> ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 167.45/167.41 ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 167.45/167.41 ! [V_B_2,V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.45/167.41 => ( V_A_2 = V_B_2 % 167.45/167.41 <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 167.45/167.41 ! [V_x_2,V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__nat__int__set__return__embed,axiom, % 167.45/167.41 ! [V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 167.45/167.41 ! [V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 167.45/167.41 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 167.45/167.41 ! [V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 167.45/167.41 ! [V_B_2,V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 167.45/167.41 ! [V_B_2,V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 167.45/167.41 ! [V_f_2,V_A_2,T_a] : % 167.45/167.41 ( ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.41 & class_Groups_Ocomm__monoid__mult(T_a) ) % 167.45/167.41 => ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 167.45/167.41 ! [V_A_2,V_x_2] : % 167.45/167.41 ( c_Nat__Transfer_Ois__nat(V_x_2) % 167.45/167.41 => ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I4_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__nonneg__leq__bound,axiom, % 167.45/167.41 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add(T_b) % 167.45/167.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 167.45/167.41 => ( ! [B_i] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 167.45/167.41 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2 % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_greaterThan__0,axiom, % 167.45/167.41 hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_sum__diff__distrib,axiom, % 167.45/167.41 ! [V_n_2,V_P_2,V_Q_2] : % 167.45/167.41 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x))) % 167.45/167.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_finite__greaterThanAtMost,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_finite__greaterThanAtMost__int,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_greaterThan__eq__iff,axiom, % 167.45/167.41 ! [V_y_2,V_x_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) % 167.45/167.41 <=> V_x_2 = V_y_2 ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I11_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I5_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 167.45/167.41 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 167.45/167.41 ! [V_y,V_x] : % 167.45/167.41 ( c_Nat__Transfer_Ois__nat(V_x) % 167.45/167.41 => ( c_Nat__Transfer_Ois__nat(V_y) % 167.45/167.41 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 167.45/167.41 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 167.45/167.41 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 167.45/167.41 ! [V_y,V_x] : % 167.45/167.41 ( c_Nat__Transfer_Ois__nat(V_x) % 167.45/167.41 => ( c_Nat__Transfer_Ois__nat(V_y) % 167.45/167.41 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 167.45/167.41 ! [V_y,V_x] : % 167.45/167.41 ( c_Nat__Transfer_Ois__nat(V_x) % 167.45/167.41 => ( c_Nat__Transfer_Ois__nat(V_y) % 167.45/167.41 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 167.45/167.41 ! [V_n,V_x] : % 167.45/167.41 ( c_Nat__Transfer_Ois__nat(V_x) % 167.45/167.41 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 167.45/167.41 ! [V_y,V_x] : % 167.45/167.41 ( c_Nat__Transfer_Ois__nat(V_x) % 167.45/167.41 => ( c_Nat__Transfer_Ois__nat(V_y) % 167.45/167.41 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_greaterThanAtMost__empty,axiom, % 167.45/167.41 ! [V_k_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 167.45/167.41 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_greaterThanAtMost__empty__iff,axiom, % 167.45/167.41 ! [V_l_2,V_k_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.41 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 167.45/167.41 ! [V_l_2,V_k_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) % 167.45/167.41 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I20_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_is__nat__def,axiom, % 167.45/167.41 ! [V_x_2] : % 167.45/167.41 ( c_Nat__Transfer_Ois__nat(V_x_2) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I14_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_card__greaterThanAtMost,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_greaterThan__iff,axiom, % 167.45/167.41 ! [V_k_2,V_i_2,T_a] : % 167.45/167.41 ( class_Orderings_Oord(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_greaterThan__subset__iff,axiom, % 167.45/167.41 ! [V_y_2,V_x_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2))) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 167.45/167.41 ! [V_x_2,V_A_2] : % 167.45/167.41 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 167.45/167.41 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_INT__greaterThan__UNIV,axiom, % 167.45/167.41 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I10_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_card__greaterThanAtMost__int,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_greaterThan__Suc,axiom, % 167.45/167.41 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I16_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 167.45/167.41 ! [V_f_2,V_A_2,T_a] : % 167.45/167.41 ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.41 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 167.45/167.41 ! [V_f_2,V_A_2,T_a] : % 167.45/167.41 ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.41 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__natinterval__difff,axiom, % 167.45/167.41 ! [V_f_2,V_n_2,V_m_2,T_a] : % 167.45/167.41 ( class_Groups_Oab__group__add(T_a) % 167.45/167.41 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 167.45/167.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_gauss__sum,axiom, % 167.45/167.41 ! [V_n_2,T_a] : % 167.45/167.41 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Groups_Oone__class_Oone(T_a))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I12_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_finite__atLeastAtMost,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeast__eq__iff,axiom, % 167.45/167.41 ! [V_y_2,V_x_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) % 167.45/167.41 <=> V_x_2 = V_y_2 ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I13_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ex__nat__less,axiom, % 167.45/167.41 ! [V_P_2,V_n_2] : % 167.45/167.41 ( ? [B_m] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 167.45/167.41 & hBOOL(hAPP(V_P_2,B_m)) ) % 167.45/167.41 <=> ? [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 167.45/167.41 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_all__nat__less,axiom, % 167.45/167.41 ! [V_P_2,V_n_2] : % 167.45/167.41 ( ! [B_m] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 167.45/167.41 => hBOOL(hAPP(V_P_2,B_m)) ) % 167.45/167.41 <=> ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 167.45/167.41 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastatMost__empty__iff2,axiom, % 167.45/167.41 ! [V_b_2,V_a_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) % 167.45/167.41 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastatMost__empty__iff,axiom, % 167.45/167.41 ! [V_b_2,V_a_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.41 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastatMost__empty,axiom, % 167.45/167.41 ! [V_a_2,V_b_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) % 167.45/167.41 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastatMost__subset__iff,axiom, % 167.45/167.41 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))) % 167.45/167.41 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 167.45/167.41 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) % 167.45/167.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastAtMost__singleton,axiom, % 167.45/167.41 ! [V_a_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastAtMost__singleton__iff,axiom, % 167.45/167.41 ! [V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.41 <=> ( V_a_2 = V_b_2 % 167.45/167.41 & V_b_2 = V_c_2 ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastAtMost__singleton_H,axiom, % 167.45/167.41 ! [V_b_2,V_a_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( V_a_2 = V_b_2 % 167.45/167.41 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_image__Suc__atLeastAtMost,axiom, % 167.45/167.41 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 167.45/167.41 ! [V_n_2,V_m_2,V_f_2,T_a] : % 167.45/167.41 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 167.45/167.41 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 167.45/167.41 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_image__add__atLeastAtMost,axiom, % 167.45/167.41 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeast__iff,axiom, % 167.45/167.41 ! [V_k_2,V_i_2,T_a] : % 167.45/167.41 ( class_Orderings_Oord(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeast__subset__iff,axiom, % 167.45/167.41 ! [V_y_2,V_x_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2))) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeast__0,axiom, % 167.45/167.41 hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_card__atLeastAtMost,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastAtMostSuc__conv,axiom, % 167.45/167.41 ! [V_n_2,V_m_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 167.45/167.41 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__head,axiom, % 167.45/167.41 ! [V_P_2,V_n_2,V_m_2,T_a] : % 167.45/167.41 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 167.45/167.41 ! [V_k_2,V_f_2] : % 167.45/167.41 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeast__Suc__greaterThan,axiom, % 167.45/167.41 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I21_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I15_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastatMost__psubset__iff,axiom, % 167.45/167.41 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))) % 167.45/167.41 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 167.45/167.41 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) % 167.45/167.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) % 167.45/167.41 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_a_2)) % 167.45/167.41 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) ) % 167.45/167.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I22_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I4_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I16_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I12_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I13_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I7_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__head__Suc,axiom, % 167.45/167.41 ! [V_f_2,V_n_2,V_m_2,T_a] : % 167.45/167.41 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I14_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I8_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_UN__atLeast__UNIV,axiom, % 167.45/167.41 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I6_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeast__Suc,axiom, % 167.45/167.41 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__cl__ivl__Suc,axiom, % 167.45/167.41 ! [V_f_2,V_m_2,V_n_2,T_a] : % 167.45/167.41 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.41 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_a) ) % 167.45/167.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__ub__add__nat,axiom, % 167.45/167.41 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] : % 167.45/167.41 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I6_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I5_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I18_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I1_J,axiom, % 167.45/167.41 ! [V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I19_J,axiom, % 167.45/167.41 ! [V_u_2,V_m_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_UN__le__eq__Un0,axiom, % 167.45/167.41 ! [V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_decr__mult__lemma,axiom, % 167.45/167.41 ! [V_k_2,V_P_2,V_d_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 167.45/167.41 => ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.41 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.41 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_incr__mult__lemma,axiom, % 167.45/167.41 ! [V_k_2,V_P_2,V_d_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 167.45/167.41 => ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.41 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.41 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ex__least__nat__less,axiom, % 167.45/167.41 ! [V_n_2,V_P_2] : % 167.45/167.41 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 167.45/167.41 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 167.45/167.41 => ? [B_k] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 167.45/167.41 & ! [B_i] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 167.45/167.41 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 167.45/167.41 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setprod__mono__one__right,axiom, % 167.45/167.41 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 167.45/167.41 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.45/167.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 167.45/167.41 => ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 167.45/167.41 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_finite__atLeastAtMost__int,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_finite__atMost,axiom, % 167.45/167.41 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atMost__eq__iff,axiom, % 167.45/167.41 ! [V_y_2,V_x_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) % 167.45/167.41 <=> V_x_2 = V_y_2 ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 167.45/167.41 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 167.45/167.41 ! [V_y_2,V_x_2] : % 167.45/167.41 ( c_Nat__Transfer_Ois__nat(V_x_2) % 167.45/167.41 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeast0AtMost,axiom, % 167.45/167.41 ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_lessThan__Suc__atMost,axiom, % 167.45/167.41 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_card__atMost,axiom, % 167.45/167.41 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atMost__Suc,axiom, % 167.45/167.41 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atMost__iff,axiom, % 167.45/167.41 ! [V_k_2,V_i_2,T_a] : % 167.45/167.41 ( class_Orderings_Oord(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atMost__subset__iff,axiom, % 167.45/167.41 ! [V_y_2,V_x_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2))) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 167.45/167.41 ! [V_y_2,V_x_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 167.45/167.41 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_UN__atMost__UNIV,axiom, % 167.45/167.41 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 167.45/167.41 ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__atMost__Suc,axiom, % 167.45/167.41 ! [V_n_2,V_f_2,T_a] : % 167.45/167.41 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atMost__0,axiom, % 167.45/167.41 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_simp__from__to,axiom, % 167.45/167.41 ! [V_i_2,V_j_2] : % 167.45/167.41 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 167.45/167.41 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) ) % 167.45/167.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 167.45/167.41 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I9_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_UN__le__add__shift,axiom, % 167.45/167.41 ! [V_k_2,V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I3_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__int_I1_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_card__atLeastAtMost__int,axiom, % 167.45/167.41 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 167.45/167.41 ! [V_n_2,V_m_2] : % 167.45/167.41 ( c_Nat__Transfer_Ois__nat(V_m_2) % 167.45/167.41 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 167.45/167.41 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I2_J,axiom, % 167.45/167.41 ! [V_u_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I10_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_atMost__Int__atLeast,axiom, % 167.45/167.41 ! [V_n_2,T_a] : % 167.45/167.41 ( class_Orderings_Oorder(T_a) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_ivl__disj__un_I7_J,axiom, % 167.45/167.41 ! [V_u_2,V_l_2,T_a] : % 167.45/167.41 ( class_Orderings_Olinorder(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_aset_I6_J,axiom, % 167.45/167.41 ! [V_A_2,V_t_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xb] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 167.45/167.41 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_bset_I8_J,axiom, % 167.45/167.41 ! [V_B_2,V_t_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xb] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 167.45/167.41 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_aset_I4_J,axiom, % 167.45/167.41 ! [V_A_2,V_t_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xb] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 167.45/167.41 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 167.45/167.41 => ( B_x != V_t_2 % 167.45/167.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_bset_I4_J,axiom, % 167.45/167.41 ! [V_B_2,V_t_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xb] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 167.45/167.41 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 167.45/167.41 => ( B_x != V_t_2 % 167.45/167.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_bset_I7_J,axiom, % 167.45/167.41 ! [V_B_2,V_t_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xb] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 167.45/167.41 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_bset_I3_J,axiom, % 167.45/167.41 ! [V_B_2,V_t_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 167.45/167.41 => ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 167.45/167.41 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 167.45/167.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_aset_I3_J,axiom, % 167.45/167.41 ! [V_A_2,V_t_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 167.45/167.41 => ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 167.45/167.41 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 167.45/167.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_aset_I5_J,axiom, % 167.45/167.41 ! [V_A_2,V_t_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xb] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 167.45/167.41 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_bset_I6_J,axiom, % 167.45/167.41 ! [V_t_2,V_B_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xb] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 167.45/167.41 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_aset_I8_J,axiom, % 167.45/167.41 ! [V_t_2,V_A_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xb] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 167.45/167.41 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_periodic__finite__ex,axiom, % 167.45/167.41 ! [V_P_2,V_d_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 167.45/167.41 => ( ! [B_x,B_k] : % 167.45/167.41 ( hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.41 <=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) ) % 167.45/167.41 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 167.45/167.41 <=> ? [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) % 167.45/167.41 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_bset_I5_J,axiom, % 167.45/167.41 ! [V_t_2,V_B_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xb] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 167.45/167.41 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_aset_I7_J,axiom, % 167.45/167.41 ! [V_t_2,V_A_2,V_D_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 167.45/167.41 => ! [B_x] : % 167.45/167.41 ( ! [B_xa] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 167.45/167.41 => ! [B_xb] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 167.45/167.41 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setprod__mono__one__left,axiom, % 167.45/167.41 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 167.45/167.41 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.45/167.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 167.45/167.41 => ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 167.45/167.41 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zero__less__imp__eq__int,axiom, % 167.45/167.41 ! [V_k] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 167.45/167.41 => ? [B_n] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 167.45/167.41 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__mono__zero__left,axiom, % 167.45/167.41 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 167.45/167.41 ( class_Groups_Ocomm__monoid__add(T_b) % 167.45/167.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 167.45/167.41 => ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 167.45/167.41 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__mono__zero__right,axiom, % 167.45/167.41 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 167.45/167.41 ( class_Groups_Ocomm__monoid__add(T_b) % 167.45/167.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 167.45/167.41 => ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 167.45/167.41 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_card__Pow,axiom, % 167.45/167.41 ! [V_A_2,T_a] : % 167.45/167.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.41 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_finite__subset__induct,axiom, % 167.45/167.41 ! [V_P_2,V_A_2,V_F_2,T_a] : % 167.45/167.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2)) % 167.45/167.41 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 167.45/167.41 => ( ! [B_a,B_F] : % 167.45/167.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 167.45/167.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F)) % 167.45/167.41 => ( hBOOL(hAPP(V_P_2,B_F)) % 167.45/167.41 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) ) % 167.45/167.41 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_field__le__mult__one__interval,axiom, % 167.45/167.41 ! [V_y,V_x,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.41 => ( ! [B_z] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y)) ) ) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_PowI,axiom, % 167.45/167.41 ! [V_B_2,V_A_2,T_a] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_image__Pow__surj,axiom, % 167.45/167.41 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 167.45/167.41 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2 % 167.45/167.41 => hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(c_Set_OPow(T_a),V_B_2) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Pow__top,axiom, % 167.45/167.41 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_A_2))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Union__Pow__eq,axiom, % 167.45/167.41 ! [V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_OPow(T_a),V_A_2)) = V_A_2 ). % 167.45/167.41 % 167.45/167.41 fof(fact_Cantors__paradox,axiom, % 167.45/167.41 ! [V_A_2,T_a] : % 167.45/167.41 ~ ? [B_f] : hAPP(c_Set_Oimage(T_a,tc_fun(T_a,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_a),V_A_2) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Pow__not__empty,axiom, % 167.45/167.41 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Pow__INT__eq,axiom, % 167.45/167.41 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Pow__bottom,axiom, % 167.45/167.41 ! [V_B_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Set_OPow(T_a),V_B_2))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_PowD,axiom, % 167.45/167.41 ! [V_B_2,V_A_2,T_a] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Pow__iff,axiom, % 167.45/167.41 ! [V_B_2,V_A_2,T_a] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Pow__mono,axiom, % 167.45/167.41 ! [V_B_2,V_A_2,T_a] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_finite__Pow__iff,axiom, % 167.45/167.41 ! [V_A_2,T_a] : % 167.45/167.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) % 167.45/167.41 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_subset__Pow__Union,axiom, % 167.45/167.41 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Pow__insert,axiom, % 167.45/167.41 ! [V_A_2,V_a_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_a),V_a_2)),hAPP(c_Set_OPow(T_a),V_A_2))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Pow__UNIV,axiom, % 167.45/167.41 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_UN__Pow__subset,axiom, % 167.45/167.41 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Pow__Int__eq,axiom, % 167.45/167.41 ! [V_B_2,V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2)) ). % 167.45/167.41 % 167.45/167.41 fof(fact_image__Pow__mono,axiom, % 167.45/167.41 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),V_B_2)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2))),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Pow__empty,axiom, % 167.45/167.41 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Un__Pow__subset,axiom, % 167.45/167.41 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Powp__Pow__eq,axiom, % 167.45/167.41 ! [V_x_2,V_A_2,T_a] : % 167.45/167.41 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2)) % 167.45/167.41 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_card__partition,axiom, % 167.45/167.41 ! [V_k_2,V_C_2,T_a] : % 167.45/167.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) % 167.45/167.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 167.45/167.41 => ( ! [B_c] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) % 167.45/167.41 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 ) % 167.45/167.41 => ( ! [B_c1] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) % 167.45/167.41 => ! [B_c2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) % 167.45/167.41 => ( B_c1 != B_c2 % 167.45/167.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 167.45/167.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 167.45/167.41 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 167.45/167.41 ( ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.41 & class_Groups_Ocomm__monoid__mult(T_a) ) % 167.45/167.41 => ( V_A_2 = V_B_2 % 167.45/167.41 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.45/167.41 => ( ! [B_x] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 167.45/167.41 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 167.45/167.41 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_split__neg__lemma,axiom, % 167.45/167.41 ! [V_n_2,V_P_2,V_k_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 167.45/167.41 <=> ! [B_i,B_j] : % 167.45/167.41 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 167.45/167.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.41 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 167.45/167.41 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_split__pos__lemma,axiom, % 167.45/167.41 ! [V_n_2,V_P_2,V_k_2] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 167.45/167.41 <=> ! [B_i,B_j] : % 167.45/167.41 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 167.45/167.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 167.45/167.41 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 167.45/167.41 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_incr__lemma,axiom, % 167.45/167.41 ! [V_x,V_z,V_d] : % 167.45/167.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__abs,axiom, % 167.45/167.41 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_setsum__abs__ge__zero,axiom, % 167.45/167.41 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__int__eq,axiom, % 167.45/167.41 ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__0,axiom, % 167.45/167.41 ! [V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__by__0,axiom, % 167.45/167.41 ! [V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__self,axiom, % 167.45/167.41 ! [V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__ge__self,axiom, % 167.45/167.41 ! [V_a,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__le__D1,axiom, % 167.45/167.41 ! [V_b,V_a,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__zero,axiom, % 167.45/167.41 ! [T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__eq__0,axiom, % 167.45/167.41 ! [V_a_2,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.41 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__add__cong,axiom, % 167.45/167.41 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 167.45/167.41 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zmod__simps_I1_J,axiom, % 167.45/167.41 ! [V_b,V_c,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zmod__simps_I2_J,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__add__eq,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__add__left__eq,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__add__right__eq,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__add__self1,axiom, % 167.45/167.41 ! [V_a,V_b,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__add__self2,axiom, % 167.45/167.41 ! [V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__mult__right__eq,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__mult__left__eq,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__mult__eq,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__mult__mult1,axiom, % 167.45/167.41 ! [V_b,V_a,V_c,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__mult__mult2,axiom, % 167.45/167.41 ! [V_b,V_c,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zmod__simps_I4_J,axiom, % 167.45/167.41 ! [V_b,V_c,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__mult__cong,axiom, % 167.45/167.41 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 167.45/167.41 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__add__abs,axiom, % 167.45/167.41 ! [V_b,V_a,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__mult,axiom, % 167.45/167.41 ! [V_b,V_a,T_a] : % 167.45/167.41 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.41 => hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__mult__self,axiom, % 167.45/167.41 ! [V_a,T_a] : % 167.45/167.41 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__mod__trivial,axiom, % 167.45/167.41 ! [V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Osemiring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__idempotent,axiom, % 167.45/167.41 ! [V_a,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__of__nat,axiom, % 167.45/167.41 ! [V_n,T_a] : % 167.45/167.41 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_power__abs,axiom, % 167.45/167.41 ! [V_n,V_a,T_a] : % 167.45/167.41 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.41 => hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__one,axiom, % 167.45/167.41 ! [T_a] : % 167.45/167.41 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zmod__zero,axiom, % 167.45/167.41 ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zmod__self,axiom, % 167.45/167.41 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__divide,axiom, % 167.45/167.41 ! [V_b,V_a,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__minus__commute,axiom, % 167.45/167.41 ! [V_b,V_a,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__diff__right__eq,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Oring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__diff__left__eq,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Oring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__diff__eq,axiom, % 167.45/167.41 ! [V_c,V_b,V_a,T_a] : % 167.45/167.41 ( class_Divides_Oring__div(T_a) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_mod__diff__cong,axiom, % 167.45/167.41 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 167.45/167.41 ( class_Divides_Oring__div(T_a) % 167.45/167.41 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 167.45/167.41 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 167.45/167.41 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zmod__zmult1__eq,axiom, % 167.45/167.41 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zmod__simps_I3_J,axiom, % 167.45/167.41 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zdiff__zmod__right,axiom, % 167.45/167.41 ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zdiff__zmod__left,axiom, % 167.45/167.41 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 167.45/167.41 % 167.45/167.41 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 167.45/167.41 ! [V_y,V_x] : % 167.45/167.41 ( c_Nat__Transfer_Ois__nat(V_x) % 167.45/167.41 => ( c_Nat__Transfer_Ois__nat(V_y) % 167.45/167.41 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zpower__zmod,axiom, % 167.45/167.41 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__setsum__abs,axiom, % 167.45/167.41 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__setprod,axiom, % 167.45/167.41 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.41 ( class_Fields_Olinordered__field(T_a) % 167.45/167.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__of__nonneg,axiom, % 167.45/167.41 ! [V_a,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__le__zero__iff,axiom, % 167.45/167.41 ! [V_a_2,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.41 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__ge__zero,axiom, % 167.45/167.41 ! [V_a,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__of__pos,axiom, % 167.45/167.41 ! [V_a,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_zero__less__abs__iff,axiom, % 167.45/167.41 ! [V_a_2,T_a] : % 167.45/167.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2))) % 167.45/167.41 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.41 % 167.45/167.41 fof(fact_abs__not__less__zero,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__mult__self2__is__0,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Divides_Osemiring__div(T_a) % 167.45/167.42 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__mult__self1__is__0,axiom, % 167.45/167.42 ! [V_a,V_b,T_a] : % 167.45/167.42 ( class_Divides_Osemiring__div(T_a) % 167.45/167.42 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__triangle__ineq,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__mult__less,axiom, % 167.45/167.42 ! [V_d,V_b,V_c,V_a,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__triangle__ineq3,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__triangle__ineq2,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__triangle__ineq2__sym,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__mult__self2,axiom, % 167.45/167.42 ! [V_c,V_b,V_a,T_a] : % 167.45/167.42 ( class_Divides_Osemiring__div(T_a) % 167.45/167.42 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__mult__self1,axiom, % 167.45/167.42 ! [V_b,V_c,V_a,T_a] : % 167.45/167.42 ( class_Divides_Osemiring__div(T_a) % 167.45/167.42 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__by__1,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Divides_Osemiring__div(T_a) % 167.45/167.42 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__div__trivial,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Divides_Osemiring__div(T_a) % 167.45/167.42 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_nonzero__abs__divide,axiom, % 167.45/167.42 ! [V_a,V_b,T_a] : % 167.45/167.42 ( class_Fields_Olinordered__field(T_a) % 167.45/167.42 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.42 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__le__nonneg__dividend,axiom, % 167.45/167.42 ! [V_k,V_m] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 167.45/167.42 ! [V_y,V_x] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_pos__mod__bound,axiom, % 167.45/167.42 ! [V_a,V_b] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__mod__bound,axiom, % 167.45/167.42 ! [V_a,V_b] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__zmult__eq__1,axiom, % 167.45/167.42 ! [V_n,V_m] : % 167.45/167.42 ( hAPP(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) % 167.45/167.42 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__eq__0__iff,axiom, % 167.45/167.42 ! [V_d_2,V_m_2] : % 167.45/167.42 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_DIVISION__BY__ZERO,axiom, % 167.45/167.42 ! [V_a] : % 167.45/167.42 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__zdiv__trivial,axiom, % 167.45/167.42 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zdiv__zadd1__eq,axiom, % 167.45/167.42 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__mult__pos,axiom, % 167.45/167.42 ! [V_y,V_x,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.45/167.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__eq__mult,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Rings_Oordered__ring__abs(T_a) % 167.45/167.42 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 167.45/167.42 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.45/167.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 167.45/167.42 => hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__diff__triangle__ineq,axiom, % 167.45/167.42 ! [V_d,V_c,V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__triangle__ineq4,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zero__le__power__abs,axiom, % 167.45/167.42 ! [V_n,V_a,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__div__pos,axiom, % 167.45/167.42 ! [V_x,V_y,T_a] : % 167.45/167.42 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.42 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_div__mod__equality,axiom, % 167.45/167.42 ! [V_c,V_b,V_a,T_a] : % 167.45/167.42 ( class_Divides_Osemiring__div(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_div__mod__equality2,axiom, % 167.45/167.42 ! [V_c,V_a,V_b,T_a] : % 167.45/167.42 ( class_Divides_Osemiring__div(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__div__equality,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Divides_Osemiring__div(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__div__equality2,axiom, % 167.45/167.42 ! [V_a,V_b,T_a] : % 167.45/167.42 ( class_Divides_Osemiring__div(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Divides_Osemiring__div(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zabs__less__one__iff,axiom, % 167.45/167.42 ! [V_z_2] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) % 167.45/167.42 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__neg__neg__trivial,axiom, % 167.45/167.42 ! [V_b,V_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__mod__conj,axiom, % 167.45/167.42 ! [V_a,V_b] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__mod__sign,axiom, % 167.45/167.42 ! [V_a,V_b] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__pos__pos__trivial,axiom, % 167.45/167.42 ! [V_b,V_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_pos__mod__conj,axiom, % 167.45/167.42 ! [V_a,V_b] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) % 167.45/167.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_pos__mod__sign,axiom, % 167.45/167.42 ! [V_a,V_b] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_nat__abs__mult__distrib,axiom, % 167.45/167.42 ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zero__le__zpower__abs,axiom, % 167.45/167.42 ! [V_n,V_x] : hBOOL(hAPP(hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__zdiv__equality,axiom, % 167.45/167.42 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zdiv__zmult1__eq,axiom, % 167.45/167.42 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zdiv__zmod__equality,axiom, % 167.45/167.42 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zdiv__zmod__equality2,axiom, % 167.45/167.42 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmult__div__cancel,axiom, % 167.45/167.42 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__zdiv__equality_H,axiom, % 167.45/167.42 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__pos__neg__trivial,axiom, % 167.45/167.42 ! [V_b,V_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zero__less__zpower__abs__iff,axiom, % 167.45/167.42 ! [V_n_2,V_x_2] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2))) % 167.45/167.42 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_split__zmod,axiom, % 167.45/167.42 ! [V_k_2,V_n_2,V_P_2] : % 167.45/167.42 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 167.45/167.42 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 167.45/167.42 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 167.45/167.42 => ! [B_i,B_j] : % 167.45/167.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 167.45/167.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 167.45/167.42 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 167.45/167.42 => hBOOL(hAPP(V_P_2,B_j)) ) ) % 167.45/167.42 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => ! [B_i,B_j] : % 167.45/167.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 167.45/167.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 167.45/167.42 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmult2__lemma__aux3,axiom, % 167.45/167.42 ! [V_q,V_b,V_r,V_c] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmult2__lemma__aux4,axiom, % 167.45/167.42 ! [V_q,V_b,V_r,V_c] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmult2__lemma__aux1,axiom, % 167.45/167.42 ! [V_q,V_r,V_b,V_c] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmult2__lemma__aux2,axiom, % 167.45/167.42 ! [V_q,V_r,V_b,V_c] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_divmod__int__rel__mod__eq,axiom, % 167.45/167.42 ! [V_y,V_q_1,V_b_1,V_a_1] : % 167.45/167.42 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y) % 167.45/167.42 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 167.45/167.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 167.45/167.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 167.45/167.42 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__zmult2__eq,axiom, % 167.45/167.42 ! [V_b,V_a,V_c] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_decr__lemma,axiom, % 167.45/167.42 ! [V_z,V_x,V_d] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 167.45/167.42 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 167.45/167.42 ( ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.42 & class_Groups_Ocomm__monoid__mult(T_a) ) % 167.45/167.42 => ( V_A_2 = V_B_2 % 167.45/167.42 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.45/167.42 => ( ! [B_x] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 167.45/167.42 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 167.45/167.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Inter__subset,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : % 167.45/167.42 ( ! [B_X] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) ) % 167.45/167.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_int__val__lemma,axiom, % 167.45/167.42 ! [V_k_2,V_f_2,V_n_2] : % 167.45/167.42 ( ! [B_i] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 167.45/167.42 => ? [B_i] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 167.45/167.42 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_nat0__intermed__int__val,axiom, % 167.45/167.42 ! [V_k_2,V_f_2,V_n_2] : % 167.45/167.42 ( ! [B_i] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 167.45/167.42 => ? [B_i] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 167.45/167.42 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_setprod__pos__nat,axiom, % 167.45/167.42 ! [V_f_2,V_S_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.45/167.42 => ( ! [B_x] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__less__eq__dividend,axiom, % 167.45/167.42 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__mult__distrib2,axiom, % 167.45/167.42 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(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)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__mult__distrib,axiom, % 167.45/167.42 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(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)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__less,axiom, % 167.45/167.42 ! [V_n,V_m] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 167.45/167.42 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__1,axiom, % 167.45/167.42 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__Suc,axiom, % 167.45/167.42 ! [V_n,V_m] : % 167.45/167.42 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.42 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__less__divisor,axiom, % 167.45/167.42 ! [V_m,V_n] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__eq__0__iff,axiom, % 167.45/167.42 ! [V_d_2,V_m_2] : % 167.45/167.42 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.42 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__geq,axiom, % 167.45/167.42 ! [V_n,V_m] : % 167.45/167.42 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__if,axiom, % 167.45/167.42 ! [V_n,V_m] : % 167.45/167.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 167.45/167.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__mult__self3,axiom, % 167.45/167.42 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ). % 167.45/167.42 % 167.45/167.42 fof(fact_le__mod__geq,axiom, % 167.45/167.42 ! [V_m,V_n] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__int,axiom, % 167.45/167.42 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 167.45/167.42 ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_div__add1__eq,axiom, % 167.45/167.42 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__le__divisor,axiom, % 167.45/167.42 ! [V_m,V_n] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__mult__self4,axiom, % 167.45/167.42 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__mult2__eq,axiom, % 167.45/167.42 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_div__mult1__eq,axiom, % 167.45/167.42 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_div__mod__equality_H,axiom, % 167.45/167.42 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mult__div__cancel,axiom, % 167.45/167.42 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Divides_Omod__div__equality_H,axiom, % 167.45/167.42 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__lemma,axiom, % 167.45/167.42 ! [V_q,V_b,V_r,V_c] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_split__mod,axiom, % 167.45/167.42 ! [V_k_2,V_n_2,V_P_2] : % 167.45/167.42 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 167.45/167.42 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.42 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 167.45/167.42 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.42 => ! [B_i,B_j] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 167.45/167.42 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) % 167.45/167.42 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Suc__times__mod__eq,axiom, % 167.45/167.42 ! [V_m,V_k] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_nat__mod__distrib,axiom, % 167.45/167.42 ! [V_y,V_x] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.42 => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 167.45/167.42 ! [V_y,V_x] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_card__less__Suc,axiom, % 167.45/167.42 ! [V_i_2,V_M_2] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 167.45/167.42 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_card__less,axiom, % 167.45/167.42 ! [V_i_2,V_M_2] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 167.45/167.42 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_card__less__Suc2,axiom, % 167.45/167.42 ! [V_i_2,V_M_2] : % 167.45/167.42 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 167.45/167.42 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_diff__nat__eq__if,axiom, % 167.45/167.42 ! [V_z_2,V_z_H_2] : % 167.45/167.42 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 167.45/167.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) ) % 167.45/167.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 167.45/167.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zdiv__zminus1__eq__if,axiom, % 167.45/167.42 ! [V_a,V_b] : % 167.45/167.42 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 167.45/167.42 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_CollectI,axiom, % 167.45/167.42 ! [T_a,V_a_2,V_P_2] : % 167.45/167.42 ( hBOOL(hAPP(V_P_2,V_a_2)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_finite__Collect__conjI,axiom, % 167.45/167.42 ! [V_Q_2,V_P_2,T_a] : % 167.45/167.42 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 167.45/167.42 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) % 167.45/167.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_negative__zle,axiom, % 167.45/167.42 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_finite__Collect__less__nat,axiom, % 167.45/167.42 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_finite__Collect__le__nat,axiom, % 167.45/167.42 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_negative__zless,axiom, % 167.45/167.42 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__minus__cong,axiom, % 167.45/167.42 ! [V_a_H,V_b,V_a,T_a] : % 167.45/167.42 ( class_Divides_Oring__div(T_a) % 167.45/167.42 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 167.45/167.42 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mod__minus__eq,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Divides_Oring__div(T_a) % 167.45/167.42 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__minus__cancel,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__zminus2,axiom, % 167.45/167.42 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__zminus__zminus,axiom, % 167.45/167.42 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zminus__zmod,axiom, % 167.45/167.42 ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zdiv__zminus2,axiom, % 167.45/167.42 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zdiv__zminus__zminus,axiom, % 167.45/167.42 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zminus__0,axiom, % 167.45/167.42 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.45/167.42 % 167.45/167.42 fof(fact_compl__eq__compl__iff,axiom, % 167.45/167.42 ! [V_y_2,V_x_2,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) % 167.45/167.42 <=> V_x_2 = V_y_2 ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_uminus__apply,axiom, % 167.45/167.42 ! [V_x_2,V_A_2,T_b,T_a] : % 167.45/167.42 ( class_Groups_Ouminus(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_double__compl,axiom, % 167.45/167.42 ! [V_x,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Collect__def,axiom, % 167.45/167.42 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ). % 167.45/167.42 % 167.45/167.42 fof(fact_fun__Compl__def,axiom, % 167.45/167.42 ! [V_x_2,V_A_2,T_b,T_a] : % 167.45/167.42 ( class_Groups_Ouminus(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__equal__iff__equal,axiom, % 167.45/167.42 ! [V_b_2,V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 167.45/167.42 <=> V_a_2 = V_b_2 ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__equation__iff,axiom, % 167.45/167.42 ! [V_b_2,V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2 % 167.45/167.42 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_equation__minus__iff,axiom, % 167.45/167.42 ! [V_b_2,V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 167.45/167.42 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__minus,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zminus__zminus,axiom, % 167.45/167.42 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__mult__right,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Rings_Oring(T_a) % 167.45/167.42 => hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__mult__left,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Rings_Oring(T_a) % 167.45/167.42 => hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__mult__commute,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Rings_Oring(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__mult__minus,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Rings_Oring(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_square__eq__iff,axiom, % 167.45/167.42 ! [V_b_2,V_a_2,T_a] : % 167.45/167.42 ( class_Rings_Oidom(T_a) % 167.45/167.42 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2) % 167.45/167.42 <=> ( V_a_2 = V_b_2 % 167.45/167.42 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__add__cancel,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_add__minus__cancel,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__add,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__add__distrib,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oab__group__add(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_less__minus__iff,axiom, % 167.45/167.42 ! [V_b_2,V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__less__iff,axiom, % 167.45/167.42 ! [V_b_2,V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__less__iff__less,axiom, % 167.45/167.42 ! [V_a_2,V_b_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__zminus__int,axiom, % 167.45/167.42 ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__zero,axiom, % 167.45/167.42 ! [T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__0__equal__iff__equal,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 167.45/167.42 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_equal__neg__zero,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.45/167.42 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 167.45/167.42 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__equal__0__iff__equal,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.42 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__equal__zero,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.45/167.42 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2 % 167.45/167.42 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_le__minus__iff,axiom, % 167.45/167.42 ! [V_b_2,V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__le__iff,axiom, % 167.45/167.42 ! [V_b_2,V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__le__iff__le,axiom, % 167.45/167.42 ! [V_a_2,V_b_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_le__imp__neg__le,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_compl__le__compl__iff,axiom, % 167.45/167.42 ! [V_y_2,V_x_2,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_compl__mono,axiom, % 167.45/167.42 ! [V_y,V_x,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_empty__Collect__eq,axiom, % 167.45/167.42 ! [V_P_2,T_a] : % 167.45/167.42 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2) % 167.45/167.42 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Collect__empty__eq,axiom, % 167.45/167.42 ! [V_P_2,T_a] : % 167.45/167.42 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__diff__eq,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oab__group__add(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__divide__right,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__divide__divide,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.42 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__divide__left,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Rings_Odivision__ring(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zminus__zadd__distrib,axiom, % 167.45/167.42 ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmult__zminus,axiom, % 167.45/167.42 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_not__neg__0,axiom, % 167.45/167.42 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_CollectE,axiom, % 167.45/167.42 ! [V_P_2,V_a_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 167.45/167.42 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_CollectD,axiom, % 167.45/167.42 ! [V_P_2,V_a_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 167.45/167.42 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_mem__Collect__eq,axiom, % 167.45/167.42 ! [V_P_2,V_a_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 167.45/167.42 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Collect__mem__eq,axiom, % 167.45/167.42 ! [V_A_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)) = V_A_2 ). % 167.45/167.42 % 167.45/167.42 fof(fact_empty__def,axiom, % 167.45/167.42 ! [T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_finite__Collect__disjI,axiom, % 167.45/167.42 ! [V_Q_2,V_P_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)))) % 167.45/167.42 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 167.45/167.42 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_not__neg__int,axiom, % 167.45/167.42 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_not__neg__1,axiom, % 167.45/167.42 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_insert__Collect,axiom, % 167.45/167.42 ! [V_P_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_UNIV__def,axiom, % 167.45/167.42 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fTrue)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Collect__disj__eq,axiom, % 167.45/167.42 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Collect__conj__eq,axiom, % 167.45/167.42 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_setsum__negf,axiom, % 167.45/167.42 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.42 ( class_Groups_Oab__group__add(T_a) % 167.45/167.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__le__self__iff,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__le__0__iff__le,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_le__minus__self__iff,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__0__le__iff__le,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_less__minus__self__iff,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__less__nonneg,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__less__0__iff__less,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__0__less__iff__less,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__unique,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_ab__left__minus,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Oab__group__add(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_left__minus,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_eq__neg__iff__add__eq__0,axiom, % 167.45/167.42 ! [V_b_2,V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 167.45/167.42 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_right__minus,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_diff__0,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_diff__minus__eq__add,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_ab__diff__minus,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oab__group__add(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_diff__def,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Ogroup__add(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 167.45/167.42 ! [V_y,V_x,T_a] : % 167.45/167.42 ( class_Rings_Ocomm__ring__1(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_square__eq__1__iff,axiom, % 167.45/167.42 ! [V_x_2,T_a] : % 167.45/167.42 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 167.45/167.42 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 167.45/167.42 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a) % 167.45/167.42 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 167.45/167.42 ! [V_x,T_a] : % 167.45/167.42 ( class_Rings_Ocomm__ring__1(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_compl__inf__bot,axiom, % 167.45/167.42 ! [V_x,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_inf__compl__bot,axiom, % 167.45/167.42 ! [V_x,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_diff__eq,axiom, % 167.45/167.42 ! [V_y,V_x,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_compl__top__eq,axiom, % 167.45/167.42 ! [T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_compl__bot__eq,axiom, % 167.45/167.42 ! [T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_compl__inf,axiom, % 167.45/167.42 ! [V_y,V_x,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_compl__sup,axiom, % 167.45/167.42 ! [V_y,V_x,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_sup__compl__top,axiom, % 167.45/167.42 ! [V_x,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_compl__sup__top,axiom, % 167.45/167.42 ! [V_x,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_nonzero__minus__divide__right,axiom, % 167.45/167.42 ! [V_a,V_b,T_a] : % 167.45/167.42 ( class_Rings_Odivision__ring(T_a) % 167.45/167.42 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_nonzero__minus__divide__divide,axiom, % 167.45/167.42 ! [V_a,V_b,T_a] : % 167.45/167.42 ( class_Rings_Odivision__ring(T_a) % 167.45/167.42 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.42 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__le__D2,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__leI,axiom, % 167.45/167.42 ! [V_b,V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__le__iff,axiom, % 167.45/167.42 ! [V_b_2,V_a_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 167.45/167.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 167.45/167.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__ge__minus__self,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__less__iff,axiom, % 167.45/167.42 ! [V_b_2,V_a_2,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 167.45/167.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 167.45/167.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_image__uminus__atLeastAtMost,axiom, % 167.45/167.42 ! [V_y_2,V_x_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__power__minus,axiom, % 167.45/167.42 ! [V_n,V_a,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zadd__zminus__inverse2,axiom, % 167.45/167.42 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.45/167.42 % 167.45/167.42 fof(fact_negative__eq__positive,axiom, % 167.45/167.42 ! [V_m_2,V_n_2] : % 167.45/167.42 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) % 167.45/167.42 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.42 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_not__int__zless__negative,axiom, % 167.45/167.42 ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__zminus2__not__zero,axiom, % 167.45/167.42 ! [V_l,V_k] : % 167.45/167.42 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__zminus1__not__zero,axiom, % 167.45/167.42 ! [V_l,V_k] : % 167.45/167.42 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_diff__int__def__symmetric,axiom, % 167.45/167.42 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) ). % 167.45/167.42 % 167.45/167.42 fof(fact_diff__int__def,axiom, % 167.45/167.42 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Ints__minus,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_image__uminus__greaterThanLessThan,axiom, % 167.45/167.42 ! [V_y_2,V_x_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_insert__compr__raw,axiom, % 167.45/167.42 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_insert__compr,axiom, % 167.45/167.42 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Un__def,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Int__Collect,axiom, % 167.45/167.42 ! [V_P_2,V_A_2,V_x_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))) % 167.45/167.42 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.42 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Int__def,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Collect__conv__if,axiom, % 167.45/167.42 ! [T_a,V_a_2,V_P_2] : % 167.45/167.42 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 167.45/167.42 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) % 167.45/167.42 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 167.45/167.42 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Collect__conv__if2,axiom, % 167.45/167.42 ! [T_a,V_a_2,V_P_2] : % 167.45/167.42 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 167.45/167.42 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) % 167.45/167.42 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 167.45/167.42 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_singleton__conv,axiom, % 167.45/167.42 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_singleton__conv2,axiom, % 167.45/167.42 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_set__diff__eq,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_finite__Collect__not,axiom, % 167.45/167.42 ! [V_P_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))) % 167.45/167.42 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_insert__def,axiom, % 167.45/167.42 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ). % 167.45/167.42 % 167.45/167.42 fof(fact_not__neg__eq__ge__0,axiom, % 167.45/167.42 ! [V_x_2] : % 167.45/167.42 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__def,axiom, % 167.45/167.42 ! [V_Z_2] : % 167.45/167.42 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_neg__nat,axiom, % 167.45/167.42 ! [V_z] : % 167.45/167.42 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 167.45/167.42 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_not__neg__nat,axiom, % 167.45/167.42 ! [V_z] : % 167.45/167.42 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 167.45/167.42 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_finite__M__bounded__by__nat,axiom, % 167.45/167.42 ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__minus__le__zero,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__of__nonpos,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.42 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__if,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Oabs__if(T_a) % 167.45/167.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.42 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 167.45/167.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.42 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_abs__of__neg,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.42 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_power__minus,axiom, % 167.45/167.42 ! [V_n,V_a,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(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),hAPP(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)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_int__zle__neg,axiom, % 167.45/167.42 ! [V_m_2,V_n_2] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))) % 167.45/167.42 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.42 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_negative__zle__0,axiom, % 167.45/167.42 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_nat__zminus__int,axiom, % 167.45/167.42 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__zminus2__eq__if,axiom, % 167.45/167.42 ! [V_b,V_a] : % 167.45/167.42 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.45/167.42 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zmod__zminus1__eq__if,axiom, % 167.45/167.42 ! [V_b,V_a] : % 167.45/167.42 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.45/167.42 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zabs__def,axiom, % 167.45/167.42 ! [V_i] : % 167.45/167.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 167.45/167.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_setsum__setsum__restrict,axiom, % 167.45/167.42 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] : % 167.45/167.42 ( class_Groups_Ocomm__monoid__add(T_c) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 167.45/167.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_c),tc_fun(tc_fun(T_a,tc_HOL_Obool),T_c),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c)),hAPP(c_COMBC(T_a,T_b,T_c),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_image__uminus__greaterThanAtMost,axiom, % 167.45/167.42 ! [V_y_2,V_x_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_image__uminus__atLeastLessThan,axiom, % 167.45/167.42 ! [V_y_2,V_x_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_if__image__distrib,axiom, % 167.45/167.42 ! [V_S_2,V_g_2,V_f_2,V_P_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Collect__all__eq,axiom, % 167.45/167.42 ! [V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),V_P_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_image__uminus__greaterThan,axiom, % 167.45/167.42 ! [V_x_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_image__uminus__lessThan,axiom, % 167.45/167.42 ! [V_x_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_image__uminus__atMost,axiom, % 167.45/167.42 ! [V_x_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_image__uminus__atLeast,axiom, % 167.45/167.42 ! [V_x_2,T_a] : % 167.45/167.42 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.42 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_nat__seg__image__imp__finite,axiom, % 167.45/167.42 ! [V_n_2,V_f_2,T_a,V_A_2] : % 167.45/167.42 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2))) % 167.45/167.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_compl__unique,axiom, % 167.45/167.42 ! [V_y,V_x,T_a] : % 167.45/167.42 ( class_Lattices_Oboolean__algebra(T_a) % 167.45/167.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 167.45/167.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_not__zle__0__negative,axiom, % 167.45/167.42 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_negative__zless__0,axiom, % 167.45/167.42 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_setsum__restrict__set_H,axiom, % 167.45/167.42 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 167.45/167.42 ( class_Groups_Ocomm__monoid__add(T_b) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_setsum__image__gen,axiom, % 167.45/167.42 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] : % 167.45/167.42 ( class_Groups_Ocomm__monoid__add(T_b) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.45/167.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),T_b,T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_a),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_S_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_nat__mult__distrib__neg,axiom, % 167.45/167.42 ! [V_z_H,V_z] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_zdiv__zminus2__eq__if,axiom, % 167.45/167.42 ! [V_a,V_b] : % 167.45/167.42 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 167.45/167.42 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.42 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_dom__if,axiom, % 167.45/167.42 ! [V_g_2,V_f_2,V_P_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_a),c_If(tc_Option_Ooption(T_b))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_g_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_z3div__def,axiom, % 167.45/167.42 ! [V_k,V_l] : % 167.45/167.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 167.45/167.42 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 167.45/167.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 167.45/167.42 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_z3mod__def,axiom, % 167.45/167.42 ! [V_k,V_l] : % 167.45/167.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 167.45/167.42 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 167.45/167.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 167.45/167.42 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_dom__override__on,axiom, % 167.45/167.42 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Fun_Ooverride__on(T_a,tc_Option_Ooption(T_b),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2)))))),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2))))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_setsum__multicount,axiom, % 167.45/167.42 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 167.45/167.42 => ( ! [B_x] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) % 167.45/167.42 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 ) % 167.45/167.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_T_2)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_ComplI,axiom, % 167.45/167.42 ! [V_A_2,V_c_2,T_a] : % 167.45/167.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_finite__Collect__subsets,axiom, % 167.45/167.42 ! [V_A_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__subset__Compl__iff,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__anti__mono,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__iff,axiom, % 167.45/167.42 ! [V_A_2,V_c_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 167.45/167.42 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_ComplD,axiom, % 167.45/167.42 ! [V_A_2,V_c_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 167.45/167.42 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_ComplE,axiom, % 167.45/167.42 ! [V_A_2,V_c_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 167.45/167.42 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Collect__neg__eq,axiom, % 167.45/167.42 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_subset__Compl__self__eq,axiom, % 167.45/167.42 ! [V_A_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 167.45/167.42 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__empty__eq,axiom, % 167.45/167.42 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__UNIV__eq,axiom, % 167.45/167.42 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_finite__compl,axiom, % 167.45/167.42 ! [V_A_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 167.45/167.42 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__disjoint,axiom, % 167.45/167.42 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__disjoint2,axiom, % 167.45/167.42 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__partition2,axiom, % 167.45/167.42 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__partition,axiom, % 167.45/167.42 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__Un,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__Int,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__eq__Diff__UNIV,axiom, % 167.45/167.42 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_A_2) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__Diff__eq,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Diff__eq,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Diff__Compl,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__eq,axiom, % 167.45/167.42 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__lessThan,axiom, % 167.45/167.42 ! [V_k_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__atLeast,axiom, % 167.45/167.42 ! [V_k_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Collect__imp__eq,axiom, % 167.45/167.42 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__atMost,axiom, % 167.45/167.42 ! [V_k_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__greaterThan,axiom, % 167.45/167.42 ! [V_k_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Pow__def,axiom, % 167.45/167.42 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__UN,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__INT,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 167.45/167.42 % 167.45/167.42 fof(fact_disjoint__eq__subset__Compl,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : % 167.45/167.42 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_surj__Compl__image__subset,axiom, % 167.45/167.42 ! [V_A_2,V_f_2,T_a,T_b] : % 167.45/167.42 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_override__on__apply__in,axiom, % 167.45/167.42 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.42 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_override__on__apply__notin,axiom, % 167.45/167.42 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 167.45/167.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.42 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_override__on__emptyset,axiom, % 167.45/167.42 ! [V_g_2,V_f_2,T_b,T_a] : c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_f_2 ). % 167.45/167.42 % 167.45/167.42 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 167.45/167.42 ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_override__on__def,axiom, % 167.45/167.42 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 167.45/167.42 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.42 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) % 167.45/167.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.42 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_setsum__cases,axiom, % 167.45/167.42 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] : % 167.45/167.42 ( class_Groups_Ocomm__monoid__add(T_b) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 167.45/167.42 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 167.45/167.42 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_setsum__multicount__gen,axiom, % 167.45/167.42 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2)) % 167.45/167.42 => ( ! [B_x] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) % 167.45/167.42 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_s_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) ) % 167.45/167.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__of__nat,axiom, % 167.45/167.42 ! [V_k,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) ) % 167.45/167.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_inf__Sup1__distrib,axiom, % 167.45/167.42 ! [V_x_2,V_A_2,T_a] : % 167.45/167.42 ( class_Lattices_Odistrib__lattice(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_inf__Sup2__distrib,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : % 167.45/167.42 ( class_Lattices_Odistrib__lattice(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Compl__eq__Compl__iff,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : % 167.45/167.42 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2) % 167.45/167.42 <=> V_A_2 = V_B_2 ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_double__complement,axiom, % 167.45/167.42 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = V_A_2 ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__int__eq,axiom, % 167.45/167.42 ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__eq__iff,axiom, % 167.45/167.42 ! [V_z_2,V_w_2,T_a] : % 167.45/167.42 ( class_Int_Oring__char__0(T_a) % 167.45/167.42 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 167.45/167.42 <=> V_w_2 = V_z_2 ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__eq__0__iff,axiom, % 167.45/167.42 ! [V_z_2,T_a] : % 167.45/167.42 ( class_Int_Oring__char__0(T_a) % 167.45/167.42 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.42 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__0__eq__iff,axiom, % 167.45/167.42 ! [V_z_2,T_a] : % 167.45/167.42 ( class_Int_Oring__char__0(T_a) % 167.45/167.42 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 167.45/167.42 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__0,axiom, % 167.45/167.42 ! [T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__le__iff,axiom, % 167.45/167.42 ! [V_z_2,V_w_2,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__less__iff,axiom, % 167.45/167.42 ! [V_z_2,V_w_2,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__add,axiom, % 167.45/167.42 ! [V_z,V_w,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__mult,axiom, % 167.45/167.42 ! [V_z,V_w,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__1,axiom, % 167.45/167.42 ! [T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__diff,axiom, % 167.45/167.42 ! [V_z,V_w,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__of__nat__eq,axiom, % 167.45/167.42 ! [V_n,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__minus,axiom, % 167.45/167.42 ! [V_z,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_finite__image__set,axiom, % 167.45/167.42 ! [V_f_2,T_b,V_P_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 167.45/167.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_a)),c_fequal)),V_f_2)))),V_P_2))))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_finite__Collect__bounded__ex,axiom, % 167.45/167.42 ! [V_Q_2,T_b,V_P_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))))) % 167.45/167.42 <=> ! [B_y] : % 167.45/167.42 ( hBOOL(hAPP(V_P_2,B_y)) % 167.45/167.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Ints__of__int,axiom, % 167.45/167.42 ! [V_z_2,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__power,axiom, % 167.45/167.42 ! [V_n,V_z,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Pow__Compl,axiom, % 167.45/167.42 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_a))))) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__setsum,axiom, % 167.45/167.42 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__setprod,axiom, % 167.45/167.42 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.42 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 167.45/167.42 & class_Rings_Oring__1(T_a) ) % 167.45/167.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__0__le__iff,axiom, % 167.45/167.42 ! [V_z_2,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__le__0__iff,axiom, % 167.45/167.42 ! [V_z_2,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__less__0__iff,axiom, % 167.45/167.42 ! [V_z_2,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__int__0__less__iff,axiom, % 167.45/167.42 ! [V_z_2,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_of__nat__nat,axiom, % 167.45/167.42 ! [V_z,T_a] : % 167.45/167.42 ( class_Rings_Oring__1(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.45/167.42 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_sup__Inf2__distrib,axiom, % 167.45/167.42 ! [V_B_2,V_A_2,T_a] : % 167.45/167.42 ( class_Lattices_Odistrib__lattice(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_sup__Inf1__distrib,axiom, % 167.45/167.42 ! [V_x_2,V_A_2,T_a] : % 167.45/167.42 ( class_Lattices_Odistrib__lattice(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_add__Min__commute,axiom, % 167.45/167.42 ! [V_k_2,V_N_2,T_a] : % 167.45/167.42 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.45/167.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_add__Max__commute,axiom, % 167.45/167.42 ! [V_k_2,V_N_2,T_a] : % 167.45/167.42 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.45/167.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_negD,axiom, % 167.45/167.42 ! [V_x] : % 167.45/167.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.42 => ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_finite__conv__nat__seg__image,axiom, % 167.45/167.42 ! [V_A_2,T_a] : % 167.45/167.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__Min__eq__Max,axiom, % 167.45/167.42 ! [V_S_2,T_a] : % 167.45/167.42 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.45/167.42 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_minus__Max__eq__Min,axiom, % 167.45/167.42 ! [V_S_2,T_a] : % 167.45/167.42 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.45/167.42 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Min_Osingleton,axiom, % 167.45/167.42 ! [V_x_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Max_Osingleton,axiom, % 167.45/167.42 ! [V_x_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Max__ge,axiom, % 167.45/167.42 ! [V_x_2,V_A_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2))) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Min__le,axiom, % 167.45/167.42 ! [V_x_2,V_A_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_x_2)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Max__in,axiom, % 167.45/167.42 ! [V_A_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Min__in,axiom, % 167.45/167.42 ! [V_A_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Min__antimono,axiom, % 167.45/167.42 ! [V_N_2,V_M_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 167.45/167.42 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_M_2))) ) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Max__mono,axiom, % 167.45/167.42 ! [V_N_2,V_M_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 167.45/167.42 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.45/167.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2))) ) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_sgn__1__neg,axiom, % 167.45/167.42 ! [V_a_2,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) % 167.45/167.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_sgn__neg,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.42 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_sgn__if,axiom, % 167.45/167.42 ! [V_x,T_a] : % 167.45/167.42 ( class_Groups_Osgn__if(T_a) % 167.45/167.42 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.42 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 167.45/167.42 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.45/167.42 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 167.45/167.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.45/167.42 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Min_Oremove,axiom, % 167.45/167.42 ! [V_x_2,V_A_2,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.42 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) % 167.45/167.42 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.42 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 167.45/167.42 ! [T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_sgn__sgn,axiom, % 167.45/167.42 ! [V_a,T_a] : % 167.45/167.42 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.42 => 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) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_Min_Oidem,axiom, % 167.45/167.42 ! [V_x,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_min__max_Oinf__assoc,axiom, % 167.45/167.42 ! [V_z,V_y,V_x,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_min__max_Oinf_Oassoc,axiom, % 167.45/167.42 ! [V_c,V_b,V_a,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.42 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ). % 167.45/167.42 % 167.45/167.42 fof(fact_min__max_Oinf__left__commute,axiom, % 167.45/167.42 ! [V_z,V_y,V_x,T_a] : % 167.45/167.42 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 167.45/167.43 ! [V_c,V_a,V_b,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__left__idem,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 167.45/167.43 ! [V_b,V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__commute,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf_Ocommute,axiom, % 167.45/167.43 ! [V_b,V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf_Oidem,axiom, % 167.45/167.43 ! [V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__add__distrib__left,axiom, % 167.45/167.43 ! [V_z,V_y,V_x,T_a] : % 167.45/167.43 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__less__iff__conj,axiom, % 167.45/167.43 ! [V_y_2,V_x_2,V_z_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2))) % 167.45/167.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__less__iff__disj,axiom, % 167.45/167.43 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) % 167.45/167.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 167.45/167.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oless__infI1,axiom, % 167.45/167.43 ! [V_b,V_x,V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oless__infI2,axiom, % 167.45/167.43 ! [V_a,V_x,V_b,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__le__iff__disj,axiom, % 167.45/167.43 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) % 167.45/167.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 167.45/167.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__le1,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__le2,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__iff__inf,axiom, % 167.45/167.43 ! [V_y_2,V_x_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.45/167.43 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__inf__iff,axiom, % 167.45/167.43 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y_2),V_z_2))) % 167.45/167.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__infI1,axiom, % 167.45/167.43 ! [V_b,V_x,V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__infI2,axiom, % 167.45/167.43 ! [V_a,V_x,V_b,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__absorb1,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__absorb2,axiom, % 167.45/167.43 ! [V_x,V_y,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__infI,axiom, % 167.45/167.43 ! [V_b,V_a,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__greatest,axiom, % 167.45/167.43 ! [V_z,V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__mono,axiom, % 167.45/167.43 ! [V_d,V_b,V_c,V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__infE,axiom, % 167.45/167.43 ! [V_b,V_a,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) % 167.45/167.43 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.45/167.43 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__Suc__Suc,axiom, % 167.45/167.43 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__0L,axiom, % 167.45/167.43 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__0R,axiom, % 167.45/167.43 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.43 % 167.45/167.43 fof(fact_inf__min,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( ( class_Lattices_Osemilattice__inf(T_a) % 167.45/167.43 & class_Orderings_Olinorder(T_a) ) % 167.45/167.43 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__diff__distrib__left,axiom, % 167.45/167.43 ! [V_z,V_y,V_x,T_a] : % 167.45/167.43 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__diff,axiom, % 167.45/167.43 ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i) ). % 167.45/167.43 % 167.45/167.43 fof(fact_sgn__0__0,axiom, % 167.45/167.43 ! [V_a_2,T_a] : % 167.45/167.43 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.43 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.43 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_sgn0,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( class_Groups_Osgn__if(T_a) % 167.45/167.43 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_sgn__times,axiom, % 167.45/167.43 ! [V_b,V_a,T_a] : % 167.45/167.43 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.43 => 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)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ofold__inf__insert,axiom, % 167.45/167.43 ! [V_a_2,V_b_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min_Oin__idem,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_sgn__greater,axiom, % 167.45/167.43 ! [V_a_2,T_a] : % 167.45/167.43 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_sgn__less,axiom, % 167.45/167.43 ! [V_a_2,T_a] : % 167.45/167.43 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Int__atLeastAtMostL1,axiom, % 167.45/167.43 ! [V_d_2,V_b_2,V_a_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Int__atLeastAtMostR1,axiom, % 167.45/167.43 ! [V_d_2,V_c_2,V_b_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min_OF__eq,axiom, % 167.45/167.43 ! [V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_mult__sgn__abs,axiom, % 167.45/167.43 ! [V_x,T_a] : % 167.45/167.43 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_abs__sgn,axiom, % 167.45/167.43 ! [V_k,T_a] : % 167.45/167.43 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.43 => hAPP(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)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__Suc1,axiom, % 167.45/167.43 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__Suc2,axiom, % 167.45/167.43 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 167.45/167.43 ! [V_b_2,V_a_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),V_b_2))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ofold1__belowI,axiom, % 167.45/167.43 ! [V_a_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_a_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Obelow__fold1__iff,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) % 167.45/167.43 <=> ! [B_x] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_fold1__below__iff,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2)) % 167.45/167.43 <=> ? [B_x] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_fold1__strict__below__iff,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2)) % 167.45/167.43 <=> ? [B_x] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_strict__below__fold1__iff,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) % 167.45/167.43 <=> ! [B_x] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min__insert,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min_Osubset__idem,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min__Un,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min_Oeq__fold__idem_H,axiom, % 167.45/167.43 ! [V_a_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_sgn__1__pos,axiom, % 167.45/167.43 ! [V_a_2,T_a] : % 167.45/167.43 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.43 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_sgn__pos,axiom, % 167.45/167.43 ! [V_a,T_a] : % 167.45/167.43 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.45/167.43 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min_Oinsert,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_fold1__antimono,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min_Oinsert__remove,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 167.45/167.43 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min_Ounion__disjoint,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min_Ounion__inter,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min_Oeq__fold_H,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_zsgn__def,axiom, % 167.45/167.43 ! [V_i] : % 167.45/167.43 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.43 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.45/167.43 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 167.45/167.43 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 167.45/167.43 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_dual__max,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => c_Orderings_Oord_Omax(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omin(T_a) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__ord__min,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( class_Orderings_Oord(T_a) % 167.45/167.43 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min_Oclosed,axiom, % 167.45/167.43 ! [V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Oremove,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) % 167.45/167.43 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_inf__nat__def,axiom, % 167.45/167.43 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 167.45/167.43 ! [V_x_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 167.45/167.43 ! [V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 167.45/167.43 ! [V_a_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 167.45/167.43 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 167.45/167.43 ! [V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),V_A_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omax(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 167.45/167.43 ! [V_N_2,V_h_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.45/167.43 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 167.45/167.43 ! [V_x,V_z,V_y,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__inf__distrib2,axiom, % 167.45/167.43 ! [V_x,V_z,V_y,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 167.45/167.43 ! [V_z,V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__inf__distrib1,axiom, % 167.45/167.43 ! [V_z,V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__sup__absorb,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__inf__absorb,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Oidem,axiom, % 167.45/167.43 ! [V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__assoc,axiom, % 167.45/167.43 ! [V_z,V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup_Oassoc,axiom, % 167.45/167.43 ! [V_c,V_b,V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__left__commute,axiom, % 167.45/167.43 ! [V_z,V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup_Oleft__commute,axiom, % 167.45/167.43 ! [V_c,V_a,V_b,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__left__idem,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup_Oleft__idem,axiom, % 167.45/167.43 ! [V_b,V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__commute,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup_Ocommute,axiom, % 167.45/167.43 ! [V_b,V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup_Oidem,axiom, % 167.45/167.43 ! [V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_max__add__distrib__left,axiom, % 167.45/167.43 ! [V_z,V_y,V_x,T_a] : % 167.45/167.43 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__max__iff__disj,axiom, % 167.45/167.43 ! [V_y_2,V_x_2,V_z_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) % 167.45/167.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 167.45/167.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_max__less__iff__conj,axiom, % 167.45/167.43 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) % 167.45/167.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oless__supI1,axiom, % 167.45/167.43 ! [V_b,V_a,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oless__supI2,axiom, % 167.45/167.43 ! [V_a,V_b,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_le__max__iff__disj,axiom, % 167.45/167.43 ! [V_y_2,V_x_2,V_z_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) % 167.45/167.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) % 167.45/167.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_le__maxI1,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_le__maxI2,axiom, % 167.45/167.43 ! [V_x,V_y,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__iff__sup,axiom, % 167.45/167.43 ! [V_y_2,V_x_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.45/167.43 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__sup__iff,axiom, % 167.45/167.43 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) % 167.45/167.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__supI1,axiom, % 167.45/167.43 ! [V_b,V_a,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__supI2,axiom, % 167.45/167.43 ! [V_a,V_b,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__absorb2,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__absorb1,axiom, % 167.45/167.43 ! [V_x,V_y,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__supI,axiom, % 167.45/167.43 ! [V_b,V_x,V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__least,axiom, % 167.45/167.43 ! [V_z,V_x,V_y,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__mono,axiom, % 167.45/167.43 ! [V_d,V_b,V_c,V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ole__supE,axiom, % 167.45/167.43 ! [V_x,V_b,V_a,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) % 167.45/167.43 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.45/167.43 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_max__Suc__Suc,axiom, % 167.45/167.43 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_max__0L,axiom, % 167.45/167.43 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 167.45/167.43 % 167.45/167.43 fof(fact_max__0R,axiom, % 167.45/167.43 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 167.45/167.43 % 167.45/167.43 fof(fact_sup__max,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( ( class_Lattices_Osemilattice__sup(T_a) % 167.45/167.43 & class_Orderings_Olinorder(T_a) ) % 167.45/167.43 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_max__diff__distrib__left,axiom, % 167.45/167.43 ! [V_z,V_y,V_x,T_a] : % 167.45/167.43 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Odistrib__inf__le,axiom, % 167.45/167.43 ! [V_z,V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Odistrib__sup__le,axiom, % 167.45/167.43 ! [V_z,V_y,V_x,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_minus__max__eq__min,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.45/167.43 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_minus__min__eq__max,axiom, % 167.45/167.43 ! [V_y,V_x,T_a] : % 167.45/167.43 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.45/167.43 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_nat__minus__add__max,axiom, % 167.45/167.43 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m) ). % 167.45/167.43 % 167.45/167.43 fof(fact_max__Suc2,axiom, % 167.45/167.43 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2) ). % 167.45/167.43 % 167.45/167.43 fof(fact_max__Suc1,axiom, % 167.45/167.43 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2) ). % 167.45/167.43 % 167.45/167.43 fof(fact_max__ord__max,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( class_Orderings_Oord(T_a) % 167.45/167.43 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ofold__sup__insert,axiom, % 167.45/167.43 ! [V_a_2,V_b_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Oin__idem,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Int__atLeastAtMost,axiom, % 167.45/167.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Int__atLeastLessThan,axiom, % 167.45/167.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Int__greaterThanAtMost,axiom, % 167.45/167.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Int__greaterThanLessThan,axiom, % 167.45/167.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Int__atLeastAtMostL2,axiom, % 167.45/167.43 ! [V_c_2,V_b_2,V_a_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_b_2) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Int__atLeastAtMostR2,axiom, % 167.45/167.43 ! [V_d_2,V_c_2,V_a_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_d_2) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_OF__eq,axiom, % 167.45/167.43 ! [V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_dual__min,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => c_Orderings_Oord_Omin(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omax(T_a) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__le__fold__sup,axiom, % 167.45/167.43 ! [V_b_2,V_a_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max__insert,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Osubset__idem,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Osup__Inf__absorb,axiom, % 167.45/167.43 ! [V_a_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = V_a_2 ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max__Un,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Oeq__fold__idem_H,axiom, % 167.45/167.43 ! [V_a_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Oinsert,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Oinsert__remove,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 167.45/167.43 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Ounion__disjoint,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Ounion__inter,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Oeq__fold_H,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Oremove,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) % 167.45/167.43 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omin(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Oclosed,axiom, % 167.45/167.43 ! [V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OInf__le__Sup,axiom, % 167.45/167.43 ! [V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_sup__nat__def,axiom, % 167.45/167.43 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 167.45/167.43 ! [V_x_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 167.45/167.43 ! [V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 167.45/167.43 ! [V_a_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = V_a_2 ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 167.45/167.43 ! [V_a_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 167.45/167.43 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 167.45/167.43 ! [V_B_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Oremove,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) % 167.45/167.43 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 167.45/167.43 ! [V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),V_A_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 167.45/167.43 ! [V_N_2,V_h_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.45/167.43 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max_Ohom__commute,axiom, % 167.45/167.43 ! [V_N_2,V_h_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.45/167.43 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min_Ohom__commute,axiom, % 167.45/167.43 ! [V_N_2,V_h_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 167.45/167.43 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.43 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_pigeonhole__infinite,axiom, % 167.45/167.43 ! [V_f_2,T_b,V_A_2,T_a] : % 167.45/167.43 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.45/167.43 => ? [B_x] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.43 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_nat__mod__eq__lemma,axiom, % 167.45/167.43 ! [V_y,V_n,V_x] : % 167.45/167.43 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 167.45/167.43 => ? [B_q] : V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_com_Osize_I5_J,axiom, % 167.45/167.43 ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_com_Osize_I13_J,axiom, % 167.45/167.43 ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_evaln_OIfFalse,axiom, % 167.45/167.43 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] : % 167.45/167.43 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_evaln_OIfTrue,axiom, % 167.45/167.43 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] : % 167.45/167.43 ( hBOOL(hAPP(V_b_2,V_s_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_evaln__elim__cases_I5_J,axiom, % 167.45/167.43 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_n_2),V_t_2)) % 167.45/167.43 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 167.45/167.43 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) ) % 167.45/167.43 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.45/167.43 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_evalc_OIfFalse,axiom, % 167.45/167.43 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] : % 167.45/167.43 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1_2),V_s_2),V_s1_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_evalc_OIfTrue,axiom, % 167.45/167.43 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] : % 167.45/167.43 ( hBOOL(hAPP(V_b_2,V_s_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c0_2),V_s_2),V_s1_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_evalc__elim__cases_I5_J,axiom, % 167.45/167.43 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2)) % 167.45/167.43 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 167.45/167.43 => ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1_2),V_s_2),V_t_2)) ) % 167.45/167.43 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.45/167.43 => ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_WTs__elim__cases_I5_J,axiom, % 167.45/167.43 ! [V_c2_2,V_c1_2,V_b_2] : % 167.45/167.43 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2))) % 167.45/167.43 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 167.45/167.43 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_evaln_Oequations_I6_J,axiom, % 167.45/167.43 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2)),V_a2_2),V_a4_2),V_a5_2)) % 167.45/167.43 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) % 167.45/167.43 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_evaln_Oequations_I5_J,axiom, % 167.45/167.43 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2)),V_a2_2),V_a4_2),V_a5_2)) % 167.45/167.43 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) % 167.45/167.43 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_com_Osimps_I4_J,axiom, % 167.45/167.43 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 167.45/167.43 ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) % 167.45/167.43 <=> ( V_fun_2 = V_fun_H_2 % 167.45/167.43 & V_com1_2 = V_com1_H_2 % 167.45/167.43 & V_com2_2 = V_com2_H_2 ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_evalc_Oequations_I5_J,axiom, % 167.45/167.43 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2)) % 167.45/167.43 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),V_a4_2)) ) % 167.45/167.43 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_evalc_Oequations_I6_J,axiom, % 167.45/167.43 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2)) % 167.45/167.43 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a5_2),V_a2_2),V_a4_2)) ) % 167.45/167.43 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_WT_Oequations_I5_J,axiom, % 167.45/167.43 ! [V_a2_2,V_a1_2,V_a3_2] : % 167.45/167.43 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) % 167.45/167.43 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 167.45/167.43 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_WT_OIf,axiom, % 167.45/167.43 ! [V_b_2,V_c1_2,V_c0_2] : % 167.45/167.43 ( hBOOL(hAPP(c_Com_OWT,V_c0_2)) % 167.45/167.43 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 167.45/167.43 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_com_Osimps_I55_J,axiom, % 167.45/167.43 ! [V_com2_2,V_com1_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 167.45/167.43 % 167.45/167.43 fof(fact_com_Osimps_I54_J,axiom, % 167.45/167.43 ! [V_pname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 167.45/167.43 % 167.45/167.43 fof(fact_com_Osimps_I53_J,axiom, % 167.45/167.43 ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 167.45/167.43 % 167.45/167.43 fof(fact_com_Osimps_I52_J,axiom, % 167.45/167.43 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 167.45/167.43 % 167.45/167.43 fof(fact_com_Osimps_I44_J,axiom, % 167.45/167.43 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 167.45/167.43 % 167.45/167.43 fof(fact_com_Osimps_I45_J,axiom, % 167.45/167.43 ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 167.45/167.43 % 167.45/167.43 fof(fact_com_Osimps_I14_J,axiom, % 167.45/167.43 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 167.45/167.43 % 167.45/167.43 fof(fact_com_Osimps_I15_J,axiom, % 167.45/167.43 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP ). % 167.45/167.43 % 167.45/167.43 fof(fact_fold__image__1,axiom, % 167.45/167.43 ! [V_f_2,V_S_2,T_a,T_b] : % 167.45/167.43 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.45/167.43 => ( ! [B_x] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 167.45/167.43 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 167.45/167.43 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_card_Oneutral,axiom, % 167.45/167.43 ! [V_A_2,T_a] : % 167.45/167.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.43 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.43 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 167.45/167.43 ! [V_c_2,V_b_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ! [B_x] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b_2),V_c_2))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 167.45/167.43 ! [V_c_2,V_b_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ! [B_x] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_c_2),V_A_2))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_mod__induct__0,axiom, % 167.45/167.43 ! [V_i_2,V_P_2,V_p_2] : % 167.45/167.43 ( ! [B_i] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 167.45/167.43 => ( hBOOL(hAPP(V_P_2,B_i)) % 167.45/167.43 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 167.45/167.43 => ( hBOOL(hAPP(V_P_2,V_i_2)) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 167.45/167.43 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_InterI,axiom, % 167.45/167.43 ! [V_A_2,V_C_2,T_a] : % 167.45/167.43 ( ! [B_X] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) ) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_fold__image__cong,axiom, % 167.45/167.43 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] : % 167.45/167.43 ( class_Groups_Oab__semigroup__mult(T_b) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ! [B_x] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.43 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 167.45/167.43 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),V_z_2),V_A_2) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Min__eqI,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ! [B_y] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Max__eqI,axiom, % 167.45/167.43 ! [V_x_2,V_A_2,T_a] : % 167.45/167.43 ( class_Orderings_Olinorder(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ! [B_y] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.43 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_inf__le__fold__inf,axiom, % 167.45/167.43 ! [V_c_2,V_b_2,V_A_2,T_a] : % 167.45/167.43 ( class_Lattices_Osemilattice__inf(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ! [B_x] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_c_2),V_A_2))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_fold__sup__le__sup,axiom, % 167.45/167.43 ! [V_c_2,V_b_2,V_A_2,T_a] : % 167.45/167.43 ( class_Lattices_Osemilattice__sup(T_a) % 167.45/167.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.43 => ( ! [B_x] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b_2),V_c_2))) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_expand__Suc,axiom, % 167.45/167.43 ! [V_v] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v))) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_of__int__number__of__eq,axiom, % 167.45/167.43 ! [V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of__eq,axiom, % 167.45/167.43 ! [V_k,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_of__nat__number__of__lemma,axiom, % 167.45/167.43 ! [V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_eq__number__of,axiom, % 167.45/167.43 ! [V_y_2,V_x_2,T_a] : % 167.45/167.43 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.43 & class_Int_Oring__char__0(T_a) ) % 167.45/167.43 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 167.45/167.43 <=> V_x_2 = V_y_2 ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of__reorient,axiom, % 167.45/167.43 ! [V_x_2,V_w_2,T_a] : % 167.45/167.43 ( class_Int_Onumber(T_a) % 167.45/167.43 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2 % 167.45/167.43 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_of__nat__number__of__eq,axiom, % 167.45/167.43 ! [V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_le__number__of__eq__not__less,axiom, % 167.45/167.43 ! [V_w_2,V_v_2,T_a] : % 167.45/167.43 ( ( class_Int_Onumber(T_a) % 167.45/167.43 & class_Orderings_Olinorder(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.45/167.43 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_right__distrib__number__of,axiom, % 167.45/167.43 ! [V_c,V_b,V_v,T_b] : % 167.45/167.43 ( ( class_Int_Onumber(T_b) % 167.45/167.43 & class_Rings_Osemiring(T_b) ) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_left__distrib__number__of,axiom, % 167.45/167.43 ! [V_v,V_b,V_a,T_b] : % 167.45/167.43 ( ( class_Int_Onumber(T_b) % 167.45/167.43 & class_Rings_Osemiring(T_b) ) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_left__diff__distrib__number__of,axiom, % 167.45/167.43 ! [V_v,V_b,V_a,T_b] : % 167.45/167.43 ( ( class_Int_Onumber(T_b) % 167.45/167.43 & class_Rings_Oring(T_b) ) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_right__diff__distrib__number__of,axiom, % 167.45/167.43 ! [V_c,V_b,V_v,T_b] : % 167.45/167.43 ( ( class_Int_Onumber(T_b) % 167.45/167.43 & class_Rings_Oring(T_b) ) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_le__number__of,axiom, % 167.45/167.43 ! [V_y_2,V_x_2,T_a] : % 167.45/167.43 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.43 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__number__of,axiom, % 167.45/167.43 ! [V_y_2,V_x_2,T_a] : % 167.45/167.43 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.43 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__number__of,axiom, % 167.45/167.43 ! [V_v,V_u,T_b] : % 167.45/167.43 ( ( class_Int_Onumber(T_b) % 167.45/167.43 & class_Orderings_Oord(T_b) ) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_max__number__of,axiom, % 167.45/167.43 ! [V_v,V_u,T_b] : % 167.45/167.43 ( ( class_Int_Onumber(T_b) % 167.45/167.43 & class_Orderings_Oord(T_b) ) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 167.45/167.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_add__number__of__left,axiom, % 167.45/167.43 ! [V_z,V_w,V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_add__number__of__eq,axiom, % 167.45/167.43 ! [V_w,V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of__add,axiom, % 167.45/167.43 ! [V_w,V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of__mult,axiom, % 167.45/167.43 ! [V_w,V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_arith__simps_I32_J,axiom, % 167.45/167.43 ! [V_w,V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_mult__number__of__left,axiom, % 167.45/167.43 ! [V_z,V_w,V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of__diff,axiom, % 167.45/167.43 ! [V_w,V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of__minus,axiom, % 167.45/167.43 ! [V_w,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_arith__simps_I30_J,axiom, % 167.45/167.43 ! [V_w,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Ints__number__of,axiom, % 167.45/167.43 ! [V_w_2,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_eq__divide__eq__number__of1,axiom, % 167.45/167.43 ! [V_w_2,V_b_2,V_a_2,T_a] : % 167.45/167.43 ( ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) % 167.45/167.43 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_b_2 ) % 167.45/167.43 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.43 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_eq__divide__eq__number__of,axiom, % 167.45/167.43 ! [V_c_2,V_b_2,V_w_2,T_a] : % 167.45/167.43 ( ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) % 167.45/167.43 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2) = V_b_2 ) % 167.45/167.43 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_divide__eq__eq__number__of,axiom, % 167.45/167.43 ! [V_w_2,V_c_2,V_b_2,T_a] : % 167.45/167.43 ( ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) % 167.45/167.43 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.43 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2) ) % 167.45/167.43 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_divide__eq__eq__number__of1,axiom, % 167.45/167.43 ! [V_a_2,V_w_2,V_b_2,T_a] : % 167.45/167.43 ( ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_a_2 % 167.45/167.43 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.43 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) % 167.45/167.43 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.43 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_add__number__of__diff1,axiom, % 167.45/167.43 ! [V_c,V_w,V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_minus__number__of__mult,axiom, % 167.45/167.43 ! [V_z,V_w,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_diff__number__of__eq,axiom, % 167.45/167.43 ! [V_w,V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__divide__eq__number__of1,axiom, % 167.45/167.43 ! [V_w_2,V_b_2,V_a_2,T_a] : % 167.45/167.43 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) % 167.45/167.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__divide__eq__number__of,axiom, % 167.45/167.43 ! [V_c_2,V_b_2,V_w_2,T_a] : % 167.45/167.43 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 167.45/167.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_divide__less__eq__number__of,axiom, % 167.45/167.43 ! [V_w_2,V_c_2,V_b_2,T_a] : % 167.45/167.43 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.45/167.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_divide__less__eq__number__of1,axiom, % 167.45/167.43 ! [V_a_2,V_w_2,V_b_2,T_a] : % 167.45/167.43 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2)) % 167.45/167.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_abs__number__of,axiom, % 167.45/167.43 ! [V_x,T_a] : % 167.45/167.43 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.43 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_add__number__of__diff2,axiom, % 167.45/167.43 ! [V_w,V_c,V_v,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_le__divide__eq__number__of1,axiom, % 167.45/167.43 ! [V_w_2,V_b_2,V_a_2,T_a] : % 167.45/167.43 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) % 167.45/167.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_le__divide__eq__number__of,axiom, % 167.45/167.43 ! [V_c_2,V_b_2,V_w_2,T_a] : % 167.45/167.43 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 167.45/167.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_divide__le__eq__number__of,axiom, % 167.45/167.43 ! [V_w_2,V_c_2,V_b_2,T_a] : % 167.45/167.43 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.45/167.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_divide__le__eq__number__of1,axiom, % 167.45/167.43 ! [V_a_2,V_w_2,V_b_2,T_a] : % 167.45/167.43 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2)) % 167.45/167.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_one__mod__nat__number__of,axiom, % 167.45/167.43 ! [V_v_H] : % 167.45/167.43 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 167.45/167.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 167.45/167.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_one__div__nat__number__of,axiom, % 167.45/167.43 ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_power__number__of__odd__number__of,axiom, % 167.45/167.43 ! [V_v_2,V_w_2,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.45/167.43 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)))),c_COMBI(T_a))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.45/167.43 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_power__nat__number__of,axiom, % 167.45/167.43 ! [V_n,V_v] : % 167.45/167.43 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_plus__numeral__code_I9_J,axiom, % 167.45/167.43 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_times__numeral__code_I5_J,axiom, % 167.45/167.43 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of__is__id,axiom, % 167.45/167.43 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__number__of__int__code,axiom, % 167.45/167.43 ! [V_l_2,V_k_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__eq__number__of__int__code,axiom, % 167.45/167.43 ! [V_l_2,V_k_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_neg__number__of__Bit1,axiom, % 167.45/167.43 ! [V_w_2] : % 167.45/167.43 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 167.45/167.43 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_minus__numeral__code_I5_J,axiom, % 167.45/167.43 ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_rel__simps_I51_J,axiom, % 167.45/167.43 ! [V_l_2,V_k_2] : % 167.45/167.43 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 167.45/167.43 <=> V_k_2 = V_l_2 ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__int__code_I16_J,axiom, % 167.45/167.43 ! [V_k2_2,V_k1_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_rel__simps_I17_J,axiom, % 167.45/167.43 ! [V_l_2,V_k_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__eq__int__code_I16_J,axiom, % 167.45/167.43 ! [V_k2_2,V_k1_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_rel__simps_I34_J,axiom, % 167.45/167.43 ! [V_l_2,V_k_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_int__number__of__def,axiom, % 167.45/167.43 ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w) ). % 167.45/167.43 % 167.45/167.43 fof(fact_bin__less__0__simps_I4_J,axiom, % 167.45/167.43 ! [V_w_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Bit1__def,axiom, % 167.45/167.43 ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k) ). % 167.45/167.43 % 167.45/167.43 fof(fact_nat__number__of,axiom, % 167.45/167.43 ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w) ). % 167.45/167.43 % 167.45/167.43 fof(fact_nat__number__of__def,axiom, % 167.45/167.43 ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_nat__number__of__Bit1,axiom, % 167.45/167.43 ! [V_w_2] : % 167.45/167.43 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of__Bit1,axiom, % 167.45/167.43 ! [V_w,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_power__number__of__odd,axiom, % 167.45/167.43 ! [V_z_2,V_w_2,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.45/167.43 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2))),c_COMBI(T_a))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.45/167.43 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_zpower__number__of__odd,axiom, % 167.45/167.43 ! [V_z_2,V_w_2] : % 167.45/167.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.45/167.43 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.45/167.43 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_minus__numeral__code_I6_J,axiom, % 167.45/167.43 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_neg__imp__number__of__eq__0,axiom, % 167.45/167.43 ! [V_v] : % 167.45/167.43 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_int__eq__iff__number__of,axiom, % 167.45/167.43 ! [V_v_2,V_m_2] : % 167.45/167.43 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) % 167.45/167.43 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 167.45/167.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_eq__nat__number__of,axiom, % 167.45/167.43 ! [V_v_H_2,V_v_2] : % 167.45/167.43 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2) % 167.45/167.43 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 167.45/167.43 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 167.45/167.43 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_nat__number__of__add__left,axiom, % 167.45/167.43 ! [V_k,V_v_H,V_v] : % 167.45/167.43 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_int__nat__number__of,axiom, % 167.45/167.43 ! [V_v] : % 167.45/167.43 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_mod__nat__number__of,axiom, % 167.45/167.43 ! [V_v_H,V_v] : % 167.45/167.43 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 167.45/167.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 167.45/167.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_div__nat__number__of,axiom, % 167.45/167.43 ! [V_v_H,V_v] : % 167.45/167.43 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_power__nat__number__of__number__of,axiom, % 167.45/167.43 ! [V_w,V_v] : % 167.45/167.43 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Suc__nat__number__of__add,axiom, % 167.45/167.43 ! [V_n,V_v] : % 167.45/167.43 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.43 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_diff__nat__number__of,axiom, % 167.45/167.43 ! [V_v_2,V_v_H_2] : % 167.45/167.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__Suc__number__of,axiom, % 167.45/167.43 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_min__number__of__Suc,axiom, % 167.45/167.43 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_succ__Pls,axiom, % 167.45/167.43 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 167.45/167.43 % 167.45/167.43 fof(fact_rel__simps_I39_J,axiom, % 167.45/167.43 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 167.45/167.43 % 167.45/167.43 fof(fact_rel__simps_I46_J,axiom, % 167.45/167.43 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 167.45/167.43 % 167.45/167.43 fof(fact_Pls__def,axiom, % 167.45/167.43 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.45/167.43 % 167.45/167.43 fof(fact_rel__simps_I19_J,axiom, % 167.45/167.43 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_rel__simps_I2_J,axiom, % 167.45/167.43 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_add__Pls__right,axiom, % 167.45/167.43 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 167.45/167.43 % 167.45/167.43 fof(fact_add__Pls,axiom, % 167.45/167.43 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 167.45/167.43 % 167.45/167.43 fof(fact_mult__Pls,axiom, % 167.45/167.43 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 167.45/167.43 % 167.45/167.43 fof(fact_succ__pred,axiom, % 167.45/167.43 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 167.45/167.43 % 167.45/167.43 fof(fact_diff__bin__simps_I1_J,axiom, % 167.45/167.43 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 167.45/167.43 % 167.45/167.43 fof(fact_minus__Pls,axiom, % 167.45/167.43 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 167.45/167.43 % 167.45/167.43 fof(fact_semiring__norm_I112_J,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of__Pls,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_add__numeral__0,axiom, % 167.45/167.43 ! [V_a,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_add__numeral__0__right,axiom, % 167.45/167.43 ! [V_a,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_bin__less__0__simps_I1_J,axiom, % 167.45/167.43 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_semiring__norm_I113_J,axiom, % 167.45/167.43 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 167.45/167.43 % 167.45/167.43 fof(fact_nat__number__of__Pls,axiom, % 167.45/167.43 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.43 % 167.45/167.43 fof(fact_zero__is__num__zero,axiom, % 167.45/167.43 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 167.45/167.43 % 167.45/167.43 fof(fact_rel__simps_I22_J,axiom, % 167.45/167.43 ! [V_k_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_rel__simps_I12_J,axiom, % 167.45/167.43 ! [V_k_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Suc__diff__number__of,axiom, % 167.45/167.43 ! [V_m,V_v] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_not__neg__number__of__Pls,axiom, % 167.45/167.43 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_nat__number__of__add__1,axiom, % 167.45/167.43 ! [V_v] : % 167.45/167.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_nat__1__add__number__of,axiom, % 167.45/167.43 ! [V_v] : % 167.45/167.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_le__iff__pred__less,axiom, % 167.45/167.43 ! [V_l_2,V_k_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_minus__Bit1,axiom, % 167.45/167.43 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_pred__def,axiom, % 167.45/167.43 ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_nat__number__of__diff__1,axiom, % 167.45/167.43 ! [V_v] : % 167.45/167.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_mult__numeral__1,axiom, % 167.45/167.43 ! [V_a,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_mult__numeral__1__right,axiom, % 167.45/167.43 ! [V_a,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_divide__Numeral0,axiom, % 167.45/167.43 ! [V_x,T_a] : % 167.45/167.43 ( ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.43 & class_Int_Onumber__ring(T_a) ) % 167.45/167.43 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_semiring__norm_I110_J,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_numeral__1__eq__1,axiom, % 167.45/167.43 ! [T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_eq__0__number__of,axiom, % 167.45/167.43 ! [V_v_2] : % 167.45/167.43 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_eq__number__of__0,axiom, % 167.45/167.43 ! [V_v_2] : % 167.45/167.43 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of2,axiom, % 167.45/167.43 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_rel__simps_I29_J,axiom, % 167.45/167.43 ! [V_k_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_rel__simps_I5_J,axiom, % 167.45/167.43 ! [V_k_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__nat__number__of,axiom, % 167.45/167.43 ! [V_v_H_2,V_v_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) % 167.45/167.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 167.45/167.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_divide__Numeral1,axiom, % 167.45/167.43 ! [V_x,T_a] : % 167.45/167.43 ( ( class_Fields_Ofield(T_a) % 167.45/167.43 & class_Int_Onumber__ring(T_a) ) % 167.45/167.43 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_divide__numeral__1,axiom, % 167.45/167.43 ! [V_a,T_a] : % 167.45/167.43 ( ( class_Fields_Ofield(T_a) % 167.45/167.43 & class_Int_Onumber__ring(T_a) ) % 167.45/167.43 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_le__nat__number__of,axiom, % 167.45/167.43 ! [V_v_H_2,V_v_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) % 167.45/167.43 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 167.45/167.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_one__is__num__one,axiom, % 167.45/167.43 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_nat__numeral__1__eq__1,axiom, % 167.45/167.43 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Numeral1__eq1__nat,axiom, % 167.45/167.43 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 167.45/167.43 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_succ__def,axiom, % 167.45/167.43 ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_le__special_I3_J,axiom, % 167.45/167.43 ! [V_x_2,T_a] : % 167.45/167.43 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.43 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_le__special_I1_J,axiom, % 167.45/167.43 ! [V_y_2,T_a] : % 167.45/167.43 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.43 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__special_I3_J,axiom, % 167.45/167.43 ! [V_x_2,T_a] : % 167.45/167.43 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.43 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__special_I1_J,axiom, % 167.45/167.43 ! [V_y_2,T_a] : % 167.45/167.43 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.43 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_less__0__number__of,axiom, % 167.45/167.43 ! [V_v_2] : % 167.45/167.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 167.45/167.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_numeral__1__eq__Suc__0,axiom, % 167.45/167.43 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.45/167.43 % 167.45/167.43 fof(fact_numeral__3__eq__3,axiom, % 167.45/167.43 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_power3__eq__cube,axiom, % 167.45/167.43 ! [V_a,T_a] : % 167.45/167.43 ( class_Groups_Omonoid__mult(T_a) % 167.45/167.43 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 167.45/167.43 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_Suc3__eq__add__3,axiom, % 167.45/167.43 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ). % 167.45/167.43 % 167.45/167.43 fof(fact_add__nat__number__of,axiom, % 167.45/167.43 ! [V_v_H,V_v] : % 167.45/167.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) % 167.45/167.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 167.45/167.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) ) ) ) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 167.45/167.43 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 167.45/167.43 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of__succ,axiom, % 167.45/167.43 ! [V_k,T_a] : % 167.45/167.43 ( class_Int_Onumber__ring(T_a) % 167.45/167.43 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ) ). % 167.45/167.43 % 167.45/167.43 fof(fact_number__of__pred,axiom, % 167.45/167.43 ! [V_w,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_le__special_I4_J,axiom, % 167.45/167.44 ! [V_x_2,T_a] : % 167.45/167.44 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.44 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_le__special_I2_J,axiom, % 167.45/167.44 ! [V_y_2,T_a] : % 167.45/167.44 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.44 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__special_I4_J,axiom, % 167.45/167.44 ! [V_x_2,T_a] : % 167.45/167.44 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.44 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__special_I2_J,axiom, % 167.45/167.44 ! [V_y_2,T_a] : % 167.45/167.44 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.44 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_add__special_I2_J,axiom, % 167.45/167.44 ! [V_w,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_add__special_I3_J,axiom, % 167.45/167.44 ! [V_v,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Suc__diff__eq__diff__pred,axiom, % 167.45/167.44 ! [V_m,V_n] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n)) % 167.45/167.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__number__of__mult__left,axiom, % 167.45/167.44 ! [V_k,V_v_H,V_v] : % 167.45/167.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mult__nat__number__of,axiom, % 167.45/167.44 ! [V_v_H,V_v] : % 167.45/167.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.45/167.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_neg__number__of__pred__iff__0,axiom, % 167.45/167.44 ! [V_v_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 167.45/167.44 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 167.45/167.44 ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Suc__mod__eq__add3__mod,axiom, % 167.45/167.44 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod__Suc__eq__mod__add3,axiom, % 167.45/167.44 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 167.45/167.44 ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Suc__div__eq__add3__div,axiom, % 167.45/167.44 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__Suc__eq__div__add3,axiom, % 167.45/167.44 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_diff__special_I1_J,axiom, % 167.45/167.44 ! [V_w,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_diff__special_I2_J,axiom, % 167.45/167.44 ! [V_v,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_eq__number__of__Suc,axiom, % 167.45/167.44 ! [V_n_2,V_v_2] : % 167.45/167.44 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Suc__eq__number__of,axiom, % 167.45/167.44 ! [V_v_2,V_n_2] : % 167.45/167.44 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__case__number__of,axiom, % 167.45/167.44 ! [V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__number__of__Suc,axiom, % 167.45/167.44 ! [V_n_2,V_v_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__Suc__number__of,axiom, % 167.45/167.44 ! [V_v_2,V_n_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_le__number__of__Suc,axiom, % 167.45/167.44 ! [V_n_2,V_v_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_le__Suc__number__of,axiom, % 167.45/167.44 ! [V_v_2,V_n_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Suc__nat__number__of,axiom, % 167.45/167.44 ! [V_v] : % 167.45/167.44 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.44 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.44 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_max__number__of__Suc,axiom, % 167.45/167.44 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_max__Suc__number__of,axiom, % 167.45/167.44 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__case__add__eq__if,axiom, % 167.45/167.44 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__rec__add__eq__if,axiom, % 167.45/167.44 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_eq__special_I2_J,axiom, % 167.45/167.44 ! [V_y_2,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 167.45/167.44 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_eq__special_I4_J,axiom, % 167.45/167.44 ! [V_x_2,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 167.45/167.44 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__rec__number__of,axiom, % 167.45/167.44 ! [V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),c_Int_Onat)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_iszero__def,axiom, % 167.45/167.44 ! [V_z_2,T_a] : % 167.45/167.44 ( class_Rings_Osemiring__1(T_a) % 167.45/167.44 => ( c_Int_Oiszero(T_a,V_z_2) % 167.45/167.44 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_iszero__0,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Rings_Osemiring__1(T_a) % 167.45/167.44 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_not__iszero__1,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Rings_Osemiring__1(T_a) % 167.45/167.44 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__rec__0,axiom, % 167.45/167.44 ! [V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__rec__Suc,axiom, % 167.45/167.44 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),V_nat_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_iszero__Numeral0,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_iszero__number__of__Bit1,axiom, % 167.45/167.44 ! [V_w,T_a] : % 167.45/167.44 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.44 & class_Int_Oring__char__0(T_a) ) % 167.45/167.44 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_not__iszero__Numeral1,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_eq__number__of__eq,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 167.45/167.44 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_eq__special_I1_J,axiom, % 167.45/167.44 ! [V_y_2,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 167.45/167.44 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_eq__special_I3_J,axiom, % 167.45/167.44 ! [V_x_2,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.44 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zmod__number__of__Bit1,axiom, % 167.45/167.44 ! [V_v,V_w] : % 167.45/167.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_neg__zmod__mult__2,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_arith__series__int,axiom, % 167.45/167.44 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_neg__zdiv__mult__2,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I49_J,axiom, % 167.45/167.44 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I50_J,axiom, % 167.45/167.44 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I31_J,axiom, % 167.45/167.44 ! [V_l_2,V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__eq__int__code_I13_J,axiom, % 167.45/167.44 ! [V_k2_2,V_k1_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I14_J,axiom, % 167.45/167.44 ! [V_l_2,V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__int__code_I13_J,axiom, % 167.45/167.44 ! [V_k2_2,V_k1_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_add__Bit0__Bit0,axiom, % 167.45/167.44 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Bit0__def,axiom, % 167.45/167.44 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I48_J,axiom, % 167.45/167.44 ! [V_l_2,V_k_2] : % 167.45/167.44 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 167.45/167.44 <=> V_k_2 = V_l_2 ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mult__Bit0,axiom, % 167.45/167.44 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_diff__bin__simps_I7_J,axiom, % 167.45/167.44 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_minus__Bit0,axiom, % 167.45/167.44 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Bit0__Pls,axiom, % 167.45/167.44 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I38_J,axiom, % 167.45/167.44 ! [V_l_2] : % 167.45/167.44 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 167.45/167.44 <=> c_Int_OPls = V_l_2 ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I44_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 167.45/167.44 <=> V_k_2 = c_Int_OPls ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_bin__less__0__simps_I3_J,axiom, % 167.45/167.44 ! [V_w_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I27_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I21_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__eq__int__code_I14_J,axiom, % 167.45/167.44 ! [V_k2_2,V_k1_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I32_J,axiom, % 167.45/167.44 ! [V_l_2,V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I10_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I4_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__int__code_I15_J,axiom, % 167.45/167.44 ! [V_k2_2,V_k1_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I16_J,axiom, % 167.45/167.44 ! [V_l_2,V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_add__Bit1__Bit0,axiom, % 167.45/167.44 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_add__Bit0__Bit1,axiom, % 167.45/167.44 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_diff__bin__simps_I3_J,axiom, % 167.45/167.44 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_diff__bin__simps_I9_J,axiom, % 167.45/167.44 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_diff__bin__simps_I10_J,axiom, % 167.45/167.44 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zdiv__number__of__Bit0,axiom, % 167.45/167.44 ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_neg__number__of__Bit0,axiom, % 167.45/167.44 ! [V_w_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 167.45/167.44 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pred__Bit1,axiom, % 167.45/167.44 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pred__Bit0,axiom, % 167.45/167.44 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_iszero__number__of__Bit0,axiom, % 167.45/167.44 ! [V_w_2,T_a] : % 167.45/167.44 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.44 & class_Int_Oring__char__0(T_a) ) % 167.45/167.44 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) % 167.45/167.44 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_succ__Bit0,axiom, % 167.45/167.44 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 167.45/167.44 % 167.45/167.44 fof(fact_succ__Bit1,axiom, % 167.45/167.44 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__number__of__Bit0,axiom, % 167.45/167.44 ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_number__of__Bit0,axiom, % 167.45/167.44 ! [V_w,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__eq__int__code_I15_J,axiom, % 167.45/167.44 ! [V_k2_2,V_k1_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I33_J,axiom, % 167.45/167.44 ! [V_l_2,V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__int__code_I14_J,axiom, % 167.45/167.44 ! [V_k2_2,V_k1_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I15_J,axiom, % 167.45/167.44 ! [V_l_2,V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_card__UNIV__bool,axiom, % 167.45/167.44 hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mult__Bit1,axiom, % 167.45/167.44 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l) ). % 167.45/167.44 % 167.45/167.44 fof(fact_diff__bin__simps_I8_J,axiom, % 167.45/167.44 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_add__Bit1__Bit1,axiom, % 167.45/167.44 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power__number__of__even,axiom, % 167.45/167.44 ! [V_w_2,V_z_2,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zpower__number__of__even,axiom, % 167.45/167.44 ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_double__number__of__Bit0,axiom, % 167.45/167.44 ! [V_w,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_number__of1,axiom, % 167.45/167.44 ! [V_n] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) % 167.45/167.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 167.45/167.44 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power__number__of__even__number__of,axiom, % 167.45/167.44 ! [V_w_2,V_v_2,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mult__2,axiom, % 167.45/167.44 ! [V_z,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mult__2__right,axiom, % 167.45/167.44 ! [V_z,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_one__add__one__is__two,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zero__eq__power2,axiom, % 167.45/167.44 ! [V_a_2,T_a] : % 167.45/167.44 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 167.45/167.44 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.44 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zero__power2,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Rings_Osemiring__1(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_semiring__norm_I115_J,axiom, % 167.45/167.44 hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_numeral__2__eq__2,axiom, % 167.45/167.44 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 167.45/167.44 ! [V_x,T_a] : % 167.45/167.44 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power2__eq__square,axiom, % 167.45/167.44 ! [V_a,T_a] : % 167.45/167.44 ( class_Groups_Omonoid__mult(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 167.45/167.44 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_add__2__eq__Suc,axiom, % 167.45/167.44 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_add__2__eq__Suc_H,axiom, % 167.45/167.44 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_one__power2,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Rings_Osemiring__1(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power2__minus,axiom, % 167.45/167.44 ! [V_a,T_a] : % 167.45/167.44 ( class_Rings_Oring__1(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__mult__2,axiom, % 167.45/167.44 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__mult__2__right,axiom, % 167.45/167.44 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power__even__eq,axiom, % 167.45/167.44 ! [V_n,V_a,T_a] : % 167.45/167.44 ( class_Groups_Omonoid__mult(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 167.45/167.44 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 167.45/167.44 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_abs__power2,axiom, % 167.45/167.44 ! [V_a,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power2__abs,axiom, % 167.45/167.44 ! [V_a,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__1__add__1,axiom, % 167.45/167.44 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod2__Suc__Suc,axiom, % 167.45/167.44 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div2__Suc__Suc,axiom, % 167.45/167.44 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zmod__number__of__Bit0,axiom, % 167.45/167.44 ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_add__self__div__2,axiom, % 167.45/167.44 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m ). % 167.45/167.44 % 167.45/167.44 fof(fact_half__gt__zero__iff,axiom, % 167.45/167.44 ! [V_r_2,T_a] : % 167.45/167.44 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.44 & class_Int_Onumber__ring(T_a) ) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_half__gt__zero,axiom, % 167.45/167.44 ! [V_r,T_a] : % 167.45/167.44 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 167.45/167.44 & class_Int_Onumber__ring(T_a) ) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power2__eq__imp__eq,axiom, % 167.45/167.44 ! [V_y,V_x,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.44 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.44 => V_x = V_y ) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power2__le__imp__le,axiom, % 167.45/167.44 ! [V_y,V_x,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zero__le__power2,axiom, % 167.45/167.44 ! [V_a,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => hBOOL(hAPP(hAPP(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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zero__less__power2,axiom, % 167.45/167.44 ! [V_a_2,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(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_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 167.45/167.44 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power2__less__0,axiom, % 167.45/167.44 ! [V_a,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_sum__power2__eq__zero__iff,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.44 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.44 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power2__eq__square__number__of,axiom, % 167.45/167.44 ! [V_w,T_b] : % 167.45/167.44 ( ( class_Groups_Omonoid__mult(T_b) % 167.45/167.44 & class_Int_Onumber(T_b) ) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__2__cases,axiom, % 167.45/167.44 ! [V_n] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) % 167.45/167.44 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.44 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__2,axiom, % 167.45/167.44 hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power2__eq__1__iff,axiom, % 167.45/167.44 ! [V_a_2,T_a] : % 167.45/167.44 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 167.45/167.44 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) % 167.45/167.44 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a) % 167.45/167.44 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 167.45/167.44 ! [V_n,V_x,T_a] : % 167.45/167.44 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power__minus__even,axiom, % 167.45/167.44 ! [V_n,V_a,T_a] : % 167.45/167.44 ( class_Rings_Oring__1(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power2__less__imp__less,axiom, % 167.45/167.44 ! [V_y,V_x,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__semidom(T_a) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_sum__power2__ge__zero,axiom, % 167.45/167.44 ! [V_y,V_x,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_sum__power2__le__zero__iff,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.44 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.44 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_sum__power2__gt__zero__iff,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) % 167.45/167.44 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.45/167.44 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_not__sum__power2__lt__zero,axiom, % 167.45/167.44 ! [V_y,V_x,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power2__sum,axiom, % 167.45/167.44 ! [V_y,V_x,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zero__le__even__power_H,axiom, % 167.45/167.44 ! [V_n,V_a,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => hBOOL(hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power__odd__eq,axiom, % 167.45/167.44 ! [V_n,V_a,T_a] : % 167.45/167.44 ( class_Groups_Omonoid__mult(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 167.45/167.44 ! [V_n,V_x,T_a] : % 167.45/167.44 ( class_Rings_Ocomm__semiring__1(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power__minus1__even,axiom, % 167.45/167.44 ! [V_n,T_a] : % 167.45/167.44 ( class_Rings_Oring__1(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zdiv__number__of__Bit1,axiom, % 167.45/167.44 ! [V_v,V_w] : % 167.45/167.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod2__gr__0,axiom, % 167.45/167.44 ! [V_m_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 167.45/167.44 <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__2__gt__zero,axiom, % 167.45/167.44 ! [V_n] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power2__diff,axiom, % 167.45/167.44 ! [V_y,V_x,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_odd__0__le__power__imp__0__le,axiom, % 167.45/167.44 ! [V_n,V_a,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(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),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))))) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_odd__power__less__zero,axiom, % 167.45/167.44 ! [V_n,V_a,T_a] : % 167.45/167.44 ( class_Rings_Olinordered__idom(T_a) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power__minus1__odd,axiom, % 167.45/167.44 ! [V_n,T_a] : % 167.45/167.44 ( class_Rings_Oring__1(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Suc__n__div__2__gt__zero,axiom, % 167.45/167.44 ! [V_n] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_of__nat__double,axiom, % 167.45/167.44 ! [V_x,T_a] : % 167.45/167.44 ( class_Rings_Osemiring__1(T_a) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.45/167.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pos__zmod__mult__2,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pos__zdiv__mult__2,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_int__of__code,axiom, % 167.45/167.44 ! [V_k] : % 167.45/167.44 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.44 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.45/167.44 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.44 => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.44 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) % 167.45/167.44 & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.44 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_of__int__num,axiom, % 167.45/167.44 ! [V_k_2,T_a] : % 167.45/167.44 ( class_Rings_Oring__1(T_a) % 167.45/167.44 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) % 167.45/167.44 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),T_a),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),tc_Int_Oint),c_COMBB(tc_fun(T_a,T_a),T_a,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,T_a),T_a),tc_Int_Oint),c_HOL_OLet(T_a,T_a)),c_Int_Oring__1__class_Oof__int(T_a)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_a)),tc_Int_Oint),c_COMBS(T_a,T_a,T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),tc_Int_Oint),c_COMBB(T_a,tc_fun(T_a,T_a),T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a))))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Oplus__class_Oplus(T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a)))),c_Groups_Oone__class_Oone(T_a))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power__m1__odd,axiom, % 167.45/167.44 ! [V_n,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I45_J,axiom, % 167.45/167.44 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I42_J,axiom, % 167.45/167.44 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I37_J,axiom, % 167.45/167.44 c_Int_OPls != c_Int_OMin ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I40_J,axiom, % 167.45/167.44 c_Int_OMin != c_Int_OPls ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I24_J,axiom, % 167.45/167.44 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I7_J,axiom, % 167.45/167.44 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_code__numeral__zero__minus__one,axiom, % 167.45/167.44 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I47_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 167.45/167.44 <=> V_k_2 = c_Int_OMin ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I43_J,axiom, % 167.45/167.44 ! [V_l_2] : % 167.45/167.44 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 167.45/167.44 <=> c_Int_OMin = V_l_2 ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Bit1__Min,axiom, % 167.45/167.44 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 167.45/167.44 % 167.45/167.44 fof(fact_bin__less__0__simps_I2_J,axiom, % 167.45/167.44 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I23_J,axiom, % 167.45/167.44 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I20_J,axiom, % 167.45/167.44 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I26_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I30_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I6_J,axiom, % 167.45/167.44 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I3_J,axiom, % 167.45/167.44 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I9_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I13_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I28_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I8_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_eq__number__of__Pls__Min,axiom, % 167.45/167.44 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Int_OMin__def,axiom, % 167.45/167.44 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mult__Min,axiom, % 167.45/167.44 ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k) ). % 167.45/167.44 % 167.45/167.44 fof(fact_neg__number__of__Min,axiom, % 167.45/167.44 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pred__Pls,axiom, % 167.45/167.44 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 167.45/167.44 % 167.45/167.44 fof(fact_add__Min,axiom, % 167.45/167.44 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 167.45/167.44 % 167.45/167.44 fof(fact_add__Min__right,axiom, % 167.45/167.44 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pred__Min,axiom, % 167.45/167.44 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nonzero__number__of__Min,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_succ__Min,axiom, % 167.45/167.44 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 167.45/167.44 % 167.45/167.44 fof(fact_diff__bin__simps_I2_J,axiom, % 167.45/167.44 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mult__minus1__right,axiom, % 167.45/167.44 ! [V_z,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mult__minus1,axiom, % 167.45/167.44 ! [V_z,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_arith__simps_I31_J,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_number__of__Min,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_abs__minus__one,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.44 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.44 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divide__minus1,axiom, % 167.45/167.44 ! [V_x,T_a] : % 167.45/167.44 ( ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.44 & class_Int_Onumber__ring(T_a) ) % 167.45/167.44 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I25_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rel__simps_I11_J,axiom, % 167.45/167.44 ! [V_k_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zmod__minus1__right,axiom, % 167.45/167.44 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.45/167.44 % 167.45/167.44 fof(fact_diff__bin__simps_I4_J,axiom, % 167.45/167.44 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_minus__Min,axiom, % 167.45/167.44 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 167.45/167.44 ! [V_n,V_m] : % 167.45/167.44 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 167.45/167.44 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 167.45/167.44 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zmult__eq__1__iff,axiom, % 167.45/167.44 ! [V_n_2,V_m_2] : % 167.45/167.44 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 167.45/167.44 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 167.45/167.44 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 167.45/167.44 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 167.45/167.44 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_diff__bin__simps_I5_J,axiom, % 167.45/167.44 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_diff__bin__simps_I6_J,axiom, % 167.45/167.44 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_of__int__m1,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zdiv__minus1__right,axiom, % 167.45/167.44 ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zero__code__numeral__code,axiom, % 167.45/167.44 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls) ). % 167.45/167.44 % 167.45/167.44 fof(fact_minus1__divide,axiom, % 167.45/167.44 ! [V_x,T_a] : % 167.45/167.44 ( ( class_Fields_Ofield__inverse__zero(T_a) % 167.45/167.44 & class_Int_Onumber__ring(T_a) ) % 167.45/167.44 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_abs__power__minus__one,axiom, % 167.45/167.44 ! [V_n,T_a] : % 167.45/167.44 ( ( class_Int_Onumber__ring(T_a) % 167.45/167.44 & class_Rings_Olinordered__idom(T_a) ) % 167.45/167.44 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__eq__minus1,axiom, % 167.45/167.44 ! [V_b] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__pos__neg__trivial,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zmod__minus1,axiom, % 167.45/167.44 ! [V_b] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_one__code__numeral__code,axiom, % 167.45/167.44 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_power__m1__even,axiom, % 167.45/167.44 ! [V_n,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_int__ge__less__than__def,axiom, % 167.45/167.44 ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_int__ge__less__than2__def,axiom, % 167.45/167.44 ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_code__numeral_Osize_I1_J,axiom, % 167.45/167.44 c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__of__aux__code,axiom, % 167.45/167.44 ! [V_n,V_i] : % 167.45/167.44 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.44 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 167.45/167.44 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.44 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__rel__def,axiom, % 167.45/167.44 ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nitpick_Oprod__def,axiom, % 167.45/167.44 ! [V_B_2,V_A_2,T_b,T_a] : c_Nitpick_Oprod(T_a,T_b,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__correct,axiom, % 167.45/167.44 ! [V_a,V_b] : % 167.45/167.44 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nitpick_OFrac__def,axiom, % 167.45/167.44 c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 167.45/167.44 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.44 => ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2) % 167.45/167.44 => c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_code__numeral_Osize_I2_J,axiom, % 167.45/167.44 ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_code__numeral_Oinject,axiom, % 167.45/167.44 ! [V_code__numeral_H_2,V_code__numeral_2] : % 167.45/167.44 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 167.45/167.44 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_code__numeral_Osimps_I3_J,axiom, % 167.45/167.44 ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.44 % 167.45/167.44 fof(fact_code__numeral_Osimps_I2_J,axiom, % 167.45/167.44 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 167.45/167.44 % 167.45/167.44 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 167.45/167.44 ! [V_z_2,V_f_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 167.45/167.44 ! [V_a2_2,V_a1_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Suc__code__numeral__minus__one,axiom, % 167.45/167.44 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n ). % 167.45/167.44 % 167.45/167.44 fof(fact_code__numeral_Osize_I4_J,axiom, % 167.45/167.44 ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nitpick_Oint__gcd__def,axiom, % 167.45/167.44 ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zmult2__lemma,axiom, % 167.45/167.44 ! [V_c,V_r,V_q,V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 167.45/167.44 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_sup__Un__eq2,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_inf__Int__eq2,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_bot__empty__eq2,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pred__equals__eq2,axiom, % 167.45/167.44 ! [V_S_2,V_R_2,T_b,T_a] : % 167.45/167.44 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2) % 167.45/167.44 <=> V_R_2 = V_S_2 ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pred__subset__eq2,axiom, % 167.45/167.44 ! [V_S_2,V_R_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__rel__0,axiom, % 167.45/167.44 ! [V_b] : % 167.45/167.44 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_self__remainder,axiom, % 167.45/167.44 ! [V_r,V_q,V_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 167.45/167.44 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_unique__quotient,axiom, % 167.45/167.44 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 167.45/167.44 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H))) % 167.45/167.44 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => V_q = V_q_H ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_unique__remainder,axiom, % 167.45/167.44 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 167.45/167.44 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H))) % 167.45/167.44 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => V_r = V_r_H ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_SUP__UN__eq2,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c))))),V_r_2)),V_x_2),V_y_2)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_INF__INT__eq2,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c))))),V_r_2)),V_x_2),V_y_2)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_self__quotient,axiom, % 167.45/167.44 ! [V_r,V_q,V_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 167.45/167.44 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__rel__mod,axiom, % 167.45/167.44 ! [V_r,V_q,V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 167.45/167.44 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__rel__div,axiom, % 167.45/167.44 ! [V_r,V_q,V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 167.45/167.44 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__mod__div,axiom, % 167.45/167.44 ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__rel__div__mod,axiom, % 167.45/167.44 ! [V_a,V_b] : % 167.45/167.44 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__gcd_Osimps,axiom, % 167.45/167.44 ! [V_x,V_y] : % 167.45/167.44 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.44 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 167.45/167.44 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.44 => c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zadd1__lemma,axiom, % 167.45/167.44 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar))) % 167.45/167.44 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br))) % 167.45/167.44 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zminus1__lemma,axiom, % 167.45/167.44 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2))) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__relI,axiom, % 167.45/167.44 ! [V_r,V_q,V_b,V_a] : % 167.45/167.44 ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) % 167.45/167.44 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 167.45/167.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 167.45/167.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_code__numeral_Osize_I3_J,axiom, % 167.45/167.44 hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.44 % 167.45/167.44 fof(fact_zmult1__lemma,axiom, % 167.45/167.44 ! [V_a,V_r,V_q,V_c,V_b] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 167.45/167.44 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pair__imageI,axiom, % 167.45/167.44 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_A_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),V_A_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_norm__frac_Osimps,axiom, % 167.45/167.44 ! [V_a_2,V_b_2] : % 167.45/167.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.45/167.44 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 167.45/167.44 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.45/167.44 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_adjust__def,axiom, % 167.45/167.44 ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_sup2CI,axiom, % 167.45/167.44 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] : % 167.45/167.44 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 167.45/167.44 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_sup2E,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 167.45/167.44 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_inf2I,axiom, % 167.45/167.44 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_inf2E,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 167.45/167.44 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 167.45/167.44 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mem__splitI,axiom, % 167.45/167.44 ! [T_c,T_b,V_b_2,V_a_2,V_c_2,V_z_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_prod__caseI,axiom, % 167.45/167.44 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_splitI,axiom, % 167.45/167.44 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_bot2E,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,T_b,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_splitD_H,axiom, % 167.45/167.44 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_c_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rev__predicate2D,axiom, % 167.45/167.44 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_predicate2D,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__by__empty,axiom, % 167.45/167.44 ! [V_B_2,T_a,V_A_2] : % 167.45/167.44 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_inf2D1,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_inf2D2,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_sup2I2,axiom, % 167.45/167.44 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_sup2I1,axiom, % 167.45/167.44 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_split__paired__All,axiom, % 167.45/167.44 ! [T_b,T_a,V_P_2] : % 167.45/167.44 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 167.45/167.44 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Pair__eq,axiom, % 167.45/167.44 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.44 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2) % 167.45/167.44 <=> ( V_a_2 = V_a_H_2 % 167.45/167.44 & V_b_2 = V_b_H_2 ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Pair__inject,axiom, % 167.45/167.44 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 167.45/167.44 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H) % 167.45/167.44 => ~ ( V_a = V_a_H % 167.45/167.44 => V_b != V_b_H ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_split__weak__cong,axiom, % 167.45/167.44 ! [V_c_2,T_c,T_b,T_a,V_q_2,V_p_2] : % 167.45/167.44 ( V_p_2 = V_q_2 % 167.45/167.44 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_q_2) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_split__twice,axiom, % 167.45/167.44 ! [V_p_2,V_g_2,T_e,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_b,T_c)),tc_fun(T_e,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2))),V_g_2)),V_p_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_prod_Osimps_I2_J,axiom, % 167.45/167.44 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_split__conv,axiom, % 167.45/167.44 ! [V_b_2,V_a_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_splitD,axiom, % 167.45/167.44 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_split__eta,axiom, % 167.45/167.44 ! [V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,T_c),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),T_c,T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b))) = V_f_2 ). % 167.45/167.44 % 167.45/167.44 fof(fact_The__split__eq,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_split__paired__The,axiom, % 167.45/167.44 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),V_P_2) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_adjust__eq,axiom, % 167.45/167.44 ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_in__rel__def,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__mod__code__numeral__def,axiom, % 167.45/167.44 ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 167.45/167.44 ! [V_w] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) % 167.45/167.44 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) % 167.45/167.44 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_negDivAlg__correct,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_negDivAlg__div__mod,axiom, % 167.45/167.44 ! [V_l,V_k] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 167.45/167.44 => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_negDivAlg__minus1,axiom, % 167.45/167.44 ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_negDivAlg_Osimps,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.44 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) % 167.45/167.44 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.44 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_negDivAlg__eqn,axiom, % 167.45/167.44 ! [V_a,V_b] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 167.45/167.44 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 167.45/167.44 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_negDivAlg__eqn__number__of,axiom, % 167.45/167.44 ! [V_w,V_v] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) % 167.45/167.44 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) % 167.45/167.44 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nitpick_Onat__lcm__def,axiom, % 167.45/167.44 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nitpick_Orefl_H__def,axiom, % 167.45/167.44 ! [V_r_2,T_a] : % 167.45/167.44 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 167.45/167.44 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 167.45/167.44 ! [V_w] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.45/167.44 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.45/167.44 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_posDivAlg__0,axiom, % 167.45/167.44 ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_posDivAlg__correct,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_posDivAlg__div__mod,axiom, % 167.45/167.44 ! [V_l,V_k] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 167.45/167.44 => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_posDivAlg__eqn,axiom, % 167.45/167.44 ! [V_a,V_b] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 167.45/167.44 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 167.45/167.44 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_posDivAlg__eqn__number__of,axiom, % 167.45/167.44 ! [V_w,V_v] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.44 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.45/167.44 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_posDivAlg_Osimps,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.44 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) % 167.45/167.44 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.44 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nitpick_Oint__lcm__def,axiom, % 167.45/167.44 ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__def,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 167.45/167.44 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__step,axiom, % 167.45/167.44 ! [V_m,V_n] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.45/167.44 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__zero,axiom, % 167.45/167.44 ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__base,axiom, % 167.45/167.44 ! [V_n,V_m] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.45/167.44 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_negateSnd__eq,axiom, % 167.45/167.44 ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__div__mod,axiom, % 167.45/167.44 ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__rel__neg,axiom, % 167.45/167.44 ! [V_qr,V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr)) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__if,axiom, % 167.45/167.44 ! [V_m_2,V_n_2] : % 167.45/167.44 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 167.45/167.44 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) ) % 167.45/167.44 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 167.45/167.44 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__pdivmod,axiom, % 167.45/167.44 ! [V_l_2,V_k_2] : % 167.45/167.44 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 167.45/167.44 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) % 167.45/167.44 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 167.45/167.44 ! [V_c,V_r,V_q,V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 167.45/167.44 ! [V_a,V_r,V_q,V_c,V_b] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_apsnd__conv,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),hAPP(V_f_2,V_y_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__rel__unique,axiom, % 167.45/167.44 ! [V_qr_H,V_qr,V_n,V_m] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 167.45/167.44 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 167.45/167.44 => V_qr = V_qr_H ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__eq,axiom, % 167.45/167.44 ! [V_qr,V_n,V_m] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 167.45/167.44 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 167.45/167.44 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__def,axiom, % 167.45/167.44 ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod__eq,axiom, % 167.45/167.44 ! [V_r,V_q,V_n,V_m] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__eq,axiom, % 167.45/167.44 ! [V_r,V_q,V_n,V_m] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_negateSnd__def,axiom, % 167.45/167.44 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__rel,axiom, % 167.45/167.44 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__rel__add1__eq,axiom, % 167.45/167.44 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar))) % 167.45/167.44 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 167.45/167.44 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pdivmod__def,axiom, % 167.45/167.44 ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pdivmod__posDivAlg,axiom, % 167.45/167.44 ! [V_k,V_l] : % 167.45/167.44 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)) ) % 167.45/167.44 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__int__code,axiom, % 167.45/167.44 ! [V_l_2,V_k_2] : % 167.45/167.44 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 167.45/167.44 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) % 167.45/167.44 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_negDivAlg_Opsimps,axiom, % 167.45/167.44 ! [V_b_2,V_a_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 167.45/167.44 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.44 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) ) % 167.45/167.44 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.44 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_posDivAlg_Opsimps,axiom, % 167.45/167.44 ! [V_b_2,V_a_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 167.45/167.44 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.44 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) ) % 167.45/167.44 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.44 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod__pos__neg__1__number__of,axiom, % 167.45/167.44 ! [V_w] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_snd__def,axiom, % 167.45/167.44 ! [V_p_2,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,T_a),hAPP(c_COMBK(tc_fun(T_a,T_a),T_b),c_COMBI(T_a))),V_p_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_apsnd__eq__conv,axiom, % 167.45/167.44 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] : % 167.45/167.44 ( hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_g_2),V_x_2) % 167.45/167.44 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_snd__apsnd,axiom, % 167.45/167.44 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapsnd(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_snd__eqD,axiom, % 167.45/167.44 ! [V_a,V_y,V_x,T_a,T_b] : % 167.45/167.44 ( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a % 167.45/167.44 => V_y = V_a ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_snd__conv,axiom, % 167.45/167.44 ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod__int__def,axiom, % 167.45/167.44 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod__neg__pos,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod__pos__pos,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod__pos__pos__1__number__of,axiom, % 167.45/167.44 ! [V_w] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod__pos__neg,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod__neg__neg,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_norm__frac_Opsimps,axiom, % 167.45/167.44 ! [V_b_2,V_a_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.45/167.44 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 167.45/167.44 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.45/167.44 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.45/167.44 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_negDivAlg_Opinduct,axiom, % 167.45/167.44 ! [V_P_2,V_a1_2,V_a0_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 167.45/167.44 => ( ! [B_a,B_b] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 167.45/167.44 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) ) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_posDivAlg_Opinduct,axiom, % 167.45/167.44 ! [V_P_2,V_a1_2,V_a0_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 167.45/167.44 => ( ! [B_a,B_b] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 167.45/167.44 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 167.45/167.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) ) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mod__nat__def,axiom, % 167.45/167.44 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_accp__subset,axiom, % 167.45/167.44 ! [V_R2_2,V_R1_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_R1_2),V_R2_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_a,V_R2_2)),c_Wellfounded_Oaccp(T_a,V_R1_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_norm__frac_Opinduct,axiom, % 167.45/167.44 ! [V_P_2,V_a1_2,V_a0_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 167.45/167.44 => ( ! [B_a,B_b] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) ) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__pos__neg__1__number__of,axiom, % 167.45/167.44 ! [V_w] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Pair__fst__snd__eq,axiom, % 167.45/167.44 ! [T_b,T_a,V_t_2,V_s_2] : % 167.45/167.44 ( V_s_2 = V_t_2 % 167.45/167.44 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) % 167.45/167.44 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_prod__eqI,axiom, % 167.45/167.44 ! [V_q,V_p,T_b,T_a] : % 167.45/167.44 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 167.45/167.44 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 167.45/167.44 => V_p = V_q ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_fst__def,axiom, % 167.45/167.44 ! [V_p_2,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_a),c_COMBK(T_a,T_b)),V_p_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_fst__eqD,axiom, % 167.45/167.44 ! [V_a,V_y,V_x,T_b,T_a] : % 167.45/167.44 ( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a % 167.45/167.44 => V_x = V_a ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_fst__conv,axiom, % 167.45/167.44 ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a ). % 167.45/167.44 % 167.45/167.44 fof(fact_fst__apsnd,axiom, % 167.45/167.44 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_a,T_c),V_x_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pair__collapse,axiom, % 167.45/167.44 ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p ). % 167.45/167.44 % 167.45/167.44 fof(fact_surjective__pairing,axiom, % 167.45/167.44 ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_prod__case__beta,axiom, % 167.45/167.44 ! [V_p_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__int__def,axiom, % 167.45/167.44 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_split__comp__eq,axiom, % 167.45/167.44 ! [V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),tc_prod(T_a,T_b)),V_f_2),hAPP(hAPP(c_COMBB(T_a,T_d,tc_prod(T_a,T_b)),V_g_2),c_Product__Type_Ofst(T_a,T_b)))),c_Product__Type_Osnd(T_a,T_b)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),T_a),V_f_2),V_g_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_split__beta,axiom, % 167.45/167.44 ! [V_z_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_z_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_z_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_split__def,axiom, % 167.45/167.44 ! [V_p_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_accp__downward,axiom, % 167.45/167.44 ! [V_a_2,V_b_2,V_r_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 167.45/167.44 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_accp_Oequations,axiom, % 167.45/167.44 ! [V_a_2,V_r_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 167.45/167.44 <=> ! [B_x] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 167.45/167.44 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_accp_Osimps,axiom, % 167.45/167.44 ! [V_a_2,V_r_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 167.45/167.44 <=> ! [B_x] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 167.45/167.44 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_The__split,axiom, % 167.45/167.44 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__neg__pos,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__pos__pos,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__pos__pos__1__number__of,axiom, % 167.45/167.44 ! [V_w] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__pos__neg,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__neg__neg,axiom, % 167.45/167.44 ! [V_b,V_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.45/167.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_prod__size__simp,axiom, % 167.45/167.44 ! [V_p_2,V_g_2,V_f_2,T_b,T_a] : c_Product__Type_Oprod_Oprod__size(T_a,T_b,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__gcd_Opsimps,axiom, % 167.45/167.44 ! [V_y_2,V_x_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2))) % 167.45/167.44 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.44 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 167.45/167.44 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.44 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_exI__realizer,axiom, % 167.45/167.44 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_div__nat__def,axiom, % 167.45/167.44 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_divmod__nat__rel__def,axiom, % 167.45/167.44 ! [V_qr_2,V_n_2,V_m_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 167.45/167.44 <=> ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) % 167.45/167.44 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.44 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.44 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) % 167.45/167.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)) ) ) % 167.45/167.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) % 167.45/167.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_conjI__realizer,axiom, % 167.45/167.44 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] : % 167.45/167.44 ( hBOOL(hAPP(V_P_2,V_p_2)) % 167.45/167.44 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 167.45/167.44 => ( hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) % 167.45/167.44 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat_Osize_I2_J,axiom, % 167.45/167.44 ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_in__measure,axiom, % 167.45/167.44 ! [V_f_2,V_y_2,V_x_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__def,axiom, % 167.45/167.44 ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Rep__Integ__inject,axiom, % 167.45/167.44 ! [V_y_2,V_x_2] : % 167.45/167.44 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 167.45/167.44 <=> V_x_2 = V_y_2 ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat_Osize_I1_J,axiom, % 167.45/167.44 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__gcd_Opinduct,axiom, % 167.45/167.44 ! [V_P_2,V_a1_2,V_a0_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2))) % 167.45/167.44 => ( ! [B_x,B_y] : % 167.45/167.44 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y))) % 167.45/167.44 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) ) % 167.45/167.44 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mlex__leq,axiom, % 167.45/167.44 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mlex__less,axiom, % 167.45/167.44 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_finite__psubset__def,axiom, % 167.45/167.44 ! [T_a] : c_Wellfounded_Ofinite__psubset(T_a) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_a)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat_Osize_I4_J,axiom, % 167.45/167.44 ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_prod_Orecs,axiom, % 167.45/167.44 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat__size,axiom, % 167.45/167.44 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat_Osize_I3_J,axiom, % 167.45/167.44 hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.44 % 167.45/167.44 fof(fact_in__finite__psubset,axiom, % 167.45/167.44 ! [V_B_2,V_A_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a))) % 167.45/167.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nats__number__of,axiom, % 167.45/167.44 ! [V_w_2,T_a] : % 167.45/167.44 ( class_Int_Onumber__ring(T_a) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 167.45/167.44 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] : % 167.45/167.44 ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) % 167.45/167.44 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.44 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 167.45/167.44 | ? [B_x,B_y] : % 167.45/167.44 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 167.45/167.44 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2)) % 167.45/167.44 & c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_in__lex__prod,axiom, % 167.45/167.44 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2))) % 167.45/167.44 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_H_2)),V_r_2)) % 167.45/167.44 | ( V_a_2 = V_a_H_2 % 167.45/167.44 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nats__0,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Rings_Osemiring__1(T_a) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nats__add,axiom, % 167.45/167.44 ! [V_b_2,V_a_2,T_a] : % 167.45/167.44 ( class_Rings_Osemiring__1(T_a) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nats__mult,axiom, % 167.45/167.44 ! [V_b_2,V_a_2,T_a] : % 167.45/167.44 ( class_Rings_Osemiring__1(T_a) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Nats__1,axiom, % 167.45/167.44 ! [T_a] : % 167.45/167.44 ( class_Rings_Osemiring__1(T_a) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_of__nat__in__Nats,axiom, % 167.45/167.44 ! [V_n_2,T_a] : % 167.45/167.44 ( class_Rings_Osemiring__1(T_a) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_same__fstI,axiom, % 167.45/167.44 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 167.45/167.44 ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_apsnd__apfst,axiom, % 167.45/167.44 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_d,T_c),V_x_2))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_apfst__apsnd,axiom, % 167.45/167.44 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_apfst__conv,axiom, % 167.45/167.44 ! [V_y_2,V_x_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_x_2)),V_y_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_snd__apfst,axiom, % 167.45/167.44 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapfst(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_c,T_a),V_x_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_apfst__eq__conv,axiom, % 167.45/167.44 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] : % 167.45/167.44 ( hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_g_2),V_x_2) % 167.45/167.44 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_fst__apfst,axiom, % 167.45/167.44 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_apsnd__apfst__commute,axiom, % 167.45/167.44 ! [V_p_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,V_g_2),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_d,V_f_2),V_p_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pair__lessI2,axiom, % 167.45/167.44 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_max__ext__additive,axiom, % 167.45/167.44 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_code__numeral_Osimps_I5_J,axiom, % 167.45/167.44 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pair__lessI1,axiom, % 167.45/167.44 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_code__numeral_Osimps_I4_J,axiom, % 167.45/167.44 ! [V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 167.45/167.44 % 167.45/167.44 fof(fact_max__extp__max__ext__eq,axiom, % 167.45/167.44 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 167.45/167.44 ( c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_R_2),V_x_2,V_xa_2) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pair__leqI2,axiom, % 167.45/167.44 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_smin__insertI,axiom, % 167.45/167.44 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_smin__emptyI,axiom, % 167.45/167.44 ! [V_X_2] : % 167.45/167.44 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pair__leqI1,axiom, % 167.45/167.44 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_wmax__insertI,axiom, % 167.45/167.44 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_wmin__insertI,axiom, % 167.45/167.44 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_smax__insertI,axiom, % 167.45/167.44 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_max__strict__def,axiom, % 167.45/167.44 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 167.45/167.44 % 167.45/167.44 fof(fact_wmax__emptyI,axiom, % 167.45/167.44 ! [V_X_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_smax__emptyI,axiom, % 167.45/167.44 ! [V_Y_2] : % 167.45/167.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 167.45/167.44 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_wmin__emptyI,axiom, % 167.45/167.44 ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_max__weak__def,axiom, % 167.45/167.44 c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_min__weak__def,axiom, % 167.45/167.44 c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_max__rpair__set,axiom, % 167.45/167.44 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_min__rpair__set,axiom, % 167.45/167.44 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_min__strict__def,axiom, % 167.45/167.44 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less__than__iff,axiom, % 167.45/167.44 ! [V_y_2,V_x_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than)) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_intrel__iff,axiom, % 167.45/167.44 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel)) % 167.45/167.44 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rp__inv__image__rp,axiom, % 167.45/167.44 ! [V_f_2,T_b,V_P_2,T_a] : % 167.45/167.44 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 167.45/167.44 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_pair__less__def,axiom, % 167.45/167.44 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mlex__prod__def,axiom, % 167.45/167.44 ! [V_R_2,V_f_2,T_a] : c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a),c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rp__inv__image__def,axiom, % 167.45/167.44 ! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_COMBS(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(T_b,T_a)),c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),c_Relation_Oinv__image(T_a,T_b))))),c_Relation_Oinv__image(T_a,T_b))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_equiv__intrel__iff,axiom, % 167.45/167.44 ! [V_y_2,V_x_2] : % 167.45/167.44 ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_measure__def,axiom, % 167.45/167.44 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Image__singleton,axiom, % 167.45/167.44 ! [V_a_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_a))),hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2))),V_r_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Image__singleton__iff,axiom, % 167.45/167.44 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_inv__image__def,axiom, % 167.45/167.44 ! [V_f_2,V_r_2,T_a,T_b] : hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_b,T_b)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),T_a),c_COMBB(T_b,tc_prod(T_b,T_b),T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_prod(T_b,T_b)),T_a),c_Product__Type_OPair(T_b,T_b)),V_f_2))),V_f_2)))),V_r_2))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Image__empty,axiom, % 167.45/167.44 ! [V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Image__Un,axiom, % 167.45/167.44 ! [V_B_2,V_A_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Image__UN,axiom, % 167.45/167.44 ! [V_B_2,V_A_2,T_c,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Image__Int__subset,axiom, % 167.45/167.44 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Image__mono,axiom, % 167.45/167.44 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Un__Image,axiom, % 167.45/167.44 ! [V_A_2,V_S_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_S_2),V_A_2)) ). % 167.45/167.44 % 167.45/167.44 fof(fact_in__inv__image,axiom, % 167.45/167.44 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Image__INT__subset,axiom, % 167.45/167.44 ! [V_B_2,V_A_2,T_c,V_r_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_rev__ImageI,axiom, % 167.45/167.44 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 167.45/167.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Image__iff,axiom, % 167.45/167.44 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 167.45/167.44 <=> ? [B_x] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.45/167.44 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Image__eq__UN,axiom, % 167.45/167.44 ! [V_B_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_of__int,axiom, % 167.45/167.44 ! [V_j_2,V_i_2,T_a] : % 167.45/167.44 ( class_Rings_Oring__1(T_a) % 167.45/167.44 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_j_2)) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_One__int__def,axiom, % 167.45/167.44 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_mult,axiom, % 167.45/167.44 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Rep__Integ__inverse,axiom, % 167.45/167.44 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 167.45/167.44 % 167.45/167.44 fof(fact_minus,axiom, % 167.45/167.44 ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_Zero__int__def,axiom, % 167.45/167.44 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_int__def,axiom, % 167.45/167.44 ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_add,axiom, % 167.45/167.44 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_nat,axiom, % 167.45/167.44 ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2) ). % 167.45/167.44 % 167.45/167.44 fof(fact_minus__int__def,axiom, % 167.45/167.44 ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ). % 167.45/167.44 % 167.45/167.44 fof(fact_less,axiom, % 167.45/167.44 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) % 167.45/167.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ). % 167.45/167.44 % 167.45/167.44 fof(fact_le,axiom, % 167.45/167.44 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 167.45/167.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_irrefl__def,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Relation_Oirrefl(T_a,V_r_2) % 167.45/167.45 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_eq__Abs__Integ,axiom, % 167.45/167.45 ! [V_z_2] : % 167.45/167.45 ~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Field__insert,axiom, % 167.45/167.45 ! [V_r_2,V_b_2,V_a_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_a),V_r_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Field__Union,axiom, % 167.45/167.45 ! [V_R_2,T_a] : hAPP(c_Relation_OField(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a)),V_R_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Field__empty,axiom, % 167.45/167.45 ! [T_a] : hAPP(c_Relation_OField(T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_mono__Field,axiom, % 167.45/167.45 ! [V_s_2,V_r_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Field__Un,axiom, % 167.45/167.45 ! [V_s_2,V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__Field,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Id__on__def,axiom, % 167.45/167.45 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_quotient__def,axiom, % 167.45/167.45 ! [V_r_2,V_A_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),c_Relation_OImage(T_a,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_ImageE,axiom, % 167.45/167.45 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 167.45/167.45 => ~ ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) % 167.45/167.45 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_quotient__empty,axiom, % 167.45/167.45 ! [V_r_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_quotient__is__empty2,axiom, % 167.45/167.45 ! [V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) % 167.45/167.45 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_quotient__is__empty,axiom, % 167.45/167.45 ! [V_r_2,V_A_2,T_a] : % 167.45/167.45 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 167.45/167.45 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Id__on__def_H,axiom, % 167.45/167.45 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),c_fequal))),V_A_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Id__on__empty,axiom, % 167.45/167.45 ! [T_a] : c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Image__Id__on,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_quotientI,axiom, % 167.45/167.45 ! [V_r_2,V_A_2,V_x_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Id__on__iff,axiom, % 167.45/167.45 ! [V_A_2,V_y_2,V_x_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2))) % 167.45/167.45 <=> ( V_x_2 = V_y_2 % 167.45/167.45 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Id__on__eqI,axiom, % 167.45/167.45 ! [V_A_2,T_a,V_b_2,V_a_2] : % 167.45/167.45 ( V_a_2 = V_b_2 % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId__on(T_a,V_A_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_singleton__quotient,axiom, % 167.45/167.45 ! [V_r_2,V_x_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equiv__class__nondisjoint,axiom, % 167.45/167.45 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_subset__equiv__class,axiom, % 167.45/167.45 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_quotientE,axiom, % 167.45/167.45 ! [V_r_2,V_A_2,V_X_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 167.45/167.45 => ~ ! [B_x] : % 167.45/167.45 ( V_X_2 = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 167.45/167.45 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equiv__intrel,axiom, % 167.45/167.45 c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Union__quotient,axiom, % 167.45/167.45 ! [V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = V_A_2 ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equiv__class__self,axiom, % 167.45/167.45 ! [V_a_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_quotient__disj,axiom, % 167.45/167.45 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 167.45/167.45 => ( V_X_2 = V_Y_2 % 167.45/167.45 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equiv__class__eq,axiom, % 167.45/167.45 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 167.45/167.45 => hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_quotient__eq__iff,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 167.45/167.45 => ( V_X_2 = V_Y_2 % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_quotient__eqI,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 167.45/167.45 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equiv__class__eq__iff,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 167.45/167.45 <=> ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 167.45/167.45 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.45 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_eq__equiv__class__iff,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 167.45/167.45 => ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_eq__equiv__class,axiom, % 167.45/167.45 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] : % 167.45/167.45 ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 167.45/167.45 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equiv__class__subset,axiom, % 167.45/167.45 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_eq__equiv__class__iff2,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 167.45/167.45 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_UN__equiv__class,axiom, % 167.45/167.45 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.45 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_UN__equiv__class2,axiom, % 167.45/167.45 ! [V_a2_2,V_a1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 167.45/167.45 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 167.45/167.45 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2)) % 167.45/167.45 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equivp__equiv,axiom, % 167.45/167.45 ! [V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 167.45/167.45 <=> c_Equiv__Relations_Oequivp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_A_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_identity__equivp,axiom, % 167.45/167.45 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equivp__def,axiom, % 167.45/167.45 ! [V_R_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 167.45/167.45 <=> ! [B_x,B_y] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 167.45/167.45 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equivp__reflp,axiom, % 167.45/167.45 ! [V_x_2,V_R_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 167.45/167.45 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equivp__symp,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_R_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equivp__transp,axiom, % 167.45/167.45 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_congruent2__implies__congruent,axiom, % 167.45/167.45 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) % 167.45/167.45 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.45 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_congruent2D,axiom, % 167.45/167.45 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_c,T_b,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y1_2),V_z1_2)),V_r1_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y2_2),V_z2_2)),V_r2_2)) % 167.45/167.45 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_congruentD,axiom, % 167.45/167.45 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_r_2)) % 167.45/167.45 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_congruent2__implies__congruent__UN,axiom, % 167.45/167.45 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 167.45/167.45 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 167.45/167.45 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2)) % 167.45/167.45 => c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_c,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_UN__equiv__class__inject,axiom, % 167.45/167.45 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 167.45/167.45 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Y_2),V_f_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 167.45/167.45 => ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => ! [B_y] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 167.45/167.45 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) ) ) ) % 167.45/167.45 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_UN__equiv__class__type2,axiom, % 167.45/167.45 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 167.45/167.45 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 167.45/167.45 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A1_2),V_r1_2))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A2_2),V_r2_2))) % 167.45/167.45 => ( ! [B_x1] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) % 167.45/167.45 => ! [B_x2] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_UN__equiv__class__type,axiom, % 167.45/167.45 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 167.45/167.45 => ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Integ__def,axiom, % 167.45/167.45 c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Id__onE,axiom, % 167.45/167.45 ! [V_A_2,V_c_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_c_2),c_Relation_OId__on(T_a,V_A_2))) % 167.45/167.45 => ~ ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_card__quotient__disjoint,axiom, % 167.45/167.45 ! [V_r_2,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2) % 167.45/167.45 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__empty,axiom, % 167.45/167.45 ! [V_f_2,T_b,T_a] : c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__uminus,axiom, % 167.45/167.45 ! [V_A_2,T_a] : % 167.45/167.45 ( class_Groups_Oordered__ab__group__add(T_a) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_subset__inj__on,axiom, % 167.45/167.45 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__Int,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__diff,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__id2,axiom, % 167.45/167.45 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__def,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 <=> ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => ! [B_xa] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 167.45/167.45 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 167.45/167.45 => B_x = B_xa ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__contraD,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( V_x_2 != V_y_2 % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 167.45/167.45 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__iff,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 167.45/167.45 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 167.45/167.45 <=> V_x_2 = V_y_2 ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__onD,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 167.45/167.45 => V_x_2 = V_y_2 ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_card__image,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__imageD,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 167.45/167.45 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__Un__image__eq__iff,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.45 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 167.45/167.45 <=> V_A_2 = V_B_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__image__eq__iff,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 167.45/167.45 <=> V_A_2 = V_B_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__fun,axiom, % 167.45/167.45 ! [T_c,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a),c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__eq,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 167.45/167.45 <=> V_x_2 = V_y_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_injD,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 167.45/167.45 => V_x_2 = V_y_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__strict__subset,axiom, % 167.45/167.45 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_range__ex1__eq,axiom, % 167.45/167.45 ! [V_b_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) % 167.45/167.45 <=> ? [B_x] : % 167.45/167.45 ( V_b_2 = hAPP(V_f_2,B_x) % 167.45/167.45 & ! [B_y] : % 167.45/167.45 ( V_b_2 = hAPP(V_f_2,B_y) % 167.45/167.45 => B_y = B_x ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__image__mem__iff,axiom, % 167.45/167.45 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__iff__surj,axiom, % 167.45/167.45 ! [V_A_H_2,T_b,T_a,V_A_2] : % 167.45/167.45 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => ( ? [B_f] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 167.45/167.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_A_H_2)) ) % 167.45/167.45 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__surj__inj,axiom, % 167.45/167.45 ! [V_f_2,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2))) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_endo__inj__surj,axiom, % 167.45/167.45 ! [V_f_2,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)),V_A_2)) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 167.45/167.45 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__UNIV__inj__surj,axiom, % 167.45/167.45 ! [V_f_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__UNIV__surj__inj,axiom, % 167.45/167.45 ! [V_f_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 167.45/167.45 => ( hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__image__subset__iff,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__image__Int,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.45/167.45 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_image__Int,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__iff__eq__card,axiom, % 167.45/167.45 ! [V_f_2,T_b,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 <=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_eq__card__imp__inj__on,axiom, % 167.45/167.45 ! [V_f_2,T_b,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__image__set__diff,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.45/167.45 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_image__set__diff,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_pigeonhole,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) % 167.45/167.45 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__fun__updI,axiom, % 167.45/167.45 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__singleton,axiom, % 167.45/167.45 ! [T_a] : c_Fun_Oinj__on(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Rep__Integ,axiom, % 167.45/167.45 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_card__bij__eq,axiom, % 167.45/167.45 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2)) % 167.45/167.45 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),V_B_2)),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 167.45/167.45 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__image__Compl__subset,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__insert,axiom, % 167.45/167.45 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) % 167.45/167.45 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 & ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__Un,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.45 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.45/167.45 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_card__inj__on__le,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2)) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__iff__card__le,axiom, % 167.45/167.45 ! [V_B_2,T_b,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 167.45/167.45 => ( ? [B_f] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 167.45/167.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_B_2)) ) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_quotient__diff1,axiom, % 167.45/167.45 ! [V_a_2,V_A_2,V_r_2,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.45 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_image__INT,axiom, % 167.45/167.45 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 167.45/167.45 => ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) ) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2)) % 167.45/167.45 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Oimage(T_a,T_b,V_f_2)),V_B_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_type__definition__Integ,axiom, % 167.45/167.45 c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg) ). % 167.45/167.45 % 167.45/167.45 fof(fact_the__inv__into__into,axiom, % 167.45/167.45 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__add__nat,axiom, % 167.45/167.45 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__Suc,axiom, % 167.45/167.45 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__of__nat,axiom, % 167.45/167.45 ! [T_a] : % 167.45/167.45 ( class_Nat_Osemiring__char__0(T_a) % 167.45/167.45 => c_Fun_Oinj__on(tc_Nat_Onat,T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__int,axiom, % 167.45/167.45 c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_swap__inj__on,axiom, % 167.45/167.45 ! [V_A_2,T_b,T_a] : c_Fun_Oinj__on(tc_prod(T_a,T_b),tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_b,T_a)),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))),V_A_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_the__inv__into__f__eq,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.45 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_the__inv__into__f__f,axiom, % 167.45/167.45 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.45 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_the__inv__f__f,axiom, % 167.45/167.45 ! [V_x_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__the__inv__into,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_the__inv__into__onto,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => hAPP(c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__graph,axiom, % 167.45/167.45 ! [T_b,T_a] : c_Fun_Oinj__on(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Set_OCollect(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool)),hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_the__inv__into__def,axiom, % 167.45/167.45 ! [V_x_2,V_f_2,V_A_2,T_b,T_a] : hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_x_2))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_f__the__inv__into__f,axiom, % 167.45/167.45 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.45/167.45 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_type__definition_OAbs__image,axiom, % 167.45/167.45 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 167.45/167.45 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 167.45/167.45 => hAPP(c_Set_Oimage(T_b,T_a,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_type__definition_ORep__range,axiom, % 167.45/167.45 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 167.45/167.45 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 167.45/167.45 => hAPP(c_Set_Oimage(T_a,T_b,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_type__definition_ORep,axiom, % 167.45/167.45 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 167.45/167.45 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_type__definition_ORep__inject,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 167.45/167.45 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 167.45/167.45 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 167.45/167.45 <=> V_x_2 = V_y_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_type__definition_ORep__inverse,axiom, % 167.45/167.45 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 167.45/167.45 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 167.45/167.45 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_type__definition_OAbs__inject,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 167.45/167.45 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 167.45/167.45 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 167.45/167.45 <=> V_x_2 = V_y_2 ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_type__definition_OAbs__inverse,axiom, % 167.45/167.45 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 167.45/167.45 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 167.45/167.45 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__vimage__singleton,axiom, % 167.45/167.45 ! [V_a_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_accp__acc__eq,axiom, % 167.45/167.45 ! [V_x_2,V_r_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2)) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_rel__comp__def,axiom, % 167.45/167.45 ! [V_s_2,V_r_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBC(T_c,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_a,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_c),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_a,T_c)))),c_Product__Type_OPair(T_a,T_c)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_s_2))))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimageI,axiom, % 167.45/167.45 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] : % 167.45/167.45 ( hAPP(V_f_2,V_a_2) = V_b_2 % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_rel__compI,axiom, % 167.45/167.45 ! [V_s_2,V_c_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_b_2),V_c_2)),V_s_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__UNIV,axiom, % 167.45/167.45 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__empty,axiom, % 167.45/167.45 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__Un,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__Collect__eq,axiom, % 167.45/167.45 ! [V_P_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),V_P_2),V_f_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__code,axiom, % 167.45/167.45 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2)) % 167.45/167.45 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__ident,axiom, % 167.45/167.45 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__Compl,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__Int,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__mono,axiom, % 167.45/167.45 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__INT,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_rel__comp__mono,axiom, % 167.45/167.45 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_H_2),V_s_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_O__assoc,axiom, % 167.45/167.45 ! [V_T_2,V_S_2,V_R_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_c),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_b),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_d,T_c,T_b),V_S_2),V_T_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_rel__comp__distrib,axiom, % 167.45/167.45 ! [V_T_2,V_S_2,V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_T_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_rel__comp__distrib2,axiom, % 167.45/167.45 ! [V_R_2,V_T_2,V_S_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_T_2),V_R_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_rel__comp__empty2,axiom, % 167.45/167.45 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_rel__comp__empty1,axiom, % 167.45/167.45 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_rel__comp__UNION__distrib,axiom, % 167.45/167.45 ! [V_r_2,V_I_2,T_d,V_s_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d),hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2)),V_r_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_rel__comp__UNION__distrib2,axiom, % 167.45/167.45 ! [V_s_2,V_r_2,V_I_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_d),c_Relation_Orel__comp(T_a,T_c,T_b)),V_r_2)),V_s_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__UN,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__Diff,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimageI2,axiom, % 167.45/167.45 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimageD,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__eq,axiom, % 167.45/167.45 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_image__vimage__subset,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))),V_A_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_surj__image__vimage__eq,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_a,T_b] : % 167.45/167.45 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = V_A_2 ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__def,axiom, % 167.45/167.45 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(T_b)),V_f_2)),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_union__comp__emptyR,axiom, % 167.45/167.45 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.45/167.45 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 167.45/167.45 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 167.45/167.45 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_union__comp__emptyL,axiom, % 167.45/167.45 ! [V_B_2,V_C_2,V_A_2,T_a] : % 167.45/167.45 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 167.45/167.45 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 167.45/167.45 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__Union,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_a,T_b,V_f_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_acc__subset,axiom, % 167.45/167.45 ! [V_R2_2,V_R1_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R1_2),V_R2_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oacc(T_a,V_R2_2)),c_Wellfounded_Oacc(T_a,V_R1_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__singleton__eq,axiom, % 167.45/167.45 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 167.45/167.45 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__insert,axiom, % 167.45/167.45 ! [V_B_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__vimageD,axiom, % 167.45/167.45 ! [V_F_2,V_h_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 167.45/167.45 => ( hAPP(c_Set_Oimage(T_a,T_b,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__subsetD,axiom, % 167.45/167.45 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] : % 167.45/167.45 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2)),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_image__vimage__eq,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__vimageI,axiom, % 167.45/167.45 ! [V_h_2,T_b,V_F_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 167.45/167.45 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__vimage__image__eq,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__const,axiom, % 167.45/167.45 ! [T_b,V_A_2,V_c_2,T_a] : % 167.45/167.45 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.45/167.45 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 167.45/167.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.45/167.45 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__eq__UN,axiom, % 167.45/167.45 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_Ovimage(T_a,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_acc__downward,axiom, % 167.45/167.45 ! [V_a_2,V_r_2,V_b_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_acc_Osimps,axiom, % 167.45/167.45 ! [V_r_2,V_a_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 167.45/167.45 <=> ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_a_2)),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__subsetI,axiom, % 167.45/167.45 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),V_A_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__if,axiom, % 167.45/167.45 ! [V_B_2,T_b,V_d_2,V_A_2,V_c_2,T_a] : % 167.45/167.45 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.45/167.45 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 167.45/167.45 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 167.45/167.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 167.45/167.45 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 167.45/167.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 167.45/167.45 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 167.45/167.45 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) ) % 167.45/167.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 167.45/167.45 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_max__ext__compat,axiom, % 167.45/167.45 ! [V_S_2,V_R_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_min__ext__compat,axiom, % 167.45/167.45 ! [V_S_2,V_R_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_a,V_R_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_pred__comp__rel__comp__eq,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_s_2)),V_x_2),V_y_2)) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_reduction__pairI,axiom, % 167.45/167.45 ! [V_S_2,V_R_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_R_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 167.45/167.45 => c_FunDef_Oreduction__pair(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_max__extp_Oequations,axiom, % 167.45/167.45 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 167.45/167.45 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 167.45/167.45 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 167.45/167.45 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 & ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 167.45/167.45 => ? [B_xa] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 167.45/167.45 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__less__than,axiom, % 167.45/167.45 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 167.45/167.45 % 167.45/167.45 fof(fact_pred__comp_Ointros,axiom, % 167.45/167.45 ! [T_c,T_b,T_a,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a_2),V_c_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__empty,axiom, % 167.45/167.45 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__inv__image,axiom, % 167.45/167.45 ! [V_f_2,T_b,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__lex__prod,axiom, % 167.45/167.45 ! [V_rb_2,T_b,V_ra_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_ra_2) % 167.45/167.45 => ( c_Wellfounded_Owf(T_b,V_rb_2) % 167.45/167.45 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__measure,axiom, % 167.45/167.45 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__comp__self,axiom, % 167.45/167.45 ! [V_R_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_R_2) % 167.45/167.45 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__less,axiom, % 167.45/167.45 c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__pair__less,axiom, % 167.45/167.45 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__mlex,axiom, % 167.45/167.45 ! [V_f_2,V_R_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_R_2) % 167.45/167.45 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_pred__comp_Oequations,axiom, % 167.45/167.45 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a1_2),V_a3_2)) % 167.45/167.45 <=> ? [B_b] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 167.45/167.45 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__Int1,axiom, % 167.45/167.45 ! [V_r_H_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__Int2,axiom, % 167.45/167.45 ! [V_r_H_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__subset,axiom, % 167.45/167.45 ! [V_p_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_p_2),V_r_2)) % 167.45/167.45 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__finite__psubset,axiom, % 167.45/167.45 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_min__ext__wf,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_max__ext__wf,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__irrefl,axiom, % 167.45/167.45 ! [V_a_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__asym,axiom, % 167.45/167.45 ! [V_x_2,V_a_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2)) % 167.45/167.45 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__not__sym,axiom, % 167.45/167.45 ! [V_x_2,V_a_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2)) % 167.45/167.45 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__not__refl,axiom, % 167.45/167.45 ! [V_a_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__int__ge__less__than,axiom, % 167.45/167.45 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__int__ge__less__than2,axiom, % 167.45/167.45 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_acc__wfD,axiom, % 167.45/167.45 ! [V_x_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__acc__iff,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__no__loop,axiom, % 167.45/167.45 ! [V_R_2,T_a] : % 167.45/167.45 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 167.45/167.45 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__union__merge,axiom, % 167.45/167.45 ! [V_S_2,V_R_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) % 167.45/167.45 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_S_2),V_R_2))),V_S_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 <=> ~ ? [B_f] : % 167.45/167.45 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wfE__pf,axiom, % 167.45/167.45 ! [V_A_2,V_R_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_R_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),V_A_2))) % 167.45/167.45 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__union__compatible,axiom, % 167.45/167.45 ! [V_S_2,V_R_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_R_2) % 167.45/167.45 => ( c_Wellfounded_Owf(T_a,V_S_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 167.45/167.45 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf,axiom, % 167.45/167.45 ! [T_a] : % 167.45/167.45 ( class_Orderings_Owellorder(T_a) % 167.45/167.45 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_a)))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_reduction__pair__def,axiom, % 167.45/167.45 ! [V_P_2,T_a] : % 167.45/167.45 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 167.45/167.45 <=> ( c_Wellfounded_Owf(T_a,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)) % 167.45/167.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_reduction__pair__lemma,axiom, % 167.45/167.45 ! [V_S_2,V_R_2,V_P_2,T_a] : % 167.45/167.45 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) % 167.45/167.45 => ( c_Wellfounded_Owf(T_a,V_S_2) % 167.45/167.45 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__lenlex,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__if__measure,axiom, % 167.45/167.45 ! [T_a,V_g_2,V_f_2,V_P_2] : % 167.45/167.45 ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) ) % 167.45/167.45 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),V_g_2))))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_max__ext_Ointros,axiom, % 167.45/167.45 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 167.45/167.45 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 167.45/167.45 => ? [B_xa] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 167.45/167.45 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) ) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_pred__nat__def,axiom, % 167.45/167.45 c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__lex,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__lexn,axiom, % 167.45/167.45 ! [V_n_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_lex__def,axiom, % 167.45/167.45 ! [V_r_2,T_a] : c_List_Olex(T_a,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_a,V_r_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_lexn_Osimps_I1_J,axiom, % 167.45/167.45 ! [V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__pred__nat,axiom, % 167.45/167.45 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__same__fst,axiom, % 167.45/167.45 ! [T_a,V_R_2,T_b,V_P_2] : % 167.45/167.45 ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.45 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) ) % 167.45/167.45 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Nitpick_Ozero__frac__def,axiom, % 167.45/167.45 ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__Inter,axiom, % 167.45/167.45 ! [V_f_2,T_b,T_a,V_S_2] : % 167.45/167.45 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 167.45/167.45 => ( ! [B_A] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) ) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Nitpick_Oone__frac__def,axiom, % 167.45/167.45 ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 167.45/167.45 ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Nitpick_Ofrac__def,axiom, % 167.45/167.45 ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Range__Collect__split,axiom, % 167.45/167.45 ! [V_P_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Set_OCollect(tc_prod(T_b,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_P_2))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_image__split__eq__Sigma,axiom, % 167.45/167.45 ! [V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Set_Oimage(T_c,tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_Oimage(T_c,T_a,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_Oimage(T_c,T_b,V_g_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_a),c_Set_Ovimage(T_c,T_a,V_f_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_A_2))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wfP__def,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_OwfP(T_a,V_r_2) % 167.45/167.45 <=> c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wfP__empty,axiom, % 167.45/167.45 ! [T_a] : c_Wellfounded_OwfP(T_a,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_SigmaI,axiom, % 167.45/167.45 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_RangeI,axiom, % 167.45/167.45 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Range__Id__on,axiom, % 167.45/167.45 ! [V_A_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ). % 167.45/167.45 % 167.45/167.45 fof(fact_wfP__accp__iff,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_OwfP(T_a,V_r_2) % 167.45/167.45 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_accp__wfPD,axiom, % 167.45/167.45 ! [V_x_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_OwfP(T_a,V_r_2) % 167.45/167.45 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Sigma__Diff__distrib2,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Times__Diff__distrib1,axiom, % 167.45/167.45 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Sigma__Diff__distrib1,axiom, % 167.45/167.45 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Times__eq__cancel2,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 167.45/167.45 => ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) % 167.45/167.45 <=> V_A_2 = V_B_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Sigma__Union,axiom, % 167.45/167.45 ! [V_B_2,V_X_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b)),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Sigma__empty1,axiom, % 167.45/167.45 ! [V_B_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_card__cartesian__product,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setsum__cartesian__product,axiom, % 167.45/167.45 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Sigma__empty2,axiom, % 167.45/167.45 ! [V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Times__empty,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,T_a] : % 167.45/167.45 ( hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) % 167.45/167.45 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Compl__Times__UNIV2,axiom, % 167.45/167.45 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Compl__Times__UNIV1,axiom, % 167.45/167.45 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setprod__cartesian__product,axiom, % 167.45/167.45 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__mult(T_a) % 167.45/167.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wfP__subset,axiom, % 167.45/167.45 ! [V_p_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_OwfP(T_a,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_p_2),V_r_2)) % 167.45/167.45 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Sigma__Un__distrib1,axiom, % 167.45/167.45 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Times__Un__distrib1,axiom, % 167.45/167.45 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Sigma__Un__distrib2,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_rel__comp__subset__Sigma,axiom, % 167.45/167.45 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)))) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_C_2)))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_swap__product,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_prod(T_a,T_b)),hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__cartesian__product,axiom, % 167.45/167.45 ! [V_B_2,T_b,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_equiv__type,axiom, % 167.45/167.45 ! [V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Sigma__Int__distrib2,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Times__Int__distrib1,axiom, % 167.45/167.45 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Sigma__Int__distrib1,axiom, % 167.45/167.45 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Id__on__subset__Times,axiom, % 167.45/167.45 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId__on(T_a,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Range__Diff__subset,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2))),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_UNIV__Times__UNIV,axiom, % 167.45/167.45 ! [T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_SigmaE2,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 167.45/167.45 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.45 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_SigmaD2,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_SigmaD1,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_mem__Sigma__iff,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 167.45/167.45 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.45 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Range__Union,axiom, % 167.45/167.45 ! [V_S_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_b,T_a)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Range__empty__iff,axiom, % 167.45/167.45 ! [V_r_2,T_a,T_b] : % 167.45/167.45 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Range__empty,axiom, % 167.45/167.45 ! [T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Range__Un__eq,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__Range,axiom, % 167.45/167.45 ! [V_r_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_snd__eq__Range,axiom, % 167.45/167.45 ! [V_R_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_a,c_Product__Type_Osnd(T_b,T_a)),V_R_2) = hAPP(c_Relation_ORange(T_b,T_a),V_R_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_card__cartesian__product__singleton,axiom, % 167.45/167.45 ! [V_A_2,V_x_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Times__subset__cancel2,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)))) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Image__subset,axiom, % 167.45/167.45 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_C_2)),V_B_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__cartesian__productD1,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 167.45/167.45 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__cartesian__productD2,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 167.45/167.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_SetCompr__Sigma__eq,axiom, % 167.45/167.45 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),V_Q_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Collect__split,axiom, % 167.45/167.45 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_OCollect(T_b),V_Q_2))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_fst__image__times,axiom, % 167.45/167.45 ! [V_A_2,T_b,T_a,V_B_2] : % 167.45/167.45 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 167.45/167.45 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = V_A_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_snd__image__times,axiom, % 167.45/167.45 ! [V_B_2,T_b,T_a,V_A_2] : % 167.45/167.45 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 167.45/167.45 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = V_B_2 ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Range__iff,axiom, % 167.45/167.45 ! [V_r_2,T_b,V_a_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 167.45/167.45 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_a_2)),V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Range__insert,axiom, % 167.45/167.45 ! [V_r_2,V_b_2,V_a_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Range__Int__subset,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_insert__times__insert,axiom, % 167.45/167.45 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__equiv__class,axiom, % 167.45/167.45 ! [V_X_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_UN__Times__distrib,axiom, % 167.45/167.45 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_b,T_a,T_d,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_c,T_d),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_c),c_Product__Type_OSigma(T_a,T_b)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),T_d),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_F_2))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Sigma__def,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__quotient,axiom, % 167.45/167.45 ! [V_r_2,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__in__rel,axiom, % 167.45/167.45 ! [V_R_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_R_2) % 167.45/167.45 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wfP__wf__eq,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_OwfP(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)) % 167.45/167.45 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setsum__mult__setsum__if__inj,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : % 167.45/167.45 ( class_Rings_Osemiring__0(T_c) % 167.45/167.45 => ( c_Fun_Oinj__on(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) % 167.45/167.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_RangeP__Range__eq,axiom, % 167.45/167.45 ! [V_x_2,V_r_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2)) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 167.45/167.45 ! [V_A_2,V_I_2,T_b,T_a] : % 167.45/167.45 ? [B_f] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,tc_prod(T_b,T_a),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) % 167.45/167.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,tc_prod(T_b,T_a),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_I_2),V_A_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_RangeP_Ointros,axiom, % 167.45/167.45 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 167.45/167.45 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_image__id,axiom, % 167.45/167.45 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ). % 167.45/167.45 % 167.45/167.45 fof(fact_of__int__eq__id,axiom, % 167.45/167.45 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__id,axiom, % 167.45/167.45 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ). % 167.45/167.45 % 167.45/167.45 fof(fact_id__apply,axiom, % 167.45/167.45 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 167.45/167.45 % 167.45/167.45 fof(fact_id__def,axiom, % 167.45/167.45 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 167.45/167.45 % 167.45/167.45 fof(fact_RangeP_Oequations,axiom, % 167.45/167.45 ! [V_a2_2,V_r_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2)) % 167.45/167.45 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_apsnd__id,axiom, % 167.45/167.45 ! [T_a,T_b] : c_Product__Type_Oapsnd(T_b,T_b,T_a,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_apfst__id,axiom, % 167.45/167.45 ! [T_b,T_a] : c_Product__Type_Oapfst(T_a,T_a,T_b,c_Fun_Oid(T_a)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__id,axiom, % 167.45/167.45 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_surj__id,axiom, % 167.45/167.45 ! [T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_split__Pair,axiom, % 167.45/167.45 ! [T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setsum__reindex__id,axiom, % 167.45/167.45 ! [V_B_2,V_f_2,T_a,T_b] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__add(T_b) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.45/167.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setprod__reindex__id,axiom, % 167.45/167.45 ! [V_B_2,V_f_2,T_a,T_b] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.45/167.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setprod__Sigma,axiom, % 167.45/167.45 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__mult(T_c) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 167.45/167.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setsum__Sigma,axiom, % 167.45/167.45 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__add(T_c) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 167.45/167.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_fold__image__Sigma,axiom, % 167.45/167.45 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__mult(T_c) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 167.45/167.45 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBC(T_a,T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),T_a),c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c))),V_g_2)),c_Groups_Oone__class_Oone(T_c))),V_B_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,tc_prod(T_a,T_b),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_g_2)),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_card__SigmaI,axiom, % 167.45/167.45 ! [V_B_2,T_b,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 167.45/167.45 => hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),V_B_2)),V_A_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__SigmaI,axiom, % 167.45/167.45 ! [V_B_2,T_b,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( ! [B_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_RangeE,axiom, % 167.45/167.45 ! [V_r_2,T_b,V_b_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 167.45/167.45 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_SigmaE,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_c_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 167.45/167.45 => ~ ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => ! [B_y] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) % 167.45/167.45 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wfP__acyclicP,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_OwfP(T_a,V_r_2) % 167.45/167.45 => c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__Un,axiom, % 167.45/167.45 ! [V_s_2,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => ( c_Wellfounded_Owf(T_a,V_s_2) % 167.45/167.45 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_DomainI,axiom, % 167.45/167.45 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_acyclic__subset,axiom, % 167.45/167.45 ! [V_r_2,V_s_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Oacyclic(T_a,V_s_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 167.45/167.45 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Domain__Id__on,axiom, % 167.45/167.45 ! [V_A_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__acyclic,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Domain__empty__iff,axiom, % 167.45/167.45 ! [V_r_2,T_b,T_a] : % 167.45/167.45 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Domain__empty,axiom, % 167.45/167.45 ! [T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Domain__mono,axiom, % 167.45/167.45 ! [V_s_2,V_r_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_s_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Domain__Un__eq,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__Domain,axiom, % 167.45/167.45 ! [V_r_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_fst__eq__Domain,axiom, % 167.45/167.45 ! [V_R_2,T_b,T_a] : hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),V_R_2) = hAPP(c_Relation_ODomain(T_a,T_b),V_R_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Domain__iff,axiom, % 167.45/167.45 ! [V_r_2,T_b,V_a_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 167.45/167.45 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Domain__insert,axiom, % 167.45/167.45 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_finite__acyclic__wf,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 167.45/167.45 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 167.45/167.45 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__iff__acyclic__if__finite,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 167.45/167.45 => ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Domain__Int__subset,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Domain__Diff__subset,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2))),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Field__def,axiom, % 167.45/167.45 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_r_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Domain__Union,axiom, % 167.45/167.45 ! [V_S_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_a,T_b)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Domain__Collect__split,axiom, % 167.45/167.45 ! [V_P_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),V_P_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_DomainP__Domain__eq,axiom, % 167.45/167.45 ! [V_x_2,V_r_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2)) % 167.45/167.45 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Nitpick_Owf_H__def,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Nitpick_Owf_H(T_a,V_r_2) % 167.45/167.45 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 167.45/167.45 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 167.45/167.45 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_DomainE,axiom, % 167.45/167.45 ! [V_r_2,T_b,V_a_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 167.45/167.45 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_DomainP_Ointros,axiom, % 167.45/167.45 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 167.45/167.45 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_DomainP_Oequations,axiom, % 167.45/167.45 ! [V_a1_2,V_r_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2)) % 167.45/167.45 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair__surj,axiom, % 167.45/167.45 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] : % 167.45/167.45 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 167.45/167.45 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair__inj__on,axiom, % 167.45/167.45 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2) % 167.45/167.45 => c_Fun_Oinj__on(tc_prod(T_a,T_c),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_a,T_b,T_c,T_d,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_2))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wf__map__pair__image,axiom, % 167.45/167.45 ! [V_f_2,T_b,V_r_2,T_a] : % 167.45/167.45 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => c_Wellfounded_Owf(T_b,hAPP(c_Set_Oimage(tc_prod(T_a,T_a),tc_prod(T_b,T_b),c_Product__Type_Omap__pair(T_a,T_b,T_a,T_b,V_f_2,V_f_2)),V_r_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair__imageI,axiom, % 167.45/167.45 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_R_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)),V_R_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair__simp,axiom, % 167.45/167.45 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair__ident,axiom, % 167.45/167.45 ! [V_z_2,T_b,T_a] : hAPP(c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)),V_z_2) = V_z_2 ). % 167.45/167.45 % 167.45/167.45 fof(fact_snd__prod__fun,axiom, % 167.45/167.45 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Omap__pair(T_c,T_b,T_d,T_a,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_fst__map__pair,axiom, % 167.45/167.45 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair_Oidentity,axiom, % 167.45/167.45 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_apfst__def,axiom, % 167.45/167.45 ! [V_f_2,T_b,T_c,T_a] : c_Product__Type_Oapfst(T_a,T_c,T_b,V_f_2) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_b,V_f_2,c_Fun_Oid(T_b)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_apsnd__def,axiom, % 167.45/167.45 ! [V_f_2,T_a,T_c,T_b] : c_Product__Type_Oapsnd(T_b,T_c,T_a,V_f_2) = c_Product__Type_Omap__pair(T_a,T_a,T_b,T_c,c_Fun_Oid(T_a),V_f_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair_Oid,axiom, % 167.45/167.45 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_Fun_Oid(T_a),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair__def,axiom, % 167.45/167.45 ! [V_g_2,V_f_2,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),T_a),c_COMBB(T_d,tc_prod(T_c,T_d),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_a),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_g_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair__surj__on,axiom, % 167.45/167.45 ! [V_B_H_2,V_B_2,V_g_2,T_c,T_d,V_A_H_2,V_A_2,V_f_2,T_a,T_b] : % 167.45/167.45 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 167.45/167.45 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2 % 167.45/167.45 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_H_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_H_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_prod__fun__imageE,axiom, % 167.45/167.45 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_c_2,T_b,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2)),V_R_2))) % 167.45/167.45 => ~ ! [B_x,B_y] : % 167.45/167.45 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 167.45/167.45 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)),V_R_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_refl__on__def,axiom, % 167.45/167.45 ! [V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 167.45/167.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 167.45/167.45 & ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Rep__Integ__induct,axiom, % 167.45/167.45 ! [V_P_2,V_y_2] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 167.45/167.45 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x))) % 167.45/167.45 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_refl__on__Id__on,axiom, % 167.45/167.45 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_refl__on__empty,axiom, % 167.45/167.45 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_refl__on__Un,axiom, % 167.45/167.45 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 167.45/167.45 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_refl__on__Int,axiom, % 167.45/167.45 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 167.45/167.45 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_refl__onD,axiom, % 167.45/167.45 ! [V_a_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_refl__onD1,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_refl__onD2,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_reflp__def,axiom, % 167.45/167.45 ! [V_r_2,T_a] : % 167.45/167.45 ( c_Predicate_Oreflp(T_a,V_r_2) % 167.45/167.45 <=> c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_refl__onI,axiom, % 167.45/167.45 ! [V_A_2,V_r_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 167.45/167.45 => ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) % 167.45/167.45 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Rep__Integ__cases,axiom, % 167.45/167.45 ! [V_y_2] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 167.45/167.45 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_reflpE,axiom, % 167.45/167.45 ! [V_x_2,V_r_2,T_a] : % 167.45/167.45 ( c_Predicate_Oreflp(T_a,V_r_2) % 167.45/167.45 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__INTER,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] : % 167.45/167.45 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => ( ! [B_i] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) % 167.45/167.45 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) ) % 167.45/167.45 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_refl__on__def_H,axiom, % 167.45/167.45 ! [V_r_2,V_A_2,T_a] : % 167.45/167.45 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 167.45/167.45 <=> ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),B_x)) ) % 167.45/167.45 & ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Abs__Integ__cases,axiom, % 167.45/167.45 ! [V_x_2] : % 167.45/167.45 ~ ! [B_y] : % 167.45/167.45 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 167.45/167.45 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_ball__empty,axiom, % 167.45/167.45 ! [V_P_2,T_a,B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 167.45/167.45 => hBOOL(hAPP(V_P_2,B_x)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Powp__def,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) % 167.45/167.45 <=> ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 167.45/167.45 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_INFI__bool__eq,axiom, % 167.45/167.45 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ). % 167.45/167.45 % 167.45/167.45 fof(fact_ball__UNIV,axiom, % 167.45/167.45 ! [V_P_2,T_a] : % 167.45/167.45 ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 167.45/167.45 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.45 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Collect__ball__eq,axiom, % 167.45/167.45 ! [V_P_2,V_A_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_congruent__def,axiom, % 167.45/167.45 ! [V_f_2,V_r_2,T_b,T_a] : % 167.45/167.45 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 167.45/167.45 <=> ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_INTER__def,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_member(T_a))),V_B_2)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Sup__Inf,axiom, % 167.45/167.45 ! [V_A_2,T_a] : % 167.45/167.45 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.45/167.45 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a)))))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Inf__Sup,axiom, % 167.45/167.45 ! [V_A_2,T_a] : % 167.45/167.45 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.45/167.45 => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_a))))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Abs__Integ__induct,axiom, % 167.45/167.45 ! [V_x_2,V_P_2] : % 167.45/167.45 ( ! [B_y] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 167.45/167.45 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 167.45/167.45 => hBOOL(hAPP(V_P_2,V_x_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__diff__nat,axiom, % 167.45/167.45 ! [V_k_2,V_N_2] : % 167.45/167.45 ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 167.45/167.45 => c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_wfP__SUP,axiom, % 167.45/167.45 ! [T_a,V_r_2,T_b] : % 167.45/167.45 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) % 167.45/167.45 => ( ! [B_i,B_j] : % 167.45/167.45 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 167.45/167.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Predicate_ODomainP(T_b,T_b,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_b,T_b,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 167.45/167.45 => c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_triples__valid__Suc,axiom, % 167.45/167.45 ! [V_n_2,V_ts_2,T_a] : % 167.45/167.45 ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 167.45/167.45 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 167.45/167.45 => ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 167.45/167.45 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_hoare__valids__def,axiom, % 167.45/167.45 ! [V_ts_2,V_Ga_2,T_a] : % 167.45/167.45 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) % 167.45/167.45 <=> ! [B_n] : % 167.45/167.45 ( ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2)) % 167.45/167.45 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) % 167.45/167.45 => ! [B_x] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 167.45/167.45 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_Inter__eq,axiom, % 167.45/167.45 ! [V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))),c_member(T_a)))) ). % 167.45/167.45 % 167.45/167.45 fof(fact_mem__splitI2,axiom, % 167.45/167.45 ! [V_c_2,V_z_2,T_c,T_b,T_a,V_p_2] : % 167.45/167.45 ( ! [B_a,B_b] : % 167.45/167.45 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) ) % 167.45/167.45 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_c_2),V_p_2))) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_mem__splitE,axiom, % 167.45/167.45 ! [V_p_2,V_c_2,T_c,T_b,V_z_2,T_a] : % 167.45/167.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),V_p_2))) % 167.45/167.45 => ~ ! [B_x,B_y] : % 167.45/167.45 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) % 167.45/167.45 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__Times,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,tc_prod(T_b,T_c),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_b,T_a,c_Product__Type_Ofst(T_b,T_c)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_c,T_a,c_Product__Type_Osnd(T_b,T_c)),V_f_2)),V_B_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair_Ocompositionality,axiom, % 167.45/167.45 ! [V_prod_2,V_i_2,V_h_2,T_f,T_e,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_e,T_a,T_f,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_e,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_g_2),V_i_2)),V_prod_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair__compose,axiom, % 167.45/167.45 ! [V_g2_2,V_g1_2,T_f,V_f2_2,V_f1_2,T_e,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_f2_2,V_g2_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_map__pair_Ocomp,axiom, % 167.45/167.45 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_b,T_a,T_d,T_c,T_f,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g_2),V_i_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_o__eq__id__dest,axiom, % 167.45/167.45 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 167.45/167.45 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_c_2) % 167.45/167.45 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_id__o,axiom, % 167.45/167.45 ! [V_g_2,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_g_2) = V_g_2 ). % 167.45/167.45 % 167.45/167.45 fof(fact_o__id,axiom, % 167.45/167.45 ! [V_f_2,T_b,T_a] : hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_f_2),c_Fun_Oid(T_a)) = V_f_2 ). % 167.45/167.45 % 167.45/167.45 fof(fact_vimage__compose,axiom, % 167.45/167.45 ! [V_x_2,V_f_2,V_g_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_a,T_c,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_g_2),V_x_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_fun__upd__comp,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_c),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_comp__cong,axiom, % 167.45/167.45 ! [T_e,T_d,T_c,T_a,T_b,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] : % 167.45/167.45 ( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2)) % 167.45/167.45 => hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2),V_g_H_2),V_x_H_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_K__record__comp,axiom, % 167.45/167.45 ! [V_x_2,V_f_2,V_c_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_f_2),V_x_2) = V_c_2 ). % 167.45/167.45 % 167.45/167.45 fof(fact_o__def,axiom, % 167.45/167.45 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_o__eq__dest__lhs,axiom, % 167.45/167.45 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 167.45/167.45 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_c_2 % 167.45/167.45 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_o__assoc,axiom, % 167.45/167.45 ! [V_h_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(c_Fun_Ocomp(T_d,T_c,T_a,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_h_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_o__apply,axiom, % 167.45/167.45 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_o__eq__dest,axiom, % 167.45/167.45 ! [V_v_2,V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 167.45/167.45 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2) % 167.45/167.45 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_o__eq__elim,axiom, % 167.45/167.45 ! [V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 167.45/167.45 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2) % 167.45/167.45 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 167.45/167.45 ! [V_x_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 167.45/167.45 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 167.45/167.45 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.45/167.45 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_apsnd__compose,axiom, % 167.45/167.45 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_a,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_x_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_apfst__compose,axiom, % 167.45/167.45 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_d,V_f_2),V_g_2)),V_x_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__imageI2,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_H_2),V_f_2),V_A_2) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__comp,axiom, % 167.45/167.45 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.45 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 167.45/167.45 => c_Fun_Oinj__on(T_c,T_b,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_image__compose,axiom, % 167.45/167.45 ! [V_r_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_a,T_b,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_r_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_comp__surj,axiom, % 167.45/167.45 ! [V_g_2,T_c,V_f_2,T_a,T_b] : % 167.45/167.45 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => ( hAPP(c_Set_Oimage(T_a,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 167.45/167.45 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_a,T_c,T_b,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_inj__on__imageI,axiom, % 167.45/167.45 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2),V_A_2) % 167.45/167.45 => c_Fun_Oinj__on(T_c,T_b,V_g_2,hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_A_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_comp__inj__on,axiom, % 167.45/167.45 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( c_Fun_Oinj__on(T_b,T_c,V_g_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) % 167.45/167.45 => c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_f_2),V_A_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_comp__inj__on__iff,axiom, % 167.45/167.45 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( c_Fun_Oinj__on(T_b,T_c,V_f_H_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) % 167.45/167.45 <=> c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_f_H_2),V_f_2),V_A_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setsum__reindex,axiom, % 167.45/167.45 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__add(T_c) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.45/167.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setprod__reindex__cong,axiom, % 167.45/167.45 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__mult(T_c) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.45 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 167.45/167.45 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2) % 167.45/167.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setprod__reindex,axiom, % 167.45/167.45 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__mult(T_c) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.45/167.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setsum_Oreindex,axiom, % 167.45/167.45 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__add(T_b) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 167.45/167.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_setprod_Oreindex,axiom, % 167.45/167.45 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 167.45/167.45 ( class_Groups_Ocomm__monoid__mult(T_b) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 167.45/167.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_the__inv__into__comp,axiom, % 167.45/167.45 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2)) % 167.45/167.45 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2)))) % 167.45/167.45 => hAPP(c_Fun_Othe__inv__into(T_c,T_b,V_A_2,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_a,T_c,T_b,c_Fun_Othe__inv__into(T_c,T_a,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_a,T_b,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding__image_Oreindex,axiom, % 167.45/167.45 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 167.45/167.45 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 167.45/167.45 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_b,T_a,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_fold__image__reindex,axiom, % 167.45/167.45 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] : % 167.45/167.45 ( class_Groups_Oab__semigroup__mult(T_c) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2) % 167.45/167.45 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Oremove,axiom, % 167.45/167.45 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.45 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Ounion,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.45 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.45 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Oinsert__remove,axiom, % 167.45/167.45 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_snd__comp__map__pair,axiom, % 167.45/167.45 ! [V_g_2,V_f_2,T_b,T_a,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_c),T_c,tc_prod(T_a,T_b),c_Product__Type_Osnd(T_d,T_c)),c_Product__Type_Omap__pair(T_a,T_d,T_b,T_c,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_c,tc_prod(T_a,T_b),V_g_2),c_Product__Type_Osnd(T_a,T_b)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_fst__comp__map__pair,axiom, % 167.45/167.45 ! [V_g_2,V_f_2,T_b,T_a,T_d,T_c] : hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,tc_prod(T_a,T_b),c_Product__Type_Ofst(T_c,T_d)),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_a,T_c,tc_prod(T_a,T_b),V_f_2),c_Product__Type_Ofst(T_a,T_b)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 167.45/167.45 ! [V_h_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e,V_F_2,V_fa_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) % 167.45/167.45 => hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),hAPP(c_Fun_Ocomp(T_f,T_e,T_c,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,V_f_2),V_g_2)),V_h_2) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Ocommute__comp,axiom, % 167.45/167.45 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Ocommute__left__comp,axiom, % 167.45/167.45 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),V_g_2)) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_UN__o,axiom, % 167.45/167.45 ! [V_f_2,V_g_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_c,tc_fun(T_a,tc_HOL_Obool),T_b,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_g_2) ). % 167.45/167.45 % 167.45/167.45 fof(fact_split__comp,axiom, % 167.45/167.45 ! [V_x_2,V_g_2,V_f_2,T_d,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_c,T_a),T_b,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_x_2))),hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 167.45/167.45 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.45 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Ocommute__comp_H_H,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.45 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Ocommute__left__comp_H,axiom, % 167.45/167.45 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Ocommute__comp_H,axiom, % 167.45/167.45 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Oempty,axiom, % 167.45/167.45 ! [V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Oeq__fold,axiom, % 167.45/167.45 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_s_2),V_A_2) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Oinsert,axiom, % 167.45/167.45 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.45 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ). % 167.45/167.45 % 167.45/167.45 fof(fact_folding_Ounion__inter,axiom, % 167.45/167.45 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.45 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.46 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Loop__sound__lemma,axiom, % 167.45/167.46 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 167.45/167.46 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.45/167.46 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_hoare__derivs_OIf,axiom, % 167.45/167.46 ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 167.45/167.46 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.45/167.46 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.45/167.46 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_peek__and__def,axiom, % 167.45/167.46 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) % 167.45/167.46 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) % 167.45/167.46 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Loop,axiom, % 167.45/167.46 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 167.45/167.46 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.45/167.46 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_setsum__reindex__nonzero,axiom, % 167.45/167.46 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] : % 167.45/167.46 ( class_Groups_Ocomm__monoid__add(T_c) % 167.45/167.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 167.45/167.46 => ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 167.45/167.46 => ! [B_y] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) % 167.45/167.46 => ( B_x != B_y % 167.45/167.46 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 167.45/167.46 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) % 167.45/167.46 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_S_2) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_folding__idem_Ounion__idem,axiom, % 167.45/167.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.46 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 167.45/167.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 167.45/167.46 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_folding__idem_Oidem__left__comp,axiom, % 167.45/167.46 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.46 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 167.45/167.46 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_folding__idem_Oidem__comp,axiom, % 167.45/167.46 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.46 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 167.45/167.46 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_folding__idem_Oin__comp__idem,axiom, % 167.45/167.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.46 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 167.45/167.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.46 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_folding__idem_Oinsert__idem,axiom, % 167.45/167.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.46 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 167.45/167.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.46 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 167.45/167.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 167.45/167.46 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 167.45/167.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.45/167.46 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_strong__setprod__reindex__cong,axiom, % 167.45/167.46 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 167.45/167.46 ( class_Groups_Ocomm__monoid__mult(T_c) % 167.45/167.46 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.46 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 167.45/167.46 => ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.46 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2),B_x) ) % 167.45/167.46 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Eps__split,axiom, % 167.45/167.46 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_tfl__some,axiom, % 167.45/167.46 ! [T_a,B_P] : % 167.45/167.46 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 167.45/167.46 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_someI,axiom, % 167.45/167.46 ! [T_a,V_x_2,V_P_2] : % 167.45/167.46 ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.46 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_someI__ex,axiom, % 167.45/167.46 ! [T_a,V_P_2] : % 167.45/167.46 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 167.45/167.46 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_some__eq__ex,axiom, % 167.45/167.46 ! [T_a,V_P_2] : % 167.45/167.46 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) % 167.45/167.46 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_some__eq__trivial,axiom, % 167.45/167.46 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ). % 167.45/167.46 % 167.45/167.46 fof(fact_some__sym__eq__trivial,axiom, % 167.45/167.46 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 167.45/167.46 % 167.45/167.46 fof(fact_exE__some,axiom, % 167.45/167.46 ! [T_a,V_c_2,V_P_2] : % 167.45/167.46 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 167.45/167.46 => ( V_c_2 = c_Hilbert__Choice_OEps(T_a,V_P_2) % 167.45/167.46 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_split__paired__Eps,axiom, % 167.45/167.46 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Eps__split__eq,axiom, % 167.45/167.46 ! [V_y_2,V_x_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_LeastM__def,axiom, % 167.45/167.46 ! [V_P_2,V_m_2,T_a,T_b] : % 167.45/167.46 ( class_Orderings_Oord(T_b) % 167.45/167.46 => c_Hilbert__Choice_OLeastM(T_a,T_b,V_m_2,V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_GreatestM__def,axiom, % 167.45/167.46 ! [V_P_2,V_m_2,T_a,T_b] : % 167.45/167.46 ( class_Orderings_Oord(T_b) % 167.45/167.46 => hAPP(c_Hilbert__Choice_OGreatestM(T_a,T_b,V_m_2),V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_LeastM__nat__le,axiom, % 167.45/167.46 ! [T_a,V_m_2,V_x_2,V_P_2] : % 167.45/167.46 ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,V_x_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_LeastM__nat__lemma,axiom, % 167.45/167.46 ! [V_m_2,T_a,V_k_2,V_P_2] : % 167.45/167.46 ( hBOOL(hAPP(V_P_2,V_k_2)) % 167.45/167.46 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) % 167.45/167.46 & ! [B_y] : % 167.45/167.46 ( hBOOL(hAPP(V_P_2,B_y)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,B_y))) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Greatest__def,axiom, % 167.45/167.46 ! [T_a] : % 167.45/167.46 ( class_Orderings_Oord(T_a) % 167.45/167.46 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_wfI__pf,axiom, % 167.45/167.46 ! [V_R_2,T_a] : % 167.45/167.46 ( ! [B_A] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),B_A))) % 167.45/167.46 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 167.45/167.46 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_LeastM__natI,axiom, % 167.45/167.46 ! [V_m_2,T_a,V_k_2,V_P_2] : % 167.45/167.46 ( hBOOL(hAPP(V_P_2,V_k_2)) % 167.45/167.46 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Sigma__mono,axiom, % 167.45/167.46 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.45/167.46 => ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_C_2),V_D_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_acc_OaccI,axiom, % 167.45/167.46 ! [V_r_2,V_x_2,T_a] : % 167.45/167.46 ( ! [B_y] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_not__acc__down,axiom, % 167.45/167.46 ! [V_R_2,V_x_2,T_a] : % 167.45/167.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) % 167.45/167.46 => ~ ! [B_z] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_max__ext_Osimps,axiom, % 167.45/167.46 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 167.45/167.46 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 167.45/167.46 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 167.45/167.46 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.46 & ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 167.45/167.46 => ? [B_xa] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_wf__no__infinite__down__chainE,axiom, % 167.45/167.46 ! [V_f_2,V_r_2,T_a] : % 167.45/167.46 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.46 => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osize_I11_J,axiom, % 167.45/167.46 ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_WTs__elim__cases_I3_J,axiom, % 167.45/167.46 ! [V_c_2,V_a_2,V_Y_2] : % 167.45/167.46 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) % 167.45/167.46 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osimps_I37_J,axiom, % 167.45/167.46 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osimps_I36_J,axiom, % 167.45/167.46 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osimps_I2_J,axiom, % 167.45/167.46 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 167.45/167.46 ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) % 167.45/167.46 <=> ( V_loc_2 = V_loc_H_2 % 167.45/167.46 & V_fun_2 = V_fun_H_2 % 167.45/167.46 & V_com_2 = V_com_H_2 ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osimps_I41_J,axiom, % 167.45/167.46 ! [V_com_2,V_fun_2,V_loc_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osimps_I40_J,axiom, % 167.45/167.46 ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_WT_Oequations_I3_J,axiom, % 167.45/167.46 ! [V_a1_2,V_a3_2,V_a2_2] : % 167.45/167.46 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) % 167.45/167.46 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_WT_OLocal,axiom, % 167.45/167.46 ! [V_a_2,V_Y_2,V_c_2] : % 167.45/167.46 ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 167.45/167.46 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osimps_I39_J,axiom, % 167.45/167.46 ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osimps_I38_J,axiom, % 167.45/167.46 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osimps_I10_J,axiom, % 167.45/167.46 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osimps_I11_J,axiom, % 167.45/167.46 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osimps_I35_J,axiom, % 167.45/167.46 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osimps_I34_J,axiom, % 167.45/167.46 ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_com_Osize_I3_J,axiom, % 167.45/167.46 ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_setsum__reindex__cong,axiom, % 167.45/167.46 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 167.45/167.46 ( class_Groups_Ocomm__monoid__add(T_c) % 167.45/167.46 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.45/167.46 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 167.45/167.46 => ( ! [B_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 167.45/167.46 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 167.45/167.46 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_scomp__unfold,axiom, % 167.45/167.46 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),hAPP(V_f_2,V_x_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_scomp__scomp,axiom, % 167.45/167.46 ! [V_h_2,V_g_2,V_f_2,T_f,T_e,T_b,T_d,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_d,T_b),hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,tc_prod(T_c,T_d)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,T_b),V_f_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),T_e),c_Product__Type_Oscomp(T_f,T_c,T_d,T_b)),V_g_2)),V_h_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_scomp__Pair,axiom, % 167.45/167.46 ! [V_x_2,T_c,T_b,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_c,tc_prod(T_b,T_c)),V_x_2),c_Product__Type_OPair(T_b,T_c)) = V_x_2 ). % 167.45/167.46 % 167.45/167.46 fof(fact_Pair__scomp,axiom, % 167.45/167.46 ! [V_f_2,V_x_2,T_b,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_a,T_b),hAPP(c_Product__Type_OPair(T_c,T_a),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_scomp__apply,axiom, % 167.45/167.46 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_scomp__def,axiom, % 167.45/167.46 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_iterate_Osimps,axiom, % 167.45/167.46 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 167.45/167.46 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.46 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2) ) % 167.45/167.46 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.46 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_a,tc_prod(T_b,T_a)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_b,T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_setsum__ivl__cong,axiom, % 167.45/167.46 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_a,T_b] : % 167.45/167.46 ( ( class_Groups_Ocomm__monoid__add(T_b) % 167.45/167.46 & class_Orderings_Oord(T_a) ) % 167.45/167.46 => ( V_a_2 = V_c_2 % 167.45/167.46 => ( V_b_2 = V_d_2 % 167.45/167.46 => ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),B_x)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2)) % 167.45/167.46 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 167.45/167.46 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)) ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_log_Osimps,axiom, % 167.45/167.46 ! [V_i,V_b] : % 167.45/167.46 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) % 167.45/167.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 167.45/167.46 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 167.45/167.46 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) % 167.45/167.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 167.45/167.46 => c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_minus__shift__def,axiom, % 167.45/167.46 ! [V_r,V_l,V_k] : % 167.45/167.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 167.45/167.46 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l) ) % 167.45/167.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 167.45/167.46 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_inc__shift__def,axiom, % 167.45/167.46 ! [V_k,V_v] : % 167.45/167.46 ( ( V_v = V_k % 167.45/167.46 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 167.45/167.46 & ( V_v != V_k % 167.45/167.46 => c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_range,axiom, % 167.45/167.46 ! [V_s,V_k] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_less__eq,axiom, % 167.45/167.46 ! [V_n_2,V_m_2] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) % 167.45/167.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nat__intermed__int__val,axiom, % 167.45/167.46 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 167.45/167.46 ( ! [B_i] : % 167.45/167.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 167.45/167.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 167.45/167.46 => ? [B_i] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 167.45/167.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 167.45/167.46 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_wf__trancl,axiom, % 167.45/167.46 ! [V_r_2,T_a] : % 167.45/167.46 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.46 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_less__than__def,axiom, % 167.45/167.46 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 167.45/167.46 % 167.45/167.46 fof(fact_acyclic__def,axiom, % 167.45/167.46 ! [V_r_2,T_a] : % 167.45/167.46 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 167.45/167.46 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl_Or__into__trancl,axiom, % 167.45/167.46 ! [V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__subset__Field2,axiom, % 167.45/167.46 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_Relation_OField(T_a),V_r_2))))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_r__into__trancl_H,axiom, % 167.45/167.46 ! [V_r_2,V_p_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__empty,axiom, % 167.45/167.46 ! [T_a] : c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__domain,axiom, % 167.45/167.46 ! [V_r_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__range,axiom, % 167.45/167.46 ! [V_r_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ORange(T_a,T_a),V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_finite__trancl,axiom, % 167.45/167.46 ! [V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 167.45/167.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_r__r__into__trancl,axiom, % 167.45/167.46 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_R_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_R_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__into__trancl2,axiom, % 167.45/167.46 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 167.45/167.46 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__trans,axiom, % 167.45/167.46 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__mono,axiom, % 167.45/167.46 ! [V_s_2,V_r_2,V_p_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__unfold,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__subset__Sigma,axiom, % 167.45/167.46 ! [V_A_2,V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__Int__subset,axiom, % 167.45/167.46 ! [V_s_2,V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__insert,axiom, % 167.45/167.46 ! [V_r_2,V_x_2,V_y_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBC(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),V_y_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_reflcl__set__eq,axiom, % 167.45/167.46 ! [V_y_2,V_x_2,V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),c_fequal),V_x_2),V_y_2)) % 167.45/167.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_r__into__rtrancl,axiom, % 167.45/167.46 ! [V_r_2,V_p_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl_Ortrancl__refl,axiom, % 167.45/167.46 ! [V_r_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_IdI,axiom, % 167.45/167.46 ! [V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Relation_OId(T_a))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__into__rtrancl,axiom, % 167.45/167.46 ! [V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__rtrancl__absorb,axiom, % 167.45/167.46 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__trancl__absorb,axiom, % 167.45/167.46 ! [V_R_2,T_a] : c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_reflcl__trancl,axiom, % 167.45/167.46 ! [V_r_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__reflcl,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__unfold__right,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__unfold__left,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__Un__subset,axiom, % 167.45/167.46 ! [V_S_2,V_R_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__subset__rtrancl,axiom, % 167.45/167.46 ! [V_s_2,V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__subset,axiom, % 167.45/167.46 ! [V_S_2,V_R_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 167.45/167.46 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__mono,axiom, % 167.45/167.46 ! [V_s_2,V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Image__closed__trancl,axiom, % 167.45/167.46 ! [V_X_2,V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),V_X_2)),V_X_2)) % 167.45/167.46 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__Int__subset,axiom, % 167.45/167.46 ! [V_r_2,V_s_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),V_s_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_refl__rtrancl,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__r__diff__Id,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__unfold,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_r__comp__rtrancl__eq,axiom, % 167.45/167.46 ! [V_r_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__idemp__self__comp,axiom, % 167.45/167.46 ! [V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_in__rtrancl__UnI,axiom, % 167.45/167.46 ! [V_S_2,V_R_2,V_x_2,T_a] : % 167.45/167.46 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 167.45/167.46 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__reflcl,axiom, % 167.45/167.46 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__Un__rtrancl,axiom, % 167.45/167.46 ! [V_S_2,V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) = c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__reflcl__absorb,axiom, % 167.45/167.46 ! [V_R_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__idemp,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 167.45/167.46 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 167.45/167.46 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__trans,axiom, % 167.45/167.46 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__empty,axiom, % 167.45/167.46 ! [T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Relation_OId(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Range__rtrancl,axiom, % 167.45/167.46 ! [V_R_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Domain__rtrancl,axiom, % 167.45/167.46 ! [V_R_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Image__Id,axiom, % 167.45/167.46 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ). % 167.45/167.46 % 167.45/167.46 fof(fact_Id__O__R,axiom, % 167.45/167.46 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_b),c_Relation_OId(T_a)),V_R_2) = V_R_2 ). % 167.45/167.46 % 167.45/167.46 fof(fact_R__O__Id,axiom, % 167.45/167.46 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_b),V_R_2),c_Relation_OId(T_b)) = V_R_2 ). % 167.45/167.46 % 167.45/167.46 fof(fact_pair__in__Id__conv,axiom, % 167.45/167.46 ! [V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId(T_a))) % 167.45/167.46 <=> V_a_2 = V_b_2 ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__eq__or__trancl,axiom, % 167.45/167.46 ! [V_R_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 167.45/167.46 <=> ( V_x_2 = V_y_2 % 167.45/167.46 | ( V_x_2 != V_y_2 % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__into__trancl2,axiom, % 167.45/167.46 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtranclD,axiom, % 167.45/167.46 ! [V_R_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 167.45/167.46 => ( V_a_2 = V_b_2 % 167.45/167.46 | ( V_a_2 != V_b_2 % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__into__trancl1,axiom, % 167.45/167.46 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__rtrancl__trancl,axiom, % 167.45/167.46 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__trancl__trancl,axiom, % 167.45/167.46 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Domain__Id,axiom, % 167.45/167.46 ! [T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Range__Id,axiom, % 167.45/167.46 ! [T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_refl__Id,axiom, % 167.45/167.46 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Relation_OId(T_a)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_pair__leq__def,axiom, % 167.45/167.46 c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Not__Domain__rtrancl,axiom, % 167.45/167.46 ! [V_y_2,V_R_2,V_x_2,T_a] : % 167.45/167.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 167.45/167.46 <=> V_x_2 = V_y_2 ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_acc__downwards,axiom, % 167.45/167.46 ! [V_b_2,V_r_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_acc__downwards__aux,axiom, % 167.45/167.46 ! [V_r_2,V_a_2,V_b_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_wf__insert,axiom, % 167.45/167.46 ! [V_r_2,V_x_2,V_y_2,T_a] : % 167.45/167.46 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) % 167.45/167.46 <=> ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.46 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_acyclic__insert,axiom, % 167.45/167.46 ! [V_r_2,V_x_2,V_y_2,T_a] : % 167.45/167.46 ( c_Wellfounded_Oacyclic(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) % 167.45/167.46 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 167.45/167.46 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_refl__reflcl,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Id__def,axiom, % 167.45/167.46 ! [T_a] : c_Relation_OId(T_a) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_a),tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),tc_prod(T_a,T_a)),c_COMBB(tc_prod(T_a,T_a),tc_HOL_Obool,T_a)),c_fequal)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_irrefl__diff__Id,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Relation_Oirrefl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_pred__nat__trancl__eq__le,axiom, % 167.45/167.46 ! [V_n_2,V_m_2] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) % 167.45/167.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__subset__Sigma__aux,axiom, % 167.45/167.46 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 167.45/167.46 => ( V_a_2 = V_b_2 % 167.45/167.46 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_irrefl__tranclI,axiom, % 167.45/167.46 ! [V_x_2,V_r_2,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_sequence__trans,axiom, % 167.45/167.46 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] : % 167.45/167.46 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__converse,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__Id,axiom, % 167.45/167.46 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_refl__on__converse,axiom, % 167.45/167.46 ! [V_r_2,V_A_2,T_a] : % 167.45/167.46 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 167.45/167.46 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__UNION,axiom, % 167.45/167.46 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__iff,axiom, % 167.45/167.46 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 167.45/167.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converseI,axiom, % 167.45/167.46 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converseD,axiom, % 167.45/167.46 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__rel__comp,axiom, % 167.45/167.46 ! [V_s_2,V_r_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_a),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_a),V_s_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__Un,axiom, % 167.45/167.46 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__Id__on,axiom, % 167.45/167.46 ! [V_A_2,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = c_Relation_OId__on(T_a,V_A_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__Int,axiom, % 167.45/167.46 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__converse,axiom, % 167.45/167.46 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = V_r_2 ). % 167.45/167.46 % 167.45/167.46 fof(fact_finite__converse,axiom, % 167.45/167.46 ! [V_r_2,T_b,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 167.45/167.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__inv__image,axiom, % 167.45/167.46 ! [V_f_2,V_R_2,T_b,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),hAPP(c_Relation_Oconverse(T_b,T_b),V_R_2)),V_f_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Field__converse,axiom, % 167.45/167.46 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_OField(T_a),V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_acyclic__converse,axiom, % 167.45/167.46 ! [V_r_2,T_a] : % 167.45/167.46 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 167.45/167.46 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__INTER,axiom, % 167.45/167.46 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__converse,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_wf__converse__trancl,axiom, % 167.45/167.46 ! [V_r_2,T_a] : % 167.45/167.46 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 167.45/167.46 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_equiv__comp__eq,axiom, % 167.45/167.46 ! [V_r_2,V_A_2,T_a] : % 167.45/167.46 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.46 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2 ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Range__converse,axiom, % 167.45/167.46 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Domain__converse,axiom, % 167.45/167.46 ! [V_r_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) = hAPP(c_Relation_ORange(T_b,T_a),V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Range__def,axiom, % 167.45/167.46 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__converseD,axiom, % 167.45/167.46 ! [V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__converseI,axiom, % 167.45/167.46 ! [V_r_2,V_x_2,V_y_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__converseD,axiom, % 167.45/167.46 ! [V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__converseI,axiom, % 167.45/167.46 ! [V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Image__subset__eq,axiom, % 167.45/167.46 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)),V_B_2)) % 167.45/167.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_refl__on__comp__subset,axiom, % 167.45/167.46 ! [V_r_2,V_A_2,T_a] : % 167.45/167.46 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_comp__equivI,axiom, % 167.45/167.46 ! [V_A_2,V_r_2,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2 % 167.45/167.46 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2 % 167.45/167.46 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_finite__acyclic__wf__converse,axiom, % 167.45/167.46 ! [V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 167.45/167.46 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 167.45/167.46 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converse__def,axiom, % 167.45/167.46 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_a)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_a)))),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))))),V_r_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Image__INT__eq,axiom, % 167.45/167.46 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] : % 167.45/167.46 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) % 167.45/167.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 167.45/167.46 => hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_total__on__diff__Id,axiom, % 167.45/167.46 ! [V_r_2,V_A_2,T_a] : % 167.45/167.46 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) % 167.45/167.46 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_single__valued__Id,axiom, % 167.45/167.46 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_single__valued__Id__on,axiom, % 167.45/167.46 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_single__valued__rel__comp,axiom, % 167.45/167.46 ! [V_s_2,T_c,V_r_2,T_b,T_a] : % 167.45/167.46 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 167.45/167.46 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 167.45/167.46 => c_Relation_Osingle__valued(T_a,T_c,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_single__valued__subset,axiom, % 167.45/167.46 ! [V_s_2,V_r_2,T_b,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 167.45/167.46 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2) % 167.45/167.46 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_total__on__empty,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_total__on__converse,axiom, % 167.45/167.46 ! [V_r_2,V_A_2,T_a] : % 167.45/167.46 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 167.45/167.46 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_single__valued__def,axiom, % 167.45/167.46 ! [V_r_2,T_b,T_a] : % 167.45/167.46 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 167.45/167.46 <=> ! [B_x,B_y] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2)) % 167.45/167.46 => ! [B_z] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2)) % 167.45/167.46 => B_y = B_z ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_single__valuedD,axiom, % 167.45/167.46 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] : % 167.45/167.46 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_z_2)),V_r_2)) % 167.45/167.46 => V_y_2 = V_z_2 ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_total__on__def,axiom, % 167.45/167.46 ! [V_r_2,V_A_2,T_a] : % 167.45/167.46 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2) % 167.45/167.46 <=> ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.46 => ! [B_xa] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 167.45/167.46 => ( B_x != B_xa % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2)) % 167.45/167.46 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2)) ) ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_single__valued__confluent,axiom, % 167.45/167.46 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 167.45/167.46 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Image__Int__eq,axiom, % 167.45/167.46 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : % 167.45/167.46 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) % 167.45/167.46 => hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 167.45/167.46 ! [V_R_2,V_p_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_acyclicI,axiom, % 167.45/167.46 ! [V_r_2,T_a] : % 167.45/167.46 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 167.45/167.46 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_single__valued__rel__pow,axiom, % 167.45/167.46 ! [V_n_2,V_R_2,T_a] : % 167.45/167.46 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2) % 167.45/167.46 => c_Relation_Osingle__valued(T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_comp__funpow,axiom, % 167.45/167.46 ! [V_f_2,V_n_2,T_b,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_a,T_b),tc_fun(T_a,T_b)),V_n_2),c_Fun_Ocomp(T_b,T_b,T_a,V_f_2)) = c_Fun_Ocomp(T_b,T_b,T_a,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_funpow__mult,axiom, % 167.45/167.46 ! [V_f_2,V_m_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_funpow__swap1,axiom, % 167.45/167.46 ! [V_x_2,V_n_2,T_a,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_wf__exp,axiom, % 167.45/167.46 ! [V_R_2,V_n_2,T_a] : % 167.45/167.46 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) % 167.45/167.46 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__1,axiom, % 167.45/167.46 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__commute,axiom, % 167.45/167.46 ! [V_n_2,V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__imp__rtrancl,axiom, % 167.45/167.46 ! [V_R_2,V_n_2,V_p_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__power,axiom, % 167.45/167.46 ! [V_R_2,V_p_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 167.45/167.46 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_relpow_Osimps_I2_J,axiom, % 167.45/167.46 ! [V_R_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__add,axiom, % 167.45/167.46 ! [V_R_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_relpow_Osimps_I1_J,axiom, % 167.45/167.46 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__0__I,axiom, % 167.45/167.46 ! [V_R_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__0__E,axiom, % 167.45/167.46 ! [V_R_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) % 167.45/167.46 => V_x_2 = V_y_2 ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__Suc__I2,axiom, % 167.45/167.46 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__Suc__I,axiom, % 167.45/167.46 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_R_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_funpow_Osimps_I2_J,axiom, % 167.45/167.46 ! [V_f_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_funpow__add,axiom, % 167.45/167.46 ! [V_f_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_funpow_Osimps_I1_J,axiom, % 167.45/167.46 ! [V_f_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_trancl__power,axiom, % 167.45/167.46 ! [V_R_2,V_p_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 167.45/167.46 <=> ? [B_n] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 167.45/167.46 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_funpow__code__def,axiom, % 167.45/167.46 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__E,axiom, % 167.45/167.46 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 167.45/167.46 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 => V_x_2 != V_z_2 ) % 167.45/167.46 => ~ ! [B_y,B_m] : % 167.45/167.46 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2))) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__E2,axiom, % 167.45/167.46 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 167.45/167.46 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 => V_x_2 != V_z_2 ) % 167.45/167.46 => ~ ! [B_y,B_m] : % 167.45/167.46 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__Un__separator__converseE,axiom, % 167.45/167.46 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2)))) % 167.45/167.46 => ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) % 167.45/167.46 => ! [B_y] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_Q_2)) % 167.45/167.46 => B_y = B_x ) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__Un__separatorE,axiom, % 167.45/167.46 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2)))) % 167.45/167.46 => ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) % 167.45/167.46 => ! [B_y] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_Q_2)) % 167.45/167.46 => B_x = B_y ) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__Suc__E,axiom, % 167.45/167.46 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 167.45/167.46 => ~ ! [B_y] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__Suc__D2,axiom, % 167.45/167.46 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 167.45/167.46 => ? [B_y] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__pow__Suc__E2,axiom, % 167.45/167.46 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 167.45/167.46 => ~ ! [B_y] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_tranclD,axiom, % 167.45/167.46 ! [V_R_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 167.45/167.46 => ? [B_z] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),V_R_2)) % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_tranclD2,axiom, % 167.45/167.46 ! [V_R_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 167.45/167.46 => ? [B_z] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),V_R_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_IdE,axiom, % 167.45/167.46 ! [V_p_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) % 167.45/167.46 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_mod__div__decomp,axiom, % 167.45/167.46 ! [V_b,V_a,T_a] : % 167.45/167.46 ( class_Divides_Osemiring__div(T_a) % 167.45/167.46 => V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_wf__eq__minimal,axiom, % 167.45/167.46 ! [V_r_2,T_a] : % 167.45/167.46 ( c_Wellfounded_Owf(T_a,V_r_2) % 167.45/167.46 <=> ! [B_Q] : % 167.45/167.46 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 167.45/167.46 => ? [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 167.45/167.46 & ! [B_y] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2)) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_transfer__nat__int__set__cong,axiom, % 167.45/167.46 ! [V_P_H_2,V_P_2] : % 167.45/167.46 ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 167.45/167.46 => ( hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.46 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 167.45/167.46 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Int__Collect__mono,axiom, % 167.45/167.46 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.46 => ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.46 => ( hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.46 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_a),V_Q_2)))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_UnionE,axiom, % 167.45/167.46 ! [V_C_2,V_A_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 167.45/167.46 => ~ ! [B_X] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_converseE,axiom, % 167.45/167.46 ! [V_r_2,V_yx_2,T_b,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_yx_2),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 167.45/167.46 => ~ ! [B_x,B_y] : % 167.45/167.46 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),B_y)),V_r_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rel__compE,axiom, % 167.45/167.46 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2))) % 167.45/167.46 => ~ ! [B_x,B_y,B_z] : % 167.45/167.46 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),B_x),B_y)),V_r_2)) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),B_z)),V_s_2)) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nitpick_Oplus__frac__def,axiom, % 167.45/167.46 ! [V_r_2,V_q_2,T_a] : c_Nitpick_Oplus__frac(T_a,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_a),V_q_2),hAPP(c_Nitpick_Odenom(T_a),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_a),tc_Int_Oint),c_Nitpick_Ofrac(T_a)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_a),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_a),V_r_2)))))),c_COMBI(tc_Int_Oint))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_setprod__pos,axiom, % 167.45/167.46 ! [V_f_2,V_A_2,T_a,T_b] : % 167.45/167.46 ( class_Rings_Olinordered__semidom(T_b) % 167.45/167.46 => ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nitpick_Otimes__frac__def,axiom, % 167.45/167.46 ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nitpick_Oof__frac__def,axiom, % 167.45/167.46 ! [V_q,T_a,T_b] : % 167.45/167.46 ( ( class_Rings_Oinverse(T_b) % 167.45/167.46 & class_Rings_Oring__1(T_b) ) % 167.45/167.46 => c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 167.45/167.46 ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 167.45/167.46 ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nitpick_Oless__frac__def,axiom, % 167.45/167.46 ! [V_r_2,V_q_2,T_a] : % 167.45/167.46 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2) % 167.45/167.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 167.45/167.46 ! [V_r_2,V_q_2,T_a] : % 167.45/167.46 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2) % 167.45/167.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nitpick_Onum__def,axiom, % 167.45/167.46 ! [T_a] : c_Nitpick_Onum(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nitpick_Odenom__def,axiom, % 167.45/167.46 ! [T_a] : c_Nitpick_Odenom(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_internal__split__def,axiom, % 167.45/167.46 ! [T_c,T_b,T_a] : c_Product__Type_Ointernal__split(T_a,T_b,T_c) = c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c) ). % 167.45/167.46 % 167.45/167.46 fof(fact_setprod__nonneg,axiom, % 167.45/167.46 ! [V_f_2,V_A_2,T_a,T_b] : % 167.45/167.46 ( class_Rings_Olinordered__semidom(T_b) % 167.45/167.46 => ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_internal__split__conv,axiom, % 167.45/167.46 ! [V_b_2,V_a_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_bool_Osize_I2_J,axiom, % 167.45/167.46 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.46 % 167.45/167.46 fof(fact_bool_Osize_I1_J,axiom, % 167.45/167.46 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.46 % 167.45/167.46 fof(fact_finite__less__ub,axiom, % 167.45/167.46 ! [V_u_2,V_f_2] : % 167.45/167.46 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 167.45/167.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lenlex__def,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_a),c_Wellfounded_Oless__than,c_List_Olex(T_a,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_a))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_COMBI(tc_List_Olist(T_a)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_neq__if__length__neq,axiom, % 167.45/167.46 ! [V_ys,V_xs,T_a] : % 167.45/167.46 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) % 167.45/167.46 => V_xs != V_ys ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lexn__length,axiom, % 167.45/167.46 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2))) % 167.45/167.46 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 % 167.45/167.46 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lenlex__conv,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_List_Olex(T_a,V_r_2)))))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_length__sublist,axiom, % 167.45/167.46 ! [V_I_2,V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lexn_Osimps_I2_J,axiom, % 167.45/167.46 ! [V_n_2,V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_a,tc_List_Olist(T_a)),tc_prod(T_a,tc_List_Olist(T_a))),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_Product__Type_Omap__pair(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),c_Wellfounded_Olex__prod(T_a,tc_List_Olist(T_a),V_r_2,hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2)))))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_impossible__Cons,axiom, % 167.45/167.46 ! [V_x,V_ys,V_xs,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) % 167.45/167.46 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list_Oinject,axiom, % 167.45/167.46 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2) % 167.45/167.46 <=> ( V_a_2 = V_a_H_2 % 167.45/167.46 & V_list_2 = V_list_H_2 ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_not__Cons__self2,axiom, % 167.45/167.46 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 167.45/167.46 % 167.45/167.46 fof(fact_not__Cons__self,axiom, % 167.45/167.46 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list_Osize_I4_J,axiom, % 167.45/167.46 ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Cons__in__lex,axiom, % 167.45/167.46 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olex(T_a,V_r_2))) % 167.45/167.46 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 167.45/167.46 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) % 167.45/167.46 | ( V_x_2 = V_y_2 % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olex(T_a,V_r_2))) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__Cons__def,axiom, % 167.45/167.46 ! [V_XS_2,V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBS(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_HOL_Obool,tc_List_Olist(T_a))),c_fequal))),c_List_Olist_OCons(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),V_XS_2)))))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_pick_Osimps,axiom, % 167.45/167.46 ! [V_xs,V_x,T_a,V_i] : % 167.45/167.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) % 167.45/167.46 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) ) % 167.45/167.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) % 167.45/167.46 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_select__weight__cons__zero,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lexord__cons__cons,axiom, % 167.45/167.46 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) % 167.45/167.46 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 167.45/167.46 | ( V_a_2 = V_b_2 % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lexord__lex,axiom, % 167.45/167.46 ! [V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olex(T_a,V_r_2))) % 167.45/167.46 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 167.45/167.46 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 167.45/167.46 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list_Osize_I2_J,axiom, % 167.45/167.46 ! [V_list_2,V_a_2,V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_a,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Cons__acc__listrel1I,axiom, % 167.45/167.46 ! [V_xs_2,V_r_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 167.45/167.46 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel1__converse,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel1__mono,axiom, % 167.45/167.46 ! [V_s_2,V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel1(T_a,V_s_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel1I2,axiom, % 167.45/167.46 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 167.45/167.46 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel1__eq__len,axiom, % 167.45/167.46 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 167.45/167.46 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__listrel1__eq__len,axiom, % 167.45/167.46 ! [V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 167.45/167.46 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_in__listrel1__converse,axiom, % 167.45/167.46 ! [V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 167.45/167.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel1I1,axiom, % 167.45/167.46 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_xs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Cons__listrel1__Cons,axiom, % 167.45/167.46 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) % 167.45/167.46 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 167.45/167.46 & V_xs_2 = V_ys_2 ) % 167.45/167.46 | ( V_x_2 = V_y_2 % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__Cons,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = c_List_Oset__Cons(T_a,hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lexord__irreflexive,axiom, % 167.45/167.46 ! [V_y_2,V_r_2,T_a] : % 167.45/167.46 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__rtrancl__refl,axiom, % 167.45/167.46 ! [V_r_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_xs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__mono,axiom, % 167.45/167.46 ! [V_s_2,V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_List_Olistrel(T_a,V_s_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 167.45/167.46 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__eq__len,axiom, % 167.45/167.46 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 167.45/167.46 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__rtrancl__trans,axiom, % 167.45/167.46 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__reflcl__if__listrel1,axiom, % 167.45/167.46 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel1__subset__listrel,axiom, % 167.45/167.46 ! [V_r_H_2,V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) % 167.45/167.46 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel(T_a,V_r_H_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 167.45/167.46 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel_OCons,axiom, % 167.45/167.46 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrelp__listrel__eq,axiom, % 167.45/167.46 ! [V_xa_2,V_x_2,V_r_2,T_a] : % 167.45/167.46 ( c_List_Olistrelp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2),V_x_2,V_xa_2) % 167.45/167.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_xa_2)),c_List_Olistrel(T_a,V_r_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__Cons2,axiom, % 167.45/167.46 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) % 167.45/167.46 => ~ ! [B_x,B_xs] : % 167.45/167.46 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_y_2)),V_r_2)) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),B_xs),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrelp_Oequations_I2_J,axiom, % 167.45/167.46 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] : % 167.45/167.46 ( c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a4_2)) % 167.45/167.46 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 167.45/167.46 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrelp_OCons,axiom, % 167.45/167.46 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 167.45/167.46 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) % 167.45/167.46 => c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__Cons1,axiom, % 167.45/167.46 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) % 167.45/167.46 => ~ ! [B_y,B_ys] : % 167.45/167.46 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),B_y)),V_r_2)) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),B_ys)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__subset,axiom, % 167.45/167.46 ! [V_A_2,V_r_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2))))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lists__UNIV,axiom, % 167.45/167.46 ! [T_a] : c_List_Olists(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lists__mono,axiom, % 167.45/167.46 ! [V_B_2,V_A_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olists(T_a,V_A_2)),c_List_Olists(T_a,V_B_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_equiv__listrel,axiom, % 167.45/167.46 ! [V_r_2,V_A_2,T_a] : % 167.45/167.46 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 167.45/167.46 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__refl__on,axiom, % 167.45/167.46 ! [V_r_2,V_A_2,T_a] : % 167.45/167.46 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 167.45/167.46 => c_Relation_Orefl__on(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Cons__in__lists__iff,axiom, % 167.45/167.46 ! [V_A_2,V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_List_Olists(T_a,V_A_2))) % 167.45/167.46 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lists__accI,axiom, % 167.45/167.46 ! [V_r_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lists__accD,axiom, % 167.45/167.46 ! [V_r_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__iff__nth,axiom, % 167.45/167.46 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 167.45/167.46 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 167.45/167.46 & ! [B_n] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_n))),V_r_2)) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lexord__linear,axiom, % 167.45/167.46 ! [V_y_2,V_x_2,V_r_2,T_a] : % 167.45/167.46 ( ! [B_a,B_b] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_b)),V_r_2)) % 167.45/167.46 | B_a = B_b % 167.45/167.46 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_b),B_a)),V_r_2)) ) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 167.45/167.46 | V_x_2 = V_y_2 % 167.45/167.46 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_x_2)),c_List_Olexord(T_a,V_r_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_infinite__UNIV__listI,axiom, % 167.45/167.46 ! [T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__eq__iff__nth__eq,axiom, % 167.45/167.46 ! [T_a,V_ys_2,V_xs_2] : % 167.45/167.46 ( V_xs_2 = V_ys_2 % 167.45/167.46 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 167.45/167.46 & ! [B_i] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__Cons__Suc,axiom, % 167.45/167.46 ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__Cons__0,axiom, % 167.45/167.46 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth_Osimps,axiom, % 167.45/167.46 ! [V_n_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_a,V_x_2,hAPP(c_List_Onth(T_a),V_xs_2),V_n_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__Cons_H,axiom, % 167.45/167.46 ! [V_xs,V_x,T_a,V_n] : % 167.45/167.46 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 167.45/167.46 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__Cons__number__of,axiom, % 167.45/167.46 ! [V_xs,V_x,T_a,V_v] : % 167.45/167.46 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x ) % 167.45/167.46 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lexord__take__index__conv,axiom, % 167.45/167.46 ! [V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 167.45/167.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2))) % 167.45/167.46 & hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),V_y_2) = V_x_2 ) % 167.45/167.46 | ? [B_i] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)))) % 167.45/167.46 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2) % 167.45/167.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_y_2),B_i))),V_r_2)) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__sublist,axiom, % 167.45/167.46 ! [V_I_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_finite__set,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__subset__Cons,axiom, % 167.45/167.46 ! [V_x_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__all,axiom, % 167.45/167.46 ! [V_n,V_xs,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) % 167.45/167.46 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__take__subset,axiom, % 167.45/167.46 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__take__subset__set__take,axiom, % 167.45/167.46 ! [V_xs_2,T_a,V_n_2,V_m_2] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__sublist__subset,axiom, % 167.45/167.46 ! [V_I_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__take,axiom, % 167.45/167.46 ! [V_xs,T_a,V_n,V_i] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__Suc__Cons,axiom, % 167.45/167.46 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_notin__set__sublistI,axiom, % 167.45/167.46 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_in__set__takeD,axiom, % 167.45/167.46 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_in__set__sublistD,axiom, % 167.45/167.46 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__ConsD,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,V_y_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) % 167.45/167.46 => ( V_y_2 = V_x_2 % 167.45/167.46 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_length__take,axiom, % 167.45/167.46 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__take,axiom, % 167.45/167.46 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs) ). % 167.45/167.46 % 167.45/167.46 fof(fact_sublist__upt__eq__take,axiom, % 167.45/167.46 ! [V_n_2,V_l_2,T_a] : c_List_Osublist(T_a,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_l_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_List_Oset_Osimps_I2_J,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_card__length,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_all__set__conv__all__nth,axiom, % 167.45/167.46 ! [V_P_2,V_xs_2,T_a] : % 167.45/167.46 ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.46 <=> ! [B_i] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__size__estimation,axiom, % 167.45/167.46 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__size__estimation_H,axiom, % 167.45/167.46 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_in__lists__conv__set,axiom, % 167.45/167.46 ! [V_A_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 167.45/167.46 <=> ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_length__pos__if__in__set,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__mem,axiom, % 167.45/167.46 ! [V_xs_2,T_a,V_n_2] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_in__set__conv__nth,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 <=> ? [B_i] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lists__eq__set,axiom, % 167.45/167.46 ! [V_A_2,T_a] : c_List_Olists(T_a,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__conv__nth,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_finite__lists__length__eq,axiom, % 167.45/167.46 ! [V_n_2,V_A_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_finite__lists__length__le,axiom, % 167.45/167.46 ! [V_n_2,V_A_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_WT__bodies__def,axiom, % 167.45/167.46 ( c_Com_OWT__bodies % 167.45/167.46 <=> ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__iff__zip,axiom, % 167.45/167.46 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 167.45/167.46 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 167.45/167.46 & ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),B_x)) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__zip,axiom, % 167.45/167.46 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_length__zip,axiom, % 167.45/167.46 ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_zip__Cons__Cons,axiom, % 167.45/167.46 ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__eq__iff__zip__eq,axiom, % 167.45/167.46 ! [T_a,V_ys_2,V_xs_2] : % 167.45/167.46 ( V_xs_2 = V_ys_2 % 167.45/167.46 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 167.45/167.46 & ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_zip__same,axiom, % 167.45/167.46 ! [V_xs_2,V_b_2,V_a_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2)))) % 167.45/167.46 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 & V_a_2 = V_b_2 ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__zip__leftD,axiom, % 167.45/167.46 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__zip__rightD,axiom, % 167.45/167.46 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_in__set__zipE,axiom, % 167.45/167.46 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 167.45/167.46 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__zip,axiom, % 167.45/167.46 ! [V_ys,T_b,V_xs,T_a,V_i] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys))) % 167.45/167.46 => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__zip,axiom, % 167.45/167.46 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_b)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_a,T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),tc_Nat_Onat),c_Product__Type_OPair(T_a,T_b)),hAPP(c_List_Onth(T_a),V_xs_2))),hAPP(c_List_Onth(T_b),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_greaterThanLessThan__upto,axiom, % 167.45/167.46 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listsum__setsum__nth,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : % 167.45/167.46 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.46 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 167.45/167.46 ! [V_ns_2] : % 167.45/167.46 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 <=> ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 167.45/167.46 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__upto,axiom, % 167.45/167.46 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_atLeastAtMost__upto,axiom, % 167.45/167.46 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_elem__le__listsum__nat,axiom, % 167.45/167.46 ! [V_ns,V_k] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listsum__simps_I2_J,axiom, % 167.45/167.46 ! [V_xs,V_x,T_a] : % 167.45/167.46 ( class_Groups_Omonoid__add(T_a) % 167.45/167.46 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_atLeastLessThan__upto,axiom, % 167.45/167.46 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_greaterThanAtMost__upto,axiom, % 167.45/167.46 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nat__list__def,axiom, % 167.45/167.46 ! [V_l_2] : % 167.45/167.46 ( c_List_Onat__list(V_l_2) % 167.45/167.46 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__size__pointwise,axiom, % 167.45/167.46 ! [V_g_2,V_f_2,V_xs_2,T_a] : % 167.45/167.46 ( ! [B_x] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_a,V_g_2,V_xs_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listsum__update__nat,axiom, % 167.45/167.46 ! [V_n,V_ns,V_k] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) % 167.45/167.46 => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_butlast__take,axiom, % 167.45/167.46 ! [V_xs,T_a,V_n] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.46 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__update__beyond,axiom, % 167.45/167.46 ! [V_x,V_i,V_xs,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)) % 167.45/167.46 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__update__id,axiom, % 167.45/167.46 ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__list__update__neq,axiom, % 167.45/167.46 ! [V_x,V_xs,T_a,V_j,V_i] : % 167.45/167.46 ( V_i != V_j % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_length__list__update,axiom, % 167.45/167.46 ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 167.45/167.46 % 167.45/167.46 fof(fact_butlast__list__update,axiom, % 167.45/167.46 ! [V_x,V_xs,T_a,V_k] : % 167.45/167.46 ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 167.45/167.46 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs) ) % 167.45/167.46 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 167.45/167.46 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_zip__update,axiom, % 167.45/167.46 ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_update__zip,axiom, % 167.45/167.46 ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__update__swap,axiom, % 167.45/167.46 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 167.45/167.46 ( V_i != V_i_H % 167.45/167.46 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__update__overwrite,axiom, % 167.45/167.46 ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__update_Osimps_I2_J,axiom, % 167.45/167.46 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,tc_List_Olist(T_a)),c_List_Olist__update(T_a,V_xs_2)),V_v_2)),V_i_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__update__code_I3_J,axiom, % 167.45/167.46 ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__update__code_I2_J,axiom, % 167.45/167.46 ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs) ). % 167.45/167.46 % 167.45/167.46 fof(fact_in__set__butlastD,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__update__subsetI,axiom, % 167.45/167.46 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_A_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__update__subset__insert,axiom, % 167.45/167.46 ! [V_x_2,V_i_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__list__update,axiom, % 167.45/167.46 ! [V_x,V_j,V_xs,T_a,V_i] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.46 => ( ( V_i = V_j % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x ) % 167.45/167.46 & ( V_i != V_j % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__update__same__conv,axiom, % 167.45/167.46 ! [V_x_2,V_xs_2,T_a,V_i_2] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 167.45/167.46 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__list__update__eq,axiom, % 167.45/167.46 ! [V_x,V_xs,T_a,V_i] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__butlast,axiom, % 167.45/167.46 ! [V_xs,T_a,V_n] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.46 => hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_length__butlast,axiom, % 167.45/167.46 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__update__memI,axiom, % 167.45/167.46 ! [V_x_2,V_xs_2,T_a,V_n_2] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_n_2),V_x_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_butlast__conv__take,axiom, % 167.45/167.46 ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel1__iff__update,axiom, % 167.45/167.46 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 167.45/167.46 <=> ? [B_y,B_n] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),B_y)),V_r_2)) % 167.45/167.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct__list__update,axiom, % 167.45/167.46 ! [V_i_2,V_a_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 167.45/167.46 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct__upto,axiom, % 167.45/167.46 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct__take,axiom, % 167.45/167.46 ! [V_i,V_xs,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.46 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct__sublistI,axiom, % 167.45/167.46 ! [V_I_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.46 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct__zipI2,axiom, % 167.45/167.46 ! [V_xs,T_b,V_ys,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 167.45/167.46 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct__zipI1,axiom, % 167.45/167.46 ! [V_ys,T_b,V_xs,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.46 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct_Osimps_I2_J,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) % 167.45/167.46 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct__card,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.46 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_card__distinct,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : % 167.45/167.46 ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) % 167.45/167.46 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct__conv__nth,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.46 <=> ! [B_i] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 => ! [B_j] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 => ( B_i != B_j % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__eq__iff__index__eq,axiom, % 167.45/167.46 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 => ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) % 167.45/167.46 <=> V_i_2 = V_j_2 ) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct__listsum__conv__Setsum,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : % 167.45/167.46 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.46 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.46 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_a),c_COMBI(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nitpick_Ocard_H__def,axiom, % 167.45/167.46 ! [V_A_2,T_a] : % 167.45/167.46 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.46 => c_Nitpick_Ocard_H(T_a,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a)))) ) % 167.45/167.46 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.46 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_dom__map__upds,axiom, % 167.45/167.46 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))),c_Map_Odom(T_a,T_b,V_m_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_map__upds__apply__nontin,axiom, % 167.45/167.46 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => hAPP(c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_map__upds__list__update2__drop,axiom, % 167.45/167.46 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_i_2)) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 167.45/167.46 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_nth__take__lemma,axiom, % 167.45/167.46 ! [V_ys,V_xs,T_a,V_k] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) % 167.45/167.46 => ( ! [B_i] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 167.45/167.46 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 167.45/167.46 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_restrict__map__upds,axiom, % 167.45/167.46 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.46 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_D_2)) % 167.45/167.46 => c_Map_Orestrict__map(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_a),V_xs_2))),V_xs_2,V_ys_2) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_restrict__map__insert,axiom, % 167.45/167.46 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_restrict__restrict,axiom, % 167.45/167.46 ! [V_B_2,V_A_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_restrict__in,axiom, % 167.45/167.46 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.46 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_dom__restrict,axiom, % 167.45/167.46 ! [V_A_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m_2)),V_A_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_fun__upd__restrict,axiom, % 167.45/167.46 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_fun__upd__restrict__conv,axiom, % 167.45/167.46 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 167.45/167.46 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_restrict__fun__upd,axiom, % 167.45/167.46 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 167.45/167.46 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 167.45/167.46 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) % 167.45/167.46 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 167.45/167.46 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__remove1__eq,axiom, % 167.45/167.46 ! [V_x_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.46 => hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__Cons__number__of,axiom, % 167.45/167.46 ! [V_xs,V_x,T_a,V_v] : % 167.45/167.46 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 167.45/167.46 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lists_ONil,axiom, % 167.45/167.46 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olists(T_a,V_A_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__Nil2,axiom, % 167.45/167.46 ! [V_r_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) % 167.45/167.46 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__Nil1,axiom, % 167.45/167.46 ! [V_r_2,V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) % 167.45/167.46 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__update__code_I1_J,axiom, % 167.45/167.46 ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__update_Osimps_I1_J,axiom, % 167.45/167.46 ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list__update__nonempty,axiom, % 167.45/167.46 ! [V_x_2,V_k_2,V_xs_2,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a) % 167.45/167.46 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_List_Oset_Osimps_I1_J,axiom, % 167.45/167.46 ! [T_a] : hAPP(c_List_Oset(T_a),c_List_Olist_ONil(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__empty2,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : % 167.45/167.46 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2) % 167.45/167.46 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__empty,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : % 167.45/167.46 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.46 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_length__0__conv,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : % 167.45/167.46 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list_Osize_I3_J,axiom, % 167.45/167.46 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listsum__simps_I1_J,axiom, % 167.45/167.46 ! [T_a] : % 167.45/167.46 ( class_Groups_Omonoid__add(T_a) % 167.45/167.46 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_zip__Nil,axiom, % 167.45/167.46 ! [V_ys,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_zip_Osimps_I1_J,axiom, % 167.45/167.46 ! [V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrelp_Oequations_I1_J,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrelp_ONil,axiom, % 167.45/167.46 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list_Osize_I1_J,axiom, % 167.45/167.46 ! [V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.46 % 167.45/167.46 fof(fact_remove1__commute,axiom, % 167.45/167.46 ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_remove1_Osimps_I1_J,axiom, % 167.45/167.46 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_sublist__nil,axiom, % 167.45/167.46 ! [V_A_2,T_a] : c_List_Osublist(T_a,c_List_Olist_ONil(T_a),V_A_2) = c_List_Olist_ONil(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__eq__Nil,axiom, % 167.45/167.46 ! [V_xs_2,V_n_2,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 167.45/167.46 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__0,axiom, % 167.45/167.46 ! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__Nil,axiom, % 167.45/167.46 ! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_upto__empty,axiom, % 167.45/167.46 ! [V_i,V_j] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 167.45/167.46 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list_Osimps_I2_J,axiom, % 167.45/167.46 ! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list_Osimps_I3_J,axiom, % 167.45/167.46 ! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_remove1_Osimps_I2_J,axiom, % 167.45/167.46 ! [V_xs,T_a,V_y,V_x] : % 167.45/167.46 ( ( V_x = V_y % 167.45/167.46 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 167.45/167.46 & ( V_x != V_y % 167.45/167.46 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_butlast_Osimps_I2_J,axiom, % 167.45/167.46 ! [V_x,T_a,V_xs] : % 167.45/167.46 ( ( V_xs = c_List_Olist_ONil(T_a) % 167.45/167.46 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 167.45/167.46 & ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.46 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_butlast_Osimps_I1_J,axiom, % 167.45/167.46 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_remove1__idem,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_notin__set__remove1,axiom, % 167.45/167.46 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_y_2,V_xs_2)))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_in__set__remove1,axiom, % 167.45/167.46 ! [V_xs_2,T_a,V_b_2,V_a_2] : % 167.45/167.46 ( V_a_2 != V_b_2 % 167.45/167.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_b_2,V_xs_2)))) % 167.45/167.46 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_map__upds__Nil1,axiom, % 167.45/167.46 ! [V_bs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,c_List_Olist_ONil(T_a),V_bs_2) = V_m_2 ). % 167.45/167.46 % 167.45/167.46 fof(fact_map__upds__Nil2,axiom, % 167.45/167.46 ! [V_as_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,c_List_Olist_ONil(T_b)) = V_m_2 ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct__remove1,axiom, % 167.45/167.46 ! [V_x,V_xs,T_a] : % 167.45/167.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.46 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct_Osimps_I1_J,axiom, % 167.45/167.46 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_distinct__butlast,axiom, % 167.45/167.46 ! [T_a,V_xs] : % 167.45/167.46 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.46 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.46 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_sublist__empty,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__remove1__subset,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_length__greater__0__conv,axiom, % 167.45/167.46 ! [V_xs_2,T_a] : % 167.45/167.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.46 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__1__Cons,axiom, % 167.45/167.46 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_not__listrel1__Nil,axiom, % 167.45/167.46 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel1(T_a,V_r_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_not__Nil__listrel1,axiom, % 167.45/167.46 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel1(T_a,V_r_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel_ONil,axiom, % 167.45/167.46 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lexord__Nil__right,axiom, % 167.45/167.46 ! [V_r_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olexord(T_a,V_r_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nil2__notin__lex,axiom, % 167.45/167.46 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olex(T_a,V_r_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Nil__notin__lex,axiom, % 167.45/167.46 ! [V_r_2,V_ys_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_ys_2)),c_List_Olex(T_a,V_r_2))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__Cons,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otake(T_a)),V_xs_2)),V_n_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_upto_Osimps,axiom, % 167.45/167.46 ! [V_j,V_i] : % 167.45/167.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 167.45/167.46 => c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j)) ) % 167.45/167.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 167.45/167.46 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_sublist__singleton,axiom, % 167.45/167.46 ! [V_x_2,T_a,V_A_2] : % 167.45/167.46 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 167.45/167.46 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) % 167.45/167.46 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 167.45/167.46 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = c_List_Olist_ONil(T_a) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_lists__empty,axiom, % 167.45/167.46 ! [T_a] : c_List_Olists(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_take__Cons_H,axiom, % 167.45/167.46 ! [V_xs,V_x,T_a,V_n] : % 167.45/167.46 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 167.45/167.46 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.46 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_upto__rec__number__of,axiom, % 167.45/167.46 ! [V_n,V_m] : % 167.45/167.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 167.45/167.46 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) ) % 167.45/167.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 167.45/167.46 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listrel__Nil,axiom, % 167.45/167.46 ! [V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__Cons__sing__Nil,axiom, % 167.45/167.46 ! [V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_a,tc_List_Olist(T_a),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))),V_A_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_length__remove1,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 167.45/167.46 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.46 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_upto_Opsimps,axiom, % 167.45/167.46 ! [V_j_2,V_i_2] : % 167.45/167.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2))) % 167.45/167.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 167.45/167.46 => c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) % 167.45/167.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 167.45/167.46 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_select,axiom, % 167.45/167.46 ! [V_s_2,T_a,V_xs_2] : % 167.45/167.46 ( V_xs_2 != c_List_Olist_ONil(T_a) % 167.45/167.46 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listset_Osimps_I1_J,axiom, % 167.45/167.46 ! [T_a] : c_List_Olistset(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_zip__Cons,axiom, % 167.45/167.46 ! [V_ys_2,V_y_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_a,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),T_a),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_a),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),c_List_Ozip(T_a,T_b)),V_ys_2))),V_xs_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list_Osimps_I5_J,axiom, % 167.45/167.46 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_list_Osimps_I4_J,axiom, % 167.45/167.46 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),c_List_Olist_ONil(T_b)) = V_f1_2 ). % 167.45/167.46 % 167.45/167.46 fof(fact_listset_Osimps_I2_J,axiom, % 167.45/167.46 ! [V_As_2,V_A_2,T_a] : c_List_Olistset(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_a,V_A_2,c_List_Olistset(T_a,V_As_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_zip__Cons1,axiom, % 167.45/167.46 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_b,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_b),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)))),hAPP(c_List_Ozip(T_a,T_b),V_xs_2))),V_ys_2) ). % 167.45/167.46 % 167.45/167.46 fof(fact_sorted__list__of__set__remove,axiom, % 167.45/167.46 ! [V_x_2,V_A_2,T_a] : % 167.45/167.46 ( class_Orderings_Olinorder(T_a) % 167.45/167.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.46 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_List_Oremove1(T_a,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_upto_Opinduct,axiom, % 167.45/167.46 ! [V_P_2,V_a1_2,V_a0_2] : % 167.45/167.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 167.45/167.46 => ( ! [B_i,B_j] : % 167.45/167.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j))) % 167.45/167.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 167.45/167.46 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) % 167.45/167.46 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_sorted__list__of__set__empty,axiom, % 167.45/167.46 ! [T_a] : % 167.45/167.46 ( class_Orderings_Olinorder(T_a) % 167.45/167.46 => c_List_Olinorder__class_Osorted__list__of__set(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_anamorph_Osimps,axiom, % 167.45/167.46 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 167.45/167.46 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.46 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2) ) % 167.45/167.46 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.46 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(tc_List_Olist(T_a),T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),c_COMBB(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),T_a),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),T_b))),c_List_Olist_OCons(T_a))))),hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_sublist__Cons,axiom, % 167.45/167.46 ! [V_A_2,V_l_2,V_x_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_a)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olist_ONil(T_a))),c_List_Osublist(T_a,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))) ). % 167.45/167.46 % 167.45/167.46 fof(fact_append__eq__Cons__conv,axiom, % 167.45/167.46 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) % 167.45/167.46 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 167.45/167.46 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) % 167.45/167.46 | ? [B_ys_H] : % 167.45/167.46 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) % 167.45/167.46 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Cons__eq__append__conv,axiom, % 167.45/167.46 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) % 167.45/167.46 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 167.45/167.46 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 ) % 167.45/167.46 | ? [B_ys_H] : % 167.45/167.46 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 % 167.45/167.46 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_append1__eq__conv,axiom, % 167.45/167.46 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) % 167.45/167.46 <=> ( V_xs_2 = V_ys_2 % 167.45/167.46 & V_x_2 = V_y_2 ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_append__Cons,axiom, % 167.45/167.46 ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_Cons__eq__appendI,axiom, % 167.45/167.46 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 167.45/167.46 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 167.45/167.46 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_set__append,axiom, % 167.45/167.46 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_zip__append,axiom, % 167.45/167.46 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 167.45/167.46 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us) % 167.45/167.46 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs) % 167.45/167.46 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs)) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_length__append,axiom, % 167.45/167.46 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ). % 167.45/167.46 % 167.45/167.46 fof(fact_listsum__append,axiom, % 167.45/167.46 ! [V_ys,V_xs,T_a] : % 167.45/167.46 ( class_Groups_Omonoid__add(T_a) % 167.45/167.46 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_append__eq__appendI,axiom, % 167.45/167.46 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 167.45/167.46 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 167.45/167.46 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_append__same__eq,axiom, % 167.45/167.46 ! [V_zs_2,V_xs_2,V_ys_2,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2) % 167.45/167.46 <=> V_ys_2 = V_zs_2 ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_same__append__eq,axiom, % 167.45/167.46 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2) % 167.45/167.46 <=> V_ys_2 = V_zs_2 ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_append__eq__append__conv2,axiom, % 167.45/167.46 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.46 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2) % 167.45/167.46 <=> ? [B_us] : % 167.45/167.46 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) % 167.45/167.46 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 ) % 167.45/167.46 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 % 167.45/167.46 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ). % 167.45/167.46 % 167.45/167.46 fof(fact_append__assoc,axiom, % 167.45/167.47 ! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__in__lists__conv,axiom, % 167.45/167.47 ! [V_A_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)),c_List_Olists(T_a,V_A_2))) % 167.45/167.47 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 167.45/167.47 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_fun__upds__append__drop,axiom, % 167.45/167.47 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.47 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_fun__upds__append2__drop,axiom, % 167.45/167.47 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.47 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_butlast__append,axiom, % 167.45/167.47 ! [V_xs,T_a,V_ys] : % 167.45/167.47 ( ( V_ys = c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 167.45/167.47 & ( V_ys != c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__Nil,axiom, % 167.45/167.47 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 167.45/167.47 % 167.45/167.47 fof(fact_Nil__is__append__conv,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_a] : % 167.45/167.47 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 167.45/167.47 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 167.45/167.47 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__Nil2,axiom, % 167.45/167.47 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 167.45/167.47 % 167.45/167.47 fof(fact_self__append__conv,axiom, % 167.45/167.47 ! [V_ys_2,T_a,V_xs_2] : % 167.45/167.47 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 167.45/167.47 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_self__append__conv2,axiom, % 167.45/167.47 ! [V_xs_2,T_a,V_ys_2] : % 167.45/167.47 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 167.45/167.47 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__is__Nil__conv,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) % 167.45/167.47 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 167.45/167.47 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__self__conv,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2 % 167.45/167.47 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__self__conv2,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2 % 167.45/167.47 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_eq__Nil__appendI,axiom, % 167.45/167.47 ! [T_a,V_ys,V_xs] : % 167.45/167.47 ( V_xs = V_ys % 167.45/167.47 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nth__append__length,axiom, % 167.45/167.47 ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x ). % 167.45/167.47 % 167.45/167.47 fof(fact_nth__append__length__plus,axiom, % 167.45/167.47 ! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n) ). % 167.45/167.47 % 167.45/167.47 fof(fact_take__append,axiom, % 167.45/167.47 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__update__append1,axiom, % 167.45/167.47 ! [V_x,V_ys,V_xs,T_a,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__update__length,axiom, % 167.45/167.47 ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remove1__append,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)),V_ys_2) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oremove1(T_a,V_x_2,V_ys_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_in__set__butlast__appendI,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 167.45/167.47 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) ) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_butlast__snoc,axiom, % 167.45/167.47 ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__listrel1I,axiom, % 167.45/167.47 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.47 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 167.45/167.47 & V_us_2 = V_vs_2 ) % 167.45/167.47 | ( V_xs_2 = V_ys_2 % 167.45/167.47 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_us_2),V_vs_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_vs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_lexord__append__leftI,axiom, % 167.45/167.47 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__append,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 167.45/167.47 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.47 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 167.45/167.47 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nth__append,axiom, % 167.45/167.47 ! [V_ys,V_xs,T_a,V_n] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__update__append,axiom, % 167.45/167.47 ! [V_x,V_ys,V_xs,T_a,V_n] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sublist__append,axiom, % 167.45/167.47 ! [V_A_2,V_l_H_2,V_l_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Osublist(T_a,V_l_2,V_A_2)),c_List_Osublist(T_a,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_l_2)))),V_A_2)))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listrel1I,axiom, % 167.45/167.47 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 167.45/167.47 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_vs_2)) % 167.45/167.47 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_vs_2)) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_lexord__append__left__rightI,axiom, % 167.45/167.47 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2)))),c_List_Olexord(T_a,V_r_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_take__Suc__conv__app__nth,axiom, % 167.45/167.47 ! [V_xs,T_a,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_snoc__listrel1__snoc__iff,axiom, % 167.45/167.47 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))))),c_List_Olistrel1(T_a,V_r_2))) % 167.45/167.47 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 167.45/167.47 & V_x_2 = V_y_2 ) % 167.45/167.47 | ( V_xs_2 = V_ys_2 % 167.45/167.47 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listrel1E,axiom, % 167.45/167.47 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 167.45/167.47 => ~ ! [B_x,B_y] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) % 167.45/167.47 => ! [B_us,B_vs] : % 167.45/167.47 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) % 167.45/167.47 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_lexord__append__leftD,axiom, % 167.45/167.47 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) % 167.45/167.47 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_a)),V_r_2)) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate1__def,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : hAPP(c_List_Orotate1(T_a),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)))),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__upds__append1,axiom, % 167.45/167.47 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 167.45/167.47 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_image__map__upd,axiom, % 167.45/167.47 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] : % 167.45/167.47 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.47 => hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),V_m_2),V_A_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__rotate1,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__rotate1,axiom, % 167.45/167.47 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 167.45/167.47 % 167.45/167.47 fof(fact_dom__const,axiom, % 167.45/167.47 ! [V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_domI,axiom, % 167.45/167.47 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 167.45/167.47 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_insert__dom,axiom, % 167.45/167.47 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] : % 167.45/167.47 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 167.45/167.47 => hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct1__rotate,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) % 167.45/167.47 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__upd__eqD1,axiom, % 167.45/167.47 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] : % 167.45/167.47 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) % 167.45/167.47 => V_x_2 = V_y_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__upd__triv,axiom, % 167.45/167.47 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] : % 167.45/167.47 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 167.45/167.47 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = V_t_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__upd__Some__unfold,axiom, % 167.45/167.47 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 167.45/167.47 <=> ( ( V_x_2 = V_a_2 % 167.45/167.47 & V_b_2 = V_y_2 ) % 167.45/167.47 | ( V_x_2 != V_a_2 % 167.45/167.47 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate1__is__Nil__conv,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 167.45/167.47 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__upds__Cons,axiom, % 167.45/167.47 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_WT_Oequations_I7_J,axiom, % 167.45/167.47 ! [V_a_2] : % 167.45/167.47 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) % 167.45/167.47 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_finite__range__updI,axiom, % 167.45/167.47 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 167.45/167.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_WT__bodiesD,axiom, % 167.45/167.47 ! [V_b,V_pn] : % 167.45/167.47 ( c_Com_OWT__bodies % 167.45/167.47 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) % 167.45/167.47 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__upds__twist,axiom, % 167.45/167.47 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] : % 167.45/167.47 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2))) % 167.45/167.47 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_restrict__upd__same,axiom, % 167.45/167.47 ! [V_y_2,V_x_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate__simps,axiom, % 167.45/167.47 ! [V_xs,V_x,T_b,T_a] : % 167.45/167.47 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 167.45/167.47 & hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate1__length01,axiom, % 167.45/167.47 ! [V_xs,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 167.45/167.47 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__upd__upds__conv__if,axiom, % 167.45/167.47 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2)))) % 167.45/167.47 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2)))) % 167.45/167.47 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option_Osize_I2_J,axiom, % 167.45/167.47 ! [V_a_2,V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,hAPP(c_Option_Ooption_OSome(T_a),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option_Osimps_I5_J,axiom, % 167.45/167.47 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option_Oinject,axiom, % 167.45/167.47 ! [V_a_H_2,V_a_2,T_a] : % 167.45/167.47 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2) % 167.45/167.47 <=> V_a_2 = V_a_H_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_inj__Some,axiom, % 167.45/167.47 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a),V_A_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_the_Osimps,axiom, % 167.45/167.47 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 167.45/167.47 % 167.45/167.47 fof(fact_WTs__elim__cases_I7_J,axiom, % 167.45/167.47 ! [V_P] : % 167.45/167.47 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) % 167.45/167.47 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_x_2,T_a] : c_Option_Oset(T_a,hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_elem__set,axiom, % 167.45/167.47 ! [V_xo_2,V_x_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2))) % 167.45/167.47 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_upd__conv__take__nth__drop,axiom, % 167.45/167.47 ! [V_a,V_xs,T_a,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_id__take__nth__drop,axiom, % 167.45/167.47 ! [V_xs,T_a,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__Nil,axiom, % 167.45/167.47 ! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__drop,axiom, % 167.45/167.47 ! [V_i,V_xs,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.47 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__butlast,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_butlast__drop,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__take,axiom, % 167.45/167.47 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_take__drop,axiom, % 167.45/167.47 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__0,axiom, % 167.45/167.47 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__drop,axiom, % 167.45/167.47 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__zip,axiom, % 167.45/167.47 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Odrop(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_b),V_n),V_ys)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__drop,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ). % 167.45/167.47 % 167.45/167.47 fof(fact_in__set__dropD,axiom, % 167.45/167.47 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__drop__subset,axiom, % 167.45/167.47 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__Suc__Cons,axiom, % 167.45/167.47 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__1__Cons,axiom, % 167.45/167.47 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ). % 167.45/167.47 % 167.45/167.47 fof(fact_nth__via__drop,axiom, % 167.45/167.47 ! [V_ys,V_y,V_xs,V_n,T_a] : % 167.45/167.47 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 167.45/167.47 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__take__drop__id,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__drop__subset__set__drop,axiom, % 167.45/167.47 ! [V_xs_2,T_a,V_m_2,V_n_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__eq__Nil,axiom, % 167.45/167.47 ! [V_xs_2,V_n_2,T_a] : % 167.45/167.47 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 167.45/167.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_n_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__all,axiom, % 167.45/167.47 ! [V_n,V_xs,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) % 167.45/167.47 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__append,axiom, % 167.45/167.47 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__eq__conv__conj,axiom, % 167.45/167.47 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2 % 167.45/167.47 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) % 167.45/167.47 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__Cons,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Odrop(T_a)),V_xs_2),V_n_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__Cons_H,axiom, % 167.45/167.47 ! [V_xs,V_x,T_a,V_n] : % 167.45/167.47 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.47 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) % 167.45/167.47 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.47 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nth__drop,axiom, % 167.45/167.47 ! [V_xs,T_a,V_i,V_n] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__eq__append__conv__if,axiom, % 167.45/167.47 ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_a] : % 167.45/167.47 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2) % 167.45/167.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) % 167.45/167.47 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) % 167.45/167.47 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) % 167.45/167.47 => ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 % 167.45/167.47 & hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2 ) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nth__drop_H,axiom, % 167.45/167.47 ! [V_xs,T_a,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__Cons__number__of,axiom, % 167.45/167.47 ! [V_xs,V_x,T_a,V_v] : % 167.45/167.47 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.47 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) % 167.45/167.47 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.47 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_take__add,axiom, % 167.45/167.47 ! [V_xs,T_a,V_j,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_zip__append1,axiom, % 167.45/167.47 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_zip__append2,axiom, % 167.45/167.47 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_take__hd__drop,axiom, % 167.45/167.47 ! [V_xs,T_a,V_n] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_hd__drop__conv__nth,axiom, % 167.45/167.47 ! [V_n,T_a,V_xs] : % 167.45/167.47 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_hd_Osimps,axiom, % 167.45/167.47 ! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ). % 167.45/167.47 % 167.45/167.47 fof(fact_hd__append,axiom, % 167.45/167.47 ! [V_ys,T_a,V_xs] : % 167.45/167.47 ( ( V_xs = c_List_Olist_ONil(T_a) % 167.45/167.47 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys) ) % 167.45/167.47 & ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_hd__append2,axiom, % 167.45/167.47 ! [V_ys,T_a,V_xs] : % 167.45/167.47 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_hd__in__set,axiom, % 167.45/167.47 ! [T_a,V_xs_2] : % 167.45/167.47 ( V_xs_2 != c_List_Olist_ONil(T_a) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_hd__conv__nth,axiom, % 167.45/167.47 ! [T_a,V_xs] : % 167.45/167.47 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate1__hd__tl,axiom, % 167.45/167.47 ! [T_a,V_xs] : % 167.45/167.47 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option_Osize_I4_J,axiom, % 167.45/167.47 ! [V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),hAPP(c_Option_Ooption_OSome(T_a),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.47 % 167.45/167.47 fof(fact_tl__drop,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__tl,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_tl_Osimps_I1_J,axiom, % 167.45/167.47 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__tl,axiom, % 167.45/167.47 ! [V_xs,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.47 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_tl_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ). % 167.45/167.47 % 167.45/167.47 fof(fact_tl__append2,axiom, % 167.45/167.47 ! [V_ys,T_a,V_xs] : % 167.45/167.47 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_take__tl,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__Suc,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_tl__append,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,hAPP(c_List_Otl(T_a),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a)),V_ys_2))),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__tl,axiom, % 167.45/167.47 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_tl__take,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_take__Suc,axiom, % 167.45/167.47 ! [V_n,T_a,V_xs] : % 167.45/167.47 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_fold1__set,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.45/167.47 => ( V_xs_2 != c_List_Olist_ONil(T_a) % 167.45/167.47 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Otl(T_a),V_xs_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_hd__rotate__conv__nth,axiom, % 167.45/167.47 ! [V_n,T_a,V_xs] : % 167.45/167.47 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__rotate,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldl__append,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2)),V_ys_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldl__Cons,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__rotate,axiom, % 167.45/167.47 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_start__le__sum,axiom, % 167.45/167.47 ! [V_ns_2,V_n_2,V_m_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldl__absorb0,axiom, % 167.45/167.47 ! [V_zs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Groups_Omonoid__add(T_a) % 167.45/167.47 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_zs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_zs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldl__assoc,axiom, % 167.45/167.47 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 167.45/167.47 ( class_Groups_Osemigroup__add(T_a) % 167.45/167.47 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_y_2),V_zs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate__rotate,axiom, % 167.45/167.47 ! [V_xs,V_n,V_m,T_a] : hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate0,axiom, % 167.45/167.47 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate__add,axiom, % 167.45/167.47 ! [V_n_2,V_m_2,T_a] : c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orotate(T_a,V_m_2)),c_List_Orotate(T_a,V_n_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__rotate,axiom, % 167.45/167.47 ! [V_xs_2,V_n_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) % 167.45/167.47 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate__is__Nil__conv,axiom, % 167.45/167.47 ! [V_xs_2,V_n_2,T_a] : % 167.45/167.47 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 167.45/167.47 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldl__Nil,axiom, % 167.45/167.47 ! [V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),c_List_Olist_ONil(T_b)) = V_a_2 ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate1__rotate__swap,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate__def,axiom, % 167.45/167.47 ! [V_n_2,T_a] : c_List_Orotate(T_a,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_n_2),c_List_Orotate1(T_a)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate__conv__mod,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate__Suc,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsum__foldl,axiom, % 167.45/167.47 ! [T_a] : % 167.45/167.47 ( class_Groups_Omonoid__add(T_a) % 167.45/167.47 => c_List_Omonoid__add__class_Olistsum(T_a) = c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sum__eq__0__conv,axiom, % 167.45/167.47 ! [V_ns_2,V_m_2] : % 167.45/167.47 ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.47 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.47 & ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 167.45/167.47 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate__id,axiom, % 167.45/167.47 ! [V_xs,T_a,V_n] : % 167.45/167.47 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.47 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate__length01,axiom, % 167.45/167.47 ! [V_n,V_xs,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 167.45/167.47 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 167.45/167.47 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 167.45/167.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Sup__set__fold,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.45/167.47 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Inf__set__fold,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.45/167.47 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Sup__fin__set__fold,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Lattices_Olattice(T_a) % 167.45/167.47 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Inf__fin__set__fold,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Lattices_Olattice(T_a) % 167.45/167.47 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Min__fin__set__fold,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Max__fin__set__fold,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_min__max_OInf__fin__set__fold,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_min__max_OSup__fin__set__fold,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_SUPR__set__fold,axiom, % 167.45/167.47 ! [V_f_2,V_xs_2,T_b,T_a] : % 167.45/167.47 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.45/167.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_INFI__set__fold,axiom, % 167.45/167.47 ! [V_f_2,V_xs_2,T_b,T_a] : % 167.45/167.47 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 167.45/167.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_f_2)),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__upds__fold__map__upd,axiom, % 167.45/167.47 ! [V_vs_2,V_ks_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),T_b))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b))))),c_Option_Ooption_OSome(T_b))),V_m_2),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ks_2),V_vs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_elem__le__sum,axiom, % 167.45/167.47 ! [V_ns_2,V_n_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate__drop__take,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_ran__def,axiom, % 167.45/167.47 ! [V_m_2,T_a,T_b] : c_Map_Oran(T_b,T_a,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_a)))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_lexord__append__rightI,axiom, % 167.45/167.47 ! [V_r_2,V_x_2,T_a,V_y_2] : % 167.45/167.47 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_ranI,axiom, % 167.45/167.47 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 167.45/167.47 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted__list__of__set__insert,axiom, % 167.45/167.47 ! [V_x_2,V_A_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.47 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_lexord__Nil__left,axiom, % 167.45/167.47 ! [V_r_2,V_y_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 167.45/167.47 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__insort,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_insort__key_Osimps_I1_J,axiom, % 167.45/167.47 ! [V_x_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_insort__key_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 167.45/167.47 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 167.45/167.47 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_ys_2)) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__insort,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_fun__left__comm__insort,axiom, % 167.45/167.47 ! [T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => c_Finite__Set_Ofun__left__comm(T_a,tc_List_Olist(T_a),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_insort__left__comm,axiom, % 167.45/167.47 ! [V_xs_2,V_y_2,V_x_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_insort__key__left__comm,axiom, % 167.45/167.47 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 167.45/167.47 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),V_xs_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remove1__insort,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) = V_xs_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_insort__not__Nil,axiom, % 167.45/167.47 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__insort,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2))) % 167.45/167.47 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_insort__insert__insort__key,axiom, % 167.45/167.47 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)))) % 167.45/167.47 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_insort__insert__insort,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__insort__insert,axiom, % 167.45/167.47 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.47 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_insort__insert__triv,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__insort__insert,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_insort__insert__key__triv,axiom, % 167.45/167.47 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)))) % 167.45/167.47 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__list__update,axiom, % 167.45/167.47 ! [V_x,V_k,T_a,V_xs] : % 167.45/167.47 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 167.45/167.47 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 167.45/167.47 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 167.45/167.47 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__conv__nth,axiom, % 167.45/167.47 ! [T_a,V_xs] : % 167.45/167.47 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__appendL,axiom, % 167.45/167.47 ! [V_xs,T_a,V_ys] : % 167.45/167.47 ( V_ys = c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__appendR,axiom, % 167.45/167.47 ! [V_xs,T_a,V_ys] : % 167.45/167.47 ( V_ys != c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__append,axiom, % 167.45/167.47 ! [V_xs,T_a,V_ys] : % 167.45/167.47 ( ( V_ys = c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 167.45/167.47 & ( V_ys != c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__ConsL,axiom, % 167.45/167.47 ! [V_x,T_a,V_xs] : % 167.45/167.47 ( V_xs = c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__ConsR,axiom, % 167.45/167.47 ! [V_x,T_a,V_xs] : % 167.45/167.47 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last_Osimps,axiom, % 167.45/167.47 ! [V_x,T_a,V_xs] : % 167.45/167.47 ( ( V_xs = c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 167.45/167.47 & ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__in__set,axiom, % 167.45/167.47 ! [T_a,V_as_2] : % 167.45/167.47 ( V_as_2 != c_List_Olist_ONil(T_a) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__snoc,axiom, % 167.45/167.47 ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__drop,axiom, % 167.45/167.47 ! [V_xs,T_a,V_n] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.47 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__butlast__last__id,axiom, % 167.45/167.47 ! [T_a,V_xs] : % 167.45/167.47 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.47 => hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_snoc__eq__iff__butlast,axiom, % 167.45/167.47 ! [V_ys_2,V_x_2,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = V_ys_2 % 167.45/167.47 <=> ( V_ys_2 != c_List_Olist_ONil(T_a) % 167.45/167.47 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2 % 167.45/167.47 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_lists_Osimps,axiom, % 167.45/167.47 ! [V_A_2,V_a_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) % 167.45/167.47 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 167.45/167.47 | ? [B_a,B_l] : % 167.45/167.47 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) % 167.45/167.47 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 167.45/167.47 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__zip__upd,axiom, % 167.45/167.47 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 167.45/167.47 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 167.45/167.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 167.45/167.47 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_z_2)) % 167.45/167.47 => hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) ) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_finite__dom__map__of,axiom, % 167.45/167.47 ! [V_l_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_l_2)))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__zip__inject,axiom, % 167.45/167.47 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 167.45/167.47 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 167.45/167.47 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 167.45/167.47 => ( hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) % 167.45/167.47 => V_ys_2 = V_zs_2 ) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_body__def,axiom, % 167.45/167.47 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__Cons__code_I2_J,axiom, % 167.45/167.47 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 167.45/167.47 ( ( V_l = V_k % 167.45/167.47 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v) ) % 167.45/167.47 & ( V_l != V_k % 167.45/167.47 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_ps),V_k) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__eq__dom,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_b,T_a] : % 167.45/167.47 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 167.45/167.47 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_finite__range__map__of,axiom, % 167.45/167.47 ! [V_xys_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__is__SomeD,axiom, % 167.45/167.47 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__SomeD,axiom, % 167.45/167.47 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xs_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_dom__map__of__conv__image__fst,axiom, % 167.45/167.47 ! [V_xys_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__zip__is__Some,axiom, % 167.45/167.47 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 <=> ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_dom__map__of__zip,axiom, % 167.45/167.47 ! [V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.47 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.47 => c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_a),V_xs_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_ps_2,V_p_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2)),hAPP(c_Option_Ooption_OSome(T_b),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_ran__distinct,axiom, % 167.45/167.47 ! [V_al_2,T_b,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_al_2))) % 167.45/167.47 => c_Map_Oran(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_al_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__map__of__compr,axiom, % 167.45/167.47 ! [V_xs_2,T_b,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) % 167.45/167.47 => hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)))),c_Option_Ooption_OSome(T_b)))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_inj__mapI,axiom, % 167.45/167.47 ! [V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.47 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsum__abs,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_a,T_a),c_Groups_Oabs__class_Oabs(T_a)),V_xs_2)))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldl__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_c,V_a_2,V_g_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,T_a)),T_a),c_COMBB(T_b,T_a,T_c)),V_g_2)),V_f_2),V_a_2),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_zip__map2,axiom, % 167.45/167.47 ! [V_ys_2,V_f_2,T_c,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_a,T_c),V_xs_2),V_ys_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__zip__map2,axiom, % 167.45/167.47 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_c)),tc_fun(T_d,T_a),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_d),V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__zip__map,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_g_2,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_c),V_f_2)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_zip__map1,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_b),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_zip__map__map,axiom, % 167.45/167.47 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),T_c),c_COMBB(T_b,tc_prod(T_a,T_b),T_d)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__map,axiom, % 167.45/167.47 ! [V_xs_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_List_Omap_Ocompositionality,axiom, % 167.45/167.47 ! [V_list_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_list_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__comp__map,axiom, % 167.45/167.47 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_List_Omap_Ocomp,axiom, % 167.45/167.47 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_List_Omap_Oid,axiom, % 167.45/167.47 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_List_Omap_Oidentity,axiom, % 167.45/167.47 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__size__map,axiom, % 167.45/167.47 ! [V_xs_2,V_g_2,T_b,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_b,hAPP(c_Fun_Ocomp(T_a,tc_Nat_Onat,T_b,V_f_2),V_g_2),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nth__map,axiom, % 167.45/167.47 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.47 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__fun__upd,axiom, % 167.45/167.47 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] : % 167.45/167.47 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => hAPP(hAPP(c_List_Omap(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__tl,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Otl(T_b),V_xs_2)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__eq__imp__length__eq,axiom, % 167.45/167.47 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_a),V_g_2),V_ys_2) % 167.45/167.47 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__append,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__update,axiom, % 167.45/167.47 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__eq__conv,axiom, % 167.45/167.47 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2) % 167.45/167.47 <=> ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 167.45/167.47 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsum__addf,axiom, % 167.45/167.47 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.47 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsum__subtractf,axiom, % 167.45/167.47 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( class_Groups_Oab__group__add(T_a) % 167.45/167.47 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsum__0,axiom, % 167.45/167.47 ! [V_xs_2,T_b,T_a] : % 167.45/167.47 ( class_Groups_Omonoid__add(T_a) % 167.45/167.47 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsum__mult__const,axiom, % 167.45/167.47 ! [V_xs_2,V_c_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( class_Rings_Osemiring__0(T_a) % 167.45/167.47 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),V_c_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsum__const__mult,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,V_c_2,T_b,T_a] : % 167.45/167.47 ( class_Rings_Osemiring__0(T_a) % 167.45/167.47 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__ident,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ). % 167.45/167.47 % 167.45/167.47 fof(fact_take__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__butlast,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Obutlast(T_b,V_xs_2)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Nil__is__map__conv,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) % 167.45/167.47 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map_Osimps_I1_J,axiom, % 167.45/167.47 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__is__Nil__conv,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a) % 167.45/167.47 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__injective,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2) % 167.45/167.47 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 167.45/167.47 => V_xs_2 = V_ys_2 ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_inj__map__eq__map,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.47 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2) % 167.45/167.47 <=> V_xs_2 = V_ys_2 ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_hd__map,axiom, % 167.45/167.47 ! [V_f_2,T_b,T_a,V_xs_2] : % 167.45/167.47 ( V_xs_2 != c_List_Olist_ONil(T_a) % 167.45/167.47 => hAPP(c_List_Ohd(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_a),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__inj__on,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2) % 167.45/167.47 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) % 167.45/167.47 => V_xs_2 = V_ys_2 ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_inj__on__map__eq__map,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2))) % 167.45/167.47 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2) % 167.45/167.47 <=> V_xs_2 = V_ys_2 ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_rotate__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(c_List_Orotate(T_a,V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 167.45/167.47 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 167.45/167.47 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__map,axiom, % 167.45/167.47 ! [V_f_2,T_b,T_a,V_xs_2] : % 167.45/167.47 ( V_xs_2 != c_List_Olist_ONil(T_a) % 167.45/167.47 => c_List_Olast(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_a,V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_uminus__listsum__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( class_Groups_Oab__group__add(T_a) % 167.45/167.47 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(T_a,T_a,T_b,c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_inj__on__mapI,axiom, % 167.45/167.47 ! [V_A_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),V_A_2))) % 167.45/167.47 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),V_A_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__fst__zip,axiom, % 167.45/167.47 ! [V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.47 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_xs_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__snd__zip,axiom, % 167.45/167.47 ! [V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.47 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_ys_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_zip__map__fst__snd,axiom, % 167.45/167.47 ! [V_zs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2)) = V_zs_2 ). % 167.45/167.47 % 167.45/167.47 fof(fact_inj__mapD,axiom, % 167.45/167.47 ! [V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) % 167.45/167.47 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_inj__map,axiom, % 167.45/167.47 ! [V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) % 167.45/167.47 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_pick__member,axiom, % 167.45/167.47 ! [V_xs_2,T_a,V_i_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Random_Opick(T_a,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 167.45/167.47 ! [V_f_2,V_xs_2,T_a,T_b] : % 167.45/167.47 ( class_Groups_Ocomm__monoid__add(T_b) % 167.45/167.47 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.47 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_zip__eq__conv,axiom, % 167.45/167.47 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.47 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2 % 167.45/167.47 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2) = V_xs_2 % 167.45/167.47 & hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2) = V_ys_2 ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsum__triv,axiom, % 167.45/167.47 ! [V_xs_2,V_r_2,T_b,T_a] : % 167.45/167.47 ( class_Rings_Osemiring__1(T_a) % 167.45/167.47 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),V_r_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__inject__set,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_b,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) % 167.45/167.47 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2))) % 167.45/167.47 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 167.45/167.47 <=> hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsum__map__remove1,axiom, % 167.45/167.47 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] : % 167.45/167.47 ( class_Groups_Ocomm__monoid__add(T_b) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_select__weight__member,axiom, % 167.45/167.47 ! [V_s_2,V_xs_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_select__weight__def,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_a,V_xs_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__mapk__SomeI,axiom, % 167.45/167.47 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.47 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_c),V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2) % 167.45/167.47 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_a),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Some__eq__map__of__iff,axiom, % 167.45/167.47 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 167.45/167.47 => ( hAPP(c_Option_Ooption_OSome(T_b),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) % 167.45/167.47 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__eq__Some__iff,axiom, % 167.45/167.47 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 167.45/167.47 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 167.45/167.47 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__is__SomeI,axiom, % 167.45/167.47 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) % 167.45/167.47 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Nitpick_Osetsum_H__def,axiom, % 167.45/167.47 ! [V_f_2,V_A_2,T_a,T_b] : % 167.45/167.47 ( class_Groups_Ocomm__monoid__add(T_b) % 167.45/167.47 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.47 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a))))) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.47 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsum__mono,axiom, % 167.45/167.47 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] : % 167.45/167.47 ( ( class_Groups_Omonoid__add(T_b) % 167.45/167.47 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 167.45/167.47 => ( ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_g_2),V_xs_2)))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_zip__same__conv__map,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__size__conv__listsum,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_a,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 167.45/167.47 ! [V_l_2,V_k_2,V_f_2,T_a] : % 167.45/167.47 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.47 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 167.45/167.47 ! [V_j_2,V_i_2,V_f_2,T_a] : % 167.45/167.47 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__map__restrict,axiom, % 167.45/167.47 ! [V_ks_2,V_f_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_a,T_b,hAPP(c_Fun_Ocomp(T_b,tc_Option_Ooption(T_b),T_a,c_Option_Ooption_OSome(T_b)),V_f_2),hAPP(c_List_Oset(T_a),V_ks_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__map__keys,axiom, % 167.45/167.47 ! [V_m_2,T_b,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2) % 167.45/167.47 => hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),T_b,T_a),c_Option_Othe(T_b)),V_m_2))),V_xs_2)) = V_m_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_select__weigth__select,axiom, % 167.45/167.47 ! [T_a,V_xs_2] : % 167.45/167.47 ( V_xs_2 != c_List_Olist_ONil(T_a) % 167.45/167.47 => c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_a,V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_pick__same,axiom, % 167.45/167.47 ! [V_xs_2,T_a,V_l_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.47 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_l_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Map_Omap__of(T_a,T_c),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Option_Omap_Ocomp,axiom, % 167.45/167.47 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Option_Omap(T_a,T_c),V_g_2)) = hAPP(c_Option_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Option_Omap_Ocompositionality,axiom, % 167.45/167.47 ! [V_option_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_option_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option__map__comp,axiom, % 167.45/167.47 ! [V_opt_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_opt_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option__map__o__map__upd,axiom, % 167.45/167.47 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_b_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_number__of__code__numeral__def,axiom, % 167.45/167.47 c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Option_Omap_Oid,axiom, % 167.45/167.47 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Option_Omap_Oidentity,axiom, % 167.45/167.47 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_code__numeral_Oof__nat__inject,axiom, % 167.45/167.47 ! [V_y_2,V_x_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 167.45/167.47 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 167.45/167.47 <=> V_x_2 = V_y_2 ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_less__code__numeral__code,axiom, % 167.45/167.47 ! [V_m_2,V_n_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) % 167.45/167.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option__map__Some,axiom, % 167.45/167.47 ! [V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f_2,V_x_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option__map__eq__Some,axiom, % 167.45/167.47 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 167.45/167.47 <=> ? [B_z] : % 167.45/167.47 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) % 167.45/167.47 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 167.45/167.47 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.47 % 167.45/167.47 fof(fact_times__code__numeral__code,axiom, % 167.45/167.47 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 167.45/167.47 ! [V_m_2,V_n_2] : % 167.45/167.47 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 167.45/167.47 <=> V_n_2 = V_m_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_dom__option__map,axiom, % 167.45/167.47 ! [V_m_2,V_f_2,T_c,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),T_a),c_Option_Omap(T_c,T_b)),V_f_2)),V_m_2)) = c_Map_Odom(T_a,T_c,V_m_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_zero__code__numeral__def,axiom, % 167.45/167.47 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_one__code__numeral__def,axiom, % 167.45/167.47 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_plus__code__numeral__code,axiom, % 167.45/167.47 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_less__eq__code__numeral__code,axiom, % 167.45/167.47 ! [V_m_2,V_n_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) % 167.45/167.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_code__numeral__not__eq__zero,axiom, % 167.45/167.47 ! [V_i_2] : % 167.45/167.47 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.45/167.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_select__def,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : c_Random_Oselect(T_a,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_a),V_xs_2)),c_Code__Numeral_Onat__of))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_subtract__code__numeral__code,axiom, % 167.45/167.47 ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_type__definition__code__numeral,axiom, % 167.45/167.47 c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_times__code__numeral__def,axiom, % 167.45/167.47 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nat__of__inverse,axiom, % 167.45/167.47 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 167.45/167.47 % 167.45/167.47 fof(fact_of__nat__nat__of,axiom, % 167.45/167.47 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 167.45/167.47 % 167.45/167.47 fof(fact_nat__of__of__nat,axiom, % 167.45/167.47 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 167.45/167.47 % 167.45/167.47 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 167.45/167.47 ! [V_l_2,V_k_2] : % 167.45/167.47 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 167.45/167.47 <=> V_k_2 = V_l_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_code__numeral_Onat__of__inject,axiom, % 167.45/167.47 ! [V_y_2,V_x_2] : % 167.45/167.47 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 167.45/167.47 <=> V_x_2 = V_y_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_less__code__numeral__def,axiom, % 167.45/167.47 ! [V_m_2,V_n_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 167.45/167.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nat__of,axiom, % 167.45/167.47 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nat__of__number,axiom, % 167.45/167.47 ! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k) ). % 167.45/167.47 % 167.45/167.47 fof(fact_int__of__def,axiom, % 167.45/167.47 c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of) ). % 167.45/167.47 % 167.45/167.47 fof(fact_less__eq__code__numeral__def,axiom, % 167.45/167.47 ! [V_m_2,V_n_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 167.45/167.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nat__of__code,axiom, % 167.45/167.47 ! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nat__of__aux__def,axiom, % 167.45/167.47 ! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Suc__code__numeral__def,axiom, % 167.45/167.47 ! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_minus__code__numeral__def,axiom, % 167.45/167.47 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_of__nat__inverse,axiom, % 167.45/167.47 ! [V_y_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 167.45/167.47 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_plus__code__numeral__def,axiom, % 167.45/167.47 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_div__code__numeral__def,axiom, % 167.45/167.47 ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_minus__code__numeral__code,axiom, % 167.45/167.47 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m) ). % 167.45/167.47 % 167.45/167.47 fof(fact_subtract__code__numeral__def,axiom, % 167.45/167.47 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.47 % 167.45/167.47 fof(fact_mod__code__numeral__def,axiom, % 167.45/167.47 ! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_code__numeral__decr,axiom, % 167.45/167.47 ! [V_k] : % 167.45/167.47 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 167.45/167.47 ! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_weak__map__of__SomeI,axiom, % 167.45/167.47 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_l_2))) % 167.45/167.47 => ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_x) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__zip__map,axiom, % 167.45/167.47 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_partition__set,axiom, % 167.45/167.47 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 167.45/167.47 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) % 167.45/167.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_yes_2)),hAPP(c_List_Oset(T_a),V_no_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option__map__o__empty,axiom, % 167.45/167.47 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),T_c,hAPP(c_Option_Omap(T_b,T_a),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option__map__is__None,axiom, % 167.45/167.47 ! [V_opt_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a) % 167.45/167.47 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option__map__None,axiom, % 167.45/167.47 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),c_Option_Ooption_ONone(T_b)) = c_Option_Ooption_ONone(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__Cons__code_I1_J,axiom, % 167.45/167.47 ! [V_k,T_a,T_b] : hAPP(hAPP(c_Map_Omap__of(T_b,T_a),c_List_Olist_ONil(tc_prod(T_b,T_a))),V_k) = c_Option_Ooption_ONone(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 167.45/167.47 ! [T_a] : c_Option_Oset(T_a,c_Option_Ooption_ONone(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__empty__eq,axiom, % 167.45/167.47 ! [V_xo_2,T_a] : % 167.45/167.47 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.47 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_empty__upd__none,axiom, % 167.45/167.47 ! [V_xa_2,V_x_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))),V_x_2),c_Option_Ooption_ONone(T_a)),V_xa_2) = c_Option_Ooption_ONone(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_dom__def,axiom, % 167.45/167.47 ! [V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_b)))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_domIff,axiom, % 167.45/167.47 ! [V_m_2,T_b,V_a_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) % 167.45/167.47 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_dom__empty,axiom, % 167.45/167.47 ! [T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_dom__eq__empty__conv,axiom, % 167.45/167.47 ! [V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.47 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_restrict__out,axiom, % 167.45/167.47 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 167.45/167.47 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.47 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_restrict__map__def,axiom, % 167.45/167.47 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.47 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.45/167.47 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_restrict__map__empty,axiom, % 167.45/167.47 ! [V_x_2,V_D_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_restrict__map__to__empty,axiom, % 167.45/167.47 ! [V_x_2,V_m_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option_Osimps_I4_J,axiom, % 167.45/167.47 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_b)) = V_f1_2 ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__upd__nonempty,axiom, % 167.45/167.47 ! [V_x_2,V_k_2,V_t_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_not__None__eq,axiom, % 167.45/167.47 ! [T_a,V_x_2] : % 167.45/167.47 ( V_x_2 != c_Option_Ooption_ONone(T_a) % 167.45/167.47 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_not__Some__eq,axiom, % 167.45/167.47 ! [T_a,V_x_2] : % 167.45/167.47 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y) % 167.45/167.47 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option_Osimps_I3_J,axiom, % 167.45/167.47 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 167.45/167.47 % 167.45/167.47 fof(fact_ran__empty,axiom, % 167.45/167.47 ! [T_a,T_b] : c_Map_Oran(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of_Osimps_I1_J,axiom, % 167.45/167.47 ! [V_x_1,T_b,T_a] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),c_List_Olist_ONil(tc_prod(T_a,T_b))),V_x_1) = c_Option_Ooption_ONone(T_b) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Option_Omap__def,axiom, % 167.45/167.47 ! [V_f_2,T_b,T_a] : hAPP(c_Option_Omap(T_a,T_b),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_a,c_Option_Ooption_ONone(T_b),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option_Osize_I3_J,axiom, % 167.45/167.47 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.47 % 167.45/167.47 fof(fact_option_Osize_I1_J,axiom, % 167.45/167.47 ! [V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.47 % 167.45/167.47 fof(fact_dom__minus,axiom, % 167.45/167.47 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] : % 167.45/167.47 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a) % 167.45/167.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),V_A_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_WT_OBody,axiom, % 167.45/167.47 ! [V_pn] : % 167.45/167.47 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) % 167.45/167.47 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_partition__P,axiom, % 167.45/167.47 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 167.45/167.47 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) % 167.45/167.47 => ( ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) % 167.45/167.47 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.47 & ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) % 167.45/167.47 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_partition_Osimps_I1_J,axiom, % 167.45/167.47 ! [V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_ran__map__upd,axiom, % 167.45/167.47 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] : % 167.45/167.47 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a) % 167.45/167.47 => c_Map_Oran(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__zip__is__None,axiom, % 167.45/167.47 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.47 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_b) % 167.45/167.47 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_partition_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),hAPP(c_If(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_List_Olist_OCons(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_List_Olist(T_a))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_List_Opartition(T_a,V_P_2,V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_dom__fun__upd,axiom, % 167.45/167.47 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] : % 167.45/167.47 ( ( V_y_2 = c_Option_Ooption_ONone(T_a) % 167.45/167.47 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) % 167.45/167.47 & ( V_y_2 != c_Option_Ooption_ONone(T_a) % 167.45/167.47 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_restrict__complement__singleton__eq,axiom, % 167.45/167.47 ! [V_x_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_b)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__eq__None__iff,axiom, % 167.45/167.47 ! [V_x_2,V_xys_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a) % 167.45/167.47 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2)))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_UNIV__option__conv,axiom, % 167.45/167.47 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_dom__eq__singleton__conv,axiom, % 167.45/167.47 ! [V_x_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Map_Odom(T_a,T_b,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.47 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),B_v)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_fun__upd__None__restrict,axiom, % 167.45/167.47 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 167.45/167.47 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 167.45/167.47 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_lists__Int__eq,axiom, % 167.45/167.47 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_B_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_lists__IntI,axiom, % 167.45/167.47 ! [V_B_2,V_A_2,V_l_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) % 167.45/167.47 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_l_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsp_ONil,axiom, % 167.45/167.47 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_append__in__listsp__conv,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_A_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 167.45/167.47 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 167.45/167.47 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsp_Oequations_I2_J,axiom, % 167.45/167.47 ! [V_a2_2,V_a1_2,V_A_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) % 167.45/167.47 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 167.45/167.47 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_in__listsp__conv__set,axiom, % 167.45/167.47 ! [V_xs_2,V_A_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 167.45/167.47 <=> ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsp__conj__eq,axiom, % 167.45/167.47 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_A_2)),V_B_2)),V_x_2)) % 167.45/167.47 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) % 167.45/167.47 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsp__inf__eq,axiom, % 167.45/167.47 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsp__infI,axiom, % 167.45/167.47 ! [V_B_2,V_l_2,V_A_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) % 167.45/167.47 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) % 167.45/167.47 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsp_Oequations_I1_J,axiom, % 167.45/167.47 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsp__mono,axiom, % 167.45/167.47 ! [V_B_2,V_A_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_listsp__lists__eq,axiom, % 167.45/167.47 ! [V_x_2,V_A_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2)) % 167.45/167.47 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_,axiom, % 167.45/167.47 ! [V_y_2,V_x_2,T_a] : c_Smallcheck_Oorelse(T_a,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,V_y_2,c_Option_Ooption_OSome(T_a)),V_x_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_product_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_a,T_b)),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_product_Osimps_I1_J,axiom, % 167.45/167.47 ! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__product,axiom, % 167.45/167.47 ! [V_ys,T_b,V_xs,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.47 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 167.45/167.47 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_product__list__set,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_List_Oset(T_b),V_ys_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sublists__powset,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_Osublists(T_a,V_xs_2))) = hAPP(c_Set_OPow(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__sublists,axiom, % 167.45/167.47 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sublists_Osimps_I1_J,axiom, % 167.45/167.47 ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sublists_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : c_Enum_Osublists(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_a)),tc_fun(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(tc_List_Olist(T_a))),c_List_Oappend(tc_List_Olist(T_a))),hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_a))))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__set__sublists,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.47 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),c_List_Oset(T_a)),c_Enum_Osublists(T_a,V_xs_2)))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__n__lists,axiom, % 167.45/167.47 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),hAPP(c_List_Oset(T_a),V_xs_2)))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__the__def,axiom, % 167.45/167.47 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__n__lists,axiom, % 167.45/167.47 ! [V_n,V_xs,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.47 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_n__lists_Osimps_I1_J,axiom, % 167.45/167.47 ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_n__lists__Nil,axiom, % 167.45/167.47 ! [T_a,V_n] : % 167.45/167.47 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.47 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ) % 167.45/167.47 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.47 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__n__lists,axiom, % 167.45/167.47 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__n__lists__elem,axiom, % 167.45/167.47 ! [V_xs_2,V_n_2,V_ys_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)))) % 167.45/167.47 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_full__small__int__def,axiom, % 167.45/167.47 ! [V_d_2,V_f_2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,V_f_2,V_d_2) = c_Smallcheck_Ofull__small_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_small_H_Osimps,axiom, % 167.45/167.47 ! [V_f_2,V_i_2,V_d_2] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 167.45/167.47 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 167.45/167.47 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_small_H_Opsimps,axiom, % 167.45/167.47 ! [V_i_2,V_d_2,V_f_2] : % 167.45/167.47 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_f_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))) % 167.45/167.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 167.45/167.47 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 167.45/167.47 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_small__int__def,axiom, % 167.45/167.47 ! [V_d_2,V_f_2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),V_f_2),V_d_2) = c_Smallcheck_Osmall_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_small__prod__def,axiom, % 167.45/167.47 ! [V_d_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( ( class_Smallcheck_Osmall(T_b) % 167.45/167.47 & class_Smallcheck_Osmall(T_a) ) % 167.45/167.47 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_a,T_b)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_a),hAPP(hAPP(c_COMBC(T_a,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),c_Smallcheck_Osmall__class_Osmall(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b)))),V_d_2)),V_d_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_small_H_Opinduct,axiom, % 167.45/167.47 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] : % 167.45/167.47 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2)))) % 167.45/167.47 => ( ! [B_f,B_d,B_i] : % 167.45/167.47 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))) % 167.45/167.47 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 167.45/167.47 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 167.45/167.47 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) % 167.45/167.47 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) ) % 167.45/167.47 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__zip__enum__inject,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_a,T_b] : % 167.45/167.47 ( ( class_Enum_Oenum(T_b) % 167.45/167.47 & class_Enum_Oenum(T_a) ) % 167.45/167.47 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)) % 167.45/167.47 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)) % 167.45/167.47 => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_xs_2))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_ys_2))) % 167.45/167.47 => V_xs_2 = V_ys_2 ) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__prod__def,axiom, % 167.45/167.47 ! [T_b,T_a] : % 167.45/167.47 ( ( class_Enum_Oenum(T_a) % 167.45/167.47 & class_Enum_Oenum(T_b) ) % 167.45/167.47 => c_Enum_Oenum__class_Oenum(tc_prod(T_a,T_b)) = c_Enum_Oproduct(T_a,T_b,c_Enum_Oenum__class_Oenum(T_a),c_Enum_Oenum__class_Oenum(T_b)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__UNIV,axiom, % 167.45/167.47 ! [T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_UNIV__enum,axiom, % 167.45/167.47 ! [T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_in__enum,axiom, % 167.45/167.47 ! [V_x_2,T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__option__def,axiom, % 167.45/167.47 ! [T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => c_Enum_Oenum__class_Oenum(tc_Option_Ooption(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(hAPP(c_List_Omap(T_a,tc_Option_Ooption(T_a)),c_Option_Ooption_OSome(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__distinct,axiom, % 167.45/167.47 ! [T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__fun__code,axiom, % 167.45/167.47 ! [T_b,T_a] : % 167.45/167.47 ( ( class_Enum_Oenum(T_a) % 167.45/167.47 & class_HOL_Oequal(T_a) % 167.45/167.47 & class_Enum_Oenum(T_b) ) % 167.45/167.47 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__fun__def,axiom, % 167.45/167.47 ! [T_b,T_a] : % 167.45/167.47 ( ( class_Enum_Oenum(T_a) % 167.45/167.47 & class_Enum_Oenum(T_b) ) % 167.45/167.47 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_all__n__lists__def,axiom, % 167.45/167.47 ! [V_n_2,V_P_2,T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2) % 167.45/167.47 <=> ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) % 167.45/167.47 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_ex__n__lists__def,axiom, % 167.45/167.47 ! [V_n_2,V_P_2,T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2) % 167.45/167.47 <=> ? [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) % 167.45/167.47 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__all__fun__def,axiom, % 167.45/167.47 ! [V_P_2,T_a,T_b] : % 167.45/167.47 ( ( class_Enum_Oenum(T_b) % 167.45/167.47 & class_Enum_Oenum(T_a) ) % 167.45/167.47 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 167.45/167.47 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__ex__fun__def,axiom, % 167.45/167.47 ! [V_P_2,T_a,T_b] : % 167.45/167.47 ( ( class_Enum_Oenum(T_b) % 167.45/167.47 & class_Enum_Oenum(T_a) ) % 167.45/167.47 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 167.45/167.47 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__all__prod__def,axiom, % 167.45/167.47 ! [V_P_2,T_a,T_b] : % 167.45/167.47 ( ( class_Enum_Oenum(T_b) % 167.45/167.47 & class_Enum_Oenum(T_a) ) % 167.45/167.47 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) % 167.45/167.47 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__all(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__ex__prod__def,axiom, % 167.45/167.47 ! [V_P_2,T_a,T_b] : % 167.45/167.47 ( ( class_Enum_Oenum(T_b) % 167.45/167.47 & class_Enum_Oenum(T_a) ) % 167.45/167.47 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) % 167.45/167.47 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__ex(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_all__code,axiom, % 167.45/167.47 ! [V_P_2,T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 167.45/167.47 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_exists__code,axiom, % 167.45/167.47 ! [V_P_2,T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 167.45/167.47 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__all,axiom, % 167.45/167.47 ! [V_P_2,T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) % 167.45/167.47 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__ex,axiom, % 167.45/167.47 ! [V_P_2,T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) % 167.45/167.47 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__all__option__def,axiom, % 167.45/167.47 ! [V_P_2,T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2)) % 167.45/167.47 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 167.45/167.47 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__ex__option__def,axiom, % 167.45/167.47 ! [V_P_2,T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2)) % 167.45/167.47 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 167.45/167.47 | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_order__fun_I1_J,axiom, % 167.45/167.47 ! [V_g_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( ( class_Orderings_Oorder(T_b) % 167.45/167.47 & class_Enum_Oenum(T_a) ) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.45/167.47 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_f_2)),V_g_2))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_order__fun_I2_J,axiom, % 167.45/167.47 ! [V_g_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( ( class_Orderings_Oorder(T_b) % 167.45/167.47 & class_Enum_Oenum(T_a) ) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.45/167.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.45/167.47 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_g_2)))) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__ex__fun__code,axiom, % 167.45/167.47 ! [V_P_2,T_a,T_b] : % 167.45/167.47 ( ( class_Enum_Oenum(T_b) % 167.45/167.47 & class_Enum_Oenum(T_a) % 167.45/167.47 & class_HOL_Oequal(T_a) ) % 167.45/167.47 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 167.45/167.47 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_enum__all__fun__code,axiom, % 167.45/167.47 ! [V_P_2,T_a,T_b] : % 167.45/167.47 ( ( class_Enum_Oenum(T_b) % 167.45/167.47 & class_Enum_Oenum(T_a) % 167.45/167.47 & class_HOL_Oequal(T_a) ) % 167.45/167.47 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 167.45/167.47 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__zip__enum__is__Some,axiom, % 167.45/167.47 ! [V_x,V_ys,T_b,T_a] : % 167.45/167.47 ( class_Enum_Oenum(T_a) % 167.45/167.47 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)) % 167.45/167.47 => ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a)),V_ys)),V_x) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__def,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 167.45/167.47 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.47 & ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__lengthD,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 167.45/167.47 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__dropI,axiom, % 167.45/167.47 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) % 167.45/167.47 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_bs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__takeI,axiom, % 167.45/167.47 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 167.45/167.47 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_ys_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__eq,axiom, % 167.45/167.47 ! [T_a,V_ys_2,V_xs_2] : % 167.45/167.47 ( V_xs_2 = V_ys_2 % 167.45/167.47 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__appendI,axiom, % 167.45/167.47 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) % 167.45/167.47 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_c_2,V_d_2) % 167.45/167.47 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__Nil,axiom, % 167.45/167.47 ! [V_ys_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) % 167.45/167.47 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__Nil2,axiom, % 167.45/167.47 ! [V_xs_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) % 167.45/167.47 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__append,axiom, % 167.45/167.47 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.47 => ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2)) % 167.45/167.47 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 167.45/167.47 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__map2,axiom, % 167.45/167.47 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_bs_2)) % 167.45/167.47 <=> c_List_Olist__all2(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_c)),V_P_2)),V_f_2),V_as_2,V_bs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__map1,axiom, % 167.45/167.47 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_as_2),V_bs_2) % 167.45/167.47 <=> c_List_Olist__all2(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),V_P_2),V_f_2),V_as_2,V_bs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__Cons,axiom, % 167.45/167.47 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) % 167.45/167.47 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 167.45/167.47 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__conv__all__nth,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 167.45/167.47 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 167.45/167.47 & ! [B_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.47 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i))) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__nthD,axiom, % 167.45/167.47 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.47 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__nthD2,axiom, % 167.45/167.47 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 167.45/167.47 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__update__cong,axiom, % 167.45/167.47 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.47 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 167.45/167.47 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2__update__cong2,axiom, % 167.45/167.47 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 167.45/167.47 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 167.45/167.47 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_list__all2I,axiom, % 167.45/167.47 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] : % 167.45/167.47 ( ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_a_2),V_b_2)))) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) % 167.45/167.47 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2) % 167.45/167.47 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_all__nth__imp__all__set,axiom, % 167.45/167.47 ! [V_x_2,V_P_2,V_xs_2,T_a] : % 167.45/167.47 ( ! [B_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.47 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 167.45/167.47 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 167.45/167.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),c_List_Oremdups(T_a,V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__removeAll__inj__on,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__remdups,axiom, % 167.45/167.47 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__remdups__leq,axiom, % 167.45/167.47 ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_removeAll__id,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remdups__id__iff__distinct,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2 % 167.45/167.47 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__removeAll,axiom, % 167.45/167.47 ! [V_x,V_xs,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.47 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__remdups__id,axiom, % 167.45/167.47 ! [V_xs,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.47 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remove1__remdups,axiom, % 167.45/167.47 ! [V_x,V_xs,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.47 => c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__remdups__eq,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) % 167.45/167.47 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__remdups,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remdups__remdups,axiom, % 167.45/167.47 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 167.45/167.47 % 167.45/167.47 fof(fact_removeAll__append,axiom, % 167.45/167.47 ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remdups_Osimps_I1_J,axiom, % 167.45/167.47 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remdups__eq__nil__right__iff,axiom, % 167.45/167.47 ! [V_x_2,T_a] : % 167.45/167.47 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2) % 167.45/167.47 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_removeAll_Osimps_I1_J,axiom, % 167.45/167.47 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remdups__eq__nil__iff,axiom, % 167.45/167.47 ! [V_x_2,T_a] : % 167.45/167.47 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a) % 167.45/167.47 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remdups__map__remdups,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremdups(T_b,V_xs_2))) = c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_removeAll_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_xs,T_a,V_y,V_x] : % 167.45/167.47 ( ( V_x = V_y % 167.45/167.47 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) % 167.45/167.47 & ( V_x != V_y % 167.45/167.47 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__remove1__removeAll,axiom, % 167.45/167.47 ! [V_x,V_xs,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.47 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remdups_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Oremdups(T_a,V_xs_2) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oremdups(T_a,V_xs_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__remdups__card__conv,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__removeAll__inj,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 167.45/167.47 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.45/167.47 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__removeAll,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__remdups__concat,axiom, % 167.45/167.47 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,c_List_Oconcat(T_a,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)),c_List_Oset(T_a))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),c_List_Oremdups(T_a,V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_concat_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__concat,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_Nil__eq__concat__conv,axiom, % 167.45/167.47 ! [V_xss_2,T_a] : % 167.45/167.47 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2) % 167.45/167.47 <=> ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 167.45/167.47 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_concat__eq__Nil__conv,axiom, % 167.45/167.47 ! [V_xss_2,T_a] : % 167.45/167.47 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a) % 167.45/167.47 <=> ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 167.45/167.47 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sort__key__simps_I1_J,axiom, % 167.45/167.47 ! [V_f_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_concat_Osimps_I1_J,axiom, % 167.45/167.47 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_concat__conv__foldl,axiom, % 167.45/167.47 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_xss_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldl__conv__concat,axiom, % 167.45/167.47 ! [V_xss_2,V_xs_2,T_a] : hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oconcat(T_a,V_xss_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__sort,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__sort,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__sort,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) % 167.45/167.47 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__concat,axiom, % 167.45/167.47 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oconcat(T_a,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xss_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__concat,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oconcat(T_a,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)),c_List_Oset(T_a)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sort__key__simps_I2_J,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_concat__append,axiom, % 167.45/167.47 ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sort__foldl__insort,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))),c_List_Olist_ONil(T_a)),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_concat__eq__concat__iff,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_a] : % 167.45/167.47 ( ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) ) % 167.45/167.47 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2) % 167.45/167.47 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 167.45/167.47 <=> V_xs_2 = V_ys_2 ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_concat__injective,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,T_a] : % 167.45/167.47 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 167.45/167.47 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2) % 167.45/167.47 => ( ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) ) % 167.45/167.47 => V_xs_2 = V_ys_2 ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_concat__map__singleton,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_b),c_List_Olist_OCons(T_a)),V_f_2)),c_List_Olist_ONil(T_a))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_n__lists_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_xs_2,V_n_2,T_a] : c_Enum_On__lists(T_a,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_List_Omap(T_a,tc_List_Olist(T_a))),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),V_xs_2)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose_Osimps_I3_J,axiom, % 167.45/167.47 ! [V_xss_2,V_xs_2,V_x_2,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose__aux__filter__head,axiom, % 167.45/167.47 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),c_List_Ohd(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter__concat,axiom, % 167.45/167.47 ! [V_xs_2,V_p_2,T_a] : hAPP(c_List_Ofilter(T_a,V_p_2),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Ofilter(T_a,V_p_2)),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter__sort,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss) ). % 167.45/167.47 % 167.45/167.47 fof(fact_partition__filter2,axiom, % 167.45/167.47 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_P_2)),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__filter,axiom, % 167.45/167.47 ! [V_P_2,V_xs_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.47 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sum__length__filter__compl,axiom, % 167.45/167.47 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__filter__le,axiom, % 167.45/167.47 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter__is__subset,axiom, % 167.45/167.47 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter__id__conv,axiom, % 167.45/167.47 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.47 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2 % 167.45/167.47 <=> ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter__insort__triv,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.47 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remove1__filter__not,axiom, % 167.45/167.47 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 167.45/167.47 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.47 => c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter__remove1,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_Q_2,T_a] : hAPP(c_List_Ofilter(T_a,V_Q_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter__filter,axiom, % 167.45/167.47 ! [V_xs_2,V_Q_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_Q_2)),V_P_2)),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_partition__filter1,axiom, % 167.45/167.47 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter__append,axiom, % 167.45/167.47 ! [V_ys_2,V_xs_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose_Osimps_I1_J,axiom, % 167.45/167.47 ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter_Osimps_I1_J,axiom, % 167.45/167.47 ! [V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter__empty__conv,axiom, % 167.45/167.47 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.47 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a) % 167.45/167.47 <=> ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 167.45/167.47 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.47 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.47 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_removeAll__filter__not__eq,axiom, % 167.45/167.47 ! [V_x_2,T_a] : c_List_OremoveAll(T_a,V_x_2) = c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(c_fequal,V_x_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_removeAll__filter__not,axiom, % 167.45/167.47 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 167.45/167.47 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.47 => hAPP(c_List_OremoveAll(T_a,V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_remdups__filter,axiom, % 167.45/167.47 ! [V_xs_2,V_P_2,T_a] : c_List_Oremdups(T_a,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oremdups(T_a,V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nth__transpose,axiom, % 167.45/167.47 ! [V_xs_2,T_a,V_i_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) % 167.45/167.47 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose__map__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),c_List_Otranspose(T_b,V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__filter,axiom, % 167.45/167.47 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)))),V_P_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__filter__map,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__filter__less,axiom, % 167.45/167.47 ! [V_P_2,V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_partition__filter__conv,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_a] : c_List_Opartition(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_f_2)),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__minus__filter__out,axiom, % 167.45/167.47 ! [V_y_2,V_xs_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_filter__in__sublist,axiom, % 167.45/167.47 ! [V_s_2,V_xs_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.47 => hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_a,V_xs_2,V_s_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose__empty,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a)) % 167.45/167.47 <=> ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.47 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__filter__conv__card,axiom, % 167.45/167.47 ! [V_xs_2,V_p_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_a),V_xs_2))))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose__aux__filter__tail,axiom, % 167.45/167.47 ! [V_xss_2,T_a] : c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otl(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose_Opsimps_I3_J,axiom, % 167.45/167.47 ! [V_xss_2,V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2))) % 167.45/167.47 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__filter__def,axiom, % 167.45/167.47 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),V_f_2)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_a)))),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__filter__simps_I2_J,axiom, % 167.45/167.47 ! [V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__of__filter__in,axiom, % 167.45/167.47 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] : % 167.45/167.47 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2)) % 167.45/167.47 => hAPP(hAPP(c_Map_Omap__of(T_b,T_a),hAPP(c_List_Ofilter(tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__filter__simps_I1_J,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_a),T_a,c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sublist__shift__lemma__Suc,axiom, % 167.45/167.47 ! [V_is_2,V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_a,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_a,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_select__weigth__drop__zero,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_pick__drop__zero,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : c_Random_Opick(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_a,V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose_Opsimps_I1_J,axiom, % 167.45/167.47 ! [T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a)))) % 167.45/167.47 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__filter__map__filter,axiom, % 167.45/167.47 ! [V_xs_2,V_P_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = c_List_Omap__filter(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_Option_Ooption(T_a)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),T_b),c_If(tc_Option_Ooption(T_a))),V_P_2)),hAPP(hAPP(c_COMBB(T_a,tc_Option_Ooption(T_a),T_b),c_Option_Ooption_OSome(T_a)),V_f_2))),c_Option_Ooption_ONone(T_a)),V_xs_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose_Opsimps_I2_J,axiom, % 167.45/167.47 ! [V_xss_2,T_a] : % 167.45/167.47 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2))) % 167.45/167.47 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2)) = c_List_Otranspose(T_a,V_xss_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose__max__length,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xs_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose__aux__max,axiom, % 167.45/167.47 ! [V_xss_2,T_b,V_xs_2,T_a] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldr__append,axiom, % 167.45/167.47 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,c_List_Ofoldr(T_b,T_a,V_f_2,V_ys_2,V_a_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldr_Osimps_I1_J,axiom, % 167.45/167.47 ! [V_a_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b),V_a_2) = V_a_2 ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldr_Osimps_I2_J,axiom, % 167.45/167.47 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldr__conv__foldl,axiom, % 167.45/167.47 ! [V_a_2,V_xs_2,T_a] : % 167.45/167.47 ( class_Groups_Oab__semigroup__add(T_a) % 167.45/167.47 => c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldr__map,axiom, % 167.45/167.47 ! [V_a_2,V_xs_2,V_f_2,T_c,V_g_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_g_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_c,T_a,hAPP(c_Fun_Ocomp(T_b,tc_fun(T_a,T_a),T_c,V_g_2),V_f_2),V_xs_2,V_a_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldl__foldr1__lemma,axiom, % 167.45/167.47 ! [V_xs_2,V_a_2,T_a] : % 167.45/167.47 ( class_Groups_Omonoid__add(T_a) % 167.45/167.47 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_foldl__foldr1,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( class_Groups_Omonoid__add(T_a) % 167.45/167.47 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_xs_2) = c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__transpose,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sublist__def,axiom, % 167.45/167.47 ! [V_A_2,V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sublist__shift__lemma,axiom, % 167.45/167.47 ! [V_i_2,V_xs_2,V_A_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_a,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_atLeastLessThan__upt,axiom, % 167.45/167.47 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_set__upt,axiom, % 167.45/167.47 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_length__upt,axiom, % 167.45/167.47 ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i) ). % 167.45/167.47 % 167.45/167.47 fof(fact_upt__Suc,axiom, % 167.45/167.47 ! [V_j,V_i] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.45/167.47 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.45/167.47 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_upt__Suc__append,axiom, % 167.45/167.47 ! [V_j,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.45/167.47 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_upt__rec,axiom, % 167.45/167.47 ! [V_j,V_i] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.45/167.47 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.45/167.47 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_upt__conv__Cons,axiom, % 167.45/167.47 ! [V_j,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.45/167.47 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_upt__conv__Nil,axiom, % 167.45/167.47 ! [V_i,V_j] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 167.45/167.47 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_upt__eq__Nil__conv,axiom, % 167.45/167.47 ! [V_j_2,V_i_2] : % 167.45/167.47 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 167.45/167.47 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.47 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_upt__0,axiom, % 167.45/167.47 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 167.45/167.47 % 167.45/167.47 fof(fact_upt__add__eq__append,axiom, % 167.45/167.47 ! [V_k,V_j,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.45/167.47 => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted__list__of__set__range,axiom, % 167.45/167.47 ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2) ). % 167.45/167.47 % 167.45/167.47 fof(fact_take__upt,axiom, % 167.45/167.47 ! [V_n,V_m,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n)) % 167.45/167.47 => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_hd__upt,axiom, % 167.45/167.47 ! [V_j,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.45/167.47 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_drop__upt,axiom, % 167.45/167.47 ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j) ). % 167.45/167.47 % 167.45/167.47 fof(fact_distinct__upt,axiom, % 167.45/167.47 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_upt__rec__number__of,axiom, % 167.45/167.47 ! [V_n,V_m] : % 167.45/167.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) % 167.45/167.47 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) ) % 167.45/167.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) % 167.45/167.47 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_upt__eq__Cons__conv,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 167.45/167.47 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 167.45/167.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 167.45/167.47 & V_i_2 = V_x_2 % 167.45/167.47 & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2 ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_last__upt,axiom, % 167.45/167.47 ! [V_j,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.45/167.47 => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__Suc__upt,axiom, % 167.45/167.47 ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_atLeastAtMost__upt,axiom, % 167.45/167.47 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_atLeast__upt,axiom, % 167.45/167.47 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nth__upt,axiom, % 167.45/167.47 ! [V_j,V_k,V_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j)) % 167.45/167.47 => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_greaterThanAtMost__upt,axiom, % 167.45/167.47 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_greaterThanLessThan__upt,axiom, % 167.45/167.47 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_atMost__upto,axiom, % 167.45/167.47 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) ). % 167.45/167.47 % 167.45/167.47 fof(fact_map__nth,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) = V_xs_2 ). % 167.45/167.47 % 167.45/167.47 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 167.45/167.47 ! [V_n_2,V_m_2,V_f_2,T_a] : % 167.45/167.47 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.47 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 167.45/167.47 ! [V_n_2,V_m_2,V_f_2,T_a] : % 167.45/167.47 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_nth__map__upt,axiom, % 167.45/167.47 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) % 167.45/167.47 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_transpose__rectangle,axiom, % 167.45/167.47 ! [V_n_2,T_a,V_xs_2] : % 167.45/167.47 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 167.45/167.47 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.47 => ( ! [B_i] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 167.45/167.47 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),B_i)) = V_n_2 ) % 167.45/167.47 => c_List_Otranspose(T_a,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_a)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_Nat_Onat,T_a),tc_Nat_Onat),c_List_Onth(T_a)),hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_insort__key__remove1,axiom, % 167.45/167.47 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] : % 167.45/167.47 ( class_Orderings_Olinorder(T_b) % 167.45/167.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 167.45/167.47 => ( hAPP(c_List_Ohd(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2 % 167.45/167.47 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted_ONil,axiom, % 167.45/167.47 ! [T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted__single,axiom, % 167.45/167.47 ! [V_x,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted__upt,axiom, % 167.45/167.47 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted__Cons,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 167.45/167.47 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 167.45/167.47 & ! [B_x] : % 167.45/167.47 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted__sort,axiom, % 167.45/167.47 ! [V_xs_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted__insort,axiom, % 167.45/167.47 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) % 167.45/167.47 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted__drop,axiom, % 167.45/167.47 ! [V_n,V_xs,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 167.45/167.47 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted__remove1,axiom, % 167.45/167.47 ! [V_a,V_xs,T_a] : % 167.45/167.47 ( class_Orderings_Olinorder(T_a) % 167.45/167.47 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 167.45/167.47 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 167.45/167.47 % 167.45/167.47 fof(fact_sorted__upto,axiom, % 167.45/167.47 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__take,axiom, % 167.45/167.48 ! [V_n,V_xs,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__tl,axiom, % 167.45/167.48 ! [V_xs,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__insort__insert,axiom, % 167.45/167.48 ! [V_x_2,V_xs_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__butlast,axiom, % 167.45/167.48 ! [V_xs,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted_Oequations_I1_J,axiom, % 167.45/167.48 ! [T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__many__eq,axiom, % 167.45/167.48 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2))) % 167.45/167.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.45/167.48 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__many,axiom, % 167.45/167.48 ! [V_zs,V_y,V_x,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__remdups,axiom, % 167.45/167.48 ! [V_l,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__distinct__set__unique,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 167.45/167.48 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 167.45/167.48 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 167.45/167.48 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 167.45/167.48 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__sort__key,axiom, % 167.45/167.48 ! [V_xs_2,V_f_2,T_b,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Osort__key(T_b,T_a,V_f_2,V_xs_2))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__insort__insert__key,axiom, % 167.45/167.48 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__map__remove1,axiom, % 167.45/167.48 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__insort__key,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2))) % 167.45/167.48 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__filter,axiom, % 167.45/167.48 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__map__same,axiom, % 167.45/167.48 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__same,axiom, % 167.45/167.48 ! [V_xs_2,V_g_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__append,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 167.45/167.48 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 167.45/167.48 & c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 167.45/167.48 & ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => ! [B_xa] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_filter__insort,axiom, % 167.45/167.48 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 167.45/167.48 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted_Oequations_I2_J,axiom, % 167.45/167.48 ! [V_a1_2,V_a2_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) % 167.45/167.48 <=> ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) % 167.45/167.48 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__list__of__set,axiom, % 167.45/167.48 ! [V_A_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.48 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 % 167.45/167.48 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) % 167.45/167.48 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_insort__remove1,axiom, % 167.45/167.48 ! [V_xs_2,V_a_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 167.45/167.48 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__equals__nth__mono,axiom, % 167.45/167.48 ! [V_xs_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 167.45/167.48 <=> ! [B_j] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.48 => ! [B_i] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j))) ) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__nth__mono,axiom, % 167.45/167.48 ! [V_j,V_i,V_xs,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__sorted__distinct__set__unique,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 167.45/167.48 ( class_Orderings_Olinorder(T_b) % 167.45/167.48 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2))) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 167.45/167.48 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)) % 167.45/167.48 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))) % 167.45/167.48 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 167.45/167.48 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_transpose__column,axiom, % 167.45/167.48 ! [V_i_2,V_xs_2,T_a] : % 167.45/167.48 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 167.45/167.48 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_nth__nth__transpose__sorted,axiom, % 167.45/167.48 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 167.45/167.48 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)))) % 167.45/167.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_j_2)),V_i_2) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_inj__on__rev,axiom, % 167.45/167.48 ! [V_A_2,T_a] : c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orev(T_a),V_A_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_distinct__rev,axiom, % 167.45/167.48 ! [V_xs_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) % 167.45/167.48 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__append,axiom, % 167.45/167.48 ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev_Osimps_I1_J,axiom, % 167.45/167.48 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 167.45/167.48 % 167.45/167.48 fof(fact_Nil__is__rev__conv,axiom, % 167.45/167.48 ! [V_xs_2,T_a] : % 167.45/167.48 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2) % 167.45/167.48 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__is__Nil__conv,axiom, % 167.45/167.48 ! [V_xs_2,T_a] : % 167.45/167.48 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 167.45/167.48 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_singleton__rev__conv,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.48 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(c_List_Orev(T_a),V_xs_2) % 167.45/167.48 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__singleton__conv,axiom, % 167.45/167.48 ! [V_x_2,V_xs_2,T_a] : % 167.45/167.48 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) % 167.45/167.48 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev_Osimps_I2_J,axiom, % 167.45/167.48 ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__eq__Cons__iff,axiom, % 167.45/167.48 ! [V_ys_2,V_y_2,V_xs_2,T_a] : % 167.45/167.48 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 167.45/167.48 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__concat,axiom, % 167.45/167.48 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Orev(T_a)),hAPP(c_List_Orev(tc_List_Olist(T_a)),V_xs_2))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__map,axiom, % 167.45/167.48 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__filter,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Orev(T_a),V_xs_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_zip__rev,axiom, % 167.45/167.48 ! [V_ys,T_b,V_xs,T_a] : % 167.45/167.48 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) % 167.45/167.48 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_set__rev,axiom, % 167.45/167.48 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__all2__rev1,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 167.45/167.48 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) % 167.45/167.48 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__all2__rev,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 167.45/167.48 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),hAPP(c_List_Orev(T_b),V_ys_2)) % 167.45/167.48 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_listsum__rev,axiom, % 167.45/167.48 ! [V_xs,T_a] : % 167.45/167.48 ( class_Groups_Ocomm__monoid__add(T_a) % 167.45/167.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__is__rev__conv,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,T_a] : % 167.45/167.48 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2) % 167.45/167.48 <=> V_xs_2 = V_ys_2 ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__swap,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,T_a] : % 167.45/167.48 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2 % 167.45/167.48 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__rev__ident,axiom, % 167.45/167.48 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 167.45/167.48 % 167.45/167.48 fof(fact_length__rev,axiom, % 167.45/167.48 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 167.45/167.48 % 167.45/167.48 fof(fact_foldl__foldr,axiom, % 167.45/167.48 ! [V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2),V_a_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_foldr__foldl,axiom, % 167.45/167.48 ! [V_a_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),V_f_2),V_a_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_last__rev,axiom, % 167.45/167.48 ! [T_a,V_xs] : % 167.45/167.48 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.48 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_hd__rev,axiom, % 167.45/167.48 ! [T_a,V_xs] : % 167.45/167.48 ( V_xs != c_List_Olist_ONil(T_a) % 167.45/167.48 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__transpose,axiom, % 167.45/167.48 ! [V_xs_2,T_a] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__foldl__cons,axiom, % 167.45/167.48 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)),V_xs_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__take,axiom, % 167.45/167.48 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__drop,axiom, % 167.45/167.48 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rotate__rev,axiom, % 167.45/167.48 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__nth,axiom, % 167.45/167.48 ! [V_xs,T_a,V_n] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__update,axiom, % 167.45/167.48 ! [V_y,V_xs,T_a,V_k] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.48 => hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__rev__nth__mono,axiom, % 167.45/167.48 ! [V_j,V_i,V_xs,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) ) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_foldr__max__sorted,axiom, % 167.45/167.48 ! [V_y_2,V_xs_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2)) % 167.45/167.48 => ( ( V_xs_2 = c_List_Olist_ONil(T_a) % 167.45/167.48 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) % 167.45/167.48 & ( V_xs_2 != c_List_Olist_ONil(T_a) % 167.45/167.48 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_length__transpose__sorted,axiom, % 167.45/167.48 ! [V_xs_2,T_a] : % 167.45/167.48 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 167.45/167.48 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 167.45/167.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.45/167.48 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) % 167.45/167.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_transpose__column__length,axiom, % 167.45/167.48 ! [V_i_2,V_xs_2,T_a] : % 167.45/167.48 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 167.45/167.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_transpose__transpose,axiom, % 167.45/167.48 ! [V_xs_2,T_a] : % 167.45/167.48 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 167.45/167.48 => c_List_Otranspose(T_a,c_List_Otranspose(T_a,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a))),V_xs_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 167.45/167.48 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__takeWhile,axiom, % 167.45/167.48 ! [V_P_2,V_xs_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_length__takeWhile__le,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__eq__all__conv,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2 % 167.45/167.48 <=> ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_set__takeWhileD,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,V_x_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_zip__takeWhile__fst,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_zip__takeWhile__snd,axiom, % 167.45/167.48 ! [V_ys_2,V_P_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__map,axiom, % 167.45/167.48 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OtakeWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__tail,axiom, % 167.45/167.48 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] : % 167.45/167.48 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2))) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile_Osimps_I2_J,axiom, % 167.45/167.48 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 167.45/167.48 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) % 167.45/167.48 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_a) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile_Osimps_I1_J,axiom, % 167.45/167.48 ! [V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__eq__take,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_distinct__takeWhile,axiom, % 167.45/167.48 ! [V_P_2,V_xs_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.48 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_return__list__def,axiom, % 167.45/167.48 ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__append1,axiom, % 167.45/167.48 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__nth,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) % 167.45/167.48 => hAPP(hAPP(c_List_Onth(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_nth__length__takeWhile,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.48 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__not__last,axiom, % 167.45/167.48 ! [T_a,V_xs_2] : % 167.45/167.48 ( V_xs_2 != c_List_Olist_ONil(T_a) % 167.45/167.48 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.48 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),c_List_Olast(T_a,V_xs_2))),V_xs_2) = c_List_Obutlast(T_a,V_xs_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 167.45/167.48 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 167.45/167.48 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2),V_xs_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_transfer__nat__int__list__return__embed,axiom, % 167.45/167.48 ! [V_l] : % 167.45/167.48 ( c_List_Onat__list(V_l) % 167.45/167.48 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 167.45/167.48 ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_embed__list__def,axiom, % 167.45/167.48 ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__neq__rev,axiom, % 167.45/167.48 ! [V_x_2,V_xs_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Otl(T_a),c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_dropWhile__neq__rev,axiom, % 167.45/167.48 ! [V_x_2,V_xs_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Orev(T_a),c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__dropWhile__id,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)) = V_xs_2 ). % 167.45/167.48 % 167.45/167.48 fof(fact_dropWhile__map,axiom, % 167.45/167.48 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OdropWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__dropWhile,axiom, % 167.45/167.48 ! [V_P_2,V_xs_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_length__dropWhile__le,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_dropWhile__eq__Nil__conv,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) % 167.45/167.48 <=> ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_dropWhile_Osimps_I2_J,axiom, % 167.45/167.48 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 167.45/167.48 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_OdropWhile(T_a,V_P_2,V_xs_2) ) % 167.45/167.48 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_dropWhile_Osimps_I1_J,axiom, % 167.45/167.48 ! [V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 167.45/167.48 % 167.45/167.48 fof(fact_distinct__dropWhile,axiom, % 167.45/167.48 ! [V_P_2,V_xs_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 167.45/167.48 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_hd__dropWhile,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) % 167.45/167.48 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_dropWhile__append1,axiom, % 167.45/167.48 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_ys_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_dropWhile__eq__Cons__conv,axiom, % 167.45/167.48 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 167.45/167.48 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) % 167.45/167.48 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_dropWhile__eq__drop,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_dropWhile__nth,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) % 167.45/167.48 => hAPP(hAPP(c_List_Onth(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_listsum__map__filter,axiom, % 167.45/167.48 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] : % 167.45/167.48 ( class_Groups_Omonoid__add(T_b) % 167.45/167.48 => ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => ( ~ hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.48 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) % 167.45/167.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted__nth__monoI,axiom, % 167.45/167.48 ! [V_xs,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( ! [B_i,B_j] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) ) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__eq__filter,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) % 167.45/167.48 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.48 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__eq__take__P__nth,axiom, % 167.45/167.48 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 167.45/167.48 ( ! [B_i] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) % 167.45/167.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.48 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) % 167.45/167.48 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_length__takeWhile__less__P__nth,axiom, % 167.45/167.48 ! [V_xs_2,T_a,V_P_2,V_j_2] : % 167.45/167.48 ( ! [B_i] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 167.45/167.48 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted_Osimps,axiom, % 167.45/167.48 ! [V_a_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2) % 167.45/167.48 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 167.45/167.48 | ? [B_xs,B_x] : % 167.45/167.48 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 167.45/167.48 & ! [B_xa] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) % 167.45/167.48 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__upds__def,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__comp__def,axiom, % 167.45/167.48 ! [V_k_2,V_g_2,V_f_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_b,c_Option_Ooption_ONone(T_a),V_f_2),hAPP(V_g_2,V_k_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__of__append,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__comp__empty_I1_J,axiom, % 167.45/167.48 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__comp__empty_I2_J,axiom, % 167.45/167.48 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_a) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__comp__simps_I2_J,axiom, % 167.45/167.48 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] : % 167.45/167.48 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2) % 167.45/167.48 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__find__right,axiom, % 167.45/167.48 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] : % 167.45/167.48 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) % 167.45/167.48 => hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__comp__Some__iff,axiom, % 167.45/167.48 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 167.45/167.48 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) % 167.45/167.48 <=> ? [B_k_H] : % 167.45/167.48 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 167.45/167.48 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__upd,axiom, % 167.45/167.48 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__SomeD,axiom, % 167.45/167.48 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 167.45/167.48 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 167.45/167.48 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 167.45/167.48 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 167.45/167.48 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__Some__iff,axiom, % 167.45/167.48 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 167.45/167.48 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 167.45/167.48 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 167.45/167.48 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 167.45/167.48 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__empty,axiom, % 167.45/167.48 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = V_m_2 ). % 167.45/167.48 % 167.45/167.48 fof(fact_empty__map__add,axiom, % 167.45/167.48 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),V_m_2) = V_m_2 ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__comp__simps_I1_J,axiom, % 167.45/167.48 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] : % 167.45/167.48 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 167.45/167.48 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__None,axiom, % 167.45/167.48 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] : % 167.45/167.48 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a) % 167.45/167.48 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 167.45/167.48 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__upds,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__upds(T_a,T_b,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_dom__map__add,axiom, % 167.45/167.48 ! [V_n_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_n_2)),c_Map_Odom(T_a,T_b,V_m_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__assoc,axiom, % 167.45/167.48 ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__add(T_a,T_b,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_m3_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 167.45/167.48 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] : % 167.45/167.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2))) % 167.45/167.48 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 167.45/167.48 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 167.45/167.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 167.45/167.48 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 167.45/167.48 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 167.45/167.48 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_inj__on__map__add__dom,axiom, % 167.45/167.48 ! [V_m_H_2,V_m_2,T_b,T_a] : % 167.45/167.48 ( c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),c_Map_Omap__add(T_a,T_b,V_m_2,V_m_H_2),c_Map_Odom(T_a,T_b,V_m_H_2)) % 167.45/167.48 <=> c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),V_m_H_2,c_Map_Odom(T_a,T_b,V_m_H_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__def,axiom, % 167.45/167.48 ! [V_x_2,V_m2_2,V_m1_2,T_a,T_b] : hAPP(c_Map_Omap__add(T_b,T_a,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_a)),hAPP(V_m2_2,V_x_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__comm,axiom, % 167.45/167.48 ! [V_m2_2,V_m1_2,T_b,T_a] : % 167.45/167.48 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m1_2)),c_Map_Odom(T_a,T_b,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.45/167.48 => c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2) = c_Map_Omap__add(T_a,T_b,V_m2_2,V_m1_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__comp__None__iff,axiom, % 167.45/167.48 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 167.45/167.48 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 167.45/167.48 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 167.45/167.48 | ? [B_k_H] : % 167.45/167.48 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 167.45/167.48 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__map__of__foldr,axiom, % 167.45/167.48 ! [V_ps_2,V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)) = c_List_Ofoldr(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)))))),c_Option_Ooption_OSome(T_b))),V_ps_2,V_m_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__add__upd__left,axiom, % 167.45/167.48 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] : % 167.45/167.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2))) % 167.45/167.48 => c_Map_Omap__add(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_finite__range__map__of__map__add,axiom, % 167.45/167.48 ! [V_l_2,V_f_2,T_b,T_a] : % 167.45/167.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 167.45/167.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),c_Map_Omap__add(T_b,T_a,V_f_2,hAPP(c_Map_Omap__of(T_b,T_a),V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_not__in__set__insert,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_List_Oinsert__def,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.48 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) % 167.45/167.48 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_distinct__insert,axiom, % 167.45/167.48 ! [V_x,V_xs,T_a] : % 167.45/167.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 167.45/167.48 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_insert__remdups,axiom, % 167.45/167.48 ! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_in__set__insert,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_List_Oset__insert,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oinsert(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_insert__Nil,axiom, % 167.45/167.48 ! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_concat__map__maps,axiom, % 167.45/167.48 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) = c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_maps__def,axiom, % 167.45/167.48 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_maps__simps_I2_J,axiom, % 167.45/167.48 ! [V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 167.45/167.48 % 167.45/167.48 fof(fact_maps__simps_I1_J,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_b,T_a,V_f_2,V_xs_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_distinct__concat,axiom, % 167.45/167.48 ! [V_xs_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) % 167.45/167.48 => ( ! [B_ys] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) ) % 167.45/167.48 => ( ! [B_ys] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.48 => ! [B_zs] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.48 => ( B_ys != B_zs % 167.45/167.48 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),B_ys)),hAPP(c_List_Oset(T_a),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 167.45/167.48 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_ran__restrictD,axiom, % 167.45/167.48 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Map_Oran(T_b,T_a,c_Map_Orestrict__map(T_b,T_a,V_m_2,V_A_2)))) % 167.45/167.48 => ? [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.45/167.48 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_measures__lesseq,axiom, % 167.45/167.48 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_measures__less,axiom, % 167.45/167.48 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_wf__measures,axiom, % 167.45/167.48 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_in__measures_I1_J,axiom, % 167.45/167.48 ! [V_y_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_Nat_Onat))))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_measures__def,axiom, % 167.45/167.48 ! [V_fs_2,T_a] : c_List_Omeasures(T_a,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_a),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_a),c_List_Omap(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_a,tc_Nat_Onat),T_a,tc_Nat_Onat),c_COMBI(tc_fun(T_a,tc_Nat_Onat))))),V_fs_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_in__measures_I2_J,axiom, % 167.45/167.48 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) % 167.45/167.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 167.45/167.48 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 167.45/167.48 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_foldl__apply,axiom, % 167.45/167.48 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] : % 167.45/167.48 ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => hAPP(c_Fun_Ocomp(T_c,T_c,T_b,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_h_2),hAPP(V_g_2,B_x)) ) % 167.45/167.48 => hAPP(c_List_Ofoldl(T_c,T_a,hAPP(c_COMBC(T_a,T_c,T_c),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_g_2),V_s_2),V_xs_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_zip__obtain__same__length,axiom, % 167.45/167.48 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 167.45/167.48 ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)) % 167.45/167.48 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)))) ) % 167.45/167.48 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_map__of__eqI,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,T_b,T_a] : % 167.45/167.48 ( hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)) = hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2)) % 167.45/167.48 => ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)))) % 167.45/167.48 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2),B_x) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),B_x) ) % 167.45/167.48 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_pos__not__random__dseq__def,axiom, % 167.45/167.48 ! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_dropWhile__append2,axiom, % 167.45/167.48 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 167.45/167.48 ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.48 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_a,V_P_2,V_ys_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__all2__all__nthI,axiom, % 167.45/167.48 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] : % 167.45/167.48 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2) % 167.45/167.48 => ( ! [B_n] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2))) % 167.45/167.48 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_b_2),B_n))) ) % 167.45/167.48 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_finite__map__freshness,axiom, % 167.45/167.48 ! [V_f_2,T_b,T_a] : % 167.45/167.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2))) % 167.45/167.48 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 167.45/167.48 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_finite__sorted__distinct__unique,axiom, % 167.45/167.48 ! [V_A_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 167.45/167.48 => ? [B_x] : % 167.45/167.48 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2 % 167.45/167.48 & c_List_Olinorder__class_Osorted(T_a,B_x) % 167.45/167.48 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x)) % 167.45/167.48 & ! [B_y] : % 167.45/167.48 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2 % 167.45/167.48 & c_List_Olinorder__class_Osorted(T_a,B_y) % 167.45/167.48 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) ) % 167.45/167.48 => B_y = B_x ) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_takeWhile__append2,axiom, % 167.45/167.48 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 167.45/167.48 ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.48 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_OtakeWhile(T_a,V_P_2,V_ys_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_insort__is__Cons,axiom, % 167.45/167.48 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] : % 167.45/167.48 ( class_Orderings_Olinorder(T_b) % 167.45/167.48 => ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 167.45/167.48 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_xs_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_filter__eq__Cons__iff,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] : % 167.45/167.48 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) % 167.45/167.48 <=> ? [B_us,B_vs] : % 167.45/167.48 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) % 167.45/167.48 & ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 167.45/167.48 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.48 & hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_Cons__eq__filter__iff,axiom, % 167.45/167.48 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 167.45/167.48 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) % 167.45/167.48 <=> ? [B_us,B_vs] : % 167.45/167.48 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) % 167.45/167.48 & ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 167.45/167.48 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.48 & hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__ball__nth,axiom, % 167.45/167.48 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.48 => ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.48 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_sorted_OCons,axiom, % 167.45/167.48 ! [V_x_2,V_xs_2,T_a] : % 167.45/167.48 ( class_Orderings_Olinorder(T_a) % 167.45/167.48 => ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) % 167.45/167.48 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 167.45/167.48 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__ex__length,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 167.45/167.48 <=> ? [B_n] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.48 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_in__set__conv__decomp,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__ex__simps_I2_J,axiom, % 167.45/167.48 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__ex__append,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 167.45/167.48 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 167.45/167.48 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__ex__iff,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 167.45/167.48 <=> ? [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__ex__rev,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 167.45/167.48 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__ex__simps_I1_J,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 167.45/167.48 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_in__set__conv__decomp__first,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 <=> ? [B_ys] : % 167.45/167.48 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) % 167.45/167.48 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_in__set__conv__decomp__last,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 <=> ? [B_ys,B_zs] : % 167.45/167.48 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) % 167.45/167.48 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_option_Orecs_I2_J,axiom, % 167.45/167.48 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_option_Orecs_I1_J,axiom, % 167.45/167.48 ! [V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_b)) = V_f1_2 ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__all__length,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 167.45/167.48 <=> ! [B_n] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_measure__function__int,axiom, % 167.45/167.48 c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__all__simps_I1_J,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 167.45/167.48 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__all__rev,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 167.45/167.48 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_Ball__set__list__all,axiom, % 167.45/167.48 ! [V_P_2,V_xs_2,T_a] : % 167.45/167.48 ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.48 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_measure__fst,axiom, % 167.45/167.48 ! [T_b,V_f_2,T_a] : % 167.45/167.48 ( c_FunDef_Ois__measure(T_a,V_f_2) % 167.45/167.48 => c_FunDef_Ois__measure(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_a,T_b)),V_f_2),c_Product__Type_Ofst(T_a,T_b))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_measure__snd,axiom, % 167.45/167.48 ! [T_b,V_f_2,T_a] : % 167.45/167.48 ( c_FunDef_Ois__measure(T_a,V_f_2) % 167.45/167.48 => c_FunDef_Ois__measure(tc_prod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_b,T_a)),V_f_2),c_Product__Type_Osnd(T_b,T_a))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__all__iff,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 167.45/167.48 <=> ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_is__measure_Osimps,axiom, % 167.45/167.48 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_is__measure_Oequations,axiom, % 167.45/167.48 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_is__measure_Ointros,axiom, % 167.45/167.48 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_measure__size,axiom, % 167.45/167.48 ! [T_a] : % 167.45/167.48 ( class_Nat_Osize(T_a) % 167.45/167.48 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__all__append,axiom, % 167.45/167.48 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 167.45/167.48 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 167.45/167.48 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__all__simps_I2_J,axiom, % 167.45/167.48 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__all__iff__raw,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 167.45/167.48 <=> ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__ex1__simps_I2_J,axiom, % 167.45/167.48 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 167.45/167.48 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => c_List_Olist__all(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) % 167.45/167.48 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_equal__fun__def,axiom, % 167.45/167.48 ! [V_g_2,V_f_2,T_a,T_b] : % 167.45/167.48 ( ( class_HOL_Oequal(T_b) % 167.45/167.48 & class_Enum_Oenum(T_a) ) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.45/167.48 <=> ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) % 167.45/167.48 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__ex1__simps_I1_J,axiom, % 167.45/167.48 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_equal,axiom, % 167.45/167.48 ! [T_a] : % 167.45/167.48 ( class_HOL_Oequal(T_a) % 167.45/167.48 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_equal__refl,axiom, % 167.45/167.48 ! [V_x,T_a] : % 167.45/167.48 ( class_HOL_Oequal(T_a) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_equal__eq,axiom, % 167.45/167.48 ! [V_y_2,V_x_2,T_a] : % 167.45/167.48 ( class_HOL_Oequal(T_a) % 167.45/167.48 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2)) % 167.45/167.48 <=> V_x_2 = V_y_2 ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__equal,axiom, % 167.45/167.48 ! [T_a] : % 167.45/167.48 ( class_HOL_Oequal(T_a) % 167.45/167.48 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_exists1__code,axiom, % 167.45/167.48 ! [V_P_2,T_a] : % 167.45/167.48 ( class_Enum_Oenum(T_a) % 167.45/167.48 => ( ? [B_x] : % 167.45/167.48 ( hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.48 & ! [B_y] : % 167.45/167.48 ( hBOOL(hAPP(V_P_2,B_y)) % 167.45/167.48 => B_y = B_x ) ) % 167.45/167.48 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_bool_Osize_I3_J,axiom, % 167.45/167.48 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(fact_bool_Osize_I4_J,axiom, % 167.45/167.48 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(fact_list__ex1__iff,axiom, % 167.45/167.48 ! [V_xs_2,V_P_2,T_a] : % 167.45/167.48 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2) % 167.45/167.48 <=> ? [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 & hBOOL(hAPP(V_P_2,B_x)) % 167.45/167.48 & ! [B_y] : % 167.45/167.48 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) % 167.45/167.48 & hBOOL(hAPP(V_P_2,B_y)) ) % 167.45/167.48 => B_y = B_x ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_size__code,axiom, % 167.45/167.48 ! [V_xq_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),T_a),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_transfer__morphism__int__nat,axiom, % 167.45/167.48 c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I7_J,axiom, % 167.45/167.48 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I11_J,axiom, % 167.45/167.48 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I13_J,axiom, % 167.45/167.48 ! [V_k2_2,V_k1_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 167.45/167.48 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I1_J,axiom, % 167.45/167.48 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I16_J,axiom, % 167.45/167.48 ! [V_k2_2,V_k1_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 167.45/167.48 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__number__of__int__code,axiom, % 167.45/167.48 ! [V_l_2,V_k_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 167.45/167.48 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I6_J,axiom, % 167.45/167.48 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I4_J,axiom, % 167.45/167.48 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I10_J,axiom, % 167.45/167.48 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_equal__int__def,axiom, % 167.45/167.48 ! [V_l_2,V_k_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) % 167.45/167.48 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I14_J,axiom, % 167.45/167.48 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OBit1(V_k2))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I15_J,axiom, % 167.45/167.48 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OBit0(V_k2))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I3_J,axiom, % 167.45/167.48 ! [V_k2_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) % 167.45/167.48 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I9_J,axiom, % 167.45/167.48 ! [V_k1_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) % 167.45/167.48 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I8_J,axiom, % 167.45/167.48 ! [V_k2_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) % 167.45/167.48 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I12_J,axiom, % 167.45/167.48 ! [V_k1_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) % 167.45/167.48 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I5_J,axiom, % 167.45/167.48 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__code_I2_J,axiom, % 167.45/167.48 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_lazy__sequence__size__code,axiom, % 167.45/167.48 ! [V_xq_2,V_s_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_a,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_a),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_seq__case,axiom, % 167.45/167.48 ! [V_xq_2,V_g_2,V_f_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f_2,V_g_2,V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(T_a,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),T_a),V_g_2)),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_eq__int__refl,axiom, % 167.45/167.48 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_yieldn__def,axiom, % 167.45/167.48 ! [T_a] : c_Lazy__Sequence_Oyieldn(T_a) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_a),T_a,c_Lazy__Sequence_Oyield(T_a)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 167.45/167.48 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 167.45/167.48 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_lazy__sequence_Oinject,axiom, % 167.45/167.48 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] : % 167.45/167.48 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H_2,V_lazy__sequence_H_2) % 167.45/167.48 <=> ( V_a_2 = V_a_H_2 % 167.45/167.48 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact__01,axiom, % 167.45/167.48 ! [V_xq,V_x,T_a] : hAPP(c_Lazy__Sequence_Oyield(T_a),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq)) = hAPP(c_Option_Ooption_OSome(tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_Product__Type_OPair(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_x),V_xq)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 167.45/167.48 ! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 167.45/167.48 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 167.45/167.48 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.48 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_a) ) % 167.45/167.48 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.48 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 167.45/167.48 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 167.45/167.48 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.48 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_a) ) % 167.45/167.48 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 167.45/167.48 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 167.45/167.48 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Opos__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 167.45/167.48 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Oneg__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 167.45/167.48 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Oneg__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_New__DSequence_Opos__empty__def,axiom, % 167.45/167.48 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 167.45/167.48 % 167.45/167.48 fof(fact_pos__empty__def,axiom, % 167.45/167.48 ! [V_seed_2,V_size_2,V_nrandom_2,T_a] : c_New__Random__Sequence_Opos__empty(T_a,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_a) ). % 167.45/167.48 % 167.45/167.48 fof(fact_neg__bind__def,axiom, % 167.45/167.48 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_New__DSequence_Opos__bind__def,axiom, % 167.45/167.48 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Opos__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_neg__map__def,axiom, % 167.45/167.48 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Oneg__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),T_b,c_New__Random__Sequence_Oneg__single(T_a)),V_f_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_neg__single__def,axiom, % 167.45/167.48 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_a,V_x_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_pos__bind__def,axiom, % 167.45/167.48 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_New__DSequence_Oneg__single__def,axiom, % 167.45/167.48 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x) ). % 167.45/167.48 % 167.45/167.48 fof(fact_pos__map__def,axiom, % 167.45/167.48 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Opos__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),T_b,c_New__Random__Sequence_Opos__single(T_a)),V_f_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_pos__single__def,axiom, % 167.45/167.48 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_a,V_x_2) ). % 167.45/167.48 % 167.45/167.48 fof(fact_length__splice,axiom, % 167.45/167.48 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_splice_Osimps_I3_J,axiom, % 167.45/167.48 ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_splice__Nil2,axiom, % 167.45/167.48 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 167.45/167.48 % 167.45/167.48 fof(fact_splice_Osimps_I1_J,axiom, % 167.45/167.48 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 167.45/167.48 % 167.45/167.48 fof(fact_splice_Osimps_I2_J,axiom, % 167.45/167.48 ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va) ). % 167.45/167.48 % 167.45/167.48 fof(fact_New__DSequence_Opos__single__def,axiom, % 167.45/167.48 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x) ). % 167.45/167.48 % 167.45/167.48 fof(fact_acyclicP__converse,axiom, % 167.45/167.48 ! [V_r_2,T_a] : % 167.45/167.48 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Predicate_Oconversep(T_a,T_a,V_r_2)))) % 167.45/167.48 <=> c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_converse__meet,axiom, % 167.45/167.48 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_converse__join,axiom, % 167.45/167.48 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_conversep__noteq,axiom, % 167.45/167.48 ! [V_y_2,V_x_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot)),c_fequal)),V_x_2),V_y_2)) % 167.45/167.48 <=> V_x_2 != V_y_2 ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_conversep__eq,axiom, % 167.45/167.48 ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal ). % 167.45/167.48 % 167.45/167.48 fof(fact_conversep__conversep,axiom, % 167.45/167.48 ! [V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Oconversep(T_a,T_b,V_r_2)) = V_r_2 ). % 167.45/167.48 % 167.45/167.48 fof(fact_conversep__iff,axiom, % 167.45/167.48 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 167.45/167.48 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_conversep_Oequations,axiom, % 167.45/167.48 ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a2_2),V_a1_2)) % 167.45/167.48 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_conversep_Ointros,axiom, % 167.45/167.48 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 167.45/167.48 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_b_2),V_a_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_conversepD,axiom, % 167.45/167.48 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 167.45/167.48 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_converse__pred__comp,axiom, % 167.45/167.48 ! [V_s_2,V_r_2,T_c,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Opred__comp(T_b,T_c,T_a,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_a,T_c,T_b,c_Predicate_Oconversep(T_c,T_a,V_s_2),c_Predicate_Oconversep(T_b,T_c,V_r_2)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_conversep__converse__eq,axiom, % 167.45/167.48 ! [V_y_2,V_x_2,V_r_2,T_b,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2),V_y_2)) % 167.45/167.48 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact__02,axiom, % 167.45/167.48 ! [V_s2_2,V_s1_2,T_b,T_a] : c_Lazy__Sequence_Oproduct(T_a,T_b,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_a,tc_prod(T_a,T_b),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_a),c_Lazy__Sequence_Obind(T_b,tc_prod(T_a,T_b),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_b),c_Lazy__Sequence_Osingle(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))) ). % 167.45/167.48 % 167.45/167.48 fof(fact_tl__replicate,axiom, % 167.45/167.48 ! [V_x,T_a,V_n] : % 167.45/167.48 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.48 => hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_zip__replicate,axiom, % 167.45/167.48 ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_replicate__app__Cons__same,axiom, % 167.45/167.48 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_replicate__Suc,axiom, % 167.45/167.48 ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_rev__replicate,axiom, % 167.45/167.48 ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x) ). % 167.45/167.48 % 167.45/167.48 fof(fact_last__replicate,axiom, % 167.45/167.48 ! [V_x,T_a,V_n] : % 167.45/167.48 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.48 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_drop__replicate,axiom, % 167.45/167.48 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x) ). % 167.45/167.48 % 167.45/167.48 fof(fact_hd__replicate,axiom, % 167.45/167.48 ! [V_x,T_a,V_n] : % 167.45/167.48 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.48 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_take__replicate,axiom, % 167.45/167.48 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x) ). % 167.45/167.48 % 167.45/167.48 fof(fact_Ball__set__replicate,axiom, % 167.45/167.48 ! [V_P_2,V_a_2,V_n_2,T_a] : % 167.45/167.48 ( ! [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) % 167.45/167.48 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.48 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 167.45/167.48 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_Bex__set__replicate,axiom, % 167.45/167.48 ! [V_P_2,V_a_2,V_n_2,T_a] : % 167.45/167.48 ( ? [B_x] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) % 167.45/167.48 & hBOOL(hAPP(V_P_2,B_x)) ) % 167.45/167.48 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 167.45/167.48 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_replicate__eq__replicate,axiom, % 167.45/167.48 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_a] : % 167.45/167.48 ( c_List_Oreplicate(T_a,V_m_2,V_x_2) = c_List_Oreplicate(T_a,V_n_2,V_y_2) % 167.45/167.48 <=> ( V_m_2 = V_n_2 % 167.45/167.48 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.45/167.48 => V_x_2 = V_y_2 ) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_nth__replicate,axiom, % 167.45/167.48 ! [V_x,T_a,V_n,V_i] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 167.45/167.48 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_in__set__replicate,axiom, % 167.45/167.48 ! [V_y_2,V_n_2,V_x_2,T_a] : % 167.45/167.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_y_2)))) % 167.45/167.48 <=> ( V_x_2 = V_y_2 % 167.45/167.48 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.45/167.48 % 167.45/167.48 fof(fact_append__replicate__commute,axiom, % 167.45/167.48 ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_replicate__add,axiom, % 167.45/167.48 ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)) ). % 167.45/167.48 % 167.45/167.48 fof(fact_filter__replicate,axiom, % 167.45/167.48 ! [V_n_2,T_a,V_x_2,V_P_2] : % 167.45/167.48 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_List_Oreplicate(T_a,V_n_2,V_x_2) ) % 167.45/167.48 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 167.45/167.48 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_List_Olist_ONil(T_a) ) ) ). % 167.45/167.48 % 167.45/167.48 %----Arity declarations (231) % 167.45/167.48 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 167.45/167.48 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Lattices_Obounded__lattice(T_1) % 167.45/167.48 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 167.45/167.48 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Lattices_Obounded__lattice(T_1) % 167.45/167.48 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Lattices_Obounded__lattice(T_1) % 167.45/167.48 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Lattices_Olattice(T_1) % 167.45/167.48 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Lattices_Olattice(T_1) % 167.45/167.48 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Lattices_Odistrib__lattice(T_1) % 167.45/167.48 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Lattices_Oboolean__algebra(T_1) % 167.45/167.48 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Orderings_Opreorder,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Orderings_Opreorder(T_1) % 167.45/167.48 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Finite__Set_Ofinite,axiom, % 167.45/167.48 ! [T_1,T_2] : % 167.45/167.48 ( ( class_Finite__Set_Ofinite(T_2) % 167.45/167.48 & class_Finite__Set_Ofinite(T_1) ) % 167.45/167.48 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Lattices_Olattice,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Lattices_Olattice(T_1) % 167.45/167.48 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Orderings_Oorder,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Orderings_Oorder(T_1) % 167.45/167.48 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Orderings_Otop,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Orderings_Otop(T_1) % 167.45/167.48 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Orderings_Oord,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Orderings_Oord(T_1) % 167.45/167.48 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Orderings_Obot,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Orderings_Obot(T_1) % 167.45/167.48 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Groups_Ouminus,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Groups_Ouminus(T_1) % 167.45/167.48 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Groups_Ominus,axiom, % 167.45/167.48 ! [T_2,T_1] : % 167.45/167.48 ( class_Groups_Ominus(T_1) % 167.45/167.48 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__HOL_Oequal,axiom, % 167.45/167.48 ! [T_1,T_2] : % 167.45/167.48 ( ( class_Enum_Oenum(T_2) % 167.45/167.48 & class_HOL_Oequal(T_1) ) % 167.45/167.48 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_fun__Enum_Oenum,axiom, % 167.45/167.48 ! [T_1,T_2] : % 167.45/167.48 ( ( class_Enum_Oenum(T_2) % 167.45/167.48 & class_Enum_Oenum(T_1) ) % 167.45/167.48 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 167.45/167.48 class_HOL_Oequal(tc_Com_Ocom) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Com__Ocom__Nat_Osize,axiom, % 167.45/167.48 class_Nat_Osize(tc_Com_Ocom) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 167.45/167.48 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 167.45/167.48 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 167.45/167.48 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 167.45/167.48 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 167.45/167.48 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 167.45/167.48 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 167.45/167.48 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 167.45/167.48 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 167.45/167.48 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 167.45/167.48 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 167.45/167.48 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 167.45/167.48 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 167.45/167.48 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 167.45/167.48 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 167.45/167.48 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 167.45/167.48 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 167.45/167.48 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 167.45/167.48 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 167.45/167.48 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 167.45/167.48 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 167.45/167.48 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 167.45/167.48 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 167.45/167.48 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 167.45/167.48 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 167.45/167.48 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 167.45/167.48 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 167.45/167.48 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 167.45/167.48 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 167.45/167.48 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 167.45/167.48 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 167.45/167.48 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 167.45/167.48 class_Divides_Osemiring__div(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 167.45/167.48 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 167.45/167.48 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 167.45/167.48 class_Groups_Oab__group__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 167.45/167.48 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 167.45/167.48 class_Rings_Oordered__ring(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 167.45/167.48 class_Orderings_Opreorder(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 167.45/167.48 class_Orderings_Olinorder(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 167.45/167.48 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 167.45/167.48 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 167.45/167.48 class_Groups_Omonoid__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 167.45/167.48 class_Smallcheck_Osmall(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 167.45/167.48 class_Rings_Osemiring__1(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 167.45/167.48 class_Rings_Osemiring__0(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 167.45/167.48 class_Lattices_Olattice(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 167.45/167.48 class_Groups_Ogroup__add(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 167.45/167.48 class_Divides_Oring__div(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 167.45/167.48 class_Rings_Omult__zero(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 167.45/167.48 class_Orderings_Oorder(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 167.45/167.48 class_Int_Oring__char__0(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 167.45/167.48 class_Int_Onumber__ring(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 167.45/167.48 class_Rings_Osemiring(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Orderings_Oord,axiom, % 167.45/167.48 class_Orderings_Oord(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 167.45/167.48 class_Groups_Ouminus(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 167.45/167.48 class_Groups_Osgn__if(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 167.45/167.48 class_Groups_Oabs__if(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 167.45/167.48 class_Rings_Oring__1(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Ominus,axiom, % 167.45/167.48 class_Groups_Ominus(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Power_Opower,axiom, % 167.45/167.48 class_Power_Opower(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Ozero,axiom, % 167.45/167.48 class_Groups_Ozero(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Oring,axiom, % 167.45/167.48 class_Rings_Oring(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Rings_Oidom,axiom, % 167.45/167.48 class_Rings_Oidom(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Int_Onumber,axiom, % 167.45/167.48 class_Int_Onumber(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__Groups_Oone,axiom, % 167.45/167.48 class_Groups_Oone(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Int__Oint__HOL_Oequal,axiom, % 167.45/167.48 class_HOL_Oequal(tc_Int_Oint) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 167.45/167.48 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 167.45/167.48 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 167.45/167.48 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 167.45/167.48 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 167.45/167.48 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 167.45/167.48 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 167.45/167.48 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 167.45/167.48 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 167.45/167.48 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 167.45/167.48 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 167.45/167.48 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 167.45/167.48 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 167.45/167.48 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 167.45/167.48 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 167.45/167.48 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 167.45/167.48 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 167.45/167.48 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 167.45/167.48 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 167.45/167.48 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 167.45/167.48 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 167.45/167.48 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 167.45/167.48 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 167.45/167.48 class_Orderings_Owellorder(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 167.45/167.48 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 167.45/167.48 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 167.45/167.48 class_Orderings_Opreorder(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 167.45/167.48 class_Orderings_Olinorder(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 167.45/167.48 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 167.45/167.48 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 167.45/167.48 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 167.45/167.48 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 167.45/167.48 class_Lattices_Olattice(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 167.45/167.48 class_Rings_Omult__zero(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 167.45/167.48 class_Orderings_Oorder(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 167.45/167.48 class_Rings_Osemiring(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 167.45/167.48 class_Orderings_Oord(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 167.45/167.48 class_Orderings_Obot(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 167.45/167.48 class_Groups_Ominus(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Power_Opower,axiom, % 167.45/167.48 class_Power_Opower(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 167.45/167.48 class_Groups_Ozero(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Int_Onumber,axiom, % 167.45/167.48 class_Int_Onumber(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Groups_Oone,axiom, % 167.45/167.48 class_Groups_Oone(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 167.45/167.48 class_HOL_Oequal(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Nat__Onat__Nat_Osize,axiom, % 167.45/167.48 class_Nat_Osize(tc_Nat_Onat) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 167.45/167.48 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 167.45/167.48 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 167.45/167.48 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 167.45/167.48 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 167.45/167.48 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 167.45/167.48 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 167.45/167.48 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 167.45/167.48 class_Orderings_Opreorder(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 167.45/167.48 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 167.45/167.48 class_Lattices_Olattice(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 167.45/167.48 class_Orderings_Oorder(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 167.45/167.48 class_Orderings_Otop(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 167.45/167.48 class_Orderings_Oord(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 167.45/167.48 class_Orderings_Obot(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 167.45/167.48 class_Groups_Ouminus(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 167.45/167.48 class_Groups_Ominus(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 167.45/167.48 class_HOL_Oequal(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 167.45/167.48 class_Enum_Oenum(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_HOL__Obool__Nat_Osize,axiom, % 167.45/167.48 class_Nat_Osize(tc_HOL_Obool) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 167.45/167.48 class_HOL_Oequal(tc_Com_Ostate) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Com__Ostate__Nat_Osize,axiom, % 167.45/167.48 class_Nat_Osize(tc_Com_Ostate) ). % 167.45/167.48 % 167.45/167.48 fof(arity_List__Olist__HOL_Oequal,axiom, % 167.45/167.48 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 167.45/167.48 % 167.45/167.48 fof(arity_List__Olist__Nat_Osize,axiom, % 167.45/167.48 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 167.45/167.48 % 167.45/167.48 fof(arity_sum__Finite__Set_Ofinite,axiom, % 167.45/167.48 ! [T_1,T_2] : % 167.45/167.48 ( ( class_Finite__Set_Ofinite(T_2) % 167.45/167.48 & class_Finite__Set_Ofinite(T_1) ) % 167.45/167.48 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_sum__HOL_Oequal,axiom, % 167.45/167.48 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 167.45/167.48 % 167.45/167.48 fof(arity_sum__Enum_Oenum,axiom, % 167.45/167.48 ! [T_1,T_2] : % 167.45/167.48 ( ( class_Enum_Oenum(T_2) % 167.45/167.48 & class_Enum_Oenum(T_1) ) % 167.45/167.48 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_sum__Nat_Osize,axiom, % 167.45/167.48 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 167.45/167.48 ! [T_1] : % 167.45/167.48 ( class_Finite__Set_Ofinite(T_1) % 167.45/167.48 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 167.45/167.48 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 167.45/167.48 ! [T_1] : % 167.45/167.48 ( class_Enum_Oenum(T_1) % 167.45/167.48 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Option__Ooption__Nat_Osize,axiom, % 167.45/167.48 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 167.45/167.48 % 167.45/167.48 fof(arity_prod__Finite__Set_Ofinite,axiom, % 167.45/167.48 ! [T_1,T_2] : % 167.45/167.48 ( ( class_Finite__Set_Ofinite(T_2) % 167.45/167.48 & class_Finite__Set_Ofinite(T_1) ) % 167.45/167.48 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_prod__Smallcheck_Osmall,axiom, % 167.45/167.48 ! [T_1,T_2] : % 167.45/167.48 ( ( class_Smallcheck_Osmall(T_2) % 167.45/167.48 & class_Smallcheck_Osmall(T_1) ) % 167.45/167.48 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_prod__HOL_Oequal,axiom, % 167.45/167.48 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 167.45/167.48 % 167.45/167.48 fof(arity_prod__Enum_Oenum,axiom, % 167.45/167.48 ! [T_1,T_2] : % 167.45/167.48 ( ( class_Enum_Oenum(T_2) % 167.45/167.48 & class_Enum_Oenum(T_1) ) % 167.45/167.48 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 167.45/167.48 % 167.45/167.48 fof(arity_prod__Nat_Osize,axiom, % 167.45/167.48 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 167.45/167.48 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 167.45/167.48 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 167.45/167.48 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 167.45/167.48 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 167.45/167.48 class_Nat_Osize(tc_Product__Type_Ounit) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 167.45/167.48 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 167.45/167.48 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 167.45/167.48 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 167.45/167.48 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 167.45/167.48 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 167.45/167.48 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 167.45/167.48 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 167.45/167.48 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 167.45/167.48 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 167.45/167.48 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 167.45/167.48 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 167.45/167.48 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 167.45/167.48 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 167.45/167.48 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 167.45/167.48 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 167.45/167.48 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 167.45/167.48 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 167.45/167.48 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 167.45/167.48 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 167.45/167.48 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 167.45/167.48 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 167.45/167.48 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 167.45/167.48 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 167.45/167.48 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 167.45/167.48 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 167.45/167.48 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 167.45/167.48 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 167.45/167.48 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 167.45/167.48 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 167.45/167.48 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 167.45/167.48 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 167.45/167.48 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 167.45/167.48 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 167.45/167.48 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 167.45/167.48 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 167.45/167.48 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 167.45/167.48 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 167.45/167.48 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 167.45/167.48 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 167.45/167.48 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 167.45/167.48 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 167.45/167.48 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 167.45/167.48 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 167.45/167.48 % 167.45/167.48 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 167.45/167.48 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 167.45/167.48 % 167.45/167.48 %----Helper facts (20) % 167.45/167.48 fof(help_c__COMBI__1,axiom, % 167.45/167.48 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 167.45/167.48 % 167.45/167.48 fof(help_c__COMBK__1,axiom, % 167.45/167.48 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 167.45/167.48 % 167.45/167.48 fof(help_c__COMBB__1,axiom, % 167.45/167.48 ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__COMBC__1,axiom, % 167.45/167.48 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__COMBS__1,axiom, % 167.45/167.48 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fequal__1,axiom, % 167.45/167.48 ! [V_y_2,V_x_2] : % 167.45/167.48 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 167.45/167.48 | V_x_2 = V_y_2 ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fequal__2,axiom, % 167.45/167.48 ! [V_y_2,V_x_2] : % 167.45/167.48 ( V_x_2 != V_y_2 % 167.45/167.48 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fFalse__1,axiom, % 167.45/167.48 ~ hBOOL(c_fFalse) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fTrue__1,axiom, % 167.45/167.48 hBOOL(c_fTrue) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fNot__1,axiom, % 167.45/167.48 ! [V_P_2] : % 167.45/167.48 ( ~ hBOOL(hAPP(c_fNot,V_P_2)) % 167.45/167.48 | ~ hBOOL(V_P_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fNot__2,axiom, % 167.45/167.48 ! [V_P_2] : % 167.45/167.48 ( ~ ~ hBOOL(V_P_2) % 167.45/167.48 | hBOOL(hAPP(c_fNot,V_P_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fconj__1,axiom, % 167.45/167.48 ! [V_Q_2,V_P_2] : % 167.45/167.48 ( ~ hBOOL(V_P_2) % 167.45/167.48 | ~ hBOOL(V_Q_2) % 167.45/167.48 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fconj__2,axiom, % 167.45/167.48 ! [V_Q_2,V_P_2] : % 167.45/167.48 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 167.45/167.48 | hBOOL(V_P_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fconj__3,axiom, % 167.45/167.48 ! [V_Q_2,V_P_2] : % 167.45/167.48 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 167.45/167.48 | hBOOL(V_Q_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fdisj__1,axiom, % 167.45/167.48 ! [V_Q_2,V_P_2] : % 167.45/167.48 ( ~ hBOOL(V_P_2) % 167.45/167.48 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fdisj__2,axiom, % 167.45/167.48 ! [V_P_2,V_Q_2] : % 167.45/167.48 ( ~ hBOOL(V_Q_2) % 167.45/167.48 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fdisj__3,axiom, % 167.45/167.48 ! [V_Q_2,V_P_2] : % 167.45/167.48 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) % 167.45/167.48 | hBOOL(V_P_2) % 167.45/167.48 | hBOOL(V_Q_2) ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fimplies__1,axiom, % 167.45/167.48 ! [V_Q_2,V_P_2] : % 167.45/167.48 ( hBOOL(V_P_2) % 167.45/167.48 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fimplies__2,axiom, % 167.45/167.48 ! [V_P_2,V_Q_2] : % 167.45/167.48 ( ~ hBOOL(V_Q_2) % 167.45/167.48 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 167.45/167.48 % 167.45/167.48 fof(help_c__fimplies__3,axiom, % 167.45/167.48 ! [V_Q_2,V_P_2] : % 167.45/167.48 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) % 167.45/167.48 | ~ hBOOL(V_P_2) % 167.45/167.48 | hBOOL(V_Q_2) ) ). % 167.45/167.48 % 167.45/167.48 %----Conjectures (3) % 167.45/167.48 fof(conj_0,hypothesis, % 167.45/167.48 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody)))),v_Procs)) ). % 167.45/167.48 % 167.45/167.48 fof(conj_1,hypothesis, % 167.45/167.48 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_Procs)) ). % 167.45/167.48 % 167.45/167.48 fof(conj_2,conjecture, % 167.45/167.48 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)) ). % 167.45/167.48 % 167.45/167.48 %------------------------------------------------------------------------------ % 167.45/167.48 %------------------------------------------- % 167.45/167.48 % Proof found % 167.45/167.48 % SZS status Theorem for theBenchmark % 167.45/167.48 % SZS output start Proof % 167.75/167.49 %ClaNum:10201(EqnAxiom:2865) % 167.75/167.49 %VarNum:70205(SingletonVarNum:20470) % 167.75/167.49 %MaxLitNum:8 % 167.75/167.49 %MaxfuncDepth:15 % 167.75/167.49 %SharedTerms:1112 % 167.75/167.49 %goalClause: 4557 % 167.75/167.49 %singleGoalClaCount:1 % 167.75/167.49 [2869]P1(a191) % 167.75/167.49 [2870]P2(a867) % 167.75/167.49 [2871]P2(a872) % 167.75/167.49 [2872]P2(a1) % 167.75/167.49 [2873]P3(a867) % 167.75/167.49 [2874]P3(a875) % 167.75/167.49 [2875]P99(a867) % 167.75/167.49 [2876]P99(a872) % 167.75/167.49 [2877]P99(a1) % 167.75/167.49 [2878]P64(a867) % 167.75/167.49 [2879]P97(a867) % 167.75/167.49 [2880]P101(a867) % 167.75/167.49 [2881]P101(a872) % 167.75/167.49 [2882]P104(a867) % 167.75/167.49 [2883]P65(a867) % 167.75/167.49 [2884]P65(a872) % 167.75/167.49 [2885]P65(a1) % 167.75/167.49 [2886]P65(a103) % 167.75/167.49 [2887]P109(a1) % 167.75/167.49 [2888]P66(a1) % 167.75/167.49 [2889]P100(a867) % 167.75/167.49 [2890]P100(a872) % 167.75/167.49 [2891]P100(a1) % 167.75/167.49 [2892]P67(a872) % 167.75/167.49 [2893]P67(a1) % 167.75/167.49 [2894]P67(a103) % 167.75/167.49 [2895]P98(a867) % 167.75/167.49 [2896]P98(a872) % 167.75/167.49 [2897]P98(a1) % 167.75/167.49 [2898]P4(a867) % 167.75/167.49 [2899]P105(a872) % 167.75/167.49 [2900]P105(a1) % 167.75/167.49 [2901]P105(a103) % 167.75/167.49 [2902]P106(a867) % 167.75/167.49 [2903]P106(a872) % 167.75/167.49 [2904]P106(a1) % 167.75/167.49 [2905]P106(a103) % 167.75/167.49 [2906]P107(a867) % 167.75/167.49 [2907]P107(a872) % 167.75/167.49 [2908]P107(a1) % 167.75/167.49 [2909]P107(a103) % 167.75/167.49 [2910]P108(a867) % 167.75/167.49 [2911]P108(a872) % 167.75/167.49 [2912]P108(a1) % 167.75/167.49 [2913]P108(a103) % 167.75/167.49 [2914]P77(a1) % 167.75/167.49 [2915]P73(a872) % 167.75/167.49 [2916]P73(a1) % 167.75/167.49 [2917]P73(a103) % 167.75/167.49 [2918]P81(a872) % 167.75/167.49 [2919]P81(a1) % 167.75/167.49 [2920]P81(a103) % 167.75/167.49 [2921]P68(a872) % 167.75/167.49 [2922]P68(a1) % 167.75/167.49 [2923]P68(a103) % 167.75/167.49 [2924]P69(a872) % 167.75/167.49 [2925]P69(a1) % 167.75/167.49 [2926]P69(a103) % 167.75/167.49 [2927]P70(a872) % 167.75/167.49 [2928]P70(a1) % 167.75/167.49 [2929]P70(a103) % 167.75/167.49 [2930]P71(a872) % 167.75/167.49 [2931]P71(a1) % 167.75/167.49 [2932]P71(a103) % 167.75/167.49 [2933]P82(a872) % 167.75/167.49 [2934]P82(a1) % 167.75/167.49 [2935]P82(a103) % 167.75/167.49 [2936]P74(a1) % 167.75/167.49 [2937]P78(a872) % 167.75/167.49 [2938]P78(a1) % 167.75/167.49 [2939]P78(a103) % 167.75/167.49 [2940]P135(a872) % 167.75/167.49 [2941]P135(a1) % 167.75/167.49 [2942]P135(a103) % 167.75/167.49 [2943]P80(a872) % 167.75/167.49 [2944]P80(a1) % 167.75/167.49 [2945]P80(a103) % 167.75/167.49 [2946]P110(a1) % 167.75/167.49 [2947]P111(a872) % 167.75/167.49 [2948]P111(a1) % 167.75/167.49 [2949]P111(a103) % 167.75/167.49 [2950]P116(a872) % 167.75/167.49 [2951]P116(a1) % 167.75/167.49 [2952]P116(a103) % 167.75/167.49 [2953]P117(a1) % 167.75/167.49 [2954]P140(a872) % 167.75/167.49 [2955]P140(a1) % 167.75/167.49 [2956]P136(a872) % 167.75/167.49 [2957]P136(a1) % 167.75/167.49 [2958]P136(a103) % 167.75/167.49 [2959]P112(a872) % 167.75/167.49 [2960]P112(a1) % 167.75/167.49 [2961]P112(a103) % 167.75/167.49 [2962]P85(a872) % 167.75/167.49 [2963]P85(a1) % 167.75/167.49 [2964]P85(a103) % 167.75/167.49 [2965]P79(a872) % 167.75/167.49 [2966]P79(a1) % 167.75/167.49 [2967]P79(a103) % 167.75/167.49 [2968]P75(a1) % 167.75/167.49 [2969]P125(a872) % 167.75/167.49 [2970]P125(a1) % 167.75/167.49 [2971]P125(a103) % 167.75/167.49 [2972]P137(a1) % 167.75/167.49 [2973]P126(a872) % 167.75/167.49 [2974]P126(a1) % 167.75/167.49 [2975]P126(a103) % 167.75/167.49 [2976]P141(a872) % 167.75/167.49 [2977]P141(a1) % 167.75/167.49 [2978]P141(a103) % 167.75/167.49 [2979]P86(a872) % 167.75/167.49 [2980]P86(a1) % 167.75/167.49 [2981]P86(a103) % 167.75/167.49 [2982]P123(a1) % 167.75/167.49 [2983]P118(a872) % 167.75/167.49 [2984]P118(a1) % 167.75/167.49 [2985]P118(a103) % 167.75/167.49 [2986]P127(a872) % 167.75/167.49 [2987]P127(a1) % 167.75/167.49 [2988]P127(a103) % 167.75/167.49 [2989]P124(a1) % 167.75/167.49 [2990]P138(a1) % 167.75/167.49 [2991]P90(a1) % 167.75/167.49 [2992]P83(a872) % 167.75/167.49 [2993]P83(a1) % 167.75/167.49 [2994]P83(a103) % 167.75/167.49 [2995]P131(a872) % 167.75/167.49 [2996]P131(a1) % 167.75/167.49 [2997]P131(a103) % 167.75/167.49 [2998]P133(a872) % 167.75/167.49 [2999]P133(a1) % 167.75/167.49 [3000]P133(a103) % 167.75/167.49 [3001]P132(a872) % 167.75/167.49 [3002]P132(a1) % 167.75/167.49 [3003]P132(a103) % 167.75/167.49 [3004]P128(a872) % 167.75/167.49 [3005]P128(a1) % 167.75/167.49 [3006]P128(a103) % 167.75/167.49 [3007]P129(a1) % 167.75/167.49 [3008]P130(a1) % 167.75/167.49 [3009]P102(a872) % 167.75/167.49 [3010]P102(a1) % 167.75/167.49 [3011]P102(a103) % 167.75/167.49 [3012]P142(a872) % 167.75/167.49 [3013]P142(a1) % 167.75/167.49 [3014]P142(a103) % 167.75/167.49 [3015]P139(a1) % 167.75/167.49 [3016]P113(a872) % 167.75/167.49 [3017]P113(a1) % 167.75/167.49 [3018]P113(a103) % 167.75/167.49 [3019]P57(a872) % 167.75/167.49 [3020]P57(a1) % 167.75/167.49 [3021]P57(a103) % 167.75/167.49 [3022]P84(a1) % 167.75/167.49 [3023]P58(a1) % 167.75/167.49 [3024]P134(a1) % 167.75/167.49 [3025]P94(a867) % 167.75/167.49 [3026]P87(a867) % 167.75/167.49 [3027]P87(a1) % 167.75/167.49 [3028]P119(a1) % 167.75/167.49 [3029]P115(a1) % 167.75/167.49 [3030]P72(a1) % 167.75/167.49 [3031]P76(a872) % 167.75/167.49 [3032]P76(a1) % 167.75/167.49 [3033]P76(a103) % 167.75/167.49 [3034]P88(a1) % 167.75/167.49 [3035]P91(a1) % 167.75/167.49 [3036]P92(a872) % 167.75/167.49 [3037]P92(a1) % 167.75/167.49 [3038]P92(a103) % 167.75/167.49 [3039]P114(a872) % 167.75/167.49 [3040]P89(a872) % 167.75/167.49 [3041]P89(a1) % 167.75/167.49 [3042]P89(a103) % 167.75/167.49 [3043]P143(a875) % 167.75/167.49 [3044]P143(a1) % 167.75/167.49 [3045]P59(a867) % 167.75/167.49 [3046]P59(a875) % 167.75/167.49 [3047]P93(a867) % 167.75/167.49 [3048]P93(a868) % 167.75/167.49 [3049]P93(a869) % 167.75/167.49 [3050]P93(a872) % 167.75/167.49 [3051]P93(a875) % 167.75/167.49 [3052]P93(a1) % 167.75/167.49 [3053]P93(a103) % 167.75/167.49 [3054]P93(a324) % 167.75/167.49 [3055]P103(a867) % 167.75/167.49 [3056]P103(a868) % 167.75/167.49 [3057]P103(a869) % 167.75/167.49 [3058]P103(a872) % 167.75/167.49 [3059]P103(a875) % 167.75/167.49 [3060]P103(a103) % 167.75/167.49 [3061]P103(a324) % 167.75/167.49 [3062]P96(a867) % 167.75/167.49 [3082]P38(a872,a247) % 167.75/167.49 [3083]P38(a872,a318) % 167.75/167.49 [4450]~E(a101,a83) % 167.75/167.49 [4451]~P1(a246) % 167.75/167.49 [2866]E(f2(a1),a83) % 167.75/167.49 [2867]E(f104(a103),a3) % 167.75/167.49 [2868]E(f22(a103),a23) % 167.75/167.49 [3063]E(f192(a872),f2(a872)) % 167.75/167.49 [3064]E(f31(a24),f2(a872)) % 167.75/167.49 [3065]E(f105(a872),f240(a872)) % 167.75/167.49 [3066]E(f114(a872),f241(a872)) % 167.75/167.49 [3067]E(f106(a1),f34(a1)) % 167.75/167.49 [3068]E(f84(a246),f2(a872)) % 167.75/167.49 [3069]E(f84(a191),f2(a872)) % 167.75/167.49 [3070]P5(f78(a1)) % 167.75/167.49 [3071]P5(f2(a1)) % 167.75/167.49 [3120]P1(f328(a25,a24)) % 167.75/167.49 [3133]P38(f878(a872,a872),a35) % 167.75/167.49 [3486]E(f321(a872,a872,a247,a247),a35) % 167.75/167.49 [4452]~E(f78(a1),f2(a1)) % 167.75/167.49 [3072]E(f4(f2(a103)),f2(a872)) % 167.75/167.49 [3073]E(f115(f2(a872)),f2(a872)) % 167.75/167.49 [3085]E(f328(f79(a1),a83),a83) % 167.75/167.49 [3088]E(f328(a116,f2(a872)),f78(a872)) % 167.75/167.49 [3089]E(f328(a108,f78(a1)),f78(a872)) % 167.75/167.49 [3090]E(f328(a3,f78(a872)),f78(a103)) % 167.75/167.49 [3092]E(f328(a3,f2(a872)),f2(a103)) % 167.75/167.49 [3094]E(f328(f107(a1),a83),f2(a1)) % 167.75/167.49 [3095]E(f328(f107(a103),a83),f2(a103)) % 167.75/167.49 [3096]E(f328(a108,f2(a1)),f2(a872)) % 167.75/167.49 [3097]E(f328(f193(a867),a246),f2(a872)) % 167.75/167.49 [3098]E(f328(f193(a867),a191),f2(a872)) % 167.75/167.49 [3099]E(f328(f193(a869),a24),f2(a872)) % 167.75/167.49 [3100]E(f328(f107(a872),a83),f2(a872)) % 167.75/167.49 [3104]E(f328(f79(a1),f78(a1)),a101) % 167.75/167.49 [3112]E(f328(f193(a103),f2(a103)),f2(a872)) % 167.75/167.49 [3113]E(f328(f104(a1),f78(a872)),f78(a1)) % 167.75/167.49 [3114]E(f328(f104(a1),f2(a872)),f2(a1)) % 167.75/167.49 [3115]E(f328(f79(a1),f2(a1)),f2(a1)) % 167.75/167.49 [3129]E(f328(a108,f78(a1)),f328(a116,f2(a872))) % 167.75/167.49 [3130]E(f328(f176(a870,a869),a27),a28) % 167.75/167.49 [3131]E(f319(f878(a872,a872),a35),a36) % 167.75/167.49 [3132]E(f320(f878(a872,a872),a35),a37) % 167.75/167.49 [3134]P1(f328(f38(a870),a880)) % 167.75/167.49 [3155]E(f328(f249(a872),f2(a872)),f192(f879(a872,a867))) % 167.75/167.49 [3156]E(f328(f250(a872),f2(a872)),f251(f879(a872,a867))) % 167.75/167.49 [3164]P39(f192(f879(a1,a867))) % 167.75/167.49 [3200]E(f328(f328(f22(a103),f2(a103)),f78(a103)),f2(a103)) % 167.75/167.49 [3277]P1(f328(f328(f243(a1),a101),f2(a1))) % 167.75/167.49 [3302]P1(f328(f328(f243(a1),f2(a1)),f78(a1))) % 167.75/167.49 [3303]P1(f328(f328(f242(a1),f2(a1)),f78(a1))) % 167.75/167.49 [3478]P1(f328(f38(a870),f182(a870,a869,a28))) % 167.75/167.49 [3516]E(f328(f328(f285(a872,a872,a872),a318),f304(a872,a318)),a247) % 167.75/167.49 [3554]P41(a1,a872,a108,f328(f242(a1),f2(a1))) % 167.75/167.49 [3558]E(f328(f328(f43(a872,f879(a872,a867)),f251(f879(a872,a867))),f300(a872)),f192(f879(a872,a867))) % 167.75/167.49 [3559]E(f328(f328(f44(a872,f879(a872,a867)),f251(f879(a872,a867))),f249(a872)),f251(f879(a872,a867))) % 167.75/167.49 [3560]E(f328(f328(f44(a872,f879(a872,a867)),f251(f879(a872,a867))),f250(a872)),f251(f879(a872,a867))) % 167.75/167.49 [3561]E(f328(f328(f44(a872,f879(a872,a867)),f251(f879(a872,a867))),f297(a872)),f251(f879(a872,a867))) % 167.75/167.49 [3577]P26(a872,a1,f104(a1),f251(f879(a872,a867))) % 167.75/167.49 [3590]P41(a872,a1,f104(a1),f328(f16(a867,a872),a191)) % 167.75/167.49 [3725]E(f328(f73(a872,a103,a1,a3),a108),f107(a103)) % 167.75/167.49 [3950]P53(a103,a872,a19,a3,f251(f879(a872,a867))) % 167.75/167.49 [3959]P53(a1,f879(f878(a872,a872),a867),a110,a89,a102) % 167.75/167.49 [4224]E(f268(a1,a1,a1,a1,f34(a1),f79(a1)),a52) % 167.75/167.49 [4475]~E(f328(f107(a1),a101),f328(f107(a1),a83)) % 167.75/167.49 [4476]~P1(f328(a197,f78(a1))) % 167.75/167.49 [4477]~P1(f328(a197,f2(a1))) % 167.75/167.49 [4518]~P1(f328(f328(f243(a1),a83),f2(a1))) % 167.75/167.49 [3147]E(f328(f328(f22(a1),a101),a101),a83) % 167.75/167.49 [3162]E(f328(f104(a1),f328(a116,f2(a872))),f78(a1)) % 167.75/167.49 [3228]E(f328(f39(a875),f251(f879(a875,a867))),f78(a872)) % 167.75/167.49 [3249]P1(f328(a197,f328(f107(a1),a101))) % 167.75/167.49 [3250]P1(f328(f328(f243(a1),a101),a83)) % 167.75/167.49 [3252]P1(f328(f328(f242(a1),a101),a83)) % 167.75/167.49 [3313]E(f328(f328(f306(a872),f2(a872)),f192(f879(a872,a867))),f328(f297(a872),f2(a872))) % 167.75/167.49 [3370]P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),a83))) % 167.75/167.49 [3382]E(f328(f307(a872,a872,a116),f251(f879(a872,a867))),f328(f300(a872),f2(a872))) % 167.75/167.49 [3422]P7(f878(a872,a872),f251(f879(f878(a872,a872),a867)),a112) % 167.75/167.49 [3733]E(f328(f73(a872,a1,a103,f104(a1)),a19),a20) % 167.75/167.49 [3793]P38(a872,f328(f248(f878(a872,a872)),f328(f267(a872,a872,a867),f243(a872)))) % 167.75/167.49 [4507]~P1(f328(a197,f328(f107(a1),a83))) % 167.75/167.49 [4508]~P1(f328(f328(f243(a1),a83),a83)) % 167.75/167.49 [4509]~P1(f328(f328(f243(a1),a83),a101)) % 167.75/167.49 [4510]~P1(f328(f328(f243(a1),a101),a101)) % 167.75/167.49 [4511]~P1(f328(f328(f242(a1),a83),a101)) % 167.75/167.49 [4512]~P1(f328(f328(f91(a1),a83),a101)) % 167.75/167.49 [4513]~P1(f328(f328(f91(a1),a101),a83)) % 167.75/167.49 [4524]~P1(f328(f38(a872),f251(f879(a872,a867)))) % 167.75/167.49 [4525]~P1(f328(f38(a1),f251(f879(a1,a867)))) % 167.75/167.49 [4395]E(f328(f267(a1,a1,a867),f328(f328(f8(f879(a1,a867),f879(a1,a867),a1),f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f243(a1),f2(a1))))),f328(f328(f7(a1,a1,f879(a1,a867)),f328(f328(f8(f879(a1,f879(a1,a867)),f879(a1,f879(a1,a867)),a1),f7(a1,a1,a867)),f328(f328(f8(f879(a1,a1),f879(a1,f879(a1,a867)),a1),f328(f8(a1,f879(a1,a867),a1),a325)),a224))),f78(a1)))),a220) % 167.75/167.49 [3460]E(f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101),f328(f79(a1),a101)) % 167.75/167.49 [3499]E(f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101),f328(f328(f22(a1),a83),a101)) % 167.75/167.49 [3659]E(f328(f328(f62(f878(a872,a872)),f251(f879(f878(a872,a872),a867))),a112),a102) % 167.75/167.49 [3688]E(f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f78(a1)) % 167.75/167.49 [3689]E(f328(f107(a103),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f78(a103)) % 167.75/167.49 [3690]E(f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f78(a872)) % 167.75/167.49 [3694]E(f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(a116,f2(a872))) % 167.75/167.49 [4084]E(f328(f328(f114(f879(f878(f878(a872,a872),f878(a872,a872)),a867)),a35),f304(f878(a872,a872),f192(f879(f878(f878(a872,a872),f878(a872,a872)),a867)))),a70) % 167.75/167.49 [4155]E(f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),f78(a872)),f2(a872))),f192(f879(f878(a872,a872),a867))))),f78(a1)) % 167.75/167.49 [4156]E(f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),f2(a872)),f2(a872))),f192(f879(f878(a872,a872),a867))))),f2(a1)) % 167.75/167.49 [4171]E(f328(f248(f878(a872,a872)),f328(f267(a872,a872,a867),f328(f328(f8(a872,f879(a872,a867),a872),f328(f7(a872,a872,a867),a325)),a116))),a318) % 167.75/167.49 [4141]E(f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),f328(a116,f328(a116,f2(a872)))) % 167.75/167.49 [4144]E(f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),f328(f328(f80(a872),f78(a872)),f78(a872))) % 167.75/167.49 [4145]E(f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),f328(f39(a867),f251(f879(a867,a867)))) % 167.75/167.49 [4210]P5(f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))) % 167.75/167.49 [4282]P27(f879(f878(a872,a872),a867),f328(f328(f263(f879(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),a867),f879(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),a867)),a36),a71)) % 167.75/167.49 [4283]P27(f879(f878(a872,a872),a867),f328(f328(f263(f879(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),a867),f879(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),a867)),a37),a69)) % 167.75/167.49 [4323]E(f328(f328(f114(f879(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),a867)),f320(f878(a872,a872),a70)),f328(f328(f306(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),f192(f879(f878(a872,a872),a867))),f192(f879(f878(a872,a872),a867)))),f192(f879(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),a867)))),a69) % 167.75/167.49 [4324]E(f328(f328(f114(f879(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),a867)),f319(f878(a872,a872),a70)),f328(f328(f306(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),f192(f879(f878(a872,a872),a867))),f192(f879(f878(a872,a872),a867)))),f192(f879(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),a867)))),a71) % 167.75/167.49 [4212]E(f328(a108,f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(a116,f328(a116,f2(a872)))) % 167.75/167.49 [4259]E(f328(f104(a1),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))) % 167.75/167.49 [4294]P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.75/167.49 [4557]~P25(a868,a881,f328(f307(a870,f871(a868),f328(f328(f18(a870,f879(a868,f879(a868,a867)),f871(a868)),f328(f328(f8(a869,f879(f879(a868,f879(a868,a867)),f871(a868)),a870),f328(f92(a868),a325)),a26)),f328(f328(f8(a869,f879(a868,f879(a868,a867)),a870),a198),a26))),a880)) % 167.75/167.49 [4295]E(f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101)),f328(a116,f328(a116,f328(a116,f2(a872))))) % 167.75/167.49 [4337]P5(f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))) % 167.75/167.49 [4416]P25(a868,f328(f328(f114(f879(f871(a868),a867)),a881),f328(f307(a870,f871(a868),f328(f328(f18(a870,f879(a868,f879(a868,a867)),f871(a868)),f328(f328(f8(a869,f879(f879(a868,f879(a868,a867)),f871(a868)),a870),f328(f92(a868),a325)),a26)),f328(f328(f8(a869,f879(a868,f879(a868,a867)),a870),a198),a26))),a880)),f328(f307(a870,f871(a868),f328(f328(f18(a870,f879(a868,f879(a868,a867)),f871(a868)),f328(f328(f8(a869,f879(f879(a868,f879(a868,a867)),f871(a868)),a870),f328(f92(a868),a325)),f328(f328(f8(f876(a869),a869,a870),f239(a869)),a28))),f328(f328(f8(a869,f879(a868,f879(a868,a867)),a870),a198),f328(f328(f8(f876(a869),a869,a870),f239(a869)),a28)))),a880)) % 167.75/167.49 [4365]E(f328(f104(a1),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))) % 167.75/167.49 [4380]P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101)))) % 167.75/167.49 [3084]P6(x30841,a325) % 167.75/167.49 [3487]P26(a872,a872,a116,x34871) % 167.75/167.49 [3074]P93(f871(x30741)) % 167.75/167.49 [3075]P93(f876(x30751)) % 167.75/167.49 [3076]P93(f873(x30761)) % 167.75/167.49 [3077]P93(f874(x30771)) % 167.75/167.49 [3078]P103(f871(x30781)) % 167.75/167.49 [3079]P103(f876(x30791)) % 167.75/167.49 [3080]P103(f873(x30801)) % 167.75/167.49 [3081]P103(f874(x30811)) % 167.75/167.49 [3101]P38(a1,f109(x31011)) % 167.75/167.49 [3102]P38(a1,f111(x31021)) % 167.75/167.49 [3152]P38(f879(x31521,a867),f303(x31521)) % 167.75/167.49 [3176]E(f252(x31761,x31761,a325),a325) % 167.75/167.49 [3191]E(f46(a1,x31911,x31911),f2(a1)) % 167.75/167.49 [3246]P16(x32461,f879(x32461,a867),f306(x32461)) % 167.75/167.49 [4454]~E(f328(a26,x44541),a24) % 167.75/167.49 [4456]~E(f328(a116,x44561),x44561) % 167.75/167.49 [4466]~E(f328(a116,x44661),f2(a872)) % 167.75/167.49 [3086]E(f328(f193(a872),x30861),x30861) % 167.75/167.49 [3087]E(f328(f107(a1),x30871),x30871) % 167.75/167.49 [3103]E(f328(a89,f329(x31031)),x31031) % 167.75/167.49 [3116]E(f118(x31161,f117(x31161)),f117(x31161)) % 167.75/167.49 [3117]E(f149(x31171,f117(x31171)),f117(x31171)) % 167.75/167.49 [3121]E(f31(f328(a26,x31211)),f2(a872)) % 167.75/167.49 [3126]E(f328(f165(x31261),f117(x31261)),f117(x31261)) % 167.75/167.49 [3127]E(f328(f169(x31271),f117(x31271)),f117(x31271)) % 167.75/167.49 [3128]E(f328(f166(x31281),f117(x31281)),f117(x31281)) % 167.75/167.49 [3135]E(f328(f107(a1),x31351),f328(f106(a1),x31351)) % 167.75/167.49 [3136]E(f328(a89,f328(a110,x31361)),x31361) % 167.75/167.49 [3138]E(f328(a3,f328(a19,x31381)),x31381) % 167.75/167.49 [3139]E(f328(a19,f328(a3,x31391)),x31391) % 167.75/167.49 [3140]P5(f328(f104(a1),x31401)) % 167.75/167.49 [3145]E(f328(f193(f876(x31451)),f205(x31451)),f2(a872)) % 167.75/167.49 [3146]E(f328(f193(f873(x31461)),f117(x31461)),f2(a872)) % 167.75/167.49 [3151]E(f328(f193(a869),f328(a26,x31511)),f2(a872)) % 167.75/167.49 [3160]E(f234(x31601,f205(x31601)),f192(f879(x31601,a867))) % 167.75/167.49 [3167]E(f328(f328(f22(a872),x31671),f2(a872)),x31671) % 167.75/167.49 [3168]E(f328(f328(f80(a872),x31681),f2(a872)),x31681) % 167.75/167.49 [3169]E(f328(f328(f80(a1),x31691),f2(a1)),x31691) % 167.75/167.49 [3170]E(f328(f328(f81(a872),x31701),f78(a872)),x31701) % 167.75/167.49 [3171]E(f328(f328(f81(a1),x31711),f78(a1)),x31711) % 167.75/167.49 [3172]E(f328(f328(f241(a872),x31721),f2(a872)),x31721) % 167.75/167.49 [3173]E(f328(f328(f81(a872),x31731),f2(a872)),f2(a872)) % 167.75/167.49 [3174]E(f328(f328(f40(a1),x31741),f2(a1)),f2(a1)) % 167.75/167.49 [3175]E(f328(f328(f240(a872),x31751),f2(a872)),f2(a872)) % 167.75/167.49 [3182]E(f328(f170(x31821),f117(x31821)),f192(f879(x31821,a867))) % 167.75/167.49 [3186]P1(f328(f134(x31861),f117(x31861))) % 167.75/167.49 [3192]E(f328(f151(x31921,x31921),f5(x31921)),f34(f873(x31921))) % 167.75/167.49 [3193]E(f328(f151(x31931,x31931),f34(x31931)),f34(f873(x31931))) % 167.75/167.49 [3194]E(f328(f206(x31941,x31941),f5(x31941)),f34(f876(x31941))) % 167.75/167.49 [3195]E(f328(f206(x31951,x31951),f34(x31951)),f34(f876(x31951))) % 167.75/167.49 [3196]E(f46(a1,x31961,f2(a1)),x31961) % 167.75/167.49 [3197]E(f328(f242(a872),f328(a116,x31971)),f328(f243(a872),x31971)) % 167.75/167.49 [3198]E(f328(f249(a872),f328(a116,x31981)),f328(f297(a872),x31981)) % 167.75/167.49 [3199]E(f328(f250(a872),f328(a116,x31991)),f328(f300(a872),x31991)) % 167.75/167.49 [3201]E(f46(a1,f2(a1),x32011),f2(a1)) % 167.75/167.49 [3212]E(f328(f328(f80(a872),x32121),f78(a872)),f328(a116,x32121)) % 167.75/167.49 [3222]E(f328(f298(a872,x32221),f2(a872)),f192(f879(a872,a867))) % 167.75/167.49 [3234]E(f299(a872,f2(a872),x32341),f328(f297(a872),x32341)) % 167.75/167.49 [3280]E(f328(f328(f22(a872),f328(a116,x32801)),f78(a872)),x32801) % 167.75/167.49 [3293]E(f48(f2(a1),x32931),f328(f328(f263(a1,a1),f2(a1)),f2(a1))) % 167.75/167.49 [3342]P1(f328(f328(f243(a872),x33421),f328(a116,x33421))) % 167.75/167.49 [3354]P1(f328(f328(f243(a872),f2(a872)),f328(a116,x33541))) % 167.75/167.49 [3645]E(f328(f328(f22(a103),f328(a3,f328(a116,f328(a19,x36451)))),f78(a103)),x36451) % 167.75/167.49 [3717]P1(f328(f328(f242(a1),f328(f79(a1),f328(f104(a1),x37171))),f2(a1))) % 167.75/167.49 [3866]P1(f328(f328(f243(a1),f328(f79(a1),f328(f104(a1),f328(a116,x38661)))),f2(a1))) % 167.75/167.49 [4482]~E(f251(f879(x44821,a867)),f192(f879(x44821,a867))) % 167.75/167.49 [4521]~P1(f328(f328(f243(a872),x45211),f2(a872))) % 167.75/167.49 [4533]~P1(f328(f328(f243(a1),f328(f104(a1),x45331)),f2(a1))) % 167.75/167.49 [3150]E(f178(x31501,f117(f873(x31501))),f117(f873(x31501))) % 167.75/167.49 [3153]E(f328(f328(f81(a1),a83),x31531),a83) % 167.75/167.49 [3154]E(f328(f328(f80(a1),a83),x31541),x31541) % 167.75/167.49 [3157]E(f328(a108,f328(f104(a1),x31571)),x31571) % 167.75/167.49 [3158]E(f328(f328(f22(a1),x31581),a83),x31581) % 167.75/167.49 [3159]E(f328(f328(f80(a1),x31591),a83),x31591) % 167.75/167.49 [3161]E(f328(f328(f22(a872),x31611),x31611),f2(a872)) % 167.75/167.49 [3165]E(f328(f39(a872),f328(f249(a872),x31651)),x31651) % 167.75/167.49 [3166]E(f328(f79(a1),f328(f79(a1),x31661)),x31661) % 167.75/167.49 [3177]E(f328(f328(f80(a872),f2(a872)),x31771),x31771) % 167.75/167.49 [3178]E(f328(f328(f80(a1),f2(a1)),x31781),x31781) % 167.75/167.49 [3179]E(f328(f328(f81(a872),f78(a872)),x31791),x31791) % 167.75/167.49 [3180]E(f328(f328(f81(a1),f78(a1)),x31801),x31801) % 167.75/167.49 [3181]E(f328(f328(f241(a872),f2(a872)),x31811),x31811) % 167.75/167.49 [3187]E(f328(f328(f22(a872),f2(a872)),x31871),f2(a872)) % 167.75/167.49 [3188]E(f328(f328(f81(a872),f2(a872)),x31881),f2(a872)) % 167.75/167.49 [3189]E(f328(f328(f40(a1),f2(a1)),x31891),f2(a1)) % 167.75/167.49 [3190]E(f328(f328(f240(a872),f2(a872)),x31901),f2(a872)) % 167.75/167.49 [3207]E(f328(f298(a872,f2(a872)),x32071),f328(f249(a872),x32071)) % 167.75/167.49 [3208]E(f328(f328(f81(a1),a101),x32081),f328(f79(a1),x32081)) % 167.75/167.49 [3214]E(f328(a108,f328(f107(a1),x32141)),f328(f107(a872),x32141)) % 167.75/167.49 [3215]E(f328(a19,f328(f107(a103),x32151)),f328(f107(a872),x32151)) % 167.75/167.49 [3216]E(f328(f39(a872),f328(f297(a872),x32161)),f328(a116,x32161)) % 167.75/167.49 [3226]E(f328(f328(f80(a872),f78(a872)),x32261),f328(a116,x32261)) % 167.75/167.49 [3230]E(f328(f75(a1),f328(f104(a1),x32301)),f328(f104(a1),x32301)) % 167.75/167.49 [3231]E(f328(f106(a1),f328(f104(a1),x32311)),f328(f104(a1),x32311)) % 167.75/167.49 [3236]E(f328(f39(x32361),f192(f879(x32361,a867))),f2(a872)) % 167.75/167.49 [3238]E(f328(f328(f40(a872),x32381),f328(a116,f2(a872))),x32381) % 167.75/167.49 [3247]E(f46(a872,x32471,f328(a116,f2(a872))),f2(a872)) % 167.75/167.49 [3248]E(f46(a1,x32481,f328(f107(a1),a101)),f2(a1)) % 167.75/167.49 [3264]E(f328(f328(f40(a1),x32641),f328(f107(a1),a101)),f328(f79(a1),x32641)) % 167.75/167.49 [3268]E(f136(a872,f328(f298(a872,x32681),f2(a872))),f117(a872)) % 167.75/167.49 [3269]E(f328(f328(f80(a1),x32691),f78(a1)),f328(f328(f22(a1),x32691),a101)) % 167.75/167.49 [3270]E(f328(f328(f22(a1),x32701),f78(a1)),f328(f328(f80(a1),x32701),a101)) % 167.75/167.49 [3274]P1(f328(f328(f242(a872),x32741),x32741)) % 167.75/167.49 [3275]P1(f328(f328(f242(a1),x32751),x32751)) % 167.75/167.49 [3276]P1(f328(f328(f91(a1),x32761),x32761)) % 167.75/167.49 [3281]E(f328(f79(a1),f328(f107(a1),x32811)),f328(f107(a1),f328(f79(a1),x32811))) % 167.75/167.49 [3282]P1(f328(f38(a872),f328(f249(a872),x32821))) % 167.75/167.49 [3283]P1(f328(f38(a872),f328(f297(a872),x32831))) % 167.75/167.49 [3291]E(f158(x32911,f251(f879(x32911,a867))),f251(f879(f873(x32911),a867))) % 167.75/167.49 [3296]P1(f328(f328(f242(a872),f2(a872)),x32961)) % 167.75/167.49 [3306]E(f328(f328(f80(a872),f115(x33061)),f328(a116,f2(a872))),f115(f328(a116,x33061))) % 167.75/167.49 [3307]E(f328(f248(x33071),f328(f16(a867,x33071),a246)),f192(f879(x33071,a867))) % 167.75/167.49 [3308]E(f328(f248(x33081),f328(f16(a867,x33081),a191)),f251(f879(x33081,a867))) % 167.75/167.49 [3312]E(f328(f328(f306(a872),x33121),f328(f249(a872),x33121)),f328(f249(a872),f328(a116,x33121))) % 167.75/167.49 [3324]E(f328(f328(f80(a1),f78(a1)),f328(f104(a1),x33241)),f328(f104(a1),f328(a116,x33241))) % 167.75/167.49 [3326]E(f328(f328(f148(f873(x33261)),f117(x33261)),f117(f873(x33261))),f55(x33261,f117(x33261))) % 167.75/167.49 [3345]E(f192(f879(f878(x33451,x33451),a867)),f260(x33451,f192(f879(x33451,a867)))) % 167.75/167.49 [3346]E(f328(f305(x33461),f251(f879(x33461,a867))),f251(f879(f879(x33461,a867),a867))) % 167.75/167.49 [3347]E(f328(f79(f879(x33471,a867)),f192(f879(x33471,a867))),f251(f879(x33471,a867))) % 167.75/167.49 [3348]E(f328(f79(f879(x33481,a867)),f251(f879(x33481,a867))),f192(f879(x33481,a867))) % 167.75/167.49 [3350]P1(f328(f38(x33501),f192(f879(x33501,a867)))) % 167.75/167.49 [3352]E(f328(f298(a872,x33521),f328(a116,x33521)),f328(f328(f306(a872),x33521),f192(f879(a872,a867)))) % 167.75/167.49 [3353]E(f85(f878(a872,a872),f49(x33531,f2(a872))),f328(f328(f263(a872,a872),f2(a872)),x33531)) % 167.75/167.49 [3365]P1(f328(f328(f328(a198,a24),x33651),x33651)) % 167.75/167.49 [3369]E(f328(f328(f306(a872),f328(a116,x33691)),f328(f297(a872),x33691)),f328(f297(a872),f328(a116,x33691))) % 167.75/167.49 [3373]P38(x33731,f192(f879(f878(x33731,x33731),a867))) % 167.75/167.49 [3376]P1(f328(f328(f242(a1),f2(a1)),f328(f104(a1),x33761))) % 167.75/167.49 [3384]E(f328(f328(f80(a872),f328(f193(a872),x33841)),f328(a116,f2(a872))),f328(f193(a872),f328(a116,x33841))) % 167.75/167.49 [3494]P39(f328(f307(a872,a1,f104(a1)),x34941)) % 167.75/167.49 [3532]P40(x35321,f192(f879(x35321,a867)),f192(f879(f878(x35321,x35321),a867))) % 167.75/167.49 [3551]E(f328(f328(f263(a1,a1),f328(f107(a1),a101)),f328(f328(f22(a1),x35511),f78(a1))),f51(f328(f107(a1),a101),x35511)) % 167.75/167.49 [3602]P56(x36021,f328(f16(f879(x36021,a867),x36021),f328(f16(a867,x36021),a246))) % 167.75/167.49 [3805]P1(f328(f328(f330(f879(f878(a872,a872),a867)),f329(x38051)),a102)) % 167.75/167.49 [3830]P1(f328(f328(f330(f879(f878(a872,a872),a867)),f328(a110,x38301)),a102)) % 167.75/167.49 [3968]P26(x39681,f879(x39681,a867),f328(f328(f7(x39681,f879(x39681,a867),f879(x39681,a867)),f306(x39681)),f192(f879(x39681,a867))),f251(f879(x39681,a867))) % 167.75/167.49 [4479]~E(f328(f328(f80(a1),x44791),x44791),a101) % 167.75/167.49 [4506]~E(f328(a3,f328(a116,f328(a19,x45061))),f2(a103)) % 167.75/167.49 [4514]~P1(f328(a197,f328(f104(a1),x45141))) % 167.75/167.49 [4517]~P1(f328(f328(f243(a872),x45171),x45171)) % 167.75/167.49 [4526]~P1(f328(f328(f242(a872),f328(a116,x45261)),x45261)) % 167.75/167.49 [3298]E(f328(a108,f328(f79(a1),f328(f104(a1),x32981))),f2(a872)) % 167.75/167.49 [3301]E(f328(f328(f80(a1),f328(f79(a1),x33011)),x33011),f2(a1)) % 167.75/167.49 [3305]E(f328(f39(a1),f328(f298(a1,f2(a1)),x33051)),f328(a108,x33051)) % 167.75/167.49 [3317]E(f328(f328(f253(a872),f328(a116,f2(a872))),x33171),f328(a116,f2(a872))) % 167.75/167.49 [3419]E(f328(f281(x34191),f192(f879(f878(x34191,x34191),a867))),f192(f879(x34191,a867))) % 167.75/167.49 [3427]E(f42(f879(x34271,a867),f192(f879(f879(x34271,a867),a867))),f251(f879(x34271,a867))) % 167.75/167.49 [3428]E(f42(f879(x34281,a867),f251(f879(f879(x34281,a867),a867))),f192(f879(x34281,a867))) % 167.75/167.49 [3429]E(f41(f879(x34291,a867),f192(f879(f879(x34291,a867),a867))),f192(f879(x34291,a867))) % 167.75/167.49 [3430]E(f41(f879(x34301,a867),f251(f879(f879(x34301,a867),a867))),f251(f879(x34301,a867))) % 167.75/167.49 [3476]E(f328(f328(f306(f873(x34761)),f117(x34761)),f192(f879(f873(x34761),a867))),f158(x34761,f192(f879(x34761,a867)))) % 167.75/167.49 [3477]E(f328(f328(f306(f873(x34771)),f117(x34771)),f192(f879(f873(x34771),a867))),f159(x34771,f117(f879(x34771,a867)))) % 167.75/167.49 [3515]E(f328(f328(f80(a872),f4(x35151)),f328(a116,f2(a872))),f4(f328(a3,f328(a116,f328(a19,x35151))))) % 167.75/167.49 [3543]E(f328(f39(a1),f328(f307(a872,a1,f104(a1)),x35431)),f328(f39(a872),x35431)) % 167.75/167.49 [3546]P1(f328(f328(f242(a872),x35461),f328(f328(f81(a872),x35461),x35461))) % 167.75/167.49 [3581]E(f328(f307(a1,a872,a108),f299(a1,f2(a1),f328(f104(a1),x35811))),f328(f297(a872),x35811)) % 167.75/167.49 [3597]E(f328(f328(f40(a872),f328(a116,f2(a872))),f328(f107(a872),x35971)),f328(a108,f328(f328(f40(a1),f78(a1)),f328(f107(a1),x35971)))) % 167.75/167.49 [3599]E(f328(f170(a872),f136(a872,f328(f298(a872,f2(a872)),f328(a116,x35991)))),f328(f297(a872),x35991)) % 167.75/167.49 [3600]E(f328(f328(f80(a872),f328(f193(a103),x36001)),f328(a116,f2(a872))),f328(f193(a103),f328(a3,f328(a116,f328(a19,x36001))))) % 167.75/167.49 [3619]E(f328(f307(a1,a872,a108),f328(f307(a872,a1,f104(a1)),x36191)),x36191) % 167.75/167.49 [3651]E(f328(f328(f306(a872),f2(a872)),f328(f307(a872,a872,a116),f328(f249(a872),x36511))),f328(f249(a872),f328(a116,x36511))) % 167.75/167.49 [3658]P51(x36581,x36581,f304(x36581,f192(f879(f878(x36581,x36581),a867)))) % 167.75/167.49 [3664]P1(f328(a197,f328(f79(a1),f328(f104(a1),f328(a116,x36641))))) % 167.75/167.49 [3675]E(f328(f328(f22(f879(a872,a867)),f328(f250(a872),x36751)),f328(f328(f306(a872),x36751),f192(f879(a872,a867)))),f328(f250(a872),f328(a116,x36751))) % 167.75/167.49 [3691]E(f328(f328(f80(a1),f328(f328(f22(a1),a83),x36911)),f328(f328(f22(a1),a83),x36911)),f328(f328(f22(a1),a83),f328(f328(f80(a1),x36911),x36911))) % 167.75/167.49 [3707]E(f328(f328(f306(f879(x37071,a867)),f192(f879(x37071,a867))),f192(f879(f879(x37071,a867),a867))),f328(f305(x37071),f192(f879(x37071,a867)))) % 167.75/167.49 [3734]E(f328(f328(f22(f879(a872,a867)),f328(f300(a872),x37341)),f328(f328(f306(a872),f328(a116,x37341)),f192(f879(a872,a867)))),f328(f300(a872),f328(a116,x37341))) % 167.75/167.49 [3743]E(f328(f328(f306(f876(x37431)),f205(x37431)),f328(f307(x37431,f876(x37431),f235(x37431)),f251(f879(x37431,a867)))),f251(f879(f876(x37431),a867))) % 167.75/167.49 [3842]E(f328(f107(a872),f328(f328(f80(a1),x38421),x38421)),f328(f328(f86(a872,a872),f328(f107(a872),x38421)),f328(f328(f18(a872,a872,a872),f80(a872)),f5(a872)))) % 167.75/167.49 [4233]P16(x42331,f879(x42331,a867),f328(f328(f8(f879(x42331,a867),f879(f879(x42331,a867),f879(x42331,a867)),x42331),f328(f7(f879(x42331,a867),f879(x42331,a867),f879(x42331,a867)),f22(f879(x42331,a867)))),f328(f328(f7(x42331,f879(x42331,a867),f879(x42331,a867)),f306(x42331)),f192(f879(x42331,a867))))) % 167.75/167.49 [4322]E(f328(f248(f878(a1,a1)),f328(f267(a1,a1,a867),f328(f328(f8(f879(a1,a867),f879(a1,a867),a1),f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),x43221)))),f243(a1)))),f111(x43221)) % 167.75/167.49 [4355]E(f328(f248(f878(a1,a1)),f328(f267(a1,a1,a867),f328(f328(f18(a1,f879(a1,a867),f879(a1,a867)),f328(f328(f8(f879(a867,a867),f879(f879(a1,a867),f879(a1,a867)),a1),f8(a867,a867,a1)),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),x43551)))),f243(a1)))),f109(x43551)) % 167.75/167.49 [4410]E(f328(f248(f878(f879(x44101,a867),f879(x44101,a867))),f328(f267(f879(x44101,a867),f879(x44101,a867),a867),f328(f328(f7(f879(x44101,a867),f879(f879(x44101,a867),a867),f879(f879(x44101,a867),a867)),f328(f328(f8(f879(f879(x44101,a867),f879(a867,a867)),f879(f879(f879(x44101,a867),a867),f879(f879(x44101,a867),a867)),f879(x44101,a867)),f18(f879(x44101,a867),a867,a867)),f328(f328(f8(f879(f879(x44101,a867),a867),f879(f879(x44101,a867),f879(a867,a867)),f879(x44101,a867)),f328(f8(a867,f879(a867,a867),f879(x44101,a867)),a326)),f243(f879(x44101,a867))))),f38(x44101)))),f303(x44101)) % 167.75/167.49 [4530]~P1(f328(f38(f873(x45301)),f251(f879(f873(x45301),a867)))) % 167.75/167.49 [4535]~P1(f328(f328(f91(a1),a101),f328(f328(f80(a1),x45351),x45351))) % 167.75/167.49 [4545]~P1(f328(f328(f242(a1),f2(a1)),f328(f79(a1),f328(f104(a1),f328(a116,x45451))))) % 167.75/167.49 [3454]E(f328(f328(f22(a1),f328(f328(f80(a1),x34541),a101)),a101),x34541) % 167.75/167.49 [3470]E(f328(f170(a872),f136(a872,f328(f298(a872,f2(a872)),x34701))),f328(f249(a872),x34701)) % 167.75/167.49 [3713]E(f328(f328(f80(a1),f328(f328(f80(a1),f78(a1)),x37131)),x37131),f328(f328(f22(a1),f328(f328(f80(a1),x37131),x37131)),a101)) % 167.75/167.49 [3760]E(f328(f283(x37601,x37601),f304(x37601,f192(f879(f878(x37601,x37601),a867)))),f304(x37601,f192(f879(f878(x37601,x37601),a867)))) % 167.75/167.49 [3808]P1(f328(f328(f242(a872),x38081),f328(f328(f81(a872),x38081),f328(f328(f81(a872),x38081),x38081)))) % 167.75/167.49 [4088]P1(f328(f38(a872),f328(f248(a872),f328(f328(f7(a872,a872,a867),f243(a872)),x40881)))) % 167.75/167.49 [4089]P1(f328(f38(a872),f328(f248(a872),f328(f328(f7(a872,a872,a867),f242(a872)),x40891)))) % 167.75/167.49 [4375]E(f328(f248(f878(x43751,x43751)),f328(f328(f8(f879(x43751,a867),a867,f878(x43751,x43751)),f87(x43751)),f328(f328(f7(f878(x43751,x43751),f879(x43751,f878(x43751,x43751)),f879(x43751,a867)),f328(f328(f8(f879(f878(x43751,x43751),a867),f879(f879(x43751,f878(x43751,x43751)),f879(x43751,a867)),f878(x43751,x43751)),f8(f878(x43751,x43751),a867,x43751)),a325)),f328(f328(f18(x43751,x43751,f878(x43751,x43751)),f263(x43751,x43751)),f5(x43751))))),f304(x43751,f192(f879(f878(x43751,x43751),a867)))) % 167.75/167.49 [4532]~E(f328(f328(f22(a1),f328(f328(f80(a1),x45321),x45321)),a101),a83) % 167.75/167.49 [4534]~E(f328(f328(f80(a1),f328(f328(f80(a1),f78(a1)),x45341)),x45341),f2(a1)) % 167.75/167.49 [4542]~P1(f328(f328(f91(a1),f328(f328(f80(a1),x45421),x45421)),a101)) % 167.75/167.49 [3855]E(f328(f328(f80(a1),f328(f328(f22(a1),a101),x38551)),f328(f328(f22(a1),a101),x38551)),f328(f328(f22(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x38551),x38551)),a101))) % 167.75/167.49 [3977]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),a101),x39771)),f328(f328(f22(a1),a101),x39771))),a101),f328(f328(f22(a1),a101),f328(f328(f80(a1),x39771),x39771))) % 167.75/167.49 [4012]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f80(a1),x40121),a101)),f328(f328(f80(a1),x40121),a101))),a101),f328(f328(f80(a1),f328(f328(f80(a1),x40121),x40121)),a101)) % 167.75/167.49 [4050]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),a101),x40501)),f328(f328(f22(a1),a101),x40501))),a101),f328(f328(f22(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x40501),x40501)),a101))) % 167.75/167.49 [4151]E(f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x41511),f2(a872))),f192(f879(f878(a872,a872),a867))))),f328(f104(a1),x41511)) % 167.75/167.49 [4161]E(f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),f333(x41611)),f523(x41611))),f192(f879(f878(a872,a872),a867))))),x41611) % 167.75/167.49 [4195]E(f328(f248(a1),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),f2(a1)))),x41951)),f328(f307(a872,a1,f104(a1)),f328(f248(a872),f328(f328(f8(a1,a867,a872),x41951),f104(a1))))) % 167.75/167.49 [4241]P39(f328(f248(a1),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),f2(a1)))),x42411))) % 167.75/167.49 [4262]P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),x42621),f192(f879(f878(a872,a872),a867)))),a71)) % 167.75/167.49 [4268]E(f328(f307(a1,a872,a108),f328(f248(a1),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),f2(a1)))),f328(f328(f8(a872,a867,a1),x42681),a108)))),f328(f248(a872),x42681)) % 167.75/167.49 [4425]E(f309(a872,f328(f328(f44(f878(a872,a872),f879(a872,a867)),f328(a110,x44251)),f328(f267(a872,a872,f879(a872,a867)),f328(f328(f7(a872,f879(a872,a867),f879(a872,f879(a872,a867))),f328(f328(f8(f879(a872,f879(f879(a872,a867),f879(a872,a867))),f879(f879(a872,a867),f879(a872,f879(a872,a867))),a872),f7(a872,f879(a872,a867),f879(a872,a867))),f328(f328(f8(f879(a872,a872),f879(a872,f879(f879(a872,a867),f879(a872,a867))),a872),f328(f8(a872,f879(f879(a872,a867),f879(a872,a867)),a872),f306(a872))),f22(a872)))),f192(f879(a872,a867)))))),f328(a108,x44251)) % 167.75/167.49 [4547]~P1(f328(f328(f91(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x45471),x45471)),a101))) % 167.75/167.49 [3900]E(f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),x39001),x39001)),a101)),a101),f328(f328(f80(a1),x39001),x39001)) % 167.75/167.49 [3951]E(f328(f328(f22(a1),f328(f328(f22(a1),f328(f328(f80(a1),x39511),x39511)),a101)),a101),f328(f328(f80(a1),f328(f328(f22(a1),x39511),a101)),f328(f328(f22(a1),x39511),a101))) % 167.75/167.49 [4169]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f80(a1),f328(f79(a1),x41691)),a101)),f328(f328(f80(a1),f328(f79(a1),x41691)),a101))),a101),f328(f79(a1),f328(f328(f22(a1),f328(f328(f80(a1),x41691),x41691)),a101))) % 167.75/167.49 [4555]~P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x45551),x45551)),a101)),a83)) % 167.75/167.49 [4213]E(f328(f328(f80(a872),x42131),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(a116,f328(a116,x42131))) % 167.75/167.49 [4214]E(f328(f328(f81(a872),x42141),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f80(a872),x42141),x42141)) % 167.75/167.49 [4215]E(f328(f328(f40(a872),f328(f328(f80(a872),x42151),x42151)),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x42151) % 167.75/167.49 [4297]E(f46(a872,f328(a116,f328(a116,x42971)),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f46(a872,x42971,f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.75/167.49 [4440]E(f328(a89,f328(f328(f44(f878(a872,a872),f879(f878(a872,a872),a867)),f328(a110,x44401)),f328(f267(a872,a872,f879(f878(a872,a872),a867)),f328(f328(f8(f879(a872,f879(f878(a872,a872),a867)),f879(a872,f879(f878(a872,a872),a867)),a872),f328(f8(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867),a872),f282(f878(a872,a872),f878(a872,a872),a112))),f328(f328(f7(a872,f879(f878(a872,a872),a867),f879(a872,f879(f878(a872,a872),a867))),f328(f328(f8(f879(a872,f879(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f879(f879(f878(a872,a872),a867),f879(a872,f879(f878(a872,a872),a867))),a872),f7(a872,f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f8(f879(a872,f878(a872,a872)),f879(a872,f879(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),a872),f328(f8(f878(a872,a872),f879(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),a872),f306(f878(a872,a872)))),f328(f7(a872,a872,f878(a872,a872)),f263(a872,a872))))),f192(f879(f878(a872,a872),a867))))))),f328(f79(a1),x44401)) % 167.75/167.49 [4292]E(f328(f328(f80(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x42921),f328(a116,f328(a116,x42921))) % 167.75/167.49 [4293]E(f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x42931),f328(f328(f80(a872),x42931),x42931)) % 167.75/167.49 [4327]E(f328(f328(f40(a872),f328(a116,f328(a116,x43271))),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(a116,f328(f328(f40(a872),x43271),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 167.75/167.49 [4381]E(f328(f328(f80(a872),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x43811),f328(a116,f328(a116,f328(a116,x43811)))) % 167.75/167.49 [4448]E(f328(f267(a1,a1,f878(a1,a1)),f328(f328(f18(a1,f879(a1,f878(a1,a1)),f879(a1,f878(a1,a1))),f328(f328(f8(f879(a1,f879(f878(a1,a1),f878(a1,a1))),f879(f879(a1,f878(a1,a1)),f879(a1,f878(a1,a1))),a1),f18(a1,f878(a1,a1),f878(a1,a1))),f328(f328(f8(f879(a1,f878(a1,a1)),f879(a1,f879(f878(a1,a1),f878(a1,a1))),a1),f328(f18(a1,f878(a1,a1),f879(f878(a1,a1),f878(a1,a1))),f328(f328(f8(a867,f879(f878(a1,a1),f879(f878(a1,a1),f878(a1,a1))),a1),f100(f878(a1,a1))),f328(f328(f8(a1,a867,a1),f328(f242(a1),f2(a1))),f328(f328(f7(a1,a1,a1),f22(a1)),x44481))))),f328(f328(f7(a1,f879(a1,a1),f879(a1,f878(a1,a1))),f328(f328(f8(f879(a1,f878(a1,a1)),f879(f879(a1,a1),f879(a1,f878(a1,a1))),a1),f8(a1,f878(a1,a1),a1)),f328(f328(f8(a1,f879(a1,f878(a1,a1)),a1),f263(a1,a1)),f328(f328(f7(a1,a1,a1),f328(f328(f8(a1,f879(a1,a1),a1),f80(a1)),f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f78(a1))))),f328(f328(f7(a1,a1,a1),f22(a1)),x44481))))),f328(f328(f8(a1,f879(a1,f878(a1,a1)),a1),f263(a1,a1)),f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))),f45(x44481)) % 167.75/167.49 [3122]P93(f877(x31221,x31222)) % 167.75/167.49 [3123]P93(f878(x31231,x31232)) % 167.75/167.49 [3124]P103(f877(x31241,x31242)) % 167.75/167.49 [3125]P103(f878(x31251,x31252)) % 167.75/167.49 [3143]P15(a1,f177(x31431,x31432)) % 167.75/167.49 [3144]P38(x31441,f150(x31441,x31442)) % 167.75/167.49 [3209]P32(x32091,x32092,f117(x32091)) % 167.75/167.49 [3242]P40(x32421,x32422,f260(x32421,x32422)) % 167.75/167.49 [3243]P51(x32431,x32431,f260(x32431,x32432)) % 167.75/167.49 [3518]P26(x35181,x35181,f5(x35181),x35182) % 167.75/167.49 [3519]P26(x35191,x35191,f34(x35191),x35192) % 167.75/167.49 [3527]P33(x35271,x35272,f117(x35271),f117(x35271)) % 167.75/167.49 [3528]P26(x35281,f876(x35281),f235(x35281),x35282) % 167.75/167.49 [3537]P26(f873(x35371),f873(x35371),f166(x35371),x35372) % 167.75/167.49 [4459]~E(f33(x44591,x44592),a24) % 167.75/167.49 [4460]~E(f32(x44601,x44602),a24) % 167.75/167.49 [4489]~P34(x44891,x44892,f117(x44891)) % 167.75/167.49 [4490]~P36(x44901,x44902,f117(x44901)) % 167.75/167.49 [3105]E(f328(f5(x31051),x31052),x31052) % 167.75/167.49 [3106]E(f328(f248(x31061),x31062),x31062) % 167.75/167.49 [3108]E(f328(f34(x31081),x31082),x31082) % 167.75/167.49 [3118]E(f328(f195(x31181),x31182),f119(x31181)) % 167.75/167.49 [3141]E(f85(x31411,f328(a325,x31412)),x31412) % 167.75/167.49 [3142]E(f90(x31421,f328(a325,x31422)),x31422) % 167.75/167.49 [3163]E(f328(f133(x31631,x31632),f117(x31631)),f117(x31631)) % 167.75/167.49 [3183]E(f304(x31831,f304(x31831,x31832)),f304(x31831,x31832)) % 167.75/167.49 [3184]E(f149(x31841,f149(x31841,x31842)),f149(x31841,x31842)) % 167.75/167.49 [3204]E(f328(f328(f125(x32041),x32042),f117(x32041)),x32042) % 167.75/167.49 [3210]E(f171(x32101,x32102,f117(x32101)),x32102) % 167.75/167.49 [3211]E(f171(x32111,f117(x32111),x32112),x32112) % 167.75/167.49 [3217]E(f328(f328(f173(x32171),x32172),f117(x32171)),f117(x32171)) % 167.75/167.49 [3218]E(f328(f328(f135(x32181),x32182),f117(x32181)),f117(x32181)) % 167.75/167.49 [3220]E(f152(x32201,x32202,f117(x32201)),f2(a872)) % 167.75/167.49 [3221]E(f236(x32211,x32212,f205(x32211)),f2(a872)) % 167.75/167.49 [3223]E(f167(x32231,x32232,f117(x32231)),f117(x32231)) % 167.75/167.49 [3224]E(f175(x32241,x32242,f117(x32241)),f117(x32241)) % 167.75/167.49 [3225]E(f174(x32251,f117(x32251),x32252),f117(x32251)) % 167.75/167.49 [3229]E(f328(f170(x32291),f149(x32291,x32292)),f328(f170(x32291),x32292)) % 167.75/167.49 [3232]E(f328(f259(x32321,x32321),f260(x32321,x32322)),x32322) % 167.75/167.49 [3233]E(f328(f261(x32331,x32331),f260(x32331,x32332)),x32332) % 167.75/167.49 [3241]E(f328(f283(x32411,x32411),f260(x32411,x32412)),f260(x32411,x32412)) % 167.75/167.49 [3256]E(f304(f873(x32561),f154(x32561,x32562)),f155(x32561,f304(x32561,x32562))) % 167.75/167.49 [3258]P1(f328(f134(a1),f177(x32581,x32582))) % 167.75/167.49 [3266]E(f328(f259(x32661,x32661),f304(x32661,x32662)),f251(f879(x32661,a867))) % 167.75/167.49 [3267]E(f328(f261(x32671,x32671),f304(x32671,x32672)),f251(f879(x32671,a867))) % 167.75/167.49 [3271]P1(f328(f134(x32711),f149(x32711,x32712))) % 167.75/167.49 [3273]P1(f328(f157(x32731,x32732),f117(x32731))) % 167.75/167.49 [3279]E(f328(f170(a1),f177(x32791,x32792)),f299(a1,x32791,x32792)) % 167.75/167.49 [3294]P52(x32941,f192(f879(x32941,a867)),x32942) % 167.75/167.49 [3299]E(f328(f266(a1,a1),f47(x32991,x32992)),f46(a1,x32991,x32992)) % 167.75/167.49 [3300]E(f328(f298(a872,x33001),f328(a116,x33002)),f299(a872,x33001,x33002)) % 167.75/167.49 [3316]E(f328(f328(f148(x33161),x33162),f117(x33161)),f137(x33161,x33162,f117(x33161))) % 167.75/167.49 [3328]E(f299(a872,f328(a116,x33281),x33282),f301(a872,x33281,x33282)) % 167.75/167.49 [3331]P40(x33311,f251(f879(x33311,a867)),f304(x33311,x33312)) % 167.75/167.49 [3396]E(f328(f328(f22(a872),x33961),f328(a116,x33962)),f328(f39(a872),f302(a872,x33962,x33961))) % 167.75/167.49 [3455]E(f164(x34551,x34552,f117(x34551)),f328(f328(f263(f873(x34551),f873(x34551)),f117(x34551)),f117(x34551))) % 167.75/167.49 [3474]E(f328(f267(x34741,x34742,f878(x34741,x34742)),f263(x34741,x34742)),f34(f878(x34741,x34742))) % 167.75/167.49 [3479]P1(f328(f328(f330(f873(x34791)),f117(x34791)),f158(x34791,x34792))) % 167.75/167.49 [3480]E(f328(f193(f873(x34801)),f118(x34801,x34802)),f328(f328(f22(a872),f328(f193(f873(x34801)),x34802)),f78(a872))) % 167.75/167.49 [3488]P1(f328(f38(a872),f302(a872,x34881,x34882))) % 167.75/167.49 [3489]P1(f328(f38(a872),f301(a872,x34891,x34892))) % 167.75/167.49 [3490]P1(f328(f38(a872),f299(a872,x34901,x34902))) % 167.75/167.49 [3491]P1(f328(f38(a1),f302(a1,x34911,x34912))) % 167.75/167.49 [3492]P1(f328(f38(a1),f301(a1,x34921,x34922))) % 167.75/167.49 [3493]P1(f328(f38(a1),f299(a1,x34931,x34932))) % 167.75/167.49 [3596]E(f328(f307(a872,a872,a116),f299(a872,x35961,x35962)),f299(a872,f328(a116,x35961),f328(a116,x35962))) % 167.75/167.49 [3616]E(f328(f328(f285(x36161,x36161,x36161),f304(x36161,x36162)),f304(x36161,x36162)),f304(x36161,x36162)) % 167.75/167.49 [3649]E(f328(f328(f263(a1,a1),f328(f328(f40(a1),x36491),x36492)),f46(a1,x36491,x36492)),f47(x36491,x36492)) % 167.75/167.49 [3650]E(f328(f328(f263(a103,a103),f328(f328(f40(a103),x36501),x36502)),f46(a103,x36501,x36502)),f21(x36501,x36502)) % 167.75/167.49 [3679]E(f328(f328(f263(a872,a872),f328(f328(f40(a872),x36791),x36792)),f46(a872,x36791,x36792)),f85(f878(a872,a872),f49(x36791,x36792))) % 167.75/167.49 [3730]P1(f328(f328(f243(a872),f328(f328(f22(a872),x37301),x37302)),f328(a116,x37301))) % 167.75/167.49 [3829]E(f328(f328(f80(a1),f328(f328(f81(a1),x38291),f328(f328(f40(a1),x38292),x38291))),f46(a1,x38292,x38291)),x38292) % 167.75/167.49 [3833]E(f328(f328(f44(a872,f879(f878(f873(x38331),f873(x38331)),a867)),f251(f879(a872,a867))),f140(x38331,x38332)),f142(x38331,x38332)) % 167.75/167.49 [4063]P1(f328(f328(f330(f878(f873(x40631),f873(x40631))),f328(f328(f263(f873(x40631),f873(x40631)),f117(x40631)),f117(x40631))),f155(x40631,x40632))) % 167.75/167.49 [4226]E(f268(x42261,x42261,x42262,x42262,f5(x42261),f5(x42262)),f34(f878(x42261,x42262))) % 167.75/167.49 [4228]E(f268(x42281,x42281,x42282,x42282,f34(x42281),f34(x42282)),f34(f878(x42281,x42282))) % 167.75/167.49 [4468]~E(f328(f235(x44681),x44682),f205(x44681)) % 167.75/167.49 [3202]E(f328(f239(x32021),f328(f235(x32021),x32022)),x32022) % 167.75/167.49 [3203]E(f328(f166(x32031),f328(f166(x32031),x32032)),x32032) % 167.75/167.49 [3205]E(f328(f328(f135(x32051),f2(a872)),x32052),x32052) % 167.75/167.49 [3219]E(f328(f328(f173(x32191),f2(a872)),x32192),f117(x32191)) % 167.75/167.49 [3227]E(f328(f328(f125(x32271),f117(x32271)),x32272),x32272) % 167.75/167.49 [3235]E(f328(f193(f876(x32351)),f328(f235(x32351),x32352)),f2(a872)) % 167.75/167.49 [3237]E(f41(f879(x32371,a867),f328(f305(x32371),x32372)),x32372) % 167.75/167.49 [3239]E(f328(f170(x32391),f328(f165(x32391),x32392)),f328(f170(x32391),x32392)) % 167.75/167.49 [3240]E(f328(f170(x32401),f328(f166(x32401),x32402)),f328(f170(x32401),x32402)) % 167.75/167.49 [3245]E(f328(f328(f22(a103),x32451),x32452),f328(f328(a23,x32451),x32452)) % 167.75/167.49 [3260]E(f328(f328(f80(a872),x32601),x32602),f328(f328(f80(a872),x32602),x32601)) % 167.75/167.49 [3261]E(f328(f328(f80(a1),x32611),x32612),f328(f328(f80(a1),x32612),x32611)) % 167.75/167.49 [3262]E(f328(f328(f81(a872),x32621),x32622),f328(f328(f81(a872),x32622),x32621)) % 167.75/167.49 [3263]E(f328(f328(f81(a1),x32631),x32632),f328(f328(f81(a1),x32632),x32631)) % 167.75/167.49 [3286]E(f328(f328(f187(x32861,x32861),f2(a872)),x32862),f34(x32861)) % 167.75/167.49 [3287]E(f328(f193(f873(x32871)),f328(f165(x32871),x32872)),f328(f193(f873(x32871)),x32872)) % 167.75/167.49 [3288]E(f328(f193(f873(x32881)),f328(f166(x32881),x32882)),f328(f193(f873(x32881)),x32882)) % 167.75/167.49 [3289]E(f174(x32891,x32892,f192(f879(a872,a867))),f117(x32891)) % 167.75/167.49 [3290]E(f328(f328(f151(x32901,x32901),f5(x32901)),x32902),x32902) % 167.75/167.49 [3292]E(f328(f262(a1,a1),f47(x32921,x32922)),f328(f328(f40(a1),x32921),x32922)) % 167.75/167.49 [3309]E(f328(f193(f873(x33091)),f149(x33091,x33092)),f328(f39(x33091),f328(f170(x33091),x33092))) % 167.75/167.49 [3310]E(f31(f32(x33101,x33102)),f328(f328(f80(a872),f31(x33102)),f328(a116,f2(a872)))) % 167.75/167.49 [3311]E(f328(f281(x33111),f328(f283(x33111,x33111),x33112)),f328(f281(x33111),x33112)) % 167.75/167.49 [3315]P1(f328(f38(x33151),f328(f170(x33151),x33152))) % 167.75/167.49 [3323]E(f328(f328(f80(a1),x33231),f328(f79(a1),x33232)),f328(f328(f22(a1),x33231),x33232)) % 167.75/167.49 [3330]P25(x33301,x33302,f192(f879(f871(x33301),a867))) % 167.75/167.49 [3332]E(f328(f307(x33321,x33321,f5(x33321)),x33322),x33322) % 167.75/167.49 [3333]E(f328(f307(x33331,x33331,f34(x33331)),x33332),x33332) % 167.75/167.49 [3334]E(f328(f308(x33341,x33341,f5(x33341)),x33342),x33342) % 167.75/167.49 [3335]E(f328(f308(x33351,x33351,f34(x33351)),x33352),x33352) % 167.75/167.49 [3336]P1(f328(f251(f879(x33361,a867)),x33362)) % 167.75/167.49 [3338]E(f328(f39(a872),f328(f298(a872,x33381),x33382)),f328(f328(f22(a872),x33382),x33381)) % 167.75/167.49 [3339]E(f328(f298(a872,f328(a116,x33391)),x33392),f302(a872,x33391,x33392)) % 167.75/167.49 [3351]E(f328(f328(f306(x33511),x33512),f192(f879(x33511,a867))),f328(f248(x33511),f328(a325,x33512))) % 167.75/167.49 [3355]E(f328(f328(f306(x33551),x33552),f192(f879(x33551,a867))),f234(x33551,f328(f235(x33551),x33552))) % 167.75/167.49 [3357]E(f304(x33571,f328(f283(x33571,x33571),x33572)),f328(f283(x33571,x33571),f304(x33571,x33572))) % 167.75/167.49 [3362]E(f328(f328(f80(a872),f328(a116,x33621)),x33622),f328(f328(f80(a872),x33621),f328(a116,x33622))) % 167.75/167.49 [3363]E(f328(f328(f22(a872),f328(a116,x33631)),f328(a116,x33632)),f328(f328(f22(a872),x33631),x33632)) % 167.75/167.49 [3371]E(f56(x33711,f2(a872),x33712),f328(f328(f148(f873(x33711)),f117(x33711)),f117(f873(x33711)))) % 167.75/167.49 [3372]E(f328(f39(a872),f301(a872,x33721,x33722)),f328(f328(f22(a872),x33722),x33721)) % 167.75/167.49 [3381]P38(x33811,f328(f328(f284(a872,x33811),a247),x33812)) % 167.75/167.49 [3383]P15(a872,f136(a872,f328(f298(a872,x33831),x33832))) % 167.75/167.49 [3385]P1(f328(f38(a872),f328(f298(a872,x33851),x33852))) % 167.75/167.49 [3386]P1(f328(f38(a1),f328(f298(a1,x33861),x33862))) % 167.75/167.49 [3389]E(f328(f283(f873(x33891),f873(x33891)),f154(x33891,x33892)),f154(x33891,f328(f283(x33891,x33891),x33892))) % 167.75/167.49 [3390]E(f328(f193(a869),f32(x33901,x33902)),f328(f328(f80(a872),f328(f193(a869),x33902)),f328(a116,f2(a872)))) % 167.75/167.49 [3392]E(f328(f298(a1,x33921),f328(f328(f80(a1),x33922),f78(a1))),f299(a1,x33921,x33922)) % 167.75/167.49 [3395]E(f328(f328(f40(a1),f328(f79(a1),x33951)),f328(f79(a1),x33952)),f328(f328(f40(a1),x33951),x33952)) % 167.75/167.49 [3403]E(f182(x34031,x34032,f328(f16(f876(x34032),x34031),f205(x34032))),f192(f879(x34031,a867))) % 167.75/167.49 [3404]E(f184(x34041,x34042,f328(f16(f876(x34042),x34041),f205(x34042))),f192(f879(x34042,a867))) % 167.75/167.49 [3405]E(f328(f328(f187(f878(x34051,x34051),a867),f78(a872)),x34052),x34052) % 167.75/167.49 [3407]E(f328(f328(f114(f879(x34071,a867)),x34072),f192(f879(x34071,a867))),x34072) % 167.75/167.49 [3408]E(f328(f328(f22(f879(x34081,a867)),x34082),f192(f879(x34081,a867))),x34082) % 167.75/167.49 [3409]E(f328(f328(f105(f879(x34091,a867)),x34092),f251(f879(x34091,a867))),x34092) % 167.75/167.49 [3410]E(f328(f262(a872,a872),f85(f878(a872,a872),f49(x34101,x34102))),f328(f328(f40(a872),x34101),x34102)) % 167.75/167.49 [3417]E(f310(x34171,f328(a20,x34172),f328(f79(a1),f328(a20,x34172))),f328(f328(f313(a1),x34171),x34172)) % 167.75/167.49 [3418]E(f299(a1,f328(f328(f80(a1),x34181),f78(a1)),x34182),f301(a1,x34181,x34182)) % 167.75/167.49 [3423]E(f328(f266(a872,a872),f85(f878(a872,a872),f49(x34231,x34232))),f46(a872,x34231,x34232)) % 167.75/167.49 [3431]E(f311(x34311,f328(a20,x34312),f328(f79(a1),f328(a20,x34312))),f312(a1,x34311,x34312)) % 167.75/167.49 [3434]P1(f328(f328(f330(x34341),x34342),f251(f879(x34341,a867)))) % 167.75/167.49 [3439]E(f328(f328(f22(a872),f328(a116,x34391)),x34392),f328(f39(a872),f299(a872,x34392,x34391))) % 167.75/167.49 [3466]E(f328(f328(f114(f879(x34661,a867)),x34662),f251(f879(x34661,a867))),f251(f879(x34661,a867))) % 167.75/167.49 [3467]E(f328(f328(f22(f879(x34671,a867)),x34672),f251(f879(x34671,a867))),f192(f879(x34671,a867))) % 167.75/167.49 [3468]E(f328(f328(f105(f879(x34681,a867)),x34682),f192(f879(x34681,a867))),f192(f879(x34681,a867))) % 167.75/167.49 [3483]E(f46(a1,f328(f104(a1),x34831),f328(f104(a1),x34832)),f328(f104(a1),f46(a872,x34831,x34832))) % 167.75/167.49 [3484]E(f46(a1,f328(f79(a1),x34841),f328(f79(a1),x34842)),f328(f79(a1),f46(a1,x34841,x34842))) % 167.75/167.49 [3495]E(f328(f193(f873(x34951)),f328(f169(x34951),x34952)),f328(f328(f22(a872),f328(f193(f873(x34951)),x34952)),f78(a872))) % 167.75/167.49 [3520]E(f328(f328(f40(a1),f46(a1,x35201,x35202)),x35202),f2(a1)) % 167.75/167.49 [3530]E(f328(a3,f46(a872,f328(a19,x35301),f328(a19,x35302))),f46(a103,x35301,x35302)) % 167.75/167.49 [3563]E(f328(a3,f328(f328(f22(a872),f328(a19,x35631)),f328(a19,x35632))),f328(f328(f22(a103),x35631),x35632)) % 167.75/167.49 [3564]E(f328(a3,f328(f328(f80(a872),f328(a19,x35641)),f328(a19,x35642))),f328(f328(f80(a103),x35641),x35642)) % 167.75/167.49 [3565]E(f328(a3,f328(f328(f81(a872),f328(a19,x35651)),f328(a19,x35652))),f328(f328(f81(a103),x35651),x35652)) % 167.75/167.49 [3566]E(f328(a3,f328(f328(f40(a872),f328(a19,x35661)),f328(a19,x35662))),f328(f328(f40(a103),x35661),x35662)) % 167.75/167.49 [3575]E(f328(f307(a872,a872,a116),f328(f298(a872,x35751),x35752)),f328(f298(a872,f328(a116,x35751)),f328(a116,x35752))) % 167.75/167.49 [3601]P1(f328(f49(x36011,x36012),f85(f878(a872,a872),f49(x36011,x36012)))) % 167.75/167.49 [3622]E(f328(f328(f80(a872),f328(f328(f80(a872),f31(x36221)),f31(x36222))),f328(a116,f2(a872))),f31(f33(x36221,x36222))) % 167.75/167.49 [3623]E(f46(a872,f328(a116,f46(a872,x36231,x36232)),x36232),f46(a872,f328(a116,x36231),x36232)) % 167.75/167.49 [3637]E(f328(f328(f43(f879(x36371,a867),f879(x36371,a867)),x36372),f5(f879(x36371,a867))),f42(f879(x36371,a867),x36372)) % 167.75/167.49 [3638]E(f328(f328(f44(f879(x36381,a867),f879(x36381,a867)),x36382),f5(f879(x36381,a867))),f41(f879(x36381,a867),x36382)) % 167.75/167.49 [3639]E(f328(f307(f873(x36391),f879(x36391,a867),f170(x36391)),f328(f170(f873(x36391)),f55(x36391,x36392))),f328(f305(x36391),f328(f170(x36391),x36392))) % 167.75/167.49 [3642]P1(f328(f328(f330(f879(x36421,a867)),x36422),f328(f305(x36421),x36422))) % 167.75/167.49 [3648]E(f46(a1,f328(f79(a1),f46(a1,x36481,x36482)),x36482),f46(a1,f328(f79(a1),x36481),x36482)) % 167.75/167.49 [3660]P1(f328(f328(f242(f879(x36601,a867)),x36602),f251(f879(x36601,a867)))) % 167.75/167.49 [3662]E(f328(f328(f285(x36621,x36621,x36621),f304(x36621,x36622)),f304(x36621,f304(x36621,x36622))),f304(x36621,x36622)) % 167.75/167.49 [3663]E(f328(f328(f114(f879(x36631,a867)),f328(f261(x36631,x36631),x36632)),f328(f259(x36631,x36631),x36632)),f328(f281(x36631),x36632)) % 167.75/167.49 [3684]E(f315(x36841,x36842,f251(f879(x36841,a867)),f251(f879(x36842,a867))),f251(f879(f877(x36841,x36842),a867))) % 167.75/167.49 [3735]P1(f328(f328(f242(a872),f46(a872,x37351,x37352)),x37351)) % 167.75/167.49 [3758]P1(f328(f328(f242(a1),f328(f79(a1),f328(f104(a1),x37581))),f328(f104(a1),x37582))) % 167.75/167.49 [3784]P1(f328(f328(f330(f879(x37841,a867)),f192(f879(x37841,a867))),f328(f305(x37841),x37842))) % 167.75/167.49 [3789]E(f304(x37891,f328(f328(f285(x37891,x37891,x37891),x37892),f304(x37891,x37892))),f304(x37891,x37892)) % 167.75/167.49 [3792]E(f328(f328(f285(x37921,x37921,x37921),f304(x37921,x37922)),x37922),f328(f328(f285(x37921,x37921,x37921),x37922),f304(x37921,x37922))) % 167.75/167.49 [3794]E(f328(a108,f328(f328(f80(a1),f328(f328(f22(a1),x37941),x37942)),f78(a1))),f328(f39(a1),f299(a1,x37942,x37941))) % 167.75/167.49 [3809]E(f328(f259(x38091,x38091),f328(f328(f285(x38091,x38091,x38091),x38092),f304(x38091,x38092))),f328(f259(x38091,x38091),x38092)) % 167.75/167.49 [3810]E(f328(f261(x38101,x38101),f328(f328(f285(x38101,x38101,x38101),x38102),f304(x38101,x38102))),f328(f261(x38101,x38101),x38102)) % 167.75/167.49 [3826]E(f328(f328(f80(a872),f328(f328(f80(a872),f328(f193(a869),x38261)),f328(f193(a869),x38262))),f328(a116,f2(a872))),f328(f193(a869),f33(x38261,x38262))) % 167.75/167.49 [3837]P26(a872,a872,f328(f328(f7(a872,a872,a872),f80(a872)),x38371),x38372) % 167.75/167.49 [3839]P15(a872,f328(f166(a872),f328(f328(f151(f873(x38391),a872),f193(f873(x38391))),f178(x38391,x38392)))) % 167.75/167.49 [3886]P1(f328(f328(f243(a1),f328(f79(a1),f328(f104(a1),f328(a116,x38861)))),f328(f104(a1),x38862))) % 167.75/167.49 [3932]E(f328(f139(f873(x39321),x39321,f328(f7(x39321,f873(x39321),f873(x39321)),f148(x39321)),f117(x39321)),x39322),f328(f166(x39321),x39322)) % 167.75/167.49 [3984]P1(f328(f328(f242(f879(f878(f873(x39841),f873(x39841)),a867)),f155(x39841,x39842)),f304(f873(x39841),f154(x39841,x39842)))) % 167.75/167.49 [4016]P1(f328(f49(x40161,x40162),f328(f328(f263(a872,a872),f328(f328(f40(a872),x40161),x40162)),f46(a872,x40161,x40162)))) % 167.75/167.49 [4027]P1(f328(f328(f242(f879(f878(f873(x40271),f873(x40271)),a867)),f154(x40271,f304(x40271,x40272))),f304(f873(x40271),f154(x40271,x40272)))) % 167.75/167.49 [4252]E(f328(f328(f269(f878(a103,a103),a103,f878(a103,a103),f878(x42521,f878(a103,a103))),f273(f328(f163(a103),f328(f328(f151(f878(a103,x42521),a103),f262(a103,x42521)),x42522)))),f328(f328(f8(x42521,f879(f878(a103,a103),f878(x42521,f878(a103,a103))),a103),f263(x42521,f878(a103,a103))),f274(x42521,x42522))),f272(x42521,x42522)) % 167.75/167.49 [4363]E(f328(f237(a872,f878(x43631,f874(x43631)),f2(a872),f328(f267(x43631,f874(x43631),a872),f328(f16(f879(f874(x43631),a872),x43631),f328(f328(f7(f874(x43631),a872,a872),f328(f328(f8(a872,f879(a872,a872),f874(x43631)),f80(a872)),f193(f874(x43631)))),f78(a872))))),f328(f132(x43631),x43632)),f328(f193(f874(x43631)),x43632)) % 167.75/167.49 [4439]E(f328(f267(f879(f878(x44391,x44391),a867),f879(f878(x44391,x44391),a867),f879(f879(x44392,x44391),f878(f879(f878(x44392,x44392),a867),f879(f878(x44392,x44392),a867)))),f328(f328(f7(f879(f878(x44391,x44391),a867),f879(f879(f878(x44391,x44391),a867),f879(f879(x44392,x44391),f879(f878(x44392,x44392),a867))),f879(f879(f878(x44391,x44391),a867),f879(f879(x44392,x44391),f878(f879(f878(x44392,x44392),a867),f879(f878(x44392,x44392),a867))))),f328(f328(f8(f879(f879(f879(x44392,x44391),f879(f878(x44392,x44392),a867)),f879(f879(x44392,x44391),f878(f879(f878(x44392,x44392),a867),f879(f878(x44392,x44392),a867)))),f879(f879(f879(f878(x44391,x44391),a867),f879(f879(x44392,x44391),f879(f878(x44392,x44392),a867))),f879(f879(f878(x44391,x44391),a867),f879(f879(x44392,x44391),f878(f879(f878(x44392,x44392),a867),f879(f878(x44392,x44392),a867))))),f879(f878(x44391,x44391),a867)),f8(f879(f879(x44392,x44391),f879(f878(x44392,x44392),a867)),f879(f879(x44392,x44391),f878(f879(f878(x44392,x44392),a867),f879(f878(x44392,x44392),a867))),f879(f878(x44391,x44391),a867))),f328(f328(f8(f879(f879(x44392,x44391),f879(f879(f878(x44392,x44392),a867),f878(f879(f878(x44392,x44392),a867),f879(f878(x44392,x44392),a867)))),f879(f879(f879(x44392,x44391),f879(f878(x44392,x44392),a867)),f879(f879(x44392,x44391),f878(f879(f878(x44392,x44392),a867),f879(f878(x44392,x44392),a867)))),f879(f878(x44391,x44391),a867)),f18(f879(x44392,x44391),f879(f878(x44392,x44392),a867),f878(f879(f878(x44392,x44392),a867),f879(f878(x44392,x44392),a867)))),f328(f328(f8(f879(f879(x44392,x44391),f879(f878(x44392,x44392),a867)),f879(f879(x44392,x44391),f879(f879(f878(x44392,x44392),a867),f878(f879(f878(x44392,x44392),a867),f879(f878(x44392,x44392),a867)))),f879(f878(x44391,x44391),a867)),f328(f8(f879(f878(x44392,x44392),a867),f879(f879(f878(x44392,x44392),a867),f878(f879(f878(x44392,x44392),a867),f879(f878(x44392,x44392),a867))),f879(x44392,x44391)),f263(f879(f878(x44392,x44392),a867),f879(f878(x44392,x44392),a867)))),f284(x44391,x44392))))),f284(x44391,x44392))),f74(x44391,x44392)) % 167.75/167.49 [4515]~E(f328(f305(x45151),x45152),f192(f879(f879(x45151,a867),a867))) % 167.75/167.49 [4529]~P1(f328(f328(f330(x45291),x45292),f192(f879(x45291,a867)))) % 167.75/167.49 [4539]~P1(f328(f328(f243(f879(x45391,a867)),x45392),f192(f879(x45391,a867)))) % 167.75/167.49 [3341]E(f328(f328(f22(a872),x33411),f328(f328(f80(a872),x33411),x33412)),f2(a872)) % 167.75/167.49 [3343]E(f328(f328(f114(f879(x33431,a867)),x33432),x33432),x33432) % 167.75/167.49 [3344]E(f328(f328(f105(f879(x33441,a867)),x33442),x33442),x33442) % 167.75/167.49 [3374]E(f328(f328(f22(f879(x33741,a867)),x33742),x33742),f192(f879(x33741,a867))) % 167.75/167.49 [3377]E(f328(f140(x33771,x33772),f2(a872)),f192(f879(f878(f873(x33771),f873(x33771)),a867))) % 167.75/167.49 [3378]E(f328(f328(f80(a872),x33781),f328(a116,x33782)),f328(a116,f328(f328(f80(a872),x33781),x33782))) % 167.75/167.49 [3391]E(f199(f328(f104(a1),x33911),f328(f104(a1),x33912)),f328(f104(a1),f328(f328(f22(a872),x33911),x33912))) % 167.75/167.49 [3394]E(f328(f328(f40(a1),f328(f79(a1),x33941)),x33942),f328(f328(f40(a1),x33941),f328(f79(a1),x33942))) % 167.75/167.49 [3398]E(f328(f39(a1),f328(f298(a1,x33981),x33982)),f328(a108,f328(f328(f22(a1),x33982),x33981))) % 167.75/167.49 [3401]E(f328(f328(f80(a872),f328(a116,x34011)),x34012),f328(a116,f328(f328(f80(a872),x34011),x34012))) % 167.75/167.49 [3406]E(f328(f79(f879(x34061,a867)),f328(f79(f879(x34061,a867)),x34062)),x34062) % 167.75/167.49 [3420]E(f178(x34201,f328(f328(f148(f873(x34201)),f117(x34201)),x34202)),f178(x34201,x34202)) % 167.75/167.49 [3424]E(f328(f328(f80(a872),x34241),f328(f328(f81(a872),x34241),x34242)),f328(f328(f81(a872),x34241),f328(a116,x34242))) % 167.75/167.49 [3432]E(f328(f328(a23,f328(a3,x34321)),f328(a3,x34322)),f328(a3,f328(f328(f22(a872),x34321),x34322))) % 167.75/167.49 [3446]E(f328(f328(f81(a1),f328(f79(a1),x34461)),x34462),f328(f79(a1),f328(f328(f81(a1),x34461),x34462))) % 167.75/167.49 [3448]E(f328(f328(f253(a1),f328(f104(a1),x34481)),x34482),f328(f104(a1),f328(f328(f253(a872),x34481),x34482))) % 167.75/167.49 [3449]E(f328(f328(f80(a103),f328(a3,x34491)),f328(a3,x34492)),f328(a3,f328(f328(f80(a872),x34491),x34492))) % 167.75/167.49 [3450]E(f328(f328(f81(a103),f328(a3,x34501)),f328(a3,x34502)),f328(a3,f328(f328(f81(a872),x34501),x34502))) % 167.75/167.49 [3451]E(f328(f328(f240(a872),f328(a116,x34511)),f328(a116,x34512)),f328(a116,f328(f328(f240(a872),x34511),x34512))) % 167.75/167.49 [3452]E(f328(f328(f241(a872),f328(a116,x34521)),f328(a116,x34522)),f328(a116,f328(f328(f241(a872),x34521),x34522))) % 167.75/167.49 [3458]E(f328(f170(a872),f136(a872,f328(f298(a872,x34581),x34582))),f328(f298(a872,x34581),x34582)) % 167.75/167.49 [3459]E(f309(x34591,f328(f328(f306(x34591),x34592),f192(f879(x34591,a867)))),x34592) % 167.75/167.49 [3464]E(f328(f259(x34641,x34642),f192(f879(f878(x34641,x34642),a867))),f192(f879(x34642,a867))) % 167.75/167.49 [3465]E(f328(f261(x34651,x34652),f192(f879(f878(x34651,x34652),a867))),f192(f879(x34651,a867))) % 167.75/167.49 [3469]E(f328(a108,f328(f328(f22(a1),x34691),x34692)),f328(f39(a1),f301(a1,x34692,x34691))) % 167.75/167.49 [3473]E(f328(f328(f80(a872),x34731),f328(f328(f81(a872),x34732),x34731)),f328(f328(f81(a872),f328(a116,x34732)),x34731)) % 167.75/167.49 [3475]E(f328(f328(f62(x34751),f192(f879(x34751,a867))),x34752),f192(f879(f879(x34751,a867),a867))) % 167.75/167.49 [3485]E(f328(f193(f873(a872)),f136(a872,f328(f298(a872,x34851),x34852))),f328(f328(f22(a872),x34852),x34851)) % 167.75/167.49 [3500]E(f328(f328(f114(f879(x35001,a867)),f192(f879(x35001,a867))),x35002),x35002) % 167.75/167.49 [3501]E(f328(f328(f105(f879(x35011,a867)),f251(f879(x35011,a867))),x35012),x35012) % 167.75/167.49 [3504]E(f328(f328(f80(a1),f328(f79(a1),x35041)),f328(f79(a1),x35042)),f328(f79(a1),f328(f328(f80(a1),x35041),x35042))) % 167.75/167.49 [3507]E(f328(f328(f80(a1),f328(f104(a1),x35071)),f328(f104(a1),x35072)),f328(f104(a1),f328(f328(f80(a872),x35071),x35072))) % 167.75/167.49 [3508]E(f328(f328(f80(a1),f328(f107(a1),x35081)),f328(f107(a1),x35082)),f328(f107(a1),f328(f328(f80(a1),x35081),x35082))) % 167.75/167.49 [3510]E(f328(f328(f81(a1),f328(f104(a1),x35101)),f328(f104(a1),x35102)),f328(f104(a1),f328(f328(f81(a872),x35101),x35102))) % 167.75/167.49 [3511]E(f328(f328(f81(a1),f328(f107(a1),x35111)),f328(f107(a1),x35112)),f328(f107(a1),f328(f328(f81(a1),x35111),x35112))) % 167.75/167.49 [3512]E(f328(f328(f40(a1),f328(f104(a1),x35121)),f328(f104(a1),x35122)),f328(f104(a1),f328(f328(f40(a872),x35121),x35122))) % 167.75/167.49 [3531]E(f328(f328(f6(x35311,a872),f328(f16(a872,x35311),f78(a872))),x35312),f328(f39(x35311),x35312)) % 167.75/167.49 [3538]E(f328(f79(a1),f46(a1,f328(f79(a1),x35381),x35382)),f46(a1,x35381,f328(f79(a1),x35382))) % 167.75/167.49 [3540]E(f328(f170(a1),f177(x35401,f328(f328(f22(a1),x35402),f78(a1)))),f328(f298(a1,x35401),x35402)) % 167.75/167.49 [3544]P1(f328(f328(f242(a872),x35441),f328(f328(f80(a872),x35442),x35441))) % 167.75/167.49 [3545]P1(f328(f328(f242(a872),x35451),f328(f328(f80(a872),x35451),x35452))) % 167.75/167.49 [3548]E(f328(f328(f114(f879(x35481,a867)),f251(f879(x35481,a867))),x35482),f251(f879(x35481,a867))) % 167.75/167.49 [3549]E(f328(f328(f22(f879(x35491,a867)),f192(f879(x35491,a867))),x35492),f192(f879(x35491,a867))) % 167.75/167.49 [3550]E(f328(f328(f105(f879(x35501,a867)),f192(f879(x35501,a867))),x35502),f192(f879(x35501,a867))) % 167.75/167.49 [3555]E(f328(f328(f263(a1,a1),x35551),f328(f79(a1),x35552)),f328(a52,f328(f328(f263(a1,a1),x35551),x35552))) % 167.75/167.49 [3556]E(f328(f298(a1,f328(f328(f80(a1),x35561),f78(a1))),x35562),f302(a1,x35561,x35562)) % 167.75/167.49 [3567]E(f328(f328(f81(a872),x35671),f328(f328(f40(a872),x35672),x35671)),f328(f328(f22(a872),x35672),f46(a872,x35672,x35671))) % 167.75/167.49 [3568]E(f328(f328(f81(a1),x35681),f328(f328(f40(a1),x35682),x35681)),f328(f328(f22(a1),x35682),f46(a1,x35682,x35681))) % 167.75/167.49 [3572]E(f328(f170(a1),f177(f328(f328(f80(a1),x35721),f78(a1)),x35722)),f301(a1,x35721,x35722)) % 167.75/167.49 [3576]P1(f328(f328(f242(f879(x35761,a867)),x35762),x35762)) % 167.75/167.49 [3579]E(f328(f328(f114(f879(x35791,a867)),x35792),f328(f79(f879(x35791,a867)),x35792)),f251(f879(x35791,a867))) % 167.75/167.49 [3580]E(f328(f328(f105(f879(x35801,a867)),x35802),f328(f79(f879(x35801,a867)),x35802)),f192(f879(x35801,a867))) % 167.75/167.49 [3588]E(f328(f328(f22(a872),f328(f328(f22(a872),x35881),f78(a872))),x35882),f328(f328(f22(a872),x35881),f328(a116,x35882))) % 167.75/167.49 [3593]E(f328(f328(f22(f879(x35931,a867)),f251(f879(x35931,a867))),x35932),f328(f79(f879(x35931,a867)),x35932)) % 167.75/167.49 [3594]E(f328(f328(f22(a1),f328(f107(a1),x35941)),f328(f107(a1),x35942)),f328(f107(a1),f328(f328(f80(a1),x35941),f328(f79(a1),x35942)))) % 167.75/167.49 [3606]E(f328(f170(a872),f136(a872,f328(f298(a872,x36061),f328(a116,x36062)))),f299(a872,x36061,x36062)) % 167.75/167.49 [3614]P1(f328(f328(f328(f328(a200,a24),x36141),x36142),x36141)) % 167.75/167.49 [3620]E(f328(f193(f873(f873(x36201))),f55(x36201,x36202)),f328(f328(f253(a872),f328(a116,f328(a116,f2(a872)))),f328(f193(f873(x36201)),x36202))) % 167.75/167.49 [3640]E(f328(f328(f187(f878(x36401,x36401),a867),f2(a872)),x36402),f304(x36401,f192(f879(f878(x36401,x36401),a867)))) % 167.75/167.49 [3644]P1(f328(f134(a872),f136(a872,f328(f298(a872,x36441),x36442)))) % 167.75/167.49 [3661]E(f328(f307(a1,a872,a108),f299(a1,f328(f104(a1),x36611),f328(f104(a1),x36612))),f299(a872,x36611,x36612)) % 167.75/167.49 [3671]E(f189(a872,f2(a872),f5(a872),f328(f328(f22(a872),x36711),x36712)),f328(f328(f22(a872),x36711),f328(a116,x36712))) % 167.75/167.49 [3672]E(f328(a108,f328(f328(f22(a1),x36721),f328(f328(f80(a1),x36722),f78(a1)))),f328(f39(a1),f302(a1,x36722,x36721))) % 167.75/167.49 [3708]E(f328(f328(f151(a872,a872),a116),f136(a872,f328(f298(a872,x37081),x37082))),f136(a872,f328(f298(a872,f328(a116,x37081)),f328(a116,x37082)))) % 167.75/167.49 [3715]E(f328(f170(a1),f177(f328(f328(f80(a1),x37151),f78(a1)),f328(f328(f22(a1),x37152),f78(a1)))),f302(a1,x37151,x37152)) % 167.75/167.49 [3726]P1(f328(f328(f242(f879(x37261,a867)),f192(f879(x37261,a867))),x37262)) % 167.75/167.49 [3731]E(f85(x37311,f328(f328(f7(x37311,x37311,a867),a325),x37312)),x37312) % 167.75/167.49 [3732]E(f90(x37321,f328(f328(f7(x37321,x37321,a867),a325),x37322)),x37322) % 167.75/167.49 [3736]E(f328(f170(a872),f136(a872,f328(f298(a872,f328(a116,x37361)),f328(a116,x37362)))),f301(a872,x37361,x37362)) % 167.75/167.49 [3761]E(f328(f328(f265(x37611,x37612),f251(f879(x37611,a867))),f328(f16(f879(x37612,a867),x37611),f251(f879(x37612,a867)))),f251(f879(f878(x37611,x37612),a867))) % 167.75/167.49 [3796]E(f328(f248(x37961),f328(f328(f8(a867,a867,x37961),a323),x37962)),f328(f79(f879(x37961,a867)),f328(f248(x37961),x37962))) % 167.75/167.49 [3799]E(f328(f248(x37991),f328(f328(f7(x37991,x37991,a867),a325),x37992)),f328(f328(f306(x37991),x37992),f192(f879(x37991,a867)))) % 167.75/167.49 [3806]E(f328(f328(f80(a1),f328(f328(f22(a1),x38061),x38062)),f328(f328(f22(a1),x38061),x38062)),f328(f328(f22(a1),f328(f328(f80(a1),x38061),x38061)),f328(f328(f80(a1),x38062),x38062))) % 167.75/167.49 [3807]E(f328(f328(f80(a1),f328(f328(f80(a1),x38071),x38071)),f328(f328(f80(a1),x38072),x38072)),f328(f328(f80(a1),f328(f328(f80(a1),x38071),x38072)),f328(f328(f80(a1),x38071),x38072))) % 167.75/167.49 [3823]P1(f328(f328(f242(a872),f328(f39(x38231),f328(f170(x38231),x38232))),f328(f193(f873(x38231)),x38232))) % 167.75/167.49 [3824]P1(f328(f328(f242(a872),f328(f193(f873(x38241)),f149(x38241,x38242))),f328(f193(f873(x38241)),x38242))) % 167.75/167.49 [3834]E(f328(f248(x38341),f328(f328(f7(x38341,f879(x38341,a867),a867),f330(x38341)),x38342)),x38342) % 167.75/167.49 [3850]E(f328(f328(f173(x38501),f328(f328(f22(a872),f328(f193(f873(x38501)),x38502)),f78(a872))),x38502),f118(x38501,x38502)) % 167.75/167.49 [3873]E(f189(a872,f2(a872),f328(f328(f8(a872,a872,a872),a116),f328(f240(a872),x38731)),x38732),f328(f328(f240(a872),f328(a116,x38731)),x38732)) % 167.75/167.49 [3877]E(f41(f879(x38771,a867),f328(f307(f879(f878(x38771,x38771),a867),f879(x38771,a867),f281(x38771)),x38772)),f328(f281(x38771),f41(f879(f878(x38771,x38771),a867),x38772))) % 167.75/167.49 [3878]E(f189(a872,f328(a116,x38781),f328(f328(f8(a872,a872,a872),a116),f328(f241(a872),x38781)),x38782),f328(f328(f241(a872),f328(a116,x38781)),x38782)) % 167.75/167.49 [3880]E(f328(f328(f263(a1,a1),f328(f328(f40(a1),f328(f75(a1),x38801)),f328(f75(a1),x38802))),f46(a1,f328(f75(a1),x38801),f328(f75(a1),x38802))),f54(x38801,x38802)) % 167.75/167.49 [3903]P1(f328(f328(f242(f879(f879(x39031,a867),a867)),x39032),f328(f305(x39031),f41(f879(x39031,a867),x39032)))) % 167.75/167.49 [3937]E(f328(f328(f44(x39371,f879(x39371,a867)),x39372),f328(f328(f7(x39371,f879(x39371,a867),f879(x39371,a867)),f306(x39371)),f192(f879(x39371,a867)))),x39372) % 167.75/167.49 [3938]E(f328(f328(f285(x39381,x39381,x39381),f328(f283(x39381,x39381),x39382)),f304(x39381,f328(f283(x39381,x39381),x39382))),f328(f283(x39381,x39381),f328(f328(f285(x39381,x39381,x39381),x39382),f304(x39381,x39382)))) % 167.75/167.49 [4007]E(f328(f170(x40071),f328(f139(f873(x40071),f873(x40071),f125(x40071),f117(x40071)),x40072)),f328(f328(f44(f873(x40071),f879(x40071,a867)),f328(f170(f873(x40071)),x40072)),f170(x40071))) % 167.75/167.49 [4039]E(f328(f328(f114(f879(f878(x40391,x40391),a867)),f304(x40391,f192(f879(f878(x40391,x40391),a867)))),f328(f328(f285(x40391,x40391,x40391),f304(x40391,x40392)),x40392)),f304(x40391,x40392)) % 167.75/167.49 [4073]E(f328(f328(f180(x40731,x40731),x40732),x40732),f328(f328(f151(x40731,f878(x40731,x40731)),f328(f328(f18(x40731,x40731,f878(x40731,x40731)),f263(x40731,x40731)),f5(x40731))),x40732)) % 167.75/167.49 [4189]E(f328(f139(a872,f873(x41891),f328(f7(f873(x41891),a872,a872),f328(f328(f8(a872,f879(a872,a872),f873(x41891)),f241(a872)),f193(f873(x41891)))),f2(a872)),f328(f166(f873(x41891)),x41892)),f328(f193(f873(f873(x41891))),f178(x41891,x41892))) % 167.75/167.49 [4267]E(f328(f328(f284(f878(a872,f873(x42671)),f873(x42671)),f321(a872,f873(x42671),a247,f142(x42671,x42672))),f328(f328(f18(f873(x42671),f873(x42671),f878(a872,f873(x42671))),f328(f328(f8(a872,f879(f873(x42671),f878(a872,f873(x42671))),f873(x42671)),f263(a872,f873(x42671))),f193(f873(x42671)))),f5(f873(x42671)))),f143(x42671,x42672)) % 167.75/167.49 [4397]E(f328(f248(x43971),f328(f328(f8(f879(f879(x43971,a867),a867),a867,x43971),f88(f879(x43971,a867))),f328(f328(f8(f879(f879(x43971,a867),a867),f879(f879(x43971,a867),a867),x43971),f328(f18(f879(x43971,a867),a867,a867),f328(f328(f8(a867,f879(a867,a867),f879(x43971,a867)),a331),f328(f328(f7(f879(x43971,a867),f879(f879(x43971,a867),a867),a867),f330(f879(x43971,a867))),x43972)))),f330(x43971)))),f42(f879(x43971,a867),x43972)) % 167.75/167.49 [4540]~P1(f328(f328(f243(a1),f328(f104(a1),x45401)),f328(f79(a1),f328(f104(a1),x45402)))) % 167.75/167.49 [4556]~P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x45561),x45561)),a101)),f328(f328(f80(a1),x45562),x45562))) % 167.75/167.49 [3471]E(f328(f328(f22(a872),f328(f328(f80(a872),x34711),x34712)),x34712),x34711) % 167.75/167.49 [3472]E(f328(f328(f22(a872),f328(f328(f80(a872),x34721),x34722)),x34721),x34722) % 167.75/167.49 [3539]E(f328(f328(f80(a872),f328(f328(f22(a872),x35391),x35392)),x35392),f328(f328(f241(a872),x35391),x35392)) % 167.75/167.49 [3647]E(f328(f328(f81(a872),f328(f328(f40(a872),x36471),x36472)),x36472),f328(f328(f22(a872),x36471),f46(a872,x36471,x36472))) % 167.75/167.49 [3676]E(f328(f170(a872),f136(a872,f328(f298(a872,f328(a116,x36761)),x36762))),f302(a872,x36761,x36762)) % 167.75/167.49 [3683]E(f328(f104(a1),f223(f328(a108,f328(f75(a1),x36831)),f328(a108,f328(f75(a1),x36832)))),f328(f328(a224,x36831),x36832)) % 167.75/167.49 [3685]E(f328(f328(f114(f879(x36851,a867)),f328(f79(f879(x36851,a867)),x36852)),x36852),f251(f879(x36851,a867))) % 167.75/167.49 [3686]E(f328(f328(f105(f879(x36861,a867)),f328(f79(f879(x36861,a867)),x36862)),x36862),f192(f879(x36861,a867))) % 167.75/167.49 [3704]P1(f328(f328(f242(a872),f328(f328(f22(a872),x37041),x37042)),x37041)) % 167.75/167.49 [3705]P1(f328(f328(f242(a872),f328(f328(f40(a872),x37051),x37052)),x37051)) % 167.75/167.49 [3728]P1(f328(f328(f243(a872),x37281),f328(a116,f328(f328(f80(a872),x37282),x37281)))) % 167.75/167.49 [3729]P1(f328(f328(f243(a872),x37291),f328(a116,f328(f328(f80(a872),x37291),x37292)))) % 167.75/167.49 [3747]E(f328(f328(f81(a872),f328(a108,f328(f75(a1),x37471))),f328(a108,f328(f75(a1),x37472))),f328(a108,f328(f75(a1),f328(f328(f81(a1),x37471),x37472)))) % 167.75/167.49 [3757]P1(f328(f328(f242(a1),f2(a1)),f328(f328(f253(a1),f328(f75(a1),x37571)),x37572))) % 167.75/167.49 [3828]E(f328(f282(f873(x38281),f873(x38281),f155(x38281,x38282)),f328(f328(f306(f873(x38281)),f117(x38281)),f192(f879(f873(x38281),a867)))),f328(f328(f306(f873(x38281)),f117(x38281)),f192(f879(f873(x38281),a867)))) % 167.75/167.49 [3848]E(f328(f328(f114(f879(f878(x38481,x38481),a867)),f304(x38481,x38482)),f304(x38481,f192(f879(f878(x38481,x38481),a867)))),f304(x38481,x38482)) % 167.75/167.49 [3863]E(f328(f328(f40(a1),f328(f107(a1),f328(f328(f80(a1),x38631),x38631))),f328(f107(a1),f328(f328(f80(a1),x38632),x38632))),f328(f328(f40(a1),f328(f107(a1),x38631)),f328(f107(a1),x38632))) % 167.75/167.49 [3927]E(f328(f328(f253(a1),x39271),f328(f107(a872),f328(f328(f80(a1),x39272),x39272))),f328(f328(f86(a1,a1),f328(f328(f253(a1),x39271),f328(f107(a872),x39272))),f328(f328(f18(a1,a1,a1),f81(a1)),f5(a1)))) % 167.75/167.49 [3933]E(f328(f248(f879(x39331,a867)),f328(f328(f7(f879(x39331,a867),f879(x39331,a867),a867),f242(f879(x39331,a867))),x39332)),f328(f305(x39331),x39332)) % 167.75/167.49 [3948]E(f328(f328(f151(a1,a872),a108),f328(f328(f125(a1),f328(f328(f151(a872,a1),f104(a1)),x39481)),f328(f328(f151(a872,a1),f104(a1)),x39482))),f328(f328(f125(a872),x39481),x39482)) % 167.75/167.49 [3983]E(f328(f307(a1,a1,f328(f328(f7(a1,a1,a1),f80(a1)),x39831)),f328(f298(a1,f2(a1)),f328(f328(f22(a1),x39832),x39831))),f328(f298(a1,x39831),x39832)) % 167.75/167.49 [3985]P42(x39851,f328(f328(f22(f879(f878(x39851,x39851),a867)),x39852),f304(x39851,f192(f879(f878(x39851,x39851),a867))))) % 167.75/167.49 [4005]E(f328(f193(f873(x40051)),f328(f139(f873(x40051),f873(x40051),f125(x40051),f117(x40051)),x40052)),f328(f163(a872),f328(f328(f151(f873(x40051),a872),f193(f873(x40051))),x40052))) % 167.75/167.49 [4010]P40(x40101,f251(f879(x40101,a867)),f328(f328(f114(f879(f878(x40101,x40101),a867)),x40102),f304(x40101,f192(f879(f878(x40101,x40101),a867))))) % 167.75/167.49 [4053]E(f189(a872,f2(a872),f328(f328(f8(a872,a872,a872),a116),f328(f328(f7(a872,a872,a872),f240(a872)),x40531)),x40532),f328(f328(f240(a872),x40532),f328(a116,x40531))) % 167.75/167.49 [4056]E(f189(a872,f328(a116,x40561),f328(f328(f8(a872,a872,a872),a116),f328(f328(f7(a872,a872,a872),f241(a872)),x40561)),x40562),f328(f328(f241(a872),x40562),f328(a116,x40561))) % 167.75/167.49 [4059]E(f328(f307(x40591,f873(x40591),f328(f328(f7(x40591,f873(x40591),f873(x40591)),f148(x40591)),f117(x40591))),x40592),f172(x40591,x40592,f328(f328(f306(f873(x40591)),f117(x40591)),f192(f879(f873(x40591),a867))))) % 167.75/167.49 [4060]E(f328(f328(f114(f879(f878(x40601,x40601),a867)),f328(f328(f285(x40601,x40601,x40601),x40602),f304(x40601,x40602))),f304(x40601,f192(f879(f878(x40601,x40601),a867)))),f304(x40601,x40602)) % 167.75/167.49 [4068]P1(f328(f328(f242(f879(f878(x40681,x40681),a867)),f260(x40681,x40682)),f328(f328(f265(x40681,x40681),x40682),f328(f16(f879(x40681,a867),x40681),x40682)))) % 167.75/167.49 [4071]E(f328(f307(a1,a872,a108),f328(f328(f114(f879(a1,a867)),f328(f307(a872,a1,f104(a1)),x40711)),f328(f307(a872,a1,f104(a1)),x40712))),f328(f328(f114(f879(a872,a867)),x40711),x40712)) % 167.75/167.49 [4072]E(f328(f307(a1,a872,a108),f328(f328(f105(f879(a1,a867)),f328(f307(a872,a1,f104(a1)),x40721)),f328(f307(a872,a1,f104(a1)),x40722))),f328(f328(f105(f879(a872,a867)),x40721),x40722)) % 167.75/167.49 [4076]E(f328(f248(x40761),f328(f328(f8(a867,a867,x40761),a323),f328(f328(f7(x40761,f879(x40761,a867),a867),f330(x40761)),x40762))),f328(f79(f879(x40761,a867)),x40762)) % 167.75/167.49 [4103]E(f328(f139(f873(x41031),f873(x41031),f125(x41031),f117(x41031)),f328(f328(f151(f873(x41031),f873(x41031)),f166(x41031)),f328(f166(f873(x41031)),x41032))),f328(f166(x41031),f328(f139(f873(x41031),f873(x41031),f125(x41031),f117(x41031)),x41032))) % 167.75/167.49 [4132]E(f328(f328(f44(a872,f879(f878(x41321,x41321),a867)),f251(f879(a872,a867))),f328(f328(f7(a872,f879(f878(x41321,x41321),a867),f879(f878(x41321,x41321),a867)),f187(f878(x41321,x41321),a867)),x41322)),f304(x41321,x41322)) % 167.75/167.49 [4152]E(f85(x41521,f328(f328(f8(f879(x41521,a867),a867,x41521),f328(a325,x41522)),f328(f328(f7(x41521,f879(x41521,a867),f879(x41521,a867)),f306(x41521)),f192(f879(x41521,a867))))),f309(x41521,x41522)) % 167.75/167.49 [4160]E(f328(f193(f873(x41601)),f149(x41601,f328(f139(f873(x41601),f873(x41601),f125(x41601),f117(x41601)),x41602))),f328(f39(x41601),f328(f328(f44(f873(x41601),f879(x41601,a867)),f328(f170(f873(x41601)),x41602)),f170(x41601)))) % 167.75/167.49 [4176]E(f328(f328(f114(f879(f878(x41761,x41761),a867)),x41762),f328(f328(f285(x41761,x41761,x41761),f328(f328(f285(x41761,x41761,x41761),x41762),f304(x41761,x41762))),x41762)),f328(f328(f285(x41761,x41761,x41761),x41762),f304(x41761,x41762))) % 167.75/167.49 [4199]P1(f328(f328(f242(f879(f878(x41991,x41991),a867)),f328(f328(f285(x41991,x41991,x41991),x41992),f304(x41991,x41992))),f328(f328(f265(x41991,x41991),f328(f281(x41991),x41992)),f328(f16(f879(x41991,a867),x41991),f328(f281(x41991),x41992))))) % 167.75/167.49 [4242]E(f328(f248(f873(x42421)),f328(f328(f7(f873(x42421),f879(x42421,a867),a867),f328(f328(f8(f879(x42421,a867),f879(f879(x42421,a867),a867),f873(x42421)),f242(f879(x42421,a867))),f170(x42421))),x42422)),f158(x42421,x42422)) % 167.75/167.49 [4254]E(f328(f153(f873(x42541),x42541,f117(x42541),f328(f328(f8(f873(x42541),f879(f873(x42541),f873(x42541)),x42541),f328(f7(f873(x42541),f873(x42541),f873(x42541)),f125(x42541))),f328(f328(f7(x42541,f873(x42541),f873(x42541)),f148(x42541)),f117(x42541)))),x42542),f328(f165(x42541),x42542)) % 167.75/167.49 [4296]P26(f879(x42961,x42962),f879(f878(x42961,x42962),a867),f328(f328(f8(f879(f878(x42961,x42962),a867),f879(f878(x42961,x42962),a867),f879(x42961,x42962)),f248(f878(x42961,x42962))),f328(f328(f8(f879(x42961,f879(x42962,a867)),f879(f878(x42961,x42962),a867),f879(x42961,x42962)),f267(x42961,x42962,a867)),f328(f8(x42962,f879(x42962,a867),x42961),f328(f7(x42962,x42962,a867),a325)))),f251(f879(f879(x42961,x42962),a867))) % 167.75/167.49 [4301]E(f46(a1,f328(f107(a1),f328(f328(f80(a1),x43011),x43011)),f328(f107(a1),f328(f328(f80(a1),x43012),x43012))),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f46(a1,f328(f107(a1),x43011),f328(f107(a1),x43012)))) % 167.75/167.49 [4344]E(f328(f328(f44(x43441,f879(f878(x43441,x43441),a867)),x43442),f328(f328(f7(x43441,f879(f878(x43441,x43441),a867),f879(f878(x43441,x43441),a867)),f328(f328(f8(f878(x43441,x43441),f879(f879(f878(x43441,x43441),a867),f879(f878(x43441,x43441),a867)),x43441),f306(f878(x43441,x43441))),f328(f328(f18(x43441,x43441,f878(x43441,x43441)),f263(x43441,x43441)),f5(x43441)))),f192(f879(f878(x43441,x43441),a867)))),f260(x43441,x43442)) % 167.75/167.49 [4352]E(f210(x43521,f328(f328(f263(a1,a1),f328(f79(a1),f328(f328(f73(f878(a1,a1),a1,x43521,f262(a1,a1)),f219(x43521)),x43522))),f328(f328(f73(f878(a1,a1),a1,x43521,f266(a1,a1)),f219(x43521)),x43522))),f227(x43521,x43522)) % 167.75/167.49 [4434]E(f328(f248(f879(x44341,a867)),f328(f328(f8(f879(f879(x44341,a867),a867),a867,f879(x44341,a867)),f87(f879(x44341,a867))),f328(f328(f7(f879(x44341,a867),f879(f879(x44341,a867),a867),f879(f879(x44341,a867),a867)),f328(f328(f8(f879(f879(x44341,a867),f879(a867,a867)),f879(f879(f879(x44341,a867),a867),f879(f879(x44341,a867),a867)),f879(x44341,a867)),f18(f879(x44341,a867),a867,a867)),f328(f328(f8(f879(f879(x44341,a867),a867),f879(f879(x44341,a867),f879(a867,a867)),f879(x44341,a867)),f328(f8(a867,f879(a867,a867),f879(x44341,a867)),a326)),f328(f328(f7(f879(x44341,a867),f879(f879(x44341,a867),f879(x44341,a867)),f879(f879(x44341,a867),a867)),f328(f328(f8(f879(f879(x44341,a867),a867),f879(f879(f879(x44341,a867),f879(x44341,a867)),f879(f879(x44341,a867),a867)),f879(x44341,a867)),f8(f879(x44341,a867),a867,f879(x44341,a867))),a325)),f79(f879(x44341,a867)))))),f328(f328(f8(f879(f879(x44341,a867),a867),a867,f879(x44341,a867)),f328(f330(f879(x44341,a867)),x44342)),f305(x44341))))),f328(f305(x44341),f328(f79(f879(x44341,a867)),x44342))) % 167.75/167.49 [4537]~E(f328(f328(f80(a1),x45371),x45371),f328(f328(f22(a1),f328(f328(f80(a1),x45372),x45372)),a101)) % 167.75/167.49 [4543]~P1(f328(f328(f243(a872),f328(f328(f80(a872),x45431),x45432)),x45432)) % 167.75/167.49 [4544]~P1(f328(f328(f243(a872),f328(f328(f80(a872),x45441),x45442)),x45441)) % 167.75/167.49 [3762]E(f328(f328(f22(a872),x37621),f328(f328(f81(a872),f328(f328(f40(a872),x37621),x37622)),x37622)),f46(a872,x37621,x37622)) % 167.75/167.49 [3763]E(f328(f328(f22(a1),x37631),f328(f328(f81(a1),f328(f328(f40(a1),x37631),x37632)),x37632)),f46(a1,x37631,x37632)) % 167.75/167.49 [3797]E(f328(f328(f151(a872,x37971),f328(f162(x37971),x37972)),f136(a872,f328(f298(a872,f2(a872)),f328(f193(f873(x37971)),x37972)))),x37972) % 167.75/167.49 [3859]E(f328(f282(x38591,x38591,f304(x38591,f192(f879(f878(x38591,x38591),a867)))),x38592),x38592) % 167.75/167.49 [3988]E(f304(x39881,f328(f328(f114(f879(f878(x39881,x39881),a867)),x39882),f304(x39881,f192(f879(f878(x39881,x39881),a867))))),f304(x39881,x39882)) % 167.75/167.49 [3989]E(f304(x39891,f328(f328(f22(f879(f878(x39891,x39891),a867)),x39892),f304(x39891,f192(f879(f878(x39891,x39891),a867))))),f304(x39891,x39892)) % 167.75/167.49 [4042]E(f328(f328(f22(a1),f328(f328(f22(a1),f328(f328(f80(a1),x40421),x40421)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x40422),x40422)),a101)),f328(f328(f80(a1),f328(f328(f22(a1),x40421),x40422)),f328(f328(f22(a1),x40421),x40422))) % 167.75/167.49 [4081]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f80(a1),x40811),x40812)),f328(f328(f80(a1),x40811),x40812))),a101),f328(f328(f80(a1),f328(f328(f80(a1),x40811),x40811)),f328(f328(f22(a1),f328(f328(f80(a1),x40812),x40812)),a101))) % 167.75/167.49 [4107]E(f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),x41071),x41071)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x41072),x41072)),a101)),f328(f328(f80(a1),f328(f328(f80(a1),x41071),f328(f328(f22(a1),x41072),a101))),f328(f328(f80(a1),x41071),f328(f328(f22(a1),x41072),a101)))) % 167.75/167.49 [4117]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),x41171),x41172)),f328(f328(f22(a1),x41171),x41172))),a101),f328(f328(f22(a1),f328(f328(f22(a1),f328(f328(f80(a1),x41171),x41171)),a101)),f328(f328(f80(a1),x41172),x41172))) % 167.75/167.49 [4118]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f80(a1),x41181),x41182)),f328(f328(f80(a1),x41181),x41182))),a101),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),x41181),x41181)),a101)),f328(f328(f80(a1),x41182),x41182))) % 167.75/167.49 [4173]E(f328(f104(a1),f328(f328(f40(a872),f328(f328(f81(a872),f328(a108,f328(f75(a1),x41731))),f328(a108,f328(f75(a1),x41732)))),f223(f328(a108,f328(f75(a1),x41731)),f328(a108,f328(f75(a1),x41732))))),f225(x41731,x41732)) % 167.75/167.49 [4219]E(f328(f328(f269(f878(a103,a103),a103,f878(a103,a103),f878(x42191,f878(a103,a103))),f273(f328(a3,f328(f193(f873(x42191)),x42192)))),f328(f328(f8(x42191,f879(f878(a103,a103),f878(x42191,f878(a103,a103))),a103),f263(x42191,f878(a103,a103))),f328(f328(f8(a872,x42191,a103),f328(f162(x42191),x42192)),a19))),f279(x42191,x42192)) % 167.75/167.49 [4302]E(f328(f139(a872,f873(x43021),f328(f7(f873(x43021),a872,a872),f328(f328(f8(a872,f879(a872,a872),f873(x43021)),f241(a872)),f193(f873(x43021)))),f2(a872)),f328(f166(f873(x43021)),f178(x43021,x43022))),f328(f193(f873(f873(x43021))),f328(f133(f873(x43021),f328(f328(f8(a867,a867,f873(x43021)),a323),f328(f328(f7(f873(x43021),f873(x43021),a867),a325),f117(x43021)))),x43022))) % 167.75/167.49 [4308]E(f328(f328(f44(a872,f879(x43081,a867)),f251(f879(a872,a867))),f328(f328(f7(a872,f879(a872,f879(x43081,a867)),f879(x43081,a867)),f328(f328(f8(f879(a872,a867),f879(f879(a872,f879(x43081,a867)),f879(x43081,a867)),a872),f44(a872,f879(x43081,a867))),f298(a872,f2(a872)))),x43082)),f328(f328(f44(a872,f879(x43081,a867)),f251(f879(a872,a867))),x43082)) % 167.75/167.49 [4328]P1(f328(f38(a872),f328(f248(a872),f328(f328(f18(a872,a867,a867),f328(f328(f8(a867,f879(a867,a867),a872),a326),x43281)),f328(f328(f7(a872,a872,a867),f243(a872)),x43282))))) % 167.75/167.49 [4445]E(f328(f248(f878(f873(x44451),f873(x44451))),f328(f267(f873(x44451),f873(x44451),a867),f328(f328(f18(f873(x44451),f879(f873(x44451),a867),f879(f873(x44451),a867)),f328(f328(f8(f879(f873(x44451),f879(a867,a867)),f879(f879(f873(x44451),a867),f879(f873(x44451),a867)),f873(x44451)),f18(f873(x44451),a867,a867)),f328(f328(f8(f879(f873(x44451),a867),f879(f873(x44451),f879(a867,a867)),f873(x44451)),f328(f8(a867,f879(a867,a867),f873(x44451)),a327)),f328(f328(f7(f873(x44451),f879(f873(x44451),a872),f879(f873(x44451),a867)),f328(f328(f8(f879(a872,a867),f879(f879(f873(x44451),a872),f879(f873(x44451),a867)),f873(x44451)),f8(a872,a867,f873(x44451))),f328(f328(f8(a872,f879(a872,a867),f873(x44451)),f243(a872)),f193(f873(x44451))))),f193(f873(x44451)))))),f328(f328(f18(f873(x44451),f879(f873(x44451),a867),f879(f873(x44451),a867)),f328(f328(f8(f879(f873(x44451),f879(a867,a867)),f879(f879(f873(x44451),a867),f879(f873(x44451),a867)),f873(x44451)),f18(f873(x44451),a867,a867)),f328(f328(f8(f879(f873(x44451),a867),f879(f873(x44451),f879(a867,a867)),f873(x44451)),f328(f8(a867,f879(a867,a867),f873(x44451)),a326)),f328(f328(f7(f873(x44451),f879(f873(x44451),a872),f879(f873(x44451),a867)),f328(f328(f8(f879(a872,a867),f879(f879(f873(x44451),a872),f879(f873(x44451),a867)),f873(x44451)),f8(a872,a867,f873(x44451))),f328(f328(f8(a872,f879(a872,a867),f873(x44451)),a325),f193(f873(x44451))))),f193(f873(x44451)))))),f328(f328(f7(f873(x44451),f879(f878(f873(x44451),f873(x44451)),a867),f879(f873(x44451),a867)),f328(f328(f8(f879(f873(x44451),f879(f879(f878(f873(x44451),f873(x44451)),a867),a867)),f879(f879(f878(f873(x44451),f873(x44451)),a867),f879(f873(x44451),a867)),f873(x44451)),f7(f873(x44451),f879(f878(f873(x44451),f873(x44451)),a867),a867)),f328(f328(f8(f879(f873(x44451),f878(f873(x44451),f873(x44451))),f879(f873(x44451),f879(f879(f878(f873(x44451),f873(x44451)),a867),a867)),f873(x44451)),f328(f8(f878(f873(x44451),f873(x44451)),f879(f879(f878(f873(x44451),f873(x44451)),a867),a867),f873(x44451)),f330(f878(f873(x44451),f873(x44451))))),f263(f873(x44451),f873(x44451))))),f142(x44451,x44452)))))),f143(x44451,x44452)) % 167.75/167.49 [4549]~P1(f328(f328(f91(a1),f328(f328(f80(a1),x45491),x45491)),f328(f328(f22(a1),f328(f328(f80(a1),x45492),x45492)),a101))) % 167.75/167.49 [4110]E(f328(f328(f80(a1),f328(f328(f80(a1),f328(f328(f81(a1),x41101),x41102)),f328(f328(f81(a1),x41101),x41102))),x41102),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f80(a1),x41101),x41101)),a101)),x41102)) % 167.75/167.49 [4217]E(f328(a108,f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x42171),x42172)),f192(f879(f878(a872,a872),a867)))))),f328(f328(f22(a872),x42171),x42172)) % 167.75/167.49 [4222]E(f328(f328(f285(x42221,x42221,x42221),f328(f328(f114(f879(f878(x42221,x42221),a867)),x42222),f304(x42221,f192(f879(f878(x42221,x42221),a867))))),f304(x42221,f328(f328(f114(f879(f878(x42221,x42221),a867)),x42222),f304(x42221,f192(f879(f878(x42221,x42221),a867)))))),f304(x42221,x42222)) % 167.75/167.49 [4260]E(f274(x42601,f328(f133(f878(a103,x42601),f328(f267(a103,x42601,a867),f328(f328(f8(a867,f879(x42601,a867),a103),f16(a867,x42601)),f328(f243(a103),f2(a103))))),x42602)),f274(x42601,x42602)) % 167.75/167.49 [4261]E(f272(x42611,f328(f133(f878(a103,x42611),f328(f267(a103,x42611,a867),f328(f328(f8(a867,f879(x42611,a867),a103),f16(a867,x42611)),f328(f243(a103),f2(a103))))),x42612)),f272(x42611,x42612)) % 167.75/167.49 [4263]E(f328(f79(a1),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x42631),x42632)),f192(f879(f878(a872,a872),a867)))))),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x42632),x42631)),f192(f879(f878(a872,a872),a867)))))) % 167.75/167.49 [4320]E(f328(f328(f284(f873(a872),x43201),f142(a872,a247)),f328(f328(f7(x43201,f873(f879(x43201,a872)),f873(a872)),f328(f328(f8(f879(f879(x43201,a872),a872),f879(f873(f879(x43201,a872)),f873(a872)),x43201),f151(f879(x43201,a872),a872)),f328(f7(f879(x43201,a872),x43201,a872),f5(f879(x43201,a872))))),x43202)),f150(x43201,x43202)) % 167.75/167.49 [4341]E(f328(f328(f86(a1,a872),f328(f107(a1),f328(f328(f80(a1),x43411),a101))),f328(f328(f18(a1,a872,a872),f328(f328(f7(a1,a872,f879(a872,a872)),f328(f328(f8(a867,f879(a872,f879(a872,a872)),a1),f100(a872)),a197)),f2(a872))),f328(f328(f8(a872,a872,a1),a116),f328(f328(f8(a872,a872,a1),f328(f240(a872),x43412)),a108)))),f328(f328(f240(a872),f328(a116,x43412)),f328(f107(a872),x43411))) % 167.75/167.49 [4342]E(f328(f328(f86(a1,a872),f328(f107(a1),f328(f328(f80(a1),x43421),a101))),f328(f328(f18(a1,a872,a872),f328(f328(f7(a1,a872,f879(a872,a872)),f328(f328(f8(a867,f879(a872,f879(a872,a872)),a1),f100(a872)),a197)),f328(a116,x43422))),f328(f328(f8(a872,a872,a1),a116),f328(f328(f8(a872,a872,a1),f328(f241(a872),x43422)),a108)))),f328(f328(f241(a872),f328(a116,x43422)),f328(f107(a872),x43421))) % 167.75/167.49 [4362]E(f328(f139(f873(x43621),f873(x43621),f125(x43621),f117(x43621)),f328(f328(f151(f873(x43621),f873(x43621)),f153(f873(x43621),x43621,f117(x43621),f328(f328(f8(f873(x43621),f879(f873(x43621),f873(x43621)),x43621),f16(f873(x43621),f873(x43621))),f328(f328(f7(x43621,f873(x43621),f873(x43621)),f148(x43621)),f117(x43621))))),x43622)),f328(f328(f151(f873(x43621),x43621),f138(x43621)),f328(f133(f873(x43621),f328(f328(f8(a867,a867,f873(x43621)),a323),f328(f328(f7(f873(x43621),f873(x43621),a867),a325),f117(x43621)))),x43622))) % 167.75/167.49 [4426]E(f328(f267(a1,a1,a867),f328(f328(f7(a1,f879(a1,a867),f879(a1,a867)),f328(f328(f8(f879(a1,f879(a867,a867)),f879(f879(a1,a867),f879(a1,a867)),a1),f18(a1,a867,a867)),f328(f328(f8(f879(a1,a867),f879(a1,f879(a867,a867)),a1),f328(f8(a867,f879(a867,a867),a1),a326)),f328(f328(f8(f879(a1,a1),f879(a1,a867),a1),f328(f8(a1,a867,a1),f328(a325,x44261))),f328(f328(f8(a1,f879(a1,a1),a1),f80(a1)),f328(f81(a1),x44262)))))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f328(f8(a867,a867,a1),f328(a331,f328(f328(f243(a1),f2(a1)),x44262))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),f2(a1)))),f328(f328(f7(a1,a1,a867),f243(a1)),x44262))))),f328(f328(f8(a867,a867,a1),f328(a331,f328(a323,f328(f328(f243(a1),f2(a1)),x44262)))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f243(a1),x44262))),f328(f328(f7(a1,a1,a867),f242(a1)),f2(a1))))))),f50(x44261,x44262)) % 167.75/167.49 [4428]E(f328(f248(x44281),f328(f328(f8(f879(a872,a867),a867,x44281),f87(a872)),f328(f328(f7(x44281,f879(a872,a867),f879(a872,a867)),f328(f328(f8(f879(a872,f879(a867,a867)),f879(f879(a872,a867),f879(a872,a867)),x44281),f18(a872,a867,a867)),f328(f328(f8(f879(a872,a867),f879(a872,f879(a867,a867)),x44281),f328(f8(a867,f879(a867,a867),a872),a326)),f328(f328(f7(x44281,f879(a872,x44281),f879(a872,a867)),f328(f328(f8(f879(x44281,a867),f879(f879(a872,x44281),f879(a872,a867)),x44281),f8(x44281,a867,a872)),a325)),f328(f162(x44281),x44282))))),f328(f328(f7(a872,a872,a867),f243(a872)),f328(f193(f873(x44281)),x44282))))),f328(f170(x44281),x44282)) % 167.75/167.49 [4232]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),x42321),a101)),x42322)),f328(f328(f22(a1),f328(f328(f80(a1),x42321),a101)),x42322))),a101),f328(f328(f22(a1),f328(f328(f80(a1),x42321),x42321)),f328(f328(f22(a1),f328(f328(f80(a1),x42322),x42322)),a101))) % 167.75/167.49 [4357]E(f328(f139(f873(f873(x43571)),f873(f873(x43571)),f125(f873(x43571)),f117(f873(x43571))),f328(f328(f151(f873(x43571),f873(f873(x43571))),f153(f873(f873(x43571)),x43571,f117(f873(x43571)),f328(f16(f879(f873(x43571),f873(f873(x43571))),x43571),f328(f328(f7(f873(x43571),f873(f873(x43571)),f873(f873(x43571))),f148(f873(x43571))),f117(f873(x43571)))))),x43572)),f328(f328(f151(f873(x43571),f873(x43571)),f169(x43571)),f328(f133(f873(x43571),f328(f328(f8(a867,a867,f873(x43571)),a323),f328(f328(f7(f873(x43571),f873(x43571),a867),a325),f117(x43571)))),x43572))) % 167.75/167.49 [4368]E(f328(f328(f86(a1,a872),f328(f107(a1),f328(f328(f80(a1),x43681),a101))),f328(f328(f18(a1,a872,a872),f328(f328(f7(a1,a872,f879(a872,a872)),f328(f328(f8(a867,f879(a872,f879(a872,a872)),a1),f100(a872)),a197)),f2(a872))),f328(f328(f8(a872,a872,a1),a116),f328(f328(f7(a1,a872,a872),f328(f328(f8(a872,f879(a872,a872),a1),f240(a872)),a108)),x43682)))),f328(f328(f240(a872),f328(f107(a872),x43681)),f328(a116,x43682))) % 167.75/167.49 [4369]E(f328(f328(f86(a1,a872),f328(f107(a1),f328(f328(f80(a1),x43691),a101))),f328(f328(f18(a1,a872,a872),f328(f328(f7(a1,a872,f879(a872,a872)),f328(f328(f8(a867,f879(a872,f879(a872,a872)),a1),f100(a872)),a197)),f328(a116,x43692))),f328(f328(f8(a872,a872,a1),a116),f328(f328(f7(a1,a872,a872),f328(f328(f8(a872,f879(a872,a872),a1),f241(a872)),a108)),x43692)))),f328(f328(f241(a872),f328(f107(a872),x43691)),f328(a116,x43692))) % 167.75/167.49 [4356]E(f328(f267(x43561,x43561,a867),f328(f328(f18(x43561,a867,f879(x43561,a867)),f328(f328(f8(f879(x43561,f879(a867,a867)),f879(a867,f879(x43561,a867)),x43561),f7(x43561,a867,a867)),f328(f328(f8(f879(x43561,a867),f879(x43561,f879(a867,a867)),x43561),f328(f8(a867,f879(a867,a867),x43561),a326)),a325))),x43562)),f260(x43561,x43562)) % 167.75/167.49 [4403]E(f328(f328(f40(a872),x44031),f328(f328(f80(a872),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x44032)),f328(f328(f40(a872),x44031),f328(a116,f328(a116,f328(a116,x44032))))) % 167.75/167.49 [4404]E(f46(a872,x44041,f328(f328(f80(a872),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x44042)),f46(a872,x44041,f328(a116,f328(a116,f328(a116,x44042))))) % 167.75/167.49 [4405]E(f46(a872,f328(f328(f80(a872),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x44051),x44052),f46(a872,f328(a116,f328(a116,f328(a116,x44051))),x44052)) % 167.75/167.49 [4419]E(f124(f328(x44191,f328(f328(f81(a103),f328(f107(a103),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x44192))),f328(f208(x44191),x44192)) % 167.75/167.49 [4420]E(f328(f328(f40(a872),f328(f328(f80(a872),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x44201)),x44202),f328(f328(f40(a872),f328(a116,f328(a116,f328(a116,x44201)))),x44202)) % 167.75/167.49 [4469]~E(f33(x44691,x44692),f328(a26,x44693)) % 167.75/167.49 [4470]~E(f32(x44701,x44702),f328(a26,x44703)) % 167.75/167.49 [4471]~E(f328(a26,x44711),f33(x44712,x44713)) % 167.75/167.49 [4472]~E(f328(a26,x44721),f32(x44722,x44723)) % 167.75/167.49 [4485]~E(f30(x44851,x44852,x44853),a24) % 167.75/167.49 [4486]~E(f29(x44861,x44862,x44863),a24) % 167.75/167.49 [3185]E(f328(f196(x31851,x31852),x31853),f122(x31851,x31852)) % 167.75/167.49 [3206]E(f328(f207(x32061,x32062),x32063),f328(f126(x32061),x32062)) % 167.75/167.49 [3284]E(f328(f328(f151(x32841,x32842),x32843),f117(x32841)),f117(x32842)) % 167.75/167.49 [3285]E(f328(f328(f206(x32851,x32852),x32853),f205(x32851)),f205(x32852)) % 167.75/167.49 [3325]E(f328(f188(x33251,x33252,x33253),f2(a872)),x33252) % 167.75/167.49 [3327]E(f328(f328(f180(x33271,x33272),x33273),f117(x33272)),f117(f878(x33271,x33272))) % 167.75/167.49 [3361]E(f85(x33611,f63(x33611,x33612,x33613)),f328(f64(x33611,x33612),x33613)) % 167.75/167.49 [3367]E(f252(x33671,x33672,f252(x33672,x33671,x33673)),x33673) % 167.75/167.49 [3387]E(f328(f166(x33871),f168(x33871,x33872,x33873)),f168(x33871,x33872,x33873)) % 167.75/167.49 [3416]E(f137(x34161,x34162,f149(x34161,x34163)),f149(x34161,f137(x34161,x34162,x34163))) % 167.75/167.49 [3435]E(f328(f262(f873(x34351),f873(x34351)),f164(x34351,x34352,x34353)),f328(f133(x34351,x34352),x34353)) % 167.75/167.49 [3481]E(f328(f328(f148(x34811),x34812),f168(x34811,x34813,x34812)),f168(x34811,f328(a116,x34813),x34812)) % 167.75/167.49 [3513]E(f189(x35131,x35132,x35133,f2(a872)),x35132) % 167.75/167.49 [3514]E(f17(x35141,x35142,x35143,f2(a103)),x35142) % 167.75/167.49 [3521]E(f160(x35211,x35212,x35213,f117(x35211)),f117(x35212)) % 167.75/167.49 [3522]E(f161(x35221,x35222,x35223,f117(x35221)),f117(x35222)) % 167.75/167.49 [3529]E(f328(f328(f162(x35291),f328(f328(f148(x35291),x35292),x35293)),f2(a872)),x35292) % 167.75/167.49 [3557]E(f61(x35571,x35572,f117(x35571),x35573),f117(f878(x35571,x35572))) % 167.75/167.49 [3578]P26(x35781,x35782,x35783,f192(f879(x35781,a867))) % 167.75/167.49 [3737]E(f328(f73(x37371,x37372,x37371,x37373),f34(x37371)),x37373) % 167.75/167.49 [3918]P1(f328(f328(f330(f878(x39181,x39181)),f328(f328(f263(x39181,x39181),x39182),x39182)),f304(x39181,x39183))) % 167.75/167.49 [4550]~P1(f328(f328(f330(f878(f873(x45501),f873(x45501))),f328(f328(f263(f873(x45501),f873(x45501)),x45502),f117(x45501))),f142(x45501,x45503))) % 167.75/167.49 [4551]~P1(f328(f328(f330(f878(f873(x45511),f873(x45511))),f328(f328(f263(f873(x45511),f873(x45511)),x45512),f117(x45511))),f144(x45511,x45513))) % 167.75/167.49 [4552]~P1(f328(f328(f330(f878(f873(x45521),f873(x45521))),f328(f328(f263(f873(x45521),f873(x45521)),x45522),f117(x45521))),f154(x45521,x45523))) % 167.75/167.49 [4553]~P1(f328(f328(f330(f878(f873(x45531),f873(x45531))),f328(f328(f263(f873(x45531),f873(x45531)),f117(x45531)),x45532)),f142(x45531,x45533))) % 167.75/167.49 [4554]~P1(f328(f328(f330(f878(f873(x45541),f873(x45541))),f328(f328(f263(f873(x45541),f873(x45541)),f117(x45541)),x45542)),f154(x45541,x45543))) % 167.75/167.49 [3259]E(f328(f328(f209(x32591),x32592),x32593),f210(x32591,f222(x32592,x32593))) % 167.75/167.49 [3314]E(f328(f283(x33141,x33142),f328(f283(x33142,x33141),x33143)),x33143) % 167.75/167.49 [3337]E(f328(f328(f180(x33371,x33372),f117(x33371)),x33373),f117(f878(x33371,x33372))) % 167.75/167.49 [3340]E(f174(x33401,x33402,f328(f249(a872),x33403)),f328(f328(f173(x33401),x33403),x33402)) % 167.75/167.49 [3358]E(f149(x33581,f328(f133(x33581,x33582),x33583)),f328(f133(x33581,x33582),f149(x33581,x33583))) % 167.75/167.49 [3359]E(f328(f259(x33591,x33592),f328(f283(x33592,x33591),x33593)),f328(f261(x33592,x33591),x33593)) % 167.75/167.49 [3360]E(f328(f261(x33601,x33602),f328(f283(x33602,x33601),x33603)),f328(f259(x33602,x33601),x33603)) % 167.75/167.49 [3379]E(f328(f133(x33791,x33792),f328(f166(x33791),x33793)),f328(f166(x33791),f328(f133(x33791,x33792),x33793))) % 167.75/167.49 [3393]E(f328(f328(f135(x33931),x33932),f328(f169(x33931),x33933)),f328(f328(f135(x33931),f328(a116,x33932)),x33933)) % 167.75/167.49 [3411]E(f31(f29(x34111,x34112,x34113)),f328(f328(f80(a872),f31(x34113)),f328(a116,f2(a872)))) % 167.75/167.49 [3412]E(f328(f307(x34121,x34122,x34123),f192(f879(x34121,a867))),f192(f879(x34122,a867))) % 167.75/167.49 [3413]E(f328(f282(x34131,x34132,x34133),f192(f879(x34131,a867))),f192(f879(x34132,a867))) % 167.75/167.49 [3414]E(f328(f308(x34141,x34142,x34143),f192(f879(x34142,a867))),f192(f879(x34141,a867))) % 167.75/167.49 [3415]E(f328(f308(x34151,x34152,x34153),f251(f879(x34152,a867))),f251(f879(x34151,a867))) % 167.75/167.49 [3444]E(f328(f328(f306(x34441),x34442),f328(f170(x34441),x34443)),f328(f170(x34441),f137(x34441,x34442,x34443))) % 167.75/167.49 [3456]E(f236(x34561,x34562,f328(f235(x34561),x34563)),f328(f328(f80(a872),f328(x34562,x34563)),f328(a116,f2(a872)))) % 167.75/167.49 [3533]E(f328(f193(a869),f29(x35331,x35332,x35333)),f328(f328(f80(a872),f328(f193(a869),x35333)),f328(a116,f2(a872)))) % 167.75/167.49 [3534]E(f328(f307(f878(x35341,x35342),x35342,f266(x35341,x35342)),x35343),f328(f259(x35341,x35342),x35343)) % 167.75/167.49 [3535]E(f328(f307(f878(x35351,x35352),x35351,f262(x35351,x35352)),x35353),f328(f261(x35351,x35352),x35353)) % 167.75/167.49 [3605]E(f328(f328(f263(x36051,x36052),f328(f262(x36051,x36052),x36053)),f328(f266(x36051,x36052),x36053)),x36053) % 167.75/167.49 [3612]E(f328(f193(f874(x36121)),f127(x36121,x36122,x36123)),f328(f328(f80(a872),f328(f193(f874(x36121)),x36123)),f328(a116,f2(a872)))) % 167.75/167.49 [3615]E(f328(f328(f267(x36151,x36152,x36151),f16(x36151,x36152)),x36153),f328(f262(x36151,x36152),x36153)) % 167.75/167.49 [3635]E(f183(x36351,x36352,x36353,f328(f16(f876(x36352),x36351),f205(x36352))),x36353) % 167.75/167.49 [3636]E(f183(x36361,x36362,f328(f16(f876(x36362),x36361),f205(x36362)),x36363),x36363) % 167.75/167.49 [3692]E(f31(f30(x36921,x36922,x36923)),f328(f328(f80(a872),f328(f328(f80(a872),f31(x36922)),f31(x36923))),f328(a116,f2(a872)))) % 167.75/167.49 [3742]E(f328(f73(x37421,x37421,x37422,f34(x37421)),x37423),x37423) % 167.75/167.49 [3851]E(f328(f193(a869),f30(x38511,x38512,x38513)),f328(f328(f80(a872),f328(f328(f80(a872),f328(f193(a869),x38512)),f328(f193(a869),x38513))),f328(a116,f2(a872)))) % 167.75/167.49 [3928]P1(f328(f328(f242(f879(x39281,a867)),f328(f170(x39281),f328(f133(x39281,x39282),x39283))),f328(f170(x39281),x39283))) % 167.75/167.49 [3973]P1(f328(f328(f242(f879(x39731,a867)),f328(f170(x39731),f328(f328(f173(x39731),x39732),x39733))),f328(f170(x39731),x39733))) % 167.75/167.49 [3974]P1(f328(f328(f242(f879(x39741,a867)),f328(f170(x39741),f328(f328(f135(x39741),x39742),x39743))),f328(f170(x39741),x39743))) % 167.75/167.49 [3979]P1(f328(f328(f242(f879(x39791,a867)),f328(f170(x39791),f174(x39791,x39792,x39793))),f328(f170(x39791),x39792))) % 167.75/167.49 [3980]P1(f328(f328(f242(f879(x39801,a867)),f328(f170(x39801),f167(x39801,x39802,x39803))),f328(f170(x39801),x39803))) % 167.75/167.49 [4003]P26(f878(x40031,x40032),f878(x40032,x40031),f328(f267(x40031,x40032,f878(x40032,x40031)),f328(f7(x40032,x40031,f878(x40032,x40031)),f263(x40032,x40031))),x40033) % 167.75/167.49 [4015]E(f328(f328(f328(f187(f873(x40151),f873(x40151)),f46(a872,x40152,f328(f193(f873(x40151)),x40153))),f165(x40151)),x40153),f328(f328(f328(f187(f873(x40151),f873(x40151)),x40152),f165(x40151)),x40153)) % 167.75/167.49 [4057]P1(f328(f328(f330(f878(f873(x40571),f873(x40571))),f328(f328(f263(f873(x40571),f873(x40571)),x40572),x40572)),f155(x40571,f304(x40571,x40573)))) % 167.75/167.49 [4202]E(f85(f878(x42021,x42022),f328(f328(f18(f878(x42021,x42022),x42022,a867),f328(f328(f8(x42021,f879(x42022,a867),f878(x42021,x42022)),x42023),f262(x42021,x42022))),f266(x42021,x42022))),f85(f878(x42021,x42022),f328(f267(x42021,x42022,a867),x42023))) % 167.75/167.49 [4203]E(f90(f878(x42031,x42032),f328(f328(f18(f878(x42031,x42032),x42032,a867),f328(f328(f8(x42031,f879(x42032,a867),f878(x42031,x42032)),x42033),f262(x42031,x42032))),f266(x42031,x42032))),f90(f878(x42031,x42032),f328(f267(x42031,x42032,a867),x42033))) % 167.75/167.49 [4239]E(f328(f328(f284(f878(a872,x42391),x42391),f321(a872,x42391,a247,x42392)),f328(f328(f18(x42391,x42391,f878(a872,x42391)),f328(f328(f8(a872,f879(x42391,f878(a872,x42391)),x42391),f263(a872,x42391)),x42393)),f5(x42391))),f322(x42391,x42393,x42392)) % 167.75/167.49 [4304]E(f328(f268(x43041,x43041,x43042,x43042,f5(x43041),f5(x43042)),x43043),x43043) % 167.75/167.49 [4379]E(f328(f139(f873(f873(x43791)),f873(f873(x43791)),f125(f873(x43791)),f117(f873(x43791))),f328(f328(f151(f873(x43791),f873(f873(x43791))),f328(f328(f7(f873(x43791),f873(x43791),f873(f873(x43791))),f328(f328(f8(f879(x43791,f873(x43791)),f879(f873(x43791),f873(f873(x43791))),f873(x43791)),f151(x43791,f873(x43791))),f328(f7(x43791,f873(x43791),f873(x43791)),f148(x43791)))),x43792)),f56(x43791,x43793,x43792))),f56(x43791,f328(a116,x43793),x43792)) % 167.75/167.49 [4441]E(f328(f237(a872,f878(x44411,f874(x44411)),f2(a872),f328(f267(x44411,f874(x44411),a872),f328(f328(f7(x44411,a872,f879(f874(x44411),a872)),f328(f328(f8(f879(f874(x44411),f879(a872,a872)),f879(a872,f879(f874(x44411),a872)),x44411),f7(f874(x44411),a872,a872)),f328(f328(f8(f879(f874(x44411),a872),f879(f874(x44411),f879(a872,a872)),x44411),f328(f8(a872,f879(a872,a872),f874(x44411)),f80(a872))),f328(f328(f7(x44411,f879(f874(x44411),a872),f879(f874(x44411),a872)),f328(f328(f8(f879(a872,a872),f879(f879(f874(x44411),a872),f879(f874(x44411),a872)),x44411),f8(a872,a872,f874(x44411))),f328(f328(f8(a872,f879(a872,a872),x44411),f80(a872)),x44412))),f129(x44411,x44412))))),f78(a872)))),f328(f132(x44411),x44413)),f328(f129(x44411,x44412),x44413)) % 167.75/167.49 [4444]E(f328(f328(f86(a1,x44441),f225(f328(f328(f73(f878(a1,a1),a1,x44441,f266(a1,a1)),f219(x44441)),x44442),f328(f328(f73(f878(a1,a1),a1,x44441,f266(a1,a1)),f219(x44441)),x44443))),f328(f328(f18(a1,a1,x44441),f328(f328(f8(a1,f879(a1,x44441),a1),f209(x44441)),f328(f328(f18(a1,a1,a1),f328(f328(f8(a1,f879(a1,a1),a1),f80(a1)),f328(f328(f8(a1,a1,a1),f328(f81(a1),f328(f328(f73(f878(a1,a1),a1,x44441,f262(a1,a1)),f219(x44441)),x44442))),f328(f328(f7(a1,a1,a1),f40(a1)),f328(f328(f73(f878(a1,a1),a1,x44441,f266(a1,a1)),f219(x44441)),x44442))))),f328(f328(f8(a1,a1,a1),f328(f81(a1),f328(f328(f73(f878(a1,a1),a1,x44441,f262(a1,a1)),f219(x44441)),x44443))),f328(f328(f7(a1,a1,a1),f40(a1)),f328(f328(f73(f878(a1,a1),a1,x44441,f266(a1,a1)),f219(x44441)),x44443)))))),f5(a1))),f230(x44441,x44442,x44443)) % 167.75/167.49 [4481]~E(f328(f328(f148(x44811),x44812),x44813),x44813) % 167.75/167.49 [4488]~E(f328(f328(f148(x44881),x44882),x44883),f117(x44881)) % 167.75/167.49 [4504]~E(f328(f328(f306(x45041),x45042),x45043),f192(f879(x45041,a867))) % 167.75/167.49 [4527]~E(f328(f307(x45271,f879(x45271,a867),x45272),x45273),f328(f305(x45271),x45273)) % 167.75/167.49 [3319]E(f328(f328(f156(x33191,f117(x33191)),x33192),x33193),f117(x33191)) % 167.75/167.49 [3320]E(f328(f138(x33201),f328(f328(f148(x33201),x33202),x33203)),x33202) % 167.75/167.49 [3321]E(f328(f169(x33211),f328(f328(f148(x33211),x33212),x33213)),x33213) % 167.75/167.49 [3366]E(f328(f328(f135(x33661),f78(a872)),f328(f328(f148(x33661),x33662),x33663)),x33663) % 167.75/167.49 [3400]E(f118(x34001,f328(f328(f135(x34001),x34002),x34003)),f328(f328(f135(x34001),x34002),f118(x34001,x34003))) % 167.75/167.49 [3402]E(f328(f328(f156(x34021,x34022),x34023),f328(f328(f162(x34021),x34022),x34023)),x34022) % 167.75/167.49 [3426]E(f328(f328(f306(x34261),x34262),f328(f328(f306(x34261),x34262),x34263)),f328(f328(f306(x34261),x34262),x34263)) % 167.75/167.49 [3437]E(f328(f328(f176(x34371,x34372),f117(f878(x34371,x34372))),x34373),f205(x34372)) % 167.75/167.49 [3440]E(f328(f328(f306(x34401),x34402),f328(f170(x34401),x34403)),f328(f170(x34401),f328(f328(f148(x34401),x34402),x34403))) % 167.75/167.49 [3442]E(f328(f328(f135(x34421),x34422),f328(f169(x34421),x34423)),f328(f169(x34421),f328(f328(f135(x34421),x34422),x34423))) % 167.75/167.49 [3453]E(f328(f328(f173(x34531),f78(a872)),f328(f328(f148(x34531),x34532),x34533)),f328(f328(f148(x34531),x34532),f117(x34531))) % 167.75/167.49 [3498]E(f328(f64(x34981,x34982),f328(f328(f306(x34981),x34983),f192(f879(x34981,a867)))),x34983) % 167.75/167.49 [3541]E(f328(f328(f80(a872),x35411),f328(f328(f80(a872),x35412),x35413)),f328(f328(f80(a872),x35412),f328(f328(f80(a872),x35411),x35413))) % 167.75/167.49 [3542]E(f328(f328(f80(a1),x35421),f328(f328(f80(a1),x35422),x35423)),f328(f328(f80(a1),x35422),f328(f328(f80(a1),x35421),x35423))) % 167.75/167.49 [3547]E(f328(f328(f265(x35471,x35472),f192(f879(x35471,a867))),x35473),f192(f879(f878(x35471,x35472),a867))) % 167.75/167.49 [3570]E(f328(f328(f114(f879(x35701,a867)),x35702),x35703),f328(f328(f114(f879(x35701,a867)),x35703),x35702)) % 167.75/167.49 [3571]E(f328(f328(f105(f879(x35711,a867)),x35712),x35713),f328(f328(f105(f879(x35711,a867)),x35713),x35712)) % 167.75/167.49 [3573]E(f328(f328(f125(x35731),x35732),f328(f328(f148(x35731),x35733),f117(x35731))),f328(f165(x35731),f328(f328(f148(x35731),x35733),x35732))) % 167.75/167.49 [3574]E(f328(f328(f125(x35741),f328(f166(x35741),x35742)),f328(f166(x35741),x35743)),f328(f166(x35741),f328(f328(f125(x35741),x35743),x35742))) % 167.75/167.49 [3584]E(f328(f169(x35841),f328(f328(f173(x35841),f328(a116,x35842)),x35843)),f328(f328(f173(x35841),x35842),f328(f169(x35841),x35843))) % 167.75/167.49 [3591]P1(f328(f328(f330(x35911),x35912),f328(f328(f306(x35911),x35912),x35913))) % 167.75/167.49 [3595]E(f328(f328(f43(x35951,f879(x35952,a867)),f192(f879(x35951,a867))),x35953),f251(f879(x35952,a867))) % 167.75/167.49 [3598]E(f328(f282(x35981,x35981,f260(x35981,x35982)),x35983),f328(f328(f105(f879(x35981,a867)),x35982),x35983)) % 167.75/167.49 [3611]E(f328(f193(f873(x36111)),f328(f328(f148(x36111),x36112),x36113)),f328(f328(f80(a872),f328(f193(f873(x36111)),x36113)),f328(a116,f2(a872)))) % 167.75/167.49 [3617]E(f118(x36171,f328(f328(f125(x36171),x36172),f328(f328(f148(x36171),x36173),f117(x36171)))),x36172) % 167.75/167.49 [3618]E(f141(x36181,f328(f328(f125(x36181),x36182),f328(f328(f148(x36181),x36183),f117(x36181)))),x36183) % 167.75/167.49 [3624]E(f328(f328(f125(x36241),f328(f328(f173(x36241),x36242),x36243)),f328(f328(f135(x36241),x36242),x36243)),x36243) % 167.75/167.49 [3633]E(f328(f328(f22(a872),f328(f328(f80(a872),x36331),x36332)),f328(f328(f80(a872),x36333),x36332)),f328(f328(f22(a872),x36331),x36333)) % 167.75/167.49 [3634]E(f328(f328(f22(a872),f328(f328(f80(a872),x36341),x36342)),f328(f328(f80(a872),x36341),x36343)),f328(f328(f22(a872),x36342),x36343)) % 167.75/167.49 [3641]E(f328(f328(f125(x36411),f328(f166(x36411),x36412)),f328(f328(f148(x36411),x36413),f117(x36411))),f328(f166(x36411),f328(f328(f148(x36411),x36413),x36412))) % 167.75/167.49 [3643]E(f328(f328(f80(a872),f328(f193(f873(x36431)),x36432)),f328(f193(f873(x36431)),x36433)),f328(f193(f873(x36431)),f328(f328(f125(x36431),x36432),x36433))) % 167.75/167.49 [3646]E(f328(f328(f80(a872),f328(f193(f873(x36461)),x36462)),f328(f193(f873(x36461)),x36463)),f328(f193(f873(x36461)),f171(x36461,x36462,x36463))) % 167.75/167.49 [3654]E(f328(f328(f114(f879(x36541,a867)),f328(f170(x36541),x36542)),f328(f170(x36541),x36543)),f328(f170(x36541),f328(f328(f125(x36541),x36542),x36543))) % 167.75/167.49 [3655]E(f46(a872,f328(f328(f81(a872),x36551),x36552),f328(f328(f81(a872),x36551),x36553)),f328(f328(f81(a872),x36551),f46(a872,x36552,x36553))) % 167.75/167.49 [3668]E(f328(f328(f173(x36681),f328(f328(f22(a872),x36682),f78(a872))),f328(f169(x36681),x36683)),f328(f169(x36681),f328(f328(f173(x36681),x36682),x36683))) % 167.75/167.49 [3673]E(f328(f328(f105(f879(x36731,a867)),x36732),f328(f79(f879(x36731,a867)),x36733)),f328(f328(f22(f879(x36731,a867)),x36732),x36733)) % 167.75/167.49 [3674]E(f328(f328(f22(f879(x36741,a867)),x36742),f328(f79(f879(x36741,a867)),x36743)),f328(f328(f105(f879(x36741,a867)),x36742),x36743)) % 167.75/167.49 [3696]E(f328(f328(f265(x36961,x36962),x36963),f328(f16(f879(x36962,a867),x36961),f192(f879(x36962,a867)))),f192(f879(f878(x36961,x36962),a867))) % 167.75/167.49 [3698]E(f328(f328(f22(a872),f328(f328(f81(a872),x36981),x36982)),f328(f328(f81(a872),x36981),x36983)),f328(f328(f81(a872),x36981),f328(f328(f22(a872),x36982),x36983))) % 167.75/167.49 [3699]E(f328(f328(f80(a872),f328(f328(f81(a872),x36991),x36992)),f328(f328(f81(a872),x36991),x36993)),f328(f328(f81(a872),x36991),f328(f328(f80(a872),x36992),x36993))) % 167.75/167.49 [3700]E(f328(f328(f22(a1),f328(f328(f81(a1),x37001),x37002)),f328(f328(f81(a1),x37001),x37003)),f328(f328(f81(a1),x37001),f328(f328(f22(a1),x37002),x37003))) % 167.75/167.49 [3701]E(f328(f328(f80(a1),f328(f328(f81(a1),x37011),x37012)),f328(f328(f81(a1),x37011),x37013)),f328(f328(f81(a1),x37011),f328(f328(f80(a1),x37012),x37013))) % 167.75/167.49 [3702]E(f328(f328(f81(a1),f328(f328(f253(a1),x37021),x37022)),f328(f328(f253(a1),x37021),x37023)),f328(f328(f253(a1),x37021),f328(f328(f80(a872),x37022),x37023))) % 167.75/167.49 [3716]E(f328(f328(f44(x37161,f879(x37162,a867)),x37163),f328(f16(f879(x37162,a867),x37161),f192(f879(x37162,a867)))),f192(f879(x37162,a867))) % 167.75/167.49 [3718]E(f46(a872,f328(f328(f81(a872),x37181),x37182),f328(f328(f81(a872),x37183),x37182)),f328(f328(f81(a872),f46(a872,x37181,x37183)),x37182)) % 167.75/167.49 [3722]E(f46(a1,f328(f328(f22(a1),x37221),f46(a1,x37222,x37223)),x37223),f46(a1,f328(f328(f22(a1),x37221),x37222),x37223)) % 167.75/167.49 [3723]E(f46(a1,f328(f328(f81(a1),x37231),f46(a1,x37232,x37233)),x37233),f46(a1,f328(f328(f81(a1),x37231),x37232),x37233)) % 167.75/167.49 [3724]P1(f328(f328(f242(f879(x37241,a867)),x37242),f328(f328(f306(x37241),x37243),x37242))) % 167.75/167.49 [3727]E(f328(f307(f878(x37271,x37272),x37271,f262(x37271,x37272)),f328(f170(f878(x37271,x37272)),x37273)),f182(x37271,x37272,f328(f176(x37271,x37272),x37273))) % 167.75/167.49 [3776]P1(f328(f38(x37761),f182(x37761,x37762,f328(f176(x37761,x37762),x37763)))) % 167.75/167.49 [3801]E(f328(f328(f43(f879(x38011,a867),f879(x38011,a867)),x38012),f328(f114(f879(x38011,a867)),x38013)),f328(f328(f114(f879(x38011,a867)),x38013),f42(f879(x38011,a867),x38012))) % 167.75/167.49 [3802]E(f328(f328(f44(f879(x38021,a867),f879(x38021,a867)),x38022),f328(f105(f879(x38021,a867)),x38023)),f328(f328(f105(f879(x38021,a867)),x38023),f41(f879(x38021,a867),x38022))) % 167.75/167.49 [3813]E(f328(f170(x38131),f328(f328(f328(f187(f873(x38131),f873(x38131)),x38132),f165(x38131)),x38133)),f328(f170(x38131),x38133)) % 167.75/167.49 [3817]E(f328(f328(f173(x38171),f328(f193(f873(x38171)),f175(x38171,x38172,x38173))),x38173),f175(x38171,x38172,x38173)) % 167.75/167.49 [3818]E(f182(x38181,x38182,f328(f328(f8(x38182,f876(x38182),x38181),f235(x38182)),x38183)),f251(f879(x38181,a867))) % 167.75/167.49 [3822]E(f328(f193(f873(x38221)),f328(f328(f328(f187(f873(x38221),f873(x38221)),x38222),f165(x38221)),x38223)),f328(f193(f873(x38221)),x38223)) % 167.75/167.49 [3825]E(f328(f328(f267(x38251,x38252,x38252),f328(f16(f879(x38252,x38252),x38251),f5(x38252))),x38253),f328(f266(x38251,x38252),x38253)) % 167.75/167.49 [3831]E(f46(a1,f328(f328(f22(a1),f46(a1,x38311,x38312)),x38313),x38312),f46(a1,f328(f328(f22(a1),x38311),x38313),x38312)) % 167.75/167.49 [3832]E(f46(a1,f328(f328(f253(a1),f46(a1,x38321,x38322)),x38323),x38322),f46(a1,f328(f328(f253(a1),x38321),x38323),x38322)) % 167.75/167.49 [3835]E(f328(f328(f44(f879(f878(x38351,x38352),a867),f879(x38352,a867)),x38353),f259(x38351,x38352)),f328(f259(x38351,x38352),f41(f879(f878(x38351,x38352),a867),x38353))) % 167.75/167.49 [3836]E(f328(f328(f44(f879(f878(x38361,x38362),a867),f879(x38361,a867)),x38363),f261(x38361,x38362)),f328(f261(x38361,x38362),f41(f879(f878(x38361,x38362),a867),x38363))) % 167.75/167.49 [3864]E(f328(f73(x38641,x38641,x38641,x38642),f328(f328(f187(x38641,x38641),x38643),x38642)),f328(f328(f187(x38641,x38641),f328(a116,x38643)),x38642)) % 167.75/167.49 [3874]E(f237(f876(x38741),x38742,f205(x38741),f328(f328(f8(x38741,f876(x38741),x38742),f235(x38741)),x38743)),f328(f206(x38742,x38741),x38743)) % 167.75/167.49 [3881]E(f328(f328(f135(x38811),f328(f328(f22(a872),f328(f193(f873(x38811)),x38812)),x38813)),f328(f166(x38811),x38812)),f328(f166(x38811),f328(f328(f173(x38811),x38813),x38812))) % 167.75/167.49 [3882]E(f328(f328(f173(x38821),f328(f328(f22(a872),f328(f193(f873(x38821)),x38822)),x38823)),f328(f166(x38821),x38822)),f328(f166(x38821),f328(f328(f135(x38821),x38823),x38822))) % 167.75/167.49 [3885]E(f328(f328(f80(a872),f328(f163(a872),f328(f328(f151(x38851,a872),x38852),x38853))),f328(f193(f873(x38851)),x38853)),f152(x38851,x38852,x38853)) % 167.75/167.49 [3904]E(f328(f165(x39041),f328(f328(f328(f187(f873(x39041),f873(x39041)),x39042),f165(x39041)),x39043)),f328(f328(f328(f187(f873(x39041),f873(x39041)),f328(a116,x39042)),f165(x39041)),x39043)) % 167.75/167.49 [3919]P1(f328(f328(f242(a872),f328(f193(f873(x39191)),f328(f133(x39191,x39192),x39193))),f328(f193(f873(x39191)),x39193))) % 167.75/167.49 [3936]E(f328(f328(f114(f879(f879(x39361,a867),a867)),f328(f305(x39361),x39362)),f328(f307(f879(x39361,a867),f879(x39361,a867),f328(f306(x39361),x39363)),f328(f305(x39361),x39362))),f328(f305(x39361),f328(f328(f306(x39361),x39363),x39362))) % 167.75/167.49 [3955]P25(x39551,x39552,f328(f328(f306(f871(x39551)),f328(f328(f328(f92(x39551),x39553),a24),x39553)),f192(f879(f871(x39551),a867)))) % 167.75/167.49 [3970]P1(f328(f328(f242(a872),f328(f193(f873(x39701)),f175(x39701,x39702,x39703))),f328(f193(f873(x39701)),x39703))) % 167.75/167.49 [3978]E(f328(f261(x39781,x39782),f328(f248(f878(x39781,x39782)),f328(f267(x39781,x39782,a867),x39783))),f328(f248(x39781),f328(f328(f8(f879(x39782,a867),a867,x39781),f87(x39782)),x39783))) % 167.75/167.49 [3990]E(f328(f307(a872,a872,f328(f328(f7(a872,a872,a872),f80(a872)),x39901)),f299(a872,x39902,x39903)),f299(a872,f328(f328(f80(a872),x39902),x39901),f328(f328(f80(a872),x39903),x39901))) % 167.75/167.49 [3993]P1(f328(f38(f876(x39931)),f328(f307(x39932,f876(x39931),f328(f176(x39932,x39931),x39933)),f251(f879(x39932,a867))))) % 167.75/167.49 [4006]E(f328(f307(a872,a872,f328(f328(f7(a872,a872,a872),f80(a872)),x40061)),f328(f298(a872,x40062),x40063)),f328(f298(a872,f328(f328(f80(a872),x40062),x40061)),f328(f328(f80(a872),x40063),x40061))) % 167.75/167.49 [4024]E(f328(f328(f180(x40241,x40242),f328(f328(f151(f878(x40241,x40242),x40241),f262(x40241,x40242)),x40243)),f328(f328(f151(f878(x40241,x40242),x40242),f266(x40241,x40242)),x40243)),x40243) % 167.75/167.49 [4029]E(f328(f328(f80(a872),f328(f328(f81(a872),x40291),f46(a872,f328(f328(f40(a872),x40292),x40291),x40293))),f46(a872,x40292,x40291)),f46(a872,x40292,f328(f328(f81(a872),x40291),x40293))) % 167.75/167.49 [4043]E(f328(f328(f125(x40431),x40432),f328(f139(f873(x40431),f873(x40431),f125(x40431),f117(x40431)),x40433)),f328(f139(f873(x40431),f873(x40431),f125(x40431),x40432),x40433)) % 167.75/167.49 [4061]P1(f328(f328(f330(f878(x40611,x40611)),f328(f328(f263(x40611,x40611),x40612),x40612)),f328(f328(f187(f878(x40611,x40611),a867),f2(a872)),x40613))) % 167.75/167.49 [4067]E(f328(f248(x40671),f328(f328(f8(f879(x40672,a867),a867,x40671),f87(x40672)),f328(f7(x40672,x40671,a867),x40673))),f328(f259(x40672,x40671),f328(f248(f878(x40672,x40671)),f328(f267(x40672,x40671,a867),x40673)))) % 167.75/167.49 [4085]E(f328(f328(f114(f879(x40851,a867)),f328(f328(f44(a872,f879(x40851,a867)),f299(a872,f78(a872),x40852)),x40853)),f328(x40853,f2(a872))),f328(f328(f44(a872,f879(x40851,a867)),f328(f297(a872),x40852)),x40853)) % 167.75/167.49 [4100]E(f328(f139(f873(x41001),f873(x41001),f125(x41001),f117(x41001)),f328(f328(f151(f873(x41001),f873(x41001)),f133(x41001,x41002)),x41003)),f328(f133(x41001,x41002),f328(f139(f873(x41001),f873(x41001),f125(x41001),f117(x41001)),x41003))) % 167.75/167.49 [4105]E(f328(f266(f873(x41051),f873(x41051)),f164(x41051,x41052,x41053)),f328(f133(x41051,f328(f73(a867,a867,x41051,a323),x41052)),x41053)) % 167.75/167.49 [4123]E(f328(f328(f43(x41231,f879(x41232,a867)),f251(f879(x41231,a867))),f328(f328(f8(f879(x41232,a867),f879(x41232,a867),x41231),f248(x41232)),f328(f7(x41232,x41231,a867),x41233))),f328(f248(x41232),f328(f328(f8(f879(x41231,a867),a867,x41232),f88(x41231)),x41233))) % 167.75/167.49 [4154]E(f328(f328(f80(a1),f328(f328(f80(a1),f328(f328(f81(a1),x41541),f328(f328(f40(a1),x41542),x41541))),f46(a1,x41542,x41541))),x41543),f328(f328(f80(a1),x41542),x41543)) % 167.75/167.49 [4191]E(f328(f328(f80(a1),f328(f328(f80(a1),f328(f328(f81(a1),f328(f328(f40(a1),x41911),x41912)),x41912)),f46(a1,x41911,x41912))),x41913),f328(f328(f80(a1),x41911),x41913)) % 167.75/167.49 [4220]E(f85(f878(x42201,x42202),f328(f267(x42201,x42202,a867),f328(f328(f8(f879(x42202,f878(x42201,x42202)),f879(x42202,a867),x42201),f328(f8(f878(x42201,x42202),a867,x42202),x42203)),f263(x42201,x42202)))),f85(f878(x42201,x42202),x42203)) % 167.75/167.49 [4221]E(f90(f878(x42211,x42212),f328(f267(x42211,x42212,a867),f328(f328(f8(f879(x42212,f878(x42211,x42212)),f879(x42212,a867),x42211),f328(f8(f878(x42211,x42212),a867,x42212),x42213)),f263(x42211,x42212)))),f90(f878(x42211,x42212),x42213)) % 167.75/167.49 [4249]P1(f328(f328(f242(f879(x42491,a867)),f41(f879(x42491,a867),f328(f328(f105(f879(f879(x42491,a867),a867)),x42492),x42493))),f328(f328(f105(f879(x42491,a867)),f41(f879(x42491,a867),x42492)),f41(f879(x42491,a867),x42493)))) % 167.75/167.49 [4250]E(f328(f166(x42501),f328(f328(f328(f187(f873(x42501),f873(x42501)),f328(f328(f22(a872),f328(f193(f873(x42501)),x42502)),f46(a872,x42503,f328(f193(f873(x42501)),x42502)))),f165(x42501)),x42502)),f328(f328(f328(f187(f873(x42501),f873(x42501)),x42503),f165(x42501)),f328(f166(x42501),x42502))) % 167.75/167.49 [4264]E(f328(f248(x42641),f328(f328(f8(a867,a867,x42641),a323),f328(f328(f7(x42641,f876(x42642),a867),f328(f328(f8(f876(x42642),f879(f876(x42642),a867),x42641),a325),x42643)),f205(x42642)))),f182(x42641,x42642,x42643)) % 167.75/167.49 [4289]P1(f328(f328(f242(a872),f328(f193(f873(x42891)),f328(f328(f135(x42891),f328(f193(f873(x42891)),f175(x42891,x42892,x42893))),x42893))),f328(f193(f873(x42891)),x42893))) % 167.75/167.49 [4330]E(f328(f248(x43301),f328(f328(f8(f879(x43302,a867),a867,x43301),f87(x43302)),f328(f328(f8(f876(x43301),f879(x43302,a867),x43301),f328(f7(x43302,f876(x43301),a867),f328(f328(f8(f876(x43301),f879(f876(x43301),a867),x43302),a325),x43303))),f235(x43301)))),f184(x43302,x43301,x43303)) % 167.75/167.49 [4541]~P1(f328(f63(x45411,x45412,f192(f879(x45411,a867))),x45413)) % 167.75/167.49 [4548]~P1(f328(f328(f330(f878(x45481,x45481)),f328(f328(f263(x45481,x45481),x45482),x45483)),f150(x45481,f117(f879(x45481,a872))))) % 167.75/167.49 [3585]E(f328(f193(f873(x35851)),f328(f328(f173(x35851),x35852),x35853)),f328(f328(f240(a872),f328(f193(f873(x35851)),x35853)),x35852)) % 167.75/167.49 [3586]E(f328(f193(f873(x35861)),f328(f328(f135(x35861),x35862),x35863)),f328(f328(f22(a872),f328(f193(f873(x35861)),x35863)),x35862)) % 167.75/167.49 [3610]E(f328(f193(f873(f873(x36101))),f56(x36101,x36102,x36103)),f328(f328(f253(a872),f328(f193(f873(x36101)),x36103)),x36102)) % 167.75/167.49 [3626]E(f328(f328(f40(a872),f328(f328(f40(a872),x36261),x36262)),x36263),f328(f328(f40(a872),x36261),f328(f328(f81(a872),x36262),x36263))) % 167.75/167.49 [3627]E(f328(f328(f22(a872),f328(f328(f22(a872),x36271),x36272)),x36273),f328(f328(f22(a872),x36271),f328(f328(f80(a872),x36272),x36273))) % 167.75/167.49 [3628]E(f328(f328(f80(a872),f328(f328(f80(a872),x36281),x36282)),x36283),f328(f328(f80(a872),x36281),f328(f328(f80(a872),x36282),x36283))) % 167.75/167.49 [3629]E(f328(f328(f80(a1),f328(f328(f80(a1),x36291),x36292)),x36293),f328(f328(f80(a1),x36291),f328(f328(f80(a1),x36292),x36293))) % 167.75/167.49 [3630]E(f328(f328(f81(a872),f328(f328(f81(a872),x36301),x36302)),x36303),f328(f328(f81(a872),x36301),f328(f328(f81(a872),x36302),x36303))) % 167.75/167.49 [3631]E(f328(f328(f81(a1),f328(f328(f81(a1),x36311),x36312)),x36313),f328(f328(f81(a1),x36311),f328(f328(f81(a1),x36312),x36313))) % 167.75/167.49 [3632]E(f328(f328(f253(a1),f328(f328(f253(a1),x36321),x36322)),x36323),f328(f328(f253(a1),x36321),f328(f328(f81(a872),x36322),x36323))) % 167.75/167.49 [3652]E(f159(x36521,f328(f328(f148(f879(x36521,a867)),x36522),x36523)),f172(x36521,x36522,f159(x36521,x36523))) % 167.75/167.49 [3697]E(f328(f328(f22(a872),f328(f328(f22(a872),x36971),x36972)),x36973),f328(f328(f22(a872),f328(f328(f22(a872),x36971),x36973)),x36972)) % 167.75/167.49 [3703]E(f328(f235(f878(x37031,f874(x37031))),f328(f328(f263(x37031,f874(x37031)),x37032),x37033)),f328(f132(x37031),f127(x37031,x37032,x37033))) % 167.75/167.49 [3706]E(f328(f328(f105(f879(x37061,a867)),x37062),f328(f328(f22(f879(x37061,a867)),x37063),x37062)),f192(f879(x37061,a867))) % 167.75/167.49 [3748]E(f42(f879(x37481,a867),f328(f328(f306(f879(x37481,a867)),x37482),x37483)),f328(f328(f105(f879(x37481,a867)),x37482),f42(f879(x37481,a867),x37483))) % 167.75/167.49 [3749]E(f41(f879(x37491,a867),f328(f328(f306(f879(x37491,a867)),x37492),x37493)),f328(f328(f114(f879(x37491,a867)),x37492),f41(f879(x37491,a867),x37493))) % 167.75/167.49 [3751]E(f328(f328(f22(a872),f328(f328(f81(a872),x37511),x37512)),f328(f328(f81(a872),x37513),x37512)),f328(f328(f81(a872),f328(f328(f22(a872),x37511),x37513)),x37512)) % 167.75/167.49 [3752]E(f328(f328(f80(a872),f328(f328(f81(a872),x37521),x37522)),f328(f328(f81(a872),x37523),x37522)),f328(f328(f81(a872),f328(f328(f80(a872),x37521),x37523)),x37522)) % 167.75/167.49 [3753]E(f328(f328(f22(a1),f328(f328(f81(a1),x37531),x37532)),f328(f328(f81(a1),x37533),x37532)),f328(f328(f81(a1),f328(f328(f22(a1),x37531),x37533)),x37532)) % 167.75/167.49 [3754]E(f328(f328(f80(a1),f328(f328(f81(a1),x37541),x37542)),f328(f328(f81(a1),x37543),x37542)),f328(f328(f81(a1),f328(f328(f80(a1),x37541),x37543)),x37542)) % 167.75/167.49 [3756]E(f328(f328(f240(a872),f328(f328(f22(a872),x37561),x37562)),f328(f328(f22(a872),x37563),x37562)),f328(f328(f22(a872),f328(f328(f240(a872),x37561),x37563)),x37562)) % 167.75/167.49 [3779]E(f328(f328(f105(f879(f873(x37791),a867)),f157(x37791,x37792)),f157(x37791,x37793)),f157(x37791,f328(f328(f105(f879(x37791,a867)),x37792),x37793))) % 167.75/167.49 [3781]E(f328(f328(f114(f879(x37811,a867)),x37812),f328(f328(f114(f879(x37811,a867)),x37812),x37813)),f328(f328(f114(f879(x37811,a867)),x37812),x37813)) % 167.75/167.49 [3782]E(f328(f328(f114(f879(x37821,a867)),x37822),f328(f328(f22(f879(x37821,a867)),x37823),x37822)),f328(f328(f114(f879(x37821,a867)),x37822),x37823)) % 167.75/167.49 [3783]E(f328(f328(f105(f879(x37831,a867)),x37832),f328(f328(f105(f879(x37831,a867)),x37832),x37833)),f328(f328(f105(f879(x37831,a867)),x37832),x37833)) % 167.75/167.49 [3795]E(f328(f328(f285(x37951,x37952,x37952),x37953),f304(x37952,f192(f879(f878(x37952,x37952),a867)))),x37953) % 167.75/167.49 [3798]E(f328(f328(f114(f879(x37981,a867)),f328(f328(f306(x37981),x37982),f192(f879(x37981,a867)))),x37983),f328(f328(f306(x37981),x37982),x37983)) % 167.75/167.49 [3816]E(f328(f328(f22(a872),f328(f328(f22(a872),f328(a116,x38161)),x38162)),f328(a116,x38163)),f328(f328(f22(a872),f328(f328(f22(a872),x38161),x38162)),x38163)) % 167.75/167.49 [3845]E(f328(f328(f105(f879(f879(x38451,a867),a867)),f328(f305(x38451),x38452)),f328(f305(x38451),x38453)),f328(f305(x38451),f328(f328(f105(f879(x38451,a867)),x38452),x38453))) % 167.75/167.49 [3849]E(f328(f328(f114(f879(x38491,a867)),f328(f79(f879(x38491,a867)),x38492)),x38493),f328(f79(f879(x38491,a867)),f328(f328(f22(f879(x38491,a867)),x38492),x38493))) % 167.75/167.49 [3861]E(f328(f328(f306(x38611),x38612),f328(f328(f22(f879(x38611,a867)),x38613),f328(f328(f306(x38611),x38612),f192(f879(x38611,a867))))),f328(f328(f306(x38611),x38612),x38613)) % 167.75/167.49 [3871]P1(f328(f328(f242(f879(x38711,a867)),x38712),f328(f328(f114(f879(x38711,a867)),x38713),x38712))) % 167.75/167.49 [3872]P1(f328(f328(f242(f879(x38721,a867)),x38722),f328(f328(f114(f879(x38721,a867)),x38722),x38723))) % 167.75/167.49 [3875]E(f328(f328(f105(f879(x38751,a867)),f328(f79(f879(x38751,a867)),x38752)),f328(f79(f879(x38751,a867)),x38753)),f328(f79(f879(x38751,a867)),f328(f328(f114(f879(x38751,a867)),x38752),x38753))) % 167.75/167.49 [3876]E(f328(f328(f114(f879(x38761,a867)),f328(f79(f879(x38761,a867)),x38762)),f328(f79(f879(x38761,a867)),x38763)),f328(f79(f879(x38761,a867)),f328(f328(f105(f879(x38761,a867)),x38762),x38763))) % 167.75/167.49 [3890]P1(f328(f328(f242(f879(x38901,a867)),f328(f170(x38901),x38902)),f328(f170(x38901),f328(f328(f148(x38901),x38903),x38902)))) % 167.75/167.49 [3901]E(f328(f328(f114(f879(x39011,a867)),f328(f328(f22(f879(x39011,a867)),x39012),x39013)),f328(f328(f105(f879(x39011,a867)),x39012),x39013)),x39012) % 167.75/167.49 [3957]E(f328(f328(f6(x39571,a1),f328(f328(f8(a872,a1,x39571),f104(a1)),x39572)),x39573),f328(f104(a1),f328(f328(f6(x39571,a872),x39572),x39573))) % 167.75/167.49 [3958]E(f328(f328(f9(x39581,a1),f328(f328(f8(a872,a1,x39581),f104(a1)),x39582)),x39583),f328(f104(a1),f328(f328(f9(x39581,a872),x39582),x39583))) % 167.75/167.49 [4008]E(f328(f328(f125(x40081),f175(x40081,x40082,x40083)),f328(f328(f135(x40081),f328(f193(f873(x40081)),f175(x40081,x40082,x40083))),x40083)),x40083) % 167.75/167.49 [4013]E(f328(f79(f879(f878(x40131,x40132),a867)),f328(f328(f265(x40131,x40132),x40133),f328(f16(f879(x40132,a867),x40131),f251(f879(x40132,a867))))),f328(f328(f265(x40131,x40132),f328(f79(f879(x40131,a867)),x40133)),f328(f16(f879(x40132,a867),x40131),f251(f879(x40132,a867))))) % 167.75/167.49 [4014]E(f328(f79(f879(f878(x40141,x40142),a867)),f328(f328(f265(x40141,x40142),f251(f879(x40141,a867))),f328(f16(f879(x40142,a867),x40141),x40143))),f328(f328(f265(x40141,x40142),f251(f879(x40141,a867))),f328(f16(f879(x40142,a867),x40141),f328(f79(f879(x40142,a867)),x40143)))) % 167.75/167.49 [4062]E(f328(f328(f44(f879(x40621,a867),f879(x40621,a867)),x40622),f328(f328(f7(f879(x40621,a867),f879(x40621,a867),f879(x40621,a867)),f105(f879(x40621,a867))),x40623)),f328(f328(f105(f879(x40621,a867)),f41(f879(x40621,a867),x40622)),x40623)) % 167.75/167.49 [4069]E(f328(f139(f873(x40691),f873(x40691),f125(x40691),f117(x40691)),f328(f328(f148(f873(x40691)),x40692),x40693)),f328(f328(f125(x40691),x40692),f328(f139(f873(x40691),f873(x40691),f125(x40691),f117(x40691)),x40693))) % 167.75/167.49 [4091]E(f328(f328(f306(f879(x40911,a867)),f328(f282(x40911,x40911,x40912),f328(f328(f306(x40911),x40913),f192(f879(x40911,a867))))),f192(f879(f879(x40911,a867),a867))),f328(f328(f62(x40911),f328(f328(f306(x40911),x40913),f192(f879(x40911,a867)))),x40912)) % 167.75/167.49 [4101]E(f328(f328(f80(a872),f328(f328(f81(a872),x41011),f328(f328(f40(a872),x41012),x41013))),f328(f328(f40(a872),f328(f328(f81(a872),x41011),f46(a872,x41012,x41013))),x41013)),f328(f328(f40(a872),f328(f328(f81(a872),x41011),x41012)),x41013)) % 167.75/167.49 [4102]E(f328(f328(f80(a1),f328(f328(f81(a1),x41021),f328(f328(f40(a1),x41022),x41023))),f328(f328(f40(a1),f328(f328(f81(a1),x41021),f46(a1,x41022,x41023))),x41023)),f328(f328(f40(a1),f328(f328(f81(a1),x41021),x41022)),x41023)) % 167.75/167.49 [4139]E(f328(f328(f22(f879(x41391,a867)),f328(f170(x41391),x41392)),f328(f328(f306(x41391),x41393),f192(f879(x41391,a867)))),f328(f170(x41391),f328(f133(x41391,f328(f328(f8(a867,a867,x41391),a323),f328(a325,x41393))),x41392))) % 167.75/167.49 [4188]E(f328(f328(f125(x41881),f328(f139(f873(x41881),f873(x41881),f125(x41881),f117(x41881)),x41882)),f328(f139(f873(x41881),f873(x41881),f125(x41881),f117(x41881)),x41883)),f328(f139(f873(x41881),f873(x41881),f125(x41881),f117(x41881)),f328(f328(f125(f873(x41881)),x41882),x41883))) % 167.75/167.49 [4193]E(f328(f328(f263(f873(x41931),f873(x41931)),f328(f133(x41931,x41932),x41933)),f328(f133(x41931,f328(f73(a867,a867,x41931,a323),x41932)),x41933)),f164(x41931,x41932,x41933)) % 167.75/167.49 [4196]E(f328(f328(f80(a872),f328(f328(f80(a872),f328(f328(f40(a872),x41961),x41962)),f328(f328(f40(a872),x41963),x41962))),f328(f328(f40(a872),f328(f328(f80(a872),f46(a872,x41961,x41962)),f46(a872,x41963,x41962))),x41962)),f328(f328(f40(a872),f328(f328(f80(a872),x41961),x41963)),x41962)) % 167.75/167.49 [4197]E(f328(f328(f80(a1),f328(f328(f80(a1),f328(f328(f40(a1),x41971),x41972)),f328(f328(f40(a1),x41973),x41972))),f328(f328(f40(a1),f328(f328(f80(a1),f46(a1,x41971,x41972)),f46(a1,x41973,x41972))),x41972)),f328(f328(f40(a1),f328(f328(f80(a1),x41971),x41973)),x41972)) % 167.75/167.49 [4253]E(f328(f328(f105(f879(f873(x42531),a867)),f328(f328(f7(f873(x42531),f879(f873(x42531),a867),a867),f330(f873(x42531))),f158(x42531,x42532))),f328(f328(f7(f873(x42531),f879(f873(x42531),a867),a867),f330(f873(x42531))),f158(x42531,x42533))),f157(x42531,f328(f328(f105(f879(x42531,a867)),f328(f328(f7(x42531,f879(x42531,a867),a867),f330(x42531)),x42532)),f328(f328(f7(x42531,f879(x42531,a867),a867),f330(x42531)),x42533)))) % 167.75/167.49 [4266]E(f328(f248(x42661),f328(f328(f18(x42661,a867,a867),f328(f328(f8(a867,f879(a867,a867),x42661),a327),f328(f328(f7(x42661,x42661,a867),a325),x42662))),f328(f328(f7(x42661,f879(x42661,a867),a867),f330(x42661)),x42663))),f328(f328(f306(x42661),x42662),x42663)) % 167.75/167.49 [4286]E(f328(f328(f86(f873(f873(x42861)),f873(f873(x42861))),f55(x42861,x42862)),f328(f328(f18(f873(f873(x42861)),f873(f873(x42861)),f873(f873(x42861))),f328(f328(f8(f873(f873(x42861)),f879(f873(f873(x42861)),f873(f873(x42861))),f873(f873(x42861))),f125(f873(x42861))),f328(f151(f873(x42861),f873(x42861)),f328(f148(x42861),x42863)))),f5(f873(f873(x42861))))),f55(x42861,f328(f328(f148(x42861),x42863),x42862))) % 167.75/167.49 [4290]E(f328(f248(x42901),f328(f328(f18(x42901,a867,a867),f328(f328(f8(a867,f879(a867,a867),x42901),a327),f328(f328(f7(x42901,f879(x42901,a867),a867),f330(x42901)),x42902))),f328(f328(f7(x42901,f879(x42901,a867),a867),f330(x42901)),x42903))),f328(f328(f114(f879(x42901,a867)),x42902),x42903)) % 167.75/167.49 [4291]E(f328(f248(x42911),f328(f328(f18(x42911,a867,a867),f328(f328(f8(a867,f879(a867,a867),x42911),a326),f328(f328(f7(x42911,f879(x42911,a867),a867),f330(x42911)),x42912))),f328(f328(f7(x42911,f879(x42911,a867),a867),f330(x42911)),x42913))),f328(f328(f105(f879(x42911,a867)),x42912),x42913)) % 167.75/167.49 [4382]E(f328(f328(f44(x43821,f879(f879(x43821,a867),a867)),x43822),f328(f328(f7(x43821,f879(f879(x43821,a867),a867),f879(f879(x43821,a867),a867)),f328(f328(f8(f879(x43821,a867),f879(f879(f879(x43821,a867),a867),f879(f879(x43821,a867),a867)),x43821),f306(f879(x43821,a867))),f328(f328(f8(f879(x43821,a867),f879(x43821,a867),x43821),f282(x43821,x43821,x43823)),f328(f328(f7(x43821,f879(x43821,a867),f879(x43821,a867)),f306(x43821)),f192(f879(x43821,a867)))))),f192(f879(f879(x43821,a867),a867)))),f328(f328(f62(x43821),x43822),x43823)) % 167.75/167.49 [4384]E(f328(f328(f209(x43841),f328(f328(f81(a1),f328(f328(f73(f878(a1,a1),a1,x43841,f262(a1,a1)),f219(x43841)),x43842)),f328(f328(f73(f878(a1,a1),a1,x43841,f262(a1,a1)),f219(x43841)),x43843))),f328(f328(f81(a1),f328(f328(f73(f878(a1,a1),a1,x43841,f266(a1,a1)),f219(x43841)),x43842)),f328(f328(f73(f878(a1,a1),a1,x43841,f266(a1,a1)),f219(x43841)),x43843))),f228(x43841,x43842,x43843)) % 167.75/167.49 [4387]E(f328(f248(f873(x43871)),f328(f328(f18(f873(x43871),a867,a867),f328(f328(f8(a867,f879(a867,a867),f873(x43871)),a326),f328(f328(f7(f873(x43871),a872,a867),f328(f328(f8(a872,f879(a872,a867),f873(x43871)),a325),f193(f873(x43871)))),x43872))),f328(f328(f7(f873(x43871),f879(x43871,a867),a867),f328(f328(f8(f879(x43871,a867),f879(f879(x43871,a867),a867),f873(x43871)),f242(f879(x43871,a867))),f170(x43871))),f328(f170(x43871),x43873)))),f328(f170(f873(x43871)),f56(x43871,x43872,x43873))) % 167.75/167.49 [3769]E(f46(a872,f328(f328(f80(a872),f328(f328(f81(a872),x37691),x37692)),x37693),x37692),f46(a872,x37693,x37692)) % 167.75/167.49 [3815]E(f136(a872,f328(f298(a872,f328(f328(f80(a872),x38151),x38152)),x38153)),f328(f328(f135(a872),x38152),f136(a872,f328(f298(a872,x38151),x38153)))) % 167.75/167.49 [3860]E(f328(f328(f80(a1),f328(f104(a1),x38601)),f328(f328(f80(a1),f328(f104(a1),x38602)),x38603)),f328(f328(f80(a1),f328(f104(a1),f328(f328(f80(a872),x38601),x38602))),x38603)) % 167.75/167.49 [3867]E(f328(f328(f114(f879(x38671,a867)),f328(f328(f22(f879(x38671,a867)),x38672),x38673)),x38673),f328(f328(f114(f879(x38671,a867)),x38672),x38673)) % 167.75/167.49 [3868]E(f328(f328(f22(f879(x38681,a867)),f328(f328(f22(f879(x38681,a867)),x38682),x38683)),x38683),f328(f328(f22(f879(x38681,a867)),x38682),x38683)) % 167.75/167.49 [3891]E(f328(f328(f285(x38911,x38911,x38912),f304(x38911,f192(f879(f878(x38911,x38911),a867)))),x38913),x38913) % 167.75/167.49 [3898]E(f328(f328(f114(f879(x38981,a867)),f328(f281(x38981),x38982)),f328(f281(x38981),x38983)),f328(f281(x38981),f328(f328(f114(f879(f878(x38981,x38981),a867)),x38982),x38983))) % 167.75/167.49 [3909]E(f272(x39091,f328(f328(f148(f878(a103,x39091)),f328(f328(f263(a103,x39091),f2(a103)),x39092)),x39093)),f272(x39091,x39093)) % 167.75/167.49 [3912]E(f328(f328(f105(f879(x39121,a867)),f42(f879(x39121,a867),x39122)),f42(f879(x39121,a867),x39123)),f42(f879(x39121,a867),f328(f328(f114(f879(f879(x39121,a867),a867)),x39122),x39123))) % 167.75/167.49 [3913]E(f328(f328(f114(f879(x39131,a867)),f41(f879(x39131,a867),x39132)),f41(f879(x39131,a867),x39133)),f41(f879(x39131,a867),f328(f328(f114(f879(f879(x39131,a867),a867)),x39132),x39133))) % 167.75/167.49 [3949]E(f328(f328(f285(x39491,x39491,x39491),f328(f328(f187(f878(x39491,x39491),a867),x39492),x39493)),x39493),f328(f328(f187(f878(x39491,x39491),a867),f328(a116,x39492)),x39493)) % 167.75/167.49 [3999]P1(f328(f328(f242(f879(x39991,a867)),f328(f328(f22(f879(x39991,a867)),x39992),x39993)),x39992)) % 167.75/167.49 [4000]P1(f328(f328(f242(f879(x40001,a867)),f328(f328(f105(f879(x40001,a867)),x40002),x40003)),x40003)) % 167.75/167.49 [4001]P1(f328(f328(f242(f879(x40011,a867)),f328(f328(f105(f879(x40011,a867)),x40012),x40013)),x40012)) % 167.75/167.49 [4026]E(f304(x40261,f328(f328(f114(f879(f878(x40261,x40261),a867)),f304(x40261,x40262)),f304(x40261,x40263))),f304(x40261,f328(f328(f114(f879(f878(x40261,x40261),a867)),x40262),x40263))) % 167.75/167.49 [4030]E(f41(f879(x40301,a867),f328(f328(f306(f879(x40301,a867)),x40302),f328(f328(f306(f879(x40301,a867)),x40303),f192(f879(f879(x40301,a867),a867))))),f328(f328(f114(f879(x40301,a867)),x40302),x40303)) % 167.75/167.49 [4031]E(f42(f879(x40311,a867),f328(f328(f306(f879(x40311,a867)),x40312),f328(f328(f306(f879(x40311,a867)),x40313),f192(f879(f879(x40311,a867),a867))))),f328(f328(f105(f879(x40311,a867)),x40312),x40313)) % 167.75/167.49 [4037]E(f328(f328(f285(x40371,x40371,x40371),f328(f328(f187(f878(x40371,x40371),a867),x40372),x40373)),x40373),f328(f328(f285(x40371,x40371,x40371),x40373),f328(f328(f187(f878(x40371,x40371),a867),x40372),x40373))) % 167.75/167.49 [4106]E(f328(f328(f114(f879(x41061,a867)),f328(f248(x41061),f328(f328(f7(x41061,x41061,a867),a325),x41062))),x41063),f328(f328(f306(x41061),x41062),x41063)) % 167.75/167.49 [4108]E(f328(a108,f328(f328(f6(x41081,a1),f328(f328(f8(a872,a1,x41081),f104(a1)),x41082)),x41083)),f328(f328(f6(x41081,a872),x41082),x41083)) % 167.75/167.49 [4109]E(f328(a108,f328(f328(f9(x41091,a1),f328(f328(f8(a872,a1,x41091),f104(a1)),x41092)),x41093)),f328(f328(f9(x41091,a872),x41092),x41093)) % 167.75/167.49 [4185]E(f328(f153(f873(x41851),x41851,f328(f169(x41851),x41852),f328(f16(f879(f873(x41851),f873(x41851)),x41851),f328(f328(f7(f873(x41851),f873(x41851),f873(x41851)),f125(x41851)),x41852))),x41853),f328(f169(x41851),f328(f328(f125(x41851),x41853),x41852))) % 167.75/167.49 [4216]P1(f328(f328(f242(f879(f879(x42161,a867),a867)),f328(f328(f114(f879(f879(x42161,a867),a867)),f328(f305(x42161),x42162)),f328(f305(x42161),x42163))),f328(f305(x42161),f328(f328(f114(f879(x42161,a867)),x42162),x42163)))) % 167.75/167.49 [4309]E(f328(f248(x43091),f328(f328(f18(x43091,a867,a867),f328(f328(f8(a867,f879(a867,a867),x43091),a326),f328(f328(f7(x43091,f879(x43091,a867),a867),f330(x43091)),x43092))),f328(f328(f8(a867,a867,x43091),a323),f328(f328(f7(x43091,f879(x43091,a867),a867),f330(x43091)),x43093)))),f328(f328(f22(f879(x43091,a867)),x43092),x43093)) % 167.75/167.49 [4331]E(f328(f39(a872),f328(f248(a872),f328(f328(f18(a872,a867,a867),f328(f328(f8(a867,f879(a867,a867),a872),a326),f328(f328(f7(a872,a872,a867),f243(a872)),f328(f193(f873(x43311)),x43312)))),f328(f328(f8(x43311,a867,a872),x43313),f328(f162(x43311),x43312))))),f328(f193(f873(x43311)),f328(f133(x43311,x43313),x43312))) % 167.75/167.49 [4333]E(f328(f193(f873(x43331)),f174(x43331,x43332,x43333)),f328(f39(a872),f328(f248(a872),f328(f328(f18(a872,a867,a867),f328(f328(f8(a867,f879(a867,a867),a872),a326),f328(f328(f7(a872,a872,a867),f243(a872)),f328(f193(f873(x43331)),x43332)))),f328(f328(f7(a872,f879(a872,a867),a867),f330(a872)),x43333))))) % 167.75/167.49 [4431]E(f328(f328(f105(f879(f878(f873(x44311),f873(x44311)),a867)),f328(f307(f878(f878(x44311,f873(x44311)),f878(x44311,f873(x44311))),f878(f873(x44311),f873(x44311)),f268(f878(x44311,f873(x44311)),f873(x44311),f878(x44311,f873(x44311)),f873(x44311),f328(f267(x44311,f873(x44311),f873(x44311)),f148(x44311)),f328(f267(x44311,f873(x44311),f873(x44311)),f148(x44311)))),f321(x44311,f873(x44311),x44312,f328(f140(x44311,x44312),x44313)))),f328(f248(f878(f873(x44311),f873(x44311))),f328(f267(f873(x44311),f873(x44311),a867),f328(f328(f7(f873(x44311),f879(f873(x44311),a867),f879(f873(x44311),a867)),f328(f328(f8(f879(a867,a867),f879(f879(f873(x44311),a867),f879(f873(x44311),a867)),f873(x44311)),f8(a867,a867,f873(x44311))),f328(f328(f8(a867,f879(a867,a867),f873(x44311)),a326),f328(f328(f7(f873(x44311),a872,a867),f328(f328(f8(a872,f879(a872,a867),f873(x44311)),a325),f193(f873(x44311)))),f328(a116,x44313))))),f328(f328(f7(f873(x44311),a872,a867),f328(f328(f8(a872,f879(a872,a867),f873(x44311)),a325),f193(f873(x44311)))),f328(a116,x44313)))))),f328(f140(x44311,x44312),f328(a116,x44313))) % 167.75/167.49 [3914]E(f46(a872,f328(a116,f328(f328(f80(a872),f328(f328(f81(a872),x39141),x39142)),x39143)),x39142),f46(a872,f328(a116,x39143),x39142)) % 167.75/167.49 [4174]E(f328(f248(x41741),f328(f328(f18(x41741,a867,a867),f328(f328(f8(a867,f879(a867,a867),x41741),a326),x41742)),x41743)),f328(f328(f105(f879(x41741,a867)),f328(f248(x41741),x41742)),f328(f248(x41741),x41743))) % 167.75/167.49 [4175]E(f328(f248(x41751),f328(f328(f18(x41751,a867,a867),f328(f328(f8(a867,f879(a867,a867),x41751),a327),x41752)),x41753)),f328(f328(f114(f879(x41751,a867)),f328(f248(x41751),x41752)),f328(f248(x41751),x41753))) % 167.75/167.49 [4177]E(f328(f328(f125(x41771),f328(f328(f135(x41771),f46(a872,x41772,f328(f193(f873(x41771)),x41773))),x41773)),f328(f328(f173(x41771),f46(a872,x41772,f328(f193(f873(x41771)),x41773))),x41773)),f328(f328(f328(f187(f873(x41771),f873(x41771)),x41772),f165(x41771)),x41773)) % 167.75/167.49 [4182]E(f328(f248(x41821),f328(f328(f18(x41821,a867,a867),f328(f328(f8(a867,f879(a867,a867),x41821),a331),x41822)),x41823)),f328(f328(f114(f879(x41821,a867)),f328(f79(f879(x41821,a867)),f328(f248(x41821),x41822))),f328(f248(x41821),x41823))) % 167.75/167.49 [4198]E(f328(f328(f80(a872),f328(f193(f873(x41981)),f328(f133(x41981,x41982),x41983))),f328(f193(f873(x41981)),f328(f133(x41981,f328(f328(f8(a867,a867,x41981),a323),x41982)),x41983))),f328(f193(f873(x41981)),x41983)) % 167.75/167.49 [4223]P1(f328(f328(f242(f879(x42231,a867)),f328(f328(f114(f879(x42231,a867)),f42(f879(x42231,a867),x42232)),f42(f879(x42231,a867),x42233))),f42(f879(x42231,a867),f328(f328(f105(f879(f879(x42231,a867),a867)),x42232),x42233)))) % 167.75/167.49 [4237]E(f328(f170(x42371),f328(f133(x42371,f328(f328(f8(a867,a867,x42371),a323),f328(f328(f7(x42371,x42371,a867),a325),x42372))),x42373)),f328(f328(f22(f879(x42371,a867)),f328(f170(x42371),x42373)),f328(f328(f306(x42371),x42372),f192(f879(x42371,a867))))) % 167.75/167.49 [4246]P1(f328(f328(f242(f879(f878(x42461,x42461),a867)),f328(f328(f114(f879(f878(x42461,x42461),a867)),f304(x42461,x42462)),f304(x42461,x42463))),f304(x42461,f328(f328(f114(f879(f878(x42461,x42461),a867)),x42462),x42463)))) % 167.75/167.49 [4271]E(f328(f328(f81(a872),f328(a116,f328(a116,f2(a872)))),f328(f328(f6(a872,a872),f328(f328(f8(a872,a872,a872),f328(f80(a872),x42711)),f328(f328(f7(a872,a872,a872),f81(a872)),x42712))),f328(f249(a872),x42713))),f328(f328(f81(a872),x42713),f328(f328(f80(a872),x42711),f328(f328(f80(a872),x42711),f328(f328(f81(a872),f328(f328(f22(a872),x42713),f78(a872))),x42712))))) % 167.75/167.49 [4281]E(f328(f248(x42811),f328(f328(f18(x42811,a867,a867),f328(f328(f8(a867,f879(a867,a867),x42811),a326),f328(f328(f7(x42811,f879(x42811,a867),a867),f330(x42811)),f328(f170(x42811),x42812)))),x42813)),f328(f170(x42811),f328(f133(x42811,x42813),x42812))) % 167.75/167.49 [4430]E(f328(f248(x44301),f328(f328(f8(f879(a872,a867),a867,x44301),f87(a872)),f328(f328(f7(x44301,f879(a872,a867),f879(a872,a867)),f328(f328(f8(f879(a872,f879(a867,a867)),f879(f879(a872,a867),f879(a872,a867)),x44301),f18(a872,a867,a867)),f328(f328(f8(f879(a872,a867),f879(a872,f879(a867,a867)),x44301),f328(f8(a867,f879(a867,a867),a872),a326)),f328(f328(f7(x44301,f879(a872,x44301),f879(a872,a867)),f328(f328(f8(f879(x44301,a867),f879(f879(a872,x44301),f879(a872,a867)),x44301),f8(x44301,a867,a872)),a325)),f328(f162(x44301),x44302))))),f328(f328(f18(a872,a867,a867),f328(f328(f8(a867,f879(a867,a867),a872),a326),f328(f328(f7(a872,a872,a867),f243(a872)),f328(f193(f873(x44301)),x44302)))),f328(f328(f7(a872,f879(a872,a867),a867),f330(a872)),x44303))))),f328(f170(x44301),f174(x44301,x44302,x44303))) % 167.75/167.49 [4321]E(f328(f248(x43211),f328(f328(f18(x43211,a867,a867),f328(f328(f8(a867,f879(a867,a867),x43211),a331),f328(f328(f8(a867,a867,x43211),a323),f328(f328(f7(x43211,x43211,a867),a325),x43212)))),x43213)),f328(f328(f306(x43211),x43212),f328(f248(x43211),x43213))) % 167.75/167.49 [4353]E(f328(f328(f151(f878(x43531,a872),x43531),f262(x43531,a872)),f328(f133(f878(x43531,a872),f328(f328(f7(f878(x43531,a872),f879(a872,a867),a867),f328(f328(f8(a872,f879(f879(a872,a867),a867),f878(x43531,a872)),f330(a872)),f266(x43531,a872))),x43532)),f328(f328(f180(x43531,a872),x43533),f136(a872,f328(f298(a872,f2(a872)),f328(f193(f873(x43531)),x43533)))))),f174(x43531,x43533,x43532)) % 167.75/167.49 [4383]E(f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f6(a872,a1),f328(f328(f8(a1,a1,a872),f328(f80(a1),x43831)),f328(f328(f7(a872,a1,a1),f328(f328(f8(a1,f879(a1,a1),a872),f81(a1)),f104(a1))),x43832))),f328(f249(a872),x43833))),f328(f328(f81(a1),f328(f104(a1),x43833)),f328(f328(f80(a1),x43831),f328(f328(f80(a1),x43831),f328(f328(f81(a1),f328(f104(a1),f328(f328(f22(a872),x43833),f78(a872)))),x43832))))) % 167.75/167.49 [4424]E(f328(f248(f878(x44241,x44242)),f328(f267(x44241,x44242,a867),f328(f328(f7(x44241,f879(f878(x44242,x44241),a867),f879(x44242,a867)),f328(f328(f8(f879(x44242,f879(f879(f878(x44242,x44241),a867),a867)),f879(f879(f878(x44242,x44241),a867),f879(x44242,a867)),x44241),f7(x44242,f879(f878(x44242,x44241),a867),a867)),f328(f328(f8(f879(x44242,f878(x44242,x44241)),f879(x44242,f879(f879(f878(x44242,x44241),a867),a867)),x44241),f328(f8(f878(x44242,x44241),f879(f879(f878(x44242,x44241),a867),a867),x44242),f330(f878(x44242,x44241)))),f328(f7(x44242,x44241,f878(x44242,x44241)),f263(x44242,x44241))))),x44243))),f328(f283(x44242,x44241),x44243)) % 167.75/167.49 [4446]E(f328(f248(f873(x44461)),f328(f328(f8(f879(x44461,a867),a867,f873(x44461)),f87(x44461)),f328(f328(f8(f879(x44461,f879(f873(x44461),a867)),f879(x44461,a867),f873(x44461)),f328(f8(f879(f873(x44461),a867),a867,x44461),f87(f873(x44461)))),f328(f328(f7(f873(x44461),f879(x44461,f879(f873(x44461),a867)),f879(x44461,f879(f873(x44461),a867))),f328(f328(f8(f879(x44461,f879(f879(f873(x44461),a867),f879(f873(x44461),a867))),f879(f879(x44461,f879(f873(x44461),a867)),f879(x44461,f879(f873(x44461),a867))),f873(x44461)),f18(x44461,f879(f873(x44461),a867),f879(f873(x44461),a867))),f328(f328(f8(f879(x44461,f879(f873(x44461),f879(a867,a867))),f879(x44461,f879(f879(f873(x44461),a867),f879(f873(x44461),a867))),f873(x44461)),f328(f8(f879(f873(x44461),f879(a867,a867)),f879(f879(f873(x44461),a867),f879(f873(x44461),a867)),x44461),f18(f873(x44461),a867,a867))),f328(f328(f8(f879(x44461,f879(f873(x44461),a867)),f879(x44461,f879(f873(x44461),f879(a867,a867))),f873(x44461)),f328(f8(f879(f873(x44461),a867),f879(f873(x44461),f879(a867,a867)),x44461),f328(f8(a867,f879(a867,a867),f873(x44461)),a326))),f328(f328(f7(f873(x44461),f879(x44461,f879(f873(x44461),f873(x44461))),f879(x44461,f879(f873(x44461),a867))),f328(f328(f8(f879(f879(f873(x44461),f873(x44461)),f879(f873(x44461),a867)),f879(f879(x44461,f879(f873(x44461),f873(x44461))),f879(x44461,f879(f873(x44461),a867))),f873(x44461)),f8(f879(f873(x44461),f873(x44461)),f879(f873(x44461),a867),x44461)),f328(f328(f8(f879(f873(x44461),a867),f879(f879(f873(x44461),f873(x44461)),f879(f873(x44461),a867)),f873(x44461)),f8(f873(x44461),a867,f873(x44461))),a325))),f148(x44461)))))),f328(f328(f7(x44461,f879(f873(x44461),a867),f879(f873(x44461),a867)),f328(f328(f8(f879(a867,a867),f879(f879(f873(x44461),a867),f879(f873(x44461),a867)),x44461),f8(a867,a867,f873(x44461))),f328(f328(f8(a867,f879(a867,a867),x44461),a326),f328(f328(f7(x44461,f879(x44461,a867),a867),f330(x44461)),x44462)))),f328(f328(f7(f873(x44461),f879(f873(x44461),a867),a867),f330(f873(x44461))),x44463)))))),f172(x44461,x44462,x44463)) % 167.75/167.49 [4443]E(f328(f328(f86(a1,f878(a1,a1)),f328(f328(f22(a1),x44431),x44432)),f328(f328(f7(a1,f878(a1,a1),f878(a1,a1)),f328(f328(f18(a1,f878(a1,a1),f879(f878(a1,a1),f878(a1,a1))),f328(f328(f8(a867,f879(f878(a1,a1),f879(f878(a1,a1),f878(a1,a1))),a1),f100(f878(a1,a1))),f328(f242(a1),f2(a1)))),f328(f263(a1,a1),f328(f328(f80(a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x44433)),f78(a1))))),f328(f328(f263(a1,a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x44433)),x44431))),f328(f45(x44432),f328(f328(f263(a1,a1),x44433),x44431))) % 167.75/167.49 [4474]~E(f32(x44741,x44742),f33(x44743,x44744)) % 167.75/167.49 [4491]~E(f328(a26,x44911),f30(x44912,x44913,x44914)) % 167.75/167.49 [4492]~E(f328(a26,x44921),f29(x44922,x44923,x44924)) % 167.75/167.49 [4493]~E(f30(x44931,x44932,x44933),f328(a26,x44934)) % 167.75/167.49 [4494]~E(f29(x44941,x44942,x44943),f328(a26,x44944)) % 167.75/167.49 [3463]E(f328(f328(f328(f72(x34631,x34632),x34633),x34634),f328(x34633,x34634)),x34633) % 167.75/167.49 [3523]E(f328(f328(f254(x35231,x35232,x35233),x35234),f2(a872)),x35232) % 167.75/167.49 [3562]E(f189(x35621,x35622,x35623,f328(a116,x35624)),f328(x35623,x35624)) % 167.75/167.49 [3603]E(f167(x36031,x36032,f167(x36031,x36033,x36034)),f167(x36031,x36033,f167(x36031,x36032,x36034))) % 167.75/167.49 [3738]E(f328(f153(x37381,x37382,x37383,x37384),f117(x37382)),x37383) % 167.75/167.49 [3739]E(f328(f237(x37391,x37392,x37393,x37394),f205(x37392)),x37393) % 167.75/167.49 [3740]E(f328(f139(x37401,x37402,x37403,x37404),f117(x37402)),x37404) % 167.75/167.49 [3844]E(f328(f328(f125(x38441),f168(x38441,x38442,x38443)),f168(x38441,x38444,x38443)),f328(f328(f125(x38441),f168(x38441,x38444,x38443)),f168(x38441,x38442,x38443))) % 167.75/167.49 [3857]E(f328(f237(f876(x38571),x38572,f205(x38571),f328(f16(f876(x38571),x38572),f205(x38571))),f328(x38573,x38574)),f205(x38571)) % 167.75/167.49 [3902]E(f328(f328(f114(f879(x39021,a867)),f182(x39021,x39022,x39023)),f182(x39021,x39022,x39024)),f182(x39021,x39022,f183(x39021,x39022,x39024,x39023))) % 167.75/167.49 [3934]E(f328(f328(f269(x39341,x39342,x39343,f878(x39342,x39343)),x39344),f263(x39342,x39343)),x39344) % 167.75/167.49 [3943]E(f185(x39431,x39432,x39433,x39434,f117(x39432)),x39433) % 167.75/167.49 [3944]E(f238(x39441,x39442,x39443,x39444,f205(x39442)),x39443) % 167.75/167.49 [3945]E(f185(x39451,x39452,x39453,f117(x39451),x39454),x39453) % 167.75/167.49 [4230]P43(x42301,x42302,x42303,x42304,f192(f879(x42301,a867)),x42304) % 167.75/167.49 [3265]E(f328(f328(f16(x32651,x32652),x32653),x32654),x32653) % 167.75/167.49 [3380]E(f328(f328(f206(x33801,x33802),x33803),f328(f235(x33801),x33804)),f328(f235(x33802),f328(x33803,x33804))) % 167.75/167.49 [3553]E(f167(x35531,x35532,f328(f133(x35531,x35533),x35534)),f328(f133(x35531,x35533),f167(x35531,x35532,x35534))) % 167.75/167.49 [3587]E(f328(f328(f65(x35871,x35872,x35873),x35874),f192(f879(x35871,a867))),x35874) % 167.75/167.49 [3609]E(f328(f328(f162(x36091),f328(f328(f148(x36091),x36092),x36093)),f328(a116,x36094)),f328(f328(f162(x36091),x36093),x36094)) % 167.75/167.49 [3653]P28(x36531,f2(a872),f328(f328(f328(f92(x36531),x36532),f328(a26,x36533)),x36534)) % 167.75/167.49 [3678]E(f328(f328(x36781,x36782),f328(f188(x36783,x36784,x36781),x36782)),f328(f188(x36783,x36784,x36781),f328(a116,x36782))) % 167.75/167.49 [3774]E(f328(f328(f156(x37741,f328(f328(f148(x37741),x37742),x37743)),f2(a872)),x37744),f328(f328(f148(x37741),x37744),x37743)) % 167.75/167.49 [3785]E(f328(f328(f44(f879(x37851,a867),f879(x37852,a867)),x37853),f307(x37851,x37852,x37854)),f328(f307(x37851,x37852,x37854),f41(f879(x37851,a867),x37853))) % 167.75/167.49 [3786]E(f328(f328(f44(f879(x37861,a867),f879(x37862,a867)),x37863),f308(x37862,x37861,x37864)),f328(f308(x37862,x37861,x37864),f41(f879(x37861,a867),x37863))) % 167.75/167.49 [3884]E(f182(x38841,x38842,f186(x38841,x38842,x38843,x38844)),f328(f328(f105(f879(x38841,a867)),f182(x38841,x38842,x38843)),x38844)) % 167.75/167.49 [3888]E(f328(f129(x38881,x38882),f127(x38881,x38883,x38884)),f328(f328(f80(a872),f328(f328(f80(a872),f328(x38882,x38883)),f328(f129(x38881,x38882),x38884))),f328(a116,f2(a872)))) % 167.75/167.49 [3908]E(f328(f139(x39081,x39082,f328(f7(x39082,x39081,x39081),x39083),x39084),f328(f166(x39082),f117(x39082))),x39084) % 167.75/167.49 [3956]E(f76(x39561,x39562,x39563,x39564,f192(f879(x39561,a867))),x39563) % 167.75/167.49 [4002]E(f328(f328(f328(f328(f72(x40021,f876(x40022)),f328(f16(f876(x40022),x40021),f205(x40022))),x40023),f205(x40022)),x40024),f205(x40022)) % 167.75/167.49 [4157]E(f328(f267(x41571,x41572,x41573),f328(f328(f8(f879(x41572,f878(x41571,x41572)),f879(x41572,x41573),x41571),f328(f8(f878(x41571,x41572),x41573,x41572),x41574)),f263(x41571,x41572))),x41574) % 167.75/167.49 [3461]E(f328(f266(x34611,x34612),f328(f328(f263(x34611,x34612),x34613),x34614)),x34614) % 167.75/167.49 [3462]E(f328(f262(x34621,x34622),f328(f328(f263(x34621,x34622),x34623),x34624)),x34623) % 167.75/167.49 [3496]E(f328(f193(f873(x34961)),f328(f328(f156(x34961,x34962),x34963),x34964)),f328(f193(f873(x34961)),x34962)) % 167.75/167.49 [3497]E(f328(f193(f873(x34971)),f328(f328(f151(x34972,x34971),x34973),x34974)),f328(f193(f873(x34972)),x34974)) % 167.75/167.49 [3517]E(f328(f328(f135(x35171),f328(a116,x35172)),f328(f328(f148(x35171),x35173),x35174)),f328(f328(f135(x35171),x35172),x35174)) % 167.75/167.49 [3582]E(f328(f328(f173(x35821),x35822),f168(x35821,x35823,x35824)),f168(x35821,f328(f328(f240(a872),x35822),x35823),x35824)) % 167.75/167.49 [3583]E(f328(f328(f135(x35831),x35832),f168(x35831,x35833,x35834)),f168(x35831,f328(f328(f22(a872),x35833),x35832),x35834)) % 167.75/167.49 [3589]E(f328(f328(f306(x35891),x35892),f328(f328(f306(x35891),x35893),x35894)),f328(f328(f306(x35891),x35893),f328(f328(f306(x35891),x35892),x35894))) % 167.75/167.49 [3592]E(f328(f328(f151(x35921,x35922),x35923),f118(x35921,x35924)),f118(x35922,f328(f328(f151(x35921,x35922),x35923),x35924))) % 167.75/167.49 [3607]E(f328(f166(x36071),f328(f328(f151(x36072,x36071),x36073),x36074)),f328(f328(f151(x36072,x36071),x36073),f328(f166(x36072),x36074))) % 167.75/167.49 [3608]E(f328(f328(f151(x36081,x36082),x36083),f328(f169(x36081),x36084)),f328(f169(x36082),f328(f328(f151(x36081,x36082),x36083),x36084))) % 167.75/167.49 [3621]E(f328(f328(f173(x36211),f328(a116,x36212)),f328(f328(f148(x36211),x36213),x36214)),f328(f328(f148(x36211),x36213),f328(f328(f173(x36211),x36212),x36214))) % 167.75/167.49 [3625]E(f328(f170(x36251),f328(f328(f151(x36252,x36251),x36253),x36254)),f328(f307(x36252,x36251,x36253),f328(f170(x36252),x36254))) % 167.75/167.49 [3677]E(f17(x36771,x36772,x36773,f328(a3,f328(a116,f328(a19,x36774)))),f328(x36773,x36774)) % 167.75/167.49 [3680]E(f328(f328(f125(x36801),f328(f133(x36801,x36802),x36803)),f328(f133(x36801,x36802),x36804)),f328(f133(x36801,x36802),f328(f328(f125(x36801),x36803),x36804))) % 167.75/167.49 [3693]E(f149(x36931,f328(f328(f151(x36932,x36931),x36933),f149(x36932,x36934))),f149(x36931,f328(f328(f151(x36932,x36931),x36933),x36934))) % 167.75/167.49 [3709]E(f328(f283(x37091,x37091),f328(f328(f284(x37092,x37091),x37093),x37094)),f328(f328(f284(x37092,x37091),f328(f283(x37092,x37092),x37093)),x37094)) % 167.75/167.49 [3719]E(f328(f328(f285(x37191,x37192,x37193),x37194),f192(f879(f878(x37192,x37193),a867))),f192(f879(f878(x37191,x37193),a867))) % 167.75/167.49 [3720]E(f328(f328(f173(x37201),f328(f328(f22(a872),x37202),x37203)),f328(f328(f135(x37201),x37203),x37204)),f328(f328(f135(x37201),x37203),f328(f328(f173(x37201),x37202),x37204))) % 167.75/167.49 [3741]E(f328(f328(f125(x37411),f168(x37411,x37412,x37413)),f168(x37411,x37414,x37413)),f168(x37411,f328(f328(f80(a872),x37412),x37414),x37413)) % 167.75/167.49 [3766]E(f42(f879(x37661,a867),f328(f307(x37662,f879(x37661,a867),x37663),x37664)),f328(f328(f43(x37662,f879(x37661,a867)),x37664),x37663)) % 167.75/167.49 [3767]E(f41(f879(x37671,a867),f328(f307(x37672,f879(x37671,a867),x37673),x37674)),f328(f328(f44(x37672,f879(x37671,a867)),x37674),x37673)) % 167.75/167.49 [3768]E(f328(f193(f873(f878(x37681,x37682))),f328(f328(f180(x37681,x37682),x37683),x37684)),f328(f328(f240(a872),f328(f193(f873(x37681)),x37683)),f328(f193(f873(x37682)),x37684))) % 167.75/167.49 [3770]E(f328(f308(x37701,x37702,x37703),f328(f79(f879(x37702,a867)),x37704)),f328(f79(f879(x37701,a867)),f328(f308(x37701,x37702,x37703),x37704))) % 167.75/167.49 [3800]E(f328(f186(x38001,x38002,x38003,f192(f879(x38001,a867))),x38004),f205(x38002)) % 167.75/167.49 [3821]E(f328(f308(x38211,x38212,x38213),f328(f248(x38212),x38214)),f328(f248(x38211),f328(f328(f8(x38212,a867,x38211),x38214),x38213))) % 167.75/167.49 [3838]E(f328(f328(f162(x38381),f328(f328(f125(x38381),x38382),f328(f328(f148(x38381),x38383),x38384))),f328(f193(f873(x38381)),x38382)),x38383) % 167.75/167.49 [3843]E(f328(f186(x38431,x38432,f328(f16(f876(x38432),x38431),f205(x38432)),x38433),x38434),f205(x38432)) % 167.75/167.49 [3865]E(f328(f307(x38651,x38652,x38653),f328(f308(x38651,x38652,x38653),x38654)),f328(f328(f105(f879(x38652,a867)),x38654),f328(f307(x38651,x38652,x38653),f251(f879(x38651,a867))))) % 167.75/167.49 [3883]P1(f328(f328(f330(x38831),f328(x38832,x38833)),f328(f307(x38834,x38831,x38832),f251(f879(x38834,a867))))) % 167.75/167.49 [3895]E(f328(f328(f125(x38951),f168(x38951,x38952,x38953)),f328(f328(f148(x38951),x38953),x38954)),f328(f328(f148(x38951),x38953),f328(f328(f125(x38951),f168(x38951,x38952,x38953)),x38954))) % 167.75/167.49 [3897]E(f328(f328(f265(x38971,x38972),f328(f170(x38971),x38973)),f328(f16(f879(x38972,a867),x38971),f328(f170(x38972),x38974))),f328(f170(f878(x38971,x38972)),f61(x38971,x38972,x38973,x38974))) % 167.75/167.49 [3911]E(f152(x39111,x39112,f328(f328(f148(x39111),x39113),x39114)),f328(f328(f80(a872),f328(f328(f80(a872),f328(x39112,x39113)),f152(x39111,x39112,x39114))),f328(a116,f2(a872)))) % 167.75/167.49 [3925]E(f189(f873(x39251),f328(f328(f148(x39251),x39252),x39253),f328(f328(f7(a872,f873(x39251),f873(x39251)),f135(x39251)),x39253),x39254),f328(f328(f135(x39251),x39254),f328(f328(f148(x39251),x39252),x39253))) % 167.75/167.49 [3926]P26(x39261,f878(x39262,x39261),f332(x39263,x39264,x39262,x39261),f328(f328(f44(x39262,f879(x39261,a867)),x39264),x39263)) % 167.75/167.49 [3935]E(f328(f328(f22(f879(x39351,a867)),f328(f328(f22(f879(x39351,a867)),x39352),x39353)),f328(f328(f306(x39351),x39354),f192(f879(x39351,a867)))),f328(f328(f22(f879(x39351,a867)),x39352),f328(f328(f306(x39351),x39354),x39353))) % 167.75/167.49 [3947]E(f328(f328(f187(f879(x39471,x39472),f879(x39471,x39472)),x39473),f73(x39472,x39472,x39471,x39474)),f73(x39472,x39472,x39471,f328(f328(f187(x39472,x39472),x39473),x39474))) % 167.75/167.49 [4025]E(f328(f328(f328(f187(f873(x40251),f873(x40251)),x40252),f165(x40251)),f328(f328(f328(f187(f873(x40251),f873(x40251)),x40253),f165(x40251)),x40254)),f328(f328(f328(f187(f873(x40251),f873(x40251)),f328(f328(f80(a872),x40252),x40253)),f165(x40251)),x40254)) % 167.75/167.49 [4111]P1(f328(f328(f242(f879(x41111,a867)),f328(f170(x41111),f328(f328(f156(x41111,x41112),x41113),x41114))),f328(f328(f306(x41111),x41114),f328(f170(x41111),x41112)))) % 167.75/167.49 [4147]E(f328(f328(f44(f879(x41471,a867),f879(f878(x41471,x41472),a867)),x41473),f328(f328(f7(f879(x41471,a867),f879(x41471,f879(x41472,a867)),f879(f878(x41471,x41472),a867)),f265(x41471,x41472)),x41474)),f328(f328(f265(x41471,x41472),f41(f879(x41471,a867),x41473)),x41474)) % 167.75/167.49 [4184]E(f216(x41841,x41842,x41843,f328(f73(x41842,f879(a103,f879(a103,f879(f878(a103,a103),f879(a103,f874(x41842))))),x41841,f215(x41842)),x41844)),f217(x41841,x41842,x41844,x41843)) % 167.75/167.49 [4201]E(f212(x42011,x42012,x42013,f328(f73(x42012,f879(a103,f879(a103,f879(f878(a103,a103),f879(a103,f874(f876(x42012)))))),x42011,f211(x42012)),x42014)),f213(x42011,x42012,x42014,x42013)) % 167.75/167.49 [4206]P1(f328(f67(x42061,x42062,x42063,x42064,f192(f879(x42061,a867))),x42064)) % 167.75/167.49 [4248]E(f328(f328(f44(x42481,f879(x42482,a867)),x42483),f328(f328(f7(x42481,f879(x42482,a867),f879(x42482,a867)),f328(f328(f8(x42482,f879(f879(x42482,a867),f879(x42482,a867)),x42481),f306(x42482)),x42484)),f192(f879(x42482,a867)))),f328(f307(x42481,x42482,x42484),x42483)) % 167.75/167.49 [4255]P1(f328(f328(f242(f879(x42551,a867)),f328(f259(x42552,x42551),f328(f328(f105(f879(f878(x42552,x42551),a867)),x42553),x42554))),f328(f328(f105(f879(x42551,a867)),f328(f259(x42552,x42551),x42553)),f328(f259(x42552,x42551),x42554)))) % 167.75/167.49 [4256]P1(f328(f328(f242(f879(x42561,a867)),f328(f261(x42561,x42562),f328(f328(f105(f879(f878(x42561,x42562),a867)),x42563),x42564))),f328(f328(f105(f879(x42561,a867)),f328(f261(x42561,x42562),x42563)),f328(f261(x42561,x42562),x42564)))) % 167.75/167.49 [4318]P1(f328(f328(f242(f879(f878(x43181,x43182),a867)),f328(f307(x43182,f878(x43181,x43182),f332(x43183,x43184,x43181,x43182)),f328(f328(f44(x43181,f879(x43182,a867)),x43184),x43183))),f328(f328(f265(x43181,x43182),x43184),x43183))) % 167.75/167.49 [4319]E(f328(f120(x43191,f878(x43191,x43192),x43193),f328(f328(f8(f879(x43192,f874(f878(x43191,x43192))),f874(f878(x43191,x43192)),x43191),f120(x43192,f878(x43191,x43192),x43194)),f328(f328(f8(f879(x43192,f878(x43191,x43192)),f879(x43192,f874(f878(x43191,x43192))),x43191),f328(f8(f878(x43191,x43192),f874(f878(x43191,x43192)),x43192),f126(f878(x43191,x43192)))),f263(x43191,x43192)))),f131(x43191,x43192,x43193,x43194)) % 167.75/167.49 [4359]E(f85(f878(x43591,x43592),f328(f267(x43591,x43592,a867),f328(f328(f7(x43591,f879(x43592,a867),f879(x43592,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x43592,a867),f879(x43592,a867)),x43591),f8(a867,a867,x43592)),f328(f328(f8(a867,f879(a867,a867),x43591),a326),f328(a325,x43593)))),f328(a325,x43594)))),f328(f328(f263(x43591,x43592),x43593),x43594)) % 167.75/167.49 [4360]E(f90(f878(x43601,x43602),f328(f267(x43601,x43602,a867),f328(f328(f7(x43601,f879(x43602,a867),f879(x43602,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x43602,a867),f879(x43602,a867)),x43601),f8(a867,a867,x43602)),f328(f328(f8(a867,f879(a867,a867),x43601),a326),f328(a325,x43603)))),f328(a325,x43604)))),f328(f328(f263(x43601,x43602),x43603),x43604)) % 167.75/167.49 [4432]E(f328(f328(f267(f873(x44321),f873(x44321),f878(f873(x44321),f873(x44321))),f328(f328(f18(f873(x44321),f879(f873(x44321),f878(f873(x44321),f873(x44321))),f879(f873(x44321),f878(f873(x44321),f873(x44321)))),f328(f328(f8(f879(f873(x44321),f879(f878(f873(x44321),f873(x44321)),f878(f873(x44321),f873(x44321)))),f879(f879(f873(x44321),f878(f873(x44321),f873(x44321))),f879(f873(x44321),f878(f873(x44321),f873(x44321)))),f873(x44321)),f18(f873(x44321),f878(f873(x44321),f873(x44321)),f878(f873(x44321),f873(x44321)))),f328(f328(f8(f879(f873(x44321),f878(f873(x44321),f873(x44321))),f879(f873(x44321),f879(f878(f873(x44321),f873(x44321)),f878(f873(x44321),f873(x44321)))),f873(x44321)),f328(f8(f878(f873(x44321),f873(x44321)),f879(f878(f873(x44321),f873(x44321)),f878(f873(x44321),f873(x44321))),f873(x44321)),f328(f100(f878(f873(x44321),f873(x44321))),f328(x44322,x44323)))),f328(f328(f8(f873(x44321),f879(f873(x44321),f878(f873(x44321),f873(x44321))),f873(x44321)),f263(f873(x44321),f873(x44321))),f328(f148(x44321),x44323))))),f328(f328(f7(f873(x44321),f879(f873(x44321),f873(x44321)),f879(f873(x44321),f878(f873(x44321),f873(x44321)))),f328(f328(f8(f879(f873(x44321),f878(f873(x44321),f873(x44321))),f879(f879(f873(x44321),f873(x44321)),f879(f873(x44321),f878(f873(x44321),f873(x44321)))),f873(x44321)),f8(f873(x44321),f878(f873(x44321),f873(x44321)),f873(x44321))),f263(f873(x44321),f873(x44321)))),f328(f148(x44321),x44323)))),f164(x44321,x44322,x44324)),f164(x44321,x44322,f328(f328(f148(x44321),x44323),x44324))) % 167.75/167.49 [4438]E(f328(f139(f879(x44381,f876(x44382)),f878(x44381,x44382),f328(f7(f878(x44381,x44382),f879(x44381,f876(x44382)),f879(x44381,f876(x44382))),f328(f267(x44381,x44382,f879(f879(x44381,f876(x44382)),f879(x44381,f876(x44382)))),f328(f328(f7(x44381,f879(x44382,f876(x44382)),f879(x44382,f879(f879(x44381,f876(x44382)),f879(x44381,f876(x44382))))),f328(f328(f8(f879(f876(x44382),f879(f879(x44381,f876(x44382)),f879(x44381,f876(x44382)))),f879(f879(x44382,f876(x44382)),f879(x44382,f879(f879(x44381,f876(x44382)),f879(x44381,f876(x44382))))),x44381),f8(f876(x44382),f879(f879(x44381,f876(x44382)),f879(x44381,f876(x44382))),x44382)),f328(f328(f8(f879(f879(x44381,f876(x44382)),f879(f876(x44382),f879(x44381,f876(x44382)))),f879(f876(x44382),f879(f879(x44381,f876(x44382)),f879(x44381,f876(x44382)))),x44381),f7(f879(x44381,f876(x44382)),f876(x44382),f879(x44381,f876(x44382)))),f328(f7(f879(x44381,f876(x44382)),x44381,f879(f876(x44382),f879(x44381,f876(x44382)))),f72(x44381,f876(x44382)))))),f235(x44382)))),x44383),f328(f166(f878(x44381,x44382)),x44384)),f183(x44381,x44382,x44383,f328(f176(x44381,x44382),x44384))) % 167.75/167.49 [3536]E(f328(f193(f871(x35361)),f328(f328(f328(f92(x35361),x35362),x35363),x35364)),f2(a872)) % 167.75/167.49 [3656]E(f328(f328(f173(x36561),x36562),f328(f328(f173(x36561),x36563),x36564)),f328(f328(f173(x36561),f328(f328(f240(a872),x36562),x36563)),x36564)) % 167.75/167.49 [3657]E(f328(f328(f135(x36571),x36572),f328(f328(f135(x36571),x36573),x36574)),f328(f328(f135(x36571),f328(f328(f80(a872),x36572),x36573)),x36574)) % 167.75/167.49 [3669]E(f328(f328(f125(x36691),f328(f328(f148(x36691),x36692),x36693)),x36694),f328(f328(f148(x36691),x36692),f328(f328(f125(x36691),x36693),x36694))) % 167.75/167.49 [3670]E(f328(f328(f125(x36701),f328(f328(f125(x36701),x36702),x36703)),x36704),f328(f328(f125(x36701),x36702),f328(f328(f125(x36701),x36703),x36704))) % 167.75/167.49 [3750]E(f328(f328(f162(x37501),f328(f328(f148(x37501),x37502),x37503)),x37504),f189(x37501,x37502,f328(f162(x37501),x37503),x37504)) % 167.75/167.49 [3759]E(f328(f328(f187(x37591,x37591),x37592),f328(f328(f187(x37591,x37591),x37593),x37594)),f328(f328(f187(x37591,x37591),f328(f328(f81(a872),x37593),x37592)),x37594)) % 167.75/167.49 [3788]E(f328(f328(f114(f879(x37881,a867)),x37882),f328(f328(f306(x37881),x37883),x37884)),f328(f328(f306(x37881),x37883),f328(f328(f114(f879(x37881,a867)),x37882),x37884))) % 167.75/167.49 [3803]E(f328(f328(f328(f187(x38031,x38031),x38032),x38033),f328(x38033,x38034)),f328(x38033,f328(f328(f328(f187(x38031,x38031),x38032),x38033),x38034))) % 167.75/167.49 [3811]E(f328(f328(f285(x38111,x38112,x38113),f192(f879(f878(x38111,x38112),a867))),x38114),f192(f879(f878(x38111,x38113),a867))) % 167.75/167.49 [3827]E(f328(f328(f114(f879(x38271,a867)),f328(f328(f306(x38271),x38272),x38273)),x38274),f328(f328(f306(x38271),x38272),f328(f328(f114(f879(x38271,a867)),x38273),x38274))) % 167.75/167.49 [3846]E(f183(x38461,x38462,f328(f176(x38461,x38462),x38463),f328(f176(x38461,x38462),x38464)),f328(f176(x38461,x38462),f328(f328(f125(f878(x38461,x38462)),x38464),x38463))) % 167.75/167.49 [3847]E(f328(f39(f878(x38471,x38472)),f328(f328(f265(x38471,x38472),x38473),f328(f16(f879(x38472,a867),x38471),x38474))),f328(f328(f81(a872),f328(f39(x38471),x38473)),f328(f39(x38472),x38474))) % 167.75/167.49 [3854]E(f328(f328(f105(f879(x38541,a867)),f328(f328(f306(x38541),x38542),x38543)),f328(f328(f306(x38541),x38542),x38544)),f328(f328(f306(x38541),x38542),f328(f328(f105(f879(x38541,a867)),x38543),x38544))) % 167.75/167.49 [3869]E(f328(f328(f114(f879(x38691,a867)),x38692),f328(f328(f114(f879(x38691,a867)),x38693),x38694)),f328(f328(f114(f879(x38691,a867)),x38693),f328(f328(f114(f879(x38691,a867)),x38692),x38694))) % 167.75/167.49 [3870]E(f328(f328(f105(f879(x38701,a867)),x38702),f328(f328(f105(f879(x38701,a867)),x38703),x38704)),f328(f328(f105(f879(x38701,a867)),x38703),f328(f328(f105(f879(x38701,a867)),x38702),x38704))) % 167.75/167.49 [3879]E(f65(x38791,x38792,f328(f328(f8(x38792,f879(x38792,x38792),x38791),x38793),x38794)),f328(f66(x38792,x38791,x38793),x38794)) % 167.75/167.49 [3889]E(f178(x38891,f328(f328(f151(f873(x38892),f873(x38891)),f328(f151(x38892,x38891),x38893)),x38894)),f328(f328(f151(f873(x38892),f873(x38891)),f328(f151(x38892,x38891),x38893)),f178(x38892,x38894))) % 167.75/167.49 [3907]E(f328(f139(f873(x39071),f873(x39071),f125(x39071),f117(x39071)),f328(f328(f151(x39072,f873(x39071)),x39073),x39074)),f161(x39072,x39071,x39073,x39074)) % 167.75/167.49 [3910]E(f186(x39101,x39102,x39103,f328(f79(f879(x39101,a867)),f328(f328(f306(x39101),x39104),f192(f879(x39101,a867))))),f328(f328(f328(f72(x39101,f876(x39102)),x39103),x39104),f205(x39102))) % 167.75/167.49 [3952]E(f328(f328(f328(f72(x39521,f876(x39522)),f328(f176(x39521,x39522),x39523)),f328(f262(x39521,x39522),x39524)),f328(f235(x39522),f328(f266(x39521,x39522),x39524))),f328(f176(x39521,x39522),f328(f328(f148(f878(x39521,x39522)),x39524),x39523))) % 167.75/167.49 [3969]E(f328(f73(x39691,x39691,x39691,f328(f328(f187(x39691,x39691),x39692),x39693)),f328(f328(f187(x39691,x39691),x39694),x39693)),f328(f328(f187(x39691,x39691),f328(f328(f80(a872),x39692),x39694)),x39693)) % 167.75/167.49 [3994]E(f328(f328(f105(f879(x39941,a867)),f328(f328(f114(f879(x39941,a867)),x39942),x39943)),f328(f328(f114(f879(x39941,a867)),x39942),x39944)),f328(f328(f114(f879(x39941,a867)),x39942),f328(f328(f105(f879(x39941,a867)),x39943),x39944))) % 167.75/167.49 [3995]E(f328(f328(f105(f879(x39951,a867)),f328(f328(f22(f879(x39951,a867)),x39952),x39953)),f328(f328(f22(f879(x39951,a867)),x39952),x39954)),f328(f328(f22(f879(x39951,a867)),x39952),f328(f328(f114(f879(x39951,a867)),x39953),x39954))) % 167.75/167.49 [3996]E(f328(f328(f114(f879(x39961,a867)),f328(f328(f22(f879(x39961,a867)),x39962),x39963)),f328(f328(f22(f879(x39961,a867)),x39962),x39964)),f328(f328(f22(f879(x39961,a867)),x39962),f328(f328(f105(f879(x39961,a867)),x39963),x39964))) % 167.75/167.49 [3997]E(f328(f328(f114(f879(x39971,a867)),f328(f328(f105(f879(x39971,a867)),x39972),x39973)),f328(f328(f105(f879(x39971,a867)),x39972),x39974)),f328(f328(f105(f879(x39971,a867)),x39972),f328(f328(f114(f879(x39971,a867)),x39973),x39974))) % 167.75/167.49 [3998]E(f328(f328(f22(f879(x39981,a867)),f328(f328(f105(f879(x39981,a867)),x39982),x39983)),f328(f328(f105(f879(x39981,a867)),x39982),x39984)),f328(f328(f105(f879(x39981,a867)),x39982),f328(f328(f22(f879(x39981,a867)),x39983),x39984))) % 167.75/167.49 [4004]E(f328(f39(f878(x40041,x40042)),f328(f328(f265(x40041,x40042),f328(f328(f306(x40041),x40043),f192(f879(x40041,a867)))),f328(f16(f879(x40042,a867),x40041),x40044))),f328(f39(x40042),x40044)) % 167.75/167.49 [4040]E(f328(f328(f44(x40401,f879(x40402,a867)),x40403),f328(f328(f8(f879(x40402,a867),f879(x40402,a867),x40401),f79(f879(x40402,a867))),x40404)),f328(f79(f879(x40402,a867)),f328(f328(f43(x40401,f879(x40402,a867)),x40403),x40404))) % 167.75/167.49 [4041]E(f328(f328(f43(x40411,f879(x40412,a867)),x40413),f328(f328(f8(f879(x40412,a867),f879(x40412,a867),x40411),f79(f879(x40412,a867))),x40414)),f328(f79(f879(x40412,a867)),f328(f328(f44(x40411,f879(x40412,a867)),x40413),x40414))) % 167.75/167.49 [4055]E(f328(f328(f285(x40551,x40551,x40551),f328(f328(f187(f878(x40551,x40551),a867),x40552),x40553)),f328(f328(f187(f878(x40551,x40551),a867),x40554),x40553)),f328(f328(f187(f878(x40551,x40551),a867),f328(f328(f80(a872),x40552),x40554)),x40553)) % 167.75/167.49 [4086]E(f328(f328(f43(x40861,f879(f879(x40862,a867),a867)),x40863),f328(f328(f8(f879(x40862,a867),f879(f879(x40862,a867),a867),x40861),f305(x40862)),x40864)),f328(f305(x40862),f328(f328(f43(x40861,f879(x40862,a867)),x40863),x40864))) % 167.75/167.49 [4115]E(f328(f328(f43(f879(x41151,a867),f879(x41152,a867)),x41153),f328(f328(f7(f879(x41151,a867),f879(x41151,f879(x41152,a867)),f879(x41152,a867)),f43(x41151,f879(x41152,a867))),x41154)),f328(f328(f43(x41151,f879(x41152,a867)),f41(f879(x41151,a867),x41153)),x41154)) % 167.75/167.49 [4116]E(f328(f328(f44(f879(x41161,a867),f879(x41162,a867)),x41163),f328(f328(f7(f879(x41161,a867),f879(x41161,f879(x41162,a867)),f879(x41162,a867)),f44(x41161,f879(x41162,a867))),x41164)),f328(f328(f44(x41161,f879(x41162,a867)),f41(f879(x41161,a867),x41163)),x41164)) % 167.75/167.49 [4121]E(f328(f328(f151(x41211,x41212),x41213),f328(f139(f873(x41211),f873(x41211),f125(x41211),f117(x41211)),x41214)),f328(f139(f873(x41212),f873(x41212),f125(x41212),f117(x41212)),f328(f328(f151(f873(x41211),f873(x41212)),f328(f151(x41211,x41212),x41213)),x41214))) % 167.75/167.49 [4125]E(f189(f873(x41251),f117(x41251),f328(f328(f8(f873(x41251),f873(x41251),a872),f328(f148(x41251),x41252)),f328(f328(f7(a872,f873(x41251),f873(x41251)),f173(x41251)),x41253)),x41254),f328(f328(f173(x41251),x41254),f328(f328(f148(x41251),x41252),x41253))) % 167.75/167.49 [4167]P1(f328(f328(f242(f879(x41671,a867)),f328(f307(x41672,x41671,x41673),f328(f308(x41672,x41671,x41673),x41674))),x41674)) % 167.75/167.49 [4170]E(f328(f307(f878(x41701,x41702),f878(x41702,x41701),f328(f267(x41701,x41702,f878(x41702,x41701)),f328(f7(x41702,x41701,f878(x41702,x41701)),f263(x41702,x41701)))),f328(f328(f265(x41701,x41702),x41703),f328(f16(f879(x41702,a867),x41701),x41704))),f328(f328(f265(x41702,x41701),x41704),f328(f16(f879(x41701,a867),x41702),x41703))) % 167.75/167.49 [4179]E(f328(f328(f44(x41791,f879(x41792,a867)),x41793),f328(f328(f8(f879(x41791,a867),f879(x41792,a867),x41791),f282(x41791,x41792,x41794)),f328(f328(f7(x41791,f879(x41791,a867),f879(x41791,a867)),f306(x41791)),f192(f879(x41791,a867))))),f328(f282(x41791,x41792,x41794),x41793)) % 167.75/167.49 [4180]E(f328(f328(f44(x41801,f879(x41802,a867)),x41803),f328(f328(f8(f879(x41801,a867),f879(x41802,a867),x41801),f308(x41802,x41801,x41804)),f328(f328(f7(x41801,f879(x41801,a867),f879(x41801,a867)),f306(x41801)),f192(f879(x41801,a867))))),f328(f308(x41802,x41801,x41804),x41803)) % 167.75/167.49 [4270]E(f328(f328(f114(f879(x42701,a867)),f328(f328(f114(f879(x42701,a867)),f328(f328(f105(f879(x42701,a867)),x42702),x42703)),f328(f328(f105(f879(x42701,a867)),x42703),x42704))),f328(f328(f105(f879(x42701,a867)),x42704),x42702)),f328(f328(f105(f879(x42701,a867)),f328(f328(f105(f879(x42701,a867)),f328(f328(f114(f879(x42701,a867)),x42702),x42703)),f328(f328(f114(f879(x42701,a867)),x42703),x42704))),f328(f328(f114(f879(x42701,a867)),x42704),x42702))) % 167.75/167.49 [4332]E(f328(f139(f873(x43321),f873(x43321),f125(x43321),f117(x43321)),f328(f328(f151(x43322,f873(x43321)),f328(f328(f7(x43322,f873(x43321),f873(x43321)),f328(f328(f8(x43321,f879(f873(x43321),f873(x43321)),x43322),f148(x43321)),x43323)),f117(x43321))),x43324)),f328(f328(f151(x43322,x43321),x43323),x43324)) % 167.75/167.49 [4343]E(f328(f328(f86(a1,x43431),f328(f107(a1),f328(f328(f80(a1),x43432),a101))),f328(f328(f18(a1,x43431,x43431),f328(f328(f7(a1,x43431,f879(x43431,x43431)),f328(f328(f8(a867,f879(x43431,f879(x43431,x43431)),a1),f100(x43431)),a197)),x43433)),f328(f328(f8(a872,x43431,a1),x43434),a108))),f189(x43431,x43433,x43434,f328(f107(a872),x43432))) % 167.75/167.49 [4546]~P1(f328(f328(f192(f879(x45461,f879(x45462,a867))),x45463),x45464)) % 167.75/167.49 [3814]E(f328(f328(f162(x38141),f328(f328(f125(x38141),x38142),x38143)),f328(f328(f80(a872),f328(f193(f873(x38141)),x38142)),x38144)),f328(f328(f162(x38141),x38143),x38144)) % 167.75/167.49 [3820]E(f328(f328(f135(x38201),x38202),f328(f328(f173(x38201),f328(f328(f80(a872),x38203),x38202)),x38204)),f328(f328(f173(x38201),x38203),f328(f328(f135(x38201),x38202),x38204))) % 167.75/167.49 [3923]E(f328(f328(f114(f879(x39231,a867)),f328(f259(x39232,x39231),x39233)),f328(f259(x39232,x39231),x39234)),f328(f259(x39232,x39231),f328(f328(f114(f879(f878(x39232,x39231),a867)),x39233),x39234))) % 167.75/167.49 [3924]E(f328(f328(f114(f879(x39241,a867)),f328(f261(x39241,x39242),x39243)),f328(f261(x39241,x39242),x39244)),f328(f261(x39241,x39242),f328(f328(f114(f879(f878(x39241,x39242),a867)),x39243),x39244))) % 167.75/167.49 [3929]E(f328(f328(f114(f879(x39291,a867)),f328(f328(f114(f879(x39291,a867)),x39292),x39293)),x39294),f328(f328(f114(f879(x39291,a867)),x39292),f328(f328(f114(f879(x39291,a867)),x39293),x39294))) % 167.75/167.49 [3930]E(f328(f328(f22(f879(x39301,a867)),f328(f328(f105(f879(x39301,a867)),x39302),x39303)),x39304),f328(f328(f105(f879(x39301,a867)),x39302),f328(f328(f22(f879(x39301,a867)),x39303),x39304))) % 167.75/167.49 [3931]E(f328(f328(f105(f879(x39311,a867)),f328(f328(f105(f879(x39311,a867)),x39312),x39313)),x39314),f328(f328(f105(f879(x39311,a867)),x39312),f328(f328(f105(f879(x39311,a867)),x39313),x39314))) % 167.75/167.49 [3971]E(f328(f328(f114(f879(f878(x39711,x39712),a867)),f328(f283(x39712,x39711),x39713)),f328(f283(x39712,x39711),x39714)),f328(f283(x39712,x39711),f328(f328(f114(f879(f878(x39712,x39711),a867)),x39713),x39714))) % 167.75/167.49 [3972]E(f328(f328(f105(f879(f878(x39721,x39722),a867)),f328(f283(x39722,x39721),x39723)),f328(f283(x39722,x39721),x39724)),f328(f283(x39722,x39721),f328(f328(f105(f879(f878(x39722,x39721),a867)),x39723),x39724))) % 167.75/167.49 [3986]E(f328(f328(f114(f879(x39861,f879(x39862,a867))),f252(x39862,x39861,x39863)),f252(x39862,x39861,x39864)),f252(x39862,x39861,f328(f328(f114(f879(x39862,f879(x39861,a867))),x39863),x39864))) % 167.75/167.49 [3987]E(f328(f328(f105(f879(x39871,f879(x39872,a867))),f252(x39872,x39871,x39873)),f252(x39872,x39871,x39874)),f252(x39872,x39871,f328(f328(f105(f879(x39872,f879(x39871,a867))),x39873),x39874))) % 167.75/167.49 [4044]E(f328(f328(f105(f879(x40441,a867)),f328(f328(f114(f879(x40441,a867)),x40442),x40443)),f328(f328(f114(f879(x40441,a867)),x40444),x40443)),f328(f328(f114(f879(x40441,a867)),f328(f328(f105(f879(x40441,a867)),x40442),x40444)),x40443)) % 167.75/167.49 [4045]E(f328(f328(f114(f879(x40451,a867)),f328(f328(f22(f879(x40451,a867)),x40452),x40453)),f328(f328(f22(f879(x40451,a867)),x40454),x40453)),f328(f328(f22(f879(x40451,a867)),f328(f328(f114(f879(x40451,a867)),x40452),x40454)),x40453)) % 167.75/167.49 [4046]E(f328(f328(f114(f879(x40461,a867)),f328(f328(f105(f879(x40461,a867)),x40462),x40463)),f328(f328(f105(f879(x40461,a867)),x40464),x40463)),f328(f328(f105(f879(x40461,a867)),f328(f328(f114(f879(x40461,a867)),x40462),x40464)),x40463)) % 167.75/167.49 [4047]E(f328(f328(f22(f879(x40471,a867)),f328(f328(f105(f879(x40471,a867)),x40472),x40473)),f328(f328(f105(f879(x40471,a867)),x40474),x40473)),f328(f328(f105(f879(x40471,a867)),f328(f328(f22(f879(x40471,a867)),x40472),x40474)),x40473)) % 167.75/167.49 [4048]E(f328(f328(f22(f879(x40481,a867)),f328(f328(f105(f879(x40481,a867)),x40482),x40483)),f328(f328(f105(f879(x40481,a867)),x40484),x40483)),f328(f328(f22(f879(x40481,a867)),f328(f328(f105(f879(x40481,a867)),x40482),x40483)),x40484)) % 167.75/167.49 [4058]E(f328(f328(f22(f879(x40581,a867)),f328(f328(f22(f879(x40581,a867)),x40582),f328(f328(f306(x40581),x40583),f192(f879(x40581,a867))))),x40584),f328(f328(f22(f879(x40581,a867)),x40582),f328(f328(f306(x40581),x40583),x40584))) % 167.75/167.49 [4112]E(f328(f328(f114(f879(x41121,a867)),f328(f328(f306(x41121),x41122),f328(f328(f306(x41121),x41123),f192(f879(x41121,a867))))),f328(f281(x41121),x41124)),f328(f281(x41121),f328(f328(f306(f878(x41121,x41121)),f328(f328(f263(x41121,x41121),x41122),x41123)),x41124))) % 167.75/167.49 [4142]E(f328(f328(f44(a872,f879(x41421,a867)),f328(f297(a872),x41422)),f328(f328(f8(a872,f879(x41421,a867),a872),x41423),f328(f328(f7(a872,a872,a872),f80(a872)),x41424))),f328(f328(f44(a872,f879(x41421,a867)),f299(a872,x41424,f328(f328(f80(a872),x41422),x41424))),x41423)) % 167.75/167.49 [4143]E(f172(x41431,f328(f282(x41431,x41431,x41432),f328(f328(f306(x41431),x41433),f192(f879(x41431,a867)))),f328(f282(f873(x41431),f873(x41431),f155(x41431,x41432)),f328(f328(f306(f873(x41431)),x41434),f192(f879(f873(x41431),a867))))),f328(f282(f873(x41431),f873(x41431),f155(x41431,x41432)),f328(f328(f306(f873(x41431)),f328(f328(f148(x41431),x41433),x41434)),f192(f879(f873(x41431),a867))))) % 167.75/167.49 [4204]E(f328(f176(x42041,x42042),f328(f328(f151(x42041,f878(x42041,x42042)),f328(f328(f18(x42041,x42042,f878(x42041,x42042)),f263(x42041,x42042)),x42043)),x42044)),f186(x42041,x42042,f328(f73(x42042,f876(x42042),x42041,f235(x42042)),x42043),f328(f170(x42041),x42044))) % 167.75/167.49 [4209]E(f328(f248(x42091),f328(f328(f7(x42091,f879(x42092,a867),a867),f328(f328(f8(x42092,f879(f879(x42092,a867),a867),x42091),f330(x42092)),x42093)),x42094)),f328(f308(x42091,x42092,x42093),x42094)) % 167.75/167.49 [4303]E(f328(f248(x43031),f328(f328(f7(x43031,f879(f878(x43032,x43031),a867),a867),f328(f328(f8(f878(x43032,x43031),f879(f879(f878(x43032,x43031),a867),a867),x43031),f330(f878(x43032,x43031))),f328(f263(x43032,x43031),x43033))),x43034)),f328(f282(x43032,x43031,x43034),f328(f328(f306(x43032),x43033),f192(f879(x43032,a867))))) % 167.75/167.49 [4317]E(f328(f328(f151(f878(x43171,a872),x43171),f262(x43171,a872)),f328(f133(f878(x43171,a872),f328(f328(f8(a872,a867,f878(x43171,a872)),x43172),f328(f328(f8(a872,a872,f878(x43171,a872)),a116),f266(x43171,a872)))),f328(f328(f180(x43171,a872),x43173),x43174))),f328(f328(f151(f878(x43171,a872),x43171),f262(x43171,a872)),f328(f133(f878(x43171,a872),f328(f328(f8(a872,a867,f878(x43171,a872)),x43172),f266(x43171,a872))),f328(f328(f180(x43171,a872),x43173),f328(f328(f151(a872,a872),a116),x43174))))) % 167.75/167.49 [4325]P1(f328(f328(f242(f879(f879(x43251,a867),a867)),f328(f328(f44(x43252,f879(f879(x43251,a867),a867)),x43253),f328(f328(f8(f879(x43251,a867),f879(f879(x43251,a867),a867),x43252),f305(x43251)),x43254))),f328(f305(x43251),f328(f328(f44(x43252,f879(x43251,a867)),x43253),x43254)))) % 167.75/167.49 [4367]E(f328(f328(f86(a1,x43671),f328(f107(a1),f328(f328(f80(a1),x43672),a101))),f328(f328(f18(a1,x43671,x43671),f328(f328(f7(a1,x43671,f879(x43671,x43671)),f328(f328(f8(a867,f879(x43671,f879(x43671,x43671)),a1),f100(x43671)),a197)),x43673)),f328(f328(f18(a1,x43671,x43671),f328(f328(f8(a872,f879(x43671,x43671),a1),x43674),a108)),f328(f328(f8(a872,x43671,a1),f188(x43671,x43673,x43674)),a108)))),f328(f188(x43671,x43673,x43674),f328(f107(a872),x43672))) % 167.75/167.49 [4370]E(f328(f328(f151(x43701,x43702),f328(f73(f876(x43702),x43702,x43701,f239(x43702)),x43703)),f328(f133(x43701,f328(f328(f8(a867,a867,x43701),a323),f328(f328(f7(x43701,f876(x43702),a867),f328(f328(f8(f876(x43702),f879(f876(x43702),a867),x43701),a325),x43703)),f205(x43702)))),x43704)),f160(x43701,x43702,x43703,x43704)) % 167.75/167.49 [4393]E(f328(f248(f878(x43931,x43932)),f328(f267(x43931,x43932,a867),f328(f328(f7(x43931,f879(x43932,a867),f879(x43932,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x43932,a867),f879(x43932,a867)),x43931),f8(a867,a867,x43932)),f328(f328(f8(a867,f879(a867,a867),x43931),a326),f328(f328(f7(x43931,f879(x43931,a867),a867),f330(x43931)),x43933)))),f328(f328(f7(x43932,f879(x43932,a867),a867),f330(x43932)),x43934)))),f229(x43931,x43932,x43933,x43934)) % 167.75/167.49 [4427]E(f328(f328(f44(x44271,f879(f878(x44271,x44272),a867)),x44273),f328(f328(f18(x44271,f879(x44272,f879(f878(x44271,x44272),a867)),f879(f878(x44271,x44272),a867)),f328(f328(f8(f879(x44272,a867),f879(f879(x44272,f879(f878(x44271,x44272),a867)),f879(f878(x44271,x44272),a867)),x44271),f44(x44272,f879(f878(x44271,x44272),a867))),x44274)),f328(f328(f7(x44271,f879(f878(x44271,x44272),a867),f879(x44272,f879(f878(x44271,x44272),a867))),f328(f328(f8(f879(x44272,f879(f879(f878(x44271,x44272),a867),f879(f878(x44271,x44272),a867))),f879(f879(f878(x44271,x44272),a867),f879(x44272,f879(f878(x44271,x44272),a867))),x44271),f7(x44272,f879(f878(x44271,x44272),a867),f879(f878(x44271,x44272),a867))),f328(f328(f8(f879(x44272,f878(x44271,x44272)),f879(x44272,f879(f879(f878(x44271,x44272),a867),f879(f878(x44271,x44272),a867))),x44271),f328(f8(f878(x44271,x44272),f879(f879(f878(x44271,x44272),a867),f879(f878(x44271,x44272),a867)),x44272),f306(f878(x44271,x44272)))),f263(x44271,x44272)))),f192(f879(f878(x44271,x44272),a867))))),f328(f328(f265(x44271,x44272),x44273),x44274)) % 167.75/167.49 [3981]E(f328(f328(f125(x39811),f328(f328(f173(x39811),x39812),x39813)),f328(f328(f173(x39811),f328(f328(f22(a872),x39812),f328(f193(f873(x39811)),x39813))),x39814)),f328(f328(f173(x39811),x39812),f328(f328(f125(x39811),x39813),x39814))) % 167.75/167.49 [3982]E(f328(f328(f125(x39821),f328(f328(f135(x39821),x39822),x39823)),f328(f328(f135(x39821),f328(f328(f22(a872),x39822),f328(f193(f873(x39821)),x39823))),x39824)),f328(f328(f135(x39821),x39822),f328(f328(f125(x39821),x39823),x39824))) % 167.75/167.49 [4034]E(f328(f328(f80(a872),f328(f328(f81(a872),x40341),x40342)),f328(f328(f80(a872),f328(f328(f81(a872),x40343),x40342)),x40344)),f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f80(a872),x40341),x40343)),x40342)),x40344)) % 167.75/167.49 [4234]P1(f328(f328(f242(f879(x42341,a867)),f328(f328(f22(f879(x42341,a867)),f328(f259(x42342,x42341),x42343)),f328(f259(x42342,x42341),x42344))),f328(f259(x42342,x42341),f328(f328(f22(f879(f878(x42342,x42341),a867)),x42343),x42344)))) % 167.75/167.49 [4235]P1(f328(f328(f242(f879(x42351,a867)),f328(f328(f22(f879(x42351,a867)),f328(f261(x42351,x42352),x42353)),f328(f261(x42351,x42352),x42354))),f328(f261(x42351,x42352),f328(f328(f22(f879(f878(x42351,x42352),a867)),x42353),x42354)))) % 167.75/167.49 [4345]E(f328(f328(f80(a1),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x43451),x43452)),f192(f879(f878(a872,a872),a867)))))),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x43453),x43454)),f192(f879(f878(a872,a872),a867)))))),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),f328(f328(f80(a872),x43451),x43453)),f328(f328(f80(a872),x43452),x43454))),f192(f879(f878(a872,a872),a867)))))) % 167.75/167.49 [4388]E(f328(f328(f81(a1),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x43881),x43882)),f192(f879(f878(a872,a872),a867)))))),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x43883),x43884)),f192(f879(f878(a872,a872),a867)))))),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),f328(f328(f80(a872),f328(f328(f81(a872),x43881),x43883)),f328(f328(f81(a872),x43882),x43884))),f328(f328(f80(a872),f328(f328(f81(a872),x43881),x43884)),f328(f328(f81(a872),x43882),x43883)))),f192(f879(f878(a872,a872),a867)))))) % 167.75/167.49 [4408]E(f328(f248(x44081),f328(f328(f8(f879(x44082,a867),a867,x44081),f88(x44082)),f328(f328(f8(f879(x44082,a867),f879(x44082,a867),x44081),f328(f18(x44082,a867,a867),f328(f328(f8(a867,f879(a867,a867),x44082),a331),f328(f328(f7(x44082,f879(x44082,a867),a867),f330(x44082)),x44083)))),f328(f328(f7(x44081,f879(x44082,f879(x44081,a867)),f879(x44082,a867)),f328(f328(f8(f879(f879(x44081,a867),a867),f879(f879(x44082,f879(x44081,a867)),f879(x44082,a867)),x44081),f8(f879(x44081,a867),a867,x44082)),f330(x44081))),x44084)))),f328(f328(f43(x44082,f879(x44081,a867)),x44083),x44084)) % 167.75/167.49 [4442]E(f328(f328(f285(x44421,x44421,x44421),f328(f328(f306(f878(x44421,x44421)),f328(f328(f263(x44421,x44421),x44422),x44423)),x44424)),f304(x44421,f328(f328(f306(f878(x44421,x44421)),f328(f328(f263(x44421,x44421),x44422),x44423)),x44424))),f328(f328(f114(f879(f878(x44421,x44421),a867)),f328(f328(f285(x44421,x44421,x44421),x44424),f304(x44421,x44424))),f328(f248(f878(x44421,x44421)),f328(f267(x44421,x44421,a867),f328(f328(f7(x44421,f879(x44421,a867),f879(x44421,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x44421,a867),f879(x44421,a867)),x44421),f8(a867,a867,x44421)),f328(f328(f8(a867,f879(a867,a867),x44421),a326),f328(f328(f7(x44421,f879(f878(x44421,x44421),a867),a867),f328(f328(f8(f878(x44421,x44421),f879(f879(f878(x44421,x44421),a867),a867),x44421),f330(f878(x44421,x44421))),f328(f328(f7(x44421,x44421,f878(x44421,x44421)),f263(x44421,x44421)),x44422))),f304(x44421,x44424))))),f328(f328(f7(x44421,f879(f878(x44421,x44421),a867),a867),f328(f328(f8(f878(x44421,x44421),f879(f879(f878(x44421,x44421),a867),a867),x44421),f330(f878(x44421,x44421))),f328(f263(x44421,x44421),x44423))),f304(x44421,x44424))))))) % 167.75/167.49 [4236]E(f328(f133(x42361,f328(f328(f18(x42361,a867,a867),f328(f328(f8(a867,f879(a867,a867),x42361),a326),x42362)),x42363)),x42364),f328(f133(x42361,x42363),f328(f133(x42361,x42362),x42364))) % 167.75/167.49 [4339]E(f328(f328(f125(x43391),f328(f328(f328(f100(f873(x43391)),f328(f328(f330(a872),f2(a872)),x43392)),f328(f328(f148(x43391),x43393),f117(x43391))),f117(x43391))),f174(x43391,x43394,f328(f248(a872),f328(f328(f7(a872,f879(a872,a867),a867),f328(f328(f8(a872,f879(f879(a872,a867),a867),a872),f330(a872)),a116)),x43392)))),f174(x43391,f328(f328(f148(x43391),x43393),x43394),x43392)) % 167.75/167.49 [4436]E(f328(f248(f878(x44361,x44362)),f328(f328(f8(f879(a872,a867),a867,f878(x44361,x44362)),f87(a872)),f328(f328(f7(f878(x44361,x44362),f879(a872,a867),f879(a872,a867)),f328(f328(f8(f879(a872,f879(a867,a867)),f879(f879(a872,a867),f879(a872,a867)),f878(x44361,x44362)),f18(a872,a867,a867)),f328(f328(f8(f879(a872,a867),f879(a872,f879(a867,a867)),f878(x44361,x44362)),f328(f8(a867,f879(a867,a867),a872),a326)),f328(f328(f7(f878(x44361,x44362),f879(a872,f878(x44361,x44362)),f879(a872,a867)),f328(f328(f8(f879(f878(x44361,x44362),a867),f879(f879(a872,f878(x44361,x44362)),f879(a872,a867)),f878(x44361,x44362)),f8(f878(x44361,x44362),a867,a872)),a325)),f328(f328(f18(a872,x44362,f878(x44361,x44362)),f328(f328(f8(x44361,f879(x44362,f878(x44361,x44362)),a872),f263(x44361,x44362)),f328(f162(x44361),x44363))),f328(f162(x44362),x44364)))))),f328(f328(f7(a872,a872,a867),f243(a872)),f328(f328(f240(a872),f328(f193(f873(x44361)),x44363)),f328(f193(f873(x44362)),x44364)))))),f328(f170(f878(x44361,x44362)),f328(f328(f180(x44361,x44362),x44363),x44364))) % 167.75/167.49 [4358]E(f328(f248(f878(x43581,x43582)),f328(f267(x43581,x43582,a867),f328(f328(f7(x43581,f879(x43582,a867),f879(x43582,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x43582,a867),f879(x43582,a867)),x43581),f8(a867,a867,x43582)),f328(f328(f8(a867,f879(a867,a867),x43581),a326),x43583))),x43584))),f328(f328(f265(x43581,x43582),f328(f248(x43581),x43583)),f328(f16(f879(x43582,a867),x43581),f328(f248(x43582),x43584)))) % 167.75/167.49 [4361]E(f328(f248(f878(x43611,x43612)),f328(f267(x43611,x43612,a867),f328(f328(f18(x43611,f879(x43612,a867),f879(x43612,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x43612,a867),f879(x43612,a867)),x43611),f8(a867,a867,x43612)),f328(f328(f8(a867,f879(a867,a867),x43611),a326),x43613))),x43614))),f328(f328(f265(x43611,x43612),f328(f248(x43611),x43613)),f328(f328(f8(f879(x43612,a867),f879(x43612,a867),x43611),f248(x43612)),x43614))) % 167.75/167.49 [4377]E(f328(f248(x43771),f328(f328(f8(f879(x43772,a867),a867,x43771),f88(x43772)),f328(f328(f8(f879(x43772,a867),f879(x43772,a867),x43771),f328(f18(x43772,a867,a867),f328(f328(f8(a867,f879(a867,a867),x43772),a331),f328(f328(f7(x43772,f879(x43772,a867),a867),f330(x43772)),x43773)))),x43774))),f328(f328(f43(x43772,f879(x43771,a867)),x43773),f328(f328(f8(f879(x43771,a867),f879(x43771,a867),x43772),f248(x43771)),f328(f7(x43771,x43772,a867),x43774)))) % 167.75/167.49 [4422]E(f328(f328(f151(f878(x44221,a872),x44221),f262(x44221,a872)),f328(f133(f878(x44221,a872),f328(f328(f7(f878(x44221,a872),f879(a872,a867),a867),f328(f328(f8(a872,f879(f879(a872,a867),a867),f878(x44221,a872)),f330(a872)),f266(x44221,a872))),x44222)),f328(f328(f180(x44221,a872),x44223),f136(a872,f328(f298(a872,x44224),f328(f328(f80(a872),x44224),f328(f193(f873(x44221)),x44223))))))),f328(f328(f151(f878(x44221,a872),x44221),f262(x44221,a872)),f328(f133(f878(x44221,a872),f328(f328(f7(f878(x44221,a872),f879(a872,a867),a867),f328(f328(f8(a872,f879(f879(a872,a867),a867),f878(x44221,a872)),f330(a872)),f328(f328(f7(f878(x44221,a872),a872,a872),f328(f328(f8(a872,f879(a872,a872),f878(x44221,a872)),f80(a872)),f266(x44221,a872))),x44224))),x44222)),f328(f328(f180(x44221,a872),x44223),f136(a872,f328(f298(a872,f2(a872)),f328(f193(f873(x44221)),x44223))))))) % 167.75/167.49 [4423]E(f328(a116,f328(f328(f241(a872),f328(f193(f873(x44231)),x44232)),f328(f139(a872,f873(x44233),f328(f7(f873(x44233),a872,a872),f328(f328(f8(a872,f879(a872,a872),f873(x44233)),f241(a872)),f328(f328(f7(f873(x44233),a872,a872),f328(f328(f8(a872,f879(a872,a872),f873(x44233)),f22(a872)),f193(f873(x44233)))),f328(a116,f2(a872))))),f2(a872)),f328(f166(f873(x44233)),f328(f133(f873(x44233),f328(f328(f8(a867,a867,f873(x44233)),a323),f328(f328(f7(f873(x44233),f873(x44233),a867),a325),f117(x44233)))),x44234))))),f328(f328(f241(a872),f328(a116,f328(f193(f873(x44231)),x44232))),f328(f139(a872,f873(x44233),f328(f7(f873(x44233),a872,a872),f328(f328(f8(a872,f879(a872,a872),f873(x44233)),f241(a872)),f193(f873(x44233)))),f2(a872)),f328(f166(f873(x44233)),x44234)))) % 167.75/167.49 [4376]E(f328(f328(f125(x43761),f174(x43761,x43762,x43763)),f174(x43761,x43764,f328(f248(a872),f328(f328(f7(a872,f879(a872,a867),a867),f328(f328(f8(a872,f879(f879(a872,a867),a867),a872),f330(a872)),f328(f328(f7(a872,a872,a872),f80(a872)),f328(f193(f873(x43761)),x43762)))),x43763)))),f174(x43761,f328(f328(f125(x43761),x43762),x43764),x43763)) % 167.75/167.49 [4429]E(f328(f328(f148(f873(x44291)),f328(f328(f148(x44291),x44292),f328(f139(f873(x44291),f873(x44291),f125(x44291),f117(x44291)),f328(f328(f151(f873(x44291),f873(x44291)),f153(f873(x44291),x44291,f117(x44291),f328(f328(f8(f873(x44291),f879(f873(x44291),f873(x44291)),x44291),f16(f873(x44291),f873(x44291))),f328(f328(f7(x44291,f873(x44291),f873(x44291)),f148(x44291)),f117(x44291))))),x44293)))),f178(x44291,f328(f328(f148(f873(x44291)),x44294),f328(f139(f873(f873(x44291)),f873(f873(x44291)),f125(f873(x44291)),f117(f873(x44291))),f328(f328(f151(f873(x44291),f873(f873(x44291))),f153(f873(f873(x44291)),x44291,f117(f873(x44291)),f328(f16(f879(f873(x44291),f873(f873(x44291))),x44291),f328(f328(f7(f873(x44291),f873(f873(x44291)),f873(f873(x44291))),f148(f873(x44291))),f117(f873(x44291)))))),x44293))))),f178(x44291,f328(f328(f148(f873(x44291)),f328(f328(f148(x44291),x44292),x44294)),x44293))) % 167.75/167.49 [4437]E(f328(f248(f878(x44371,x44371)),f328(f267(x44371,x44371,a867),f328(f328(f7(x44371,f879(f878(x44372,x44372),a867),f879(x44371,a867)),f328(f328(f8(f879(x44371,f879(f879(f878(x44372,x44372),a867),a867)),f879(f879(f878(x44372,x44372),a867),f879(x44371,a867)),x44371),f7(x44371,f879(f878(x44372,x44372),a867),a867)),f328(f328(f8(f879(x44371,f878(x44372,x44372)),f879(x44371,f879(f879(f878(x44372,x44372),a867),a867)),x44371),f328(f8(f878(x44372,x44372),f879(f879(f878(x44372,x44372),a867),a867),x44371),f330(f878(x44372,x44372)))),f328(f328(f7(x44371,f879(x44371,x44372),f879(x44371,f878(x44372,x44372))),f328(f328(f8(f879(x44372,f878(x44372,x44372)),f879(f879(x44371,x44372),f879(x44371,f878(x44372,x44372))),x44371),f8(x44372,f878(x44372,x44372),x44371)),f328(f328(f8(x44372,f879(x44372,f878(x44372,x44372)),x44371),f263(x44372,x44372)),x44373))),x44373)))),x44374))),f328(f328(f284(x44372,x44371),x44374),x44373)) % 167.75/167.49 [4495]~E(f33(x44951,x44952),f30(x44953,x44954,x44955)) % 167.75/167.49 [4496]~E(f33(x44961,x44962),f29(x44963,x44964,x44965)) % 167.75/167.49 [4497]~E(f32(x44971,x44972),f30(x44973,x44974,x44975)) % 167.75/167.49 [4498]~E(f32(x44981,x44982),f29(x44983,x44984,x44985)) % 167.75/167.49 [4499]~E(f30(x44991,x44992,x44993),f33(x44994,x44995)) % 167.75/167.49 [4500]~E(f30(x45001,x45002,x45003),f32(x45004,x45005)) % 167.75/167.49 [4501]~E(f29(x45011,x45012,x45013),f33(x45014,x45015)) % 167.75/167.49 [4502]~E(f29(x45021,x45022,x45023),f32(x45024,x45025)) % 167.75/167.49 [3921]E(f328(f183(x39211,x39212,x39213,x39214),x39215),f328(f237(f876(x39212),x39212,f328(x39213,x39215),f235(x39212)),f328(x39214,x39215))) % 167.75/167.49 [4009]E(f183(x40091,x40092,f183(x40091,x40092,x40093,x40094),x40095),f183(x40091,x40092,x40093,f183(x40091,x40092,x40094,x40095))) % 167.75/167.49 [4183]E(f264(x41831,x41832,x41833,f252(x41832,x41831,x41834),f252(x41833,x41832,x41835)),f252(x41833,x41831,f264(x41833,x41832,x41831,x41835,x41834))) % 167.75/167.49 [4190]E(f328(f328(f114(f879(x41901,a867)),f328(f170(x41901),f328(f328(f173(x41901),f328(f193(f873(x41902)),x41903)),x41904))),f182(x41901,x41902,x41905)),f182(x41901,x41902,f185(x41901,x41902,x41905,x41904,x41903))) % 167.75/167.49 [3746]E(f328(f328(f267(x37461,x37462,x37463),x37464),x37465),f328(f328(x37464,f328(f262(x37461,x37462),x37465)),f328(f266(x37461,x37462),x37465))) % 167.75/167.49 [3771]E(f328(f237(x37711,x37712,x37713,x37714),f328(f235(x37712),x37715)),f328(x37714,x37715)) % 167.75/167.49 [3780]E(f328(f328(f328(f66(x37801,x37802,x37803),x37804),x37805),f192(f879(x37802,a867))),x37805) % 167.75/167.49 [3953]E(f238(x39531,x39532,x39533,x39534,f328(f235(x39532),x39535)),f328(x39534,x39535)) % 167.75/167.49 [4064]E(f328(f73(f876(x40641),f876(x40642),f876(x40643),f328(f206(x40641,x40642),x40644)),f328(f206(x40643,x40641),x40645)),f328(f206(x40643,x40642),f328(f73(x40641,x40642,x40643,x40644),x40645))) % 167.75/167.49 [4066]E(f328(f73(f873(x40661),f873(x40662),f873(x40663),f328(f151(x40661,x40662),x40664)),f328(f151(x40663,x40661),x40665)),f328(f151(x40663,x40662),f328(f73(x40661,x40662,x40663,x40664),x40665))) % 167.75/167.49 [4122]E(f328(f237(x41221,f878(x41222,f874(x41222)),x41223,f328(f267(x41222,f874(x41222),x41221),x41224)),f328(f132(x41222),x41225)),f130(x41221,x41222,x41223,x41224,x41225)) % 167.75/167.49 [4146]E(f85(x41461,f67(x41462,x41461,x41463,x41464,x41465)),f328(f328(f65(x41462,x41461,x41463),x41464),x41465)) % 167.75/167.49 [4181]E(f328(f328(f80(a872),f328(f328(f80(a872),f328(x41811,f328(f262(x41812,x41813),x41814))),f328(x41815,f328(f266(x41812,x41813),x41814)))),f328(a116,f2(a872))),f271(x41812,x41813,x41811,x41815,x41814)) % 167.75/167.49 [4372]E(f160(x43721,x43722,f328(f328(f7(x43721,f876(x43722),f876(x43722)),f328(f328(f18(x43721,f876(x43722),f879(f876(x43722),f876(x43722))),f328(f328(f8(a867,f879(f876(x43722),f879(f876(x43722),f876(x43722))),x43721),f100(f876(x43722))),x43723)),f328(f328(f8(x43722,f876(x43722),x43721),f235(x43722)),x43724))),f205(x43722)),x43725),f328(f328(f151(x43721,x43722),x43724),f328(f133(x43721,x43723),x43725))) % 167.75/167.49 [4538]~E(f328(f328(f328(f72(x45381,f876(x45382)),x45383),x45384),f328(f235(x45382),x45385)),f328(f16(f876(x45382),x45381),f205(x45382))) % 167.75/167.49 [3681]E(f328(f328(f173(x36811),x36812),f328(f328(f151(x36813,x36811),x36814),x36815)),f328(f328(f151(x36813,x36811),x36814),f328(f328(f173(x36813),x36812),x36815))) % 167.75/167.49 [3682]E(f328(f328(f135(x36821),x36822),f328(f328(f151(x36823,x36821),x36824),x36825)),f328(f328(f151(x36823,x36821),x36824),f328(f328(f135(x36823),x36822),x36825))) % 167.75/167.49 [3714]E(f328(f328(f151(x37141,x37142),x37143),f328(f328(f148(x37141),x37144),x37145)),f328(f328(f148(x37142),f328(x37143,x37144)),f328(f328(f151(x37141,x37142),x37143),x37145))) % 167.75/167.49 [3775]E(f328(f307(x37751,x37752,x37753),f328(f328(f306(x37751),x37754),x37755)),f328(f328(f306(x37752),f328(x37753,x37754)),f328(f307(x37751,x37752,x37753),x37755))) % 167.75/167.49 [3804]E(f171(x38041,f328(f328(f148(x38041),x38042),x38043),f328(f328(f148(x38041),x38044),x38045)),f328(f328(f148(x38041),x38042),f328(f328(f148(x38041),x38044),f171(x38041,x38043,x38045)))) % 167.75/167.49 [3840]E(f328(f328(f180(x38401,x38402),f328(f328(f173(x38401),x38403),x38404)),f328(f328(f173(x38402),x38403),x38405)),f328(f328(f173(f878(x38401,x38402)),x38403),f328(f328(f180(x38401,x38402),x38404),x38405))) % 167.75/167.49 [3841]E(f328(f328(f180(x38411,x38412),f328(f328(f135(x38411),x38413),x38414)),f328(f328(f135(x38412),x38413),x38415)),f328(f328(f135(f878(x38411,x38412)),x38413),f328(f328(f180(x38411,x38412),x38414),x38415))) % 167.75/167.49 [3853]E(f328(f328(f156(x38531,f328(f328(f148(x38531),x38532),x38533)),f328(a116,x38534)),x38535),f328(f328(f148(x38531),x38532),f328(f328(f156(x38531,x38533),x38534),x38535))) % 167.75/167.49 [3856]E(f328(f237(f876(x38561),x38562,f205(x38561),x38563),f328(f328(f16(f876(x38562),x38564),f205(x38562)),x38565)),f205(x38561)) % 167.75/167.49 [3858]E(f328(f328(f125(x38581),f328(f328(f151(x38582,x38581),x38583),x38584)),f328(f328(f151(x38582,x38581),x38583),x38585)),f328(f328(f151(x38582,x38581),x38583),f328(f328(f125(x38582),x38584),x38585))) % 167.75/167.49 [3862]E(f328(f328(x38621,x38622),f328(f328(f254(x38623,x38624,x38621),x38622),x38625)),f328(f328(f254(x38623,x38624,x38621),x38622),f328(a116,x38625))) % 167.75/167.49 [3892]E(f161(x38921,x38922,x38923,f328(f328(f148(x38921),x38924),x38925)),f328(f328(f125(x38922),f328(x38923,x38924)),f161(x38921,x38922,x38923,x38925))) % 167.75/167.49 [3905]E(f328(f328(f285(x39051,x39052,x39053),f328(f283(x39052,x39051),x39054)),f328(f283(x39053,x39052),x39055)),f328(f283(x39053,x39051),f328(f328(f285(x39053,x39052,x39051),x39055),x39054))) % 167.75/167.49 [3939]E(f328(f328(f328(f187(f873(x39391),f873(x39391)),x39392),f165(x39391)),f328(f328(f151(x39393,x39391),x39394),x39395)),f328(f328(f151(x39393,x39391),x39394),f328(f328(f328(f187(f873(x39393),f873(x39393)),x39392),f165(x39393)),x39395))) % 167.75/167.49 [3940]E(f328(f328(f269(x39401,x39402,x39401,x39403),f328(f263(x39402,x39401),x39404)),x39405),f328(x39405,x39404)) % 167.75/167.49 [3967]E(f152(x39671,x39672,f328(f328(f151(x39673,x39671),x39674),x39675)),f152(x39673,f328(f73(x39671,a872,x39673,x39672),x39674),x39675)) % 167.75/167.49 [4032]E(f328(f328(f73(f876(x40321),f876(x40322),x40323,f328(f206(x40321,x40322),x40324)),f328(f16(f876(x40321),x40323),f205(x40321))),x40325),f205(x40322)) % 167.75/167.49 [4033]E(f175(f878(x40331,x40332),f328(f73(x40332,a867,f878(x40331,x40332),x40333),f266(x40331,x40332)),f328(f328(f180(x40331,x40332),x40334),x40335)),f328(f328(f180(x40331,x40332),x40334),f175(x40332,x40333,x40335))) % 167.75/167.49 [4038]E(f328(f307(x40381,x40382,f328(f328(f8(x40383,x40382,x40381),x40384),x40385)),f251(f879(x40381,a867))),f328(f307(x40383,x40382,x40384),f328(f307(x40381,x40383,x40385),f251(f879(x40381,a867))))) % 167.75/167.49 [4051]E(f175(f878(x40511,x40512),f328(f73(x40511,a867,f878(x40511,x40512),x40513),f262(x40511,x40512)),f328(f328(f180(x40511,x40512),x40514),x40515)),f328(f328(f180(x40511,x40512),f175(x40511,x40513,x40514)),x40515)) % 167.75/167.49 [4070]E(f328(f328(f114(f879(x40701,a867)),f328(f308(x40701,x40702,x40703),f328(f328(f306(x40702),x40704),f192(f879(x40702,a867))))),f328(f308(x40701,x40702,x40703),x40705)),f328(f308(x40701,x40702,x40703),f328(f328(f306(x40702),x40704),x40705))) % 167.75/167.49 [4130]E(f328(f328(f125(f878(x41301,x41302)),f328(f328(f151(x41302,f878(x41301,x41302)),f328(f263(x41301,x41302),x41303)),x41304)),f61(x41301,x41302,x41305,x41304)),f61(x41301,x41302,f328(f328(f148(x41301),x41303),x41305),x41304)) % 167.75/167.49 [4131]E(f328(f328(f151(x41311,x41312),x41313),f175(x41311,f328(f73(x41312,a867,x41311,x41314),x41313),x41315)),f175(x41312,x41314,f328(f328(f151(x41311,x41312),x41313),x41315))) % 167.75/167.49 [4137]E(f328(f139(x41371,x41372,f328(f7(x41372,x41371,x41371),f328(f7(x41371,x41372,x41371),x41373)),x41374),f328(f166(x41372),f328(f166(x41372),x41375))),f328(f139(x41371,x41372,x41373,x41374),x41375)) % 167.75/167.49 [4138]E(f328(f328(f328(f72(x41381,f876(x41382)),f186(x41381,x41382,x41383,x41384)),x41385),f328(x41383,x41385)),f186(x41381,x41382,x41383,f328(f328(f306(x41381),x41385),x41384))) % 167.75/167.49 [4207]E(f328(f237(f873(x42071),x42071,f160(x42072,x42071,x42073,x42074),f328(f328(f7(x42071,f873(x42071),f873(x42071)),f148(x42071)),f160(x42072,x42071,x42073,x42074))),f328(x42073,x42075)),f160(x42072,x42071,x42073,f328(f328(f148(x42072),x42075),x42074))) % 167.75/167.49 [4244]P1(f328(f328(f242(f879(x42441,a867)),f328(f307(x42442,x42441,x42443),f328(f328(f105(f879(x42442,a867)),x42444),x42445))),f328(f328(f105(f879(x42441,a867)),f328(f307(x42442,x42441,x42443),x42444)),f328(f307(x42442,x42441,x42443),x42445)))) % 167.75/167.49 [4245]P1(f328(f328(f242(f879(x42451,a867)),f328(f282(x42452,x42451,x42453),f328(f328(f105(f879(x42452,a867)),x42454),x42455))),f328(f328(f105(f879(x42451,a867)),f328(f282(x42452,x42451,x42453),x42454)),f328(f282(x42452,x42451,x42453),x42455)))) % 167.75/167.49 [4346]E(f328(f266(x43461,x43462),f328(f268(x43463,x43461,x43462,x43462,x43464,f34(x43462)),x43465)),f328(f266(x43463,x43462),x43465)) % 167.75/167.49 [4347]E(f328(f262(x43471,x43472),f328(f268(x43471,x43471,x43473,x43472,f34(x43471),x43474),x43475)),f328(f262(x43471,x43473),x43475)) % 167.75/167.49 [4433]E(f328(f139(f879(x44331,f876(x44332)),f878(x44331,x44332),f328(f328(f8(f879(x44331,f879(x44332,f879(x44331,f876(x44332)))),f879(f878(x44331,x44332),f879(x44331,f876(x44332))),f879(x44331,f876(x44332))),f267(x44331,x44332,f879(x44331,f876(x44332)))),f328(f328(f7(f879(x44331,f876(x44332)),f879(x44332,f876(x44332)),f879(x44331,f879(x44332,f879(x44331,f876(x44332))))),f328(f328(f8(f879(x44331,f879(f879(x44332,f876(x44332)),f879(x44332,f879(x44331,f876(x44332))))),f879(f879(x44332,f876(x44332)),f879(x44331,f879(x44332,f879(x44331,f876(x44332))))),f879(x44331,f876(x44332))),f7(x44331,f879(x44332,f876(x44332)),f879(x44332,f879(x44331,f876(x44332))))),f328(f328(f8(f879(x44331,f879(f876(x44332),f879(x44331,f876(x44332)))),f879(x44331,f879(f879(x44332,f876(x44332)),f879(x44332,f879(x44331,f876(x44332))))),f879(x44331,f876(x44332))),f328(f8(f879(f876(x44332),f879(x44331,f876(x44332))),f879(f879(x44332,f876(x44332)),f879(x44332,f879(x44331,f876(x44332)))),x44331),f8(f876(x44332),f879(x44331,f876(x44332)),x44332))),f72(x44331,f876(x44332))))),f235(x44332))),x44333),f328(f328(f180(x44331,x44332),x44334),x44335)),f185(x44331,x44332,x44333,x44334,x44335)) % 167.75/167.49 [4435]P25(x44351,x44352,f328(f328(f306(f871(x44351)),f328(f328(f328(f92(x44351),f328(f328(f7(x44351,f879(a868,a867),f879(a868,a867)),f328(f328(f8(f879(a868,f879(a867,a867)),f879(f879(a868,a867),f879(a868,a867)),x44351),f18(a868,a867,a867)),f328(f328(f8(f879(a868,a867),f879(a868,f879(a867,a867)),x44351),f328(f8(a867,f879(a867,a867),a868),a326)),x44353))),f328(f328(f8(a867,a867,a868),a323),x44354))),f32(x44354,x44355)),x44353)),f192(f879(f871(x44351),a867)))) % 167.75/167.49 [3524]E(f328(f328(f328(f328(f211(x35241),x35242),x35243),x35244),x35245),f196(x35241,x35242)) % 167.75/167.49 [3525]E(f328(f328(f328(f328(f215(x35251),x35252),x35253),x35254),x35255),f207(x35251,x35252)) % 167.75/167.49 [3569]E(f97(x35691,x35692,f328(f328(f328(f92(x35691),x35693),x35694),x35695)),f2(a872)) % 167.75/167.49 [3665]E(f328(f328(f328(f328(f72(x36651,x36652),x36653),x36654),x36655),x36654),x36655) % 167.75/167.49 [3893]E(f328(f328(f43(x38931,f879(x38932,a867)),f328(f328(f306(x38931),x38933),x38934)),x38935),f328(f328(f105(f879(x38932,a867)),f328(x38935,x38933)),f328(f328(f43(x38931,f879(x38932,a867)),x38934),x38935))) % 167.75/167.49 [3894]E(f328(f328(f44(x38941,f879(x38942,a867)),f328(f328(f306(x38941),x38943),x38944)),x38945),f328(f328(f114(f879(x38942,a867)),f328(x38945,x38943)),f328(f328(f44(x38941,f879(x38942,a867)),x38944),x38945))) % 167.75/167.49 [3946]E(f328(f120(x39461,x39462,f328(x39463,x39464)),f328(f328(f7(x39461,a103,f874(x39462)),x39465),x39464)),f328(f203(x39461,x39462,x39463,x39465),x39464)) % 167.75/167.49 [3960]E(f328(f328(f114(f879(x39601,a867)),f328(f307(x39602,x39601,x39603),x39604)),f328(f307(x39602,x39601,x39603),x39605)),f328(f307(x39602,x39601,x39603),f328(f328(f114(f879(x39602,a867)),x39604),x39605))) % 167.75/167.49 [3961]E(f328(f328(f114(f879(x39611,a867)),f328(f282(x39612,x39611,x39613),x39614)),f328(f282(x39612,x39611,x39613),x39615)),f328(f282(x39612,x39611,x39613),f328(f328(f114(f879(x39612,a867)),x39614),x39615))) % 167.75/167.49 [3962]E(f328(f328(f114(f879(x39621,a867)),f328(f308(x39621,x39622,x39623),x39624)),f328(f308(x39621,x39622,x39623),x39625)),f328(f308(x39621,x39622,x39623),f328(f328(f114(f879(x39622,a867)),x39624),x39625))) % 167.75/167.49 [3963]E(f328(f328(f22(f879(x39631,a867)),f328(f308(x39631,x39632,x39633),x39634)),f328(f308(x39631,x39632,x39633),x39635)),f328(f308(x39631,x39632,x39633),f328(f328(f22(f879(x39632,a867)),x39634),x39635))) % 167.75/167.49 [3964]E(f328(f328(f105(f879(x39641,a867)),f328(f308(x39641,x39642,x39643),x39644)),f328(f308(x39641,x39642,x39643),x39645)),f328(f308(x39641,x39642,x39643),f328(f328(f105(f879(x39642,a867)),x39644),x39645))) % 167.75/167.49 [3966]E(f186(x39661,x39662,f186(x39661,x39662,x39663,x39664),x39665),f186(x39661,x39662,x39663,f328(f328(f105(f879(x39661,a867)),x39664),x39665))) % 167.75/167.49 [4028]E(f328(f328(f156(x40281,f328(f328(f125(x40281),x40282),f328(f328(f148(x40281),x40283),x40284))),f328(f193(f873(x40281)),x40282)),x40285),f328(f328(f125(x40281),x40282),f328(f328(f148(x40281),x40285),x40284))) % 167.75/167.49 [4036]E(f328(f328(f43(x40361,f879(x40362,a867)),x40363),f328(f328(f8(f879(x40362,a867),f879(x40362,a867),x40361),f328(f306(x40362),x40364)),x40365)),f328(f328(f306(x40362),x40364),f328(f328(f43(x40361,f879(x40362,a867)),x40363),x40365))) % 167.75/167.49 [4104]E(f186(x41041,x41042,f328(f328(f328(f72(x41041,f876(x41042)),x41043),x41044),f328(f235(x41042),x41045)),f328(f79(f879(x41041,a867)),f328(f328(f306(x41041),x41044),f192(f879(x41041,a867))))),f186(x41041,x41042,x41043,f328(f79(f879(x41041,a867)),f328(f328(f306(x41041),x41044),f192(f879(x41041,a867)))))) % 167.75/167.49 [4194]E(f328(f328(f151(x41941,x41942),x41943),f328(f133(x41941,f328(f73(x41942,a867,x41941,x41944),x41943)),x41945)),f328(f133(x41942,x41944),f328(f328(f151(x41941,x41942),x41943),x41945))) % 167.75/167.49 [4200]E(f328(f193(f873(x42001)),f328(f133(x42001,x42002),f328(f328(f151(x42003,x42001),x42004),x42005))),f328(f193(f873(x42003)),f328(f133(x42003,f328(f73(x42001,a867,x42003,x42002),x42004)),x42005))) % 167.75/167.49 [4338]E(f328(f328(f114(f879(x43381,a867)),f328(f328(f22(f879(x43381,a867)),f182(x43381,x43382,x43383)),f328(f248(x43381),f328(f328(f7(x43381,f879(x43381,a867),a867),f330(x43381)),f328(f328(f22(f879(x43381,a867)),x43384),f182(x43381,x43382,x43385)))))),f328(f248(x43381),f328(f328(f7(x43381,f879(x43381,a867),a867),f330(x43381)),f328(f328(f105(f879(x43381,a867)),x43384),f182(x43381,x43382,x43385))))),f182(x43381,x43382,f76(x43381,f876(x43382),x43383,x43385,x43384))) % 167.75/167.49 [4413]E(f328(f153(f873(f878(x44131,x44132)),x44132,f117(f878(x44131,x44132)),f328(f328(f7(x44132,f879(f873(x44132),f873(f878(x44131,x44132))),f879(f873(x44132),f873(f878(x44131,x44132)))),f328(f328(f8(f879(f873(f878(x44131,x44132)),f873(f878(x44131,x44132))),f879(f879(f873(x44132),f873(f878(x44131,x44132))),f879(f873(x44132),f873(f878(x44131,x44132)))),x44132),f8(f873(f878(x44131,x44132)),f873(f878(x44131,x44132)),f873(x44132))),f328(f328(f8(f878(x44131,x44132),f879(f873(f878(x44131,x44132)),f873(f878(x44131,x44132))),x44132),f148(f878(x44131,x44132))),f328(f263(x44131,x44132),x44133)))),f328(f180(x44131,x44132),x44134))),x44135),f328(f328(f180(x44131,x44132),f328(f328(f148(x44131),x44133),x44134)),x44135)) % 167.75/167.49 [3887]E(f328(f328(f156(x38871,f328(f328(f156(x38871,x38872),x38873),x38874)),x38873),x38875),f328(f328(f156(x38871,x38872),x38873),x38875)) % 167.75/167.49 [3941]E(f328(f259(x39411,x39412),f328(f328(f306(f878(x39411,x39412)),f328(f328(f263(x39411,x39412),x39413),x39414)),x39415)),f328(f328(f306(x39412),x39414),f328(f259(x39411,x39412),x39415))) % 167.75/167.49 [3942]E(f328(f261(x39421,x39422),f328(f328(f306(f878(x39421,x39422)),f328(f328(f263(x39421,x39422),x39423),x39424)),x39425)),f328(f328(f306(x39421),x39423),f328(f261(x39421,x39422),x39425))) % 167.75/167.49 [3991]E(f123(x39911,x39912,f328(x39913,x39914),f328(f328(f7(x39911,a103,f874(f876(x39912))),x39915),x39914)),f328(f201(x39911,x39912,x39913,x39915),x39914)) % 167.75/167.49 [4021]E(f328(f328(f114(f879(f878(x40211,x40212),a867)),f328(f328(f265(x40211,x40212),x40213),x40214)),f328(f328(f265(x40211,x40212),x40215),x40214)),f328(f328(f265(x40211,x40212),f328(f328(f114(f879(x40211,a867)),x40213),x40215)),x40214)) % 167.75/167.49 [4022]E(f328(f328(f22(f879(f878(x40221,x40222),a867)),f328(f328(f265(x40221,x40222),x40223),x40224)),f328(f328(f265(x40221,x40222),x40225),x40224)),f328(f328(f265(x40221,x40222),f328(f328(f22(f879(x40221,a867)),x40223),x40225)),x40224)) % 167.75/167.49 [4023]E(f328(f328(f105(f879(f878(x40231,x40232),a867)),f328(f328(f265(x40231,x40232),x40233),x40234)),f328(f328(f265(x40231,x40232),x40235),x40234)),f328(f328(f265(x40231,x40232),f328(f328(f105(f879(x40231,a867)),x40233),x40235)),x40234)) % 167.75/167.49 [4082]E(f328(f328(f105(f879(x40821,a867)),f328(f328(f43(x40822,f879(x40821,a867)),x40823),x40824)),f328(f328(f43(x40822,f879(x40821,a867)),x40825),x40824)),f328(f328(f43(x40822,f879(x40821,a867)),f328(f328(f114(f879(x40822,a867)),x40823),x40825)),x40824)) % 167.75/167.49 [4083]E(f328(f328(f114(f879(x40831,a867)),f328(f328(f44(x40832,f879(x40831,a867)),x40833),x40834)),f328(f328(f44(x40832,f879(x40831,a867)),x40835),x40834)),f328(f328(f44(x40832,f879(x40831,a867)),f328(f328(f114(f879(x40832,a867)),x40833),x40835)),x40834)) % 167.75/167.49 [4097]E(f328(f328(f43(x40971,f879(x40972,a867)),x40973),f328(f328(f8(f879(x40972,a867),f879(x40972,a867),x40971),f328(f114(f879(x40972,a867)),x40974)),x40975)),f328(f328(f114(f879(x40972,a867)),x40974),f328(f328(f43(x40971,f879(x40972,a867)),x40973),x40975))) % 167.75/167.49 [4098]E(f328(f328(f44(x40981,f879(x40982,a867)),x40983),f328(f328(f8(f879(x40982,a867),f879(x40982,a867),x40981),f328(f22(f879(x40982,a867)),x40984)),x40985)),f328(f328(f22(f879(x40982,a867)),x40984),f328(f328(f43(x40981,f879(x40982,a867)),x40983),x40985))) % 167.75/167.49 [4099]E(f328(f328(f44(x40991,f879(x40992,a867)),x40993),f328(f328(f8(f879(x40992,a867),f879(x40992,a867),x40991),f328(f105(f879(x40992,a867)),x40994)),x40995)),f328(f328(f105(f879(x40992,a867)),x40994),f328(f328(f44(x40991,f879(x40992,a867)),x40993),x40995))) % 167.75/167.49 [4136]E(f183(x41361,x41362,x41363,f328(f176(x41361,x41362),f328(f166(f878(x41361,x41362)),f328(f328(f180(x41361,x41362),x41364),x41365)))),f185(x41361,x41362,x41363,x41364,x41365)) % 167.75/167.49 [4158]E(f189(f873(x41581),f328(f328(f148(x41581),x41582),x41583),f328(f328(f8(f873(x41581),f873(x41581),a872),f328(f148(x41581),x41584)),f328(f328(f7(a872,x41581,f873(x41581)),f156(x41581,x41583)),x41582)),x41585),f328(f328(f156(x41581,f328(f328(f148(x41581),x41584),x41583)),x41585),x41582)) % 167.75/167.49 [4162]E(f328(f328(f43(x41621,f879(f878(x41622,x41623),a867)),x41624),f328(f328(f8(f879(f878(x41623,x41622),a867),f879(f878(x41622,x41623),a867),x41621),f283(x41623,x41622)),x41625)),f328(f283(x41623,x41622),f328(f328(f43(x41621,f879(f878(x41623,x41622),a867)),x41624),x41625))) % 167.75/167.49 [4163]E(f328(f328(f44(x41631,f879(f878(x41632,x41633),a867)),x41634),f328(f328(f8(f879(f878(x41633,x41632),a867),f879(f878(x41632,x41633),a867),x41631),f283(x41633,x41632)),x41635)),f328(f283(x41633,x41632),f328(f328(f44(x41631,f879(f878(x41633,x41632),a867)),x41634),x41635))) % 167.75/167.49 [4218]E(f182(x42181,x42182,f328(f328(f18(x42181,f876(x42183),f876(x42182)),f328(f328(f8(f879(x42183,x42182),f879(f876(x42183),f876(x42182)),x42181),f206(x42183,x42182)),x42184)),x42185)),f182(x42181,x42183,x42185)) % 167.75/167.49 [4269]P1(f328(f328(f242(f879(x42691,a867)),f328(f328(f22(f879(x42691,a867)),f328(f307(x42692,x42691,x42693),x42694)),f328(f307(x42692,x42691,x42693),x42695))),f328(f307(x42692,x42691,x42693),f328(f328(f22(f879(x42692,a867)),x42694),x42695)))) % 167.75/167.49 [4418]E(f328(f153(f873(f878(x44181,x44182)),x44181,f117(f878(x44181,x44182)),f328(f328(f7(x44181,f879(f873(x44181),f873(f878(x44181,x44182))),f879(f873(x44181),f873(f878(x44181,x44182)))),f328(f328(f8(f879(f873(f878(x44181,x44182)),f873(f878(x44181,x44182))),f879(f879(f873(x44181),f873(f878(x44181,x44182))),f879(f873(x44181),f873(f878(x44181,x44182)))),x44181),f8(f873(f878(x44181,x44182)),f873(f878(x44181,x44182)),f873(x44181))),f328(f328(f8(f878(x44181,x44182),f879(f873(f878(x44181,x44182)),f873(f878(x44181,x44182))),x44181),f148(f878(x44181,x44182))),f328(f328(f7(x44181,x44182,f878(x44181,x44182)),f263(x44181,x44182)),x44183)))),f328(f328(f7(f873(x44181),f873(x44182),f873(f878(x44181,x44182))),f180(x44181,x44182)),x44184))),x44185),f328(f328(f180(x44181,x44182),x44185),f328(f328(f148(x44182),x44183),x44184))) % 167.75/167.49 [4124]E(f328(f328(f114(f879(x41241,a867)),f328(f282(x41242,x41241,x41243),x41244)),f328(f282(x41242,x41241,x41245),x41244)),f328(f282(x41242,x41241,f328(f328(f114(f879(f878(x41242,x41241),a867)),x41243),x41245)),x41244)) % 167.75/167.49 [4165]E(f328(f328(f125(f878(x41651,x41652)),f328(f328(f180(x41651,x41652),x41653),f328(f328(f173(x41652),f328(f193(f873(x41651)),x41653)),x41654))),f328(f328(f180(x41651,x41652),x41655),f328(f328(f135(x41652),f328(f193(f873(x41651)),x41653)),x41654))),f328(f328(f180(x41651,x41652),f328(f328(f125(x41651),x41653),x41655)),x41654)) % 167.75/167.49 [4272]E(f328(f328(f265(x42721,x42722),x42723),f328(f328(f18(x42721,f879(x42722,a867),f879(x42722,a867)),f328(f328(f8(f879(x42722,a867),f879(f879(x42722,a867),f879(x42722,a867)),x42721),f114(f879(x42722,a867))),x42724)),x42725)),f328(f328(f114(f879(f878(x42721,x42722),a867)),f328(f328(f265(x42721,x42722),x42723),x42724)),f328(f328(f265(x42721,x42722),x42723),x42725))) % 167.75/167.49 [4273]E(f328(f328(f265(x42731,x42732),x42733),f328(f328(f18(x42731,f879(x42732,a867),f879(x42732,a867)),f328(f328(f8(f879(x42732,a867),f879(f879(x42732,a867),f879(x42732,a867)),x42731),f22(f879(x42732,a867))),x42734)),x42735)),f328(f328(f22(f879(f878(x42731,x42732),a867)),f328(f328(f265(x42731,x42732),x42733),x42734)),f328(f328(f265(x42731,x42732),x42733),x42735))) % 167.75/167.49 [4274]E(f328(f328(f265(x42741,x42742),x42743),f328(f328(f18(x42741,f879(x42742,a867),f879(x42742,a867)),f328(f328(f8(f879(x42742,a867),f879(f879(x42742,a867),f879(x42742,a867)),x42741),f105(f879(x42742,a867))),x42744)),x42745)),f328(f328(f105(f879(f878(x42741,x42742),a867)),f328(f328(f265(x42741,x42742),x42743),x42744)),f328(f328(f265(x42741,x42742),x42743),x42745))) % 167.75/167.49 [4278]E(f328(f328(f43(x42781,f879(x42782,a867)),x42783),f328(f328(f7(x42781,f879(x42782,a867),f879(x42782,a867)),f328(f328(f8(f879(x42782,a867),f879(f879(x42782,a867),f879(x42782,a867)),x42781),f114(f879(x42782,a867))),x42784)),x42785)),f328(f328(f114(f879(x42782,a867)),f328(f328(f43(x42781,f879(x42782,a867)),x42783),x42784)),x42785)) % 167.75/167.49 [4279]E(f328(f328(f44(x42791,f879(x42792,a867)),x42793),f328(f328(f7(x42791,f879(x42792,a867),f879(x42792,a867)),f328(f328(f8(f879(x42792,a867),f879(f879(x42792,a867),f879(x42792,a867)),x42791),f22(f879(x42792,a867))),x42794)),x42795)),f328(f328(f22(f879(x42792,a867)),f328(f328(f44(x42791,f879(x42792,a867)),x42793),x42794)),x42795)) % 167.75/167.49 [4280]E(f328(f328(f44(x42801,f879(x42802,a867)),x42803),f328(f328(f7(x42801,f879(x42802,a867),f879(x42802,a867)),f328(f328(f8(f879(x42802,a867),f879(f879(x42802,a867),f879(x42802,a867)),x42801),f105(f879(x42802,a867))),x42804)),x42805)),f328(f328(f105(f879(x42802,a867)),f328(f328(f44(x42801,f879(x42802,a867)),x42803),x42804)),x42805)) % 167.75/167.49 [4284]E(f328(f328(f43(x42841,f879(x42842,a867)),x42843),f328(f328(f18(x42841,f879(x42842,a867),f879(x42842,a867)),f328(f328(f8(f879(x42842,a867),f879(f879(x42842,a867),f879(x42842,a867)),x42841),f105(f879(x42842,a867))),x42844)),x42845)),f328(f328(f105(f879(x42842,a867)),f328(f328(f43(x42841,f879(x42842,a867)),x42843),x42844)),f328(f328(f43(x42841,f879(x42842,a867)),x42843),x42845))) % 167.75/167.49 [4285]E(f328(f328(f44(x42851,f879(x42852,a867)),x42853),f328(f328(f18(x42851,f879(x42852,a867),f879(x42852,a867)),f328(f328(f8(f879(x42852,a867),f879(f879(x42852,a867),f879(x42852,a867)),x42851),f114(f879(x42852,a867))),x42854)),x42855)),f328(f328(f114(f879(x42852,a867)),f328(f328(f44(x42851,f879(x42852,a867)),x42853),x42854)),f328(f328(f44(x42851,f879(x42852,a867)),x42853),x42855))) % 167.75/167.49 [4299]E(f328(f328(f43(x42991,f879(x42992,a867)),x42993),f328(f328(f18(x42991,f879(x42992,a867),f879(x42992,a867)),f328(f328(f8(f879(x42992,a867),f879(f879(x42992,a867),f879(x42992,a867)),x42991),f105(f879(x42992,a867))),x42994)),x42995)),f328(f328(f105(f879(x42992,a867)),f42(f879(x42992,a867),f328(f307(x42991,f879(x42992,a867),x42994),x42993))),f42(f879(x42992,a867),f328(f307(x42991,f879(x42992,a867),x42995),x42993)))) % 167.75/167.49 [4300]E(f328(f328(f44(x43001,f879(x43002,a867)),x43003),f328(f328(f18(x43001,f879(x43002,a867),f879(x43002,a867)),f328(f328(f8(f879(x43002,a867),f879(f879(x43002,a867),f879(x43002,a867)),x43001),f114(f879(x43002,a867))),x43004)),x43005)),f328(f328(f114(f879(x43002,a867)),f41(f879(x43002,a867),f328(f307(x43001,f879(x43002,a867),x43004),x43003))),f41(f879(x43002,a867),f328(f307(x43001,f879(x43002,a867),x43005),x43003)))) % 167.75/167.49 [4334]E(f328(f328(f135(x43341),f328(f193(f873(x43341)),f175(x43341,x43342,f328(f328(f151(x43343,x43341),x43344),x43345)))),f328(f328(f151(x43343,x43341),x43344),x43345)),f328(f328(f151(x43343,x43341),x43344),f328(f328(f135(x43343),f328(f193(f873(x43343)),f175(x43343,f328(f73(x43341,a867,x43343,x43342),x43344),x43345))),x43345))) % 167.75/167.49 [4208]E(f328(f328(f125(f878(x42081,x42082)),f328(f328(f180(x42081,x42082),f328(f328(f173(x42081),f328(f193(f873(x42082)),x42083)),x42084)),x42083)),f328(f328(f180(x42081,x42082),f328(f328(f135(x42081),f328(f193(f873(x42082)),x42083)),x42084)),x42085)),f328(f328(f180(x42081,x42082),x42084),f328(f328(f125(x42082),x42083),x42085))) % 167.75/167.49 [4326]E(f85(x43261,f328(f328(f18(x43261,a867,a867),f328(f328(f8(a867,f879(a867,a867),x43261),a326),f328(f328(f7(x43261,f879(x43261,a867),a867),f330(x43261)),x43262))),f328(f328(f7(x43261,x43263,a867),f328(f328(f8(x43263,f879(x43263,a867),x43261),a325),x43264)),x43265))),f328(f77(x43261,x43263,x43262,x43264),x43265)) % 167.75/167.49 [4378]E(f328(f328(f86(a1,x43781),f328(f107(a1),f328(f328(f80(a1),x43782),a101))),f328(f328(f18(a1,x43781,x43781),f328(f328(f7(a1,x43781,f879(x43781,x43781)),f328(f328(f8(a867,f879(x43781,f879(x43781,x43781)),a1),f100(x43781)),a197)),f189(x43781,x43783,x43784,x43785))),f328(f328(f8(a872,x43781,a1),x43784),f328(f328(f7(a1,a872,a872),f328(f328(f8(a872,f879(a872,a872),a1),f80(a872)),a108)),x43785)))),f189(x43781,x43783,x43784,f328(f328(f80(a872),f328(f107(a872),x43782)),x43785))) % 167.75/167.49 [4414]E(f328(f176(x44141,x44142),f328(f328(f151(f878(x44141,x44143),f878(x44141,x44142)),f328(f267(x44141,x44143,f878(x44141,x44142)),f328(f328(f7(x44141,f879(x44143,x44142),f879(x44143,f878(x44141,x44142))),f328(f328(f8(f879(x44142,f878(x44141,x44142)),f879(f879(x44143,x44142),f879(x44143,f878(x44141,x44142))),x44141),f8(x44142,f878(x44141,x44142),x44143)),f263(x44141,x44142))),x44144))),x44145)),f328(f73(f876(x44143),f876(x44142),x44141,f328(f206(x44143,x44142),x44144)),f328(f176(x44141,x44143),x44145))) % 167.75/167.49 [4371]E(f182(x43711,x43712,f328(f328(f18(x43711,f876(x43712),f876(x43712)),f328(f328(f18(x43711,f876(x43712),f879(f876(x43712),f876(x43712))),f328(f328(f8(a867,f879(f876(x43712),f879(f876(x43712),f876(x43712))),x43711),f100(f876(x43712))),x43713)),x43714)),x43715)),f328(f328(f114(f879(x43711,a867)),f328(f328(f105(f879(x43711,a867)),f182(x43711,x43712,x43714)),f328(f248(x43711),x43713))),f328(f328(f105(f879(x43711,a867)),f182(x43711,x43712,x43715)),f328(f248(x43711),f328(f328(f8(a867,a867,x43711),a323),x43713))))) % 167.75/167.49 [4412]E(f328(f328(f86(a1,x44121),f328(f107(a1),f328(f328(f80(a1),x44122),a101))),f328(f328(f18(a1,x44121,x44121),f328(f328(f7(a1,x44121,f879(x44121,x44121)),f328(f328(f8(a867,f879(x44121,f879(x44121,x44121)),a1),f100(x44121)),a197)),f328(f188(x44121,x44123,x44124),x44125))),f328(f328(f18(a1,x44121,x44121),f328(f328(f8(a872,f879(x44121,x44121),a1),x44124),f328(f328(f7(a1,a872,a872),f328(f328(f8(a872,f879(a872,a872),a1),f80(a872)),a108)),x44125))),f328(f328(f8(a872,x44121,a1),f188(x44121,x44123,x44124)),f328(f328(f7(a1,a872,a872),f328(f328(f8(a872,f879(a872,a872),a1),f80(a872)),a108)),x44125))))),f328(f188(x44121,x44123,x44124),f328(f328(f80(a872),f328(f107(a872),x44122)),x44125))) % 167.75/167.49 [4447]E(f328(f248(f878(x44471,x44472)),f328(f267(x44471,x44472,a867),f328(f328(f8(f879(x44472,f879(x44473,a867)),f879(x44472,a867),x44471),f328(f8(f879(x44473,a867),a867,x44472),f87(x44473))),f328(f328(f7(x44471,f879(x44472,f879(x44473,a867)),f879(x44472,f879(x44473,a867))),f328(f328(f8(f879(f879(x44473,a867),f879(x44473,a867)),f879(f879(x44472,f879(x44473,a867)),f879(x44472,f879(x44473,a867))),x44471),f8(f879(x44473,a867),f879(x44473,a867),x44472)),f328(f328(f8(f879(x44473,f879(a867,a867)),f879(f879(x44473,a867),f879(x44473,a867)),x44471),f18(x44473,a867,a867)),f328(f328(f8(f879(x44473,a867),f879(x44473,f879(a867,a867)),x44471),f328(f8(a867,f879(a867,a867),x44473),a326)),f328(f328(f7(x44471,f879(f878(x44471,x44473),a867),f879(x44473,a867)),f328(f328(f8(f879(x44473,f879(f879(f878(x44471,x44473),a867),a867)),f879(f879(f878(x44471,x44473),a867),f879(x44473,a867)),x44471),f7(x44473,f879(f878(x44471,x44473),a867),a867)),f328(f328(f8(f879(x44473,f878(x44471,x44473)),f879(x44473,f879(f879(f878(x44471,x44473),a867),a867)),x44471),f328(f8(f878(x44471,x44473),f879(f879(f878(x44471,x44473),a867),a867),x44473),f330(f878(x44471,x44473)))),f263(x44471,x44473)))),x44474))))),f328(f328(f7(x44472,f879(f878(x44473,x44472),a867),f879(x44473,a867)),f328(f328(f8(f879(x44473,f879(f879(f878(x44473,x44472),a867),a867)),f879(f879(f878(x44473,x44472),a867),f879(x44473,a867)),x44472),f7(x44473,f879(f878(x44473,x44472),a867),a867)),f328(f328(f8(f879(x44473,f878(x44473,x44472)),f879(x44473,f879(f879(f878(x44473,x44472),a867),a867)),x44472),f328(f8(f878(x44473,x44472),f879(f879(f878(x44473,x44472),a867),a867),x44473),f330(f878(x44473,x44472)))),f328(f7(x44473,x44472,f878(x44473,x44472)),f263(x44473,x44472))))),x44475))))),f328(f328(f285(x44471,x44473,x44472),x44474),x44475)) % 167.75/167.49 [4523]~E(f29(x45231,x45232,x45233),f30(x45234,x45235,x45236)) % 167.75/167.49 [3976]E(f130(x39761,x39762,x39763,x39764,f127(x39762,x39765,x39766)),f328(f328(x39764,x39765),x39766)) % 167.75/167.49 [4192]E(f185(x41921,x41922,f183(x41921,x41922,x41923,x41924),x41925,x41926),f183(x41921,x41922,x41923,f185(x41921,x41922,x41924,x41925,x41926))) % 167.75/167.49 [4315]E(f328(f73(f878(x43151,x43152),x43152,f878(x43153,x43154),f266(x43151,x43152)),f268(x43153,x43151,x43154,x43152,x43155,x43156)),f328(f73(x43154,x43152,f878(x43153,x43154),x43156),f266(x43153,x43154))) % 167.75/167.49 [4316]E(f328(f73(f878(x43161,x43162),x43161,f878(x43163,x43164),f262(x43161,x43162)),f268(x43163,x43161,x43164,x43162,x43165,x43166)),f328(f73(x43163,x43161,f878(x43163,x43164),x43165),f262(x43163,x43164))) % 167.75/167.49 [3916]E(f328(f328(f73(x39161,x39162,x39163,x39164),x39165),x39166),f328(x39164,f328(x39165,x39166))) % 167.75/167.49 [3712]E(f328(f328(f267(x37121,x37122,x37123),x37124),f328(f328(f263(x37121,x37122),x37125),x37126)),f328(f328(x37124,x37125),x37126)) % 167.75/167.49 [3772]E(f328(f328(f328(f8(x37721,x37722,x37723),x37724),x37725),x37726),f328(x37724,f328(x37725,x37726))) % 167.75/167.49 [3773]E(f328(f328(f328(f7(x37731,x37732,x37733),x37734),x37735),x37736),f328(f328(x37734,x37736),x37735)) % 167.75/167.49 [3790]E(f328(f328(f328(f18(x37901,x37902,x37903),x37904),x37905),x37906),f328(f328(x37904,x37906),f328(x37905,x37906))) % 167.75/167.49 [3812]E(f328(f153(x38121,x38122,x38123,x38124),f328(f328(f148(x38122),x38125),x38126)),f328(f328(x38124,x38125),x38126)) % 167.75/167.49 [3852]E(f168(f878(x38521,x38522),f328(f328(f240(a872),x38523),x38524),f328(f328(f263(x38521,x38522),x38525),x38526)),f328(f328(f180(x38521,x38522),f168(x38521,x38523,x38525)),f168(x38522,x38524,x38526))) % 167.75/167.49 [3920]E(f328(f328(f148(f878(x39201,x39202)),f328(f328(f263(x39201,x39202),x39203),x39204)),f328(f328(f180(x39201,x39202),x39205),x39206)),f328(f328(f180(x39201,x39202),f328(f328(f148(x39201),x39203),x39205)),f328(f328(f148(x39202),x39204),x39206))) % 167.75/167.49 [3922]E(f328(f328(f151(x39221,x39222),x39223),f328(f328(f156(x39221,x39224),x39225),x39226)),f328(f328(f156(x39222,f328(f328(f151(x39221,x39222),x39223),x39224)),x39225),f328(x39223,x39226))) % 167.75/167.49 [3965]E(f328(f139(x39651,x39652,x39653,x39654),f328(f328(f148(x39652),x39655),x39656)),f328(f139(x39651,x39652,x39653,f328(f328(x39653,x39654),x39655)),x39656)) % 167.75/167.49 [3992]E(f270(x39921,x39922,x39923,x39924,f328(f328(f263(x39921,x39922),x39925),x39926)),f328(f328(x39924,x39925),x39926)) % 167.75/167.49 [4075]E(f328(f328(f44(x40751,f879(x40752,a867)),x40753),f328(f73(x40754,f879(x40752,a867),x40751,x40755),x40756)),f328(f328(f44(x40754,f879(x40752,a867)),f328(f307(x40751,x40754,x40756),x40753)),x40755)) % 167.75/167.49 [4127]E(f328(f328(f151(x41271,x41272),x41273),f328(f328(f151(x41274,x41271),x41275),x41276)),f328(f328(f151(x41274,x41272),f328(f73(x41271,x41272,x41274,x41273),x41275)),x41276)) % 167.75/167.49 [4129]E(f328(f328(f206(x41291,x41292),x41293),f328(f328(f206(x41294,x41291),x41295),x41296)),f328(f328(f206(x41294,x41292),f328(f73(x41291,x41292,x41294,x41293),x41295)),x41296)) % 167.75/167.49 [4134]E(f328(f307(x41341,x41342,f328(f73(x41343,x41342,x41341,x41344),x41345)),x41346),f328(f307(x41343,x41342,x41344),f328(f307(x41341,x41343,x41345),x41346))) % 167.75/167.49 [4135]E(f328(f308(x41351,x41352,f328(f73(x41353,x41352,x41351,x41354),x41355)),x41356),f328(f308(x41351,x41353,x41355),f328(f308(x41353,x41352,x41354),x41356))) % 167.75/167.49 [4164]E(f183(x41641,x41642,x41643,f328(f328(f328(f72(x41641,f876(x41642)),x41644),x41645),f328(f235(x41642),x41646))),f328(f328(f328(f72(x41641,f876(x41642)),f183(x41641,x41642,x41643,x41644)),x41645),f328(f235(x41642),x41646))) % 167.75/167.49 [4166]E(f328(f139(x41661,x41662,x41663,f328(f139(x41661,x41662,x41663,x41664),x41665)),x41666),f328(f139(x41661,x41662,x41663,x41664),f328(f328(f125(x41662),x41665),x41666))) % 167.75/167.49 [4305]E(f328(f268(x43051,x43051,x43052,x43053,f34(x43051),x43054),f328(f328(f263(x43051,x43052),x43055),x43056)),f328(f328(f263(x43051,x43053),x43055),f328(x43054,x43056))) % 167.75/167.49 [4306]E(f328(f268(x43061,x43062,x43063,x43063,x43064,f34(x43063)),f328(f328(f263(x43061,x43063),x43065),x43066)),f328(f328(f263(x43062,x43063),f328(x43064,x43065)),x43066)) % 167.75/167.49 [4396]E(f328(f328(f151(f878(x43961,x43962),f878(x43961,x43963)),f328(f267(x43961,x43962,f878(x43961,x43963)),f328(f328(f7(x43961,f879(x43962,x43963),f879(x43962,f878(x43961,x43963))),f328(f328(f8(f879(x43963,f878(x43961,x43963)),f879(f879(x43962,x43963),f879(x43962,f878(x43961,x43963))),x43961),f8(x43963,f878(x43961,x43963),x43962)),f263(x43961,x43963))),x43964))),f328(f328(f180(x43961,x43962),x43965),x43966)),f328(f328(f180(x43961,x43963),x43965),f328(f328(f151(x43962,x43963),x43964),x43966))) % 167.75/167.49 [3777]E(f98(x37771,x37772,x37773,f328(f328(f328(f92(x37771),x37774),x37775),x37776)),f328(f328(f328(x37773,x37774),x37775),x37776)) % 167.75/167.49 [3778]E(f99(x37781,x37782,x37783,f328(f328(f328(f92(x37781),x37784),x37785),x37786)),f328(f328(f328(x37783,x37784),x37785),x37786)) % 167.75/167.49 [3975]E(f328(f328(f73(x39751,x39752,x39753,f328(f16(x39752,x39751),x39754)),x39755),x39756),x39754) % 167.75/167.49 [4011]E(f328(f307(x40111,x40112,x40113),f328(f307(x40114,x40111,x40115),x40116)),f328(f307(x40114,x40112,f328(f328(f8(x40111,x40112,x40114),x40113),x40115)),x40116)) % 167.75/167.49 [4017]E(f328(f328(f43(x40171,f879(x40172,a867)),f328(f307(x40173,x40171,x40174),x40175)),x40176),f328(f328(f43(x40173,f879(x40172,a867)),x40175),f328(f328(f8(x40171,f879(x40172,a867),x40173),x40176),x40174))) % 167.75/167.49 [4018]E(f328(f328(f44(x40181,f879(x40182,a867)),f328(f307(x40183,x40181,x40184),x40185)),x40186),f328(f328(f44(x40183,f879(x40182,a867)),x40185),f328(f328(f8(x40181,f879(x40182,a867),x40183),x40186),x40184))) % 167.75/167.49 [4019]E(f328(f328(f43(x40191,f879(x40192,a867)),x40193),f328(f328(f8(x40194,f879(x40192,a867),x40191),x40195),x40196)),f328(f328(f43(x40194,f879(x40192,a867)),f328(f307(x40191,x40194,x40196),x40193)),x40195)) % 167.75/167.49 [4020]E(f328(f328(f44(x40201,f879(x40202,a867)),x40203),f328(f328(f8(x40204,f879(x40202,a867),x40201),x40205),x40206)),f328(f328(f44(x40204,f879(x40202,a867)),f328(f307(x40201,x40204,x40206),x40203)),x40205)) % 167.75/167.49 [4077]E(f328(f328(f44(x40771,f879(x40772,a867)),x40773),f328(f328(f8(f879(x40774,a867),f879(x40772,a867),x40771),f307(x40774,x40772,x40775)),x40776)),f328(f307(x40774,x40772,x40775),f328(f328(f44(x40771,f879(x40774,a867)),x40773),x40776))) % 167.75/167.49 [4078]E(f328(f328(f44(x40781,f879(x40782,a867)),x40783),f328(f328(f8(f879(x40784,a867),f879(x40782,a867),x40781),f282(x40784,x40782,x40785)),x40786)),f328(f282(x40784,x40782,x40785),f328(f328(f44(x40781,f879(x40784,a867)),x40783),x40786))) % 167.75/167.49 [4079]E(f328(f328(f43(x40791,f879(x40792,a867)),x40793),f328(f328(f8(f879(x40794,a867),f879(x40792,a867),x40791),f308(x40792,x40794,x40795)),x40796)),f328(f308(x40792,x40794,x40795),f328(f328(f43(x40791,f879(x40794,a867)),x40793),x40796))) % 167.75/167.49 [4080]E(f328(f328(f44(x40801,f879(x40802,a867)),x40803),f328(f328(f8(f879(x40804,a867),f879(x40802,a867),x40801),f308(x40802,x40804,x40805)),x40806)),f328(f308(x40802,x40804,x40805),f328(f328(f44(x40801,f879(x40804,a867)),x40803),x40806))) % 167.75/167.49 [4172]E(f328(f139(x41721,x41722,f328(f7(x41722,x41721,x41721),x41723),x41724),f328(f166(x41722),f328(f328(f148(x41722),x41725),x41726))),f328(f328(x41723,x41725),f328(f139(x41721,x41722,f328(f7(x41722,x41721,x41721),x41723),x41724),f328(f166(x41722),x41726)))) % 167.75/167.49 [4231]E(f328(f328(f18(f878(x42311,x42312),x42312,x42313),f328(f328(f8(x42314,f879(x42312,x42313),f878(x42311,x42312)),x42315),f328(f328(f8(x42311,x42314,f878(x42311,x42312)),x42316),f262(x42311,x42312)))),f266(x42311,x42312)),f328(f267(x42311,x42312,x42313),f328(f328(f8(x42314,f879(x42312,x42313),x42311),x42315),x42316))) % 167.75/167.49 [4238]E(f328(f139(x42381,x42382,f328(f7(x42382,x42381,x42381),x42383),f328(f139(x42381,x42382,f328(f7(x42382,x42381,x42381),x42383),x42384),f328(f166(x42382),x42385))),f328(f166(x42382),x42386)),f328(f139(x42381,x42382,f328(f7(x42382,x42381,x42381),x42383),x42384),f328(f166(x42382),f328(f328(f125(x42382),x42386),x42385)))) % 167.75/167.49 [4240]E(f328(f328(f151(f878(x42401,x42402),f878(x42403,x42402)),f328(f267(x42401,x42402,f878(x42403,x42402)),f328(f328(f8(x42403,f879(x42402,f878(x42403,x42402)),x42401),f263(x42403,x42402)),x42404))),f328(f328(f180(x42401,x42402),x42405),x42406)),f328(f328(f180(x42403,x42402),f328(f328(f151(x42401,x42403),x42404),x42405)),x42406)) % 167.75/167.49 [4288]P1(f328(f328(f242(f879(x42881,a867)),f328(f282(x42882,x42881,x42883),f328(f328(f43(x42884,f879(x42882,a867)),x42885),x42886))),f328(f328(f43(x42884,f879(x42881,a867)),x42885),f328(f328(f8(f879(x42882,a867),f879(x42881,a867),x42884),f282(x42882,x42881,x42883)),x42886)))) % 167.75/167.49 [4090]E(f328(f328(f180(x40901,x40902),f328(f328(f156(x40901,x40903),x40904),f328(f262(x40901,x40902),x40905))),f328(f328(f156(x40902,x40906),x40904),f328(f266(x40901,x40902),x40905))),f328(f328(f156(f878(x40901,x40902),f328(f328(f180(x40901,x40902),x40903),x40906)),x40904),x40905)) % 167.75/167.49 [4153]E(f328(f328(f114(f879(f878(x41531,x41532),a867)),f328(f328(f285(x41531,x41533,x41532),x41534),x41535)),f328(f328(f285(x41531,x41533,x41532),x41534),x41536)),f328(f328(f285(x41531,x41533,x41532),x41534),f328(f328(f114(f879(f878(x41533,x41532),a867)),x41535),x41536))) % 167.75/167.49 [4251]E(f328(f328(f306(f878(x42511,x42512)),f328(f328(f263(x42511,x42512),x42513),x42514)),f328(f328(f114(f879(f878(x42511,x42512),a867)),f328(f328(f265(x42511,x42512),x42515),f328(f16(f879(x42512,a867),x42511),f328(f328(f306(x42512),x42514),x42516)))),f328(f328(f265(x42511,x42512),f328(f328(f306(x42511),x42513),x42515)),f328(f16(f879(x42512,a867),x42511),x42516)))),f328(f328(f265(x42511,x42512),f328(f328(f306(x42511),x42513),x42515)),f328(f16(f879(x42512,a867),x42511),f328(f328(f306(x42512),x42514),x42516)))) % 167.75/167.49 [4329]E(f328(f328(f105(f879(x43291,a867)),f328(f308(x43291,x43292,f328(f73(f878(x43292,x43293),x43292,x43291,f262(x43292,x43293)),x43294)),x43295)),f328(f308(x43291,x43293,f328(f73(f878(x43292,x43293),x43293,x43291,f266(x43292,x43293)),x43294)),x43296)),f328(f308(x43291,f878(x43292,x43293),x43294),f328(f328(f265(x43292,x43293),x43295),f328(f16(f879(x43293,a867),x43292),x43296)))) % 167.75/167.49 [4074]E(f328(f328(f328(f72(x40741,x40742),f328(f328(f328(f72(x40741,x40742),x40743),x40744),x40745)),x40744),x40746),f328(f328(f328(f72(x40741,x40742),x40743),x40744),x40746)) % 167.75/167.49 [4178]E(f328(f328(f114(f879(f878(x41781,x41782),a867)),f328(f328(f285(x41781,x41783,x41782),x41784),x41785)),f328(f328(f285(x41781,x41783,x41782),x41786),x41785)),f328(f328(f285(x41781,x41783,x41782),f328(f328(f114(f879(f878(x41781,x41783),a867)),x41784),x41786)),x41785)) % 167.75/167.49 [4313]E(f328(f328(f43(x43131,f879(x43132,a867)),x43133),f328(f328(f7(x43131,f879(x43134,f879(x43132,a867)),f879(x43132,a867)),f328(f328(f8(f879(x43134,a867),f879(f879(x43134,f879(x43132,a867)),f879(x43132,a867)),x43131),f43(x43134,f879(x43132,a867))),x43135)),x43136)),f328(f328(f43(x43134,f879(x43132,a867)),f328(f328(f44(x43131,f879(x43134,a867)),x43133),x43135)),x43136)) % 167.75/167.49 [4314]E(f328(f328(f44(x43141,f879(x43142,a867)),x43143),f328(f328(f7(x43141,f879(x43144,f879(x43142,a867)),f879(x43142,a867)),f328(f328(f8(f879(x43144,a867),f879(f879(x43144,f879(x43142,a867)),f879(x43142,a867)),x43141),f44(x43144,f879(x43142,a867))),x43145)),x43146)),f328(f328(f44(x43144,f879(x43142,a867)),f328(f328(f44(x43141,f879(x43144,a867)),x43143),x43145)),x43146)) % 167.75/167.49 [4366]E(f328(f267(x43661,x43662,f878(x43663,x43664)),f328(f328(f7(x43661,f879(x43662,x43664),f879(x43662,f878(x43663,x43664))),f328(f328(f8(f879(x43664,f878(x43663,x43664)),f879(f879(x43662,x43664),f879(x43662,f878(x43663,x43664))),x43661),f8(x43664,f878(x43663,x43664),x43662)),f328(f328(f8(x43663,f879(x43664,f878(x43663,x43664)),x43661),f263(x43663,x43664)),x43665))),x43666)),f268(x43661,x43663,x43662,x43664,x43665,x43666)) % 167.75/167.49 [4287]E(f328(f328(f328(f72(x42871,f876(x42872)),f186(x42871,x42872,x42873,f328(f328(f22(f879(x42871,a867)),x42874),f328(f328(f306(x42871),x42875),f192(f879(x42871,a867)))))),x42875),x42876),f328(f328(f328(f72(x42871,f876(x42872)),f186(x42871,x42872,x42873,x42874)),x42875),x42876)) % 167.75/167.49 [4391]E(f328(f307(x43911,x43912,f328(f328(f18(x43911,x43912,x43912),f328(f328(f18(x43911,x43912,f879(x43912,x43912)),f328(f328(f8(a867,f879(x43912,f879(x43912,x43912)),x43911),f100(x43912)),x43913)),x43914)),x43915)),x43916),f328(f328(f114(f879(x43912,a867)),f328(f307(x43911,x43912,x43914),f328(f328(f105(f879(x43911,a867)),x43916),f328(f248(x43911),x43913)))),f328(f307(x43911,x43912,x43915),f328(f328(f105(f879(x43911,a867)),x43916),f328(f248(x43911),f328(f328(f8(a867,a867,x43911),a323),x43913)))))) % 167.75/167.49 [4402]E(f328(f307(x44021,f878(x44022,x44023),f328(f328(f18(x44021,x44023,f878(x44022,x44023)),f328(f328(f8(x44022,f879(x44023,f878(x44022,x44023)),x44021),f263(x44022,x44023)),x44024)),x44025)),x44026),f328(f328(f265(x44022,x44023),f328(f307(x44021,x44022,x44024),x44026)),f328(f328(f8(f879(x44021,a867),f879(x44023,a867),x44022),f307(x44021,x44023,x44025)),f328(f328(f7(x44022,f879(x44021,a867),f879(x44021,a867)),f328(f328(f8(f879(x44021,a867),f879(f879(x44021,a867),f879(x44021,a867)),x44022),f105(f879(x44021,a867))),f328(f328(f8(f879(x44022,a867),f879(x44021,a867),x44022),f308(x44021,x44022,x44024)),f328(f328(f7(x44022,f879(x44022,a867),f879(x44022,a867)),f306(x44022)),f192(f879(x44022,a867)))))),x44026)))) % 167.75/167.49 [4348]E(f328(f266(x43481,x43482),f328(f268(x43483,x43481,x43484,x43482,x43485,x43486),x43487)),f328(x43486,f328(f266(x43483,x43484),x43487))) % 167.75/167.49 [4349]E(f328(f262(x43491,x43492),f328(f268(x43493,x43491,x43494,x43492,x43495,x43496),x43497)),f328(x43495,f328(f262(x43493,x43494),x43497))) % 167.75/167.49 [4052]E(f328(f328(f180(x40521,x40522),f328(f328(f156(x40521,x40523),x40524),x40525)),f328(f328(f156(x40522,x40526),x40524),x40527)),f328(f328(f156(f878(x40521,x40522),f328(f328(f180(x40521,x40522),x40523),x40526)),x40524),f328(f328(f263(x40521,x40522),x40525),x40527))) % 167.75/167.49 [4120]E(f328(f328(f328(f269(x41201,x41202,x41203,x41204),x41205),x41206),x41207),f328(f328(f267(x41202,x41203,x41204),x41206),f328(x41205,x41207))) % 167.75/167.49 [4133]E(f328(f328(f328(f269(x41331,x41332,x41333,x41334),x41335),x41336),x41337),f328(f328(x41336,f328(f262(x41332,x41333),f328(x41335,x41337))),f328(f266(x41332,x41333),f328(x41335,x41337)))) % 167.75/167.49 [4168]E(f185(x41681,x41682,f328(f328(f328(f72(x41681,f876(x41682)),x41683),x41684),f328(f235(x41682),x41685)),x41686,x41687),f185(x41681,x41682,x41683,f328(f328(f148(x41681),x41684),x41686),f328(f328(f148(x41682),x41685),x41687))) % 167.75/167.49 [4186]E(f328(f73(x41861,x41862,x41863,x41864),f328(f73(x41865,x41861,x41863,x41866),x41867)),f328(f73(x41865,x41862,x41863,f328(f73(x41861,x41862,x41865,x41864),x41866)),x41867)) % 167.75/167.49 [4247]E(f328(f73(f876(x42471),f876(x42472),x42473,f328(f206(x42471,x42472),x42474)),f328(f328(f328(f72(x42473,f876(x42471)),x42475),x42476),f328(f235(x42471),x42477))),f328(f328(f328(f72(x42473,f876(x42472)),f328(f73(f876(x42471),f876(x42472),x42473,f328(f206(x42471,x42472),x42474)),x42475)),x42476),f328(f235(x42472),f328(x42474,x42477)))) % 167.75/167.49 [4373]E(f328(f268(x43731,x43732,x43733,x43733,x43734,f34(x43733)),f328(f268(x43731,x43731,x43735,x43733,f34(x43731),x43736),x43737)),f328(f328(f263(x43732,x43733),f328(x43734,f328(f262(x43731,x43735),x43737))),f328(x43736,f328(f266(x43731,x43735),x43737)))) % 167.75/167.49 [4374]E(f328(f268(x43741,x43741,x43742,x43743,f34(x43741),x43744),f328(f268(x43745,x43741,x43742,x43742,x43746,f34(x43742)),x43747)),f328(f328(f263(x43741,x43743),f328(x43746,f328(f262(x43745,x43742),x43747))),f328(x43744,f328(f266(x43745,x43742),x43747)))) % 167.75/167.49 [4389]E(f328(f268(x43891,x43892,x43893,x43893,x43894,f34(x43893)),f328(f268(x43895,x43891,x43893,x43893,x43896,f34(x43893)),x43897)),f328(f268(x43895,x43892,x43893,x43893,f328(f73(x43891,x43892,x43895,x43894),x43896),f34(x43893)),x43897)) % 167.75/167.49 [4390]E(f328(f268(x43901,x43901,x43902,x43903,f34(x43901),x43904),f328(f268(x43901,x43901,x43905,x43902,f34(x43901),x43906),x43907)),f328(f268(x43901,x43901,x43905,x43903,f34(x43901),f328(f73(x43902,x43903,x43905,x43904),x43906)),x43907)) % 167.75/167.49 [4399]E(f328(f268(x43991,x43992,x43993,x43993,x43994,f34(x43993)),f328(f268(x43991,x43991,x43995,x43993,f34(x43991),x43996),x43997)),f328(f268(x43992,x43992,x43995,x43993,f34(x43992),x43996),f328(f268(x43991,x43992,x43995,x43995,x43994,f34(x43995)),x43997))) % 167.75/167.49 [4087]E(f328(f328(f285(x40871,x40872,x40873),f328(f328(f285(x40871,x40874,x40872),x40875),x40876)),x40877),f328(f328(f285(x40871,x40874,x40873),x40875),f328(f328(f285(x40874,x40872,x40873),x40876),x40877))) % 167.75/167.49 [4159]E(f328(f328(f267(x41591,x41592,x41593),f328(f73(x41594,f879(x41592,x41593),x41591,x41595),x41596)),x41597),f328(f328(x41595,f328(x41596,f328(f262(x41591,x41592),x41597))),f328(f266(x41591,x41592),x41597))) % 167.75/167.49 [4211]E(f328(f73(x42111,x42112,x42113,x42114),f328(f328(f328(f72(x42113,x42111),x42115),x42116),x42117)),f328(f328(f328(f72(x42113,x42112),f328(f73(x42111,x42112,x42113,x42114),x42115)),x42116),f328(x42114,x42117))) % 167.75/167.49 [4243]E(f328(f139(x42431,x42432,f328(f7(x42432,x42431,x42431),x42433),x42434),f328(f166(x42432),f328(f328(f151(x42435,x42432),x42436),x42437))),f328(f139(x42431,x42435,f328(f7(x42435,x42431,x42431),f328(f73(x42432,f879(x42431,x42431),x42435,x42433),x42436)),x42434),f328(f166(x42435),x42437))) % 167.75/167.49 [4187]E(f328(f328(f44(x41871,f879(f878(x41872,x41873),a867)),x41874),f328(f328(f8(f879(f878(x41875,x41873),a867),f879(f878(x41872,x41873),a867),x41871),f328(f285(x41872,x41875,x41873),x41876)),x41877)),f328(f328(f285(x41872,x41875,x41873),x41876),f328(f328(f44(x41871,f879(f878(x41875,x41873),a867)),x41874),x41877))) % 167.75/167.49 [4335]E(f328(f328(f44(x43351,f879(f878(x43352,x43353),a867)),x43354),f328(f328(f7(x43351,f879(f878(x43355,x43353),a867),f879(f878(x43352,x43353),a867)),f328(f328(f8(f879(f878(x43352,x43355),a867),f879(f879(f878(x43355,x43353),a867),f879(f878(x43352,x43353),a867)),x43351),f285(x43352,x43355,x43353)),x43356)),x43357)),f328(f328(f285(x43352,x43355,x43353),f328(f328(f44(x43351,f879(f878(x43352,x43355),a867)),x43354),x43356)),x43357)) % 167.75/167.49 [4336]E(f328(f139(x43361,x43362,f328(f328(f7(x43361,f879(x43362,x43363),f879(x43362,x43361)),f328(f328(f8(f879(x43363,x43361),f879(f879(x43362,x43363),f879(x43362,x43361)),x43361),f8(x43363,x43361,x43362)),x43364)),x43365),x43366),x43367),f328(f139(x43361,x43363,x43364,x43366),f328(f328(f151(x43362,x43363),x43365),x43367))) % 167.75/167.49 [4400]E(f328(f328(f43(x44001,f879(x44002,a867)),x44003),f328(f328(f8(f879(x44004,f879(x44002,a867)),f879(x44002,a867),x44001),f328(f43(x44004,f879(x44002,a867)),x44005)),f328(f328(f7(x44001,f879(x44004,f879(x44002,a867)),f879(x44004,f879(x44002,a867))),f328(f328(f8(f879(f879(x44002,a867),f879(x44002,a867)),f879(f879(x44004,f879(x44002,a867)),f879(x44004,f879(x44002,a867))),x44001),f8(f879(x44002,a867),f879(x44002,a867),x44004)),f328(f328(f8(f879(x44002,a867),f879(f879(x44002,a867),f879(x44002,a867)),x44001),f114(f879(x44002,a867))),x44006))),x44007))),f328(f328(f114(f879(x44002,a867)),f328(f328(f43(x44001,f879(x44002,a867)),x44003),x44006)),f328(f328(f43(x44004,f879(x44002,a867)),x44005),x44007))) % 167.75/167.49 [4401]E(f328(f328(f44(x44011,f879(x44012,a867)),x44013),f328(f328(f8(f879(x44014,f879(x44012,a867)),f879(x44012,a867),x44011),f328(f44(x44014,f879(x44012,a867)),x44015)),f328(f328(f7(x44011,f879(x44014,f879(x44012,a867)),f879(x44014,f879(x44012,a867))),f328(f328(f8(f879(f879(x44012,a867),f879(x44012,a867)),f879(f879(x44014,f879(x44012,a867)),f879(x44014,f879(x44012,a867))),x44011),f8(f879(x44012,a867),f879(x44012,a867),x44014)),f328(f328(f8(f879(x44012,a867),f879(f879(x44012,a867),f879(x44012,a867)),x44011),f105(f879(x44012,a867))),x44016))),x44017))),f328(f328(f105(f879(x44012,a867)),f328(f328(f44(x44011,f879(x44012,a867)),x44013),x44016)),f328(f328(f44(x44014,f879(x44012,a867)),x44015),x44017))) % 167.75/167.49 [4394]E(f203(x43941,x43942,f328(f328(f328(x43943,x43944),x43945),x43946),f328(f328(f7(x43941,f878(a103,a103),f879(a103,f874(x43942))),f328(f328(f7(x43941,a103,f879(f878(a103,a103),f879(a103,f874(x43942)))),f328(f328(f7(x43941,a103,f879(a103,f879(f878(a103,a103),f879(a103,f874(x43942))))),x43947),x43944)),x43945)),x43946)),f328(f328(f328(f216(x43941,x43942,x43943,x43947),x43944),x43945),x43946)) % 167.75/167.49 [4407]E(f204(x44071,x44072,f328(f328(f328(x44073,x44074),x44075),x44076),f328(f328(f7(x44071,f878(a103,a103),f879(a103,f874(x44072))),f328(f328(f7(x44071,a103,f879(f878(a103,a103),f879(a103,f874(x44072)))),f328(f328(f7(x44071,a103,f879(a103,f879(f878(a103,a103),f879(a103,f874(x44072))))),x44077),x44074)),x44075)),x44076)),f218(x44071,x44072,x44073,x44077,x44074,x44075,x44076)) % 167.75/167.49 [4398]E(f201(x43981,x43982,f328(f328(f328(x43983,x43984),x43985),x43986),f328(f328(f7(x43981,f878(a103,a103),f879(a103,f874(f876(x43982)))),f328(f328(f7(x43981,a103,f879(f878(a103,a103),f879(a103,f874(f876(x43982))))),f328(f328(f7(x43981,a103,f879(a103,f879(f878(a103,a103),f879(a103,f874(f876(x43982)))))),x43987),x43984)),x43985)),x43986)),f328(f328(f328(f212(x43981,x43982,x43983,x43987),x43984),x43985),x43986)) % 167.75/167.49 [4409]E(f202(x44091,x44092,f328(f328(f328(x44093,x44094),x44095),x44096),f328(f328(f7(x44091,f878(a103,a103),f879(a103,f874(f876(x44092)))),f328(f328(f7(x44091,a103,f879(f878(a103,a103),f879(a103,f874(f876(x44092))))),f328(f328(f7(x44091,a103,f879(a103,f879(f878(a103,a103),f879(a103,f874(f876(x44092)))))),x44097),x44094)),x44095)),x44096)),f214(x44091,x44092,x44093,x44097,x44094,x44095,x44096)) % 167.75/167.49 [4307]E(f328(f268(x43071,x43072,x43073,x43074,x43075,x43076),f328(f328(f263(x43071,x43073),x43077),x43078)),f328(f328(f263(x43072,x43074),f328(x43075,x43077)),f328(x43076,x43078))) % 167.75/167.49 [4411]E(f328(f328(f151(f878(x44111,x44112),f878(x44113,x44114)),f328(f267(x44111,x44112,f878(x44113,x44114)),f328(f328(f7(x44111,f879(x44112,x44114),f879(x44112,f878(x44113,x44114))),f328(f328(f8(f879(x44114,f878(x44113,x44114)),f879(f879(x44112,x44114),f879(x44112,f878(x44113,x44114))),x44111),f8(x44114,f878(x44113,x44114),x44112)),f328(f328(f8(x44113,f879(x44114,f878(x44113,x44114)),x44111),f263(x44113,x44114)),x44115))),x44116))),f328(f328(f180(x44111,x44112),x44117),x44118)),f328(f328(f180(x44113,x44114),f328(f328(f151(x44111,x44113),x44115),x44117)),f328(f328(f151(x44112,x44114),x44116),x44118))) % 167.75/167.49 [4415]E(f328(f328(f151(f878(x44151,x44152),x44153),f328(f267(x44151,x44152,x44153),f328(f328(f8(f879(x44152,f878(x44151,x44154)),f879(x44152,x44153),x44151),f328(f8(f878(x44151,x44154),x44153,x44152),x44155)),f328(f328(f7(x44151,f879(x44152,x44154),f879(x44152,f878(x44151,x44154))),f328(f328(f8(f879(x44154,f878(x44151,x44154)),f879(f879(x44152,x44154),f879(x44152,f878(x44151,x44154))),x44151),f8(x44154,f878(x44151,x44154),x44152)),f263(x44151,x44154))),x44156)))),f328(f328(f180(x44151,x44152),x44157),x44158)),f328(f328(f151(f878(x44151,x44154),x44153),x44155),f328(f328(f180(x44151,x44154),x44157),f328(f328(f151(x44152,x44154),x44156),x44158)))) % 167.75/167.49 [4340]E(f328(f328(f151(f878(x43401,x43402),x43403),f328(f267(x43401,x43402,x43403),f328(f328(f8(f879(x43402,f878(x43404,x43402)),f879(x43402,x43403),x43401),f328(f8(f878(x43404,x43402),x43403,x43402),x43405)),f328(f328(f8(x43404,f879(x43402,f878(x43404,x43402)),x43401),f263(x43404,x43402)),x43406)))),f328(f328(f180(x43401,x43402),x43407),x43408)),f328(f328(f151(f878(x43404,x43402),x43403),x43405),f328(f328(f180(x43404,x43402),f328(f328(f151(x43401,x43404),x43406),x43407)),x43408))) % 167.75/167.49 [4298]E(f328(f328(f267(x42981,x42982,x42983),f328(f328(f8(f879(x42982,f878(x42984,x42985)),f879(x42982,x42983),x42981),f328(f8(f878(x42984,x42985),x42983,x42982),f328(f267(x42984,x42985,x42983),x42986))),x42987)),x42988),f328(f328(f267(x42984,x42985,x42983),x42986),f328(f328(f267(x42981,x42982,f878(x42984,x42985)),x42987),x42988))) % 167.75/167.49 [4417]E(f328(f328(f44(f878(x44171,x44172),f879(f878(x44173,x44174),a867)),f328(f328(f265(x44171,x44172),x44175),f328(f16(f879(x44172,a867),x44171),x44176))),f328(f267(x44171,x44172,f879(f878(x44173,x44174),a867)),f328(f328(f7(x44171,f879(x44172,f879(x44173,f879(x44174,a867))),f879(x44172,f879(f878(x44173,x44174),a867))),f328(f328(f8(f879(f879(x44173,f879(x44174,a867)),f879(f878(x44173,x44174),a867)),f879(f879(x44172,f879(x44173,f879(x44174,a867))),f879(x44172,f879(f878(x44173,x44174),a867))),x44171),f8(f879(x44173,f879(x44174,a867)),f879(f878(x44173,x44174),a867),x44172)),f328(f328(f8(f879(x44173,a867),f879(f879(x44173,f879(x44174,a867)),f879(f878(x44173,x44174),a867)),x44171),f265(x44173,x44174)),x44177))),f328(f328(f8(f879(x44174,a867),f879(x44173,f879(x44174,a867)),x44172),f16(f879(x44174,a867),x44173)),x44178)))),f328(f328(f265(x44173,x44174),f328(f328(f44(x44171,f879(x44173,a867)),x44175),x44177)),f328(f16(f879(x44174,a867),x44173),f328(f328(f44(x44172,f879(x44174,a867)),x44176),x44178)))) % 167.75/167.49 [4354]E(f328(f328(f269(x43541,x43542,x43543,x43544),f328(f328(f269(x43541,x43545,x43546,f878(x43542,x43543)),x43547),x43548)),x43549),f328(f328(f269(x43541,x43545,x43546,x43544),x43547),f328(f328(f7(x43545,f879(x43542,f879(x43543,x43544)),f879(x43546,x43544)),f328(f328(f8(f879(x43546,f878(x43542,x43543)),f879(f879(x43542,f879(x43543,x43544)),f879(x43546,x43544)),x43545),f269(x43546,x43542,x43543,x43544)),x43548)),x43549))) % 167.75/167.49 [4386]E(f328(f73(f878(x43861,x43862),f878(x43863,x43864),f878(x43865,x43866),f268(x43861,x43863,x43862,x43864,x43867,x43868)),f268(x43865,x43861,x43866,x43862,x43869,x438610)),f268(x43865,x43863,x43866,x43864,f328(f73(x43861,x43863,x43865,x43867),x43869),f328(f73(x43862,x43864,x43866,x43868),x438610))) % 167.75/167.49 [4392]E(f328(f268(x43921,x43922,x43923,x43924,x43925,x43926),f328(f268(x43927,x43921,x43928,x43923,x43929,x439210),x439211)),f328(f268(x43927,x43922,x43928,x43924,f328(f73(x43921,x43922,x43927,x43925),x43929),f328(f73(x43923,x43924,x43928,x43926),x439210)),x439211)) % 167.75/167.49 [6440]P8(a5000)+P1(f328(f328(f330(f878(a870,a869)),a678),f328(f170(f878(a870,a869)),a27))) % 167.75/167.49 [8445]P8(a5000)+~P1(f328(f328(f267(a870,a869,a867),f328(f16(f879(a869,a867),a870),a25)),a678)) % 167.75/167.49 [4559]~P93(x45591)+E(f91(x45591),a325) % 167.75/167.49 [4560]~P3(x45601)+P3(f876(x45601)) % 167.75/167.49 [4561]~P59(x45611)+P59(f876(x45611)) % 167.75/167.49 [4564]~P141(x45641)+~E(f78(x45641),f2(x45641)) % 167.75/167.49 [4566]~E(x45661,f2(a103))+E(f328(a20,x45661),f2(a1)) % 167.75/167.49 [4567]~E(x45671,f2(a1))+E(f82(a1,x45671),f2(a1)) % 167.75/167.49 [4573]~P142(x45731)+P31(x45731,f2(x45731)) % 167.75/167.49 [4575]~P105(x45751)+P15(x45751,f117(x45751)) % 167.75/167.49 [4584]P1(x45841)+P1(f328(a323,x45841)) % 167.75/167.49 [4627]~P142(x46271)+~P31(x46271,f78(x46271)) % 167.75/167.49 [4673]~P1(x46731)+~P1(f328(a323,x46731)) % 167.75/167.49 [4696]E(f328(a108,x46961),f2(a872))+~P1(f328(a197,x46961)) % 167.75/167.49 [4760]~P99(x47601)+P16(x47601,x47601,f114(x47601)) % 167.75/167.49 [4761]~P100(x47611)+P16(x47611,x47611,f105(x47611)) % 167.75/167.49 [4762]~P95(x47621)+P16(x47621,x47621,f81(x47621)) % 167.75/167.49 [4763]~P105(x47631)+P16(x47631,x47631,f240(x47631)) % 167.75/167.49 [4764]~P105(x47641)+P16(x47641,x47641,f241(x47641)) % 167.75/167.49 [4765]~P69(x47651)+P17(x47651,x47651,f81(x47651)) % 167.75/167.49 [4570]~E(x45701,f2(a872))+E(f328(f104(a1),x45701),f2(a1)) % 167.75/167.49 [4577]~P91(x45771)+E(f328(f107(x45771),a83),f2(x45771)) % 167.75/167.49 [4580]~E(f582(x45801),f2(a872))+E(f328(f163(a872),x45801),f2(a872)) % 167.75/167.49 [4581]~P108(x45811)+E(f244(x45811,f242(x45811)),f240(x45811)) % 167.75/167.49 [4582]~P108(x45821)+E(f245(x45821,f242(x45821)),f241(x45821)) % 167.75/167.49 [4583]~P88(x45831)+E(f82(x45831,f2(x45831)),f2(x45831)) % 167.75/167.49 [4592]~P142(x45921)+E(f328(f104(x45921),f78(a872)),f78(x45921)) % 167.75/167.49 [4593]~P142(x45931)+E(f328(f104(x45931),f2(a872)),f2(x45931)) % 167.75/167.49 [4594]~P138(x45941)+E(f328(f106(x45941),f78(a1)),f78(x45941)) % 167.75/167.49 [4595]~P138(x45951)+E(f328(f106(x45951),f2(a1)),f2(x45951)) % 167.75/167.49 [4596]E(x45961,f2(a872))+~E(f328(f104(a1),x45961),f2(a1)) % 167.75/167.49 [4621]~P117(x46211)+E(f328(f75(x46211),f78(x46211)),f78(x46211)) % 167.75/167.49 [4622]~P84(x46221)+E(f328(f75(x46221),f2(x46221)),f2(x46221)) % 167.75/167.49 [4623]~P94(x46231)+E(f328(f79(x46231),f192(x46231)),f251(x46231)) % 167.75/167.49 [4624]~P94(x46241)+E(f328(f79(x46241),f251(x46241)),f192(x46241)) % 167.75/167.49 [4625]~P74(x46251)+E(f328(f79(x46251),f2(x46251)),f2(x46251)) % 167.75/167.49 [4626]~P79(x46261)+E(f328(f163(x46261),f117(x46261)),f2(x46261)) % 167.75/167.49 [4647]~P37(x46471)+P39(f328(f170(a1),x46471)) % 167.75/167.49 [4678]~P91(x46781)+E(f328(f79(x46781),f78(x46781)),f328(f107(x46781),a101)) % 167.75/167.49 [4695]~P91(x46951)+P31(x46951,f328(f107(x46951),a83)) % 167.75/167.49 [4712]~P59(x47121)+E(f328(f170(x47121),f57(x47121)),f251(f879(x47121,a867))) % 167.75/167.49 [4722]P37(x47221)+~P39(f328(f170(a1),x47221)) % 167.75/167.49 [4723]~P59(x47231)+P1(f328(f134(x47231),f57(x47231))) % 167.75/167.49 [4766]E(f328(f104(a1),f328(a108,x47661)),x47661)+P1(f328(a197,x47661)) % 167.75/167.49 [4783]~P108(x47831)+E(f93(x47831,x47831,f5(x47831)),f94(x47831)) % 167.75/167.49 [4836]~P113(x48361)+E(f254(x48361,f78(x48361),f81(x48361)),f253(x48361)) % 167.75/167.49 [4866]~P91(x48661)+~P31(x48661,f328(f107(x48661),a101)) % 167.75/167.49 [4876]E(f328(a28,x48761),f205(a869))+P1(f328(a25,f328(a26,x48761))) % 167.75/167.49 [5007]E(f328(f75(a1),x50071),x50071)+P1(f328(f328(f243(a1),x50071),f2(a1))) % 167.75/167.49 [5028]~E(f328(a108,x50281),f2(a872))+P1(f328(f328(f242(a1),x50281),f2(a1))) % 167.75/167.49 [5090]~P1(f328(a197,x50901))+P1(f328(f328(f243(a1),x50901),f2(a1))) % 167.75/167.49 [5130]~P138(x51301)+P1(f328(f328(f330(x51301),f78(x51301)),f113(x51301))) % 167.75/167.49 [5131]~P142(x51311)+P1(f328(f328(f330(x51311),f78(x51311)),f190(x51311))) % 167.75/167.49 [5132]~P138(x51321)+P1(f328(f328(f330(x51321),f2(x51321)),f113(x51321))) % 167.75/167.49 [5133]~P142(x51331)+P1(f328(f328(f330(x51331),f2(x51331)),f190(x51331))) % 167.75/167.49 [5134]~P116(x51341)+P1(f328(f328(f243(x51341),f2(x51341)),f78(x51341))) % 167.75/167.49 [5135]~P116(x51351)+P1(f328(f328(f242(x51351),f2(x51351)),f78(x51351))) % 167.75/167.49 [5137]E(f328(f235(a869),f688(x51371)),f328(a28,x51371))+~P1(f328(a25,f328(a26,x51371))) % 167.75/167.49 [5138]E(f328(f235(a869),f702(x51381)),f328(a28,x51381))+~P1(f328(a25,f328(a26,x51381))) % 167.75/167.49 [5193]E(x51931,f2(a872))+~P1(f328(f328(f242(a872),x51931),f2(a872))) % 167.75/167.49 [5237]E(f328(a108,x52371),f2(a872))+~P1(f328(f328(f242(a1),x52371),f2(a1))) % 167.75/167.49 [5300]P1(f328(a197,x53001))+~P1(f328(f328(f243(a1),x53001),f2(a1))) % 167.75/167.49 [5305]~P105(x53051)+P17(x53051,f873(x53051),f145(x53051,x53051,f5(x53051))) % 167.75/167.49 [5322]P39(x53221)+~P1(f328(f328(f242(a1),f2(a1)),f336(x53221))) % 167.75/167.49 [5328]E(f328(f75(a1),x53281),f328(f79(a1),x53281))+~P1(f328(f328(f243(a1),x53281),f2(a1))) % 167.75/167.49 [5500]~P116(x55001)+~P1(f328(f328(f243(x55001),f78(x55001)),f2(x55001))) % 167.75/167.49 [5501]~P116(x55011)+~P1(f328(f328(f242(x55011),f78(x55011)),f2(x55011))) % 167.75/167.49 [5511]~E(x55111,f2(a1))+P1(f328(f328(f243(a1),f328(f75(a1),x55111)),f78(a1))) % 167.75/167.49 [5512]~E(x55121,f2(a872))+P1(f328(f328(f242(a1),f328(f104(a1),x55121)),f2(a1))) % 167.75/167.49 [5632]~P79(x56321)+E(f139(x56321,x56321,f80(x56321),f2(x56321)),f163(x56321)) % 167.75/167.49 [5804]~P102(x58041)+P26(a872,x58041,f104(x58041),f251(f879(a872,a867))) % 167.75/167.49 [5996]E(x59961,f2(a872))+~P1(f328(f328(f242(a1),f328(f104(a1),x59961)),f2(a1))) % 167.75/167.49 [5997]E(x59971,f2(a1))+~P1(f328(f328(f243(a1),f328(f75(a1),x59971)),f78(a1))) % 167.75/167.49 [6796]~P1(f328(f328(f243(a1),x67961),f2(a1)))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x67961),x67961)),f2(a1))) % 167.75/167.49 [7344]P1(f328(f328(f243(a1),x73441),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x73441),x73441)),f2(a1))) % 167.75/167.49 [7904]E(x79041,f328(a3,f2(a872)))+P1(f328(f328(f243(a872),f328(f328(f22(a872),f328(a19,x79041)),f328(a116,f2(a872)))),f328(a19,x79041))) % 167.75/167.49 [8678]~P1(f328(f328(f243(a1),x86781),f2(a1)))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86781),x86781)),a101)),f2(a1))) % 167.75/167.49 [8764]~P1(f328(f328(f243(a1),x87641),f2(a1)))+P1(f328(f328(f243(a1),f328(f328(f80(a1),f328(f328(f80(a1),f78(a1)),x87641)),x87641)),f2(a1))) % 167.75/167.49 [9088]P1(f328(f328(f243(a1),x90881),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90881),x90881)),a101)),f2(a1))) % 167.75/167.49 [9151]P1(f328(f328(f243(a1),x91511),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),f328(f328(f80(a1),f78(a1)),x91511)),x91511)),f2(a1))) % 167.75/167.49 [4666]~E(a83,x46661)+E(f328(f328(f80(a1),x46661),x46661),a83) % 167.75/167.49 [4667]~E(x46671,a83)+E(f328(f328(f80(a1),x46671),x46671),a83) % 167.75/167.49 [4681]E(x46811,f2(a1))+E(f328(f328(f40(a1),x46811),x46811),f78(a1)) % 167.75/167.49 [4812]E(x48121,a83)+~E(f328(f328(f80(a1),x48121),x48121),a83) % 167.75/167.49 [4813]E(a83,x48131)+~E(f328(f328(f80(a1),x48131),x48131),a83) % 167.75/167.49 [4826]~P4(x48261)+E(f42(x48261,f192(f879(x48261,a867))),f251(x48261)) % 167.75/167.49 [4827]~P4(x48271)+E(f42(x48271,f251(f879(x48271,a867))),f192(x48271)) % 167.75/167.49 [4828]~P4(x48281)+E(f41(x48281,f192(f879(x48281,a867))),f192(x48281)) % 167.75/167.49 [4829]~P4(x48291)+E(f41(x48291,f251(f879(x48291,a867))),f251(x48291)) % 167.75/167.49 [4830]~P105(x48301)+E(f136(x48301,f192(f879(x48301,a867))),f117(x48301)) % 167.75/167.49 [4965]E(x49651,f2(a872))+P1(f328(f328(f243(a872),f2(a872)),x49651)) % 167.75/167.49 [4984]~P5(x49841)+P1(f328(f328(f242(a1),f2(a1)),x49841)) % 167.75/167.49 [5019]~E(f328(f107(a872),x50191),f2(a872))+P1(f328(f328(f242(a1),x50191),a83)) % 167.75/167.49 [5024]P39(x50241)+P1(f328(f328(f330(a1),f336(x50241)),x50241)) % 167.75/167.49 [5025]E(x50251,f328(a3,f2(a872)))+P1(f328(f328(f242(a103),f78(a103)),x50251)) % 167.75/167.49 [5064]P1(f328(a197,x50641))+P1(f328(f328(f242(a1),f2(a1)),x50641)) % 167.75/167.49 [5112]E(f328(f104(a1),f328(a108,x51121)),f2(a1))+P1(f328(f328(f242(a1),f2(a1)),x51121)) % 167.75/167.49 [5179]E(f328(f104(a1),f328(f107(a872),x51791)),f328(f107(a1),x51791))+P1(f328(a197,f328(f107(a1),x51791))) % 167.75/167.49 [5199]E(f328(f107(a872),x51991),f2(a872))+~P1(f328(a197,f328(f107(a1),x51991))) % 167.75/167.49 [5200]E(f328(f107(a872),x52001),f2(a872))+~P1(f328(f328(f242(a1),x52001),a83)) % 167.75/167.49 [5234]P5(x52341)+~P1(f328(f328(f242(a1),f2(a1)),x52341)) % 167.75/167.49 [5308]E(f328(a116,f803(x53081)),x53081)+~P1(f328(f328(f243(a872),f2(a872)),x53081)) % 167.75/167.49 [5316]E(f328(a116,f328(f107(a872),x53161)),f78(a872))+~P1(f328(a197,f328(f107(a1),x53161))) % 167.75/167.49 [5324]E(f328(f104(a1),f387(x53241)),x53241)+~P1(f328(f328(f243(a1),f2(a1)),x53241)) % 167.75/167.49 [5331]~E(x53311,f328(a3,f2(a872)))+~P1(f328(f328(f242(a103),f78(a103)),x53311)) % 167.75/167.49 [5338]E(f328(f104(a1),f328(f107(a872),x53381)),f2(a1))+~P1(f328(a197,f328(f107(a1),x53381))) % 167.75/167.49 [5364]E(f328(f163(a872),x53641),f2(a872))+P1(f328(f328(f330(a872),f582(x53641)),f328(f170(a872),x53641))) % 167.75/167.49 [5385]E(f328(f104(a1),f328(a108,x53851)),x53851)+~P1(f328(f328(f242(a1),f2(a1)),x53851)) % 167.75/167.49 [5394]~P1(f328(a197,x53941))+~P1(f328(f328(f242(a1),f2(a1)),x53941)) % 167.75/167.49 [5493]E(f328(f328(f80(a872),f78(a872)),f328(f107(a872),x54931)),f78(a872))+~P1(f328(f328(f243(a1),x54931),a83)) % 167.75/167.49 [5551]E(x55511,f2(a872))+~P1(f328(f328(f243(a872),x55511),f328(a116,f2(a872)))) % 167.75/167.49 [5591]E(f328(f328(f22(a872),f328(f107(a872),x55911)),f78(a872)),f2(a872))+~P1(f328(f328(f242(a1),x55911),a83)) % 167.75/167.49 [5592]E(f328(f328(f80(a872),f328(f107(a872),x55921)),f78(a872)),f78(a872))+~P1(f328(f328(f243(a1),x55921),a83)) % 167.75/167.49 [5602]~P39(x56021)+E(f328(f39(a872),f328(f307(a1,a872,a108),x56021)),f328(f39(a1),x56021)) % 167.75/167.49 [5633]~P105(x56331)+E(f245(x56331,f328(f7(x56331,x56331,a867),f242(x56331))),f240(x56331)) % 167.75/167.49 [5634]~P105(x56341)+E(f244(x56341,f328(f7(x56341,x56341,a867),f242(x56341))),f241(x56341)) % 167.75/167.49 [5644]E(f46(a872,f328(a116,f2(a872)),f328(f107(a872),x56441)),f328(a116,f2(a872)))+~P1(f328(a197,f328(f107(a1),x56441))) % 167.75/167.49 [5653]P1(f328(f328(f243(a1),f2(a1)),x56531))+~P1(f328(f328(f242(a1),f78(a1)),x56531)) % 167.75/167.49 [5654]~P1(f328(f328(f243(a1),f2(a1)),x56541))+P1(f328(f328(f242(a1),f78(a1)),x56541)) % 167.75/167.49 [5665]E(f328(a116,f328(f328(f22(a872),x56651),f78(a872))),x56651)+~P1(f328(f328(f243(a872),f2(a872)),x56651)) % 167.75/167.49 [5723]P1(f328(f328(f243(a872),f2(a872)),f387(x57231)))+~P1(f328(f328(f243(a1),f2(a1)),x57231)) % 167.75/167.49 [5782]E(f46(a1,f328(f107(a1),a101),x57821),f328(f328(f22(a1),x57821),f78(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x57821)) % 167.75/167.49 [5816]~P1(f328(f328(f243(a1),a83),x58161))+P1(f328(f328(f243(a872),f2(a872)),f328(f107(a872),x58161))) % 167.75/167.49 [5866]P1(f328(f328(f243(a872),f2(a872)),f328(a108,x58661)))+~P1(f328(f328(f243(a1),f2(a1)),x58661)) % 167.75/167.49 [5917]~P1(f328(f328(f243(a872),f2(a872)),x59171))+P1(f328(f328(f243(a1),f2(a1)),f328(f104(a1),x59171))) % 167.75/167.49 [5953]~P1(f328(f328(f243(a872),f2(a872)),f328(a108,x59531)))+P1(f328(f328(f243(a1),f2(a1)),x59531)) % 167.75/167.49 [5967]~P39(x59671)+E(f328(f307(a872,a1,f104(a1)),f328(f307(a1,a872,a108),x59671)),x59671) % 167.75/167.49 [5977]P1(f328(f328(f243(a1),a83),x59771))+~P1(f328(f328(f243(a872),f2(a872)),f328(f107(a872),x59771))) % 167.75/167.49 [6025]~P59(x60251)+E(f328(f328(f148(f876(x60251)),f205(x60251)),f328(f328(f151(x60251,f876(x60251)),f235(x60251)),f57(x60251))),f57(f876(x60251))) % 167.75/167.49 [6036]P1(f328(f328(f243(a872),f2(a872)),x60361))+~P1(f328(f328(f243(a1),f2(a1)),f328(f104(a1),x60361))) % 167.75/167.49 [6151]E(f328(f307(a872,a1,f104(a1)),f328(f249(a872),f328(a108,x61511))),f328(f298(a1,f2(a1)),x61511))+~P1(f328(f328(f242(a1),f2(a1)),x61511)) % 167.75/167.49 [6169]~P116(x61691)+P1(f328(f328(f243(x61691),f2(x61691)),f328(f328(f80(x61691),f78(x61691)),f78(x61691)))) % 167.75/167.49 [6220]P1(f328(f328(f243(a872),f328(a116,f2(a872))),f328(a108,x62201)))+~P1(f328(f328(f243(a1),f78(a1)),x62201)) % 167.75/167.49 [6315]E(x63151,f2(a1))+P1(f328(f50(f2(a1),x63151),f328(f328(f263(a1,a1),f2(a1)),f2(a1)))) % 167.75/167.49 [6479]~P1(f328(f328(f243(a872),f328(a116,f2(a872))),f328(a108,x64791)))+P1(f328(f328(f243(a1),f78(a1)),x64791)) % 167.75/167.49 [6907]~P114(x69071)+P38(x69071,f328(f248(f878(x69071,x69071)),f328(f267(x69071,x69071,a867),f243(x69071)))) % 167.75/167.49 [5538]E(f328(f107(a872),f328(f328(f22(a1),x55381),a101)),f328(a116,f328(f107(a872),x55381)))+P1(f328(a197,f328(f107(a1),x55381))) % 167.75/167.49 [5554]~P37(x55541)+E(f328(f328(f151(a872,a1),f104(a1)),f328(f328(f151(a1,a872),a108),x55541)),x55541) % 167.75/167.49 [5671]E(f328(f79(a1),f328(f104(a1),f328(a116,f460(x56711)))),x56711)+~P1(f328(f328(f243(a1),x56711),f2(a1))) % 167.75/167.49 [5681]E(f328(f328(f80(a872),f78(a872)),f328(f107(a872),x56811)),f328(f107(a872),f328(f328(f22(a1),x56811),a101)))+P1(f328(f328(f243(a1),x56811),a83)) % 167.75/167.49 [5725]E(f328(f328(f40(a1),f328(f107(a1),a101)),x57251),f328(f107(a1),a101))+~P1(f328(f328(f243(a1),f2(a1)),x57251)) % 167.75/167.49 [5812]E(f328(f328(f22(a872),f328(f107(a872),x58121)),f78(a872)),f328(f107(a872),f328(f328(f80(a1),x58121),a101)))+P1(f328(f328(f242(a1),x58121),a83)) % 167.75/167.49 [5813]E(f328(f328(f80(a872),f328(f107(a872),x58131)),f78(a872)),f328(f107(a872),f328(f328(f22(a1),x58131),a101)))+P1(f328(f328(f243(a1),x58131),a83)) % 167.75/167.49 [5854]E(f328(a108,f328(f328(f80(a1),f78(a1)),x58541)),f328(a116,f328(a108,x58541)))+~P1(f328(f328(f242(a1),f2(a1)),x58541)) % 167.75/167.49 [5890]E(f328(a116,f328(f328(f22(a872),x58901),f328(a116,f2(a872)))),x58901)+~P1(f328(f328(f243(a872),f2(a872)),x58901)) % 167.75/167.49 [6096]E(f46(a872,f328(a116,f2(a872)),f328(f107(a872),x60961)),f328(a108,f46(a1,f78(a1),f328(f107(a1),x60961))))+P1(f328(a197,f328(f107(a1),x60961))) % 167.75/167.49 [6141]~P1(f328(f328(f243(a1),a83),x61411))+P1(f328(f328(f243(a1),a83),f328(f328(f80(a1),x61411),x61411))) % 167.75/167.49 [6142]~P1(f328(f328(f243(a1),a101),x61421))+P1(f328(f328(f243(a1),a101),f328(f328(f80(a1),x61421),x61421))) % 167.75/167.49 [6143]~P1(f328(f328(f242(a1),a83),x61431))+P1(f328(f328(f242(a1),a83),f328(f328(f80(a1),x61431),x61431))) % 167.75/167.49 [6144]~P1(f328(f328(f243(a1),a101),x61441))+P1(f328(f328(f242(a1),a101),f328(f328(f80(a1),x61441),x61441))) % 167.75/167.49 [6145]~P1(f328(f328(f91(a1),a83),x61451))+P1(f328(f328(f91(a1),a83),f328(f328(f80(a1),x61451),x61451))) % 167.75/167.49 [6328]~P1(f328(f38(x63281),f251(f879(x63281,a867))))+P1(f328(f38(f876(x63281)),f251(f879(f876(x63281),a867)))) % 167.75/167.49 [6412]~P1(f328(f328(f242(a1),f2(a1)),x64121))+P1(f328(f328(f243(a1),f2(a1)),f328(f328(f80(a1),f78(a1)),x64121))) % 167.75/167.49 [6419]E(f328(f262(a1,a1),f48(f78(a1),f328(f107(a1),x64191))),f328(f328(f40(a1),f78(a1)),f328(f107(a1),x64191)))+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x64191))) % 167.75/167.49 [6439]E(f328(f266(a1,a1),f48(f78(a1),f328(f107(a1),x64391))),f46(a1,f78(a1),f328(f107(a1),x64391)))+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x64391))) % 167.75/167.49 [6451]P1(f328(f38(x64511),f251(f879(x64511,a867))))+~P1(f328(f38(f876(x64511)),f251(f879(f876(x64511),a867)))) % 167.75/167.49 [6480]P1(f328(f328(f243(a1),a83),x64801))+~P1(f328(f328(f243(a1),a83),f328(f328(f80(a1),x64801),x64801))) % 167.75/167.49 [6481]P1(f328(f328(f243(a1),a101),x64811))+~P1(f328(f328(f243(a1),a101),f328(f328(f80(a1),x64811),x64811))) % 167.75/167.49 [6482]P1(f328(f328(f243(a1),a101),x64821))+~P1(f328(f328(f242(a1),a101),f328(f328(f80(a1),x64821),x64821))) % 167.75/167.49 [6483]P1(f328(f328(f242(a1),a83),x64831))+~P1(f328(f328(f242(a1),a83),f328(f328(f80(a1),x64831),x64831))) % 167.75/167.49 [6484]P1(f328(f328(f91(a1),a83),x64841))+~P1(f328(f328(f91(a1),a83),f328(f328(f80(a1),x64841),x64841))) % 167.75/167.49 [6800]~P1(f328(f38(x68001),f251(f879(x68001,a867))))+P1(f328(f328(f243(a872),f2(a872)),f328(f39(x68001),f251(f879(x68001,a867))))) % 167.75/167.49 [7386]P1(f328(f38(a872),x73861))+~P1(f328(f38(a1),f328(f307(a872,a1,f104(a1)),x73861))) % 167.75/167.49 [5468]~E(a101,x54681)+E(f328(f328(f22(a1),f328(f328(f80(a1),x54681),x54681)),a101),a101) % 167.75/167.49 [5469]~E(x54691,a101)+E(f328(f328(f22(a1),f328(f328(f80(a1),x54691),x54691)),a101),a101) % 167.75/167.49 [5972]E(x59721,a101)+~E(f328(f328(f22(a1),f328(f328(f80(a1),x59721),x59721)),a101),a101) % 167.75/167.49 [5973]E(a101,x59731)+~E(f328(f328(f22(a1),f328(f328(f80(a1),x59731),x59731)),a101),a101) % 167.75/167.49 [6381]~E(f328(f107(a872),x63811),f2(a872))+P1(f328(a197,f328(f107(a1),f328(f328(f80(a1),x63811),a101)))) % 167.75/167.49 [6726]~P1(f328(a197,f328(f107(a1),x67261)))+P1(f328(a197,f328(f107(a1),f328(f328(f80(a1),x67261),x67261)))) % 167.75/167.49 [6727]~P1(f328(f328(f243(a1),x67271),a83))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x67271),x67271)),a83)) % 167.75/167.49 [6728]~P1(f328(f328(f242(a1),x67281),a101))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x67281),x67281)),a101)) % 167.75/167.49 [6729]~P1(f328(f328(f242(a1),x67291),a83))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x67291),x67291)),a83)) % 167.75/167.49 [6730]~P1(f328(f328(f242(a1),x67301),a101))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x67301),x67301)),a101)) % 167.75/167.49 [6731]~P1(f328(f328(f91(a1),x67311),a83))+P1(f328(f328(f91(a1),f328(f328(f80(a1),x67311),x67311)),a83)) % 167.75/167.49 [7052]E(f328(f107(a872),x70521),f2(a872))+~P1(f328(a197,f328(f107(a1),f328(f328(f80(a1),x70521),a101)))) % 167.75/167.49 [7293]~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x72931)))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),f328(f328(f80(a1),x72931),x72931)))) % 167.75/167.49 [7294]P1(f328(a197,f328(f107(a1),x72941)))+~P1(f328(a197,f328(f107(a1),f328(f328(f80(a1),x72941),x72941)))) % 167.75/167.49 [7295]P1(f328(f328(f243(a1),x72951),a83))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x72951),x72951)),a83)) % 167.75/167.49 [7296]P1(f328(f328(f242(a1),x72961),a83))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x72961),x72961)),a83)) % 167.75/167.49 [7297]P1(f328(f328(f242(a1),x72971),a101))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x72971),x72971)),a101)) % 167.75/167.49 [7298]P1(f328(f328(f242(a1),x72981),a101))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x72981),x72981)),a101)) % 167.75/167.49 [7299]P1(f328(f328(f91(a1),x72991),a83))+~P1(f328(f328(f91(a1),f328(f328(f80(a1),x72991),x72991)),a83)) % 167.75/167.49 [7669]E(f328(a110,f572(x76691)),x76691)+~P1(f328(f328(f330(f879(f878(a872,a872),a867)),x76691),a102)) % 167.75/167.49 [6301]~P91(x63011)+E(f328(f107(x63011),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f78(x63011)) % 167.75/167.49 [6778]~P1(f328(a197,f328(f107(a1),x67781)))+E(f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),x67781),x67781)),a101)),f2(a872)) % 167.75/167.49 [7849]~P1(f328(f328(f243(a1),f328(f107(a1),x78491)),f2(a1)))+E(f328(f262(a1,a1),f328(a52,f51(f328(f79(a1),f78(a1)),f328(f79(a1),f328(f107(a1),x78491))))),f328(f328(f40(a1),f78(a1)),f328(f107(a1),x78491))) % 167.75/167.49 [7862]~P1(f328(f328(f243(a1),f328(f107(a1),x78621)),f2(a1)))+E(f328(f266(a1,a1),f328(a52,f51(f328(f79(a1),f78(a1)),f328(f79(a1),f328(f107(a1),x78621))))),f46(a1,f78(a1),f328(f107(a1),x78621))) % 167.75/167.49 [7910]~P1(f328(f328(f242(a1),a83),x79101))+P1(f328(f328(f243(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x79101),x79101)),a101))) % 167.75/167.49 [7911]~P1(f328(f328(f243(a1),a101),x79111))+P1(f328(f328(f243(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x79111),x79111)),a101))) % 167.75/167.49 [7912]~P1(f328(f328(f242(a1),a83),x79121))+P1(f328(f328(f242(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x79121),x79121)),a101))) % 167.75/167.49 [7913]~P1(f328(f328(f242(a1),a101),x79131))+P1(f328(f328(f242(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x79131),x79131)),a101))) % 167.75/167.49 [7914]~P1(f328(f328(f91(a1),a101),x79141))+P1(f328(f328(f91(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x79141),x79141)),a101))) % 167.75/167.49 [8225]~P91(x82251)+~P31(x82251,f328(f107(x82251),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))) % 167.75/167.49 [8404]P1(f328(f328(f243(a1),a101),x84041))+~P1(f328(f328(f243(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x84041),x84041)),a101))) % 167.75/167.49 [8405]P1(f328(f328(f242(a1),a83),x84051))+~P1(f328(f328(f243(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x84051),x84051)),a101))) % 167.75/167.49 [8406]P1(f328(f328(f242(a1),a83),x84061))+~P1(f328(f328(f242(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x84061),x84061)),a101))) % 167.75/167.49 [8407]P1(f328(f328(f242(a1),a101),x84071))+~P1(f328(f328(f242(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x84071),x84071)),a101))) % 167.75/167.49 [8408]P1(f328(f328(f91(a1),a101),x84081))+~P1(f328(f328(f91(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x84081),x84081)),a101))) % 167.75/167.49 [8722]E(f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),x87221),x87221)),a101)),f328(f328(f86(a872,a872),f328(f107(a872),x87221)),f328(f328(f8(a872,a872,a872),a116),f328(f328(f18(a872,a872,a872),f80(a872)),f5(a872)))))+P1(f328(a197,f328(f107(a1),x87221))) % 167.75/167.49 [9569]E(x95691,f192(f879(f878(a872,a872),a867)))+P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),x95691),f192(f879(f878(a872,a872),a867)))),a36)) % 167.75/167.49 [8653]~P1(f328(a197,f328(f107(a1),x86531)))+P1(f328(a197,f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86531),x86531)),a101)))) % 167.75/167.49 [8654]~P1(f328(f328(f243(a1),x86541),a83))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86541),x86541)),a101)),a83)) % 167.75/167.49 [8655]~P1(f328(f328(f243(a1),x86551),a101))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86551),x86551)),a101)),a101)) % 167.75/167.49 [8656]~P1(f328(f328(f243(a1),x86561),a83))+P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86561),x86561)),a101)),a83)) % 167.75/167.49 [8657]~P1(f328(f328(f242(a1),x86571),a101))+P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86571),x86571)),a101)),a101)) % 167.75/167.49 [8658]~P1(f328(f328(f91(a1),x86581),a101))+P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86581),x86581)),a101)),a101)) % 167.75/167.49 [8757]~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x87571)))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x87571),x87571)),a101)))) % 167.75/167.49 [8916]~P91(x89161)+E(f328(f328(f80(x89161),f78(x89161)),f78(x89161)),f328(f107(x89161),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))) % 167.75/167.49 [9072]P1(f328(a197,f328(f107(a1),x90721)))+~P1(f328(a197,f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90721),x90721)),a101)))) % 167.75/167.49 [9073]P1(f328(f328(f243(a1),x90731),a83))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90731),x90731)),a101)),a83)) % 167.75/167.49 [9074]P1(f328(f328(f243(a1),x90741),a83))+~P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90741),x90741)),a101)),a83)) % 167.75/167.49 [9075]P1(f328(f328(f243(a1),x90751),a101))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90751),x90751)),a101)),a101)) % 167.75/167.49 [9076]P1(f328(f328(f242(a1),x90761),a101))+~P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90761),x90761)),a101)),a101)) % 167.75/167.49 [9077]P1(f328(f328(f91(a1),x90771),a101))+~P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90771),x90771)),a101)),a101)) % 167.75/167.49 [9615]~P1(f328(f38(f878(a872,a872)),x96151))+P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),f192(f879(f878(a872,a872),a867))),x96151)),a69)) % 167.75/167.49 [9399]~P142(x93991)+E(f328(f328(f253(x93991),f78(x93991)),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(x93991)) % 167.75/167.49 [9400]~P142(x94001)+E(f328(f328(f253(x94001),f2(x94001)),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f2(x94001)) % 167.75/167.49 [9845]~P1(f328(f328(f243(a872),f78(a872)),x98451))+P1(f328(f328(f243(a872),f2(a872)),f328(f328(f40(a872),x98451),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 167.75/167.49 [9857]~P1(f328(f328(f243(a872),f2(a872)),x98571))+P1(f328(f328(f243(a872),f2(a872)),f328(f328(f40(a872),f328(f328(f80(a872),x98571),f78(a872))),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 167.75/167.49 [9899]~E(f46(a872,x98991,f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(a872))+P1(f328(f328(f243(a872),f2(a872)),f46(a872,x98991,f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 167.75/167.49 [9918]E(f46(a872,x99181,f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(a872))+~P1(f328(f328(f243(a872),f2(a872)),f46(a872,x99181,f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 167.75/167.49 [4600]~P38(x46001,x46002)+P54(x46001,x46002) % 167.75/167.49 [4601]~P44(x46011,x46012)+P54(x46011,x46012) % 167.75/167.49 [4562]~E(x45621,x45622)+E(f275(x45621,x45622),f78(a103)) % 167.75/167.49 [4565]E(f223(x45651,x45652),x45651)+~E(x45652,f2(a872)) % 167.75/167.49 [4572]~E(x45722,f117(x45721))+E(f149(x45721,x45722),f117(x45721)) % 167.75/167.49 [4591]~E(f149(x45912,x45911),f117(x45912))+E(x45911,f117(x45912)) % 167.75/167.49 [4605]~P2(x46052)+P2(f879(x46051,x46052)) % 167.75/167.49 [4606]~P2(x46062)+P99(f879(x46061,x46062)) % 167.75/167.49 [4607]~P96(x46072)+P64(f879(x46071,x46072)) % 167.75/167.49 [4608]~P96(x46082)+P97(f879(x46081,x46082)) % 167.75/167.49 [4609]~P101(x46092)+P101(f879(x46091,x46092)) % 167.75/167.49 [4610]~P104(x46102)+P104(f879(x46101,x46102)) % 167.75/167.49 [4611]~P65(x46112)+P65(f879(x46111,x46112)) % 167.75/167.49 [4612]~P2(x46122)+P100(f879(x46121,x46122)) % 167.75/167.49 [4613]~P98(x46132)+P98(f879(x46131,x46132)) % 167.75/167.49 [4614]~P4(x46142)+P4(f879(x46141,x46142)) % 167.75/167.49 [4615]~P106(x46152)+P106(f879(x46151,x46152)) % 167.75/167.49 [4616]~P107(x46162)+P107(f879(x46161,x46162)) % 167.75/167.49 [4617]~P108(x46172)+P108(f879(x46171,x46172)) % 167.75/167.49 [4618]~P94(x46182)+P94(f879(x46181,x46182)) % 167.75/167.49 [4619]~P87(x46192)+P87(f879(x46191,x46192)) % 167.75/167.49 [4620]~P96(x46202)+P96(f879(x46201,x46202)) % 167.75/167.49 [4632]E(x46321,x46322)+~E(f328(a26,x46321),f328(a26,x46322)) % 167.75/167.49 [4634]E(x46341,x46342)+~E(f328(a116,x46341),f328(a116,x46342)) % 167.75/167.49 [4635]E(x46351,x46352)+~E(f328(a110,x46351),f328(a110,x46352)) % 167.75/167.49 [4636]E(x46361,x46362)+~E(f328(a3,x46361),f328(a3,x46362)) % 167.75/167.49 [4638]E(x46381,x46382)+~E(f328(a19,x46381),f328(a19,x46382)) % 167.75/167.49 [4739]~P57(x47391)+E(f46(x47391,x47392,x47392),f2(x47391)) % 167.75/167.49 [4773]~P38(x47731,x47732)+P38(f873(x47731),f143(x47731,x47732)) % 167.75/167.49 [4774]~P38(x47741,x47742)+P38(f873(x47741),f142(x47741,x47742)) % 167.75/167.49 [4871]~P38(x48711,x48712)+P38(f879(x48711,a867),f320(x48711,x48712)) % 167.75/167.49 [4872]~P38(x48721,x48722)+P38(f879(x48721,a867),f319(x48721,x48722)) % 167.75/167.49 [4990]~P5(x49901)+P39(f299(a1,x49901,x49902)) % 167.75/167.49 [5093]~P38(x50931,x50932)+P56(x50931,f68(x50931,x50931,x50932)) % 167.75/167.49 [5596]~P77(x55961)+P26(x55961,x55961,f79(x55961),x55962) % 167.75/167.49 [4586]~E(x45862,f117(x45861))+E(f328(f165(x45861),x45862),f117(x45861)) % 167.75/167.49 [4587]~E(x45872,f117(x45871))+E(f328(f166(x45871),x45872),f117(x45871)) % 167.75/167.49 [4642]E(x46421,f328(a108,x46422))+~E(f328(f104(a1),x46421),x46422) % 167.75/167.49 [4645]E(x46451,f117(x46452))+~E(f328(f165(x46452),x46451),f117(x46452)) % 167.75/167.49 [4646]E(x46461,f117(x46462))+~E(f328(f166(x46462),x46461),f117(x46462)) % 167.75/167.49 [4663]~P91(x46631)+E(f328(f107(x46631),x46632),f328(f106(x46631),x46632)) % 167.75/167.49 [4670]~E(x46702,f205(x46701))+E(f234(x46701,x46702),f192(f879(x46701,a867))) % 167.75/167.49 [4672]~P3(x46721)+P1(f328(f38(x46721),x46722)) % 167.75/167.49 [4679]E(x46791,f205(x46792))+E(f328(f235(x46792),f681(x46792,x46791)),x46791) % 167.75/167.49 [4680]E(x46801,f205(x46802))+E(f328(f235(x46802),f714(x46802,x46801)),x46801) % 167.75/167.49 [4682]~E(f715(x46822,x46821),f117(x46821))+E(f178(x46821,x46822),f117(f873(x46821))) % 167.75/167.49 [4691]~E(x46912,f117(x46911))+E(f328(f170(x46911),x46912),f192(f879(x46911,a867))) % 167.75/167.49 [4692]~E(x46922,f117(x46921))+E(f192(f879(x46921,a867)),f328(f170(x46921),x46922)) % 167.75/167.49 [4694]E(x46941,x46942)+~E(f328(f104(a1),x46941),f328(f104(a1),x46942)) % 167.75/167.49 [4697]E(f221(x46971,x46972),f2(a872))+P1(f328(f38(x46971),x46972)) % 167.75/167.49 [4717]~P117(x47171)+E(f82(x47171,f82(x47171,x47172)),f82(x47171,x47172)) % 167.75/167.49 [4730]~P78(x47301)+E(f328(f328(f253(x47301),x47302),f78(a872)),x47302) % 167.75/167.49 [4731]~P111(x47311)+E(f328(f328(f253(x47311),x47312),f78(a872)),x47312) % 167.75/167.49 [4733]E(x47331,x47332)+E(f275(x47331,x47332),f328(f328(f80(a103),x47332),f78(a103))) % 167.75/167.49 [4736]E(f328(f39(x47361),x47362),f2(a872))+P1(f328(f38(x47361),x47362)) % 167.75/167.49 [4740]~E(f149(x47401,x47402),x47402)+P1(f328(f134(x47401),x47402)) % 167.75/167.49 [4743]~P64(x47431)+E(f328(f328(f114(x47431),x47432),f192(x47431)),x47432) % 167.75/167.49 [4744]~P74(x47441)+E(f328(f328(f22(x47441),x47442),f2(x47441)),x47442) % 167.75/167.49 [4745]~P97(x47451)+E(f328(f328(f105(x47451),x47452),f251(x47451)),x47452) % 167.75/167.49 [4746]~P67(x47461)+E(f328(f328(f80(x47461),x47462),f2(x47461)),x47462) % 167.75/167.49 [4747]~P111(x47471)+E(f328(f328(f80(x47471),x47472),f2(x47471)),x47472) % 167.75/167.49 [4748]~P79(x47481)+E(f328(f328(f80(x47481),x47482),f2(x47481)),x47482) % 167.75/167.49 [4749]~P73(x47491)+E(f328(f328(f81(x47491),x47492),f78(x47491)),x47492) % 167.75/167.49 [4750]~P78(x47501)+E(f328(f328(f81(x47501),x47502),f78(x47501)),x47502) % 167.75/167.49 [4751]~P111(x47511)+E(f328(f328(f81(x47511),x47512),f78(x47511)),x47512) % 167.75/167.49 [4752]~P57(x47521)+E(f328(f328(f40(x47521),x47522),f78(x47521)),x47522) % 167.75/167.49 [4753]~P120(x47531)+E(f328(f328(f286(x47531),x47532),f78(x47531)),x47532) % 167.75/167.49 [4754]~P111(x47541)+E(f328(f328(f253(x47541),x47542),f2(a872)),f78(x47541)) % 167.75/167.49 [4755]~P113(x47551)+E(f328(f328(f253(x47551),x47552),f2(a872)),f78(x47551)) % 167.75/167.49 [4756]~E(x47562,f192(f879(x47561,a867)))+E(f328(f39(x47561),x47562),f2(a872)) % 167.75/167.49 [4767]~P57(x47671)+E(f46(x47671,x47672,f2(x47671)),x47672) % 167.75/167.49 [4775]~P97(x47751)+E(f328(f328(f114(x47751),x47752),f251(x47751)),f251(x47751)) % 167.75/167.49 [4776]~P64(x47761)+E(f328(f328(f105(x47761),x47762),f192(x47761)),f192(x47761)) % 167.75/167.49 [4777]~P111(x47771)+E(f328(f328(f81(x47771),x47772),f2(x47771)),f2(x47771)) % 167.75/167.49 [4778]~P126(x47781)+E(f328(f328(f81(x47781),x47782),f2(x47781)),f2(x47781)) % 167.75/167.49 [4779]~P57(x47791)+E(f328(f328(f40(x47791),x47792),f2(x47791)),f2(x47791)) % 167.75/167.49 [4780]~P121(x47801)+E(f328(f328(f286(x47801),x47802),f2(x47801)),f2(x47801)) % 167.75/167.49 [4781]E(x47811,f205(x47812))+~E(f234(x47812,x47811),f192(f879(x47812,a867))) % 167.75/167.49 [4784]~P57(x47841)+E(f46(x47841,x47842,f78(x47841)),f2(x47841)) % 167.75/167.49 [4785]~P57(x47851)+E(f46(x47851,f2(x47851),x47852),f2(x47851)) % 167.75/167.49 [4814]E(x48141,f2(a872))+E(f56(x48142,x48141,f117(x48142)),f117(f873(x48142))) % 167.75/167.49 [4838]P38(x48381,x48382)+~E(f583(x48382,x48381),f192(f879(x48381,a867))) % 167.75/167.49 [4839]E(x48391,f117(x48392))+~E(f328(f170(x48392),x48391),f192(f879(x48392,a867))) % 167.75/167.49 [4840]E(x48401,f117(x48402))+~E(f192(f879(x48402,a867)),f328(f170(x48402),x48401)) % 167.75/167.49 [4843]~E(x48431,x48432)+P1(f328(f328(a325,x48431),x48432)) % 167.75/167.49 [4853]P1(x48531)+P1(f328(f328(a331,x48531),x48532)) % 167.75/167.49 [4854]E(x48541,f117(x48542))+E(f328(f328(f162(x48542),x48541),f2(a872)),f328(f138(x48542),x48541)) % 167.75/167.49 [4857]E(f149(x48571,x48572),x48572)+~P1(f328(f134(x48571),x48572)) % 167.75/167.49 [4862]~P1(x48622)+P1(f328(f328(a331,x48621),x48622)) % 167.75/167.49 [4863]~P1(x48632)+P1(f328(f328(a327,x48631),x48632)) % 167.75/167.49 [4864]~P1(x48641)+P1(f328(f328(a327,x48641),x48642)) % 167.75/167.49 [4874]~E(f682(x48742,x48741),f686(x48742,x48741))+P1(f328(f134(x48741),x48742)) % 167.75/167.49 [4882]E(f328(f248(x48821),x48822),f192(f879(x48821,a867)))+P1(f328(x48822,f334(x48822))) % 167.75/167.49 [4883]E(f192(f879(x48831,a867)),f328(f248(x48831),x48832))+P1(f328(x48832,f335(x48832))) % 167.75/167.49 [4947]~P117(x49471)+E(f328(f328(f81(x49471),x49472),f82(x49471,x49472)),f328(f75(x49471),x49472)) % 167.75/167.49 [4958]~E(x49581,f2(a1))+E(f47(x49581,x49582),f328(f328(f263(a1,a1),f2(a1)),f2(a1))) % 167.75/167.49 [4989]~P54(x49891,x49892)+P54(x49891,f328(f283(x49891,x49891),x49892)) % 167.75/167.49 [5008]~E(f328(a28,x50081),f328(f235(a869),x50082))+P1(f328(a25,f328(a26,x50081))) % 167.75/167.49 [5013]E(x50131,x50132)+~P1(f328(f328(a325,x50131),x50132)) % 167.75/167.49 [5017]~P1(f328(a25,x50172))+P1(f328(a25,f32(x50171,x50172))) % 167.75/167.49 [5026]P1(x50261)+~P1(f328(f328(a326,x50262),x50261)) % 167.75/167.49 [5027]P1(x50271)+~P1(f328(f328(a326,x50271),x50272)) % 167.75/167.49 [5032]~P104(x50321)+P1(f328(f328(f242(x50321),x50322),f251(x50321))) % 167.75/167.49 [5036]E(x50361,x50362)+~E(f328(x50361,f386(x50362,x50361)),f328(x50362,f386(x50362,x50361))) % 167.75/167.49 [5066]E(x50661,f2(a872))+E(f223(x50661,f46(a872,x50662,x50661)),f223(x50662,x50661)) % 167.75/167.49 [5071]~P105(x50711)+P15(x50711,f328(f328(f148(x50711),x50712),f117(x50711))) % 167.75/167.49 [5073]E(x50731,f2(a1))+P1(f328(f50(x50732,x50731),f47(x50732,x50731))) % 167.75/167.49 [5091]~E(x50911,x50912)+P1(f328(f328(f243(a872),x50911),f328(a116,x50912))) % 167.75/167.49 [5101]~E(x51011,f2(a872))+P1(f328(f328(f243(a872),x51011),f328(a116,x51012))) % 167.75/167.49 [5111]P1(f328(x51111,x51112))+P1(f328(f328(f242(a1),f2(a1)),f377(x51111))) % 167.75/167.49 [5147]P1(f328(a25,x51471))+~P1(f328(a25,f32(x51472,x51471))) % 167.75/167.49 [5149]P1(f328(a25,x51491))+~P1(f328(a25,f33(x51492,x51491))) % 167.75/167.49 [5151]P1(f328(a25,x51511))+~P1(f328(a25,f33(x51511,x51512))) % 167.75/167.49 [5183]P54(x51831,x51832)+~P54(x51831,f328(f283(x51831,x51831),x51832)) % 167.75/167.49 [5186]~E(f46(a872,x51862,x51861),f2(a872))+E(f328(f328(f81(a872),x51861),f447(x51861,x51862)),x51862) % 167.75/167.49 [5187]~E(f46(a1,x51872,x51871),f2(a1))+E(f328(f328(f81(a1),x51871),f448(x51871,x51872)),x51872) % 167.75/167.49 [5213]~P1(f328(x52131,x52132))+P1(f328(f328(f242(a1),f2(a1)),f337(x52131))) % 167.75/167.49 [5225]E(f328(f328(f22(a872),f328(a108,x52251)),f328(a108,x52252)),f328(a108,x52251))+~P1(f328(a197,x52252)) % 167.75/167.49 [5255]E(f276(x52551,x52552),f78(a103))+~P1(f328(f328(f242(a103),x52551),f78(a103))) % 167.75/167.49 [5350]E(f328(f328(f162(x53501),x53502),f682(x53502,x53501)),f328(f328(f162(x53501),x53502),f686(x53502,x53501)))+P1(f328(f134(x53501),x53502)) % 167.75/167.49 [5395]~P1(f328(x53951,f90(x53952,x53951)))+P1(f328(x53951,f586(x53952,x53951))) % 167.75/167.49 [5458]P56(x54581,x54582)+~P1(f328(f316(x54581,x54582),f528(x54582,x54581))) % 167.75/167.49 [5603]~E(f328(a116,f46(a872,x56031,x56032)),x56032)+E(f46(a872,f328(a116,x56031),x56032),f2(a872)) % 167.75/167.49 [5660]P38(x56601,x56602)+P1(f328(f328(f330(x56601),f626(x56602,x56601)),f627(x56602,x56601))) % 167.75/167.49 [5667]~P138(x56671)+P1(f328(f328(f330(x56671),f328(f104(x56671),x56672)),f113(x56671))) % 167.75/167.49 [5668]~P142(x56681)+P1(f328(f328(f330(x56681),f328(f104(x56681),x56682)),f190(x56681))) % 167.75/167.49 [5669]~P138(x56691)+P1(f328(f328(f330(x56691),f328(f106(x56691),x56692)),f113(x56691))) % 167.75/167.49 [5670]~P91(x56701)+P1(f328(f328(f330(x56701),f328(f107(x56701),x56702)),f113(x56701))) % 167.75/167.49 [5815]E(f328(a116,f46(a872,x58151,x58152)),x58152)+E(f46(a872,f328(a116,x58151),x58152),f328(a116,f46(a872,x58151,x58152))) % 167.75/167.49 [6232]P38(x62321,x62322)+~P1(f328(f328(f330(x62321),f529(x62322,x62321)),f317(x62321,x62322))) % 167.75/167.49 [6267]~P116(x62671)+~P1(f328(f328(f243(x62671),f328(f104(x62671),x62672)),f2(x62671))) % 167.75/167.49 [6268]~P84(x62681)+~P1(f328(f328(f243(x62681),f328(f75(x62681),x62682)),f2(x62681))) % 167.75/167.49 [6354]P1(f328(f328(f243(a1),x63541),f46(a1,x63542,x63541)))+~P1(f328(f328(f243(a1),x63541),f2(a1))) % 167.75/167.49 [6453]E(f328(f328(f306(a872),f328(a116,x64531)),f299(a872,x64532,x64531)),f299(a872,x64532,f328(a116,x64531)))+~P1(f328(f328(f242(a872),x64532),f328(a116,x64531))) % 167.75/167.49 [6540]~P105(x65401)+P15(x65401,f147(x65401,x65401,f5(x65401),x65402)) % 167.75/167.49 [6670]E(f328(f165(x66701),x66702),x66702)+~P1(f328(f328(f242(a872),f328(f193(f873(x66701)),x66702)),f78(a872))) % 167.75/167.49 [6690]~P84(x66901)+P1(f328(f328(f242(x66901),f328(f79(x66901),f328(f75(x66901),x66902))),f2(x66901))) % 167.75/167.49 [6723]~P38(x67231,x67232)+P38(x67231,f328(f328(f285(x67231,x67231,x67231),x67232),f304(x67231,x67232))) % 167.75/167.49 [6945]~P1(f328(f328(f243(a1),x69452),f2(a1)))+P1(f328(f328(f242(a1),f46(a1,x69451,x69452)),f2(a1))) % 167.75/167.49 [7341]~P142(x73411)+E(f194(x73411,f328(f328(f7(x73411,x73411,x73411),f80(x73411)),f78(x73411)),x73412,f2(x73411)),f328(f104(x73411),x73412)) % 167.75/167.49 [7369]~P124(x73691)+~P1(f328(f328(f243(x73691),f328(f328(f81(x73691),x73692),x73692)),f2(x73691))) % 167.75/167.49 [10008]~P117(x100081)+~P1(f328(f328(f243(x100081),f328(f328(f253(x100081),x100082),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f2(x100081))) % 167.75/167.49 [4643]~E(x46432,f117(x46431))+E(f328(f193(f873(x46431)),x46432),f2(a872)) % 167.75/167.49 [4683]~E(x46831,f2(a872))+E(f328(f328(f80(a872),x46831),x46832),x46832) % 167.75/167.49 [4684]~E(x46842,f2(a872))+E(f328(f328(f81(a872),x46841),x46842),f2(a872)) % 167.75/167.49 [4686]~E(x46861,f2(a872))+E(f328(f328(f81(a872),x46861),x46862),f2(a872)) % 167.75/167.49 [4687]~E(x46872,f2(a872))+E(f328(f328(f253(a872),x46871),x46872),f78(a872)) % 167.75/167.49 [4688]~E(x46882,f2(a1))+E(f328(f328(f40(a1),x46881),x46882),f2(a1)) % 167.75/167.49 [4698]E(x46981,f117(x46982))+~E(f328(f193(f873(x46982)),x46981),f2(a872)) % 167.75/167.49 [4699]~P2(x46991)+E(f328(f328(f114(x46991),x46992),x46992),x46992) % 167.75/167.49 [4701]~P99(x47011)+E(f328(f328(f114(x47011),x47012),x47012),x47012) % 167.75/167.49 [4702]~P2(x47021)+E(f328(f328(f105(x47021),x47022),x47022),x47022) % 167.75/167.49 [4704]~P100(x47041)+E(f328(f328(f105(x47041),x47042),x47042),x47042) % 167.75/167.49 [4706]~P95(x47061)+E(f328(f328(f81(x47061),x47062),x47062),x47062) % 167.75/167.49 [4708]~P105(x47081)+E(f328(f328(f240(x47081),x47082),x47082),x47082) % 167.75/167.49 [4710]~P105(x47101)+E(f328(f328(f241(x47101),x47102),x47102),x47102) % 167.75/167.49 [4729]~P74(x47291)+E(f328(f328(f22(x47291),x47292),x47292),f2(x47291)) % 167.75/167.49 [4741]~P74(x47411)+E(f328(f79(x47411),f328(f79(x47411),x47412)),x47412) % 167.75/167.49 [4742]~P94(x47421)+E(f328(f79(x47421),f328(f79(x47421),x47422)),x47422) % 167.75/167.49 [4759]~E(x47592,f2(a872))+E(f328(f328(f253(a872),x47591),x47592),f328(a116,f2(a872))) % 167.75/167.49 [4793]~P64(x47931)+E(f328(f328(f114(x47931),f192(x47931)),x47932),x47932) % 167.75/167.49 [4794]~P97(x47941)+E(f328(f328(f105(x47941),f251(x47941)),x47942),x47942) % 167.75/167.49 [4795]~P67(x47951)+E(f328(f328(f80(x47951),f2(x47951)),x47952),x47952) % 167.75/167.49 [4796]~P111(x47961)+E(f328(f328(f80(x47961),f2(x47961)),x47962),x47962) % 167.75/167.49 [4797]~P79(x47971)+E(f328(f328(f80(x47971),f2(x47971)),x47972),x47972) % 167.75/167.49 [4798]~P73(x47981)+E(f328(f328(f81(x47981),f78(x47981)),x47982),x47982) % 167.75/167.49 [4799]~P78(x47991)+E(f328(f328(f81(x47991),f78(x47991)),x47992),x47992) % 167.75/167.49 [4800]~P111(x48001)+E(f328(f328(f81(x48001),f78(x48001)),x48002),x48002) % 167.75/167.49 [4819]~P97(x48191)+E(f328(f328(f114(x48191),f251(x48191)),x48192),f251(x48191)) % 167.75/167.49 [4820]~P64(x48201)+E(f328(f328(f105(x48201),f192(x48201)),x48202),f192(x48201)) % 167.75/167.49 [4821]~P111(x48211)+E(f328(f328(f81(x48211),f2(x48211)),x48212),f2(x48211)) % 167.75/167.49 [4822]~P126(x48221)+E(f328(f328(f81(x48221),f2(x48221)),x48222),f2(x48221)) % 167.75/167.49 [4823]~P78(x48231)+E(f328(f328(f253(x48231),f78(x48231)),x48232),f78(x48231)) % 167.75/167.49 [4824]~P57(x48241)+E(f328(f328(f40(x48241),f2(x48241)),x48242),f2(x48241)) % 167.75/167.49 [4825]~P120(x48251)+E(f328(f328(f286(x48251),f2(x48251)),x48252),f2(x48251)) % 167.75/167.49 [4833]E(x48331,f117(x48332))+E(f141(x48332,f328(f166(x48332),x48331)),f328(f138(x48332),x48331)) % 167.75/167.49 [4834]E(x48341,f117(x48342))+E(f328(f138(x48342),f328(f166(x48342),x48341)),f141(x48342,x48341)) % 167.75/167.49 [4835]E(x48351,f2(a872))+~E(f328(f328(f80(a872),x48352),x48351),x48352) % 167.75/167.49 [4841]~P138(x48411)+E(f328(f106(x48411),f328(f104(a1),x48412)),f328(f104(x48411),x48412)) % 167.75/167.49 [4842]~P91(x48421)+E(f328(f106(x48421),f328(f107(a1),x48422)),f328(f107(x48421),x48422)) % 167.75/167.49 [4849]E(x48491,f78(a872))+~E(f328(f328(f81(a872),x48492),x48491),f78(a872)) % 167.75/167.49 [4850]E(x48501,f78(a872))+~E(f328(f328(f81(a872),x48501),x48502),f78(a872)) % 167.75/167.49 [4851]E(x48511,f2(a872))+~E(f328(f328(f80(a872),x48512),x48511),f2(a872)) % 167.75/167.49 [4852]E(x48521,f2(a872))+~E(f328(f328(f80(a872),x48521),x48522),f2(a872)) % 167.75/167.49 [4867]~P117(x48671)+E(f328(f75(x48671),f328(f104(x48671),x48672)),f328(f104(x48671),x48672)) % 167.75/167.49 [4868]~P84(x48681)+E(f328(f75(x48681),f328(f75(x48681),x48682)),f328(f75(x48681),x48682)) % 167.75/167.49 [4869]~P84(x48691)+E(f328(f75(x48691),f328(f79(x48691),x48692)),f328(f75(x48691),x48692)) % 167.75/167.49 [4870]~P67(x48701)+E(f328(f163(x48701),f328(f166(x48701),x48702)),f328(f163(x48701),x48702)) % 167.75/167.49 [4875]~E(x48751,f328(a116,f2(a872)))+E(f328(f328(f253(a872),x48751),x48752),f328(a116,f2(a872))) % 167.75/167.49 [4885]~P74(x48851)+E(f328(f328(f22(x48851),f2(x48851)),x48852),f328(f79(x48851),x48852)) % 167.75/167.49 [4886]~E(x48862,f2(a872))+E(f136(a872,f328(f298(a872,x48861),x48862)),f117(a872)) % 167.75/167.49 [4895]~P91(x48951)+E(f328(f328(f80(x48951),x48952),f328(f107(x48951),a83)),x48952) % 167.75/167.49 [4896]E(x48961,f2(a1))+E(f48(f328(f75(a1),x48962),f328(f75(a1),x48961)),f54(x48962,x48961)) % 167.75/167.49 [4910]~E(x49101,x49102)+P1(f328(f328(f242(a872),x49101),x49102)) % 167.75/167.49 [4917]~E(x49171,f2(a103))+E(f328(f328(f80(a872),f328(a19,x49171)),x49172),x49172) % 167.75/167.49 [4918]~E(f328(f107(a1),x49182),f328(f104(a1),x49181))+E(x49181,f328(a108,f328(f107(a1),x49182))) % 167.75/167.49 [4927]~P5(x49271)+P5(f328(f328(f253(a1),x49271),x49272)) % 167.75/167.49 [4928]~P94(x49281)+E(f328(f328(f114(x49281),x49282),f328(f79(x49281),x49282)),f251(x49281)) % 167.75/167.49 [4929]~P94(x49291)+E(f328(f328(f105(x49291),x49292),f328(f79(x49291),x49292)),f192(x49291)) % 167.75/167.49 [4930]~P74(x49301)+E(f328(f328(f80(x49301),x49302),f328(f79(x49301),x49302)),f2(x49301)) % 167.75/167.49 [4955]E(x49551,f2(a872))+~E(f328(f79(a1),f328(f104(a1),x49552)),f328(f104(a1),x49551)) % 167.75/167.49 [4956]E(x49561,f2(a872))+~E(f328(f79(a1),f328(f104(a1),x49561)),f328(f104(a1),x49562)) % 167.75/167.49 [4966]E(f199(x49661,x49662),f2(a1))+P1(f328(f328(f242(a1),x49662),x49661)) % 167.75/167.49 [4967]E(f177(x49671,x49672),f117(a1))+P1(f328(f328(f242(a1),x49671),x49672)) % 167.75/167.49 [4980]E(x49801,f328(a116,f2(a872)))+~E(f328(f328(f81(a872),x49802),x49801),f328(a116,f2(a872))) % 167.75/167.49 [4981]E(x49811,f328(a116,f2(a872)))+~E(f328(f328(f81(a872),x49811),x49812),f328(a116,f2(a872))) % 167.75/167.49 [4982]~P106(x49821)+P1(f328(f328(f242(x49821),x49822),x49822)) % 167.75/167.49 [4983]~P93(x49831)+P1(f328(f328(f91(x49831),x49832),x49832)) % 167.75/167.49 [4986]~P91(x49861)+E(f328(f328(f81(x49861),x49862),f328(f107(x49861),a101)),f328(f79(x49861),x49862)) % 167.75/167.49 [5004]~P138(x50041)+E(f328(f79(x50041),f328(f106(x50041),x50042)),f328(f106(x50041),f328(f79(a1),x50042))) % 167.75/167.49 [5005]~P91(x50051)+E(f328(f79(x50051),f328(f107(x50051),x50052)),f328(f107(x50051),f328(f79(a1),x50052))) % 167.75/167.49 [5037]~E(x50371,f328(a116,x50372))+P1(f328(f328(f243(a872),f2(a872)),x50371)) % 167.75/167.49 [5054]~P105(x50541)+E(f328(f79(f879(x50541,a867)),f328(f249(x50541),x50542)),f328(f250(x50541),x50542)) % 167.75/167.49 [5055]~P105(x50551)+E(f328(f79(f879(x50551,a867)),f328(f300(x50551),x50552)),f328(f297(x50551),x50552)) % 167.75/167.49 [5056]~P105(x50561)+E(f328(f79(f879(x50561,a867)),f328(f250(x50561),x50562)),f328(f249(x50561),x50562)) % 167.75/167.49 [5057]~P105(x50571)+E(f328(f79(f879(x50571,a867)),f328(f297(x50571),x50572)),f328(f300(x50571),x50572)) % 167.75/167.49 [5065]~E(f328(f104(a1),x50652),x50651)+P1(f328(f328(f242(a1),f2(a1)),x50651)) % 167.75/167.49 [5072]~E(x50722,f2(a1))+E(f54(x50721,x50722),f328(f328(f263(a1,a1),f2(a1)),f328(f75(a1),x50721))) % 167.75/167.49 [5074]~P101(x50741)+P1(f328(f328(f242(x50741),f192(x50741)),x50742)) % 167.75/167.49 [5106]E(x51061,x51062)+~E(f328(f328(f80(a1),x51061),x51061),f328(f328(f80(a1),x51062),x51062)) % 167.75/167.49 [5110]~P1(f328(x51101,x51102))+P1(f328(x51101,f328(a108,f337(x51101)))) % 167.75/167.49 [5136]~P117(x51361)+E(f328(f328(f81(x51361),f82(x51361,x51362)),f328(f75(x51361),x51362)),x51362) % 167.75/167.49 [5145]~E(x51452,f2(a872))+E(f85(f878(a872,a872),f49(x51451,x51452)),f328(f328(f263(a872,a872),f2(a872)),x51451)) % 167.75/167.49 [5156]~E(x51561,x51562)+~P1(f328(f328(f243(a872),x51561),x51562)) % 167.75/167.49 [5157]~E(x51571,x51572)+~P1(f328(f328(f243(a1),x51571),x51572)) % 167.75/167.49 [5160]~P142(x51601)+E(f328(f328(f80(x51601),f78(x51601)),f328(f104(x51601),x51602)),f328(f104(x51601),f328(a116,x51602))) % 167.75/167.49 [5164]~E(x51641,f2(a872))+~P1(f328(f328(f243(a872),x51642),x51641)) % 167.75/167.49 [5180]E(f149(x51801,x51802),x51802)+~E(f328(f193(f873(x51801)),f149(x51801,x51802)),f328(f193(f873(x51801)),x51802)) % 167.75/167.49 [5181]E(f328(f39(x51811),f328(f170(x51811),x51812)),f328(f193(f873(x51811)),x51812))+~P1(f328(f134(x51811),x51812)) % 167.75/167.49 [5191]~P1(f328(x51911,f338(x51911)))+P1(f328(x51911,f328(f104(a1),x51912))) % 167.75/167.49 [5202]E(f276(x52021,x52022),f78(a103))+~P1(f328(f328(f243(a103),x52022),x52021)) % 167.75/167.49 [5203]E(f177(x52031,x52032),f117(a1))+~P1(f328(f328(f243(a1),x52032),x52031)) % 167.75/167.49 [5206]~P107(x52061)+E(f299(x52061,x52062,x52062),f328(f328(f306(x52061),x52062),f192(f879(x52061,a867)))) % 167.75/167.49 [5228]~E(f328(f328(f22(a872),x52281),x52282),f2(a872))+P1(f328(f328(f242(a872),x52281),x52282)) % 167.75/167.49 [5229]~E(f328(f328(f22(a1),x52291),x52292),f2(a1))+P1(f328(f328(f91(a1),x52291),x52292)) % 167.75/167.49 [5252]~E(x52522,f2(a872))+E(f56(x52521,x52522,f117(x52521)),f328(f328(f148(f873(x52521)),f117(x52521)),f117(f873(x52521)))) % 167.75/167.49 [5256]~P106(x52561)+~P1(f328(f328(f243(x52561),x52562),x52562)) % 167.75/167.49 [5259]~E(f46(a1,x52591,x52592),f2(a1))+E(f46(a1,x52591,f328(f79(a1),x52592)),f2(a1)) % 167.75/167.49 [5261]~E(f46(a1,x52611,x52612),f2(a1))+E(f46(a1,f328(f79(a1),x52611),x52612),f2(a1)) % 167.75/167.49 [5270]E(f328(f298(a872,x52701),f328(a116,x52702)),f192(f879(a872,a867)))+P1(f328(f328(f242(a872),x52701),x52702)) % 167.75/167.49 [5291]E(f136(a872,f328(f298(a872,x52911),x52912)),f117(a872))+P1(f328(f328(f243(a872),x52911),x52912)) % 167.75/167.49 [5296]~E(f328(f39(x52961),f328(f170(x52961),x52962)),f328(f193(f873(x52961)),x52962))+P1(f328(f134(x52961),x52962)) % 167.75/167.49 [5301]~P1(f328(f134(x53011),x53012))+P1(f328(f134(x53011),f328(f165(x53011),x53012))) % 167.75/167.49 [5302]~P1(f328(f134(x53021),x53022))+P1(f328(f134(x53021),f328(f169(x53021),x53022))) % 167.75/167.49 [5303]~P1(f328(f134(x53031),x53032))+P1(f328(f134(x53031),f328(f166(x53031),x53032))) % 167.75/167.49 [5310]P1(f328(x53101,x53102))+~P1(f328(x53101,f328(a108,f377(x53101)))) % 167.75/167.49 [5311]P1(f328(f328(f242(a872),x53112),x53111))+P1(f328(f328(f242(a872),x53111),x53112)) % 167.75/167.49 [5312]P1(f328(f328(f242(a1),x53122),x53121))+P1(f328(f328(f242(a1),x53121),x53122)) % 167.75/167.49 [5314]~P84(x53141)+P1(f328(f328(f242(x53141),x53142),f328(f75(x53141),x53142))) % 167.75/167.49 [5317]P1(f328(x53171,f339(x53171)))+~P1(f328(x53171,f328(f104(a1),x53172))) % 167.75/167.49 [5342]E(f328(f328(f22(a872),x53421),x53422),f2(a872))+~P1(f328(f328(f242(a872),x53421),x53422)) % 167.75/167.49 [5343]E(f328(f328(f22(a1),x53431),x53432),f2(a1))+~P1(f328(f328(f91(a1),x53431),x53432)) % 167.75/167.49 [5344]E(f328(f328(f40(a872),x53441),x53442),f2(a872))+~P1(f328(f328(f243(a872),x53441),x53442)) % 167.75/167.49 [5362]E(f46(a872,x53621,x53622),x53621)+~P1(f328(f328(f243(a872),x53621),x53622)) % 167.75/167.49 [5371]E(f46(a1,x53711,f328(f79(a1),x53712)),f287(x53711,x53712))+P1(f328(f328(f242(a1),f2(a1)),x53712)) % 167.75/167.49 [5383]E(f328(f328(f22(a1),x53831),x53832),f199(x53831,x53832))+~P1(f328(f328(f242(a1),x53832),x53831)) % 167.75/167.49 [5402]P1(f328(f328(f242(a1),f2(a1)),f338(x54021)))+P1(f328(x54021,f328(f104(a1),x54022))) % 167.75/167.49 [5414]~P59(x54141)+P1(f328(f328(f330(x54141),x54142),f328(f170(x54141),f57(x54141)))) % 167.75/167.49 [5416]~P116(x54161)+P1(f328(f328(f242(x54161),f2(x54161)),f328(f104(x54161),x54162))) % 167.75/167.49 [5417]~P84(x54171)+P1(f328(f328(f242(x54171),f2(x54171)),f328(f75(x54171),x54172))) % 167.75/167.49 [5444]E(f328(f328(f80(a872),x54441),f340(x54442,x54441)),x54442)+~P1(f328(f328(f242(a872),x54441),x54442)) % 167.75/167.49 [5456]~E(f328(f107(a1),x54561),f328(f104(a1),x54562))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x54561))) % 167.75/167.49 [5459]E(f299(a1,x54591,x54592),f192(f879(a1,a867)))+~P1(f328(f328(f243(a1),x54592),x54591)) % 167.75/167.49 [5461]~P117(x54611)+E(f328(f328(f81(x54611),f328(f75(x54611),x54612)),f328(f75(x54611),x54612)),f328(f328(f81(x54611),x54612),x54612)) % 167.75/167.49 [5467]E(f136(a872,f328(f298(a872,x54671),f328(a116,x54672))),f117(a872))+P1(f328(f328(f242(a872),x54671),x54672)) % 167.75/167.49 [5471]E(f328(f328(f40(a1),x54711),x54712),f288(x54711,x54712))+~P1(f328(f328(f242(a1),f2(a1)),x54712)) % 167.75/167.49 [5491]P1(f328(f134(x54911),x54912))+~P1(f328(f134(x54911),f328(f165(x54911),x54912))) % 167.75/167.49 [5492]P1(f328(f134(x54921),x54922))+~P1(f328(f134(x54921),f328(f166(x54921),x54922))) % 167.75/167.49 [5513]P1(f328(f38(a872),x55131))+P1(f328(f328(f330(a872),f341(x55131,x55132)),x55131)) % 167.75/167.49 [5514]P1(f328(f38(a872),x55141))+P1(f328(f328(f330(a872),f345(x55141,x55142)),x55141)) % 167.75/167.49 [5515]P1(f328(f328(f243(a872),x55152),f328(a116,x55151)))+P1(f328(f328(f243(a872),x55151),x55152)) % 167.75/167.49 [5516]E(f46(a1,x55161,x55162),f287(x55161,x55162))+~P1(f328(f328(f242(a1),f2(a1)),x55162)) % 167.75/167.49 [5519]E(f136(a872,f328(f298(a872,x55191),x55192)),f117(a872))+~P1(f328(f328(f242(a872),x55192),x55191)) % 167.75/167.49 [5520]~P77(x55201)+E(f328(f307(x55201,x55201,f79(x55201)),f328(f249(x55201),x55202)),f328(f300(x55201),f328(f79(x55201),x55202))) % 167.75/167.49 [5521]~P77(x55211)+E(f328(f307(x55211,x55211,f79(x55211)),f328(f300(x55211),x55212)),f328(f249(x55211),f328(f79(x55211),x55212))) % 167.75/167.49 [5522]~P77(x55221)+E(f328(f307(x55221,x55221,f79(x55221)),f328(f250(x55221),x55222)),f328(f297(x55221),f328(f79(x55221),x55222))) % 167.75/167.49 [5523]~P77(x55231)+E(f328(f307(x55231,x55231,f79(x55231)),f328(f297(x55231),x55232)),f328(f250(x55231),f328(f79(x55231),x55232))) % 167.75/167.49 [5534]E(x55341,f192(f879(x55342,a867)))+P1(f328(f328(f330(x55342),f847(x55341,x55342)),x55341)) % 167.75/167.49 [5535]E(x55351,f192(f879(x55352,a867)))+P1(f328(f328(f330(x55352),f860(x55351,x55352)),x55351)) % 167.75/167.49 [5546]~P1(f328(f328(f243(a872),x55461),x55462))+P1(f328(f328(f242(a872),x55461),x55462)) % 167.75/167.49 [5547]~P1(f328(f328(f243(a1),x55471),x55472))+P1(f328(f328(f242(a1),x55471),x55472)) % 167.75/167.49 [5563]E(f48(x55631,x55632),f328(f328(f263(a1,a1),f2(a1)),x55631))+~P1(f328(f328(f243(a1),x55631),x55632)) % 167.75/167.49 [5565]E(f222(f328(f79(a1),x55651),f328(f79(a1),x55652)),f222(x55651,x55652))+~P1(f328(f328(f243(a1),x55652),f2(a1))) % 167.75/167.49 [5573]E(x55731,x55732)+~P1(f328(f328(f328(a198,a24),x55731),x55732)) % 167.75/167.49 [5577]E(x55771,x55772)+~E(f328(a3,f328(a116,f328(a19,x55771))),f328(a3,f328(a116,f328(a19,x55772)))) % 167.75/167.49 [5582]E(f48(x55821,x55822),f328(f328(f263(a1,a1),f2(a1)),x55821))+~P1(f328(f328(f242(a1),x55822),f2(a1))) % 167.75/167.49 [5609]E(f46(a872,f328(f107(a872),x56091),f328(f107(a872),x56092)),f2(a872))+~P1(f328(a197,f328(f107(a1),x56091))) % 167.75/167.49 [5624]P1(f328(f328(f242(a1),f2(a1)),f339(x56241)))+~P1(f328(x56241,f328(f104(a1),x56242))) % 167.75/167.49 [5658]P39(f299(a1,x56581,x56582))+~P1(f328(f328(f242(a1),f2(a1)),x56581)) % 167.75/167.49 [5663]~P1(f328(f38(x56631),x56632))+P1(f328(f38(f879(x56631,a867)),f328(f305(x56631),x56632))) % 167.75/167.49 [5676]E(f328(f328(f80(a1),x56761),f328(f104(a1),f357(x56762,x56761))),x56762)+~P1(f328(f328(f242(a1),x56761),x56762)) % 167.75/167.49 [5684]P1(f328(f328(f242(a872),x56841),x56842))+P1(f328(f328(f242(a872),f328(a116,x56842)),x56841)) % 167.75/167.49 [5729]E(f328(f328(f40(a872),f328(f107(a872),x57291)),f328(f107(a872),x57292)),f2(a872))+~P1(f328(a197,f328(f107(a1),x57291))) % 167.75/167.49 [5730]E(f328(f328(f81(a872),f328(f107(a872),x57301)),f328(f107(a872),x57302)),f2(a872))+~P1(f328(f328(f243(a1),x57301),a83)) % 167.75/167.49 [5732]P1(f328(f328(f243(a872),x57321),f328(a116,x57322)))+~P1(f328(f328(f243(a872),x57321),x57322)) % 167.75/167.49 [5734]P1(f328(f328(f243(a872),x57341),f328(a116,x57342)))+~P1(f328(f328(f242(a872),x57341),x57342)) % 167.75/167.49 [5736]P1(f328(f328(f242(a872),x57361),f328(a116,x57362)))+~P1(f328(f328(f242(a872),x57361),x57362)) % 167.75/167.49 [5739]~E(x57391,x57392)+P1(f328(f328(f243(a1),x57391),f328(f328(f80(a1),x57392),f78(a1)))) % 167.75/167.49 [5742]E(f46(a1,x57421,x57422),f2(a1))+E(f328(f328(f22(a1),x57422),f46(a1,x57421,x57422)),f46(a1,f328(f79(a1),x57421),x57422)) % 167.75/167.49 [5751]E(x57511,f117(x57512))+P1(f328(f328(f330(x57512),f141(x57512,x57511)),f328(f170(x57512),x57511))) % 167.75/167.49 [5763]E(f85(f878(a872,a872),f49(x57631,x57632)),f328(f328(f263(a872,a872),f2(a872)),x57631))+~P1(f328(f328(f243(a872),x57631),x57632)) % 167.75/167.49 [5796]E(f328(f328(f22(a872),f328(f107(a872),x57961)),f328(f107(a872),x57962)),f328(f107(a872),x57961))+~P1(f328(f328(f243(a1),x57962),a83)) % 167.75/167.49 [5797]E(f328(f328(f80(a872),f328(f107(a872),x57971)),f328(f107(a872),x57972)),f328(f107(a872),x57972))+~P1(f328(f328(f243(a1),x57971),a83)) % 167.75/167.49 [5802]E(f328(a116,f328(f328(f80(a872),x58021),f804(x58022,x58021))),x58022)+~P1(f328(f328(f243(a872),x58021),x58022)) % 167.75/167.49 [5825]P1(f328(x58251,x58252))+~P1(f328(x58251,f328(a89,f587(x58252,x58251)))) % 167.75/167.49 [5833]~P1(f328(f328(f243(a872),x58331),f328(a116,x58332)))+P1(f328(f328(f242(a872),x58331),x58332)) % 167.75/167.49 [5879]E(f328(f328(f306(a872),x58791),f328(f298(a872,x58792),x58791)),f328(f298(a872,x58792),f328(a116,x58791)))+~P1(f328(f328(f242(a872),x58792),x58791)) % 167.75/167.49 [5883]E(x58831,f117(x58832))+E(f328(f328(f125(x58832),f118(x58832,x58831)),f328(f328(f148(x58832),f141(x58832,x58831)),f117(x58832))),x58831) % 167.75/167.49 [5897]P1(f328(f38(x58971),x58972))+~P1(f328(f328(f243(a872),f2(a872)),f328(f39(x58971),x58972))) % 167.75/167.49 [5899]~E(x58991,f192(f879(x58992,a867)))+~P1(f328(f328(f243(a872),f2(a872)),f328(f39(x58992),x58991))) % 167.75/167.49 [5911]~P1(f328(f328(f243(a872),x59111),x59112))+P1(f328(f328(f242(a872),f328(a116,x59111)),x59112)) % 167.75/167.49 [5918]~P105(x59181)+E(f147(x59181,x59181,f5(x59181),f149(x59181,x59182)),f136(x59181,f328(f170(x59181),x59182))) % 167.75/167.49 [5921]E(x59211,f117(x59212))+P1(f328(f328(f330(x59212),f328(f138(x59212),x59211)),f328(f170(x59212),x59211))) % 167.75/167.49 [5927]~P116(x59271)+P1(f328(f328(f243(x59271),x59272),f328(f328(f80(x59271),x59272),f78(x59271)))) % 167.75/167.49 [5929]~P84(x59291)+P1(f328(f328(f242(x59291),f328(f79(x59291),x59292)),f328(f75(x59291),x59292))) % 167.75/167.49 [5960]P1(f328(f38(a872),x59601))+~P1(f328(f328(f243(a872),f345(x59601,x59602)),x59602)) % 167.75/167.49 [5961]P1(f328(f38(a872),x59611))+~P1(f328(f328(f242(a872),f341(x59611,x59612)),x59612)) % 167.75/167.49 [5964]~P1(f328(f38(f878(x59641,x59641)),x59642))+P1(f328(f38(x59641),f328(f281(x59641),x59642))) % 167.75/167.49 [6017]~P1(f328(f328(f243(a872),x60172),f328(a116,x60171)))+~P1(f328(f328(f243(a872),x60171),x60172)) % 167.75/167.49 [6018]~P107(x60181)+E(f328(f328(f105(f879(x60181,a867)),f328(f297(x60181),x60182)),f328(f250(x60181),x60182)),f328(f328(f306(x60181),x60182),f192(f879(x60181,a867)))) % 167.75/167.49 [6031]P1(f328(f38(x60311),x60312))+~P1(f328(f38(f879(x60311,a867)),f328(f305(x60311),x60312))) % 167.75/167.49 [6056]P1(f328(f328(f243(a872),f328(a116,x60561)),f328(a116,x60562)))+~P1(f328(f328(f243(a872),x60561),x60562)) % 167.75/167.49 [6057]P1(f328(f328(f243(a872),f328(a19,x60571)),f328(a19,x60572)))+~P1(f328(f328(f243(a103),x60571),x60572)) % 167.75/167.49 [6058]P1(f328(f328(f243(a103),f328(a3,x60581)),f328(a3,x60582)))+~P1(f328(f328(f243(a872),x60581),x60582)) % 167.75/167.49 [6059]P1(f328(f328(f242(a872),f328(a116,x60591)),f328(a116,x60592)))+~P1(f328(f328(f242(a872),x60591),x60592)) % 167.75/167.49 [6060]P1(f328(f328(f242(a872),f328(a19,x60601)),f328(a19,x60602)))+~P1(f328(f328(f242(a103),x60601),x60602)) % 167.75/167.49 [6061]P1(f328(f328(f242(a103),f328(a3,x60611)),f328(a3,x60612)))+~P1(f328(f328(f242(a872),x60611),x60612)) % 167.75/167.49 [6064]E(x60641,x60642)+~E(f328(f307(a872,a1,f104(a1)),x60641),f328(f307(a872,a1,f104(a1)),x60642)) % 167.75/167.49 [6080]P1(f328(f328(f243(a872),x60801),x60802))+~P1(f328(f328(f243(a872),f328(a116,x60801)),x60802)) % 167.75/167.49 [6083]P1(f328(f328(f243(a872),x60831),x60832))+~P1(f328(f328(f242(a872),f328(a116,x60831)),x60832)) % 167.75/167.49 [6084]P1(f328(f328(f242(a872),x60841),x60842))+~P1(f328(f328(f242(a872),f328(a116,x60841)),x60842)) % 167.75/167.49 [6099]E(f46(a1,x60991,x60992),f2(a1))+E(f328(f328(f22(a1),f46(a1,x60991,x60992)),x60992),f46(a1,x60991,f328(f79(a1),x60992))) % 167.75/167.49 [6172]E(f328(f39(f879(x61721,a867)),f328(f305(x61721),x61722)),f328(f328(f253(a872),f328(a116,f328(a116,f2(a872)))),f328(f39(x61721),x61722)))+~P1(f328(f38(x61721),x61722)) % 167.75/167.49 [6175]E(x61751,f117(x61752))+E(f328(f328(f162(x61752),x61751),f328(f328(f22(a872),f328(f193(f873(x61752)),x61751)),f78(a872))),f141(x61752,x61751)) % 167.75/167.49 [6200]E(x62001,f117(x62002))+E(f328(f328(f125(x62002),f328(f169(x62002),x62001)),f328(f328(f148(x62002),f328(f138(x62002),x62001)),f117(x62002))),f328(f165(x62002),x62001)) % 167.75/167.49 [6229]~P1(f328(f38(x62291),f41(f879(x62291,a867),x62292)))+P1(f328(f38(f879(x62291,a867)),x62292)) % 167.75/167.49 [6252]P1(f328(f328(f242(a872),f328(f107(a872),x62521)),f328(f107(a872),x62522)))+~P1(f328(f328(f242(a1),x62521),a83)) % 167.75/167.49 [6269]~P1(f328(f328(f243(a1),x62691),x62692))+P1(f328(f328(f243(a1),x62691),f328(f328(f80(a1),x62692),f78(a1)))) % 167.75/167.49 [6270]~P1(f328(f328(f242(a1),x62701),x62702))+P1(f328(f328(f243(a1),x62701),f328(f328(f80(a1),x62702),f78(a1)))) % 167.75/167.49 [6271]~P1(f328(f328(f243(a1),x62711),x62712))+P1(f328(f328(f242(a1),x62711),f328(f328(f22(a1),x62712),f78(a1)))) % 167.75/167.49 [6274]~P1(f328(f328(f243(a872),x62741),x62742))+P1(f328(f328(f243(a1),f328(f104(a1),x62741)),f328(f104(a1),x62742))) % 167.75/167.49 [6275]~P1(f328(f328(f243(a1),x62751),x62752))+P1(f328(f328(f243(a1),f328(f107(a1),x62751)),f328(f107(a1),x62752))) % 167.75/167.49 [6276]~P1(f328(f328(f242(a1),x62761),x62762))+P1(f328(f328(f242(a872),f328(f107(a872),x62761)),f328(f107(a872),x62762))) % 167.75/167.49 [6278]~P1(f328(f328(f242(a872),x62781),x62782))+P1(f328(f328(f242(a1),f328(f104(a1),x62781)),f328(f104(a1),x62782))) % 167.75/167.49 [6279]~P1(f328(f328(f242(a1),x62791),x62792))+P1(f328(f328(f242(a1),f328(f107(a1),x62791)),f328(f107(a1),x62792))) % 167.75/167.49 [6280]~P1(f328(f328(f91(a1),x62801),x62802))+P1(f328(f328(f91(a1),f328(f107(a1),x62801)),f328(f107(a1),x62802))) % 167.75/167.49 [6298]~P1(f328(f328(f242(a872),x62981),x62982))+~P1(f328(f328(f242(a872),f328(a116,x62982)),x62981)) % 167.75/167.50 [6341]~P1(f328(f328(f243(a872),f328(a116,x63411)),f328(a116,x63412)))+P1(f328(f328(f243(a872),x63411),x63412)) % 167.75/167.50 [6342]~P1(f328(f328(f243(a103),f328(a3,x63421)),f328(a3,x63422)))+P1(f328(f328(f243(a872),x63421),x63422)) % 167.75/167.50 [6343]~P1(f328(f328(f243(a872),f328(a108,x63431)),f328(a108,x63432)))+P1(f328(f328(f243(a1),x63431),x63432)) % 167.75/167.50 [6344]~P1(f328(f328(f243(a872),f328(a19,x63441)),f328(a19,x63442)))+P1(f328(f328(f243(a103),x63441),x63442)) % 167.75/167.50 [6345]~P1(f328(f328(f242(a872),f328(a116,x63451)),f328(a116,x63452)))+P1(f328(f328(f242(a872),x63451),x63452)) % 167.75/167.50 [6346]~P1(f328(f328(f242(a103),f328(a3,x63461)),f328(a3,x63462)))+P1(f328(f328(f242(a872),x63461),x63462)) % 167.75/167.50 [6347]~P1(f328(f328(f242(a872),f328(a19,x63471)),f328(a19,x63472)))+P1(f328(f328(f242(a103),x63471),x63472)) % 167.75/167.50 [6387]~P1(f328(f328(f243(a872),f328(a108,x63872)),f328(a108,x63871)))+P1(f328(f328(f243(a1),f2(a1)),x63871)) % 167.75/167.50 [6418]P1(f328(f328(f242(a1),f2(a1)),f46(a1,x64181,x64182)))+~P1(f328(f328(f243(a1),f2(a1)),x64182)) % 167.75/167.50 [6575]P38(x65751,x65752)+~E(f328(f328(f285(x65751,x65751,x65751),x65752),x65752),f192(f879(f878(x65751,x65751),a867))) % 167.75/167.50 [6587]~P38(x65871,x65872)+P38(x65871,f328(f328(f285(x65871,x65871,x65871),x65872),x65872)) % 167.75/167.50 [6599]P1(f328(f328(f243(a1),x65991),x65992))+~P1(f328(f328(f242(a1),x65991),f328(f328(f22(a1),x65992),f78(a1)))) % 167.75/167.50 [6600]P1(f328(f328(f242(a1),x66001),x66002))+~P1(f328(f328(f243(a1),x66001),f328(f328(f80(a1),x66002),f78(a1)))) % 167.75/167.50 [6603]P1(f328(f328(f243(a872),x66031),x66032))+~P1(f328(f328(f243(a1),f328(f104(a1),x66031)),f328(f104(a1),x66032))) % 167.75/167.50 [6604]P1(f328(f328(f243(a1),x66041),x66042))+~P1(f328(f328(f243(a872),f328(f107(a872),x66041)),f328(f107(a872),x66042))) % 167.75/167.50 [6605]P1(f328(f328(f243(a1),x66051),x66052))+~P1(f328(f328(f243(a1),f328(f107(a1),x66051)),f328(f107(a1),x66052))) % 167.75/167.50 [6607]P1(f328(f328(f242(a872),x66071),x66072))+~P1(f328(f328(f242(a1),f328(f104(a1),x66071)),f328(f104(a1),x66072))) % 167.75/167.50 [6608]P1(f328(f328(f242(a1),x66081),x66082))+~P1(f328(f328(f242(a1),f328(f107(a1),x66081)),f328(f107(a1),x66082))) % 167.75/167.50 [6609]P1(f328(f328(f91(a1),x66091),x66092))+~P1(f328(f328(f91(a1),f328(f107(a1),x66091)),f328(f107(a1),x66092))) % 167.75/167.50 [6703]~E(f730(x67032,x67031),f117(x67031))+E(f328(f139(f873(x67031),f873(x67031),f125(x67031),f117(x67031)),x67032),f117(x67031)) % 167.75/167.50 [6704]~E(f737(x67042,x67041),f117(x67041))+E(f328(f139(f873(x67041),f873(x67041),f125(x67041),f117(x67041)),x67042),f117(x67041)) % 167.75/167.50 [6711]~P4(x67111)+E(f328(f139(x67111,x67111,f105(x67111),f251(x67111)),x67112),f42(x67111,f328(f170(x67111),x67112))) % 167.75/167.50 [6712]~P4(x67121)+E(f328(f139(x67121,x67121,f114(x67121),f192(x67121)),x67122),f41(x67121,f328(f170(x67121),x67122))) % 167.75/167.50 [6724]E(x67241,f2(a103))+E(f328(f328(f80(a872),f328(a19,f328(f328(f22(a103),x67241),f78(a103)))),f328(a116,x67242)),f328(f328(f80(a872),f328(a19,x67241)),x67242)) % 167.75/167.50 [6774]P1(f328(f328(f243(a1),f328(f328(f22(a1),x67741),x67742)),f2(a1)))+~P1(f328(f328(f243(a1),x67741),x67742)) % 167.75/167.50 [6802]~P105(x68021)+E(f328(f328(f114(f879(x68021,a867)),f328(f328(f306(x68021),x68022),f192(f879(x68021,a867)))),f328(f300(x68021),x68022)),f328(f250(x68021),x68022)) % 167.75/167.50 [6878]~P56(x68781,x68782)+P38(x68781,f328(f248(f878(x68781,x68781)),f328(f267(x68781,x68781,a867),x68782))) % 167.75/167.50 [6879]~P56(x68791,x68792)+P54(x68791,f328(f248(f878(x68791,x68791)),f328(f267(x68791,x68791,a867),x68792))) % 167.75/167.50 [6880]E(x68801,f192(f879(x68802,a867)))+~P1(f328(f328(f242(f879(x68802,a867)),x68801),f192(f879(x68802,a867)))) % 167.75/167.50 [6961]~P1(f328(f328(f243(a872),f2(a872)),x69612))+P1(f328(f328(f243(a872),f46(a872,x69611,x69612)),x69612)) % 167.75/167.50 [6963]~P1(f328(f328(f243(a1),f2(a1)),x69632))+P1(f328(f328(f243(a1),f46(a1,x69631,x69632)),x69632)) % 167.75/167.50 [6964]~P1(f328(f328(f243(a872),f2(a872)),x69642))+P1(f328(f328(f242(a872),f46(a872,x69641,x69642)),x69642)) % 167.75/167.50 [6965]~P1(f328(f328(f242(a1),f2(a1)),x69651))+P1(f328(f328(f242(a1),f46(a1,x69651,x69652)),x69651)) % 167.75/167.50 [7041]~P107(x70411)+E(f328(f328(f22(f879(x70411,a867)),f328(f328(f306(x70411),x70412),f192(f879(x70411,a867)))),f328(f249(x70411),x70412)),f328(f328(f306(x70411),x70412),f192(f879(x70411,a867)))) % 167.75/167.50 [7114]~P49(x71141,x71142)+P40(x71141,f251(f879(x71141,a867)),f328(f248(f878(x71141,x71141)),f328(f267(x71141,x71141,a867),x71142))) % 167.75/167.50 [7115]P1(f328(x71151,x71152))+P1(f328(f328(f330(f879(f878(a872,a872),a867)),f587(x71152,x71151)),a102)) % 167.75/167.50 [7160]E(f328(f328(f125(a872),f136(a872,f328(f298(a872,x71601),x71602))),f328(f328(f148(a872),x71602),f117(a872))),f136(a872,f328(f298(a872,x71601),f328(a116,x71602))))+~P1(f328(f328(f242(a872),x71601),x71602)) % 167.75/167.50 [7303]E(x73031,f2(a872))+~E(f328(f139(a872,a872,f80(a872),x73031),x73032),f2(a872)) % 167.75/167.50 [7331]~P1(f328(f328(f243(a1),f328(f328(f22(a1),x73311),x73312)),f2(a1)))+P1(f328(f328(f243(a1),x73311),x73312)) % 167.75/167.50 [7360]P38(x73601,x73602)+~P38(x73601,f328(f328(f285(x73601,x73601,x73601),x73602),x73602)) % 167.75/167.50 [7389]~P1(f328(f328(f242(a872),f328(a116,x73891)),x73892))+P1(f189(a867,a246,f328(f242(a872),x73891),x73892)) % 167.75/167.50 [7546]P26(a872,a872,f328(f328(f7(a872,a872,a872),f22(a872)),x75461),x75462)+P1(f328(f328(f330(a872),f593(x75461,x75462)),x75462)) % 167.75/167.50 [7604]E(f328(f328(f328(f66(a872,x76041,f80(a872)),f328(f16(a872,x76041),f78(a872))),f2(a872)),x76042),f328(f39(x76041),x76042))+~P1(f328(f38(x76041),x76042)) % 167.75/167.50 [7646]P26(a872,a872,f328(f328(f7(a872,a872,a872),f22(a872)),x76461),x76462)+~P1(f328(f328(f242(a872),x76461),f593(x76461,x76462))) % 167.75/167.50 [7704]P38(x77041,x77042)+P1(f328(f328(f242(f879(x77041,a867)),f583(x77042,x77041)),f328(f282(x77041,x77041,x77042),f583(x77042,x77041)))) % 167.75/167.50 [7709]P56(x77091,x77092)+~P38(x77091,f328(f248(f878(x77091,x77091)),f328(f267(x77091,x77091,a867),x77092))) % 167.75/167.50 [7781]P1(f328(f328(f242(a872),f328(a116,x77811)),x77812))+~P1(f189(a867,a246,f328(f242(a872),x77811),x77812)) % 167.75/167.50 [7837]P1(f328(f328(f330(f878(a872,a872)),f328(f328(f263(a872,a872),x78371),x78372)),f304(a872,a318)))+~P1(f328(f328(f242(a872),x78371),x78372)) % 167.75/167.50 [7934]P49(x79341,x79342)+~P40(x79341,f251(f879(x79341,a867)),f328(f248(f878(x79341,x79341)),f328(f267(x79341,x79341,a867),x79342))) % 167.75/167.50 [7988]~P1(f328(f134(x79881),x79882))+P1(f328(f134(f879(x79881,a867)),f328(f328(f151(f873(x79881),f879(x79881,a867)),f170(x79881)),f55(x79881,x79882)))) % 167.75/167.50 [8199]~P38(x81991,f328(f283(x81991,x81991),x81992))+P38(x81991,f328(f283(x81991,x81991),f328(f328(f285(x81991,x81991,x81991),x81992),f304(x81991,x81992)))) % 167.75/167.50 [8322]P1(f328(f38(f878(x83221,x83221)),f328(f328(f285(x83221,x83221,x83221),x83222),f304(x83221,x83222))))+~P1(f328(f38(f878(x83221,x83221)),x83222)) % 167.75/167.50 [8353]E(x83531,f2(a1))+P1(f328(f50(x83532,x83531),f328(f328(f263(a1,a1),f328(f328(f40(a1),x83532),x83531)),f46(a1,x83532,x83531)))) % 167.75/167.50 [8364]~P1(f328(f328(f330(f878(a872,a872)),f328(f328(f263(a872,a872),x83641),x83642)),f304(a872,a318)))+P1(f328(f328(f242(a872),x83641),x83642)) % 167.75/167.50 [8379]~P79(x83791)+E(f328(f139(x83791,x83791,f328(f7(x83791,x83791,x83791),f80(x83791)),f2(x83791)),f328(f166(x83791),x83792)),f328(f139(x83791,x83791,f80(x83791),f2(x83791)),x83792)) % 167.75/167.50 [8559]~P105(x85591)+E(f328(f139(f873(x85591),x85591,f328(f7(x85591,f873(x85591),f873(x85591)),f145(x85591,x85591,f5(x85591))),f117(x85591)),x85592),f147(x85591,x85591,f5(x85591),x85592)) % 167.75/167.50 [8663]~P54(x86631,f328(f248(f878(x86631,x86631)),f328(f267(x86631,x86631,a867),x86632)))+P54(x86631,f328(f248(f878(x86631,x86631)),f328(f267(x86631,x86631,a867),f252(x86631,x86631,x86632)))) % 167.75/167.50 [8677]P1(f328(f328(f330(f878(a872,a872)),f328(f328(f263(a872,a872),x86771),x86772)),f328(f328(f285(a872,a872,a872),a318),f304(a872,a318))))+~P1(f328(f328(f243(a872),x86771),x86772)) % 167.75/167.50 [8720]~P1(f328(f38(f878(x87201,x87201)),f328(f328(f285(x87201,x87201,x87201),x87202),f304(x87201,x87202))))+P1(f328(f38(f878(x87201,x87201)),x87202)) % 167.75/167.50 [8771]~P54(x87711,f328(f248(f878(x87711,x87711)),f328(f267(x87711,x87711,a867),f252(x87711,x87711,x87712))))+P54(x87711,f328(f248(f878(x87711,x87711)),f328(f267(x87711,x87711,a867),x87712))) % 167.75/167.50 [8973]P54(x89731,x89732)+P1(f328(f328(f330(f878(x89731,x89731)),f328(f328(f263(x89731,x89731),f620(x89732,x89731)),f620(x89732,x89731))),f328(f328(f285(x89731,x89731,x89731),x89732),f304(x89731,x89732)))) % 167.75/167.50 [8974]P54(x89741,x89742)+P1(f328(f328(f330(f878(x89741,x89741)),f328(f328(f263(x89741,x89741),f632(x89742,x89741)),f632(x89742,x89741))),f328(f328(f285(x89741,x89741,x89741),x89742),f304(x89741,x89742)))) % 167.75/167.50 [9091]~P1(f328(f328(f330(f878(a872,a872)),f328(f328(f263(a872,a872),x90911),x90912)),f328(f328(f285(a872,a872,a872),a318),f304(a872,a318))))+P1(f328(f328(f243(a872),x90911),x90912)) % 167.75/167.50 [5050]~P91(x50501)+E(f328(f328(f80(x50501),f328(f107(x50501),a83)),x50502),x50502) % 167.75/167.50 [5079]~P94(x50791)+E(f328(f328(f114(x50791),f328(f79(x50791),x50792)),x50792),f251(x50791)) % 167.75/167.50 [5080]~P94(x50801)+E(f328(f328(f105(x50801),f328(f79(x50801),x50802)),x50802),f192(x50801)) % 167.75/167.50 [5081]~P66(x50811)+E(f328(f328(f80(x50811),f328(f79(x50811),x50812)),x50812),f2(x50811)) % 167.75/167.50 [5082]~P74(x50821)+E(f328(f328(f80(x50821),f328(f79(x50821),x50822)),x50822),f2(x50821)) % 167.75/167.50 [5114]~P91(x51141)+E(f328(f328(f81(x51141),f328(f107(x51141),a101)),x51142),f328(f79(x51141),x51142)) % 167.75/167.50 [5284]~P115(x52841)+E(f328(f328(f81(x52841),f328(f79(x52841),f78(x52841))),x52842),f328(f79(x52841),x52842)) % 167.75/167.50 [5327]E(f328(f75(a1),x53271),f78(a1))+~E(f328(f75(a1),f328(f328(f81(a1),x53271),x53272)),f78(a1)) % 167.75/167.50 [5419]~P91(x54191)+E(f328(f328(f80(x54191),f78(x54191)),f328(f107(x54191),x54192)),f328(f107(x54191),f328(f328(f22(a1),x54192),a101))) % 167.75/167.50 [5472]~P2(x54721)+E(f13(x54721,f328(f328(f306(x54721),x54722),f192(f879(x54721,a867)))),x54722) % 167.75/167.50 [5473]~P2(x54731)+E(f10(x54731,f328(f328(f306(x54731),x54732),f192(f879(x54731,a867)))),x54732) % 167.75/167.50 [5474]~P4(x54741)+E(f42(x54741,f328(f328(f306(x54741),x54742),f192(f879(x54741,a867)))),x54742) % 167.75/167.50 [5475]~P4(x54751)+E(f41(x54751,f328(f328(f306(x54751),x54752),f192(f879(x54751,a867)))),x54752) % 167.75/167.50 [5476]~P105(x54761)+E(f14(x54761,f328(f328(f306(x54761),x54762),f192(f879(x54761,a867)))),x54762) % 167.75/167.50 [5477]~P105(x54771)+E(f15(x54771,f328(f328(f306(x54771),x54772),f192(f879(x54771,a867)))),x54772) % 167.75/167.50 [5499]E(f328(f328(f80(a872),x54991),f328(f328(f22(a872),x54992),x54991)),x54992)+P1(f328(f328(f243(a872),x54992),x54991)) % 167.75/167.50 [5529]E(x55291,f117(x55292))+P1(f328(f328(f243(a872),f2(a872)),f328(f193(f873(x55292)),x55291))) % 167.75/167.50 [5655]~P105(x56551)+E(f11(x56551,f240(x56551),f328(f328(f306(x56551),x56552),f192(f879(x56551,a867)))),x56552) % 167.75/167.50 [5656]~P105(x56561)+E(f12(x56561,f241(x56561),f328(f328(f306(x56561),x56562),f192(f879(x56561,a867)))),x56562) % 167.75/167.50 [5719]E(f328(f328(f22(a872),x57191),f328(f328(f22(a872),x57191),x57192)),x57192)+~P1(f328(f328(f242(a872),x57192),x57191)) % 167.75/167.50 [5720]E(f328(f328(f80(a872),x57201),f328(f328(f22(a872),x57202),x57201)),x57202)+~P1(f328(f328(f242(a872),x57201),x57202)) % 167.75/167.50 [5741]E(f46(a872,f328(f328(f22(a872),x57411),x57412),x57412),f46(a872,x57411,x57412))+P1(f328(f328(f243(a872),x57411),x57412)) % 167.75/167.50 [5752]E(f328(f79(a1),f328(f328(f40(a1),x57521),f328(f79(a1),x57522))),f288(x57521,x57522))+P1(f328(f328(f242(a1),f2(a1)),x57522)) % 167.75/167.50 [5754]~E(x57542,f2(a872))+P1(f328(f328(f243(a872),f2(a872)),f328(f328(f253(a872),x57541),x57542))) % 167.75/167.50 [5805]~P91(x58051)+E(f328(f328(f80(x58051),f328(f79(x58051),f78(x58051))),f328(f107(x58051),x58052)),f328(f107(x58051),f328(f328(f80(a1),x58052),a101))) % 167.75/167.50 [5806]E(f328(f328(f253(a872),f328(f107(a872),x58061)),x58062),f328(f328(f253(a872),f2(a872)),x58062))+~P1(f328(a197,f328(f107(a1),x58061))) % 167.75/167.50 [5903]E(f328(f138(a872),f136(a872,f328(f298(a872,x59031),x59032))),x59031)+~P1(f328(f328(f243(a872),x59031),x59032)) % 167.75/167.50 [5922]E(f328(f328(f81(a872),f328(f107(a872),x59221)),f328(f107(a872),x59222)),f328(f107(a872),f328(f328(f81(a1),x59221),x59222)))+P1(f328(f328(f243(a1),x59221),a83)) % 167.75/167.50 [5928]~P124(x59281)+P1(f328(f328(f242(x59281),f2(x59281)),f328(f328(f81(x59281),x59282),x59282))) % 167.75/167.50 [5940]E(f328(f328(f22(a872),f328(a116,x59401)),x59402),f328(a116,f328(f328(f22(a872),x59401),x59402)))+~P1(f328(f328(f242(a872),x59402),x59401)) % 167.75/167.50 [5943]E(f46(a872,f328(f328(f22(a872),x59431),x59432),x59432),f46(a872,x59431,x59432))+~P1(f328(f328(f242(a872),x59432),x59431)) % 167.75/167.50 [5992]E(f328(f328(f253(a872),f328(a108,x59921)),x59922),f328(a108,f328(f328(f253(a1),x59921),x59922)))+~P1(f328(f328(f242(a1),f2(a1)),x59921)) % 167.75/167.50 [6008]P1(f328(f134(x60081),x60082))+P1(f328(f328(f243(a872),f682(x60082,x60081)),f328(f193(f873(x60081)),x60082))) % 167.75/167.50 [6009]P1(f328(f134(x60091),x60092))+P1(f328(f328(f243(a872),f686(x60092,x60091)),f328(f193(f873(x60091)),x60092))) % 167.75/167.50 [6024]~E(x60241,f117(x60242))+~P1(f328(f328(f243(a872),f2(a872)),f328(f193(f873(x60242)),x60241))) % 167.75/167.50 [6038]E(f141(a872,f136(a872,f328(f298(a872,x60381),x60382))),f328(f328(f22(a872),x60382),f78(a872)))+~P1(f328(f328(f243(a872),x60381),x60382)) % 167.75/167.50 [6041]E(f328(f328(f80(a1),x60411),f328(f104(a1),f328(a116,f358(x60412,x60411)))),x60412)+~P1(f328(f328(f243(a1),x60411),x60412)) % 167.75/167.50 [6048]E(x60481,f2(a872))+E(f328(f328(f81(a872),x60482),f328(f328(f253(a872),x60482),f328(f328(f22(a872),x60481),f78(a872)))),f328(f328(f253(a872),x60482),x60481)) % 167.75/167.50 [6074]E(f328(f328(f81(a872),f328(a108,x60741)),f328(a108,x60742)),f328(a108,f328(f328(f81(a1),x60741),x60742)))+~P1(f328(f328(f242(a1),f2(a1)),x60741)) % 167.75/167.50 [6075]E(f328(f328(f40(a872),f328(a108,x60751)),f328(a108,x60752)),f328(a108,f328(f328(f40(a1),x60751),x60752)))+~P1(f328(f328(f242(a1),f2(a1)),x60751)) % 167.75/167.50 [6089]~P111(x60891)+E(f328(f328(f80(x60891),x60892),x60892),f328(f328(f81(x60891),f328(f328(f80(x60891),f78(x60891)),f78(x60891))),x60892)) % 167.75/167.50 [6106]E(f328(f328(f22(a1),f328(f104(a1),x61061)),f328(f104(a1),x61062)),f328(f104(a1),f328(f328(f22(a872),x61061),x61062)))+~P1(f328(f328(f242(a872),x61062),x61061)) % 167.75/167.50 [6108]E(f328(f328(f263(a1,a1),f328(f107(a1),a101)),f328(f328(f80(a1),x61081),x61082)),f51(x61081,x61082))+~P1(f328(f328(f242(a1),x61082),f2(a1))) % 167.75/167.50 [6148]E(f178(x61481,x61482),f117(f873(x61481)))+P1(f328(f328(f330(f873(x61481)),f715(x61482,x61481)),f328(f170(f873(x61481)),x61482))) % 167.75/167.50 [6235]E(f328(f328(f148(a1),x62351),f177(f328(f328(f80(a1),x62351),f78(a1)),x62352)),f177(x62351,x62352))+~P1(f328(f328(f242(a1),x62351),x62352)) % 167.75/167.50 [6272]~P1(f328(f328(f243(a872),x62722),x62721))+P1(f328(f328(f243(a872),f2(a872)),f328(f328(f22(a872),x62721),x62722))) % 167.75/167.50 [6303]~P1(f328(f328(f243(a872),x63031),f328(a108,x63032)))+P1(f328(f328(f243(a1),f328(f104(a1),x63031)),x63032)) % 167.75/167.50 [6332]~P105(x63321)+E(f328(f328(f114(f879(x63321,a867)),f328(f249(x63321),x63322)),f328(f328(f306(x63321),x63322),f192(f879(x63321,a867)))),f328(f297(x63321),x63322)) % 167.75/167.50 [6335]~P1(f328(f328(f243(a872),f2(a872)),x63351))+P1(f328(f328(f243(a872),f2(a872)),f328(f328(f253(a872),x63351),x63352))) % 167.75/167.50 [6336]~P1(f328(f328(f242(a1),f2(a1)),x63361))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f253(a1),x63361),x63362))) % 167.75/167.50 [6363]~E(f328(x63631,f2(a872)),f2(a872))+E(f328(f328(f6(a872,a872),x63631),f299(a872,f328(a116,f2(a872)),x63632)),f328(f328(f6(a872,a872),x63631),f299(a872,f2(a872),x63632))) % 167.75/167.50 [6426]~P91(x64261)+E(f328(f328(f81(x64261),f328(f328(f80(x64261),f78(x64261)),f78(x64261))),f328(f107(x64261),x64262)),f328(f107(x64261),f328(f328(f80(a1),x64262),x64262))) % 167.75/167.50 [6442]E(f328(f328(f306(a1),x64421),f299(a1,f328(f328(f80(a1),x64421),f78(a1)),x64422)),f299(a1,x64421,x64422))+P1(f328(f328(f243(a1),x64422),x64421)) % 167.75/167.50 [6443]P1(f328(f328(f243(a872),x64431),f328(a108,x64432)))+~P1(f328(f328(f243(a1),f328(f104(a1),x64431)),x64432)) % 167.75/167.50 [6543]E(f328(a108,f328(f328(f40(a1),f328(f107(a1),x65431)),f328(f107(a1),x65432))),f328(f328(f40(a872),f328(f107(a872),x65431)),f328(f107(a872),x65432)))+P1(f328(a197,f328(f107(a1),x65431))) % 167.75/167.50 [6601]P1(f328(f328(f243(a872),x66011),x66012))+~P1(f328(f328(f243(a872),f2(a872)),f328(f328(f22(a872),x66012),x66011))) % 167.75/167.50 [6646]P1(f328(f328(f243(a872),f2(a872)),x66461))+~P1(f328(f328(f243(a872),f2(a872)),f328(f328(f81(a872),x66462),x66461))) % 167.75/167.50 [6647]P1(f328(f328(f243(a872),f2(a872)),x66471))+~P1(f328(f328(f243(a872),f2(a872)),f328(f328(f81(a872),x66471),x66472))) % 167.75/167.50 [6664]~P1(f328(f328(f242(a1),x66641),f2(a1)))+E(f328(f328(f81(a872),f328(a108,f328(f79(a1),x66641))),f328(a108,f328(f79(a1),x66642))),f328(a108,f328(f328(f81(a1),x66641),x66642))) % 167.75/167.50 [6722]~E(x67222,f192(f879(x67221,a867)))+P1(f328(f328(f242(f879(x67221,a867)),x67222),f328(f79(f879(x67221,a867)),x67222))) % 167.75/167.50 [6785]~P91(x67851)+E(f328(f328(f80(x67851),f328(f328(f80(x67851),f2(x67851)),f328(f107(x67851),x67852))),f328(f107(x67851),x67852)),f328(f107(x67851),f328(f328(f80(a1),x67852),x67852))) % 167.75/167.50 [6842]~P1(f328(f328(f243(a1),x68421),x68422))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x68421),f78(a1))),x68422)) % 167.75/167.50 [6908]E(x69081,f2(a872))+~P1(f328(f328(f242(a1),f328(f104(a1),x69082)),f328(f79(a1),f328(f104(a1),x69081)))) % 167.75/167.50 [6909]E(x69091,f2(a872))+~P1(f328(f328(f242(a1),f328(f104(a1),x69091)),f328(f79(a1),f328(f104(a1),x69092)))) % 167.75/167.50 [7012]E(f328(f328(f263(a1,a1),f328(f107(a1),a101)),f328(f328(f80(a1),x70121),x70122)),f51(x70121,x70122))+~P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),x70121),x70122))) % 167.75/167.50 [7054]~P27(x70541,x70542)+P38(x70541,f328(f262(f879(f878(x70541,x70541),a867),f879(f878(x70541,x70541),a867)),x70542)) % 167.75/167.50 [7072]~P1(f328(f328(f242(a872),f328(a116,f2(a872))),x70721))+P1(f328(f328(f242(a872),f328(a116,f2(a872))),f328(f328(f253(a872),x70721),x70722))) % 167.75/167.50 [7237]~P1(f328(f328(f243(a1),x72371),x72372))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x72371),x72371)),f328(f328(f80(a1),x72372),x72372))) % 167.75/167.50 [7249]~P1(f328(f328(f242(a1),x72491),x72492))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x72491),x72491)),f328(f328(f80(a1),x72492),x72492))) % 167.75/167.50 [7250]~P1(f328(f328(f91(a1),x72501),x72502))+P1(f328(f328(f91(a1),f328(f328(f80(a1),x72501),x72501)),f328(f328(f80(a1),x72502),x72502))) % 167.75/167.50 [7305]~P1(f328(f328(f243(a872),f2(a872)),x73051))+P1(f328(f328(f243(a872),f328(f328(f22(a872),x73051),f328(a116,x73052))),x73051)) % 167.75/167.50 [7342]P1(f328(f328(f242(a872),f328(a116,f2(a872))),x73421))+~P1(f328(f328(f242(a872),f328(a116,f2(a872))),f328(f328(f81(a872),x73422),x73421))) % 167.75/167.50 [7343]P1(f328(f328(f242(a872),f328(a116,f2(a872))),x73431))+~P1(f328(f328(f242(a872),f328(a116,f2(a872))),f328(f328(f81(a872),x73431),x73432))) % 167.75/167.50 [7347]P1(f328(f328(f242(a872),f328(f328(f162(a872),x73471),x73472)),f328(f163(a872),x73471)))+~P1(f328(f328(f243(a872),x73472),f328(f193(f873(a872)),x73471))) % 167.75/167.50 [7388]P1(f328(f328(f243(a1),x73881),x73882))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x73881),f78(a1))),x73882)) % 167.75/167.50 [7432]P1(f328(f38(x74321),f251(f879(x74321,a867))))+~P1(f328(f38(f879(x74322,x74321)),f251(f879(f879(x74322,x74321),a867)))) % 167.75/167.50 [7433]P1(f328(f38(x74331),f251(f879(x74331,a867))))+~P1(f328(f38(f877(x74332,x74331)),f251(f879(f877(x74332,x74331),a867)))) % 167.75/167.50 [7434]P1(f328(f38(x74341),f251(f879(x74341,a867))))+~P1(f328(f38(f877(x74341,x74342)),f251(f879(f877(x74341,x74342),a867)))) % 167.75/167.50 [7476]E(x74761,f192(f879(x74762,a867)))+~P1(f328(f328(f242(f879(x74762,a867)),x74761),f328(f79(f879(x74762,a867)),x74761))) % 167.75/167.50 [7614]E(f328(f139(f873(x76141),f873(x76141),f125(x76141),f117(x76141)),x76142),f117(x76141))+P1(f328(f328(f330(f873(x76141)),f730(x76142,x76141)),f328(f170(f873(x76141)),x76142))) % 167.75/167.50 [7615]E(f328(f139(f873(x76151),f873(x76151),f125(x76151),f117(x76151)),x76152),f117(x76151))+P1(f328(f328(f330(f873(x76151)),f737(x76152,x76151)),f328(f170(f873(x76151)),x76152))) % 167.75/167.50 [7856]P1(f328(f328(f243(a1),x78561),x78562))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x78561),x78561)),f328(f328(f80(a1),x78562),x78562))) % 167.75/167.50 [7859]P1(f328(f328(f242(a1),x78591),x78592))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x78591),x78591)),f328(f328(f80(a1),x78592),x78592))) % 167.75/167.50 [7860]P1(f328(f328(f91(a1),x78601),x78602))+~P1(f328(f328(f91(a1),f328(f328(f80(a1),x78601),x78601)),f328(f328(f80(a1),x78602),x78602))) % 167.75/167.50 [7954]~P111(x79541)+E(f328(f328(f81(x79541),f328(f328(f80(x79541),f78(x79541)),f78(x79541))),f328(f328(f6(a872,x79541),f104(x79541)),f299(a872,f78(a872),x79542))),f328(f328(f81(x79541),f328(f104(x79541),x79542)),f328(f328(f80(x79541),f328(f104(x79541),x79542)),f78(x79541)))) % 167.75/167.50 [8002]P1(f328(f328(f330(a872),x80021),x80022))+~P1(f328(f328(f330(a1),f328(f104(a1),x80021)),f328(f307(a872,a1,f104(a1)),x80022))) % 167.75/167.50 [8167]~P1(f328(f38(x81671),x81672))+E(f328(f307(a872,x81671,f468(x81672,x81671)),f328(f248(a872),f328(f328(f7(a872,a872,a867),f243(a872)),f469(x81672,x81671)))),x81672) % 167.75/167.50 [8454]P42(x84541,x84542)+P1(f328(f328(f330(f878(x84541,x84541)),f328(f328(f263(x84541,x84541),f522(x84542,x84541)),f522(x84542,x84541))),x84542)) % 167.75/167.50 [8600]~P91(x86001)+E(f328(f328(f22(x86001),f78(x86001)),f328(f107(x86001),x86002)),f328(f107(x86001),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f79(a1),x86002)))) % 167.75/167.50 [8716]~P1(f328(f328(f243(f879(a872,a867)),x87161),x87162))+P1(f328(f328(f243(f879(a1,a867)),f328(f307(a872,a1,f104(a1)),x87161)),f328(f307(a872,a1,f104(a1)),x87162))) % 167.75/167.50 [8745]~P1(f328(f328(f243(a1),x87451),x87452))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x87451),x87451)),a101)),f328(f328(f80(a1),x87452),x87452))) % 167.75/167.50 [8747]~P1(f328(f328(f243(a1),x87471),x87472))+P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x87471),x87471)),a101)),f328(f328(f80(a1),x87472),x87472))) % 167.75/167.50 [8817]~P1(f328(f328(f330(a872),x88171),f328(f170(a872),x88172)))+P1(f328(f328(f242(a872),x88171),f328(f139(a872,a872,f80(a872),f2(a872)),x88172))) % 167.75/167.50 [8909]P46(x89091,x89092)+~P1(f328(f328(f330(f878(x89091,x89091)),f328(f328(f263(x89091,x89091),f506(x89092,x89091)),f506(x89092,x89091))),x89092)) % 167.75/167.50 [9055]~P1(f328(f328(f243(f879(a1,a867)),f328(f307(a872,a1,f104(a1)),x90551)),f328(f307(a872,a1,f104(a1)),x90552)))+P1(f328(f328(f243(f879(a872,a867)),x90551),x90552)) % 167.75/167.50 [9056]~P1(f328(f328(f242(f879(a1,a867)),f328(f307(a872,a1,f104(a1)),x90561)),f328(f307(a872,a1,f104(a1)),x90562)))+P1(f328(f328(f242(f879(a872,a867)),x90561),x90562)) % 167.75/167.50 [9138]P1(f328(f328(f243(a1),x91381),x91382))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x91381),x91381)),a101)),f328(f328(f80(a1),x91382),x91382))) % 167.75/167.50 [9140]P1(f328(f328(f243(a1),x91401),x91402))+~P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x91401),x91401)),a101)),f328(f328(f80(a1),x91402),x91402))) % 167.75/167.50 [10049]~P1(f328(f38(x100491),x100492))+E(f328(f193(f873(x100491)),f90(f873(x100491),f328(f328(f18(f873(x100491),a867,a867),f328(f328(f8(a867,f879(a867,a867),f873(x100491)),a326),f328(f328(f7(f873(x100491),f879(x100491,a867),a867),f328(f328(f8(f879(x100491,a867),f879(f879(x100491,a867),a867),f873(x100491)),a325),f170(x100491))),x100492))),f134(x100491)))),f221(x100491,x100492)) % 167.75/167.50 [10185]~P25(a868,x101851,f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),a325),x101852),f328(a198,x101852))),f192(f879(f871(a868),a867))))+P25(a868,x101851,f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),f328(f328(f8(f879(a868,f879(a868,a867)),f879(a868,a867),a868),f328(f8(f879(a868,a867),a867,a868),f88(a868))),f328(f328(f8(f879(a868,a867),f879(a868,f879(a868,a867)),a868),f328(f7(a868,f879(a868,a867),f879(a868,a867)),f328(f328(f8(f879(a868,f879(a867,a867)),f879(f879(a868,a867),f879(a868,a867)),a868),f18(a868,a867,a867)),f328(f328(f8(f879(a868,a867),f879(a868,f879(a867,a867)),a868),f328(f8(a867,f879(a867,a867),a868),a331)),f328(a198,x101852))))),a325))),x101852),a325)),f192(f879(f871(a868),a867)))) % 167.75/167.50 [6037]E(f328(f328(f80(a872),f328(f328(f22(a872),x60371),x60372)),x60372),x60371)+~P1(f328(f328(f242(a872),x60372),x60371)) % 167.75/167.50 [6102]E(f328(f328(f40(a872),f328(f328(f81(a872),x61021),x61022)),x61022),x61021)+~P1(f328(f328(f243(a872),f2(a872)),x61022)) % 167.75/167.50 [6103]E(f328(f328(f40(a872),f328(f328(f81(a872),x61031),x61032)),x61031),x61032)+~P1(f328(f328(f243(a872),f2(a872)),x61031)) % 167.75/167.50 [6107]~P67(x61071)+E(f328(f328(f6(a872,x61071),f328(f162(x61071),x61072)),f328(f298(a872,f2(a872)),f328(f193(f873(x61071)),x61072))),f328(f163(x61071),x61072)) % 167.75/167.50 [6227]E(f46(a872,f328(a116,f328(f328(f81(a872),x62271),x62272)),x62271),f78(a872))+~P1(f328(f328(f243(a872),f78(a872)),x62271)) % 167.75/167.50 [6233]E(f328(a116,f328(f328(f80(a872),f328(f107(a872),x62331)),x62332)),f328(f328(f80(a872),f78(a872)),x62332))+~P1(f328(a197,f328(f107(a1),x62331))) % 167.75/167.50 [6261]E(f328(a108,f328(f328(f253(a1),f328(f107(a1),x62611)),x62612)),f328(f328(f253(a872),f328(f107(a872),x62611)),x62612))+P1(f328(a197,f328(f107(a1),x62611))) % 167.75/167.50 [6496]E(f328(f328(f22(a872),x64961),f328(f107(a872),f328(f328(f80(a1),x64962),a101))),f328(f328(f22(a872),f328(a116,x64961)),f328(f107(a872),x64962)))+~P1(f328(f328(f243(a1),a83),x64962)) % 167.75/167.50 [6574]E(x65741,f2(a872))+E(f328(a116,f328(f328(f80(a872),f328(f328(f22(a872),x65741),f78(a872))),x65742)),f328(f328(f80(a872),x65741),x65742)) % 167.75/167.50 [6615]E(x66151,f2(a1))+P1(f328(f328(f243(a1),f2(a1)),f328(f328(f253(a1),f328(f75(a1),x66151)),x66152))) % 167.75/167.50 [6631]~E(x66312,f2(a872))+P1(f328(f328(f243(a1),f2(a1)),f328(f328(f253(a1),f328(f75(a1),x66311)),x66312))) % 167.75/167.50 [6668]E(x66681,f2(a872))+E(f328(f328(f80(a872),x66682),f328(f328(f81(a872),f328(f328(f22(a872),x66681),f78(a872))),x66682)),f328(f328(f81(a872),x66681),x66682)) % 167.75/167.50 [6716]~P1(f328(f328(f242(a1),x67161),x67162))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x67161),a101)),x67162)) % 167.75/167.50 [6845]E(f328(f328(f148(a872),x68451),f136(a872,f328(f298(a872,f328(a116,x68451)),x68452))),f136(a872,f328(f298(a872,x68451),x68452)))+~P1(f328(f328(f243(a872),x68451),x68452)) % 167.75/167.50 [7045]E(x70451,x70452)+~E(f328(f328(f22(a1),f328(f328(f80(a1),x70451),x70451)),a101),f328(f328(f22(a1),f328(f328(f80(a1),x70452),x70452)),a101)) % 167.75/167.50 [7048]E(x70481,f117(x70482))+E(f272(x70482,f328(f328(f151(x70482,f878(a103,x70482)),f328(f263(a103,x70482),f78(a103))),x70481)),f279(x70482,x70481)) % 167.75/167.50 [7274]P1(f328(f328(f242(a1),x72741),x72742))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x72741),a101)),x72742)) % 167.75/167.50 [7758]~P1(f328(f328(f243(a872),x77581),x77582))+P1(f328(f328(f330(f878(a872,a872)),f328(f328(f263(a872,a872),x77581),x77582)),a247)) % 167.75/167.50 [7979]~P1(f328(f328(f243(a103),f2(a103)),x79791))+P1(f328(f328(f243(a103),f328(f262(a103,f878(a103,a103)),f328(f273(x79791),x79792))),x79791)) % 167.75/167.50 [8300]~P84(x83001)+P1(f328(f328(f242(x83001),f328(f75(x83001),f328(f163(x83001),x83002))),f328(f163(x83001),f328(f328(f151(x83001,x83001),f75(x83001)),x83002)))) % 167.75/167.50 [8324]P1(f328(f328(f243(a872),x83241),x83242))+~P1(f328(f328(f330(f878(a872,a872)),f328(f328(f263(a872,a872),x83241),x83242)),a247)) % 167.75/167.50 [8475]E(f328(f328(f263(x84751,x84751),f645(x84752,x84751)),f645(x84752,x84751)),x84752)+~P1(f328(f328(f330(f878(x84751,x84751)),x84752),f304(x84751,f192(f879(f878(x84751,x84751),a867))))) % 167.75/167.50 [8518]E(f328(f298(a872,x85181),f328(f328(f80(a872),x85181),f328(f39(a872),x85182))),x85182)+~P1(f328(f328(f242(f879(a872,a867)),x85182),f328(f298(a872,x85181),f328(f328(f80(a872),x85181),f328(f39(a872),x85182))))) % 167.75/167.50 [8856]E(f328(f328(f40(a1),f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x88561),x88561)),a101))),f328(f107(a1),f328(f328(f80(a1),x88562),x88562))),f328(f328(f40(a1),f328(f107(a1),x88561)),f328(f107(a1),x88562)))+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x88562))) % 167.75/167.50 [8984]E(f175(f873(x89841),f328(f328(f8(a867,a867,f873(x89841)),a323),f328(f328(f7(f873(x89841),f873(x89841),a867),a325),f117(x89841))),x89842),f178(x89841,f178(x89841,x89842)))+~P15(a872,f328(f166(a872),f328(f328(f151(f873(x89841),a872),f193(f873(x89841))),x89842))) % 167.75/167.50 [8987]E(f328(f328(f40(a1),f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x89871),x89871)),a101))),f328(f107(a1),f328(f328(f80(a1),x89872),x89872))),f328(f328(f40(a1),f328(f328(f80(a1),f328(f107(a1),x89871)),f78(a1))),f328(f107(a1),x89872)))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x89872))) % 167.75/167.50 [9675]P25(a868,x96751,f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),a325),f328(a26,x96752)),f328(a198,f328(a26,x96752)))),f192(f879(f871(a868),a867))))+~P25(a868,f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),a325),f328(a26,x96752)),f328(a198,f328(a26,x96752)))),x96751),f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),a325),f328(f239(a869),f328(a28,x96752))),f328(a198,f328(f239(a869),f328(a28,x96752))))),f192(f879(f871(a868),a867)))) % 167.75/167.50 [9825]P1(f328(a197,x98252))+E(f328(f328(f86(a1,a872),f328(f328(f22(a1),x98251),x98252)),f328(f328(f18(a1,a872,a872),f328(f328(f7(a1,a872,f879(a872,a872)),f328(f328(f8(a867,f879(a872,f879(a872,a872)),a1),f100(a872)),a197)),f2(a872))),a108)),f328(f328(f22(a872),f328(a108,x98251)),f328(a108,x98252))) % 167.75/167.50 [9833]E(f328(f328(f86(a1,a872),f328(f107(a1),f328(f328(f80(a1),x98331),f328(f79(a1),x98332)))),f328(f328(f18(a1,a872,a872),f328(f328(f7(a1,a872,f879(a872,a872)),f328(f328(f8(a867,f879(a872,f879(a872,a872)),a1),f100(a872)),a197)),f2(a872))),a108)),f328(f328(f22(a872),f328(f107(a872),x98331)),f328(f107(a872),x98332)))+P1(f328(f328(f243(a1),x98332),a83)) % 167.75/167.50 [9834]~P27(x98341,x98342)+P1(f328(f328(f242(f879(f878(x98341,x98341),a867)),f328(f328(f285(x98341,x98341,x98341),f328(f262(f879(f878(x98341,x98341),a867),f879(f878(x98341,x98341),a867)),x98342)),f328(f266(f879(f878(x98341,x98341),a867),f879(f878(x98341,x98341),a867)),x98342))),f328(f262(f879(f878(x98341,x98341),a867),f879(f878(x98341,x98341),a867)),x98342))) % 167.75/167.50 [9900]~E(f328(f39(a872),f328(f248(a872),f328(f328(f18(a872,a867,a867),f328(f328(f8(a867,f879(a867,a867),a872),a326),f328(f328(f7(a872,f879(a872,a867),a867),f330(a872)),x99001))),f328(f328(f7(a872,a872,a867),f243(a872)),f328(a116,x99002))))),f2(a872))+~P1(f328(f328(f330(a872),f2(a872)),x99001)) % 167.75/167.50 [9956]E(f46(a1,f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x99561),x99561)),a101)),f328(f107(a1),f328(f328(f80(a1),x99562),x99562))),f328(f328(f80(a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f46(a1,f328(f107(a1),x99561),f328(f107(a1),x99562)))),f78(a1)))+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x99562))) % 167.75/167.50 [9965]E(f46(a1,f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x99651),x99651)),a101)),f328(f107(a1),f328(f328(f80(a1),x99652),x99652))),f328(f328(f22(a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f46(a1,f328(f328(f80(a1),f328(f107(a1),x99651)),f78(a1)),f328(f107(a1),x99652)))),f78(a1)))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x99652))) % 167.75/167.50 [10017]~P4(x100171)+E(f41(x100171,f328(f248(x100171),f328(f328(f8(f879(x100171,a867),a867,x100171),f88(x100171)),f328(f328(f8(f879(x100171,a867),f879(x100171,a867),x100171),f328(f18(x100171,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100171),a331),f328(f328(f7(x100171,f879(x100171,a867),a867),f330(x100171)),x100172)))),f242(x100171))))),f42(x100171,x100172)) % 167.75/167.50 [10042]~P38(x100421,x100422)+P56(x100421,f328(f328(f7(x100421,f879(f878(x100421,x100421),a867),f879(x100421,a867)),f328(f328(f8(f879(x100421,f879(f879(f878(x100421,x100421),a867),a867)),f879(f879(f878(x100421,x100421),a867),f879(x100421,a867)),x100421),f7(x100421,f879(f878(x100421,x100421),a867),a867)),f328(f328(f8(f879(x100421,f878(x100421,x100421)),f879(x100421,f879(f879(f878(x100421,x100421),a867),a867)),x100421),f328(f8(f878(x100421,x100421),f879(f879(f878(x100421,x100421),a867),a867),x100421),f330(f878(x100421,x100421)))),f263(x100421,x100421)))),x100422)) % 167.75/167.50 [10043]~P7(x100431,f251(f879(x100431,a867)),x100432)+P6(x100431,f328(f328(f7(x100431,f879(f878(x100431,x100431),a867),f879(x100431,a867)),f328(f328(f8(f879(x100431,f879(f879(f878(x100431,x100431),a867),a867)),f879(f879(f878(x100431,x100431),a867),f879(x100431,a867)),x100431),f7(x100431,f879(f878(x100431,x100431),a867),a867)),f328(f328(f8(f879(x100431,f878(x100431,x100431)),f879(x100431,f879(f879(f878(x100431,x100431),a867),a867)),x100431),f328(f8(f878(x100431,x100431),f879(f879(f878(x100431,x100431),a867),a867),x100431),f330(f878(x100431,x100431)))),f263(x100431,x100431)))),x100432)) % 167.75/167.50 [10080]P38(x100801,x100802)+~P56(x100801,f328(f328(f7(x100801,f879(f878(x100801,x100801),a867),f879(x100801,a867)),f328(f328(f8(f879(x100801,f879(f879(f878(x100801,x100801),a867),a867)),f879(f879(f878(x100801,x100801),a867),f879(x100801,a867)),x100801),f7(x100801,f879(f878(x100801,x100801),a867),a867)),f328(f328(f8(f879(x100801,f878(x100801,x100801)),f879(x100801,f879(f879(f878(x100801,x100801),a867),a867)),x100801),f328(f8(f878(x100801,x100801),f879(f879(f878(x100801,x100801),a867),a867),x100801),f330(f878(x100801,x100801)))),f263(x100801,x100801)))),x100802)) % 167.75/167.50 [10081]P7(x100811,f251(f879(x100811,a867)),x100812)+~P6(x100811,f328(f328(f7(x100811,f879(f878(x100811,x100811),a867),f879(x100811,a867)),f328(f328(f8(f879(x100811,f879(f879(f878(x100811,x100811),a867),a867)),f879(f879(f878(x100811,x100811),a867),f879(x100811,a867)),x100811),f7(x100811,f879(f878(x100811,x100811),a867),a867)),f328(f328(f8(f879(x100811,f878(x100811,x100811)),f879(x100811,f879(f879(f878(x100811,x100811),a867),a867)),x100811),f328(f8(f878(x100811,x100811),f879(f879(f878(x100811,x100811),a867),a867),x100811),f330(f878(x100811,x100811)))),f263(x100811,x100811)))),x100812)) % 167.75/167.50 [7225]E(f328(f328(f80(a872),f328(f107(a872),f328(f328(f22(a1),x72251),a101))),x72252),f328(a116,f328(f328(f80(a872),f328(f107(a872),x72251)),x72252)))+P1(f328(a197,f328(f107(a1),x72251))) % 167.75/167.50 [7673]~P91(x76731)+E(f328(f328(f80(x76731),f328(f328(f80(x76731),f78(x76731)),f328(f107(x76731),x76732))),f328(f107(x76731),x76732)),f328(f107(x76731),f328(f328(f22(a1),f328(f328(f80(a1),x76732),x76732)),a101))) % 167.75/167.50 [8326]~P1(f328(f328(f242(a1),x83261),x83262))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x83261),x83261)),f328(f328(f22(a1),f328(f328(f80(a1),x83262),x83262)),a101))) % 167.75/167.50 [8328]~P1(f328(f328(f242(a1),x83281),x83282))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x83281),x83281)),f328(f328(f22(a1),f328(f328(f80(a1),x83282),x83282)),a101))) % 167.75/167.50 [8749]P1(f328(f328(f242(a1),x87491),x87492))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x87491),x87491)),f328(f328(f22(a1),f328(f328(f80(a1),x87492),x87492)),a101))) % 167.75/167.50 [8751]P1(f328(f328(f242(a1),x87511),x87512))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x87511),x87511)),f328(f328(f22(a1),f328(f328(f80(a1),x87512),x87512)),a101))) % 167.75/167.50 [9043]~P1(f328(f328(f243(a1),x90431),x90432))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90431),x90431)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x90432),x90432)),a101))) % 167.75/167.50 [9045]~P1(f328(f328(f242(a1),x90451),x90452))+P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90451),x90451)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x90452),x90452)),a101))) % 167.75/167.50 [9046]~P1(f328(f328(f91(a1),x90461),x90462))+P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90461),x90461)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x90462),x90462)),a101))) % 167.75/167.50 [9311]P1(f328(f328(f243(a1),x93111),x93112))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x93111),x93111)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x93112),x93112)),a101))) % 167.75/167.50 [9313]P1(f328(f328(f242(a1),x93131),x93132))+~P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x93131),x93131)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x93132),x93132)),a101))) % 167.75/167.50 [9314]P1(f328(f328(f91(a1),x93141),x93142))+~P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x93141),x93141)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x93142),x93142)),a101))) % 167.75/167.50 [9346]~P1(f328(f38(x93461),x93462))+P1(f328(f38(f879(x93461,a867)),f328(f248(f879(x93461,a867)),f328(f328(f7(f879(x93461,a867),f879(x93461,a867),a867),f242(f879(x93461,a867))),x93462)))) % 167.75/167.50 [9394]~E(f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),x93941),f192(f879(f878(a872,a872),a867)))),f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),x93942),f192(f879(f878(a872,a872),a867)))))+P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),x93941),x93942)),a112)) % 167.75/167.50 [9478]E(f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),x94781),f192(f879(f878(a872,a872),a867)))),f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),x94782),f192(f879(f878(a872,a872),a867)))))+~P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),x94781),x94782)),a112)) % 167.75/167.50 [9516]P1(f328(f328(f242(a1),f2(a1)),f652(x95161,x95162)))+E(f328(f248(a1),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),f2(a1)))),x95161)),f328(f248(a1),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),f2(a1)))),x95162))) % 167.75/167.50 [10027]~P4(x100271)+E(f42(x100271,f328(f248(x100271),f328(f328(f8(f879(x100271,a867),a867,x100271),f88(x100271)),f328(f328(f8(f879(x100271,a867),f879(x100271,a867),x100271),f328(f18(x100271,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100271),a331),f328(f328(f7(x100271,f879(x100271,a867),a867),f330(x100271)),x100272)))),f328(f7(x100271,x100271,a867),f242(x100271)))))),f41(x100271,x100272)) % 167.75/167.50 [10048]P1(f328(f328(f330(a872),f2(a872)),x100481))+E(f328(f39(a872),f328(f248(a872),f328(f328(f18(a872,a867,a867),f328(f328(f8(a867,f879(a867,a867),a872),a326),f328(f328(f7(a872,f879(a872,a867),a867),f328(f328(f8(a872,f879(f879(a872,a867),a867),a872),f330(a872)),a116)),x100481))),f328(f328(f7(a872,a872,a867),f243(a872)),x100482)))),f328(f39(a872),f328(f248(a872),f328(f328(f18(a872,a867,a867),f328(f328(f8(a867,f879(a867,a867),a872),a326),f328(f328(f7(a872,f879(a872,a867),a867),f330(a872)),x100481))),f328(f328(f7(a872,a872,a867),f243(a872)),f328(a116,x100482)))))) % 167.75/167.50 [7540]~P91(x75401)+E(f328(f328(f81(x75401),x75402),f328(f107(x75401),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),x75402) % 167.75/167.50 [7807]~P91(x78071)+E(f328(f328(f80(x78071),f328(f107(x78071),x78072)),f78(x78071)),f328(f107(x78071),f328(f328(f80(a1),x78072),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))) % 167.75/167.50 [7952]P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x79522)))+E(f328(f328(f253(a1),x79521),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),x79522),x79522)),a101))),f78(a1)) % 167.75/167.50 [9371]~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x93712)))+E(f328(f328(f253(a1),x93711),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),x93712),x93712)),a101))),f328(f328(f86(a1,a1),f328(f328(f253(a1),x93711),f328(f107(a872),x93712))),f328(f328(f18(a1,a1,a1),f328(f328(f8(a1,f879(a1,a1),a1),f81(a1)),f328(f81(a1),x93711))),f5(a1)))) % 167.75/167.50 [9740]~P1(f328(f328(f242(a872),f664(x97402,x97401)),f328(x97401,f664(x97402,x97401))))+P1(f328(f38(a872),f328(f248(a872),f328(f328(f7(a872,a872,a867),f328(f328(f8(a872,f879(a872,a867),a872),f242(a872)),x97401)),x97402)))) % 167.75/167.50 [9890]~P1(f328(f328(f243(a872),f328(f107(a872),x98901)),f328(a116,x98902)))+P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x98901),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f7(a1,a872,a867),f328(f328(f8(a872,f879(a872,a867),a1),f243(a872)),a108)),x98902)))) % 167.75/167.50 [9891]~P1(f328(f328(f242(a872),f328(f107(a872),x98911)),f328(a116,x98912)))+P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x98911),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f7(a1,a872,a867),f328(f328(f8(a872,f879(a872,a867),a1),f242(a872)),a108)),x98912)))) % 167.75/167.50 [9940]P1(f328(f328(f243(a872),f328(f107(a872),x99401)),f328(a116,x99402)))+~P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x99401),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f7(a1,a872,a867),f328(f328(f8(a872,f879(a872,a867),a1),f243(a872)),a108)),x99402)))) % 167.75/167.50 [9941]P1(f328(f328(f242(a872),f328(f107(a872),x99411)),f328(a116,x99412)))+~P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x99411),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f7(a1,a872,a867),f328(f328(f8(a872,f879(a872,a867),a1),f242(a872)),a108)),x99412)))) % 167.75/167.50 [9971]~P1(f328(f328(f243(a872),f328(a116,x99712)),f328(f107(a872),x99711)))+P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x99711),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f8(a872,a867,a1),f328(f243(a872),x99712)),a108))))) % 167.75/167.50 [9972]~P1(f328(f328(f242(a872),f328(a116,x99722)),f328(f107(a872),x99721)))+P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x99721),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f8(a872,a867,a1),f328(f242(a872),x99722)),a108))))) % 167.75/167.50 [10015]P1(f328(f328(f243(a872),f328(a116,x100151)),f328(f107(a872),x100152)))+~P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x100152),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f8(a872,a867,a1),f328(f243(a872),x100151)),a108))))) % 167.75/167.50 [10016]P1(f328(f328(f242(a872),f328(a116,x100161)),f328(f107(a872),x100162)))+~P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x100162),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f8(a872,a867,a1),f328(f242(a872),x100161)),a108))))) % 167.75/167.50 [10088]~P1(f328(f328(f330(a872),f2(a872)),x100881))+E(f328(a116,f328(f39(a872),f328(f248(a872),f328(f328(f18(a872,a867,a867),f328(f328(f8(a867,f879(a867,a867),a872),a326),f328(f328(f7(a872,f879(a872,a867),a867),f328(f328(f8(a872,f879(f879(a872,a867),a867),a872),f330(a872)),a116)),x100881))),f328(f328(f7(a872,a872,a867),f243(a872)),x100882))))),f328(f39(a872),f328(f248(a872),f328(f328(f18(a872,a867,a867),f328(f328(f8(a867,f879(a867,a867),a872),a326),f328(f328(f7(a872,f879(a872,a867),a867),f330(a872)),x100881))),f328(f328(f7(a872,a872,a867),f243(a872)),f328(a116,x100882)))))) % 167.75/167.50 [8502]~P91(x85021)+E(f328(f328(f81(x85021),f328(f107(x85021),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),x85022),x85022) % 167.75/167.50 [8568]~P91(x85681)+E(f328(f328(f80(x85681),f78(x85681)),f328(f107(x85681),x85682)),f328(f107(x85681),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),x85682))) % 167.75/167.50 [8626]~P91(x86261)+E(f328(f328(f22(x86261),f328(f107(x86261),x86262)),f78(x86261)),f328(f107(x86261),f328(f328(f80(a1),x86262),f328(f79(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.75/167.50 [8767]~P1(f328(f328(f243(a872),f328(f107(a872),a83)),x87672))+E(f328(f328(f22(a872),x87671),f328(f328(f22(a872),x87672),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f22(a872),f328(a116,x87671)),x87672)) % 167.75/167.50 [9410]~P111(x94101)+E(f328(f328(f81(x94101),x94102),x94102),f328(f328(f253(x94101),x94102),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.75/167.50 [9411]~P78(x94111)+E(f328(f328(f253(x94111),x94112),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f81(x94111),x94112),x94112)) % 167.75/167.50 [9413]~P91(x94131)+E(f328(f328(f81(x94131),x94132),f328(f107(x94131),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f80(x94131),x94132),x94132)) % 167.75/167.50 [9658]~P117(x96581)+E(f328(f328(f253(x96581),f328(f75(x96581),x96582)),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f253(x96581),x96582),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.75/167.50 [9659]~P138(x96591)+E(f328(f328(f253(x96591),f328(f79(x96591),x96592)),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f253(x96591),x96592),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.75/167.50 [9655]~P91(x96551)+E(f328(f328(f81(x96551),f328(f107(x96551),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x96552),f328(f328(f80(x96551),x96552),x96552)) % 167.75/167.50 [9780]~P117(x97801)+E(f328(f75(x97801),f328(f328(f253(x97801),x97802),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x97801),x97802),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.75/167.50 [9842]~P117(x98421)+P1(f328(f328(f242(x98421),f2(x98421)),f328(f328(f253(x98421),x98422),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 167.75/167.50 [10006]~E(f328(a116,x100062),f328(f107(a872),x100061))+P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x100061),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f7(a1,a872,a867),f328(f328(f8(a872,f879(a872,a867),a1),a325),a108)),x100062))))) % 167.75/167.50 [10007]~E(f328(f107(a872),x100071),f328(a116,x100072))+P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x100071),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f7(a1,a872,a867),f328(f328(f8(a872,f879(a872,a867),a1),a325),a108)),x100072))))) % 167.75/167.50 [10051]E(f328(a116,x100511),f328(f107(a872),x100512))+~P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x100512),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f7(a1,a872,a867),f328(f328(f8(a872,f879(a872,a867),a1),a325),a108)),x100511))))) % 167.75/167.50 [10052]E(f328(f107(a872),x100521),f328(a116,x100522))+~P1(f328(f328(f86(a1,a867),f328(f107(a1),f328(f328(f80(a1),x100521),a101))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a331),f328(f328(f8(a867,a867,a1),a323),a197))),f328(f328(f7(a1,a872,a867),f328(f328(f8(a872,f879(a872,a867),a1),a325),a108)),x100522))))) % 167.75/167.50 [9839]~P91(x98391)+E(f328(f328(f253(x98391),f328(f107(x98391),a101)),f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x98392)),f78(x98391)) % 167.75/167.50 [9840]~P138(x98401)+E(f328(f328(f253(x98401),f328(f79(x98401),f78(x98401))),f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x98402)),f78(x98401)) % 167.75/167.50 [9844]~P78(x98441)+E(f328(f328(f253(x98441),x98442),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),f328(f328(f81(x98441),f328(f328(f81(x98441),x98442),x98442)),x98442)) % 167.75/167.50 [10030]~P1(f328(f328(f242(a1),f2(a1)),x100302))+E(f46(a1,f328(f328(f80(a1),f78(a1)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100301)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100302)),f328(f328(f80(a1),f78(a1)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f46(a1,x100301,x100302)))) % 167.75/167.50 [10054]~P1(f328(f328(f242(a1),f2(a1)),x100542))+E(f328(f328(f40(a1),f328(f328(f80(a1),f78(a1)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100541))),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100542)),f328(f328(f40(a1),x100541),x100542)) % 167.75/167.50 [10056]~P1(f328(f328(f242(a1),x100562),f2(a1)))+E(f328(f328(f40(a1),f328(f328(f80(a1),f78(a1)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100561))),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100562)),f328(f328(f40(a1),f328(f328(f80(a1),x100561),f78(a1))),x100562)) % 167.75/167.50 [10057]~P1(f328(f328(f242(a1),x100572),f2(a1)))+E(f46(a1,f328(f328(f80(a1),f78(a1)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100571)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100572)),f328(f328(f22(a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f46(a1,f328(f328(f80(a1),x100571),f78(a1)),x100572))),f78(a1))) % 167.75/167.50 [9931]~P91(x99311)+E(f328(f328(f253(x99311),f328(f107(x99311),a101)),f328(a116,f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99312))),f328(f107(x99311),a101)) % 167.75/167.50 [9933]~P138(x99331)+E(f328(f328(f253(x99331),f328(f79(x99331),f78(x99331))),f328(a116,f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99332))),f328(f79(x99331),f78(x99331))) % 167.75/167.50 [5087]~P25(x50871,x50872,x50873)+P29(x50871,x50872,x50873) % 167.75/167.50 [8017]~E(x80172,x80173)+P35(x80171,x80171,a325,x80172,x80173) % 167.75/167.50 [8581]E(x85811,x85812)+~P35(x85813,x85813,a325,x85811,x85812) % 167.75/167.50 [5092]~P38(x50921,x50923)+P38(x50921,f322(x50921,x50922,x50923)) % 167.75/167.50 [5264]P28(x52641,x52642,x52643)+~P28(x52641,f328(a116,x52642),x52643) % 167.75/167.50 [5351]~P7(x53511,x53512,x53513)+P7(f873(x53511),f158(x53511,x53512),f155(x53511,x53513)) % 167.75/167.50 [5352]~P40(x53521,x53522,x53523)+P40(f873(x53521),f158(x53521,x53522),f155(x53521,x53523)) % 167.75/167.50 [5464]P51(x54641,x54642,x54643)+~E(f607(x54643,x54642,x54641),f608(x54643,x54642,x54641)) % 167.75/167.50 [5465]P52(x54651,x54652,x54653)+~E(f624(x54653,x54652,x54651),f625(x54653,x54652,x54651)) % 167.75/167.50 [6401]P29(x64011,x64012,x64013)+~P28(x64011,f591(x64013,x64012,x64011),f598(x64013,x64012,x64011)) % 167.75/167.50 [4640]~E(x46401,f205(x46402))+~E(x46401,f328(f235(x46402),x46403)) % 167.75/167.50 [4689]~E(f328(f166(x46892),x46891),x46893)+E(x46891,f328(f166(x46892),x46893)) % 167.75/167.50 [4690]~E(x46902,f328(f166(x46901),x46903))+E(f328(f166(x46901),x46902),x46903) % 167.75/167.50 [4737]E(x47371,x47372)+~E(f328(f235(x47373),x47371),f328(f235(x47373),x47372)) % 167.75/167.50 [4738]E(x47381,x47382)+~E(f328(f166(x47383),x47381),f328(f166(x47383),x47382)) % 167.75/167.50 [4943]~P6(x49433,x49431)+P1(f328(f328(x49431,x49432),x49432)) % 167.75/167.50 [4944]~P49(x49443,x49441)+P1(f328(f328(x49441,x49442),x49442)) % 167.75/167.50 [4946]~P56(x49461,x49462)+P1(f328(f316(x49461,x49462),x49463)) % 167.75/167.50 [5009]~P38(x50091,x50092)+P38(f873(x50091),f328(f140(x50091,x50092),x50093)) % 167.75/167.50 [5014]~P1(f328(x50142,x50143))+~E(f328(f248(x50141),x50142),f192(f879(x50141,a867))) % 167.75/167.50 [5015]~P1(f328(x50152,x50153))+~E(f192(f879(x50151,a867)),f328(f248(x50151),x50152)) % 167.75/167.50 [5029]E(x50291,f2(a872))+E(f141(x50292,f168(x50292,x50291,x50293)),x50293) % 167.75/167.50 [5047]~P1(f328(x50471,x50473))+P1(f328(x50471,f90(x50472,x50471))) % 167.75/167.50 [5059]E(x50591,f2(a872))+E(f328(f138(x50592),f168(x50592,x50591,x50593)),x50593) % 167.75/167.50 [5172]~E(x51722,x51723)+P1(f328(f328(f330(x51721),x51722),f328(a325,x51723))) % 167.75/167.50 [5184]P1(f328(x51841,x51842))+~P1(f328(x51841,f584(x51841,x51843))) % 167.75/167.50 [5230]E(f328(f166(x52301),x52302),f328(f328(f148(x52301),x52303),f117(x52301)))+~E(x52302,f328(f328(f148(x52301),x52303),f117(x52301))) % 167.75/167.50 [5231]~E(x52313,f328(f328(f148(x52311),x52312),f117(x52311)))+E(f328(f328(f148(x52311),x52312),f117(x52311)),f328(f166(x52311),x52313)) % 167.75/167.50 [5257]~E(x52573,f328(f16(f876(x52572),x52571),f205(x52572)))+E(f182(x52571,x52572,x52573),f192(f879(x52571,a867))) % 167.75/167.50 [5279]~P34(x52791,x52792,x52793)+P34(x52791,x52792,f328(f166(x52791),x52793)) % 167.75/167.50 [5280]~P32(x52801,x52802,x52803)+P32(x52801,x52802,f328(f166(x52801),x52803)) % 167.75/167.50 [5283]E(f328(f39(x52831),f773(x52832,x52833,x52831)),x52832)+~E(f328(f39(x52831),x52833),f328(a116,x52832)) % 167.75/167.50 [5289]~P38(x52891,x52893)+P1(f328(f328(f330(x52891),x52892),f317(x52891,x52893))) % 167.75/167.50 [5293]~E(f328(f166(x52932),x52931),f328(f328(f148(x52932),x52933),f117(x52932)))+E(x52931,f328(f328(f148(x52932),x52933),f117(x52932))) % 167.75/167.50 [5294]~E(f328(f328(f148(x52942),x52943),f117(x52942)),f328(f166(x52942),x52941))+E(x52941,f328(f328(f148(x52942),x52943),f117(x52942))) % 167.75/167.50 [5309]E(x53091,f328(f16(f876(x53092),x53093),f205(x53092)))+~E(f182(x53093,x53092,x53091),f192(f879(x53093,a867))) % 167.75/167.50 [5315]E(f85(f878(a872,a872),f49(x53151,x53152)),x53153)+~P1(f328(f49(x53151,x53152),x53153)) % 167.75/167.50 [5323]~E(x53233,f328(f235(x53231),x53232))+P1(f328(f328(f330(x53231),x53232),f234(x53231,x53233))) % 167.75/167.50 [5355]P34(x53551,x53552,x53553)+~P34(x53551,x53552,f328(f166(x53551),x53553)) % 167.75/167.50 [5356]P32(x53561,x53562,x53563)+~P32(x53561,x53562,f328(f166(x53561),x53563)) % 167.75/167.50 [5418]~E(x54182,f117(x54181))+P1(f328(f328(f330(f873(x54181)),x54182),f158(x54181,x54183))) % 167.75/167.50 [5425]~P40(x54251,x54252,x54253)+P40(x54251,x54252,f328(f283(x54251,x54251),x54253)) % 167.75/167.50 [5426]~P52(x54261,x54262,x54263)+P52(x54261,x54262,f328(f283(x54261,x54261),x54263)) % 167.75/167.50 [5445]~P57(x54451)+E(f46(x54451,f46(x54451,x54452,x54453),x54453),f46(x54451,x54452,x54453)) % 167.75/167.50 [5540]E(x55401,x55402)+~P1(f328(f328(f330(x55403),x55401),f328(a325,x55402))) % 167.75/167.50 [5587]~P142(x55871)+E(f194(x55871,x55872,f2(a872),x55873),x55873) % 167.75/167.50 [5607]P40(x56071,x56072,x56073)+~P40(x56071,x56072,f328(f283(x56071,x56071),x56073)) % 167.75/167.50 [5608]P52(x56081,x56082,x56083)+~P52(x56081,x56082,f328(f283(x56081,x56081),x56083)) % 167.75/167.50 [5612]~P105(x56122)+E(f147(x56121,x56122,x56123,f117(x56121)),f117(x56121)) % 167.75/167.50 [5625]E(f167(x56251,x56252,f149(x56251,x56253)),f149(x56251,f167(x56251,x56252,x56253)))+~P1(f328(f134(x56251),x56253)) % 167.75/167.50 [5631]E(x56311,f328(f235(x56312),x56313))+~P1(f328(f328(f330(x56312),x56313),f234(x56312,x56311))) % 167.75/167.50 [5717]~P1(f328(a25,x57173))+P1(f328(a25,f29(x57171,x57172,x57173))) % 167.75/167.50 [5728]E(f328(f133(x57281,x57282),x57283),f117(x57281))+P1(f328(x57282,f728(x57283,x57282,x57281))) % 167.75/167.50 [5871]~P1(f328(f134(x58711),x58712))+P1(f328(f134(x58711),f174(x58711,x58712,x58713))) % 167.75/167.50 [5872]~P1(f328(f134(x58721),x58723))+P1(f328(f134(x58721),f167(x58721,x58722,x58723))) % 167.75/167.50 [5873]~P1(f328(f134(x58731),x58733))+P1(f328(f134(x58731),f175(x58731,x58732,x58733))) % 167.75/167.50 [5874]~P1(f328(f134(x58741),x58743))+P1(f328(f134(x58741),f137(x58741,x58742,x58743))) % 167.75/167.50 [5875]~P144(x58751,x58752,x58753)+P1(f328(x58751,f46(a1,x58752,x58753))) % 167.75/167.50 [5894]~P34(x58943,x58941,x58942)+P1(f328(x58941,f776(x58942,x58941,x58943))) % 167.75/167.50 [5895]~P36(x58953,x58951,x58952)+P1(f328(x58951,f805(x58952,x58951,x58953))) % 167.75/167.50 [5916]E(f328(f133(x59161,x59162),x59163),f175(x59161,x59162,x59163))+P1(f328(x59162,f755(x59163,x59162,x59161))) % 167.75/167.50 [5956]~P1(f328(f134(x59561),x59563))+P1(f328(f134(f873(x59561)),f56(x59561,x59562,x59563))) % 167.75/167.50 [5987]~P107(x59871)+E(f328(f328(f105(f879(x59871,a867)),f328(f249(x59871),x59872)),f299(x59871,x59872,x59873)),f192(f879(x59871,a867))) % 167.75/167.50 [5988]~P107(x59881)+E(f328(f328(f105(f879(x59881,a867)),f328(f297(x59881),x59882)),f302(x59881,x59882,x59883)),f192(f879(x59881,a867))) % 167.75/167.50 [5989]~P107(x59891)+E(f328(f328(f105(f879(x59891,a867)),f328(f297(x59891),x59892)),f301(x59891,x59892,x59893)),f192(f879(x59891,a867))) % 167.75/167.50 [6136]P1(f328(a25,x61361))+~P1(f328(a25,f29(x61362,x61363,x61361))) % 167.75/167.50 [6138]P1(f328(a25,x61381))+~P1(f328(a25,f30(x61382,x61383,x61381))) % 167.75/167.50 [6140]P1(f328(a25,x61401))+~P1(f328(a25,f30(x61402,x61401,x61403))) % 167.75/167.50 [6223]E(f328(f133(x62231,x62232),x62233),x62233)+~P1(f328(x62232,f729(x62233,x62232,x62231))) % 167.75/167.50 [6225]E(f328(f328(f306(x62251),f857(x62252,x62253,x62251)),f773(x62252,x62253,x62251)),x62253)+~E(f328(f39(x62251),x62253),f328(a116,x62252)) % 167.75/167.50 [6241]P144(x62411,x62412,x62413)+~P1(f328(x62411,f46(a1,x62412,x62413))) % 167.75/167.50 [6288]P32(x62881,x62882,x62883)+~P1(f328(x62882,f793(x62882,x62883,x62881))) % 167.75/167.50 [6289]P32(x62891,x62892,x62893)+~P1(f328(x62892,f799(x62893,x62892,x62891))) % 167.75/167.50 [6290]P32(x62901,x62902,x62903)+~P1(f328(x62902,f801(x62903,x62902,x62901))) % 167.75/167.50 [6292]E(f175(x62921,x62922,x62923),x62923)+~P1(f328(x62922,f750(x62923,x62922,x62921))) % 167.75/167.50 [6370]~P1(f328(x63702,f585(x63703,x63702,x63701)))+P1(f328(f256(x63701,x63702),x63703)) % 167.75/167.50 [6371]~P1(f328(x63712,f720(x63713,x63712,x63711)))+P1(f328(f157(x63711,x63712),x63713)) % 167.75/167.50 [6616]~P1(f328(f316(x66161,x66162),f496(x66163,x66162,x66161)))+P1(f328(f316(x66161,x66162),x66163)) % 167.75/167.50 [6617]~P1(f328(f316(x66171,x66172),f515(x66173,x66172,x66171)))+P1(f328(f316(x66171,x66172),x66173)) % 167.75/167.50 [7226]~P57(x72261)+E(f328(f328(f80(x72261),f328(f328(f81(x72261),x72262),f328(f328(f40(x72261),x72263),x72262))),f46(x72261,x72263,x72262)),x72263) % 167.75/167.50 [7696]E(f328(f328(f263(x76961,x76961),f531(x76962,x76963,x76961)),f531(x76962,x76963,x76961)),x76963)+~P1(f328(f328(f330(f878(x76961,x76961)),x76963),f260(x76961,x76962))) % 167.75/167.50 [7815]~P1(f328(f328(f330(x78151),f543(x78153,x78152,x78151)),f317(x78151,x78153)))+P1(f328(f328(f330(x78151),x78152),f317(x78151,x78153))) % 167.75/167.50 [7816]~P1(f328(f328(f330(x78161),f611(x78163,x78162,x78161)),f317(x78161,x78163)))+P1(f328(f328(f330(x78161),x78162),f317(x78161,x78163))) % 167.75/167.50 [7817]~P1(f328(f328(f330(x78171),f612(x78173,x78172,x78171)),f317(x78171,x78173)))+P1(f328(f328(f330(x78171),x78172),f317(x78171,x78173))) % 167.75/167.50 [7998]~P57(x79981)+E(f328(f328(f80(x79981),f328(f328(f81(x79981),f328(f328(f40(x79981),x79982),x79983)),x79983)),f46(x79981,x79982,x79983)),x79982) % 167.75/167.50 [8043]~E(f328(f39(x80431),x80432),f328(a116,x80433))+~P1(f328(f328(f330(x80431),f857(x80433,x80432,x80431)),f773(x80433,x80432,x80431))) % 167.75/167.50 [8679]P1(f328(f328(f242(f879(f878(x86791,x86791),a867)),f304(x86791,x86792)),f304(x86791,x86793)))+~P1(f328(f328(f242(f879(f878(x86791,x86791),a867)),x86792),f304(x86791,x86793))) % 167.75/167.50 [8953]E(x89531,f117(x89532))+~P1(f328(f328(f330(f878(f873(x89532),f873(x89532))),f328(f328(f263(f873(x89532),f873(x89532)),x89531),f117(x89532))),f155(x89532,x89533))) % 167.75/167.50 [8978]E(x89781,f117(x89782))+~P1(f328(f328(f330(f878(f873(x89782),f873(x89782))),f328(f328(f263(f873(x89782),f873(x89782)),f117(x89782)),x89781)),f155(x89782,x89783))) % 167.75/167.50 [9102]E(f328(f328(f148(x91021),f706(x91022,x91023,x91021)),f707(x91022,x91023,x91021)),x91023)+~P1(f328(f328(f330(f878(f873(x91021),f873(x91021))),f328(f328(f263(f873(x91021),f873(x91021)),f117(x91021)),x91023)),f144(x91021,x91022))) % 167.75/167.50 [9339]~P124(x93391)+~P1(f328(f328(f243(x93391),f328(f328(f80(x93391),f328(f328(f81(x93391),x93392),x93392)),f328(f328(f81(x93391),x93393),x93393))),f2(x93391))) % 167.75/167.50 [9388]P1(f328(f38(x93881),x93882))+~P1(f328(f328(f330(f878(f879(x93881,a867),f879(x93881,a867))),f328(f328(f263(f879(x93881,a867),f879(x93881,a867)),x93883),x93882)),f303(x93881))) % 167.75/167.50 [9681]~P47(x96811,x96812,x96813)+P1(f328(f328(f243(a1),f328(f328(f73(f878(a1,a1),a1,x96811,f262(a1,a1)),f219(x96811)),f230(x96811,x96812,f227(x96811,x96813)))),f2(a1))) % 167.75/167.50 [9682]~P48(x96821,x96822,x96823)+P1(f328(f328(f242(a1),f328(f328(f73(f878(a1,a1),a1,x96821,f262(a1,a1)),f219(x96821)),f230(x96821,x96822,f227(x96821,x96823)))),f2(a1))) % 167.75/167.50 [9809]P47(x98091,x98092,x98093)+~P1(f328(f328(f243(a1),f328(f328(f73(f878(a1,a1),a1,x98091,f262(a1,a1)),f219(x98091)),f230(x98091,x98092,f227(x98091,x98093)))),f2(a1))) % 167.75/167.50 [9810]P48(x98101,x98102,x98103)+~P1(f328(f328(f242(a1),f328(f328(f73(f878(a1,a1),a1,x98101,f262(a1,a1)),f219(x98101)),f230(x98101,x98102,f227(x98101,x98103)))),f2(a1))) % 167.75/167.50 [10131]~P117(x101311)+~P1(f328(f328(f243(x101311),f328(f328(f80(x101311),f328(f328(f253(x101311),x101312),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x101311),x101313),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f2(x101311))) % 167.75/167.50 [4720]~E(x47203,f117(x47201))+E(f328(f328(f125(x47201),x47202),x47203),x47202) % 167.75/167.50 [4721]~E(x47212,f117(x47211))+E(f328(f328(f125(x47211),x47212),x47213),x47213) % 167.75/167.50 [4728]~E(x47282,f2(a872))+E(f328(f328(f173(x47281),x47282),x47283),f117(x47281)) % 167.75/167.50 [4732]~E(x47323,f117(x47321))+E(f328(f328(f173(x47321),x47322),x47323),f117(x47321)) % 167.75/167.50 [4772]~E(x47721,x47723)+E(x47721,f328(f328(f125(x47722),f117(x47722)),x47723)) % 167.75/167.50 [4860]~P101(x48602)+E(f328(f192(f879(x48601,x48602)),x48603),f192(x48602)) % 167.75/167.50 [4861]~P104(x48612)+E(f328(f251(f879(x48611,x48612)),x48613),f251(x48612)) % 167.75/167.50 [4880]E(x48801,f117(x48802))+~E(f328(f328(f125(x48802),x48803),x48801),x48803) % 167.75/167.50 [4881]E(x48811,f117(x48812))+~E(f328(f328(f125(x48812),x48811),x48813),x48813) % 167.75/167.50 [4889]E(x48891,f117(x48892))+~E(f328(f328(f125(x48892),x48893),x48891),f117(x48892)) % 167.75/167.50 [4890]E(x48901,f117(x48902))+~E(f328(f328(f125(x48902),x48901),x48903),f117(x48902)) % 167.75/167.50 [4913]~E(x49132,f2(a872))+E(f328(f328(f81(a872),x49131),x49132),f328(f328(f81(a872),x49133),x49132)) % 167.75/167.50 [4915]~E(x49151,f2(a872))+E(f328(f328(f81(a872),x49151),x49152),f328(f328(f81(a872),x49151),x49153)) % 167.75/167.50 [4968]~P2(x49681)+E(f328(f328(f114(x49681),x49682),x49683),f328(f328(f114(x49681),x49683),x49682)) % 167.75/167.50 [4970]~P99(x49701)+E(f328(f328(f114(x49701),x49702),x49703),f328(f328(f114(x49701),x49703),x49702)) % 167.75/167.50 [4971]~P2(x49711)+E(f328(f328(f105(x49711),x49712),x49713),f328(f328(f105(x49711),x49713),x49712)) % 167.75/167.50 [4973]~P100(x49731)+E(f328(f328(f105(x49731),x49732),x49733),f328(f328(f105(x49731),x49733),x49732)) % 167.75/167.50 [4974]~P111(x49741)+E(f328(f328(f80(x49741),x49742),x49743),f328(f328(f80(x49741),x49743),x49742)) % 167.75/167.50 [4975]~P111(x49751)+E(f328(f328(f81(x49751),x49752),x49753),f328(f328(f81(x49751),x49753),x49752)) % 167.75/167.50 [4977]~P105(x49771)+E(f328(f328(f240(x49771),x49772),x49773),f328(f328(f240(x49771),x49773),x49772)) % 167.75/167.50 [4979]~P105(x49791)+E(f328(f328(f241(x49791),x49792),x49793),f328(f328(f241(x49791),x49793),x49792)) % 167.75/167.50 [5042]E(f46(a872,x50421,x50422),f2(a872))+~E(x50421,f328(f328(f81(a872),x50422),x50423)) % 167.75/167.50 [5043]E(f46(a1,x50431,x50432),f2(a1))+~E(x50431,f328(f328(f81(a1),x50432),x50433)) % 167.75/167.50 [5104]E(x51041,x51042)+~E(f328(f328(f80(a872),x51043),x51041),f328(f328(f80(a872),x51043),x51042)) % 167.75/167.50 [5105]E(x51051,x51052)+~E(f328(f328(f80(a872),x51051),x51053),f328(f328(f80(a872),x51052),x51053)) % 167.75/167.50 [5115]~P94(x51151)+E(f328(f328(f105(x51151),x51152),f328(f79(x51151),x51153)),f328(f328(f22(x51151),x51152),x51153)) % 167.75/167.50 [5116]~P66(x51161)+E(f328(f328(f80(x51161),x51162),f328(f79(x51161),x51163)),f328(f328(f22(x51161),x51162),x51163)) % 167.75/167.50 [5117]~P74(x51171)+E(f328(f328(f80(x51171),x51172),f328(f79(x51171),x51173)),f328(f328(f22(x51171),x51172),x51173)) % 167.75/167.50 [5118]~P115(x51181)+E(f328(f328(f80(x51181),x51182),f328(f79(x51181),x51183)),f328(f328(f22(x51181),x51182),x51183)) % 167.75/167.50 [5119]~P74(x51191)+E(f328(f328(f22(x51191),x51192),f328(f79(x51191),x51193)),f328(f328(f80(x51191),x51192),x51193)) % 167.75/167.50 [5165]~P1(f328(x51653,x51652))+P1(f328(f328(f330(x51651),x51652),x51653)) % 167.75/167.50 [5167]~P67(x51672)+E(f328(f328(f6(x51671,x51672),x51673),f192(f879(x51671,a867))),f2(x51672)) % 167.75/167.50 [5169]~P73(x51692)+E(f328(f328(f9(x51691,x51692),x51693),f192(f879(x51691,a867))),f78(x51692)) % 167.75/167.50 [5218]~E(x52182,f328(f328(f80(a872),x52181),x52183))+P1(f328(f328(f242(a872),x52181),x52182)) % 167.75/167.50 [5221]~E(x52212,f192(f879(x52211,a867)))+E(f328(f328(f62(x52211),x52212),x52213),f192(f879(f879(x52211,a867),a867))) % 167.75/167.50 [5222]~E(x52222,f192(f879(x52221,a867)))+E(f192(f879(f879(x52221,a867),a867)),f328(f328(f62(x52221),x52222),x52223)) % 167.75/167.50 [5298]~E(f328(f259(x52982,x52983),x52981),f192(f879(x52983,a867)))+E(x52981,f192(f879(f878(x52982,x52983),a867))) % 167.75/167.50 [5299]~E(f328(f261(x52992,x52993),x52991),f192(f879(x52992,a867)))+E(x52991,f192(f879(f878(x52992,x52993),a867))) % 167.75/167.50 [5329]E(f328(f259(x53291,x53292),x53293),f192(f879(x53292,a867)))+~E(x53293,f192(f879(f878(x53291,x53292),a867))) % 167.75/167.50 [5330]E(f328(f261(x53301,x53302),x53303),f192(f879(x53301,a867)))+~E(x53303,f192(f879(f878(x53301,x53302),a867))) % 167.75/167.50 [5333]E(f278(x53331,x53332,x53333),f328(f328(f22(a103),x53332),x53333))+P1(f328(f328(f243(a103),x53332),x53333)) % 167.75/167.50 [5349]P1(f328(x53491,x53492))+~P1(f328(f328(f330(x53493),x53492),x53491)) % 167.75/167.50 [5388]E(x53881,x53882)+~E(f328(f79(f879(x53883,a867)),x53881),f328(f79(f879(x53883,a867)),x53882)) % 167.75/167.50 [5393]E(f310(x53931,x53932,x53933),f205(f873(a324)))+~P1(f328(f328(f243(a1),x53932),x53933)) % 167.75/167.50 [5398]~E(x53981,f192(f879(x53982,a867)))+~P1(f328(f328(f330(x53982),x53983),x53981)) % 167.75/167.50 [5427]~E(x54272,f328(f328(f80(a1),x54271),f328(f104(a1),x54273)))+P1(f328(f328(f242(a1),x54271),x54272)) % 167.75/167.50 [5443]E(f328(f328(f306(x54431),x54432),x54433),x54433)+~P1(f328(f328(f330(x54431),x54432),x54433)) % 167.75/167.50 [5454]E(x54541,f192(f879(x54542,a867)))+~E(f328(f328(f62(x54542),x54541),x54543),f192(f879(f879(x54542,a867),a867))) % 167.75/167.50 [5455]E(x54551,f192(f879(x54552,a867)))+~E(f192(f879(f879(x54552,a867),a867)),f328(f328(f62(x54552),x54551),x54553)) % 167.75/167.50 [5462]~P109(x54621)+E(f328(f328(f81(x54621),f328(f79(x54621),x54622)),f328(f79(x54621),x54623)),f328(f328(f81(x54621),x54622),x54623)) % 167.75/167.50 [5463]~P60(x54631)+E(f328(f328(f286(x54631),f328(f79(x54631),x54632)),f328(f79(x54631),x54633)),f328(f328(f286(x54631),x54632),x54633)) % 167.75/167.50 [5495]~P1(f328(x54953,x54952))+P1(f328(f328(f330(x54951),x54952),f328(f248(x54951),x54953))) % 167.75/167.50 [5533]E(f167(x55331,x55332,x55333),x55333)+P1(f328(f328(f330(x55331),x55332),f328(f170(x55331),x55333))) % 167.75/167.50 [5616]~P1(f328(f134(x56161),x56163))+P1(f328(f134(x56161),f328(f133(x56161,x56162),x56163))) % 167.75/167.50 [5661]~P57(x56611)+E(f328(f328(f40(x56611),f46(x56611,x56612,x56613)),x56613),f2(x56611)) % 167.75/167.50 [5680]E(f174(x56801,f328(f328(f148(x56801),x56802),f117(x56801)),x56803),f117(x56801))+P1(f328(f328(f330(a872),f2(a872)),x56803)) % 167.75/167.50 [5686]E(x56861,f2(a872))+E(f328(f169(x56862),f168(x56862,x56861,x56863)),f168(x56862,f328(f328(f22(a872),x56861),f78(a872)),x56863)) % 167.75/167.50 [5738]E(f328(f328(f148(x57381),x57382),x57383),f137(x57381,x57382,x57383))+P1(f328(f328(f330(x57381),x57382),f328(f170(x57381),x57383))) % 167.75/167.50 [5747]E(x57471,x57472)+~E(f328(f328(f81(a872),f328(a116,x57473)),x57471),f328(f328(f81(a872),f328(a116,x57473)),x57472)) % 167.75/167.50 [5748]~E(x57482,f328(f328(f80(a1),x57481),f328(f104(a1),f328(a116,x57483))))+P1(f328(f328(f243(a1),x57481),x57482)) % 167.75/167.50 [5853]~E(x58533,f117(x58531))+E(f328(f328(f328(f187(f873(x58531),f873(x58531)),x58532),f165(x58531)),x58533),f117(x58531)) % 167.75/167.50 [5857]P1(f328(x58571,x58572))+~P1(f328(f328(f330(x58573),x58572),f328(f248(x58573),x58571))) % 167.75/167.50 [5889]E(x58891,x58892)+~E(f328(f328(f306(x58893),x58891),f192(f879(x58893,a867))),f328(f328(f306(x58893),x58892),f192(f879(x58893,a867)))) % 167.75/167.50 [5900]~P107(x59001)+E(f328(f328(f105(f879(x59001,a867)),f328(f249(x59001),x59002)),f328(f298(x59001,x59002),x59003)),f192(f879(x59001,a867))) % 167.75/167.50 [5942]E(f137(x59421,x59422,x59423),x59423)+~P1(f328(f328(f330(x59421),x59422),f328(f170(x59421),x59423))) % 167.75/167.50 [5963]~P77(x59631)+E(f328(f307(x59631,x59631,f79(x59631)),f328(f298(x59631,x59632),x59633)),f301(x59631,f328(f79(x59631),x59633),f328(f79(x59631),x59632))) % 167.75/167.50 [5971]E(f328(f193(f873(x59711)),f167(x59711,x59712,x59713)),f328(f193(f873(x59711)),x59713))+P1(f328(f328(f330(x59711),x59712),f328(f170(x59711),x59713))) % 167.75/167.50 [6023]~P107(x60231)+E(f328(f328(f105(f879(x60231,a867)),f328(f298(x60231,x60232),x60233)),f328(f250(x60231),x60233)),f192(f879(x60231,a867))) % 167.75/167.50 [6046]~P77(x60461)+E(f328(f307(x60461,x60461,f79(x60461)),f302(x60461,x60462,x60463)),f302(x60461,f328(f79(x60461),x60463),f328(f79(x60461),x60462))) % 167.75/167.50 [6047]~P77(x60471)+E(f328(f307(x60471,x60471,f79(x60471)),f299(x60471,x60472,x60473)),f299(x60471,f328(f79(x60471),x60473),f328(f79(x60471),x60472))) % 167.75/167.50 [6104]E(f174(x61041,f328(f328(f148(x61041),x61042),f117(x61041)),x61043),f328(f328(f148(x61041),x61042),f117(x61041)))+~P1(f328(f328(f330(a872),f2(a872)),x61043)) % 167.75/167.50 [6111]~P77(x61111)+E(f328(f307(x61111,x61111,f79(x61111)),f301(x61111,x61112,x61113)),f328(f298(x61111,f328(f79(x61111),x61113)),f328(f79(x61111),x61112))) % 167.75/167.50 [6131]~P58(x61311)+E(f46(x61311,f328(f79(x61311),f46(x61311,x61312,x61313)),x61313),f46(x61311,f328(f79(x61311),x61312),x61313)) % 167.75/167.50 [6238]~P1(f328(f38(f878(x62382,x62381)),x62383))+P1(f328(f38(x62381),f328(f259(x62382,x62381),x62383))) % 167.75/167.50 [6239]~P1(f328(f38(f878(x62391,x62392)),x62393))+P1(f328(f38(x62391),f328(f261(x62391,x62392),x62393))) % 167.75/167.50 [6245]~P107(x62451)+E(f328(f328(f105(f879(x62451,a867)),f302(x62451,x62452,x62453)),f328(f250(x62451),x62453)),f192(f879(x62451,a867))) % 167.75/167.50 [6246]~P107(x62461)+E(f328(f328(f105(f879(x62461,a867)),f301(x62461,x62462,x62463)),f328(f300(x62461),x62463)),f192(f879(x62461,a867))) % 167.75/167.50 [6247]~P107(x62471)+E(f328(f328(f105(f879(x62471,a867)),f299(x62471,x62472,x62473)),f328(f300(x62471),x62473)),f192(f879(x62471,a867))) % 167.75/167.50 [6313]E(f328(f328(f162(x63131),x63132),f648(x63132,x63133,x63131)),x63133)+~P1(f328(f328(f330(x63131),x63133),f328(f170(x63131),x63132))) % 167.75/167.50 [6452]E(x64521,f117(x64522))+~E(f328(f328(f328(f187(f873(x64522),f873(x64522)),x64523),f165(x64522)),x64521),f117(x64522)) % 167.75/167.50 [6553]~P1(f328(f38(f878(x65532,x65531)),x65533))+P1(f328(f38(f878(x65531,x65532)),f328(f283(x65532,x65531),x65533))) % 167.75/167.50 [6705]P52(x67051,x67052,x67053)+P1(f328(f328(f330(x67051),f625(x67053,x67052,x67051)),x67052)) % 167.75/167.50 [6706]P52(x67061,x67062,x67063)+P1(f328(f328(f330(x67061),f624(x67063,x67062,x67061)),x67062)) % 167.75/167.50 [6718]P1(f328(f316(x67181,x67182),x67183))+P1(f328(f328(x67182,f496(x67183,x67182,x67181)),x67183)) % 167.75/167.50 [6719]P1(f328(f316(x67191,x67192),x67193))+P1(f328(f328(x67192,f515(x67193,x67192,x67191)),x67193)) % 167.75/167.50 [6750]E(f328(f193(f873(x67501)),f167(x67501,x67502,x67503)),f328(f328(f22(a872),f328(f193(f873(x67501)),x67503)),f78(a872)))+~P1(f328(f328(f330(x67501),x67502),f328(f170(x67501),x67503))) % 167.75/167.50 [6790]P1(f328(f256(x67901,x67902),x67903))+P1(f328(f328(f330(x67901),f585(x67903,x67902,x67901)),x67903)) % 167.75/167.50 [6801]~P1(f328(f38(f878(x68012,x68011)),f328(f283(x68011,x68012),x68013)))+P1(f328(f38(f878(x68011,x68012)),x68013)) % 167.75/167.50 [6858]~P1(f328(f328(f330(x68581),x68582),f328(f170(x68581),f118(x68581,x68583))))+P1(f328(f328(f330(x68581),x68582),f328(f170(x68581),x68583))) % 167.75/167.50 [6863]P29(x68631,x68632,x68633)+P1(f328(f328(f330(f871(x68631)),f598(x68633,x68632,x68631)),x68633)) % 167.75/167.50 [6891]E(f328(f133(x68911,x68912),x68913),x68913)+P1(f328(f328(f330(x68911),f729(x68913,x68912,x68911)),f328(f170(x68911),x68913))) % 167.75/167.50 [6906]E(f328(f133(x69061,x69062),x69063),f117(x69061))+P1(f328(f328(f330(x69061),f728(x69063,x69062,x69061)),f328(f170(x69061),x69063))) % 167.75/167.50 [6929]P32(x69291,x69292,x69293)+P1(f328(f328(f330(x69291),f799(x69293,x69292,x69291)),f328(f170(x69291),x69293))) % 167.75/167.50 [6930]P32(x69301,x69302,x69303)+P1(f328(f328(f330(x69301),f801(x69303,x69302,x69301)),f328(f170(x69301),x69303))) % 167.75/167.50 [6931]P32(x69311,x69312,x69313)+P1(f328(f328(f330(x69311),f793(x69312,x69313,x69311)),f328(f170(x69311),x69313))) % 167.75/167.50 [6934]E(f175(x69341,x69342,x69343),x69343)+P1(f328(f328(f330(x69341),f750(x69343,x69342,x69341)),f328(f170(x69341),x69343))) % 167.75/167.50 [7013]P1(f328(f157(x70131,x70132),x70133))+P1(f328(f328(f330(x70131),f720(x70133,x70132,x70131)),f328(f170(x70131),x70133))) % 167.75/167.50 [7022]~P34(x70221,x70223,x70222)+P1(f328(f328(f330(x70221),f776(x70222,x70223,x70221)),f328(f170(x70221),x70222))) % 167.75/167.50 [7023]~P36(x70231,x70233,x70232)+P1(f328(f328(f330(x70231),f805(x70232,x70233,x70231)),f328(f170(x70231),x70232))) % 167.75/167.50 [7058]P1(f328(f328(f330(x70581),x70582),f650(x70583,x70582,x70581)))+~P1(f328(f328(f330(x70581),x70582),f41(f879(x70581,a867),x70583))) % 167.75/167.50 [7059]~P67(x70591)+E(f328(f328(f80(x70591),f328(f328(f6(a872,x70591),x70592),f328(f249(a872),x70593))),f328(x70592,x70593)),f328(f328(f6(a872,x70591),x70592),f328(f249(a872),f328(a116,x70593)))) % 167.75/167.50 [7148]~P34(x71482,x71481,x71483)+P1(f328(x71481,f328(f328(f162(x71482),x71483),f789(x71483,x71481,x71482)))) % 167.75/167.50 [7161]~P1(f328(f328(f330(x71611),x71612),f497(x71612,x71613,x71611)))+P1(f328(f328(f330(x71611),x71612),f42(f879(x71611,a867),x71613))) % 167.75/167.50 [7193]~P67(x71931)+E(f328(f328(f80(x71931),f328(f328(f6(a872,x71931),x71932),f328(f297(a872),x71933))),f328(x71932,f328(a116,x71933))),f328(f328(f6(a872,x71931),x71932),f328(f297(a872),f328(a116,x71933)))) % 167.75/167.50 [7328]P1(f328(f328(f330(f873(x73281)),x73282),f158(x73281,x73283)))+P1(f328(f328(f330(x73281),f673(x73283,x73282,x73281)),f328(f170(x73281),x73282))) % 167.75/167.50 [7345]~P1(f328(f328(f330(f873(x73451)),x73452),f158(x73451,f317(x73451,x73453))))+P1(f328(f328(f330(f873(x73451)),x73452),f317(f873(x73451),f154(x73451,x73453)))) % 167.75/167.50 [7370]~P1(f328(f328(f330(f873(x73701)),x73702),f317(f873(x73701),f154(x73701,x73703))))+P1(f328(f328(f330(f873(x73701)),x73702),f158(x73701,f317(x73701,x73703)))) % 167.75/167.50 [7406]E(f328(f328(f328(f187(f873(x74061),f873(x74061)),x74062),f165(x74061)),x74063),x74063)+~P1(f328(f328(f242(a872),f328(f193(f873(x74061)),x74063)),f78(a872))) % 167.75/167.50 [7441]E(f328(f328(f125(x74411),f791(x74412,x74413,x74411)),f328(f328(f148(x74411),x74413),f792(x74412,x74413,x74411))),x74412)+~P1(f328(f328(f330(x74411),x74413),f328(f170(x74411),x74412))) % 167.75/167.50 [7442]E(f328(f328(f125(x74421),f795(x74422,x74423,x74421)),f328(f328(f148(x74421),x74423),f796(x74422,x74423,x74421))),x74422)+~P1(f328(f328(f330(x74421),x74423),f328(f170(x74421),x74422))) % 167.75/167.50 [7443]E(f328(f328(f125(x74431),f797(x74432,x74433,x74431)),f328(f328(f148(x74431),x74433),f798(x74432,x74433,x74431))),x74432)+~P1(f328(f328(f330(x74431),x74433),f328(f170(x74431),x74432))) % 167.75/167.50 [7467]~P26(x74671,x74672,x74673,f251(f879(x74671,a867)))+P26(f873(x74671),f873(x74672),f328(f151(x74671,x74672),x74673),f251(f879(f873(x74671),a867))) % 167.75/167.50 [7617]E(x76171,f328(f328(f80(a872),f328(f328(f81(a872),f328(f262(a872,a872),x76172)),x76173)),f328(f266(a872,a872),x76172)))+~P1(f328(f49(x76171,x76173),x76172)) % 167.75/167.50 [7625]P26(x76251,x76252,x76253,f251(f879(x76251,a867)))+~P26(f873(x76251),f873(x76252),f328(f151(x76251,x76252),x76253),f251(f879(f873(x76251),a867))) % 167.75/167.50 [7668]P1(f328(f328(f330(f879(x76681,a867)),f497(x76682,x76683,x76681)),x76683))+P1(f328(f328(f330(x76681),x76682),f42(f879(x76681,a867),x76683))) % 167.75/167.50 [7762]P1(f328(f328(f330(f873(x77621)),x77622),f158(x77621,x77623)))+~P1(f328(f328(f330(x77621),f673(x77623,x77622,x77621)),x77623)) % 167.75/167.50 [7804]P1(f328(f328(f328(f328(a200,x78041),x78042),f473(x78043,x78042,x78041)),x78043))+~P1(f328(f328(f328(a198,x78041),x78042),x78043)) % 167.75/167.50 [7864]P32(x78641,x78642,x78643)+~P1(f328(x78642,f328(f328(f162(x78641),x78643),f794(x78643,x78642,x78641)))) % 167.75/167.50 [7889]E(x78891,x78892)+~E(f328(f328(f7(x78893,f879(x78893,a867),a867),f330(x78893)),x78891),f328(f328(f7(x78893,f879(x78893,a867),a867),f330(x78893)),x78892)) % 167.75/167.50 [7895]~P1(f328(f328(f330(f878(x78951,x78951)),x78953),f260(x78951,x78952)))+P1(f328(f328(f330(x78951),f531(x78952,x78953,x78951)),x78952)) % 167.75/167.50 [7897]~P1(f328(f328(f330(x78971),x78973),f41(f879(x78971,a867),x78972)))+P1(f328(f328(f330(f879(x78971,a867)),f650(x78972,x78973,x78971)),x78972)) % 167.75/167.50 [8071]~P1(f328(f328(f330(x80711),x80712),f328(f170(x80711),f795(x80713,x80712,x80711))))+~P1(f328(f328(f330(x80711),x80712),f328(f170(x80711),x80713))) % 167.75/167.50 [8072]~P1(f328(f328(f330(x80721),x80722),f328(f170(x80721),f798(x80723,x80722,x80721))))+~P1(f328(f328(f330(x80721),x80722),f328(f170(x80721),x80723))) % 167.75/167.50 [8166]E(f328(f237(f876(f873(a324)),f873(a324),f310(x81661,x81662,f328(f328(f80(a1),x81663),f78(a1))),f235(f873(a324))),f328(x81661,x81663)),f310(x81661,x81662,x81663))+P1(f328(f328(f243(a1),x81662),x81663)) % 167.75/167.50 [8272]E(x82721,f117(x82722))+P1(f328(f328(f330(x82722),f328(f262(x82722,f878(a103,a103)),f328(f279(x82722,x82721),x82723))),f328(f170(x82722),x82721))) % 167.75/167.50 [8369]~P68(x83691)+E(f328(f139(x83691,x83691,f328(f7(x83691,x83691,x83691),f80(x83691)),x83692),f328(f166(x83691),x83693)),f328(f139(x83691,x83691,f80(x83691),x83692),x83693)) % 167.75/167.50 [8862]~P105(x88621)+E(f328(f170(x88621),f146(x88621,x88621,f5(x88621),x88622,x88623)),f328(f328(f306(x88621),x88622),f328(f170(x88621),x88623))) % 167.75/167.50 [8873]P1(f328(f328(f243(a872),f2(a872)),f633(x88731,x88732,x88733)))+~P1(f328(f328(f330(f878(x88733,x88733)),x88732),f328(f328(f285(x88733,x88733,x88733),x88731),f304(x88733,x88731)))) % 167.75/167.50 [9162]~P54(x91621,x91622)+~P1(f328(f328(f330(f878(x91621,x91621)),f328(f328(f263(x91621,x91621),x91623),x91623)),f328(f328(f285(x91621,x91621,x91621),x91622),f304(x91621,x91622)))) % 167.75/167.50 [9294]~E(f328(f328(f105(f879(f878(x92941,x92941),a867)),f328(f283(x92941,x92941),x92942)),f304(x92941,x92942)),f192(f879(f878(x92941,x92941),a867)))+~P1(f328(f328(f330(f878(x92941,x92941)),f328(f328(f263(x92941,x92941),x92943),x92943)),f328(f328(f285(x92941,x92941,x92941),x92942),f304(x92941,x92942)))) % 167.75/167.50 [9473]~P1(f328(f38(x94731),x94732))+P1(f328(f328(f242(a872),f328(f39(x94731),f328(f328(f22(f879(x94731,a867)),x94732),f328(f328(f306(x94731),x94733),f192(f879(x94731,a867)))))),f328(f39(x94731),x94732))) % 167.75/167.50 [5031]~E(x50313,f117(x50311))+E(f141(x50311,f328(f328(f148(x50311),x50312),x50313)),x50312) % 167.75/167.50 [5039]~E(x50393,f117(x50391))+E(f118(x50391,f328(f328(f148(x50391),x50392),x50393)),f117(x50391)) % 167.75/167.50 [5068]E(x50681,f117(x50682))+E(f141(x50682,f328(f328(f148(x50682),x50683),x50681)),f141(x50682,x50681)) % 167.75/167.50 [5070]E(x50701,f117(x50702))+E(f141(x50702,f328(f328(f125(x50702),x50703),x50701)),f141(x50702,x50701)) % 167.75/167.50 [5075]~E(x50753,f117(x50751))+E(f118(x50751,f328(f328(f125(x50751),x50752),x50753)),f118(x50751,x50752)) % 167.75/167.50 [5077]~E(x50773,f117(x50771))+E(f141(x50771,f328(f328(f125(x50771),x50772),x50773)),f141(x50771,x50772)) % 167.75/167.50 [5109]E(x51091,f117(x51092))+E(f328(f138(x51092),f328(f328(f125(x51092),x51091),x51093)),f328(f138(x51092),x51091)) % 167.75/167.50 [5139]~E(x51392,f117(x51391))+E(f328(f138(x51391),f328(f328(f125(x51391),x51392),x51393)),f328(f138(x51391),x51393)) % 167.75/167.50 [5194]~P2(x51941)+E(f328(f328(f114(x51941),x51942),f328(f328(f105(x51941),x51942),x51943)),x51942) % 167.75/167.50 [5195]~P2(x51951)+E(f328(f328(f105(x51951),x51952),f328(f328(f114(x51951),x51952),x51953)),x51952) % 167.75/167.50 [5196]~P105(x51961)+E(f328(f328(f240(x51961),x51962),f328(f328(f241(x51961),x51962),x51963)),x51962) % 167.75/167.50 [5197]~P105(x51971)+E(f328(f328(f241(x51971),x51972),f328(f328(f240(x51971),x51972),x51973)),x51972) % 167.75/167.50 [5216]~P57(x52161)+E(f46(x52161,f328(f328(f81(x52161),x52162),x52163),x52163),f2(x52161)) % 167.75/167.50 [5217]~P57(x52171)+E(f46(x52171,f328(f328(f81(x52171),x52172),x52173),x52172),f2(x52171)) % 167.75/167.50 [5292]~P66(x52921)+E(f328(f79(x52921),f328(f328(f22(x52921),x52922),x52923)),f328(f328(f22(x52921),x52923),x52922)) % 167.75/167.50 [5353]E(x53531,f117(x53532))+E(f118(x53532,f328(f328(f148(x53532),x53533),x53531)),f328(f328(f148(x53532),x53533),f118(x53532,x53531))) % 167.75/167.50 [5354]E(x53541,f117(x53542))+E(f118(x53542,f328(f328(f125(x53542),x53543),x53541)),f328(f328(f125(x53542),x53543),f118(x53542,x53541))) % 167.75/167.50 [5357]~P4(x53571)+E(f42(x53571,f328(f328(f306(x53571),x53572),x53573)),f328(f328(f105(x53571),x53572),f42(x53571,x53573))) % 167.75/167.50 [5358]~P4(x53581)+E(f41(x53581,f328(f328(f306(x53581),x53582),x53583)),f328(f328(f114(x53581),x53582),f41(x53581,x53583))) % 167.75/167.50 [5403]~P2(x54031)+E(f328(f328(f114(x54031),x54032),f328(f328(f114(x54031),x54032),x54033)),f328(f328(f114(x54031),x54032),x54033)) % 167.75/167.50 [5405]~P99(x54051)+E(f328(f328(f114(x54051),x54052),f328(f328(f114(x54051),x54052),x54053)),f328(f328(f114(x54051),x54052),x54053)) % 167.75/167.50 [5406]~P2(x54061)+E(f328(f328(f105(x54061),x54062),f328(f328(f105(x54061),x54062),x54063)),f328(f328(f105(x54061),x54062),x54063)) % 167.75/167.50 [5408]~P100(x54081)+E(f328(f328(f105(x54081),x54082),f328(f328(f105(x54081),x54082),x54083)),f328(f328(f105(x54081),x54082),x54083)) % 167.75/167.50 [5409]~P95(x54091)+E(f328(f328(f81(x54091),x54092),f328(f328(f81(x54091),x54092),x54093)),f328(f328(f81(x54091),x54092),x54093)) % 167.75/167.50 [5411]~P105(x54111)+E(f328(f328(f240(x54111),x54112),f328(f328(f240(x54111),x54112),x54113)),f328(f328(f240(x54111),x54112),x54113)) % 167.75/167.50 [5413]~P105(x54131)+E(f328(f328(f241(x54131),x54132),f328(f328(f241(x54131),x54132),x54133)),f328(f328(f241(x54131),x54132),x54133)) % 167.75/167.50 [5421]~P57(x54211)+E(f46(x54211,f328(f328(f80(x54211),x54212),x54213),x54213),f46(x54211,x54212,x54213)) % 167.75/167.50 [5422]~P57(x54221)+E(f46(x54221,f328(f328(f80(x54221),x54222),x54223),x54222),f46(x54221,x54223,x54222)) % 167.75/167.50 [5428]~P109(x54281)+E(f328(f328(f81(x54281),x54282),f328(f79(x54281),x54283)),f328(f79(x54281),f328(f328(f81(x54281),x54282),x54283))) % 167.75/167.50 [5429]~P60(x54291)+E(f328(f328(f286(x54291),x54292),f328(f79(x54291),x54293)),f328(f79(x54291),f328(f328(f286(x54291),x54292),x54293))) % 167.75/167.50 [5430]~P79(x54301)+E(f328(f328(f80(x54301),x54302),f328(f163(x54301),x54303)),f328(f163(x54301),f328(f328(f148(x54301),x54302),x54303))) % 167.75/167.50 [5460]~P109(x54601)+E(f328(f328(f81(x54601),f328(f79(x54601),x54602)),x54603),f328(f328(f81(x54601),x54602),f328(f79(x54601),x54603))) % 167.75/167.50 [5466]~P7(x54661,x54662,x54663)+E(f41(f879(x54661,a867),f328(f328(f62(x54661),x54662),x54663)),x54662) % 167.75/167.50 [5525]~P113(x55251)+E(f328(f328(f81(x55251),x55252),f328(f328(f253(x55251),x55252),x55253)),f328(f328(f253(x55251),x55252),f328(a116,x55253))) % 167.75/167.50 [5526]~P111(x55261)+E(f328(f328(f81(x55261),x55262),f328(f328(f253(x55261),x55262),x55263)),f328(f328(f253(x55261),x55262),f328(a116,x55263))) % 167.75/167.50 [5536]~P74(x55361)+E(f328(f328(f80(x55361),f328(f79(x55361),x55362)),f328(f328(f80(x55361),x55362),x55363)),x55363) % 167.75/167.50 [5559]~P142(x55591)+E(f328(f328(f253(x55591),f328(f104(x55591),x55592)),x55593),f328(f104(x55591),f328(f328(f253(a872),x55592),x55593))) % 167.75/167.50 [5560]~P138(x55601)+E(f328(f328(f253(x55601),f328(f106(x55601),x55602)),x55603),f328(f106(x55601),f328(f328(f253(a1),x55602),x55603))) % 167.75/167.50 [5566]~P84(x55661)+E(f328(f75(x55661),f328(f328(f22(x55661),x55662),x55663)),f328(f75(x55661),f328(f328(f22(x55661),x55663),x55662))) % 167.75/167.50 [5568]~P117(x55681)+E(f328(f328(f81(x55681),f82(x55681,x55682)),f82(x55681,x55683)),f82(x55681,f328(f328(f81(x55681),x55682),x55683))) % 167.75/167.50 [5572]E(x55721,f117(x55722))+E(f328(f328(f125(x55722),f328(f169(x55722),x55721)),x55723),f328(f169(x55722),f328(f328(f125(x55722),x55721),x55723))) % 167.75/167.50 [5578]~E(x55782,f328(a116,f328(f328(f80(a872),x55781),x55783)))+P1(f328(f328(f243(a872),x55781),x55782)) % 167.75/167.50 [5579]~P117(x55791)+E(f328(f328(f253(x55791),f328(f75(x55791),x55792)),x55793),f328(f75(x55791),f328(f328(f253(x55791),x55792),x55793))) % 167.75/167.50 [5580]~P109(x55801)+E(f328(f328(f81(x55801),f328(f79(x55801),x55802)),x55803),f328(f79(x55801),f328(f328(f81(x55801),x55802),x55803))) % 167.75/167.50 [5581]~P120(x55811)+E(f328(f328(f286(x55811),f328(f79(x55811),x55812)),x55813),f328(f79(x55811),f328(f328(f286(x55811),x55812),x55813))) % 167.75/167.50 [5679]E(f689(x56791,x56792,x56793),f703(x56791,x56792,x56793))+E(f328(f328(f105(f879(x56793,a867)),x56792),x56791),f192(f879(x56793,a867))) % 167.75/167.50 [5694]~P67(x56942)+E(f328(f328(f6(x56941,x56942),f328(f16(x56942,x56941),f2(x56942))),x56943),f2(x56942)) % 167.75/167.50 [5695]~P73(x56952)+E(f328(f328(f9(x56951,x56952),f328(f16(x56952,x56951),f78(x56952))),x56953),f78(x56952)) % 167.75/167.50 [5697]~P142(x56971)+E(f328(f328(f80(x56971),f328(f104(x56971),x56972)),f328(f104(x56971),x56973)),f328(f104(x56971),f328(f328(f80(a872),x56972),x56973))) % 167.75/167.50 [5698]~P142(x56981)+E(f328(f328(f81(x56981),f328(f104(x56981),x56982)),f328(f104(x56981),x56983)),f328(f104(x56981),f328(f328(f81(a872),x56982),x56983))) % 167.75/167.50 [5699]~P138(x56991)+E(f328(f328(f22(x56991),f328(f106(x56991),x56992)),f328(f106(x56991),x56993)),f328(f106(x56991),f328(f328(f22(a1),x56992),x56993))) % 167.75/167.50 [5700]~P138(x57001)+E(f328(f328(f80(x57001),f328(f106(x57001),x57002)),f328(f106(x57001),x57003)),f328(f106(x57001),f328(f328(f80(a1),x57002),x57003))) % 167.75/167.50 [5701]~P138(x57011)+E(f328(f328(f81(x57011),f328(f106(x57011),x57012)),f328(f106(x57011),x57013)),f328(f106(x57011),f328(f328(f81(a1),x57012),x57013))) % 167.75/167.50 [5702]~P91(x57021)+E(f328(f328(f22(x57021),f328(f107(x57021),x57022)),f328(f107(x57021),x57023)),f328(f107(x57021),f328(f328(f22(a1),x57022),x57023))) % 167.75/167.50 [5705]~P91(x57051)+E(f328(f328(f80(x57051),f328(f107(x57051),x57052)),f328(f107(x57051),x57053)),f328(f107(x57051),f328(f328(f80(a1),x57052),x57053))) % 167.75/167.50 [5706]~P91(x57061)+E(f328(f328(f81(x57061),f328(f107(x57061),x57062)),f328(f107(x57061),x57063)),f328(f107(x57061),f328(f328(f81(a1),x57062),x57063))) % 167.75/167.50 [5755]~E(x57553,x57552)+P1(f328(f328(f242(f879(x57551,a867)),x57552),x57553)) % 167.75/167.50 [5761]~E(x57612,x57613)+P1(f328(f328(f242(f879(x57611,a867)),x57612),x57613)) % 167.75/167.50 [5766]~P117(x57661)+E(f328(f328(f81(x57661),f328(f75(x57661),x57662)),f328(f75(x57661),x57663)),f328(f75(x57661),f328(f328(f81(x57661),x57662),x57663))) % 167.75/167.50 [5767]~P62(x57671)+E(f328(f328(f286(x57671),f328(f75(x57671),x57672)),f328(f75(x57671),x57673)),f328(f75(x57671),f328(f328(f286(x57671),x57672),x57673))) % 167.75/167.50 [5768]~P94(x57681)+E(f328(f328(f105(x57681),f328(f79(x57681),x57682)),f328(f79(x57681),x57683)),f328(f79(x57681),f328(f328(f114(x57681),x57682),x57683))) % 167.75/167.50 [5769]~P94(x57691)+E(f328(f328(f114(x57691),f328(f79(x57691),x57692)),f328(f79(x57691),x57693)),f328(f79(x57691),f328(f328(f105(x57691),x57692),x57693))) % 167.75/167.50 [5770]~P74(x57701)+E(f328(f328(f80(x57701),f328(f79(x57701),x57702)),f328(f79(x57701),x57703)),f328(f79(x57701),f328(f328(f80(x57701),x57703),x57702))) % 167.75/167.50 [5771]~P66(x57711)+E(f328(f328(f80(x57711),f328(f79(x57711),x57712)),f328(f79(x57711),x57713)),f328(f79(x57711),f328(f328(f80(x57711),x57712),x57713))) % 167.75/167.50 [5772]~P75(x57721)+E(f328(f328(f241(x57721),f328(f79(x57721),x57722)),f328(f79(x57721),x57723)),f328(f79(x57721),f328(f328(f240(x57721),x57722),x57723))) % 167.75/167.50 [5773]~P75(x57731)+E(f328(f328(f240(x57731),f328(f79(x57731),x57732)),f328(f79(x57731),x57733)),f328(f79(x57731),f328(f328(f241(x57731),x57732),x57733))) % 167.75/167.50 [5774]~P79(x57741)+E(f328(f328(f80(x57741),f328(f163(x57741),x57742)),f328(f163(x57741),x57743)),f328(f163(x57741),f328(f328(f125(x57741),x57742),x57743))) % 167.75/167.50 [5775]E(x57751,f192(f879(x57752,a867)))+~E(f328(f328(f114(f879(x57752,a867)),x57753),x57751),f192(f879(x57752,a867))) % 167.75/167.50 [5776]E(x57761,f192(f879(x57762,a867)))+~E(f328(f328(f114(f879(x57762,a867)),x57761),x57763),f192(f879(x57762,a867))) % 167.75/167.50 [5777]~P145(x57771,x57772,x57773)+P1(f328(x57771,f328(f328(f40(a1),x57772),x57773))) % 167.75/167.50 [5827]~P1(f328(f38(x58271),x58273))+P1(f328(f38(x58271),f328(f328(f306(x58271),x58272),x58273))) % 167.75/167.50 [5828]~P1(f328(f134(x58281),x58283))+P1(f328(f134(x58281),f328(f328(f173(x58281),x58282),x58283))) % 167.75/167.50 [5829]~P1(f328(f134(x58291),x58293))+P1(f328(f134(x58291),f328(f328(f135(x58291),x58292),x58293))) % 167.75/167.50 [5858]~P2(x58581)+P1(f328(f328(f242(x58581),x58582),f328(f328(f114(x58581),x58583),x58582))) % 167.75/167.50 [5859]~P99(x58591)+P1(f328(f328(f242(x58591),x58592),f328(f328(f114(x58591),x58593),x58592))) % 167.75/167.50 [5860]~P2(x58601)+P1(f328(f328(f242(x58601),x58602),f328(f328(f114(x58601),x58602),x58603))) % 167.75/167.50 [5861]~P99(x58611)+P1(f328(f328(f242(x58611),x58612),f328(f328(f114(x58611),x58612),x58613))) % 167.75/167.50 [5862]~P105(x58621)+P1(f328(f328(f242(x58621),x58622),f328(f328(f241(x58621),x58623),x58622))) % 167.75/167.50 [5863]~P105(x58631)+P1(f328(f328(f242(x58631),x58632),f328(f328(f241(x58631),x58632),x58633))) % 167.75/167.50 [5877]~E(x58771,f2(a872))+E(f328(f328(f40(a872),f328(f328(f81(a872),x58771),x58772)),f328(f328(f81(a872),x58771),x58773)),f2(a872)) % 167.75/167.50 [5958]~P91(x59581)+E(f328(f328(f22(x59581),f328(f107(x59581),x59582)),f328(f107(x59581),x59583)),f328(f107(x59581),f328(f328(f80(a1),x59582),f328(f79(a1),x59583)))) % 167.75/167.50 [6010]E(x60101,f2(a872))+E(f328(f328(f40(a872),f328(f328(f81(a872),x60101),x60102)),f328(f328(f81(a872),x60101),x60103)),f328(f328(f40(a872),x60102),x60103)) % 167.75/167.50 [6044]E(f149(x60441,f328(f328(f148(x60441),x60442),x60443)),f328(f328(f148(x60441),x60442),f149(x60441,x60443)))+P1(f328(f328(f330(x60441),x60442),f328(f170(x60441),x60443))) % 167.75/167.50 [6078]P145(x60781,x60782,x60783)+~P1(f328(x60781,f328(f328(f40(a1),x60782),x60783))) % 167.75/167.50 [6153]E(x61531,f117(x61532))+E(f328(f328(f148(x61532),f328(f138(x61532),x61531)),f328(f328(f173(x61532),x61533),f328(f169(x61532),x61531))),f328(f328(f173(x61532),f328(a116,x61533)),x61531)) % 167.75/167.50 [6158]P1(f328(x61581,x61582))+P1(f328(f328(f328(a198,f32(x61581,x61583)),x61582),x61582)) % 167.75/167.50 [6161]E(f328(f328(f22(f879(x61611,a867)),x61612),x61613),x61612)+~E(f328(f328(f105(f879(x61611,a867)),x61612),x61613),f192(f879(x61611,a867))) % 167.75/167.50 [6176]E(f149(x61761,f328(f328(f148(x61761),x61762),x61763)),f149(x61761,x61763))+~P1(f328(f328(f330(x61761),x61762),f328(f170(x61761),x61763))) % 167.75/167.50 [6208]~P1(f328(f328(f243(a872),x62081),x62083))+P1(f328(f328(f243(a872),x62081),f328(f328(f80(a872),x62082),x62083))) % 167.75/167.50 [6210]~P1(f328(f328(f243(a872),x62101),x62102))+P1(f328(f328(f243(a872),x62101),f328(f328(f80(a872),x62102),x62103))) % 167.75/167.50 [6212]~P1(f328(f328(f242(a872),x62121),x62123))+P1(f328(f328(f242(a872),x62121),f328(f328(f80(a872),x62122),x62123))) % 167.75/167.50 [6214]~P1(f328(f328(f242(a872),x62141),x62142))+P1(f328(f328(f242(a872),x62141),f328(f328(f80(a872),x62142),x62143))) % 167.75/167.50 [6253]P1(f328(f38(x62531),x62532))+~P1(f328(f38(x62531),f328(f328(f306(x62531),x62533),x62532))) % 167.75/167.50 [6254]P1(f328(f134(x62541),x62542))+~P1(f328(f134(x62541),f328(f328(f148(x62541),x62543),x62542))) % 167.75/167.50 [6255]P1(f328(f134(x62551),x62552))+~P1(f328(f134(x62551),f328(f328(f125(x62551),x62553),x62552))) % 167.75/167.50 [6256]P1(f328(f134(x62561),x62562))+~P1(f328(f134(x62561),f328(f328(f125(x62561),x62562),x62563))) % 167.75/167.50 [6302]~P111(x63021)+E(f328(f328(f80(x63021),x63022),f328(f328(f81(x63021),x63023),x63022)),f328(f328(f81(x63021),f328(f328(f80(x63021),x63023),f78(x63021))),x63022)) % 167.75/167.50 [6348]~E(x63481,x63482)+~P1(f328(f328(f243(f879(x63483,a867)),x63481),x63482)) % 167.75/167.50 [6392]P1(f328(f328(f330(x63921),x63922),x63923))+P1(f328(f328(f330(x63921),x63922),f328(f79(f879(x63921,a867)),x63923))) % 167.75/167.50 [6398]E(f141(x63981,f328(f328(f135(x63981),x63982),x63983)),f141(x63981,x63983))+~P1(f328(f328(f243(a872),x63982),f328(f193(f873(x63981)),x63983))) % 167.75/167.50 [6399]E(f328(f328(f173(x63991),x63992),f118(x63991,x63993)),f328(f328(f173(x63991),x63992),x63993))+~P1(f328(f328(f243(a872),x63992),f328(f193(f873(x63991)),x63993))) % 167.75/167.50 [6454]E(f328(f328(f328(f187(f873(x64541),f873(x64541)),x64542),f165(x64541)),x64543),x64543)+~E(f46(a872,x64542,f328(f193(f873(x64541)),x64543)),f2(a872)) % 167.75/167.50 [6461]~P7(x64611,x64613,x64612)+E(f328(f328(f285(x64611,x64611,x64611),f328(f283(x64611,x64611),x64612)),x64612),x64612) % 167.75/167.50 [6503]~E(f328(f328(f114(f879(x65031,a867)),x65032),x65033),x65033)+P1(f328(f328(f242(f879(x65031,a867)),x65032),x65033)) % 167.75/167.50 [6508]~P51(x65081,x65081,x65083)+P51(x65081,x65081,f328(f328(f187(f878(x65081,x65081),a867),x65082),x65083)) % 167.75/167.50 [6510]~P1(f328(f328(f330(x65101),x65103),f328(f170(x65101),x65102)))+P1(f328(f328(f243(a872),f2(a872)),f328(f193(f873(x65101)),x65102))) % 167.75/167.50 [6536]~P84(x65361)+E(f328(f75(x65361),f328(f328(f80(x65361),f328(f75(x65361),x65362)),f328(f75(x65361),x65363))),f328(f328(f80(x65361),f328(f75(x65361),x65362)),f328(f75(x65361),x65363))) % 167.75/167.50 [6546]E(f328(f328(f40(a872),f328(f328(f81(a872),x65461),x65462)),f328(f328(f81(a872),x65461),x65463)),f328(f328(f40(a872),x65462),x65463))+~P1(f328(f328(f243(a872),f2(a872)),x65461)) % 167.75/167.50 [6594]E(x65941,x65942)+~P1(f328(f328(f328(f328(a200,a24),x65941),x65943),x65942)) % 167.75/167.50 [6684]~P1(f328(f38(x66841),x66843))+E(f328(f328(f65(x66841,f879(x66841,a867),f306(x66841)),x66842),x66843),f328(f328(f114(f879(x66841,a867)),x66843),x66842)) % 167.75/167.50 [6743]E(f328(f328(f114(f879(x67431,a867)),x67432),x67433),x67432)+~P1(f328(f328(f242(f879(x67431,a867)),x67433),x67432)) % 167.75/167.50 [6745]E(f328(f328(f114(f879(x67451,a867)),x67452),x67453),x67453)+~P1(f328(f328(f242(f879(x67451,a867)),x67452),x67453)) % 167.75/167.50 [6746]E(f328(f328(f105(f879(x67461,a867)),x67462),x67463),x67463)+~P1(f328(f328(f242(f879(x67461,a867)),x67463),x67462)) % 167.75/167.50 [6747]E(f328(f328(f105(f879(x67471,a867)),x67472),x67473),x67472)+~P1(f328(f328(f242(f879(x67471,a867)),x67472),x67473)) % 167.75/167.50 [6799]~P1(f328(f134(x67991),x67992))+E(f328(f328(f22(f879(x67991,a867)),f328(f170(x67991),x67992)),f328(f328(f306(x67991),x67993),f192(f879(x67991,a867)))),f328(f170(x67991),f167(x67991,x67993,x67992))) % 167.75/167.50 [6852]P38(x68521,x68522)+~P38(x68521,f328(f328(f187(f878(x68521,x68521),a867),x68523),x68522)) % 167.75/167.50 [6917]P1(f328(f50(x69171,x69172),f328(a52,x69173)))+~P1(f328(f50(f328(f79(a1),x69171),f328(f79(a1),x69172)),x69173)) % 167.75/167.50 [6922]E(f328(f328(f22(f879(x69221,a867)),f328(f328(f306(x69221),x69222),x69223)),f328(f328(f306(x69221),x69222),f192(f879(x69221,a867)))),x69223)+P1(f328(f328(f330(x69221),x69222),x69223)) % 167.75/167.50 [6943]E(f328(f328(f105(f879(x69431,a867)),f328(f170(x69431),x69432)),f328(f170(x69431),x69433)),f192(f879(x69431,a867)))+~P1(f328(f134(x69431),f328(f328(f125(x69431),x69432),x69433))) % 167.75/167.50 [6959]~P1(f328(f328(f330(x69591),x69592),f328(f170(x69591),x69593)))+~P1(f328(f134(x69591),f328(f328(f148(x69591),x69592),x69593))) % 167.75/167.50 [7029]P32(x70291,x70292,x70293)+P1(f328(f328(f243(a872),f794(x70293,x70292,x70291)),f328(f193(f873(x70291)),x70293))) % 167.75/167.50 [7039]E(f328(f328(f105(f879(x70391,a867)),x70392),x70393),f192(f879(x70391,a867)))+P1(f328(f328(f330(x70391),f689(x70393,x70392,x70391)),x70392)) % 167.75/167.50 [7040]E(f328(f328(f105(f879(x70401,a867)),x70402),x70403),f192(f879(x70401,a867)))+P1(f328(f328(f330(x70401),f703(x70403,x70402,x70401)),x70403)) % 167.75/167.50 [7044]E(f118(x70441,f328(f328(f173(x70441),x70442),x70443)),f328(f328(f173(x70441),f328(f328(f22(a872),x70442),f78(a872))),x70443))+~P1(f328(f328(f242(a872),x70442),f328(f193(f873(x70441)),x70443))) % 167.75/167.50 [7103]~P34(x71033,x71032,x71031)+P1(f328(f328(f243(a872),f789(x71031,x71032,x71033)),f328(f193(f873(x71033)),x71031))) % 167.75/167.50 [7121]P1(f328(f328(f243(a872),f2(a872)),x71211))+P1(f328(f328(f242(a872),f328(f328(f81(a872),x71212),x71211)),f328(f328(f81(a872),x71213),x71211))) % 167.75/167.50 [7122]P1(f328(f328(f243(a872),f2(a872)),x71221))+P1(f328(f328(f242(a872),f328(f328(f81(a872),x71221),x71222)),f328(f328(f81(a872),x71221),x71223))) % 167.75/167.50 [7125]~P1(f328(f328(f330(x71251),x71252),x71253))+~P1(f328(f328(f330(x71251),x71252),f328(f79(f879(x71251,a867)),x71253))) % 167.75/167.50 [7132]~P1(f328(f328(f243(f879(x71321,a867)),x71322),x71323))+P1(f328(f328(f242(f879(x71321,a867)),x71322),x71323)) % 167.75/167.50 [7233]~P1(f328(f328(f243(a872),x72332),x72333))+P1(f328(f328(f243(a872),f328(f328(f80(a872),x72331),x72332)),f328(f328(f80(a872),x72331),x72333))) % 167.75/167.50 [7234]~P1(f328(f328(f243(a872),x72341),x72343))+P1(f328(f328(f243(a872),f328(f328(f80(a872),x72341),x72342)),f328(f328(f80(a872),x72343),x72342))) % 167.75/167.50 [7235]~P1(f328(f328(f243(a1),x72351),x72353))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x72351),x72352)),f328(f328(f80(a1),x72353),x72352))) % 167.75/167.50 [7238]~P1(f328(f328(f242(a872),x72383),x72382))+P1(f328(f328(f242(a872),f328(f328(f22(a872),x72381),x72382)),f328(f328(f22(a872),x72381),x72383))) % 167.75/167.50 [7239]~P1(f328(f328(f242(a872),x72391),x72393))+P1(f328(f328(f242(a872),f328(f328(f22(a872),x72391),x72392)),f328(f328(f22(a872),x72393),x72392))) % 167.75/167.50 [7240]~P1(f328(f328(f242(a872),x72402),x72403))+P1(f328(f328(f242(a872),f328(f328(f80(a872),x72401),x72402)),f328(f328(f80(a872),x72401),x72403))) % 167.75/167.50 [7241]~P1(f328(f328(f242(a872),x72411),x72413))+P1(f328(f328(f242(a872),f328(f328(f80(a872),x72411),x72412)),f328(f328(f80(a872),x72413),x72412))) % 167.75/167.50 [7243]~P1(f328(f328(f242(a872),x72432),x72433))+P1(f328(f328(f242(a872),f328(f328(f81(a872),x72431),x72432)),f328(f328(f81(a872),x72431),x72433))) % 167.75/167.50 [7245]~P1(f328(f328(f242(a872),x72451),x72453))+P1(f328(f328(f242(a872),f328(f328(f81(a872),x72451),x72452)),f328(f328(f81(a872),x72453),x72452))) % 167.75/167.50 [7246]~P1(f328(f328(f242(a872),x72461),x72463))+P1(f328(f328(f242(a872),f328(f328(f40(a872),x72461),x72462)),f328(f328(f40(a872),x72463),x72462))) % 167.75/167.50 [7247]~P1(f328(f328(f242(a1),x72472),x72473))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x72471),x72472)),f328(f328(f80(a1),x72471),x72473))) % 167.75/167.50 [7327]E(x73271,x73272)+~P1(f328(f328(f330(x73273),x73271),f328(f328(f306(x73273),x73272),f192(f879(x73273,a867))))) % 167.75/167.50 [7329]~E(f328(f328(f105(f879(x73291,a867)),x73292),x73293),f192(f879(x73291,a867)))+P1(f328(f328(f242(f879(x73291,a867)),x73292),f328(f79(f879(x73291,a867)),x73293))) % 167.75/167.50 [7337]P1(f328(f328(f330(f879(x73371,a867)),x73372),f328(f305(x73371),x73373)))+~P1(f328(f328(f242(f879(x73371,a867)),x73372),x73373)) % 167.75/167.50 [7390]E(f328(f328(f148(x73901),f328(f328(f162(x73901),x73902),x73903)),f328(f328(f135(x73901),f328(a116,x73903)),x73902)),f328(f328(f135(x73901),x73903),x73902))+~P1(f328(f328(f243(a872),x73903),f328(f193(f873(x73901)),x73902))) % 167.75/167.50 [7417]P1(f328(f328(f330(f878(x74171,x74171)),x74172),f304(x74171,x74173)))+~P1(f328(f328(f330(f878(x74171,x74171)),x74172),x74173)) % 167.75/167.50 [7427]~P1(f328(f328(f330(f879(x74271,a867)),x74272),f328(f305(x74271),x74273)))+P1(f328(f328(f242(f879(x74271,a867)),x74272),x74273)) % 167.75/167.50 [7473]P1(f328(f328(f242(f879(x74731,a867)),x74732),f41(f879(x74731,a867),x74733)))+~P1(f328(f328(f330(f879(x74731,a867)),x74732),x74733)) % 167.75/167.50 [7498]~P138(x74981)+E(f328(f328(f81(x74981),f328(f328(f253(x74981),f328(f79(x74981),f78(x74981))),x74982)),f328(f328(f253(x74981),x74983),x74982)),f328(f328(f253(x74981),f328(f79(x74981),x74983)),x74982)) % 167.75/167.50 [7519]E(f328(f328(f162(x75191),x75192),f328(f328(f22(a872),f328(f193(f873(x75191)),x75192)),f328(a116,x75193))),f328(f328(f162(x75191),f328(f166(x75191),x75192)),x75193))+~P1(f328(f328(f243(a872),x75193),f328(f193(f873(x75191)),x75192))) % 167.75/167.50 [7536]~E(f328(f328(f105(f879(x75361,a867)),f837(x75363,x75362,x75361)),x75363),f192(f879(x75361,a867)))+E(f328(f328(f105(f879(x75361,a867)),f41(f879(x75361,a867),x75362)),x75363),f192(f879(x75361,a867))) % 167.75/167.50 [7599]~P1(f328(f328(f330(x75993),x75992),f328(f170(x75993),x75991)))+P1(f328(f328(f243(a872),f648(x75991,x75992,x75993)),f328(f193(f873(x75993)),x75991))) % 167.75/167.50 [7607]P1(f328(f328(f330(x76071),f328(f328(f162(x76071),x76072),x76073)),f328(f170(x76071),x76072)))+~P1(f328(f328(f243(a872),x76073),f328(f193(f873(x76071)),x76072))) % 167.75/167.50 [7707]~P1(f328(x77072,f751(x77073,x77072,x77071)))+E(f328(f328(f135(x77071),f328(f193(f873(x77071)),f175(x77071,x77072,x77073))),x77073),f117(x77071)) % 167.75/167.50 [7718]P1(f328(f328(f242(f879(f873(x77181),a867)),f158(x77181,x77182)),f158(x77181,x77183)))+~P1(f328(f328(f242(f879(x77181,a867)),x77182),x77183)) % 167.75/167.50 [7719]P1(f328(f328(f242(f879(f873(x77191),a867)),f157(x77191,x77192)),f157(x77191,x77193)))+~P1(f328(f328(f242(f879(x77191,a867)),x77192),x77193)) % 167.75/167.50 [7746]E(f328(f328(f105(f879(x77461,a867)),f41(f879(x77461,a867),x77462)),x77463),f192(f879(x77461,a867)))+P1(f328(f328(f330(f879(x77461,a867)),f837(x77463,x77462,x77461)),x77462)) % 167.75/167.50 [7749]~P1(f328(f328(f330(f879(x77491,a867)),x77493),x77492))+P1(f328(f328(f242(f879(x77491,a867)),f42(f879(x77491,a867),x77492)),x77493)) % 167.75/167.50 [7751]E(f328(f328(f105(f879(x77511,a867)),x77512),x77513),f192(f879(x77511,a867)))+~P1(f328(f328(f242(f879(x77511,a867)),x77512),f328(f79(f879(x77511,a867)),x77513))) % 167.75/167.50 [7801]E(f328(f328(f22(a872),f328(f328(f80(a872),f328(f163(a872),x78011)),x78012)),f328(f328(f162(a872),x78011),x78013)),f328(f163(a872),f328(f328(f156(a872,x78011),x78013),x78012)))+~P1(f328(f328(f243(a872),x78013),f328(f193(f873(a872)),x78011))) % 167.75/167.50 [7852]P1(f328(f328(f243(a872),x78521),x78522))+~P1(f328(f328(f243(a872),f328(f328(f80(a872),x78523),x78521)),f328(f328(f80(a872),x78523),x78522))) % 167.75/167.50 [7853]P1(f328(f328(f243(a872),x78531),x78532))+~P1(f328(f328(f243(a872),f328(f328(f81(a872),x78533),x78531)),f328(f328(f81(a872),x78533),x78532))) % 167.75/167.50 [7854]P1(f328(f328(f243(a872),x78541),x78542))+~P1(f328(f328(f243(a872),f328(f328(f81(a872),x78541),x78543)),f328(f328(f81(a872),x78542),x78543))) % 167.75/167.50 [7857]P1(f328(f328(f242(a872),x78571),x78572))+~P1(f328(f328(f242(a872),f328(f328(f80(a872),x78573),x78571)),f328(f328(f80(a872),x78573),x78572))) % 167.75/167.50 [7887]P1(f328(f328(f243(a872),f2(a872)),x78871))+~P1(f328(f328(f243(a872),f328(f328(f81(a872),x78872),x78871)),f328(f328(f81(a872),x78873),x78871))) % 167.75/167.50 [7888]P1(f328(f328(f243(a872),f2(a872)),x78881))+~P1(f328(f328(f243(a872),f328(f328(f81(a872),x78881),x78882)),f328(f328(f81(a872),x78881),x78883))) % 167.75/167.50 [7961]E(f255(x79611,x79612,x79613),x79612)+~P1(f328(f328(f242(f879(x79611,a867)),x79613),f328(f328(f306(x79611),x79612),f192(f879(x79611,a867))))) % 167.75/167.50 [8011]~P1(f328(f134(x80111),x80113))+E(f328(f133(x80111,f328(f328(f8(a867,a867,x80111),a323),f328(a325,x80112))),x80113),f167(x80111,x80112,x80113)) % 167.75/167.50 [8034]E(f328(f328(f135(x80341),f328(f193(f873(x80341)),f175(x80341,x80342,x80343))),x80343),f117(x80341))+P1(f328(f328(f330(x80341),f751(x80343,x80342,x80341)),f328(f170(x80341),x80343))) % 167.75/167.50 [8038]E(f328(f328(f125(x80381),f328(f328(f173(x80381),x80382),x80383)),f328(f328(f148(x80381),f328(f328(f162(x80381),x80383),x80382)),f117(x80381))),f328(f328(f173(x80381),f328(a116,x80382)),x80383))+~P1(f328(f328(f243(a872),x80382),f328(f193(f873(x80381)),x80383))) % 167.75/167.50 [8101]E(f328(f133(x81011,f328(f328(f8(a867,a867,x81011),a323),f328(a325,x81012))),x81013),x81013)+P1(f328(f328(f330(x81011),x81012),f328(f170(x81011),x81013))) % 167.75/167.50 [8109]P1(f328(f328(f242(f879(f879(x81091,a867),a867)),f256(x81091,x81092)),f256(x81091,x81093)))+~P1(f328(f328(f242(f879(x81091,a867)),x81092),x81093)) % 167.75/167.50 [8154]~P1(f328(f134(x81541),x81543))+P1(f328(f134(x81541),f328(f328(f328(f187(f873(x81541),f873(x81541)),x81542),f165(x81541)),x81543))) % 167.75/167.50 [8162]~P1(f328(f328(f243(a872),x81622),x81623))+P1(f328(f328(f243(a872),f328(f328(f81(a872),f328(a116,x81621)),x81622)),f328(f328(f81(a872),f328(a116,x81621)),x81623))) % 167.75/167.50 [8185]P1(f328(f328(f242(f879(f879(x81851,a867),a867)),f328(f305(x81851),x81852)),f328(f305(x81851),x81853)))+~P1(f328(f328(f242(f879(x81851,a867)),x81852),x81853)) % 167.75/167.50 [8352]~P1(f328(f328(f242(f879(x83521,a867)),x83523),x83522))+P1(f328(f328(f242(f879(x83521,a867)),f328(f79(f879(x83521,a867)),x83522)),f328(f79(f879(x83521,a867)),x83523))) % 167.75/167.50 [8382]E(f328(f307(a872,a872,f328(f328(f7(a872,a872,a872),f22(a872)),x83821)),f328(f298(a872,x83822),x83823)),f328(f298(a872,f328(f328(f22(a872),x83822),x83821)),f328(f328(f22(a872),x83823),x83821)))+~P1(f328(f328(f243(a872),x83821),x83823)) % 167.75/167.50 [8412]~P79(x84121)+E(f328(f328(f80(x84121),x84122),f328(f139(x84121,x84121,f80(x84121),f2(x84121)),x84123)),f328(f139(x84121,x84121,f80(x84121),x84122),x84123)) % 167.75/167.50 [8487]~P84(x84871)+P1(f328(f328(f242(x84871),f328(f75(x84871),f328(f328(f22(x84871),x84872),x84873))),f328(f328(f80(x84871),f328(f75(x84871),x84872)),f328(f75(x84871),x84873)))) % 167.75/167.50 [8488]~P84(x84881)+P1(f328(f328(f242(x84881),f328(f75(x84881),f328(f328(f80(x84881),x84882),x84883))),f328(f328(f80(x84881),f328(f75(x84881),x84882)),f328(f75(x84881),x84883)))) % 167.75/167.50 [8500]E(f328(f328(f80(a1),f328(f328(f81(a1),x85001),f46(a1,f328(f328(f40(a1),x85002),x85001),x85003))),f46(a1,x85002,x85001)),f46(a1,x85002,f328(f328(f81(a1),x85001),x85003)))+~P1(f328(f328(f243(a1),f2(a1)),x85003)) % 167.75/167.50 [8506]E(f328(f328(f125(x85061),f328(f328(f173(x85061),x85062),x85063)),f328(f328(f148(x85061),f328(f138(x85061),f328(f328(f135(x85061),x85062),x85063))),f117(x85061))),f328(f328(f173(x85061),f328(a116,x85062)),x85063))+~P1(f328(f328(f243(a872),x85062),f328(f193(f873(x85061)),x85063))) % 167.75/167.50 [8526]E(f328(f274(x85261,f328(f328(f151(x85261,f878(a103,x85261)),f328(f263(a103,x85261),f78(a103))),x85262)),f328(a3,x85263)),f328(f328(f162(x85261),x85262),x85263))+~P1(f328(f328(f243(a872),x85263),f328(f193(f873(x85261)),x85262))) % 167.75/167.50 [8597]P1(f328(f328(f330(f878(x85971,x85971)),x85972),f328(f328(f285(x85971,x85971,x85971),x85973),f304(x85971,x85973))))+~P1(f328(f328(f330(f878(x85971,x85971)),x85972),x85973)) % 167.75/167.50 [8617]P1(f328(f328(f242(a872),x86171),x86172))+~P1(f328(f328(f242(a872),f328(f328(f81(a872),f328(a116,x86173)),x86171)),f328(f328(f81(a872),f328(a116,x86173)),x86172))) % 167.75/167.50 [8634]P1(f328(f328(f242(f879(x86341,a867)),x86342),x86343))+~P1(f328(f328(f242(f879(x86341,a867)),f328(f79(f879(x86341,a867)),x86343)),f328(f79(f879(x86341,a867)),x86342))) % 167.75/167.50 [8652]P1(f328(f134(x86521),x86522))+~P1(f328(f134(x86521),f328(f328(f328(f187(f873(x86521),f873(x86521)),x86523),f165(x86521)),x86522))) % 167.75/167.50 [8712]E(f328(f307(f878(x87121,x87122),x87122,f266(x87121,x87122)),f328(f170(f878(x87121,x87122)),x87123)),f184(x87121,x87122,f328(f176(x87121,x87122),x87123)))+~P1(f328(f134(x87121),f328(f328(f151(f878(x87121,x87122),x87121),f262(x87121,x87122)),x87123))) % 167.75/167.50 [8721]E(f328(f282(x87211,x87211,f304(x87211,x87212)),x87213),x87213)+~P1(f328(f328(f242(f879(x87211,a867)),f328(f282(x87211,x87211,x87212),x87213)),x87213)) % 167.75/167.50 [8763]~P105(x87631)+P15(x87631,f328(f133(x87631,f328(f328(f7(x87631,x87631,a867),a325),f328(x87632,x87633))),x87633)) % 167.75/167.50 [8769]~P1(f328(f328(f242(a872),x87691),x87692))+P1(f328(f328(f242(a872),x87691),f328(f139(a872,a872,f80(a872),x87692),x87693))) % 167.75/167.50 [8846]~P1(f328(f328(f330(f878(x88461,x88461)),x88462),f304(x88461,x88463)))+P1(f328(f328(f330(f878(x88461,x88461)),x88462),f328(f328(f187(f878(x88461,x88461),a867),f631(x88463,x88462,x88461)),x88463))) % 167.75/167.50 [8939]~P79(x89391)+E(f328(f328(f80(x89391),x89392),f328(f139(x89391,x89391,f328(f7(x89391,x89391,x89391),f80(x89391)),f2(x89391)),f328(f166(x89391),x89393))),f328(f139(x89391,x89391,f80(x89391),x89392),x89393)) % 167.75/167.50 [9208]P51(x92081,x92082,x92083)+P1(f328(f328(f330(f878(x92081,x92082)),f328(f328(f263(x92081,x92082),f621(x92083,x92082,x92081)),f608(x92083,x92082,x92081))),x92083)) % 167.75/167.50 [9209]P51(x92091,x92092,x92093)+P1(f328(f328(f330(f878(x92091,x92092)),f328(f328(f263(x92091,x92092),f621(x92093,x92092,x92091)),f607(x92093,x92092,x92091))),x92093)) % 167.75/167.50 [9279]~P1(f328(f328(f330(f878(x92791,x92791)),x92792),f328(f328(f285(x92791,x92791,x92791),x92793),f304(x92791,x92793))))+P1(f328(f328(f330(f878(x92791,x92791)),x92792),f328(f328(f187(f878(x92791,x92791),a867),f633(x92793,x92792,x92791)),x92793))) % 167.75/167.50 [9280]~P1(f328(x92801,f328(f328(f162(x92802),x92803),f328(f193(f873(x92802)),f175(x92802,x92801,x92803)))))+~P1(f328(f328(f243(a872),f328(f193(f873(x92802)),f175(x92802,x92801,x92803))),f328(f193(f873(x92802)),x92803))) % 167.75/167.50 [9369]~P1(f328(f328(f242(f879(x93691,a867)),x93692),x93693))+P1(f328(f328(f242(f879(x93691,a867)),f328(f328(f7(x93691,f879(x93691,a867),a867),f330(x93691)),x93692)),f328(f328(f7(x93691,f879(x93691,a867),a867),f330(x93691)),x93693))) % 167.75/167.50 [9422]~P1(f328(f328(f330(f878(f879(x94221,a867),f879(x94221,a867))),f328(f328(f263(f879(x94221,a867),f879(x94221,a867)),x94222),x94223)),f303(x94221)))+P1(f328(f328(f243(f879(x94221,a867)),x94222),x94223)) % 167.75/167.50 [9447]P52(x94471,x94472,x94473)+~P1(f328(f328(f330(f878(x94471,x94471)),f328(f328(f263(x94471,x94471),f625(x94473,x94472,x94471)),f624(x94473,x94472,x94471))),x94473)) % 167.75/167.50 [9448]P52(x94481,x94482,x94483)+~P1(f328(f328(f330(f878(x94481,x94481)),f328(f328(f263(x94481,x94481),f624(x94483,x94482,x94481)),f625(x94483,x94482,x94481))),x94483)) % 167.75/167.50 [9484]~P1(f328(f328(f330(f878(f873(x94841),f873(x94841))),f328(f328(f263(f873(x94841),f873(x94841)),x94842),x94842)),f144(x94841,x94843)))+P1(f328(f328(f330(f878(x94841,x94841)),f328(f328(f263(x94841,x94841),f663(x94842,x94843,x94841)),f663(x94842,x94843,x94841))),x94843)) % 167.75/167.50 [9538]P1(f328(f328(f242(f879(x95381,a867)),x95382),x95383))+~P1(f328(f328(f242(f879(x95381,a867)),f328(f328(f7(x95381,f879(x95381,a867),a867),f330(x95381)),x95382)),f328(f328(f7(x95381,f879(x95381,a867),a867),f330(x95381)),x95383))) % 167.75/167.50 [9619]E(f328(f328(f22(a872),f328(f328(f6(a872,a872),x96191),f328(f249(a872),x96192))),f328(f328(f6(a872,a872),x96193),f328(f249(a872),x96192))),f328(f328(f6(a872,a872),f328(f328(f18(a872,a872,a872),f328(f328(f8(a872,f879(a872,a872),a872),f22(a872)),x96191)),x96193)),f328(f249(a872),x96192)))+~P1(f328(f328(f242(a872),f328(x96193,f391(x96192,x96191,x96193))),f328(x96191,f391(x96192,x96191,x96193)))) % 167.75/167.50 [9925]E(f328(f248(f878(x99251,x99252)),f328(f267(x99251,x99252,a867),f328(f328(f7(x99251,f879(x99252,f876(x99252)),f879(x99252,a867)),f328(f328(f8(f879(f876(x99252),a867),f879(f879(x99252,f876(x99252)),f879(x99252,a867)),x99251),f8(f876(x99252),a867,x99252)),f328(f328(f8(f876(x99252),f879(f876(x99252),a867),x99251),a325),f328(f176(x99251,x99252),x99253)))),f235(x99252)))),f328(f170(f878(x99251,x99252)),x99253))+~P1(f328(f134(x99251),f328(f328(f151(f878(x99251,x99252),x99251),f262(x99251,x99252)),x99253))) % 167.75/167.50 [5613]~P74(x56131)+E(f328(f328(f22(x56131),f328(f328(f80(x56131),x56132),x56133)),x56133),x56132) % 167.75/167.50 [5614]~P74(x56141)+E(f328(f328(f80(x56141),f328(f328(f22(x56141),x56142),x56143)),x56143),x56142) % 167.75/167.50 [5835]~P74(x58351)+E(f328(f328(f80(x58351),x58352),f328(f328(f80(x58351),f328(f79(x58351),x58352)),x58353)),x58353) % 167.75/167.50 [5919]~P78(x59191)+E(f328(f328(f81(x59191),f328(f328(f253(x59191),x59192),x59193)),x59192),f328(f328(f253(x59191),x59192),f328(a116,x59193))) % 167.75/167.50 [5920]~P111(x59201)+E(f328(f328(f81(x59201),f328(f328(f253(x59201),x59202),x59203)),x59202),f328(f328(f253(x59201),x59202),f328(a116,x59203))) % 167.75/167.50 [6128]~P117(x61281)+E(f328(f75(x61281),f328(f328(f253(x61281),f328(f79(x61281),x61282)),x61283)),f328(f75(x61281),f328(f328(f253(x61281),x61282),x61283))) % 167.75/167.50 [6190]~P78(x61901)+E(f328(f328(f81(x61901),f328(f328(f253(x61901),x61902),x61903)),x61902),f328(f328(f81(x61901),x61902),f328(f328(f253(x61901),x61902),x61903))) % 167.75/167.50 [6244]E(f328(f328(f22(a103),f328(f328(f80(a103),x62441),x62442)),x62443),f278(x62441,x62442,x62443))+~P1(f328(f328(f243(a103),x62442),x62443)) % 167.75/167.50 [6265]~E(f328(f328(f135(x62651),x62653),x62652),f117(x62651))+P1(f328(f328(f242(a872),f328(f193(f873(x62651)),x62652)),x62653)) % 167.75/167.50 [6397]E(f328(f328(f81(a872),f328(f107(a872),x63971)),f328(f328(f81(a872),f328(f107(a872),x63972)),x63973)),f2(a872))+~P1(f328(f328(f243(a1),x63971),a83)) % 167.75/167.50 [6413]~P60(x64131)+E(f328(f328(f253(x64131),f328(f328(f286(x64131),f78(x64131)),x64132)),x64133),f328(f328(f286(x64131),f78(x64131)),f328(f328(f253(x64131),x64132),x64133))) % 167.75/167.50 [6490]E(f328(f328(f22(a872),f328(f328(f80(a872),x64901),x64902)),x64903),f328(f328(f22(a872),x64901),f328(f328(f22(a872),x64903),x64902)))+~P1(f328(f328(f242(a872),x64902),x64903)) % 167.75/167.50 [6492]E(f328(f328(f22(a872),f328(f328(f80(a872),x64921),x64922)),x64923),f328(f328(f80(a872),x64921),f328(f328(f22(a872),x64922),x64923)))+~P1(f328(f328(f242(a872),x64923),x64922)) % 167.75/167.50 [6527]~P2(x65271)+P1(f328(f328(f242(x65271),f328(f328(f105(x65271),x65272),x65273)),x65273)) % 167.75/167.50 [6528]~P100(x65281)+P1(f328(f328(f242(x65281),f328(f328(f105(x65281),x65282),x65283)),x65283)) % 167.75/167.50 [6529]~P2(x65291)+P1(f328(f328(f242(x65291),f328(f328(f105(x65291),x65292),x65293)),x65292)) % 167.75/167.50 [6530]~P100(x65301)+P1(f328(f328(f242(x65301),f328(f328(f105(x65301),x65302),x65303)),x65302)) % 167.75/167.50 [6531]~P105(x65311)+P1(f328(f328(f242(x65311),f328(f328(f240(x65311),x65312),x65313)),x65313)) % 167.75/167.50 [6532]~P105(x65321)+P1(f328(f328(f242(x65321),f328(f328(f240(x65321),x65322),x65323)),x65322)) % 167.75/167.50 [6545]E(f328(f328(f40(a1),f328(f328(f40(a1),x65451),x65452)),x65453),f328(f328(f40(a1),x65451),f328(f328(f81(a1),x65452),x65453)))+~P1(f328(f328(f243(a1),f2(a1)),x65453)) % 167.75/167.50 [6597]~P111(x65971)+E(f328(f328(f80(x65971),f328(f328(f81(x65971),x65972),x65973)),x65973),f328(f328(f81(x65971),f328(f328(f80(x65971),x65972),f78(x65971))),x65973)) % 167.75/167.50 [6598]~P91(x65981)+E(f328(f328(f81(x65981),f328(f79(x65981),f328(f107(x65981),x65982))),x65983),f328(f328(f81(x65981),f328(f107(x65981),f328(f79(a1),x65982))),x65983)) % 167.75/167.50 [6671]~P79(x66711)+E(f328(f163(x66711),f328(f328(f151(x66712,x66711),f328(f16(x66711,x66712),f2(x66711))),x66713)),f2(x66711)) % 167.75/167.50 [6687]E(f328(f328(f80(a872),f328(f107(a872),x66871)),f328(f328(f80(a872),f328(f107(a872),x66872)),x66873)),f328(f328(f80(a872),f328(f107(a872),x66872)),x66873))+~P1(f328(a197,f328(f107(a1),x66871))) % 167.75/167.50 [6701]~P4(x67011)+E(f42(x67011,f328(f328(f306(x67011),x67012),f328(f328(f306(x67011),x67013),f192(f879(x67011,a867))))),f328(f328(f105(x67011),x67012),x67013)) % 167.75/167.50 [6702]~P4(x67021)+E(f41(x67021,f328(f328(f306(x67021),x67022),f328(f328(f306(x67021),x67023),f192(f879(x67021,a867))))),f328(f328(f114(x67021),x67022),x67023)) % 167.75/167.50 [6725]E(f328(f328(f173(x67251),x67252),x67253),x67253)+~P1(f328(f328(f242(a872),f328(f193(f873(x67251)),x67253)),x67252)) % 167.75/167.50 [6738]E(f328(f328(f135(x67381),x67382),x67383),f117(x67381))+~P1(f328(f328(f242(a872),f328(f193(f873(x67381)),x67383)),x67382)) % 167.75/167.50 [6749]E(f328(f328(f80(a872),f328(f328(f22(a872),x67491),x67492)),x67493),f328(f328(f22(a872),f328(f328(f80(a872),x67491),x67493)),x67492))+~P1(f328(f328(f242(a872),x67492),x67491)) % 167.75/167.50 [6763]~P1(f328(f328(f243(a872),x67631),x67633))+P1(f328(f328(f243(a872),f328(f328(f22(a872),x67631),x67632)),x67633)) % 167.75/167.50 [6791]~P105(x67911)+E(f167(x67911,x67912,f328(f328(f145(x67911,x67911,f5(x67911)),x67912),x67913)),x67913) % 167.75/167.50 [6881]E(f328(f328(f22(a872),f328(f328(f80(a872),x68811),x68812)),f328(a116,x68813)),f328(f328(f22(a872),x68811),f328(a116,f328(f328(f22(a872),x68813),x68812))))+~P1(f328(f328(f242(a872),x68812),x68813)) % 167.75/167.50 [6882]~P117(x68821)+P1(f328(f328(f242(x68821),f2(x68821)),f328(f328(f253(x68821),f328(f75(x68821),x68822)),x68823))) % 167.75/167.50 [6927]P25(x69271,x69272,x69273)+~P1(f328(f328(f242(f879(f871(x69271),a867)),x69273),x69272)) % 167.75/167.50 [6970]~P1(f328(f38(x69701),x69702))+P1(f328(f38(x69701),f328(f328(f22(f879(x69701,a867)),x69702),x69703))) % 167.75/167.50 [6971]~P1(f328(f38(x69711),x69713))+P1(f328(f38(x69711),f328(f328(f105(f879(x69711,a867)),x69712),x69713))) % 167.75/167.50 [6972]~P1(f328(f38(x69721),x69722))+P1(f328(f38(x69721),f328(f328(f105(f879(x69721,a867)),x69722),x69723))) % 167.75/167.50 [7111]~P38(x71111,x71113)+P38(x71111,f328(f328(f105(f879(f878(x71111,x71111),a867)),x71112),x71113)) % 167.75/167.50 [7112]~P38(x71121,x71122)+P38(x71121,f328(f328(f105(f879(f878(x71121,x71121),a867)),x71122),x71123)) % 167.75/167.50 [7229]~P2(x72291)+E(f13(x72291,f328(f170(x72291),f328(f328(f148(x72291),x72292),x72293))),f328(f139(x72291,x72291,f114(x72291),x72292),x72293)) % 167.75/167.50 [7230]~P2(x72301)+E(f10(x72301,f328(f170(x72301),f328(f328(f148(x72301),x72302),x72303))),f328(f139(x72301,x72301,f105(x72301),x72302),x72303)) % 167.75/167.50 [7231]~P105(x72311)+E(f14(x72311,f328(f170(x72311),f328(f328(f148(x72311),x72312),x72313))),f328(f139(x72311,x72311,f240(x72311),x72312),x72313)) % 167.75/167.50 [7232]~P105(x72321)+E(f15(x72321,f328(f170(x72321),f328(f328(f148(x72321),x72322),x72323))),f328(f139(x72321,x72321,f241(x72321),x72322),x72323)) % 167.75/167.50 [7292]~P1(f328(f38(x72921),x72922))+P1(f328(f328(f242(a872),f328(f39(x72921),x72922)),f328(f39(x72921),f328(f328(f306(x72921),x72923),x72922)))) % 167.75/167.50 [7300]E(f328(f328(f114(f879(a872,a867)),f328(f298(a872,x73001),x73002)),f328(f298(a872,x73002),f328(f328(f80(a872),x73002),x73003))),f328(f298(a872,x73001),f328(f328(f80(a872),x73002),x73003)))+~P1(f328(f328(f242(a872),x73001),x73002)) % 167.75/167.50 [7308]P1(f328(f328(f243(a872),x73081),x73082))+~P1(f328(f328(f243(a872),f328(f328(f80(a872),x73081),x73083)),x73082)) % 167.75/167.50 [7311]P1(f328(f328(f242(a872),x73111),x73112))+~P1(f328(f328(f242(a872),f328(f328(f80(a872),x73113),x73111)),x73112)) % 167.75/167.50 [7312]P1(f328(f328(f242(a872),x73121),x73122))+~P1(f328(f328(f242(a872),f328(f328(f80(a872),x73121),x73123)),x73122)) % 167.75/167.50 [7354]~P105(x73541)+E(f11(x73541,f240(x73541),f328(f170(x73541),f328(f328(f148(x73541),x73542),x73543))),f328(f139(x73541,x73541,f240(x73541),x73542),x73543)) % 167.75/167.50 [7355]~P105(x73551)+E(f12(x73551,f241(x73551),f328(f170(x73551),f328(f328(f148(x73551),x73552),x73553))),f328(f139(x73551,x73551,f241(x73551),x73552),x73553)) % 167.75/167.50 [7359]~E(x73592,f192(f879(f878(x73591,x73591),a867)))+P1(f328(f328(f242(f879(f878(x73591,x73591),a867)),x73592),x73593)) % 167.75/167.50 [7468]E(f328(f328(f114(f879(x74681,a867)),x74682),f328(f328(f22(f879(x74681,a867)),x74683),x74682)),x74683)+~P1(f328(f328(f242(f879(x74681,a867)),x74682),x74683)) % 167.75/167.50 [7469]~P1(f328(f328(f243(a872),x74691),f328(f328(f22(a872),x74693),x74692)))+P1(f328(f328(f243(a872),f328(f328(f80(a872),x74691),x74692)),x74693)) % 167.75/167.50 [7470]~P1(f328(f328(f242(a872),x74701),f328(f328(f80(a872),x74703),x74702)))+P1(f328(f328(f242(a872),f328(f328(f22(a872),x74701),x74702)),x74703)) % 167.75/167.50 [7526]E(x75261,f117(x75262))+E(f328(f138(x75262),f328(f328(f328(f187(f873(x75262),f873(x75262)),x75263),f165(x75262)),x75261)),f328(f328(f162(x75262),x75261),f46(a872,x75263,f328(f193(f873(x75262)),x75261)))) % 167.75/167.50 [7535]E(f328(f328(f306(x75351),x75352),f328(f328(f22(f879(x75351,a867)),x75353),f328(f328(f306(x75351),x75352),f192(f879(x75351,a867))))),x75353)+~P1(f328(f328(f330(x75351),x75352),x75353)) % 167.75/167.50 [7698]P1(f328(f328(f243(a872),x76981),f328(f328(f22(a872),x76982),x76983)))+~P1(f328(f328(f243(a872),f328(f328(f80(a872),x76981),x76983)),x76982)) % 167.75/167.50 [7699]P1(f328(f328(f242(a872),x76991),f328(f328(f80(a872),x76992),x76993)))+~P1(f328(f328(f242(a872),f328(f328(f22(a872),x76991),x76993)),x76992)) % 167.75/167.50 [7722]P1(f328(f38(x77221),x77222))+~P1(f328(f38(x77221),f328(f328(f114(f879(x77221,a867)),x77223),x77222))) % 167.75/167.50 [7723]P1(f328(f38(x77231),x77232))+~P1(f328(f38(x77231),f328(f328(f114(f879(x77231,a867)),x77232),x77233))) % 167.75/167.50 [7800]~P46(x78001,x78003)+P1(f328(f328(f330(f878(x78001,x78001)),f328(f328(f263(x78001,x78001),x78002),x78002)),x78003)) % 167.75/167.50 [7935]E(f328(f328(f162(a872),f136(a872,f328(f298(a872,x79351),x79352))),x79353),f328(f328(f80(a872),x79351),x79353))+~P1(f328(f328(f243(a872),f328(f328(f80(a872),x79351),x79353)),x79352)) % 167.75/167.50 [8000]E(f328(f328(f173(a872),x80001),f136(a872,f328(f298(a872,x80002),x80003))),f136(a872,f328(f298(a872,x80002),f328(f328(f80(a872),x80002),x80001))))+~P1(f328(f328(f242(a872),f328(f328(f80(a872),x80002),x80001)),x80003)) % 167.75/167.50 [8053]~P91(x80531)+E(f328(f328(f253(x80531),x80532),f328(f107(a872),f328(f328(f80(a1),x80533),x80533))),f328(f328(f86(x80531,x80531),f328(f328(f253(x80531),x80532),f328(f107(a872),x80533))),f328(f328(f18(x80531,x80531,x80531),f81(x80531)),f5(x80531)))) % 167.75/167.50 [8207]~P1(f328(f328(f328(a198,f328(a26,x82071)),x82072),x82073))+P1(f328(f328(f328(a198,f328(f239(a869),f328(a28,x82071))),x82072),x82073)) % 167.75/167.50 [8332]E(f328(f328(f125(x83321),f328(f328(f173(x83321),x83322),x83323)),f328(f328(f148(x83321),f328(f328(f162(x83321),x83323),x83322)),f328(f328(f135(x83321),f328(a116,x83322)),x83323))),x83323)+~P1(f328(f328(f243(a872),x83322),f328(f193(f873(x83321)),x83323))) % 167.75/167.50 [8339]P1(f328(f328(f242(f879(x83391,a867)),f316(x83391,x83392)),f316(x83391,x83393)))+~P1(f328(f328(f242(f879(x83391,f879(x83391,a867))),x83393),x83392)) % 167.75/167.50 [8341]~P52(x83411,x83412,x83413)+P52(x83411,x83412,f328(f328(f22(f879(f878(x83411,x83411),a867)),x83413),f304(x83411,f192(f879(f878(x83411,x83411),a867))))) % 167.75/167.50 [8358]P1(f328(f328(f242(f879(x83581,a867)),f317(x83581,x83582)),f317(x83581,x83583)))+~P1(f328(f328(f242(f879(f878(x83581,x83581),a867)),x83583),x83582)) % 167.75/167.50 [8365]~P124(x83651)+P1(f328(f328(f242(x83651),f2(x83651)),f328(f328(f80(x83651),f328(f328(f81(x83651),x83652),x83652)),f328(f328(f81(x83651),x83653),x83653)))) % 167.75/167.50 [8386]P1(f328(f328(f328(a198,f328(a26,x83861)),x83862),x83863))+~P1(f328(f328(f328(a198,f328(f239(a869),f328(a28,x83861))),x83862),x83863)) % 167.75/167.50 [8400]P1(f328(f328(f242(f879(x84001,a867)),f328(f281(x84001),x84002)),f328(f281(x84001),x84003)))+~P1(f328(f328(f242(f879(f878(x84001,x84001),a867)),x84002),x84003)) % 167.75/167.50 [8430]~P42(x84301,x84302)+~P1(f328(f328(f330(f878(x84301,x84301)),f328(f328(f263(x84301,x84301),x84303),x84303)),x84302)) % 167.75/167.50 [8432]~P38(x84321,x84322)+~P1(f328(f328(f330(f878(x84321,x84321)),f328(f328(f263(x84321,x84321),x84323),x84323)),x84322)) % 167.75/167.50 [8489]P1(f328(f328(f242(f879(x84891,a867)),f42(f879(x84891,a867),x84892)),f42(f879(x84891,a867),x84893)))+~P1(f328(f328(f242(f879(f879(x84891,a867),a867)),x84893),x84892)) % 167.75/167.50 [8490]P1(f328(f328(f242(f879(x84901,a867)),f41(f879(x84901,a867),x84902)),f41(f879(x84901,a867),x84903)))+~P1(f328(f328(f242(f879(f879(x84901,a867),a867)),x84902),x84903)) % 167.75/167.50 [8548]~P7(x85481,x85483,x85482)+P1(f328(f328(f242(f879(f878(x85481,x85481),a867)),x85482),f328(f328(f265(x85481,x85481),x85483),f328(f16(f879(x85481,a867),x85481),x85483)))) % 167.75/167.50 [8549]~P40(x85491,x85493,x85492)+P1(f328(f328(f242(f879(f878(x85491,x85491),a867)),x85492),f328(f328(f265(x85491,x85491),x85493),f328(f16(f879(x85491,a867),x85491),x85493)))) % 167.75/167.50 [8598]~P84(x85981)+P1(f328(f328(f242(x85981),f328(f328(f22(x85981),f328(f75(x85981),x85982)),f328(f75(x85981),x85983))),f328(f75(x85981),f328(f328(f22(x85981),x85983),x85982)))) % 167.75/167.50 [8599]~P84(x85991)+P1(f328(f328(f242(x85991),f328(f328(f22(x85991),f328(f75(x85991),x85992)),f328(f75(x85991),x85993))),f328(f75(x85991),f328(f328(f22(x85991),x85992),x85993)))) % 167.75/167.50 [8632]P1(f328(f328(f242(f879(f878(x86321,x86321),a867)),f304(x86321,x86322)),f304(x86321,x86323)))+~P1(f328(f328(f242(f879(f878(x86321,x86321),a867)),x86322),x86323)) % 167.75/167.50 [8787]P52(x87871,x87872,x87873)+~P52(x87871,x87872,f328(f328(f22(f879(f878(x87871,x87871),a867)),x87873),f304(x87871,f192(f879(f878(x87871,x87871),a867))))) % 167.75/167.50 [8805]P1(f328(f328(f242(f879(f878(f873(x88051),f873(x88051)),a867)),f154(x88051,x88052)),f154(x88051,x88053)))+~P1(f328(f328(f242(f879(f878(x88051,x88051),a867)),x88052),x88053)) % 167.75/167.50 [8806]P1(f328(f328(f242(f879(f878(f873(x88061),f873(x88061)),a867)),f155(x88061,x88062)),f155(x88061,x88063)))+~P1(f328(f328(f242(f879(f878(x88061,x88061),a867)),x88062),x88063)) % 167.75/167.50 [8825]~P40(x88251,x88253,x88252)+P1(f328(f328(f242(f879(f878(x88251,x88251),a867)),x88252),f328(f328(f285(x88251,x88251,x88251),f328(f283(x88251,x88251),x88252)),x88252))) % 167.75/167.50 [8874]~P1(f328(f134(x88741),x88742))+E(f328(f133(x88741,f328(f328(f7(x88741,f879(x88741,a867),a867),f330(x88741)),f328(f170(x88741),f174(x88741,x88742,x88743)))),x88742),f174(x88741,x88742,x88743)) % 167.75/167.50 [8937]E(x89371,x89372)+~P1(f328(f328(f330(f878(x89373,x89373)),f328(f328(f263(x89373,x89373),x89371),x89372)),f304(x89373,f192(f879(f878(x89373,x89373),a867))))) % 167.75/167.50 [9021]P1(f328(f328(f330(x90211),x90212),f317(x90211,x90213)))+P1(f328(f328(f330(f878(x90211,x90211)),f328(f328(f263(x90211,x90211),f543(x90213,x90212,x90211)),x90212)),x90213)) % 167.75/167.50 [9022]P1(f328(f328(f330(x90221),x90222),f317(x90221,x90223)))+P1(f328(f328(f330(f878(x90221,x90221)),f328(f328(f263(x90221,x90221),f611(x90223,x90222,x90221)),x90222)),x90223)) % 167.75/167.50 [9023]P1(f328(f328(f330(x90231),x90232),f317(x90231,x90233)))+P1(f328(f328(f330(f878(x90231,x90231)),f328(f328(f263(x90231,x90231),f612(x90233,x90232,x90231)),x90232)),x90233)) % 167.75/167.50 [9111]~P1(f328(f328(f330(f873(x91111)),x91113),f158(x91111,x91112)))+P1(f328(f157(x91111,f328(f328(f7(x91111,f879(x91111,a867),a867),f330(x91111)),x91112)),x91113)) % 167.75/167.50 [9132]P1(f328(x91323,x91322))+E(f328(f248(x91321),f328(f328(f18(x91321,a867,a867),f328(f328(f8(a867,f879(a867,a867),x91321),a326),f328(a325,x91322))),x91323)),f192(f879(x91321,a867))) % 167.75/167.50 [9153]~P84(x91531)+P1(f328(f328(f242(x91531),f328(f75(x91531),f328(f328(f22(x91531),f328(f75(x91531),x91532)),f328(f75(x91531),x91533)))),f328(f75(x91531),f328(f328(f22(x91531),x91532),x91533)))) % 167.75/167.50 [9167]~P1(f328(x91673,x91672))+E(f328(f248(x91671),f328(f328(f18(x91671,a867,a867),f328(f328(f8(a867,f879(a867,a867),x91671),a326),f328(a325,x91672))),x91673)),f328(f328(f306(x91671),x91672),f192(f879(x91671,a867)))) % 167.75/167.50 [9174]~P1(f328(f328(f330(f879(x91741,a867)),x91743),f328(f305(x91741),x91742)))+P1(f328(f256(x91741,f328(f328(f7(x91741,f879(x91741,a867),a867),f330(x91741)),x91742)),x91743)) % 167.75/167.50 [9207]P38(x92071,x92072)+P1(f328(f328(f330(f878(x92071,x92071)),f328(f328(f263(x92071,x92071),f328(f553(x92072,x92071),f328(a116,x92073))),f328(f553(x92072,x92071),x92073))),x92072)) % 167.75/167.50 [9348]P1(f328(f328(f330(f873(x93481)),x93482),f158(x93481,x93483)))+~P1(f328(f157(x93481,f328(f328(f7(x93481,f879(x93481,a867),a867),f330(x93481)),x93483)),x93482)) % 167.75/167.50 [9361]P1(f328(f328(f330(f879(x93611,a867)),x93612),f328(f305(x93611),x93613)))+~P1(f328(f256(x93611,f328(f328(f7(x93611,f879(x93611,a867),a867),f330(x93611)),x93613)),x93612)) % 167.75/167.50 [9418]P1(f328(f328(f330(x94181),f328(f274(x94181,x94182),x94183)),f328(f170(x94181),f328(f328(f151(f878(a103,x94181),x94181),f266(a103,x94181)),x94182))))+~P1(f328(f328(f243(a103),x94183),f328(f163(a103),f328(f328(f151(f878(a103,x94181),a103),f262(a103,x94181)),x94182)))) % 167.75/167.50 [9466]P1(f328(f328(f242(f879(f878(f873(x94661),f873(x94661)),a867)),f155(x94661,x94662)),f328(f328(f265(f873(x94661),f873(x94661)),f158(x94661,x94663)),f328(f16(f879(f873(x94661),a867),f873(x94661)),f158(x94661,x94663)))))+~P1(f328(f328(f242(f879(f878(x94661,x94661),a867)),x94662),f328(f328(f265(x94661,x94661),x94663),f328(f16(f879(x94661,a867),x94661),x94663)))) % 167.75/167.50 [9487]P1(f328(f328(f330(x94871),f328(f262(x94871,f878(a103,a103)),f328(f272(x94871,x94872),x94873))),f328(f170(x94871),f328(f328(f151(f878(a103,x94871),x94871),f266(a103,x94871)),x94872))))+~P1(f328(f328(f243(a103),f2(a103)),f328(f163(a103),f328(f328(f151(f878(a103,x94871),a103),f262(a103,x94871)),x94872)))) % 167.75/167.50 [9506]~P1(f328(f328(f242(f879(f878(x95061,x95061),a867)),x95062),f328(f328(f265(x95061,x95061),x95063),f328(f16(f879(x95061,a867),x95061),x95063))))+P1(f328(f328(f242(f879(f878(x95061,x95061),a867)),f328(f328(f285(x95061,x95061,x95061),x95062),f304(x95061,x95062))),f328(f328(f265(x95061,x95061),x95063),f328(f16(f879(x95061,a867),x95061),x95063)))) % 167.75/167.50 [9812]~P38(x98121,x98122)+~P1(f328(f328(f330(f878(x98121,x98121)),f328(f328(f263(x98121,x98121),f328(x98123,f328(a116,f554(x98122,x98121,x98123)))),f328(x98123,f554(x98122,x98121,x98123)))),x98122)) % 167.75/167.50 [9813]~P38(x98131,x98132)+~P1(f328(f328(f330(f878(x98131,x98131)),f328(f328(f263(x98131,x98131),f328(x98133,f328(a116,f617(x98133,x98132,x98131)))),f328(x98133,f617(x98133,x98132,x98131)))),x98132)) % 167.75/167.50 [10065]P1(f328(f328(f242(f879(f878(f879(x100651,a867),f879(x100651,a867)),a867)),f328(f328(f285(f879(x100651,a867),f879(x100651,a867),f879(x100651,a867)),f320(x100651,x100652)),f328(f328(f114(f879(f878(f879(x100651,a867),f879(x100651,a867)),a867)),f320(x100651,x100653)),f328(f328(f306(f878(f879(x100651,a867),f879(x100651,a867))),f328(f328(f263(f879(x100651,a867),f879(x100651,a867)),f192(f879(x100651,a867))),f192(f879(x100651,a867)))),f192(f879(f878(f879(x100651,a867),f879(x100651,a867)),a867)))))),f320(x100651,x100652)))+~P1(f328(f328(f242(f879(f878(x100651,x100651),a867)),f328(f328(f285(x100651,x100651,x100651),x100652),x100653)),x100652)) % 167.75/167.50 [10066]P1(f328(f328(f242(f879(f878(f879(x100661,a867),f879(x100661,a867)),a867)),f328(f328(f285(f879(x100661,a867),f879(x100661,a867),f879(x100661,a867)),f319(x100661,x100662)),f328(f328(f114(f879(f878(f879(x100661,a867),f879(x100661,a867)),a867)),f319(x100661,x100663)),f328(f328(f306(f878(f879(x100661,a867),f879(x100661,a867))),f328(f328(f263(f879(x100661,a867),f879(x100661,a867)),f192(f879(x100661,a867))),f192(f879(x100661,a867)))),f192(f879(f878(f879(x100661,a867),f879(x100661,a867)),a867)))))),f319(x100661,x100662)))+~P1(f328(f328(f242(f879(f878(x100661,x100661),a867)),f328(f328(f285(x100661,x100661,x100661),x100662),x100663)),x100662)) % 167.75/167.50 [7228]~P1(f328(f328(f242(a872),x72282),x72281))+E(f328(f328(f22(a872),f328(a116,f328(f328(f22(a872),x72281),x72282))),x72283),f328(f328(f22(a872),f328(a116,x72281)),f328(f328(f80(a872),x72282),x72283))) % 167.75/167.50 [7267]~P57(x72671)+E(f328(f328(f80(x72671),f46(x72671,x72672,x72673)),f328(f328(f81(x72671),f328(f328(f40(x72671),x72672),x72673)),x72673)),x72672) % 167.75/167.50 [7474]E(f328(f328(f81(a872),f328(f107(a872),x74741)),f328(f328(f81(a872),f328(f107(a872),x74742)),x74743)),f328(f328(f81(a872),f328(f107(a872),f328(f328(f81(a1),x74741),x74742))),x74743))+P1(f328(f328(f243(a1),x74741),a83)) % 167.75/167.50 [7944]~P1(f328(f328(f242(a872),x79443),x79442))+P1(f328(f328(f242(a872),x79441),f328(f328(f22(a872),f328(f328(f80(a872),x79442),x79441)),x79443))) % 167.75/167.50 [8144]~P1(f328(f328(f242(a872),x81441),x81442))+E(f328(f328(f125(a872),f136(a872,f328(f298(a872,x81441),x81442))),f136(a872,f328(f298(a872,x81442),f328(f328(f80(a872),x81442),x81443)))),f136(a872,f328(f298(a872,x81441),f328(f328(f80(a872),x81442),x81443)))) % 167.75/167.50 [8409]~P1(f328(f38(x84091),x84092))+E(f328(a116,f328(f39(x84091),f328(f328(f22(f879(x84091,a867)),x84092),f328(f328(f306(x84091),x84093),f192(f879(x84091,a867)))))),f328(f39(x84091),f328(f328(f306(x84091),x84093),x84092))) % 167.75/167.50 [8451]~P1(f328(f38(x84511),x84512))+E(f328(f328(f80(a872),f78(a872)),f328(f39(x84511),f328(f328(f22(f879(x84511,a867)),x84512),f328(f328(f306(x84511),x84513),f192(f879(x84511,a867)))))),f328(f39(x84511),f328(f328(f306(x84511),x84513),x84512))) % 167.75/167.50 [8641]E(f328(f328(f22(a872),f328(f39(x86411),x86412)),f328(f39(x86411),f328(f328(f105(f879(x86411,a867)),x86412),x86413))),f328(f39(x86411),f328(f328(f22(f879(x86411,a867)),x86412),x86413)))+~P1(f328(f38(x86411),f328(f328(f105(f879(x86411,a867)),x86412),x86413))) % 167.75/167.50 [8870]~P5(f328(x88702,f389(x88702,x88703,x88701)))+E(f328(f104(a1),f328(f328(f6(x88701,a872),f328(f328(f8(a1,a872,x88701),a108),x88702)),x88703)),f328(f328(f6(x88701,a1),x88702),x88703)) % 167.75/167.50 [8871]~P5(f328(x88712,f390(x88712,x88713,x88711)))+E(f328(f104(a1),f328(f328(f9(x88711,a872),f328(f328(f8(a1,a872,x88711),a108),x88712)),x88713)),f328(f328(f9(x88711,a1),x88712),x88713)) % 167.75/167.50 [8919]~P1(f328(f38(x89191),x89193))+P1(f328(f328(f242(a872),f328(f328(f22(a872),f328(f39(x89191),x89192)),f328(f39(x89191),x89193))),f328(f39(x89191),f328(f328(f22(f879(x89191,a867)),x89192),x89193)))) % 167.75/167.50 [8945]P1(f328(f328(f330(x89451),f389(x89452,x89453,x89451)),x89453))+E(f328(f104(a1),f328(f328(f6(x89451,a872),f328(f328(f8(a1,a872,x89451),a108),x89452)),x89453)),f328(f328(f6(x89451,a1),x89452),x89453)) % 167.75/167.50 [8946]P1(f328(f328(f330(x89461),f390(x89462,x89463,x89461)),x89463))+E(f328(f104(a1),f328(f328(f9(x89461,a872),f328(f328(f8(a1,a872,x89461),a108),x89462)),x89463)),f328(f328(f9(x89461,a1),x89462),x89463)) % 167.75/167.50 [9013]E(f85(x90131,f328(f328(f7(x90131,f879(x90131,a867),a867),f330(x90131)),f328(f328(f22(f879(x90131,a867)),x90132),f328(f328(f306(x90131),x90133),f192(f879(x90131,a867)))))),f255(x90131,x90133,x90132))+P1(f328(f328(f242(f879(x90131,a867)),x90132),f328(f328(f306(x90131),x90133),f192(f879(x90131,a867))))) % 167.75/167.50 [9362]E(f328(f328(f151(f873(x93621),x93621),f328(f328(f7(f873(x93621),a872,x93621),f162(x93621)),x93622)),f328(f133(f873(x93621),f328(f328(f8(a872,a867,f873(x93621)),f328(f243(a872),x93622)),f193(f873(x93621)))),x93623)),f328(f328(f162(f873(x93621)),f178(x93621,x93623)),x93622))+~P1(f328(f328(f243(a872),x93622),f328(f193(f873(f873(x93621))),f178(x93621,x93623)))) % 167.75/167.50 [9435]E(f328(f133(x94351,x94352),x94353),f175(x94351,x94352,x94353))+P1(f328(f328(f330(x94351),f755(x94353,x94352,x94351)),f328(f170(x94351),f328(f328(f135(x94351),f328(f193(f873(x94351)),f175(x94351,x94352,x94353))),x94353)))) % 167.75/167.50 [9578]E(f328(f328(f135(x95781),f328(f193(f873(x95781)),f175(x95781,x95782,x95783))),x95783),f117(x95781))+~P1(f328(x95782,f328(f138(x95781),f328(f328(f135(x95781),f328(f193(f873(x95781)),f175(x95781,x95782,x95783))),x95783)))) % 167.75/167.50 [9673]~P1(f328(f328(f330(f878(x96731,x96731)),x96732),f304(x96731,x96733)))+P1(f328(f328(f330(f878(x96731,x96731)),x96732),f328(f328(f44(a872,f879(f878(x96731,x96731),a867)),f251(f879(a872,a867))),f328(f328(f7(a872,f879(f878(x96731,x96731),a867),f879(f878(x96731,x96731),a867)),f187(f878(x96731,x96731),a867)),x96733)))) % 167.75/167.50 [9730]~P1(f328(f328(f242(f879(x97301,a867)),f328(f328(f44(a872,f879(x97301,a867)),f328(f298(a872,f2(a872)),f374(x97303,x97302,x97301))),x97302)),x97303))+P1(f328(f328(f242(f879(x97301,a867)),f328(f328(f44(a872,f879(x97301,a867)),f251(f879(a872,a867))),x97302)),x97303)) % 167.75/167.50 [9788]~P1(f328(f328(f243(a1),f2(a1)),x97883))+P1(f328(f328(f243(a1),x97881),f328(f328(f80(a1),x97882),f328(f328(f81(a1),f328(f328(f80(a1),f328(f75(a1),f328(f328(f22(a1),x97882),x97881))),f78(a1))),x97883)))) % 167.75/167.50 [9799]~P38(x97991,f328(f328(f114(f879(f878(x97991,x97991),a867)),x97992),x97993))+P38(x97991,f328(f328(f114(f879(f878(x97991,x97991),a867)),f328(f328(f114(f879(f878(x97991,x97991),a867)),f328(f328(f285(x97991,x97991,x97991),x97992),x97992)),f328(f328(f285(x97991,x97991,x97991),x97993),x97992))),x97993)) % 167.75/167.50 [9881]P38(x98811,f328(f328(f114(f879(f878(x98811,x98811),a867)),x98812),x98813))+~P38(x98811,f328(f328(f114(f879(f878(x98811,x98811),a867)),f328(f328(f114(f879(f878(x98811,x98811),a867)),f328(f328(f285(x98811,x98811,x98811),x98812),x98812)),f328(f328(f285(x98811,x98811,x98811),x98813),x98812))),x98813)) % 167.75/167.50 [9439]~P138(x94391)+E(f328(f106(x94391),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x94392),x94393)),f192(f879(f878(a872,a872),a867)))))),f328(f328(f22(x94391),f328(f104(x94391),x94392)),f328(f104(x94391),x94393))) % 167.75/167.50 [9524]P1(f328(x95243,x95242))+E(f328(f248(x95241),f328(f328(f18(x95241,a867,a867),f328(f328(f8(a867,f879(a867,a867),x95241),a326),f328(f328(f7(x95241,x95241,a867),a325),x95242))),x95243)),f192(f879(x95241,a867))) % 167.75/167.50 [9527]~P1(f328(x95273,x95272))+E(f328(f248(x95271),f328(f328(f18(x95271,a867,a867),f328(f328(f8(a867,f879(a867,a867),x95271),a326),f328(f328(f7(x95271,x95271,a867),a325),x95272))),x95273)),f328(f328(f306(x95271),x95272),f192(f879(x95271,a867)))) % 167.75/167.50 [9766]E(x97661,x97662)+P1(f328(f328(f252(x97663,x97663,f328(f328(f8(f879(x97663,a867),f879(x97663,a867),x97663),f328(f8(a867,a867,x97663),a323)),a325)),x97661),x97662)) % 167.75/167.50 [9859]~E(x98591,x98592)+~P1(f328(f328(f252(x98593,x98593,f328(f328(f8(f879(x98593,a867),f879(x98593,a867),x98593),f328(f8(a867,a867,x98593),a323)),a325)),x98591),x98592)) % 167.75/167.50 [9873]~P1(f328(f38(x98731),x98733))+E(f328(f328(f65(x98731,f879(x98731,a867),f328(f328(f8(f879(x98731,a867),f879(f879(x98731,a867),f879(x98731,a867)),x98731),f328(f7(f879(x98731,a867),f879(x98731,a867),f879(x98731,a867)),f22(f879(x98731,a867)))),f328(f328(f7(x98731,f879(x98731,a867),f879(x98731,a867)),f306(x98731)),f192(f879(x98731,a867))))),x98732),x98733),f328(f328(f22(f879(x98731,a867)),x98732),x98733)) % 167.75/167.50 [9905]~P1(f328(f328(f243(a1),f2(a1)),x99053))+P1(f328(f328(f243(a1),f328(f328(f22(a1),x99051),f328(f328(f81(a1),f328(f328(f80(a1),f328(f75(a1),f328(f328(f22(a1),x99051),x99052))),f78(a1))),x99053))),x99052)) % 167.75/167.50 [10127]~P1(f328(f328(f330(x101271),x101273),f317(x101271,x101272)))+P1(f328(f316(x101271,f328(f328(f7(x101271,f879(f878(x101271,x101271),a867),f879(x101271,a867)),f328(f328(f8(f879(x101271,f879(f879(f878(x101271,x101271),a867),a867)),f879(f879(f878(x101271,x101271),a867),f879(x101271,a867)),x101271),f7(x101271,f879(f878(x101271,x101271),a867),a867)),f328(f328(f8(f879(x101271,f878(x101271,x101271)),f879(x101271,f879(f879(f878(x101271,x101271),a867),a867)),x101271),f328(f8(f878(x101271,x101271),f879(f879(f878(x101271,x101271),a867),a867),x101271),f330(f878(x101271,x101271)))),f263(x101271,x101271)))),x101272)),x101273)) % 167.75/167.50 [10139]P1(f328(f328(f330(x101391),x101392),f317(x101391,x101393)))+~P1(f328(f316(x101391,f328(f328(f7(x101391,f879(f878(x101391,x101391),a867),f879(x101391,a867)),f328(f328(f8(f879(x101391,f879(f879(f878(x101391,x101391),a867),a867)),f879(f879(f878(x101391,x101391),a867),f879(x101391,a867)),x101391),f7(x101391,f879(f878(x101391,x101391),a867),a867)),f328(f328(f8(f879(x101391,f878(x101391,x101391)),f879(x101391,f879(f879(f878(x101391,x101391),a867),a867)),x101391),f328(f8(f878(x101391,x101391),f879(f879(f878(x101391,x101391),a867),a867),x101391),f330(f878(x101391,x101391)))),f263(x101391,x101391)))),x101393)),x101392)) % 167.75/167.50 [9728]~P1(f328(f38(x97281),f328(f248(x97281),x97283)))+P1(f328(f38(x97281),f328(f248(x97281),f328(f328(f18(x97281,a867,a867),f328(f328(f8(a867,f879(a867,a867),x97281),a326),x97282)),x97283)))) % 167.75/167.50 [9729]~P1(f328(f38(x97291),f328(f248(x97291),x97292)))+P1(f328(f38(x97291),f328(f248(x97291),f328(f328(f18(x97291,a867,a867),f328(f328(f8(a867,f879(a867,a867),x97291),a326),x97292)),x97293)))) % 167.75/167.50 [9831]P1(f328(f38(x98311),f328(f248(x98311),x98312)))+~P1(f328(f38(x98311),f328(f248(x98311),f328(f328(f18(x98311,a867,a867),f328(f328(f8(a867,f879(a867,a867),x98311),a327),x98313)),x98312)))) % 167.75/167.50 [9832]P1(f328(f38(x98321),f328(f248(x98321),x98322)))+~P1(f328(f38(x98321),f328(f248(x98321),f328(f328(f18(x98321,a867,a867),f328(f328(f8(a867,f879(a867,a867),x98321),a327),x98322)),x98323)))) % 167.75/167.50 [10114]~P1(f328(f38(x101141),x101142))+P1(f328(f38(f873(x101141)),f328(f248(f873(x101141)),f328(f328(f18(f873(x101141),a867,a867),f328(f328(f8(a867,f879(a867,a867),f873(x101141)),a326),f328(f328(f7(f873(x101141),f879(x101141,a867),a867),f328(f328(f8(f879(x101141,a867),f879(f879(x101141,a867),a867),f873(x101141)),f242(f879(x101141,a867))),f170(x101141))),x101142))),f328(f328(f7(f873(x101141),a872,a867),f328(f328(f8(a872,f879(a872,a867),f873(x101141)),a325),f193(f873(x101141)))),x101143))))) % 167.75/167.50 [10115]~P1(f328(f38(x101151),x101152))+P1(f328(f38(f873(x101151)),f328(f248(f873(x101151)),f328(f328(f18(f873(x101151),a867,a867),f328(f328(f8(a867,f879(a867,a867),f873(x101151)),a326),f328(f328(f7(f873(x101151),f879(x101151,a867),a867),f328(f328(f8(f879(x101151,a867),f879(f879(x101151,a867),a867),f873(x101151)),f242(f879(x101151,a867))),f170(x101151))),x101152))),f328(f328(f7(f873(x101151),a872,a867),f328(f328(f8(a872,f879(a872,a867),f873(x101151)),f242(a872)),f193(f873(x101151)))),x101153))))) % 167.75/167.50 [9846]~P111(x98461)+E(f328(f328(f253(x98461),x98462),f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x98463)),f328(f328(f81(x98461),f328(f328(f253(x98461),x98462),x98463)),f328(f328(f253(x98461),x98462),x98463))) % 167.75/167.50 [9886]~P78(x98861)+E(f328(f328(f253(x98861),f328(f328(f253(x98861),x98862),x98863)),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f253(x98861),x98862),f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x98863))) % 167.75/167.50 [9932]~P138(x99321)+E(f328(f328(f253(x99321),f328(f79(x99321),x99322)),f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99323)),f328(f328(f253(x99321),x99322),f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99323))) % 167.75/167.50 [10072]~P117(x100721)+P1(f328(f328(f242(x100721),f2(x100721)),f328(f328(f80(x100721),f328(f328(f253(x100721),x100722),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100721),x100723),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))) % 167.75/167.50 [9942]~P111(x99421)+E(f328(f328(f253(x99421),x99422),f328(a116,f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99423))),f328(f328(f81(x99421),x99422),f328(f328(f81(x99421),f328(f328(f253(x99421),x99422),x99423)),f328(f328(f253(x99421),x99422),x99423)))) % 167.75/167.50 [9991]~P78(x99911)+E(f328(f328(f81(x99911),x99912),f328(f328(f253(x99911),f328(f328(f253(x99911),x99912),x99913)),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x99911),x99912),f328(a116,f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99913)))) % 167.75/167.50 [10029]~P117(x100291)+P1(f328(f328(f242(x100291),f2(x100291)),f328(f328(f253(x100291),x100292),f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100293)))) % 167.75/167.50 [10095]~P91(x100951)+E(f328(f328(f22(x100951),f328(f328(f80(x100951),f328(f328(f253(x100951),x100952),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100951),x100953),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f328(f328(f81(x100951),f328(f328(f81(x100951),f328(f107(x100951),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100952)),x100953)),f328(f328(f253(x100951),f328(f328(f22(x100951),x100952),x100953)),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.75/167.50 [10096]~P91(x100961)+E(f328(f328(f80(x100961),f328(f328(f80(x100961),f328(f328(f253(x100961),x100962),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100961),x100963),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f328(f328(f81(x100961),f328(f328(f81(x100961),f328(f107(x100961),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100962)),x100963)),f328(f328(f253(x100961),f328(f328(f80(x100961),x100962),x100963)),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.75/167.50 [10194]~P28(x101941,x101942,x101943)+P1(f99(x101941,a867,f328(f328(f8(f879(a869,f879(f879(x101941,f879(a868,a867)),f879(x101941,a867))),f879(a869,f879(f879(x101941,f879(a868,a867)),a867)),f879(x101941,f879(a868,a867))),f328(f8(f879(f879(x101941,f879(a868,a867)),f879(x101941,a867)),f879(f879(x101941,f879(a868,a867)),a867),a869),f328(f8(f879(x101941,a867),a867,f879(x101941,f879(a868,a867))),f88(x101941)))),f328(f328(f8(f879(a869,f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867)))),f879(a869,f879(f879(x101941,f879(a868,a867)),f879(x101941,a867))),f879(x101941,f879(a868,a867))),f328(f8(f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867))),f879(f879(x101941,f879(a868,a867)),f879(x101941,a867)),a869),f328(f8(f879(x101941,f879(a868,a867)),f879(x101941,a867),f879(x101941,f879(a868,a867))),f328(f8(f879(a868,a867),a867,x101941),f88(a868))))),f328(f328(f7(f879(x101941,f879(a868,a867)),f879(a869,f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867)))),f879(a869,f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867))))),f328(f328(f8(f879(f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867))),f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867)))),f879(f879(a869,f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867)))),f879(a869,f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867))))),f879(x101941,f879(a868,a867))),f8(f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867))),f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867))),a869)),f328(f328(f8(f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867))),f879(f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867))),f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867)))),f879(x101941,f879(a868,a867))),f8(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867)))),f328(f328(f8(f879(x101941,f879(f879(a868,a867),f879(a868,a867))),f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867))),f879(x101941,f879(a868,a867))),f18(x101941,f879(a868,a867),f879(a868,a867))),f328(f328(f8(f879(x101941,f879(a868,f879(a867,a867))),f879(x101941,f879(f879(a868,a867),f879(a868,a867))),f879(x101941,f879(a868,a867))),f328(f8(f879(a868,f879(a867,a867)),f879(f879(a868,a867),f879(a868,a867)),x101941),f18(a868,a867,a867))),f328(f8(f879(a868,a867),f879(a868,f879(a867,a867)),x101941),f328(f8(a867,f879(a867,a867),a868),a331))))))),f328(f328(f8(f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,f879(a868,a867)))),f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867))),a869),f328(f8(f879(x101941,f879(a868,f879(a868,a867))),f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,a867))),f328(f8(f879(a868,f879(a868,a867)),f879(a868,a867),x101941),f328(f8(f879(a868,a867),a867,a868),f88(a868))))),f328(f328(f8(f879(f879(a868,a867),f879(a868,f879(a868,a867))),f879(f879(x101941,f879(a868,a867)),f879(x101941,f879(a868,f879(a868,a867)))),a869),f8(f879(a868,a867),f879(a868,f879(a868,a867)),x101941)),f328(f328(f8(f879(a868,f879(f879(a868,a867),f879(a868,a867))),f879(f879(a868,a867),f879(a868,f879(a868,a867))),a869),f7(a868,f879(a868,a867),f879(a868,a867))),f328(f328(f8(f879(a868,f879(a868,f879(a867,a867))),f879(a868,f879(f879(a868,a867),f879(a868,a867))),a869),f328(f8(f879(a868,f879(a867,a867)),f879(f879(a868,a867),f879(a868,a867)),a868),f18(a868,a867,a867))),f328(f328(f8(f879(a868,f879(a868,a867)),f879(a868,f879(a868,f879(a867,a867))),a869),f328(f8(f879(a868,a867),f879(a868,f879(a867,a867)),a868),f328(f8(a867,f879(a867,a867),a868),a331))),f328(f328(f7(a869,a872,f879(a868,f879(a868,a867))),f328(f328(f8(f879(a868,f879(a872,f879(a868,a867))),f879(a872,f879(a868,f879(a868,a867))),a869),f7(a868,a872,f879(a868,a867))),a200)),x101942))))))))),x101943)) % 167.75/167.50 [10196]P28(x101961,x101962,x101963)+~P1(f99(x101961,a867,f328(f328(f8(f879(a869,f879(f879(x101961,f879(a868,a867)),f879(x101961,a867))),f879(a869,f879(f879(x101961,f879(a868,a867)),a867)),f879(x101961,f879(a868,a867))),f328(f8(f879(f879(x101961,f879(a868,a867)),f879(x101961,a867)),f879(f879(x101961,f879(a868,a867)),a867),a869),f328(f8(f879(x101961,a867),a867,f879(x101961,f879(a868,a867))),f88(x101961)))),f328(f328(f8(f879(a869,f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867)))),f879(a869,f879(f879(x101961,f879(a868,a867)),f879(x101961,a867))),f879(x101961,f879(a868,a867))),f328(f8(f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867))),f879(f879(x101961,f879(a868,a867)),f879(x101961,a867)),a869),f328(f8(f879(x101961,f879(a868,a867)),f879(x101961,a867),f879(x101961,f879(a868,a867))),f328(f8(f879(a868,a867),a867,x101961),f88(a868))))),f328(f328(f7(f879(x101961,f879(a868,a867)),f879(a869,f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867)))),f879(a869,f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867))))),f328(f328(f8(f879(f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867))),f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867)))),f879(f879(a869,f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867)))),f879(a869,f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867))))),f879(x101961,f879(a868,a867))),f8(f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867))),f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867))),a869)),f328(f328(f8(f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867))),f879(f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867))),f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867)))),f879(x101961,f879(a868,a867))),f8(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867)))),f328(f328(f8(f879(x101961,f879(f879(a868,a867),f879(a868,a867))),f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867))),f879(x101961,f879(a868,a867))),f18(x101961,f879(a868,a867),f879(a868,a867))),f328(f328(f8(f879(x101961,f879(a868,f879(a867,a867))),f879(x101961,f879(f879(a868,a867),f879(a868,a867))),f879(x101961,f879(a868,a867))),f328(f8(f879(a868,f879(a867,a867)),f879(f879(a868,a867),f879(a868,a867)),x101961),f18(a868,a867,a867))),f328(f8(f879(a868,a867),f879(a868,f879(a867,a867)),x101961),f328(f8(a867,f879(a867,a867),a868),a331))))))),f328(f328(f8(f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,f879(a868,a867)))),f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867))),a869),f328(f8(f879(x101961,f879(a868,f879(a868,a867))),f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,a867))),f328(f8(f879(a868,f879(a868,a867)),f879(a868,a867),x101961),f328(f8(f879(a868,a867),a867,a868),f88(a868))))),f328(f328(f8(f879(f879(a868,a867),f879(a868,f879(a868,a867))),f879(f879(x101961,f879(a868,a867)),f879(x101961,f879(a868,f879(a868,a867)))),a869),f8(f879(a868,a867),f879(a868,f879(a868,a867)),x101961)),f328(f328(f8(f879(a868,f879(f879(a868,a867),f879(a868,a867))),f879(f879(a868,a867),f879(a868,f879(a868,a867))),a869),f7(a868,f879(a868,a867),f879(a868,a867))),f328(f328(f8(f879(a868,f879(a868,f879(a867,a867))),f879(a868,f879(f879(a868,a867),f879(a868,a867))),a869),f328(f8(f879(a868,f879(a867,a867)),f879(f879(a868,a867),f879(a868,a867)),a868),f18(a868,a867,a867))),f328(f328(f8(f879(a868,f879(a868,a867)),f879(a868,f879(a868,f879(a867,a867))),a869),f328(f8(f879(a868,a867),f879(a868,f879(a867,a867)),a868),f328(f8(a867,f879(a867,a867),a868),a331))),f328(f328(f7(a869,a872,f879(a868,f879(a868,a867))),f328(f328(f8(f879(a868,f879(a872,f879(a868,a867))),f879(a872,f879(a868,f879(a868,a867))),a869),f7(a868,a872,f879(a868,a867))),a200)),x101962))))))))),x101963)) % 167.75/167.50 [4659]E(x46591,x46592)+~E(f33(x46593,x46591),f33(x46594,x46592)) % 167.75/167.50 [4660]E(x46601,x46602)+~E(f33(x46601,x46603),f33(x46602,x46604)) % 167.75/167.50 [4661]E(x46611,x46612)+~E(f32(x46613,x46611),f32(x46614,x46612)) % 167.75/167.50 [4662]E(x46621,x46622)+~E(f32(x46621,x46623),f32(x46622,x46624)) % 167.75/167.50 [7740]P26(x77401,x77402,x77403,x77404)+~E(f538(x77404,x77403,x77402,x77401),f539(x77404,x77403,x77402,x77401)) % 167.75/167.50 [8032]P35(x80321,x80322,x80323,x80324,f117(x80322))+~E(x80324,f117(x80321)) % 167.75/167.50 [8033]P35(x80331,x80332,x80333,f117(x80331),x80334)+~E(x80334,f117(x80332)) % 167.75/167.50 [8258]~P26(x82581,f876(x82582),x82584,f182(x82581,x82582,x82584))+P26(x82581,f876(x82582),f183(x82581,x82582,x82583,x82584),f182(x82581,x82582,x82584)) % 167.75/167.50 [8465]~P26(x84651,f876(x84652),f183(x84651,x84652,x84654,x84653),f182(x84651,x84652,x84653))+P26(x84651,f876(x84652),x84653,f182(x84651,x84652,x84653)) % 167.75/167.50 [8588]~P35(x85882,x85883,x85884,x85881,f117(x85883))+E(x85881,f117(x85882)) % 167.75/167.50 [8589]~P35(x85893,x85892,x85894,f117(x85893),x85891)+E(x85891,f117(x85892)) % 167.75/167.50 [5035]~P18(x50353,x50351,x50354)+E(f328(f328(x50351,x50352),x50352),x50352) % 167.75/167.50 [5290]P1(f328(x52902,x52904))+E(f328(f133(x52901,x52902),f168(x52901,x52903,x52904)),f117(x52901)) % 167.75/167.50 [5326]~E(x53264,f192(f879(x53261,a867)))+E(f328(f307(x53261,x53262,x53263),x53264),f192(f879(x53262,a867))) % 167.75/167.50 [5564]~P1(f328(x55642,x55644))+E(f328(f133(x55641,x55642),f168(x55641,x55643,x55644)),f168(x55641,x55643,x55644)) % 167.75/167.50 [5594]~E(f328(f307(x55942,x55943,x55944),x55941),f192(f879(x55943,a867)))+E(x55941,f192(f879(x55942,a867))) % 167.75/167.50 [5878]~P105(x58782)+E(f328(f328(f145(x58781,x58782,x58783),x58784),f117(x58781)),f328(f328(f148(x58781),x58784),f117(x58781))) % 167.75/167.50 [5915]E(f328(x59151,x59152),f205(x59153))+P1(f328(f328(f330(x59154),x59152),f182(x59154,x59153,x59151))) % 167.75/167.50 [6237]~E(x62371,f192(f879(x62372,a867)))+~P1(f328(f63(x62372,x62373,x62371),x62374)) % 167.75/167.50 [6259]~P55(x62591,x62593,x62594,x62592)+P1(f328(f38(x62591),x62592)) % 167.75/167.50 [6260]~P55(x62601,x62603,x62602,x62604)+P1(f328(f38(x62601),x62602)) % 167.75/167.50 [6266]~P55(x62662,x62663,x62664,x62661)+~E(x62661,f192(f879(x62662,a867))) % 167.75/167.50 [6297]~P107(x62971)+E(f328(f328(f105(f879(x62971,a867)),f328(f298(x62971,x62972),x62973)),f299(x62971,x62973,x62974)),f192(f879(x62971,a867))) % 167.75/167.50 [6324]~P1(f328(f328(x63243,x63244),x63242))+P1(f328(f328(f330(x63241),x63242),f289(x63241,x63243,x63244))) % 167.75/167.50 [6325]~P1(f328(f328(x63253,x63254),x63252))+P1(f328(f328(f330(x63251),x63252),f290(x63251,x63253,x63254))) % 167.75/167.50 [6326]~P1(f328(f328(x63263,x63262),x63264))+P1(f328(f328(f330(x63261),x63262),f291(x63261,x63263,x63264))) % 167.75/167.50 [6327]~P1(f328(f328(x63273,x63272),x63274))+P1(f328(f328(f330(x63271),x63272),f294(x63271,x63273,x63274))) % 167.75/167.50 [6465]~P107(x64651)+E(f328(f328(f105(f879(x64651,a867)),f302(x64651,x64652,x64653)),f299(x64651,x64653,x64654)),f192(f879(x64651,a867))) % 167.75/167.50 [6466]~P107(x64661)+E(f328(f328(f105(f879(x64661,a867)),f301(x64661,x64662,x64663)),f302(x64661,x64663,x64664)),f192(f879(x64661,a867))) % 167.75/167.50 [6467]~P107(x64671)+E(f328(f328(f105(f879(x64671,a867)),f301(x64671,x64672,x64673)),f301(x64671,x64673,x64674)),f192(f879(x64671,a867))) % 167.75/167.50 [6468]~P107(x64681)+E(f328(f328(f105(f879(x64681,a867)),f299(x64681,x64682,x64683)),f302(x64681,x64683,x64684)),f192(f879(x64681,a867))) % 167.75/167.50 [6469]~P107(x64691)+E(f328(f328(f105(f879(x64691,a867)),f299(x64691,x64692,x64693)),f301(x64691,x64693,x64694)),f192(f879(x64691,a867))) % 167.75/167.50 [6506]P1(f328(f328(x65061,x65062),f559(x65062,x65061)))+~P1(f328(f257(x65063,x65064,x65061),x65062)) % 167.75/167.50 [6554]~E(f328(x65541,x65542),f205(x65543))+~P1(f328(f328(f330(x65544),x65542),f182(x65544,x65543,x65541))) % 167.75/167.50 [6583]~P105(x65832)+E(f328(f170(x65831),f147(x65831,x65832,x65833,x65834)),f328(f170(x65831),x65834)) % 167.75/167.50 [6636]~P142(x66361)+E(f194(x66361,x66362,f328(a116,x66363),x66364),f194(x66361,x66362,x66363,f328(x66362,x66364))) % 167.75/167.50 [6696]~P1(f328(f328(f330(x66964),x66963),f289(x66964,x66961,x66962)))+P1(f328(f328(x66961,x66962),x66963)) % 167.75/167.50 [6697]~P1(f328(f328(f330(x66974),x66973),f290(x66974,x66971,x66972)))+P1(f328(f328(x66971,x66972),x66973)) % 167.75/167.50 [6698]~P1(f328(f328(f330(x66984),x66982),f291(x66984,x66981,x66983)))+P1(f328(f328(x66981,x66982),x66983)) % 167.75/167.50 [6699]~P1(f328(f328(f330(x66994),x66992),f294(x66994,x66991,x66993)))+P1(f328(f328(x66991,x66992),x66993)) % 167.75/167.50 [6776]E(f328(f39(f877(x67761,x67762)),f315(x67761,x67762,x67763,x67764)),f2(a872))+P1(f328(f38(x67762),x67764)) % 167.75/167.50 [6777]E(f328(f39(f877(x67771,x67772)),f315(x67771,x67772,x67773,x67774)),f2(a872))+P1(f328(f38(x67771),x67773)) % 167.75/167.50 [6979]~P16(x69794,x69791,x69792)+E(f328(f73(x69791,x69791,x69791,f328(x69792,x69793)),f328(x69792,x69793)),f328(x69792,x69793)) % 167.75/167.50 [7780]~P1(f328(x77801,x77804))+P1(f328(x77801,f96(x77802,a872,x77803,x77801))) % 167.75/167.50 [7865]~E(x78652,x78653)+P1(f328(f328(f330(f878(x78651,x78651)),f328(f328(f263(x78651,x78651),x78652),x78653)),f304(x78651,x78654))) % 167.75/167.50 [7894]~P26(x78941,x78942,x78943,f251(f879(x78941,a867)))+E(f328(f77(x78941,x78942,f251(f879(x78941,a867)),x78943),f328(x78943,x78944)),x78944) % 167.75/167.50 [7983]~P1(f328(f328(f330(f873(x79831)),f328(f328(f148(x79831),x79834),x79832)),f158(x79831,x79833)))+P1(f328(f328(f330(f873(x79831)),x79832),f158(x79831,x79833))) % 167.75/167.50 [7984]~P1(f328(f328(f330(f873(x79841)),f328(f328(f125(x79841),x79844),x79842)),f158(x79841,x79843)))+P1(f328(f328(f330(f873(x79841)),x79842),f158(x79841,x79843))) % 167.75/167.50 [7985]~P1(f328(f328(f330(f873(x79851)),f328(f328(f125(x79851),x79852),x79854)),f158(x79851,x79853)))+P1(f328(f328(f330(f873(x79851)),x79852),f158(x79851,x79853))) % 167.75/167.50 [7996]~P105(x79961)+P15(x79961,f328(f328(f151(x79962,x79961),x79963),f147(x79962,x79961,x79963,x79964))) % 167.75/167.50 [8095]P26(x80954,x80953,x80951,x80952)+E(f328(x80951,f538(x80952,x80951,x80953,x80954)),f328(x80951,f539(x80952,x80951,x80953,x80954))) % 167.75/167.50 [8108]E(f183(x81081,x81082,x81083,x81084),f183(x81081,x81082,x81084,x81083))+~E(f328(f328(f105(f879(x81081,a867)),f182(x81081,x81082,x81083)),f182(x81081,x81082,x81084)),f192(f879(x81081,a867))) % 167.75/167.50 [8220]~P26(x82202,x82201,x82204,x82203)+P26(x82201,x82202,f77(x82202,x82201,x82203,x82204),f328(f307(x82202,x82201,x82204),x82203)) % 167.75/167.50 [8356]P38(f878(x83562,x83564),f280(x83562,x83564,x83561,x83563))+P1(f328(x83561,f550(x83562,x83563,x83564,x83561))) % 167.75/167.50 [8473]E(x84731,x84732)+~P1(f328(f328(f330(f878(x84733,x84733)),f328(f328(f263(x84733,x84733),x84731),x84732)),f260(x84733,x84734))) % 167.75/167.50 [8540]~P1(f328(f38(f877(x85403,x85401)),f315(x85403,x85401,x85404,x85402)))+P1(f328(f38(x85401),x85402)) % 167.75/167.50 [8541]~P1(f328(f38(f877(x85411,x85413)),f315(x85411,x85413,x85412,x85414)))+P1(f328(f38(x85411),x85412)) % 167.75/167.50 [8724]P38(f878(x87241,x87242),f280(x87241,x87242,x87243,x87244))+~P38(x87242,f328(x87244,f550(x87241,x87244,x87242,x87243))) % 167.75/167.50 [9284]E(f328(f328(f156(x92841,x92842),f684(x92843,x92844,x92842,x92841)),f685(x92843,x92844,x92842,x92841)),x92844)+~P1(f328(f328(f330(f878(f873(x92841),f873(x92841))),f328(f328(f263(f873(x92841),f873(x92841)),x92842),x92844)),f154(x92841,x92843))) % 167.75/167.50 [9285]~P1(f328(x92853,x92854))+P1(f328(f328(f242(a872),f328(x92851,f96(x92852,a872,x92851,x92853))),f328(x92851,x92854))) % 167.75/167.50 [9291]~P1(f328(f328(f330(f878(f873(x92911),f873(x92911))),f328(f328(f263(f873(x92911),f873(x92911)),x92912),x92913)),f142(x92911,x92914)))+P1(f328(f328(f330(f878(f873(x92911),f873(x92911))),f328(f328(f263(f873(x92911),f873(x92911)),x92912),x92913)),f144(x92911,x92914))) % 167.75/167.50 [9397]P1(f328(f38(x93971),x93972))+~P1(f328(f328(f330(f878(f879(x93971,a867),f879(x93971,a867))),f328(f328(f263(f879(x93971,a867),f879(x93971,a867)),x93973),x93972)),f320(x93971,x93974))) % 167.75/167.50 [9398]P1(f328(f38(x93981),x93982))+~P1(f328(f328(f330(f878(f879(x93981,a867),f879(x93981,a867))),f328(f328(f263(f879(x93981,a867),f879(x93981,a867)),x93982),x93983)),f320(x93981,x93984))) % 167.75/167.50 [9401]~E(x94011,f192(f879(x94012,a867)))+~P1(f328(f328(f330(f878(f879(x94012,a867),f879(x94012,a867))),f328(f328(f263(f879(x94012,a867),f879(x94012,a867)),x94013),x94011)),f320(x94012,x94014))) % 167.75/167.50 [10041]P13(x100411,x100412,x100413,x100414)+~P1(f328(f328(f267(x100411,x100411,a867),f328(f328(f7(x100411,f879(x100411,x100412),f879(x100411,a867)),f328(f328(f8(f879(x100412,a867),f879(f879(x100411,x100412),f879(x100411,a867)),x100411),f8(x100412,a867,x100411)),f328(f328(f8(x100412,f879(x100412,a867),x100411),a325),x100414))),x100414)),f589(x100414,x100413,x100412,x100411))) % 167.75/167.50 [4934]~E(x49342,f117(x49341))+E(f328(f328(f156(x49341,x49342),x49343),x49344),f117(x49341)) % 167.75/167.50 [4935]~E(x49354,f117(x49351))+E(f328(f328(f151(x49351,x49352),x49353),x49354),f117(x49352)) % 167.75/167.50 [4936]~E(x49364,f205(x49361))+E(f328(f328(f206(x49361,x49362),x49363),x49364),f205(x49362)) % 167.75/167.50 [5174]E(x51741,f117(x51742))+~E(f328(f328(f151(x51742,x51743),x51744),x51741),f117(x51743)) % 167.75/167.50 [5175]E(x51751,f205(x51752))+~E(f328(f328(f206(x51752,x51753),x51754),x51751),f205(x51753)) % 167.75/167.50 [5176]E(x51761,f117(x51762))+~E(f328(f328(f156(x51762,x51761),x51763),x51764),f117(x51762)) % 167.75/167.50 [5208]E(x52081,x52082)+~E(f328(f328(f125(x52083),x52084),x52081),f328(f328(f125(x52083),x52084),x52082)) % 167.75/167.50 [5209]E(x52091,x52092)+~E(f328(f328(f125(x52093),x52091),x52094),f328(f328(f125(x52093),x52092),x52094)) % 167.75/167.50 [5363]P1(f328(x53633,x53632))+E(f167(x53631,x53632,f328(f133(x53631,x53633),x53634)),f328(f133(x53631,x53633),x53634)) % 167.75/167.50 [5366]~P1(f328(x53662,x53663))+P34(x53661,x53662,f328(f328(f148(x53661),x53663),x53664)) % 167.75/167.50 [5375]E(x53751,x53752)+~E(f136(a872,f328(f298(a872,x53751),x53753)),f328(f328(f148(a872),x53752),x53754)) % 167.75/167.50 [5423]~P27(x54232,x54233)+P27(x54231,f328(f328(f74(x54232,x54231),x54233),x54234)) % 167.75/167.50 [5424]~P38(x54242,x54243)+P38(x54241,f328(f328(f284(x54242,x54241),x54243),x54244)) % 167.75/167.50 [5548]~P34(x55481,x55482,x55484)+P34(x55481,x55482,f328(f328(f148(x55481),x55483),x55484)) % 167.75/167.50 [5549]~P34(x55491,x55492,x55494)+P34(x55491,x55492,f328(f328(f125(x55491),x55493),x55494)) % 167.75/167.50 [5550]~P34(x55501,x55502,x55503)+P34(x55501,x55502,f328(f328(f125(x55501),x55503),x55504)) % 167.75/167.50 [5637]~E(x56371,f117(x56372))+~E(f328(f328(f125(x56372),x56373),f328(f328(f148(x56372),x56374),f117(x56372))),x56371) % 167.75/167.50 [5662]~P32(x56623,x56621,f328(f328(f148(x56623),x56622),x56624))+P1(f328(x56621,x56622)) % 167.75/167.50 [5672]E(f118(x56721,x56722),x56723)+~E(f328(f328(f125(x56721),x56723),f328(f328(f148(x56721),x56724),f117(x56721))),x56722) % 167.75/167.50 [5673]E(f141(x56731,x56732),x56733)+~E(f328(f328(f125(x56731),x56734),f328(f328(f148(x56731),x56733),f117(x56731))),x56732) % 167.75/167.50 [5783]~E(f136(a872,f328(f298(a872,x57831),x57832)),f328(f328(f148(a872),x57833),x57834))+P1(f328(f328(f243(a872),x57831),x57832)) % 167.75/167.50 [5791]P32(x57911,x57912,x57913)+~P32(x57911,x57912,f328(f328(f148(x57911),x57914),x57913)) % 167.75/167.50 [5792]P32(x57921,x57922,x57923)+~P32(x57921,x57922,f328(f328(f125(x57921),x57924),x57923)) % 167.75/167.50 [5793]P32(x57931,x57932,x57933)+~P32(x57931,x57932,f328(f328(f125(x57931),x57933),x57934)) % 167.75/167.50 [5978]E(x59781,f328(f328(f125(x59782),f328(f166(x59782),x59783)),f328(f328(f148(x59782),x59784),f117(x59782))))+~E(f328(f166(x59782),x59781),f328(f328(f148(x59782),x59784),x59783)) % 167.75/167.50 [6155]~P107(x61551)+E(f328(f328(f105(f879(x61551,a867)),f328(f298(x61551,x61552),x61553)),f328(f298(x61551,x61553),x61554)),f192(f879(x61551,a867))) % 167.75/167.50 [6168]E(f328(f328(f162(x61681),f168(x61681,x61682,x61683)),x61684),x61683)+~P1(f328(f328(f243(a872),x61684),x61682)) % 167.75/167.50 [6195]~P67(x61951)+E(f328(f163(x61951),f328(f328(f151(a1,x61951),x61952),f177(x61953,x61954))),f328(f328(f6(a1,x61951),x61952),f328(f170(a1),f177(x61953,x61954)))) % 167.75/167.50 [6196]~P67(x61961)+E(f328(f328(f6(a1,x61961),x61962),f328(f170(a1),f177(x61963,x61964))),f328(f163(x61961),f328(f328(f151(a1,x61961),x61962),f177(x61963,x61964)))) % 167.75/167.50 [6337]~E(x63372,f328(f328(f125(x63371),f328(f166(x63371),x63374)),f328(f328(f148(x63371),x63373),f117(x63371))))+E(f328(f166(x63371),x63372),f328(f328(f148(x63371),x63373),x63374)) % 167.75/167.50 [6352]~P20(x63522,x63523,x63524,x63521)+E(f328(x63521,f192(f879(x63522,a867))),f34(x63523)) % 167.75/167.50 [6378]~P107(x63781)+E(f328(f328(f105(f879(x63781,a867)),f302(x63781,x63782,x63783)),f328(f298(x63781,x63783),x63784)),f192(f879(x63781,a867))) % 167.75/167.50 [6584]E(x65841,f192(f879(x65842,a867)))+~E(f315(x65843,x65842,x65844,x65841),f192(f879(f877(x65843,x65842),a867))) % 167.75/167.50 [6585]E(x65851,f192(f879(x65852,a867)))+~E(f315(x65852,x65853,x65851,x65854),f192(f879(f877(x65852,x65853),a867))) % 167.75/167.50 [6655]~P105(x66552)+E(f328(f193(f873(x66551)),f147(x66551,x66552,x66553,x66554)),f328(f193(f873(x66551)),x66554)) % 167.75/167.50 [6667]~P1(f328(f258(x66673,x66674,x66671),x66672))+P1(f328(f328(x66671,f560(x66672,x66671)),x66672)) % 167.75/167.50 [6707]~P1(f328(f38(x67072),x67074))+P1(f328(f38(x67071),f328(f307(x67072,x67071,x67073),x67074))) % 167.75/167.50 [6939]~P26(x69392,x69391,x69393,x69394)+E(f328(f39(x69391),f328(f307(x69392,x69391,x69393),x69394)),f328(f39(x69392),x69394)) % 167.75/167.50 [6958]E(f328(f307(x69581,x69582,x69583),f328(f308(x69581,x69582,x69583),x69584)),x69584)+~E(f328(f307(x69581,x69582,x69583),f251(f879(x69581,a867))),f251(f879(x69582,a867))) % 167.75/167.50 [7368]~P26(x73681,x73682,x73683,f251(f879(x73681,a867)))+E(f328(f308(x73681,x73682,x73683),f328(f307(x73681,x73682,x73683),x73684)),x73684) % 167.75/167.50 [7656]E(x76561,x76562)+~P1(f328(f328(f330(x76563),x76561),f328(f170(x76563),f168(x76563,x76564,x76562)))) % 167.75/167.50 [7665]~E(x76651,f2(a872))+~P1(f328(f328(f330(x76652),x76653),f328(f170(x76652),f168(x76652,x76651,x76654)))) % 167.75/167.50 [7701]P1(f328(x77011,x77012))+~P1(f328(f328(f330(x77013),x77012),f328(f170(x77013),f175(x77013,x77011,x77014)))) % 167.75/167.50 [7812]~P1(f328(f328(f330(f873(x78121)),f328(f328(f148(x78121),x78122),x78124)),f158(x78121,x78123)))+P1(f328(f328(f330(x78121),x78122),x78123)) % 167.75/167.50 [7941]~P1(f328(f328(f330(x79411),x79412),f328(f170(x79411),f174(x79411,x79413,x79414))))+P1(f328(f328(f330(x79411),x79412),f328(f170(x79411),x79413))) % 167.75/167.50 [7942]~P1(f328(f328(f330(x79421),x79422),f328(f170(x79421),f167(x79421,x79424,x79423))))+P1(f328(f328(f330(x79421),x79422),f328(f170(x79421),x79423))) % 167.75/167.50 [7943]~P1(f328(f328(f330(x79431),x79432),f328(f170(x79431),f175(x79431,x79434,x79433))))+P1(f328(f328(f330(x79431),x79432),f328(f170(x79431),x79433))) % 167.75/167.50 [7953]E(f328(f193(f873(x79531)),x79532),x79533)+~P1(f328(f328(f330(f873(x79531)),x79532),f328(f170(f873(x79531)),f56(x79531,x79533,x79534)))) % 167.75/167.50 [8044]P1(f328(x80443,x80442))+E(f328(f133(x80441,f328(f328(f8(a867,a867,x80441),a323),f328(a325,x80442))),f328(f133(x80441,x80443),x80444)),f328(f133(x80441,x80443),x80444)) % 167.75/167.50 [8164]E(f328(f328(f162(x81641),f175(x81641,x81642,x81643)),x81644),f328(f328(f162(x81641),x81643),x81644))+~P1(f328(f328(f243(a872),x81644),f328(f193(f873(x81641)),f175(x81641,x81642,x81643)))) % 167.75/167.50 [8256]~P67(x82561)+E(f328(f328(f6(a872,x82561),f328(f328(f8(a872,x82561,a872),x82562),a116)),f328(f298(a872,x82563),x82564)),f328(f328(f6(a872,x82561),x82562),f328(f298(a872,f328(a116,x82563)),f328(a116,x82564)))) % 167.75/167.50 [8265]~P67(x82651)+E(f328(f328(f6(a872,x82651),f328(f328(f8(a872,x82651,a872),x82652),a116)),f299(a872,x82653,x82654)),f328(f328(f6(a872,x82651),x82652),f299(a872,f328(a116,x82653),f328(a116,x82654)))) % 167.75/167.50 [8393]~P26(x83931,x83933,x83934,f251(f879(x83931,a867)))+P26(x83931,f879(x83932,x83933),f328(f328(f8(x83933,f879(x83932,x83933),x83931),f16(x83933,x83932)),x83934),f251(f879(x83931,a867))) % 167.75/167.50 [8478]~P26(x84782,x84781,x84784,x84783)+E(f328(f307(x84781,x84782,f77(x84782,x84781,x84783,x84784)),f328(f307(x84782,x84781,x84784),x84783)),x84783) % 167.75/167.50 [8542]~P1(f328(f328(f330(f878(x85421,x85421)),f328(f328(f263(x85421,x85421),x85422),x85424)),f260(x85421,x85423)))+P1(f328(f328(f330(x85421),x85422),x85423)) % 167.75/167.50 [8637]E(f328(f328(f328(f72(x86371,f876(x86372)),f328(f16(f876(x86372),x86371),f205(x86372))),x86373),f328(f235(x86372),f721(x86373,x86374,x86372,x86371))),x86374)+~E(f182(x86371,x86372,x86374),f328(f328(f306(x86371),x86373),f192(f879(x86371,a867)))) % 167.75/167.50 [8759]~E(f328(f328(f6(x87591,a872),x87594),x87593),f328(a116,x87592))+P1(f328(f328(f330(x87591),f862(x87592,x87593,x87594,x87591)),x87593)) % 167.75/167.50 [8779]~E(f328(f328(f6(x87794,a872),x87791),x87793),f328(a116,x87792))+P1(f328(f328(f243(a872),f2(a872)),f328(x87791,f862(x87792,x87793,x87791,x87794)))) % 167.75/167.50 [8790]~P1(f328(f38(x87902),x87904))+P1(f328(f328(f242(a872),f328(f39(x87901),f328(f307(x87902,x87901,x87903),x87904))),f328(f39(x87902),x87904))) % 167.75/167.50 [8791]E(f328(f328(f263(x87911,x87912),f656(x87913,x87914,x87912,x87911)),f657(x87913,x87914,x87912,x87911)),x87914)+~P1(f328(f328(f330(f878(x87911,x87912)),x87914),f328(f283(x87912,x87911),x87913))) % 167.75/167.50 [8799]P26(x87991,x87992,x87993,x87994)+P1(f328(f328(f330(x87991),f538(x87994,x87993,x87992,x87991)),x87994)) % 167.75/167.50 [8800]P26(x88001,x88002,x88003,x88004)+P1(f328(f328(f330(x88001),f539(x88004,x88003,x88002,x88001)),x88004)) % 167.75/167.50 [8861]P13(x88611,x88612,x88613,x88614)+P1(f328(f328(f330(f878(x88611,x88611)),f589(x88614,x88613,x88612,x88611)),x88613)) % 167.75/167.50 [8923]P1(f328(x89231,x89232))+~P1(f328(x89231,f328(f328(f263(x89233,x89234),f507(x89234,x89233,x89231)),f508(x89234,x89233,x89231)))) % 167.75/167.50 [8940]E(f328(f193(f873(x89401)),x89402),f328(f193(f873(x89401)),x89403))+~P1(f328(f328(f330(f878(f873(x89401),f873(x89401))),f328(f328(f263(f873(x89401),f873(x89401)),x89402),x89403)),f142(x89401,x89404))) % 167.75/167.50 [8941]E(f328(f193(f873(x89411)),x89412),f328(f193(f873(x89411)),x89413))+~P1(f328(f328(f330(f878(f873(x89411),f873(x89411))),f328(f328(f263(f873(x89411),f873(x89411)),x89412),x89413)),f154(x89411,x89414))) % 167.75/167.50 [8944]E(f328(f193(f873(x89441)),x89442),f328(f193(f873(x89441)),x89443))+~P1(f328(f328(f330(f878(f873(x89441),f873(x89441))),f328(f328(f263(f873(x89441),f873(x89441)),x89442),x89443)),f155(x89441,x89444))) % 167.75/167.50 [9017]P1(f328(f328(f242(a872),f152(x90171,x90172,x90173)),f152(x90171,x90174,x90173)))+P1(f328(f328(f330(x90171),f683(x90174,x90172,x90173,x90171)),f328(f170(x90171),x90173))) % 167.75/167.50 [9020]E(f328(f193(f873(x90201)),x90202),f328(f193(f873(x90201)),x90203))+~P1(f328(f328(f330(f878(f873(x90201),f873(x90201))),f328(f328(f263(f873(x90201),f873(x90201)),x90202),x90203)),f304(f873(x90201),f154(x90201,x90204)))) % 167.75/167.50 [9256]~P26(x92561,x92562,x92563,x92564)+~P1(f328(f328(f243(a872),f328(f39(x92562),f328(f307(x92561,x92562,x92563),x92564))),f328(f39(x92561),x92564))) % 167.75/167.50 [9302]~P1(f328(f328(f330(f878(f873(x93021),f873(x93021))),f328(f328(f263(f873(x93021),f873(x93021)),x93022),x93023)),f154(x93021,x93024)))+P1(f328(f328(f330(f878(f873(x93021),f873(x93021))),f328(f328(f263(f873(x93021),f873(x93021)),x93022),x93023)),f155(x93021,f304(x93021,x93024)))) % 167.75/167.50 [9306]~P1(f328(f328(f330(f878(f873(x93061),f873(x93061))),f328(f328(f263(f873(x93061),f873(x93061)),x93062),x93063)),f155(x93061,x93064)))+P1(f328(f328(f330(f878(f873(x93061),f873(x93061))),f328(f328(f263(f873(x93061),f873(x93061)),x93062),x93063)),f304(f873(x93061),f154(x93061,x93064)))) % 167.75/167.50 [9323]P1(f328(f328(f330(f878(x93231,x93231)),f328(f328(f263(x93231,x93231),x93232),x93233)),f304(x93231,x93234)))+~P1(f328(f328(f330(f878(x93231,x93231)),f328(f328(f263(x93231,x93231),x93232),x93233)),f328(f328(f285(x93231,x93231,x93231),x93234),f304(x93231,x93234)))) % 167.75/167.50 [9507]E(f328(f328(f125(x95071),f699(x95072,x95073,x95074,x95071)),f328(f328(f148(x95071),f697(x95072,x95073,x95074,x95071)),f700(x95072,x95073,x95074,x95071))),x95074)+~P1(f328(f328(f330(f878(f873(x95071),f873(x95071))),f328(f328(f263(f873(x95071),f873(x95071)),x95074),x95073)),f154(x95071,x95072))) % 167.75/167.50 [9508]E(f328(f328(f125(x95081),f699(x95082,x95083,x95084,x95081)),f328(f328(f148(x95081),f698(x95082,x95083,x95084,x95081)),f700(x95082,x95083,x95084,x95081))),x95083)+~P1(f328(f328(f330(f878(f873(x95081),f873(x95081))),f328(f328(f263(f873(x95081),f873(x95081)),x95084),x95083)),f154(x95081,x95082))) % 167.75/167.50 [9585]P1(f328(f328(f330(f878(x95851,x95851)),f328(f328(f263(x95851,x95851),x95852),f647(x95853,x95854,x95852,x95851))),f304(x95851,x95853)))+~P1(f328(f328(f330(f878(x95851,x95851)),f328(f328(f263(x95851,x95851),x95852),x95854)),f328(f328(f285(x95851,x95851,x95851),x95853),f304(x95851,x95853)))) % 167.75/167.50 [9656]P1(f328(f328(f242(a872),f152(x96561,x96562,x96563)),f152(x96561,x96564,x96563)))+~P1(f328(f328(f243(a872),f328(x96562,f683(x96564,x96562,x96563,x96561))),f328(x96564,f683(x96564,x96562,x96563,x96561)))) % 167.75/167.50 [9724]P1(f328(f328(f330(f878(x97241,x97241)),f328(f328(f263(x97241,x97241),f646(x97242,x97243,x97244,x97241)),x97243)),f304(x97241,x97242)))+~P1(f328(f328(f330(f878(x97241,x97241)),f328(f328(f263(x97241,x97241),x97244),x97243)),f328(f328(f285(x97241,x97241,x97241),x97242),f304(x97241,x97242)))) % 167.75/167.50 [5190]~E(x51902,x51903)+E(f167(x51901,x51902,f328(f328(f148(x51901),x51903),x51904)),x51904) % 167.75/167.50 [5318]P1(f328(x53182,x53183))+E(f175(x53181,x53182,f328(f328(f148(x53181),x53183),x53184)),f117(x53181)) % 167.75/167.50 [5387]~P87(x53872)+E(f328(f328(f79(f879(x53871,x53872)),x53873),x53874),f328(f79(x53872),f328(x53873,x53874))) % 167.75/167.50 [5399]~E(x53992,f2(a872))+E(f328(f328(f135(x53991),x53992),f328(f328(f148(x53991),x53993),x53994)),f328(f328(f148(x53991),x53993),x53994)) % 167.75/167.50 [5400]P1(f328(x54002,x54003))+E(f328(f133(x54001,x54002),f328(f328(f148(x54001),x54003),x54004)),f328(f133(x54001,x54002),x54004)) % 167.75/167.50 [5531]~E(x55312,x55314)+P1(f328(f328(f328(f306(x55311),x55312),x55313),x55314)) % 167.75/167.50 [5539]E(x55391,f117(x55392))+E(f141(x55393,f328(f328(f151(x55392,x55393),x55394),x55391)),f328(x55394,f141(x55392,x55391))) % 167.75/167.50 [5553]~E(x55531,f64(x55532,x55534))+E(f328(x55531,f328(f328(f306(x55532),x55533),f192(f879(x55532,a867)))),x55533) % 167.75/167.50 [5589]E(x55891,f117(x55892))+E(f328(f138(x55893),f328(f328(f151(x55892,x55893),x55894),x55891)),f328(x55894,f328(f138(x55892),x55891))) % 167.75/167.50 [5692]~P1(f328(x56923,x56924))+P1(f328(f328(f328(f306(x56921),x56922),x56923),x56924)) % 167.75/167.50 [5808]~P19(x58082,x58084,x58081)+E(f328(x58081,f328(f328(f306(x58082),x58083),f192(f879(x58082,a867)))),x58083) % 167.75/167.50 [5832]~E(x58322,x58323)+P1(f328(f328(f330(x58321),x58322),f328(f328(f306(x58321),x58323),x58324))) % 167.75/167.50 [5836]~P2(x58361)+E(f328(f328(f114(x58361),x58362),f328(f328(f114(x58361),x58363),x58364)),f328(f328(f114(x58361),x58363),f328(f328(f114(x58361),x58362),x58364))) % 167.75/167.50 [5838]~P99(x58381)+E(f328(f328(f114(x58381),x58382),f328(f328(f114(x58381),x58383),x58384)),f328(f328(f114(x58381),x58383),f328(f328(f114(x58381),x58382),x58384))) % 167.75/167.50 [5839]~P2(x58391)+E(f328(f328(f105(x58391),x58392),f328(f328(f105(x58391),x58393),x58394)),f328(f328(f105(x58391),x58393),f328(f328(f105(x58391),x58392),x58394))) % 167.75/167.50 [5841]~P100(x58411)+E(f328(f328(f105(x58411),x58412),f328(f328(f105(x58411),x58413),x58414)),f328(f328(f105(x58411),x58413),f328(f328(f105(x58411),x58412),x58414))) % 167.75/167.50 [5842]~P111(x58421)+E(f328(f328(f80(x58421),x58422),f328(f328(f80(x58421),x58423),x58424)),f328(f328(f80(x58421),x58423),f328(f328(f80(x58421),x58422),x58424))) % 167.75/167.50 [5843]~P111(x58431)+E(f328(f328(f81(x58431),x58432),f328(f328(f81(x58431),x58433),x58434)),f328(f328(f81(x58431),x58433),f328(f328(f81(x58431),x58432),x58434))) % 167.75/167.50 [5845]~P105(x58451)+E(f328(f328(f240(x58451),x58452),f328(f328(f240(x58451),x58453),x58454)),f328(f328(f240(x58451),x58453),f328(f328(f240(x58451),x58452),x58454))) % 167.75/167.50 [5847]~P105(x58471)+E(f328(f328(f241(x58471),x58472),f328(f328(f241(x58471),x58473),x58474)),f328(f328(f241(x58471),x58473),f328(f328(f241(x58471),x58472),x58474))) % 167.75/167.50 [5852]E(x58521,x58522)+E(f167(x58523,x58521,f328(f328(f148(x58523),x58522),x58524)),f328(f328(f148(x58523),x58522),f167(x58523,x58521,x58524))) % 167.75/167.50 [5865]~P1(f328(x58652,x58653))+E(f328(f133(x58651,x58652),f328(f328(f148(x58651),x58653),x58654)),f328(f328(f148(x58651),x58653),f328(f133(x58651,x58652),x58654))) % 167.75/167.50 [5998]~P1(f328(x59982,x59983))+E(f175(x59981,x59982,f328(f328(f148(x59981),x59983),x59984)),f328(f328(f148(x59981),x59983),f175(x59981,x59982,x59984))) % 167.75/167.50 [6049]P25(x60491,x60492,x60493)+~P25(x60491,x60492,f328(f328(f306(f871(x60491)),x60494),x60493)) % 167.75/167.50 [6062]E(x60621,f192(f879(x60622,a867)))+E(f328(f328(f43(x60622,f879(x60623,a867)),x60621),f328(f16(f879(x60623,a867),x60622),x60624)),x60624) % 167.75/167.50 [6063]E(x60631,f192(f879(x60632,a867)))+E(f328(f328(f44(x60632,f879(x60633,a867)),x60631),f328(f16(f879(x60633,a867),x60632),x60634)),x60634) % 167.75/167.50 [6072]~E(x60724,f192(f879(x60722,a867)))+E(f328(f328(f265(x60721,x60722),x60723),f328(f16(f879(x60722,a867),x60721),x60724)),f192(f879(f878(x60721,x60722),a867))) % 167.75/167.50 [6073]~E(x60733,f192(f879(x60731,a867)))+E(f328(f328(f265(x60731,x60732),x60733),f328(f16(f879(x60732,a867),x60731),x60734)),f192(f879(f878(x60731,x60732),a867))) % 167.75/167.50 [6119]E(x61191,f2(a872))+E(f328(f328(f135(x61192),x61191),f328(f328(f148(x61192),x61193),x61194)),f328(f328(f135(x61192),f328(f328(f22(a872),x61191),f78(a872))),x61194)) % 167.75/167.50 [6149]E(x61491,f192(f879(x61492,a867)))+E(f328(f307(x61492,x61493,f328(f16(x61493,x61492),x61494)),x61491),f328(f328(f306(x61493),x61494),f192(f879(x61493,a867)))) % 167.75/167.50 [6152]E(f328(f308(x61521,x61522,f328(f16(x61522,x61521),x61523)),x61524),f192(f879(x61521,a867)))+P1(f328(f328(f330(x61522),x61523),x61524)) % 167.75/167.50 [6221]~E(x62213,f192(f879(x62211,a867)))+E(f328(f328(f43(x62211,f879(x62212,a867)),x62213),f328(f16(f879(x62212,a867),x62211),x62214)),f251(f879(x62212,a867))) % 167.75/167.50 [6222]~E(x62223,f192(f879(x62221,a867)))+E(f328(f328(f44(x62221,f879(x62222,a867)),x62223),f328(f16(f879(x62222,a867),x62221),x62224)),f192(f879(x62222,a867))) % 167.75/167.50 [6224]~P57(x62241)+E(f46(x62241,f328(f328(f81(x62241),x62242),x62243),f328(f328(f81(x62241),x62242),x62244)),f328(f328(f81(x62241),x62242),f46(x62241,x62243,x62244))) % 167.75/167.50 [6388]E(f328(f308(x63881,x63882,f328(f16(x63882,x63881),x63883)),x63884),f251(f879(x63881,a867)))+~P1(f328(f328(f330(x63882),x63883),x63884)) % 167.75/167.50 [6411]~P1(f328(f328(f330(x64111),x64112),x64114))+P1(f328(f328(f330(x64111),x64112),f328(f328(f306(x64111),x64113),x64114))) % 167.75/167.50 [6416]P1(f328(x64161,x64162))+~P1(f328(f157(x64163,x64161),f328(f328(f148(x64163),x64162),x64164))) % 167.75/167.50 [6425]~E(x64253,f328(f328(f22(a872),f328(f193(f873(x64251)),x64252)),f78(a872)))+E(f118(x64251,f328(f328(f156(x64251,x64252),x64253),x64254)),f118(x64251,x64252)) % 167.75/167.50 [6444]~P105(x64441)+E(f328(f328(f105(f879(x64441,a867)),f328(f297(x64441),x64442)),f299(x64441,x64443,x64444)),f299(x64441,x64443,f328(f328(f240(x64441),x64442),x64444))) % 167.75/167.50 [6445]~P105(x64451)+E(f328(f328(f105(f879(x64451,a867)),f328(f250(x64451),x64452)),f299(x64451,x64453,x64454)),f299(x64451,f328(f328(f241(x64451),x64452),x64453),x64454)) % 167.75/167.50 [6460]E(f328(f328(f105(f879(x64601,a867)),x64602),f328(f328(f306(x64601),x64603),x64604)),f328(f328(f105(f879(x64601,a867)),x64602),x64604))+P1(f328(f328(f330(x64601),x64603),x64602)) % 167.75/167.50 [6472]E(f167(x64721,x64722,f328(f328(f125(x64721),x64723),x64724)),f328(f328(f125(x64721),x64723),f167(x64721,x64722,x64724)))+P1(f328(f328(f330(x64721),x64722),f328(f170(x64721),x64723))) % 167.75/167.50 [6476]~P78(x64761)+E(f328(f328(f81(x64761),f328(f328(f253(x64761),x64762),x64763)),f328(f328(f253(x64761),x64762),x64764)),f328(f328(f253(x64761),x64762),f328(f328(f80(a872),x64763),x64764))) % 167.75/167.50 [6477]~P111(x64771)+E(f328(f328(f81(x64771),f328(f328(f253(x64771),x64772),x64773)),f328(f328(f253(x64771),x64772),x64774)),f328(f328(f253(x64771),x64772),f328(f328(f80(a872),x64773),x64774))) % 167.75/167.50 [6513]~P98(x65131)+E(f328(f328(f105(x65131),f328(f328(f114(x65131),x65132),x65133)),f328(f328(f114(x65131),x65132),x65134)),f328(f328(f114(x65131),x65132),f328(f328(f105(x65131),x65133),x65134))) % 167.75/167.50 [6514]~P98(x65141)+E(f328(f328(f114(x65141),f328(f328(f105(x65141),x65142),x65143)),f328(f328(f105(x65141),x65142),x65144)),f328(f328(f105(x65141),x65142),f328(f328(f114(x65141),x65143),x65144))) % 167.75/167.50 [6515]~P111(x65151)+E(f328(f328(f80(x65151),f328(f328(f81(x65151),x65152),x65153)),f328(f328(f81(x65151),x65152),x65154)),f328(f328(f81(x65151),x65152),f328(f328(f80(x65151),x65153),x65154))) % 167.75/167.50 [6516]~P105(x65161)+E(f328(f328(f241(x65161),f328(f328(f240(x65161),x65162),x65163)),f328(f328(f240(x65161),x65162),x65164)),f328(f328(f240(x65161),x65162),f328(f328(f241(x65161),x65163),x65164))) % 167.75/167.50 [6517]~P105(x65171)+E(f328(f328(f240(x65171),f328(f328(f241(x65171),x65172),x65173)),f328(f328(f241(x65171),x65172),x65174)),f328(f328(f241(x65171),x65172),f328(f328(f240(x65171),x65173),x65174))) % 167.75/167.50 [6548]~P57(x65481)+E(f46(x65481,f328(f328(f81(x65481),x65482),x65483),f328(f328(f81(x65481),x65484),x65483)),f328(f328(f81(x65481),f46(x65481,x65482,x65484)),x65483)) % 167.75/167.50 [6551]~E(f328(f193(f873(x65511)),x65513),f328(f193(f873(x65512)),x65514))+E(f328(f328(f151(f878(x65511,x65512),x65512),f266(x65511,x65512)),f328(f328(f180(x65511,x65512),x65513),x65514)),x65514) % 167.75/167.50 [6552]~E(f328(f193(f873(x65521)),x65523),f328(f193(f873(x65522)),x65524))+E(f328(f328(f151(f878(x65521,x65522),x65521),f262(x65521,x65522)),f328(f328(f180(x65521,x65522),x65523),x65524)),x65523) % 167.75/167.50 [6558]P1(f328(f157(x65581,x65582),x65583))+~P1(f328(f157(x65581,x65582),f328(f328(f148(x65581),x65584),x65583))) % 167.75/167.50 [6559]P1(f328(f157(x65591,x65592),x65593))+~P1(f328(f157(x65591,x65592),f328(f328(f125(x65591),x65594),x65593))) % 167.75/167.50 [6560]P1(f328(f157(x65601,x65602),x65603))+~P1(f328(f157(x65601,x65602),f328(f328(f125(x65601),x65603),x65604))) % 167.75/167.50 [6565]~P58(x65651)+E(f46(x65651,f328(f328(f22(x65651),x65652),f46(x65651,x65653,x65654)),x65654),f46(x65651,f328(f328(f22(x65651),x65652),x65653),x65654)) % 167.75/167.50 [6567]~P57(x65671)+E(f46(x65671,f328(f328(f81(x65671),x65672),f46(x65671,x65673,x65674)),x65674),f46(x65671,f328(f328(f81(x65671),x65672),x65673),x65674)) % 167.75/167.50 [6568]~P57(x65681)+E(f46(x65681,f328(f328(f80(x65681),x65682),f46(x65681,x65683,x65684)),x65684),f46(x65681,f328(f328(f80(x65681),x65682),x65683),x65684)) % 167.75/167.50 [6649]~P105(x66491)+E(f328(f328(f105(f879(x66491,a867)),f299(x66491,x66492,x66493)),f328(f297(x66491),x66494)),f299(x66491,x66492,f328(f328(f240(x66491),x66493),x66494))) % 167.75/167.50 [6650]~P105(x66501)+E(f328(f328(f105(f879(x66501,a867)),f299(x66501,x66502,x66503)),f328(f250(x66501),x66504)),f299(x66501,f328(f328(f241(x66501),x66502),x66504),x66503)) % 167.75/167.50 [6653]~E(f328(f193(f873(x66531)),x66533),f328(f193(f873(x66532)),x66534))+E(f328(f328(f180(x66531,x66532),f328(f166(x66531),x66533)),f328(f166(x66532),x66534)),f328(f166(f878(x66531,x66532)),f328(f328(f180(x66531,x66532),x66533),x66534))) % 167.75/167.50 [6663]E(x66631,f328(f328(f22(a872),f328(f193(f873(x66632)),x66633)),f78(a872)))+E(f118(x66632,f328(f328(f156(x66632,x66633),x66631),x66634)),f328(f328(f156(x66632,f118(x66632,x66633)),x66631),x66634)) % 167.75/167.50 [6678]~P1(f328(f134(x66782),x66784))+P1(f328(f134(f878(x66781,x66782)),f328(f328(f180(x66781,x66782),x66783),x66784))) % 167.75/167.50 [6679]~P1(f328(f134(x66791),x66793))+P1(f328(f134(f878(x66791,x66792)),f328(f328(f180(x66791,x66792),x66793),x66794))) % 167.75/167.50 [6942]E(f328(f328(f40(a872),x69421),x69422),x69423)+~P1(f328(f49(x69421,x69422),f328(f328(f263(a872,a872),x69423),x69424))) % 167.75/167.50 [6966]E(f46(a872,x69661,x69662),x69663)+~P1(f328(f49(x69661,x69662),f328(f328(f263(a872,a872),x69664),x69663))) % 167.75/167.50 [6969]P1(f328(f134(x69691),x69692))+~P1(f328(f134(x69693),f328(f328(f151(x69691,x69693),x69694),x69692))) % 167.75/167.50 [6977]~P25(x69771,x69772,f328(f328(f306(f871(x69771)),x69773),x69774))+P25(x69771,x69772,f328(f328(f306(f871(x69771)),x69773),f192(f879(f871(x69771),a867)))) % 167.75/167.50 [7053]E(f167(x70531,x70532,f328(f328(f125(x70531),x70533),x70534)),f328(f328(f125(x70531),f167(x70531,x70532,x70533)),x70534))+~P1(f328(f328(f330(x70531),x70532),f328(f170(x70531),x70533))) % 167.75/167.50 [7143]~P58(x71431)+E(f46(x71431,f328(f328(f22(x71431),f46(x71431,x71432,x71433)),x71434),x71433),f46(x71431,f328(f328(f22(x71431),x71432),x71434),x71433)) % 167.75/167.50 [7146]~P57(x71461)+E(f46(x71461,f328(f328(f80(x71461),f46(x71461,x71462,x71463)),x71464),x71463),f46(x71461,f328(f328(f80(x71461),x71462),x71464),x71463)) % 167.75/167.50 [7147]~P57(x71471)+E(f46(x71471,f328(f328(f81(x71471),f46(x71471,x71472,x71473)),x71474),x71473),f46(x71471,f328(f328(f81(x71471),x71472),x71474),x71473)) % 167.75/167.50 [7164]P1(f328(f328(f328(a198,x71641),x71642),x71643))+~P1(f328(f328(f328(f328(a200,x71641),x71642),x71644),x71643)) % 167.75/167.50 [7339]~E(x73391,f328(f328(f148(x73392),x73393),x73394))+~P1(f328(f328(f242(a872),f328(f193(f873(x73392)),x73391)),f328(f193(f873(x73392)),x73394))) % 167.75/167.50 [7414]~E(f328(f176(x74141,x74142),x74143),f328(f176(x74141,x74142),x74144))+E(f328(f307(f878(x74141,x74142),x74141,f262(x74141,x74142)),f328(f170(f878(x74141,x74142)),x74143)),f328(f307(f878(x74141,x74142),x74141,f262(x74141,x74142)),f328(f170(f878(x74141,x74142)),x74144))) % 167.75/167.50 [7547]P26(x75471,x75472,x75473,f328(f170(x75471),x75474))+~P1(f328(f134(x75472),f328(f328(f151(x75471,x75472),x75473),x75474))) % 167.75/167.50 [7623]~P1(f328(f328(f242(f879(x76231,a867)),x76232),x76234))+P1(f328(f328(f242(f879(x76231,a867)),x76232),f328(f328(f306(x76231),x76233),x76234))) % 167.75/167.50 [7657]~P58(x76571)+E(f46(x76571,f328(f328(f22(x76571),f46(x76571,x76572,x76573)),f46(x76571,x76574,x76573)),x76573),f46(x76571,f328(f328(f22(x76571),x76572),x76574),x76573)) % 167.75/167.50 [7658]~P57(x76581)+E(f46(x76581,f328(f328(f80(x76581),f46(x76581,x76582,x76583)),f46(x76581,x76584,x76583)),x76583),f46(x76581,f328(f328(f80(x76581),x76582),x76584),x76583)) % 167.75/167.50 [7659]~P57(x76591)+E(f46(x76591,f328(f328(f81(x76591),f46(x76591,x76592,x76593)),f46(x76591,x76594,x76593)),x76593),f46(x76591,f328(f328(f81(x76591),x76592),x76594),x76593)) % 167.75/167.50 [7759]P1(f328(f328(f328(f328(a200,x77591),x77592),f328(a116,x77593)),x77594))+~P1(f328(f328(f328(f328(a200,x77591),x77592),x77593),x77594)) % 167.75/167.50 [7766]~E(f328(x77664,f819(x77664,x77663,x77661,x77662)),f192(f879(x77662,a867)))+E(f328(f328(f44(x77661,f879(x77662,a867)),x77663),x77664),f192(f879(x77662,a867))) % 167.75/167.50 [7767]~E(f328(x77674,f822(x77674,x77673,x77671,x77672)),f251(f879(x77672,a867)))+E(f328(f328(f43(x77671,f879(x77672,a867)),x77673),x77674),f251(f879(x77672,a867))) % 167.75/167.50 [7768]~E(f328(x77684,f823(x77684,x77683,x77682,x77681)),f251(f879(x77682,a867)))+E(f328(f328(f43(x77681,f879(x77682,a867)),x77683),x77684),f251(f879(x77682,a867))) % 167.75/167.50 [7769]~E(f328(x77694,f820(x77694,x77693,x77692,x77691)),f192(f879(x77692,a867)))+E(f328(f328(f44(x77691,f879(x77692,a867)),x77693),x77694),f192(f879(x77692,a867))) % 167.75/167.50 [8165]P1(f328(x81651,x81652))+~P1(f328(f328(f330(x81653),x81652),f328(f328(f105(f879(x81653,a867)),x81654),f328(f248(x81653),x81651)))) % 167.75/167.50 [8209]~P1(f328(f328(f242(f879(x82091,a867)),x82093),x82094))+P1(f328(f328(f242(f879(x82091,a867)),f328(f328(f306(x82091),x82092),x82093)),f328(f328(f306(x82091),x82092),x82094))) % 167.75/167.50 [8383]P1(f328(x83832,x83833))+E(f328(f328(f135(x83831),f328(f193(f873(x83831)),f175(x83831,x83832,f328(f328(f148(x83831),x83833),x83834)))),f328(f328(f148(x83831),x83833),x83834)),f328(f328(f148(x83831),x83833),x83834)) % 167.75/167.50 [8492]P1(f328(f328(f328(a198,x84921),x84922),f630(x84923,x84922,x84924,x84921)))+~P1(f328(f328(f328(a198,f33(x84921,x84924)),x84922),x84923)) % 167.75/167.50 [8493]~P1(f328(f328(f243(a872),f328(x84934,x84932)),f328(x84934,x84933)))+P1(f328(f328(f330(f878(x84931,x84931)),f328(f328(f263(x84931,x84931),x84932),x84933)),f328(f328(f284(a872,x84931),a247),x84934))) % 167.75/167.50 [8591]~P1(f328(x85912,f778(x85914,x85912,x85913,x85911)))+E(f175(x85911,x85912,f328(f328(f125(x85911),x85913),x85914)),f328(f328(f125(x85911),x85913),f175(x85911,x85912,x85914))) % 167.75/167.50 [8664]P26(f873(x86641),f873(x86642),f328(f151(x86641,x86642),x86643),x86644)+~P26(x86641,x86642,x86643,f41(f879(x86641,a867),f328(f307(f873(x86641),f879(x86641,a867),f170(x86641)),x86644))) % 167.75/167.50 [8731]~P1(f328(x87312,x87313))+E(f328(f328(f135(x87311),f328(f193(f873(x87311)),f175(x87311,x87312,f328(f328(f148(x87311),x87313),x87314)))),f328(f328(f148(x87311),x87313),x87314)),f328(f328(f135(x87311),f328(f193(f873(x87311)),f175(x87311,x87312,x87314))),x87314)) % 167.75/167.50 [8770]~E(x87702,x87703)+E(f328(f133(x87701,f328(f328(f8(a867,a867,x87701),a323),f328(a325,x87702))),f328(f328(f148(x87701),x87703),x87704)),f328(f133(x87701,f328(f328(f8(a867,a867,x87701),a323),f328(a325,x87702))),x87704)) % 167.75/167.50 [8780]E(f328(f328(f44(x87801,f879(x87802,a867)),x87803),x87804),f192(f879(x87802,a867)))+P1(f328(f328(f330(x87801),f819(x87804,x87803,x87801,x87802)),x87803)) % 167.75/167.50 [8781]E(f328(f328(f43(x87811,f879(x87812,a867)),x87813),x87814),f251(f879(x87812,a867)))+P1(f328(f328(f330(x87811),f822(x87814,x87813,x87811,x87812)),x87813)) % 167.75/167.50 [8782]E(f328(f328(f43(x87821,f879(x87822,a867)),x87823),x87824),f251(f879(x87822,a867)))+P1(f328(f328(f330(x87821),f823(x87824,x87823,x87822,x87821)),x87823)) % 167.75/167.50 [8783]E(f328(f328(f44(x87831,f879(x87832,a867)),x87833),x87834),f192(f879(x87832,a867)))+P1(f328(f328(f330(x87831),f820(x87834,x87833,x87832,x87831)),x87833)) % 167.75/167.50 [8819]P1(f328(f328(f243(a872),f328(x88191,x88192)),f328(x88191,x88193)))+~P1(f328(f328(f330(f878(x88194,x88194)),f328(f328(f263(x88194,x88194),x88192),x88193)),f328(f328(f284(a872,x88194),a247),x88191))) % 167.75/167.50 [8840]E(f175(x88401,x88402,f328(f328(f125(x88401),x88403),x88404)),f328(f328(f125(x88401),x88403),f175(x88401,x88402,x88404)))+P1(f328(f328(f330(x88401),f778(x88404,x88402,x88403,x88401)),f328(f170(x88401),x88403))) % 167.75/167.50 [8957]P1(f328(f328(f328(a198,x89571),f630(x89572,x89573,x89571,x89574)),x89572))+~P1(f328(f328(f328(a198,f33(x89574,x89571)),x89573),x89572)) % 167.75/167.50 [9006]P1(f328(f328(f330(x90061),f525(x90062,x90063,x90064,x90061)),x90063))+~P1(f328(f328(f330(f879(x90061,a867)),x90064),f328(f328(f62(x90061),x90063),x90062))) % 167.75/167.50 [9009]E(x90091,x90092)+~P1(f328(f328(f330(f878(x90093,x90093)),f328(f328(f263(x90093,x90093),x90091),x90092)),f328(f328(f187(f878(x90093,x90093),a867),f2(a872)),x90094))) % 167.75/167.50 [9090]E(f328(f282(x90901,x90901,x90902),f328(f328(f306(x90901),f525(x90902,x90903,x90904,x90901)),f192(f879(x90901,a867)))),x90904)+~P1(f328(f328(f330(f879(x90901,a867)),x90904),f328(f328(f62(x90901),x90903),x90902))) % 167.75/167.50 [9095]~P1(f328(f328(f330(f878(x90951,x90951)),f328(f328(f263(x90951,x90951),x90953),x90952)),f304(x90951,x90954)))+P1(f328(f328(f330(f878(x90951,x90951)),f328(f328(f263(x90951,x90951),x90952),x90953)),f304(x90951,f328(f283(x90951,x90951),x90954)))) % 167.75/167.50 [9107]~P57(x91071)+E(f328(f328(f80(x91071),f328(f328(f80(x91071),f328(f328(f81(x91071),x91072),f328(f328(f40(x91071),x91073),x91072))),f46(x91071,x91073,x91072))),x91074),f328(f328(f80(x91071),x91073),x91074)) % 167.75/167.50 [9117]~P1(f328(f328(f330(x91171),x91173),x91174))+P1(f328(f328(f330(f879(x91171,a867)),f328(f282(x91171,x91171,x91172),f328(f328(f306(x91171),x91173),f192(f879(x91171,a867))))),f328(f328(f62(x91171),x91174),x91172))) % 167.75/167.50 [9128]P1(f328(f328(f330(f878(x91281,x91281)),f328(f328(f263(x91281,x91281),x91282),x91283)),f304(x91281,x91284)))+~P1(f328(f328(f330(f878(x91281,x91281)),f328(f328(f263(x91281,x91281),x91283),x91282)),f304(x91281,f328(f283(x91281,x91281),x91284)))) % 167.75/167.50 [9220]E(f328(f328(f156(x92201,f328(f166(x92201),x92202)),f328(f328(f22(a872),f328(f328(f22(a872),f328(f193(f873(x92201)),x92202)),x92203)),f78(a872))),x92204),f328(f166(x92201),f328(f328(f156(x92201,x92202),x92203),x92204)))+~P1(f328(f328(f243(a872),x92203),f328(f193(f873(x92201)),x92202))) % 167.75/167.50 [9223]~P1(f328(x92232,f771(x92234,x92232,x92233,x92231)))+E(f328(f328(f135(x92231),f328(f193(f873(x92231)),f175(x92231,x92232,f328(f328(f125(x92231),x92233),x92234)))),f328(f328(f125(x92231),x92233),x92234)),f328(f328(f135(x92231),f328(f193(f873(x92231)),f175(x92231,x92232,x92234))),x92234)) % 167.75/167.50 [9262]~P26(x92622,x92621,x92623,f251(f879(x92622,a867)))+P1(f328(f328(f242(f879(x92621,a867)),f328(f307(x92622,x92621,x92623),f328(f79(f879(x92622,a867)),x92624))),f328(f79(f879(x92621,a867)),f328(f307(x92622,x92621,x92623),x92624)))) % 167.75/167.50 [9275]~P4(x92751)+E(f328(f139(x92751,x92752,f328(f7(x92752,x92751,x92751),f328(f328(f8(x92751,f879(x92751,x92751),x92752),f105(x92751)),x92753)),f251(x92751)),x92754),f328(f328(f43(x92752,x92751),f328(f170(x92752),x92754)),x92753)) % 167.75/167.50 [9276]~P4(x92761)+E(f328(f139(x92761,x92762,f328(f7(x92762,x92761,x92761),f328(f328(f8(x92761,f879(x92761,x92761),x92762),f114(x92761)),x92763)),f192(x92761)),x92764),f328(f328(f44(x92762,x92761),f328(f170(x92762),x92764)),x92763)) % 167.75/167.50 [9288]E(f328(f328(f135(x92881),f328(f193(f873(x92881)),f175(x92881,x92882,f328(f328(f125(x92881),x92883),x92884)))),f328(f328(f125(x92881),x92883),x92884)),f328(f328(f135(x92881),f328(f193(f873(x92881)),f175(x92881,x92882,x92884))),x92884))+P1(f328(f328(f330(x92881),f771(x92884,x92882,x92883,x92881)),f328(f170(x92881),x92883))) % 167.75/167.50 [9356]~P1(f328(f328(f330(f878(f873(x93564),f873(x93564))),f328(f328(f263(f873(x93564),f873(x93564)),x93563),x93562)),f154(x93564,x93561)))+P1(f328(f328(f243(a872),f684(x93561,x93562,x93563,x93564)),f328(f193(f873(x93564)),x93563))) % 167.75/167.50 [9357]~P57(x93571)+E(f328(f328(f80(x93571),f328(f328(f80(x93571),f328(f328(f81(x93571),f328(f328(f40(x93571),x93572),x93573)),x93573)),f46(x93571,x93572,x93573))),x93574),f328(f328(f80(x93571),x93572),x93574)) % 167.75/167.50 [9384]~P1(f328(f328(f330(f878(f873(x93841),f873(x93841))),f328(f328(f263(f873(x93841),f873(x93841)),x93842),x93843)),f328(f283(f873(x93841),f873(x93841)),f154(x93841,x93844))))+P1(f328(f328(f330(f878(f873(x93841),f873(x93841))),f328(f328(f263(f873(x93841),f873(x93841)),x93842),x93843)),f154(x93841,f328(f283(x93841,x93841),x93844)))) % 167.75/167.50 [9385]P1(f328(f328(f330(f878(f873(x93851),f873(x93851))),f328(f328(f263(f873(x93851),f873(x93851)),x93852),x93853)),f328(f283(f873(x93851),f873(x93851)),f154(x93851,x93854))))+~P1(f328(f328(f330(f878(f873(x93851),f873(x93851))),f328(f328(f263(f873(x93851),f873(x93851)),x93852),x93853)),f154(x93851,f328(f283(x93851,x93851),x93854)))) % 167.75/167.50 [9420]~P1(f328(f328(f330(x94201),x94203),f328(f261(x94201,x94202),x94204)))+P1(f328(f328(f330(f878(x94201,x94202)),f328(f328(f263(x94201,x94202),x94203),f567(x94204,x94202,x94203,x94201))),x94204)) % 167.75/167.50 [9421]~P1(f328(f328(f330(x94211),x94213),f328(f261(x94211,x94212),x94214)))+P1(f328(f328(f330(f878(x94211,x94212)),f328(f328(f263(x94211,x94212),x94213),f571(x94214,x94212,x94213,x94211))),x94214)) % 167.75/167.50 [9533]~P1(f328(f38(f876(x95331)),f328(f307(x95332,f876(x95331),x95333),f251(f879(x95332,a867)))))+P1(f328(f38(f876(x95331)),f328(f307(x95332,f876(x95331),f183(x95332,x95331,x95333,f328(f176(x95332,x95331),x95334))),f251(f879(x95332,a867))))) % 167.75/167.50 [9580]~P1(f328(f328(f330(f878(x95801,x95801)),f328(f328(f263(x95801,x95801),x95802),x95804)),f328(f328(f285(x95801,x95801,x95801),x95803),f304(x95801,x95803))))+P1(f328(f328(f330(f878(x95801,x95801)),f328(f328(f263(x95801,x95801),x95802),f646(x95803,x95804,x95802,x95801))),x95803)) % 167.75/167.50 [9751]~P1(f328(f328(f330(f878(x97512,x97511)),x97514),f328(f283(x97511,x97512),x97513)))+P1(f328(f328(f330(f878(x97511,x97512)),f328(f328(f263(x97511,x97512),f657(x97513,x97514,x97511,x97512)),f656(x97513,x97514,x97511,x97512))),x97513)) % 167.75/167.50 [9779]~P1(f328(f328(f330(f878(f873(x97791),f873(x97791))),f328(f328(f263(f873(x97791),f873(x97791)),x97794),x97793)),f154(x97791,x97792)))+P1(f328(f328(f330(f878(x97791,x97791)),f328(f328(f263(x97791,x97791),f697(x97792,x97793,x97794,x97791)),f698(x97792,x97793,x97794,x97791))),x97792)) % 167.75/167.50 [9875]~P1(f328(f328(f330(f878(f873(x98751),f873(x98751))),f328(f328(f263(f873(x98751),f873(x98751)),x98752),x98754)),f154(x98751,x98753)))+P1(f328(f328(f330(f878(x98751,x98751)),f328(f328(f263(x98751,x98751),f328(f328(f162(x98751),x98752),f684(x98753,x98754,x98752,x98751))),f685(x98753,x98754,x98752,x98751))),x98753)) % 167.75/167.50 [9897]~P1(f328(f38(x98972),x98974))+E(f328(f328(f328(f66(f879(x98971,a867),x98972,f114(f879(x98971,a867))),f328(f328(f7(x98972,f879(x98971,a867),f879(x98971,a867)),f328(f328(f8(x98971,f879(f879(x98971,a867),f879(x98971,a867)),x98972),f306(x98971)),x98973)),f192(f879(x98971,a867)))),f192(f879(x98971,a867))),x98974),f328(f307(x98972,x98971,x98973),x98974)) % 167.75/167.50 [9992]~P26(x99921,x99922,x99923,f251(f879(x99921,a867)))+P1(f328(f328(f242(f879(x99921,a867)),f328(f308(x99921,x99922,x99923),f328(f328(f306(x99922),x99924),f192(f879(x99922,a867))))),f328(f328(f306(x99921),f85(x99921,f328(f328(f7(x99921,x99922,a867),f328(f328(f8(x99922,f879(x99922,a867),x99921),a325),x99923)),x99924))),f192(f879(x99921,a867))))) % 167.75/167.50 [5598]~E(f328(f328(f125(x55981),x55982),x55984),x55983)+E(f328(f328(f173(x55981),f328(f193(f873(x55981)),x55982)),x55983),x55982) % 167.75/167.50 [5599]~E(f328(f328(f125(x55992),x55993),x55991),x55994)+E(x55991,f328(f328(f135(x55992),f328(f193(f873(x55992)),x55993)),x55994)) % 167.75/167.50 [5610]~E(x56104,f2(a872))+E(f328(f328(f162(x56101),f328(f328(f148(x56101),x56102),x56103)),x56104),x56102) % 167.75/167.50 [6132]~P111(x61321)+E(f328(f328(f253(x61321),f328(f328(f253(x61321),x61322),x61323)),x61324),f328(f328(f253(x61321),x61322),f328(f328(f81(a872),x61323),x61324))) % 167.75/167.50 [6133]~P78(x61331)+E(f328(f328(f253(x61331),f328(f328(f253(x61331),x61332),x61333)),x61334),f328(f328(f253(x61331),x61332),f328(f328(f81(a872),x61333),x61334))) % 167.75/167.50 [6150]E(x61501,f2(a872))+E(f328(f328(f162(x61502),f328(f328(f148(x61502),x61503),x61504)),x61501),f328(f328(f162(x61502),x61504),f328(f328(f22(a872),x61501),f78(a872)))) % 167.75/167.50 [6179]~P120(x61791)+E(f328(f328(f286(x61791),f328(f328(f81(x61791),x61792),x61793)),x61794),f328(f328(f81(x61791),x61792),f328(f328(f286(x61791),x61793),x61794))) % 167.75/167.50 [6180]~P2(x61801)+E(f328(f328(f114(x61801),f328(f328(f114(x61801),x61802),x61803)),x61804),f328(f328(f114(x61801),x61802),f328(f328(f114(x61801),x61803),x61804))) % 167.75/167.50 [6182]~P99(x61821)+E(f328(f328(f114(x61821),f328(f328(f114(x61821),x61822),x61823)),x61824),f328(f328(f114(x61821),x61822),f328(f328(f114(x61821),x61823),x61824))) % 167.75/167.50 [6183]~P2(x61831)+E(f328(f328(f105(x61831),f328(f328(f105(x61831),x61832),x61833)),x61834),f328(f328(f105(x61831),x61832),f328(f328(f105(x61831),x61833),x61834))) % 167.75/167.50 [6185]~P100(x61851)+E(f328(f328(f105(x61851),f328(f328(f105(x61851),x61852),x61853)),x61854),f328(f328(f105(x61851),x61852),f328(f328(f105(x61851),x61853),x61854))) % 167.75/167.50 [6186]~P68(x61861)+E(f328(f328(f80(x61861),f328(f328(f80(x61861),x61862),x61863)),x61864),f328(f328(f80(x61861),x61862),f328(f328(f80(x61861),x61863),x61864))) % 167.75/167.50 [6187]~P111(x61871)+E(f328(f328(f80(x61871),f328(f328(f80(x61871),x61872),x61873)),x61874),f328(f328(f80(x61871),x61872),f328(f328(f80(x61871),x61873),x61874))) % 167.75/167.50 [6188]~P69(x61881)+E(f328(f328(f81(x61881),f328(f328(f81(x61881),x61882),x61883)),x61884),f328(f328(f81(x61881),x61882),f328(f328(f81(x61881),x61883),x61884))) % 167.75/167.50 [6189]~P111(x61891)+E(f328(f328(f81(x61891),f328(f328(f81(x61891),x61892),x61893)),x61894),f328(f328(f81(x61891),x61892),f328(f328(f81(x61891),x61893),x61894))) % 167.75/167.50 [6192]~P105(x61921)+E(f328(f328(f240(x61921),f328(f328(f240(x61921),x61922),x61923)),x61924),f328(f328(f240(x61921),x61922),f328(f328(f240(x61921),x61923),x61924))) % 167.75/167.50 [6194]~P105(x61941)+E(f328(f328(f241(x61941),f328(f328(f241(x61941),x61942),x61943)),x61944),f328(f328(f241(x61941),x61942),f328(f328(f241(x61941),x61943),x61944))) % 167.75/167.50 [6205]~P57(x62051)+E(f46(x62051,f328(f328(f80(x62051),x62052),f328(f328(f81(x62051),x62053),x62054)),x62054),f46(x62051,x62052,x62054)) % 167.75/167.50 [6206]~P57(x62061)+E(f46(x62061,f328(f328(f80(x62061),x62062),f328(f328(f81(x62061),x62063),x62064)),x62063),f46(x62061,x62062,x62063)) % 167.75/167.50 [6338]E(f328(f328(f162(x63381),f328(f328(f173(x63381),x63382),x63383)),x63384),f328(f328(f162(x63381),x63383),x63384))+~P1(f328(f328(f243(a872),x63384),x63382)) % 167.75/167.50 [6511]~P111(x65111)+E(f328(f328(f80(x65111),f328(f328(f80(x65111),x65112),x65113)),x65114),f328(f328(f80(x65111),f328(f328(f80(x65111),x65112),x65114)),x65113)) % 167.75/167.50 [6512]~P111(x65121)+E(f328(f328(f81(x65121),f328(f328(f81(x65121),x65122),x65123)),x65124),f328(f328(f81(x65121),f328(f328(f81(x65121),x65122),x65124)),x65123)) % 167.75/167.50 [6571]~P142(x65712)+E(f328(f328(f6(x65711,x65712),f328(f16(x65712,x65711),x65713)),x65714),f328(f328(f81(x65712),f328(f104(x65712),f328(f39(x65711),x65714))),x65713)) % 167.75/167.50 [6741]E(f328(f328(f105(f879(x67411,a867)),f328(f328(f306(x67411),x67412),x67413)),x67414),f328(f328(f105(f879(x67411,a867)),x67413),x67414))+P1(f328(f328(f330(x67411),x67412),x67414)) % 167.75/167.50 [6811]~P98(x68111)+E(f328(f328(f105(x68111),f328(f328(f114(x68111),x68112),x68113)),f328(f328(f114(x68111),x68114),x68113)),f328(f328(f114(x68111),f328(f328(f105(x68111),x68112),x68114)),x68113)) % 167.75/167.50 [6812]~P77(x68121)+E(f328(f328(f240(x68121),f328(f328(f22(x68121),x68122),x68123)),f328(f328(f22(x68121),x68124),x68123)),f328(f328(f22(x68121),f328(f328(f240(x68121),x68122),x68124)),x68123)) % 167.75/167.50 [6813]~P77(x68131)+E(f328(f328(f241(x68131),f328(f328(f22(x68131),x68132),x68133)),f328(f328(f22(x68131),x68134),x68133)),f328(f328(f22(x68131),f328(f328(f241(x68131),x68132),x68134)),x68133)) % 167.75/167.50 [6814]~P98(x68141)+E(f328(f328(f114(x68141),f328(f328(f105(x68141),x68142),x68143)),f328(f328(f105(x68141),x68144),x68143)),f328(f328(f105(x68141),f328(f328(f114(x68141),x68142),x68144)),x68143)) % 167.75/167.50 [6815]~P82(x68151)+E(f328(f328(f240(x68151),f328(f328(f80(x68151),x68152),x68153)),f328(f328(f80(x68151),x68154),x68153)),f328(f328(f80(x68151),f328(f328(f240(x68151),x68152),x68154)),x68153)) % 167.75/167.50 [6816]~P82(x68161)+E(f328(f328(f241(x68161),f328(f328(f80(x68161),x68162),x68163)),f328(f328(f80(x68161),x68164),x68163)),f328(f328(f80(x68161),f328(f328(f241(x68161),x68162),x68164)),x68163)) % 167.75/167.50 [6818]~P112(x68181)+E(f328(f328(f80(x68181),f328(f328(f81(x68181),x68182),x68183)),f328(f328(f81(x68181),x68184),x68183)),f328(f328(f81(x68181),f328(f328(f80(x68181),x68182),x68184)),x68183)) % 167.75/167.50 [6819]~P73(x68191)+E(f328(f328(f81(x68191),f328(f328(f253(x68191),x68192),x68193)),f328(f328(f253(x68191),x68194),x68193)),f328(f328(f253(x68191),f328(f328(f81(x68191),x68192),x68194)),x68193)) % 167.75/167.50 [6820]~P111(x68201)+E(f328(f328(f81(x68201),f328(f328(f253(x68201),x68202),x68203)),f328(f328(f253(x68201),x68204),x68203)),f328(f328(f253(x68201),f328(f328(f81(x68201),x68202),x68204)),x68203)) % 167.75/167.50 [6821]~P60(x68211)+E(f328(f328(f286(x68211),f328(f328(f253(x68211),x68212),x68213)),f328(f328(f253(x68211),x68214),x68213)),f328(f328(f253(x68211),f328(f328(f286(x68211),x68212),x68214)),x68213)) % 167.75/167.50 [6822]~P120(x68221)+E(f328(f328(f22(x68221),f328(f328(f286(x68221),x68222),x68223)),f328(f328(f286(x68221),x68224),x68223)),f328(f328(f286(x68221),f328(f328(f22(x68221),x68222),x68224)),x68223)) % 167.75/167.50 [6823]~P120(x68231)+E(f328(f328(f80(x68231),f328(f328(f286(x68231),x68232),x68233)),f328(f328(f286(x68231),x68234),x68233)),f328(f328(f286(x68231),f328(f328(f80(x68231),x68232),x68234)),x68233)) % 167.75/167.50 [6824]~P105(x68241)+E(f328(f328(f241(x68241),f328(f328(f240(x68241),x68242),x68243)),f328(f328(f240(x68241),x68244),x68243)),f328(f328(f240(x68241),f328(f328(f241(x68241),x68242),x68244)),x68243)) % 167.75/167.50 [6825]~P105(x68251)+E(f328(f328(f240(x68251),f328(f328(f241(x68251),x68252),x68253)),f328(f328(f241(x68251),x68254),x68253)),f328(f328(f241(x68251),f328(f328(f240(x68251),x68252),x68254)),x68253)) % 167.75/167.50 [6826]~P111(x68261)+E(f328(f328(f80(x68261),f328(f328(f81(x68261),x68262),x68263)),f328(f328(f81(x68261),x68264),x68263)),f328(f328(f81(x68261),f328(f328(f80(x68261),x68262),x68264)),x68263)) % 167.75/167.50 [6859]E(f328(f328(f156(x68591,x68592),x68593),x68594),x68592)+~P1(f328(f328(f242(a872),f328(f193(f873(x68591)),x68592)),x68593)) % 167.75/167.50 [6884]~P1(f328(x68843,x68844))+P1(f328(f328(f328(f114(f879(x68841,a867)),x68842),x68843),x68844)) % 167.75/167.50 [6886]~P1(f328(x68862,x68864))+P1(f328(f328(f328(f114(f879(x68861,a867)),x68862),x68863),x68864)) % 167.75/167.50 [6905]E(f328(f328(f162(x69051),f328(f328(f125(x69051),x69052),x69053)),x69054),f328(f328(f162(x69051),x69052),x69054))+~P1(f328(f328(f243(a872),x69054),f328(f193(f873(x69051)),x69052))) % 167.75/167.50 [6915]E(f328(f328(f22(f879(x69151,a867)),f328(f328(f306(x69151),x69152),x69153)),x69154),f328(f328(f22(f879(x69151,a867)),x69153),x69154))+~P1(f328(f328(f330(x69151),x69152),x69154)) % 167.75/167.50 [6956]~E(f136(a872,f328(f298(a872,x69561),x69562)),f328(f328(f148(a872),x69564),x69563))+E(f136(a872,f328(f298(a872,f328(f328(f80(a872),x69561),f78(a872))),x69562)),x69563) % 167.75/167.50 [7027]E(x70271,f2(a872))+E(f328(f328(f148(x70272),x70273),f328(f328(f173(x70272),f328(f328(f22(a872),x70271),f78(a872))),x70274)),f328(f328(f173(x70272),x70271),f328(f328(f148(x70272),x70273),x70274))) % 167.75/167.50 [7127]E(f328(f328(f162(x71271),x71272),f328(f328(f22(a872),x71273),f328(f193(f873(x71271)),x71274))),f328(f328(f162(x71271),f328(f328(f125(x71271),x71274),x71272)),x71273))+P1(f328(f328(f243(a872),x71273),f328(f193(f873(x71271)),x71274))) % 167.75/167.50 [7157]E(f328(f328(f105(f879(x71571,a867)),x71572),f328(f328(f306(x71571),x71573),x71574)),f328(f328(f306(x71571),x71573),f328(f328(f105(f879(x71571,a867)),x71572),x71574)))+~P1(f328(f328(f330(x71571),x71573),x71572)) % 167.75/167.50 [7194]E(f328(f328(f162(x71941),f328(f328(f156(x71941,x71942),x71943),x71944)),x71943),x71944)+~P1(f328(f328(f243(a872),x71943),f328(f193(f873(x71941)),x71942))) % 167.75/167.50 [7215]E(x72151,f192(f879(x72152,a867)))+E(f328(f307(f878(x72153,x72152),x72153,f262(x72153,x72152)),f328(f328(f265(x72153,x72152),x72154),f328(f16(f879(x72152,a867),x72153),x72151))),x72154) % 167.75/167.50 [7216]E(x72161,f192(f879(x72162,a867)))+E(f328(f307(f878(x72162,x72163),x72163,f266(x72162,x72163)),f328(f328(f265(x72162,x72163),x72161),f328(f16(f879(x72163,a867),x72162),x72164))),x72164) % 167.75/167.50 [7283]E(f328(f328(f22(f879(x72831,a867)),f328(f328(f306(x72831),x72832),x72833)),x72834),f328(f328(f306(x72831),x72832),f328(f328(f22(f879(x72831,a867)),x72833),x72834)))+P1(f328(f328(f330(x72831),x72832),x72834)) % 167.75/167.50 [7315]P1(f328(x73151,x73152))+P1(f328(f328(f328(f328(a200,f32(x73151,x73153)),x73152),x73154),x73152)) % 167.75/167.50 [7322]~E(x73224,f192(f879(x73222,a867)))+E(f328(f307(f878(x73221,x73222),x73221,f262(x73221,x73222)),f328(f328(f265(x73221,x73222),x73223),f328(f16(f879(x73222,a867),x73221),x73224))),f192(f879(x73221,a867))) % 167.75/167.50 [7323]~E(x73233,f192(f879(x73231,a867)))+E(f328(f307(f878(x73231,x73232),x73232,f266(x73231,x73232)),f328(f328(f265(x73231,x73232),x73233),f328(f16(f879(x73232,a867),x73231),x73234))),f192(f879(x73232,a867))) % 167.75/167.50 [7379]~P1(f328(f328(f330(x73791),x73792),x73794))+P1(f328(f328(f330(x73791),x73792),f328(f328(f114(f879(x73791,a867)),x73793),x73794))) % 167.75/167.50 [7382]~P1(f328(f328(f330(x73821),x73822),x73823))+P1(f328(f328(f330(x73821),x73822),f328(f328(f114(f879(x73821,a867)),x73823),x73824))) % 167.75/167.50 [7401]E(f328(f328(f105(f879(x74011,a867)),f328(f328(f306(x74011),x74012),x74013)),x74014),f328(f328(f306(x74011),x74012),f328(f328(f105(f879(x74011,a867)),x74013),x74014)))+~P1(f328(f328(f330(x74011),x74012),x74014)) % 167.75/167.50 [7680]P1(f328(x76801,x76802))+~P1(f328(f328(f328(f105(f879(x76803,a867)),x76804),x76801),x76802)) % 167.75/167.50 [7681]P1(f328(x76811,x76812))+~P1(f328(f328(f328(f105(f879(x76813,a867)),x76811),x76814),x76812)) % 167.75/167.50 [7684]E(f328(f328(f6(x76841,a872),x76842),f328(f328(f22(f879(x76841,a867)),x76843),f328(f328(f306(x76841),x76844),f192(f879(x76841,a867))))),f328(f328(f6(x76841,a872),x76842),x76843))+P1(f328(f328(f330(x76841),x76844),x76843)) % 167.75/167.50 [7689]~P67(x76891)+E(f328(f163(x76891),f328(f328(f151(a872,x76891),x76892),f136(a872,f328(f298(a872,x76893),x76894)))),f328(f328(f6(a872,x76891),x76892),f328(f170(a872),f136(a872,f328(f298(a872,x76893),x76894))))) % 167.75/167.50 [7690]~P67(x76901)+E(f328(f328(f6(a872,x76901),x76902),f328(f170(a872),f136(a872,f328(f298(a872,x76903),x76904)))),f328(f163(x76901),f328(f328(f151(a872,x76901),x76902),f136(a872,f328(f298(a872,x76903),x76904))))) % 167.75/167.50 [7805]~E(x78053,x78054)+P1(f328(f63(x78051,x78052,f328(f328(f306(x78051),x78053),f192(f879(x78051,a867)))),x78054)) % 167.75/167.50 [7902]P1(f328(f328(f330(x79021),x79022),f328(f170(x79021),x79023)))+~P1(f328(f328(f330(x79021),x79022),f328(f170(x79021),f328(f328(f173(x79021),x79024),x79023)))) % 167.75/167.50 [7903]P1(f328(f328(f330(x79031),x79032),f328(f170(x79031),x79033)))+~P1(f328(f328(f330(x79031),x79032),f328(f170(x79031),f328(f328(f135(x79031),x79034),x79033)))) % 167.75/167.50 [7973]P1(f328(f328(f330(x79731),x79732),x79733))+~P1(f328(f328(f330(x79731),x79732),f328(f328(f22(f879(x79731,a867)),x79733),x79734))) % 167.75/167.50 [7975]P1(f328(f328(f330(x79751),x79752),x79753))+~P1(f328(f328(f330(x79751),x79752),f328(f328(f105(f879(x79751,a867)),x79754),x79753))) % 167.75/167.50 [7978]P1(f328(f328(f330(x79781),x79782),x79783))+~P1(f328(f328(f330(x79781),x79782),f328(f328(f105(f879(x79781,a867)),x79783),x79784))) % 167.75/167.50 [7993]E(f328(f328(f125(x79931),f328(f328(f173(x79931),x79932),x79933)),f328(f328(f148(x79931),x79934),f328(f328(f135(x79931),f328(a116,x79932)),x79933))),f328(f328(f156(x79931,x79933),x79932),x79934))+~P1(f328(f328(f243(a872),x79932),f328(f193(f873(x79931)),x79933))) % 167.75/167.50 [8016]P1(f328(f328(f330(x80161),x80162),x80163))+~P1(f328(f328(f242(f879(x80161,a867)),f328(f328(f306(x80161),x80162),x80164)),x80163)) % 167.75/167.50 [8049]~P1(f328(f328(f330(x80491),x80492),x80493))+~P1(f328(f328(f330(x80491),x80492),f328(f328(f22(f879(x80491,a867)),x80494),x80493))) % 167.75/167.50 [8083]~P1(f328(f328(f243(a872),x80834),f328(f193(f873(x80831)),x80833)))+P1(f328(f328(f330(x80831),x80832),f328(f170(x80831),f328(f328(f156(x80831,x80833),x80834),x80832)))) % 167.75/167.50 [8139]E(f328(f328(f162(x81391),f328(f328(f135(x81391),x81392),x81393)),x81394),f328(f328(f162(x81391),x81393),f328(f328(f80(a872),x81392),x81394)))+~P1(f328(f328(f242(a872),f328(f328(f80(a872),x81392),x81394)),f328(f193(f873(x81391)),x81393))) % 167.75/167.50 [8149]~P142(x81492)+E(f328(f328(f6(x81491,x81492),f328(f328(f8(a872,x81492,x81491),f104(x81492)),x81493)),x81494),f328(f104(x81492),f328(f328(f6(x81491,a872),x81493),x81494))) % 167.75/167.50 [8150]~P138(x81502)+E(f328(f328(f6(x81501,x81502),f328(f328(f8(a1,x81502,x81501),f106(x81502)),x81503)),x81504),f328(f106(x81502),f328(f328(f6(x81501,a1),x81503),x81504))) % 167.75/167.50 [8211]~P63(x82112)+E(f328(f328(f9(x82111,x82112),f328(f328(f8(x82112,x82112,x82111),f75(x82112)),x82113)),x82114),f328(f75(x82112),f328(f328(f9(x82111,x82112),x82113),x82114))) % 167.75/167.50 [8212]~P66(x82122)+E(f328(f328(f6(x82121,x82122),f328(f328(f8(x82122,x82122,x82121),f79(x82122)),x82123)),x82124),f328(f79(x82122),f328(f328(f6(x82121,x82122),x82123),x82124))) % 167.75/167.50 [8214]E(f328(f328(f6(x82141,a872),x82142),f328(f328(f22(f879(x82141,a867)),x82143),f328(f328(f306(x82141),x82144),f192(f879(x82141,a867))))),f328(f328(f22(a872),f328(f328(f6(x82141,a872),x82142),x82143)),f328(x82142,x82144)))+~P1(f328(f328(f330(x82141),x82144),x82143)) % 167.75/167.50 [8235]P1(f328(f328(f242(f879(x82351,a867)),x82352),x82353))+~P1(f328(f328(f242(f879(x82351,a867)),f328(f328(f306(x82351),x82354),x82352)),x82353)) % 167.75/167.50 [8438]E(f328(a116,f516(x84381,x84382,x84383,x84384)),x84382)+~P1(f328(f328(f328(f328(a200,f328(a26,x84384)),x84383),x84382),x84381)) % 167.75/167.50 [8440]E(f328(f328(f176(x84401,x84402),x84403),x84404),f205(x84402))+P1(f328(f328(f330(x84401),x84404),f328(f307(f878(x84401,x84402),x84401,f262(x84401,x84402)),f328(f170(f878(x84401,x84402)),x84403)))) % 167.75/167.50 [8441]P38(x84411,x84412)+~P38(x84411,f328(f328(f306(f878(x84411,x84411)),f328(f328(f263(x84411,x84411),x84413),x84414)),x84412)) % 167.75/167.50 [8442]P54(x84421,x84422)+~P54(x84421,f328(f328(f306(f878(x84421,x84421)),f328(f328(f263(x84421,x84421),x84423),x84424)),x84422)) % 167.75/167.50 [8448]~P105(x84481)+E(f328(f328(f145(x84481,x84481,f5(x84481)),x84482),f328(f328(f145(x84481,x84481,f5(x84481)),x84483),x84484)),f328(f328(f145(x84481,x84481,f5(x84481)),x84483),f328(f328(f145(x84481,x84481,f5(x84481)),x84482),x84484))) % 167.75/167.50 [8458]E(x84581,x84582)+~P1(f328(f63(x84583,x84584,f328(f328(f306(x84583),x84581),f192(f879(x84583,a867)))),x84582)) % 167.75/167.50 [8469]E(f328(f328(f125(x84691),f328(f328(f173(x84691),x84692),x84693)),f328(f328(f173(x84691),x84694),f328(f328(f135(x84691),x84692),x84693))),f328(f328(f173(x84691),f328(f328(f80(a872),x84692),x84694)),x84693))+~P1(f328(f328(f242(a872),f328(f328(f80(a872),x84692),x84694)),f328(f193(f873(x84691)),x84693))) % 167.75/167.50 [8508]P1(f328(f38(x85081),x85082))+~E(x85082,f328(f307(a872,x85081,x85083),f328(f248(a872),f328(f328(f7(a872,a872,a867),f243(a872)),x85084)))) % 167.75/167.50 [8529]~P89(x85291)+E(f328(f139(x85291,x85291,f80(x85291),f328(f328(f80(x85291),x85292),x85293)),x85294),f328(f328(f80(x85291),x85292),f328(f139(x85291,x85291,f80(x85291),x85293),x85294))) % 167.75/167.50 [8569]P1(f328(f328(f242(f879(x85691,a867)),f328(f261(x85691,x85692),x85693)),f328(f261(x85691,x85692),x85694)))+~P1(f328(f328(f242(f879(f878(x85691,x85692),a867)),x85693),x85694)) % 167.75/167.50 [8582]~P1(f328(f328(f242(a872),x85822),x85824))+P1(f328(f328(f242(f879(x85821,a867)),f328(f170(x85821),f328(f328(f173(x85821),x85822),x85823))),f328(f170(x85821),f328(f328(f173(x85821),x85824),x85823)))) % 167.75/167.50 [8583]~P1(f328(f328(f242(a872),x85834),x85832))+P1(f328(f328(f242(f879(x85831,a867)),f328(f170(x85831),f328(f328(f135(x85831),x85832),x85833))),f328(f170(x85831),f328(f328(f135(x85831),x85834),x85833)))) % 167.75/167.50 [8639]~P1(f328(f38(x86391),f328(f328(f22(f879(x86391,a867)),x86392),x86394)))+P1(f328(f38(x86391),f328(f328(f22(f879(x86391,a867)),x86392),f328(f328(f306(x86391),x86393),x86394)))) % 167.75/167.50 [8675]P1(f328(f328(f330(f878(x86751,x86751)),x86752),f304(x86751,x86753)))+~P1(f328(f328(f330(f878(x86751,x86751)),x86752),f328(f328(f187(f878(x86751,x86751),a867),x86754),x86753))) % 167.75/167.50 [8752]~P1(f328(f38(x87521),f328(f328(f22(f879(x87521,a867)),x87522),f328(f328(f306(x87521),x87524),x87523))))+P1(f328(f38(x87521),f328(f328(f22(f879(x87521,a867)),x87522),x87523))) % 167.75/167.50 [8898]~E(f328(f328(f176(x88981,x88982),x88983),x88984),f205(x88982))+~P1(f328(f328(f330(x88981),x88984),f328(f307(f878(x88981,x88982),x88981,f262(x88981,x88982)),f328(f170(f878(x88981,x88982)),x88983)))) % 167.75/167.50 [8967]~P2(x89671)+P1(f328(f328(f242(x89671),f328(f328(f114(x89671),x89672),f328(f328(f105(x89671),x89673),x89674))),f328(f328(f105(x89671),f328(f328(f114(x89671),x89672),x89673)),f328(f328(f114(x89671),x89672),x89674)))) % 167.75/167.50 [8968]~P105(x89681)+P1(f328(f328(f242(x89681),f328(f328(f241(x89681),x89682),f328(f328(f240(x89681),x89683),x89684))),f328(f328(f240(x89681),f328(f328(f241(x89681),x89682),x89683)),f328(f328(f241(x89681),x89682),x89684)))) % 167.75/167.50 [9113]E(x91131,x91132)+~P1(f328(f328(f330(f878(x91133,x91133)),f328(f328(f263(x91133,x91133),x91131),x91132)),f328(f170(f878(x91133,x91133)),f328(f328(f180(x91133,x91133),x91134),x91134)))) % 167.75/167.50 [9146]~P1(f328(f328(f330(f878(x91461,x91461)),f328(f328(f263(x91461,x91461),x91463),x91462)),f304(x91461,x91464)))+~P38(x91461,f328(f328(f306(f878(x91461,x91461)),f328(f328(f263(x91461,x91461),x91462),x91463)),x91464)) % 167.75/167.50 [9147]~P1(f328(f328(f330(f878(x91471,x91471)),f328(f328(f263(x91471,x91471),x91473),x91472)),f304(x91471,x91474)))+~P54(x91471,f328(f328(f306(f878(x91471,x91471)),f328(f328(f263(x91471,x91471),x91472),x91473)),x91474)) % 167.75/167.50 [9152]E(x91521,x91522)+E(f328(f133(x91523,f328(f328(f8(a867,a867,x91523),a323),f328(a325,x91521))),f328(f328(f148(x91523),x91522),x91524)),f328(f328(f148(x91523),x91522),f328(f133(x91523,f328(f328(f8(a867,a867,x91523),a323),f328(a325,x91521))),x91524))) % 167.75/167.50 [9196]~P2(x91961)+P1(f328(f328(f242(x91961),f328(f328(f114(x91961),f328(f328(f105(x91961),x91962),x91963)),f328(f328(f105(x91961),x91962),x91964))),f328(f328(f105(x91961),x91962),f328(f328(f114(x91961),x91963),x91964)))) % 167.75/167.50 [9197]~P105(x91971)+P1(f328(f328(f242(x91971),f328(f328(f241(x91971),f328(f328(f240(x91971),x91972),x91973)),f328(f328(f240(x91971),x91972),x91974))),f328(f328(f240(x91971),x91972),f328(f328(f241(x91971),x91973),x91974)))) % 167.75/167.50 [9271]~E(f328(f307(x92712,x92711,x92713),f251(f879(x92712,a867))),f251(f879(x92711,a867)))+P1(f328(f328(f242(f879(x92711,a867)),f328(f79(f879(x92711,a867)),f328(f307(x92712,x92711,x92713),x92714))),f328(f307(x92712,x92711,x92713),f328(f79(f879(x92712,a867)),x92714)))) % 167.75/167.50 [9349]P1(f328(f328(f328(f328(a200,f328(f239(a869),f328(a28,x93491))),x93492),f516(x93493,x93494,x93492,x93491)),x93493))+~P1(f328(f328(f328(f328(a200,f328(a26,x93491)),x93492),x93494),x93493)) % 167.75/167.50 [9594]P1(f328(f328(f330(f878(x95941,x95941)),f328(f328(f263(x95941,x95941),x95942),x95943)),f328(f283(x95941,x95941),f328(f328(f285(x95941,x95941,x95941),x95944),f304(x95941,x95944)))))+~P1(f328(f328(f330(f878(x95941,x95941)),f328(f328(f263(x95941,x95941),x95942),x95943)),f328(f328(f285(x95941,x95941,x95941),f328(f283(x95941,x95941),x95944)),f304(x95941,f328(f283(x95941,x95941),x95944))))) % 167.75/167.50 [9595]~P1(f328(f328(f330(f878(x95951,x95951)),f328(f328(f263(x95951,x95951),x95952),x95953)),f328(f283(x95951,x95951),f328(f328(f285(x95951,x95951,x95951),x95954),f304(x95951,x95954)))))+P1(f328(f328(f330(f878(x95951,x95951)),f328(f328(f263(x95951,x95951),x95952),x95953)),f328(f328(f285(x95951,x95951,x95951),f328(f283(x95951,x95951),x95954)),f304(x95951,f328(f283(x95951,x95951),x95954))))) % 167.75/167.50 [9616]~P1(f328(f328(f330(x96162),x96164),f328(f259(x96161,x96162),x96163)))+P1(f328(f328(f330(f878(x96161,x96162)),f328(f328(f263(x96161,x96162),f558(x96163,x96161,x96164,x96162)),x96164)),x96163)) % 167.75/167.50 [9617]~P1(f328(f328(f330(x96172),x96174),f328(f259(x96171,x96172),x96173)))+P1(f328(f328(f330(f878(x96171,x96172)),f328(f328(f263(x96171,x96172),f569(x96173,x96171,x96174,x96172)),x96174)),x96173)) % 167.75/167.50 [9644]~P1(f328(f328(f330(x96441),x96444),f328(f328(f114(f879(x96441,a867)),x96442),x96443)))+P1(f328(f328(f328(f114(f879(x96441,a867)),f328(f328(f7(x96441,f879(x96441,a867),a867),f330(x96441)),x96442)),f328(f328(f7(x96441,f879(x96441,a867),a867),f330(x96441)),x96443)),x96444)) % 167.75/167.50 [9645]~P1(f328(f328(f330(x96451),x96454),f328(f328(f105(f879(x96451,a867)),x96452),x96453)))+P1(f328(f328(f328(f105(f879(x96451,a867)),f328(f328(f7(x96451,f879(x96451,a867),a867),f330(x96451)),x96452)),f328(f328(f7(x96451,f879(x96451,a867),a867),f330(x96451)),x96453)),x96454)) % 167.75/167.50 [9722]~P1(f328(f328(f330(f878(x97221,x97221)),f328(f328(f263(x97221,x97221),x97224),x97223)),f328(f328(f285(x97221,x97221,x97221),x97222),f304(x97221,x97222))))+P1(f328(f328(f330(f878(x97221,x97221)),f328(f328(f263(x97221,x97221),f647(x97222,x97223,x97224,x97221)),x97223)),x97222)) % 167.75/167.50 [9767]P1(f328(f328(f330(x97671),x97672),f328(f328(f114(f879(x97671,a867)),x97673),x97674)))+~P1(f328(f328(f328(f114(f879(x97671,a867)),f328(f328(f7(x97671,f879(x97671,a867),a867),f330(x97671)),x97673)),f328(f328(f7(x97671,f879(x97671,a867),a867),f330(x97671)),x97674)),x97672)) % 167.75/167.50 [9768]P1(f328(f328(f330(x97681),x97682),f328(f328(f105(f879(x97681,a867)),x97683),x97684)))+~P1(f328(f328(f328(f105(f879(x97681,a867)),f328(f328(f7(x97681,f879(x97681,a867),a867),f330(x97681)),x97683)),f328(f328(f7(x97681,f879(x97681,a867),a867),f330(x97681)),x97684)),x97682)) % 167.75/167.50 [10046]P33(x100461,f328(f328(f7(x100461,f879(f878(x100461,x100461),a867),f879(x100461,a867)),f328(f328(f8(f879(x100461,f879(f879(f878(x100461,x100461),a867),a867)),f879(f879(f878(x100461,x100461),a867),f879(x100461,a867)),x100461),f7(x100461,f879(f878(x100461,x100461),a867),a867)),f328(f328(f8(f879(x100461,f878(x100461,x100461)),f879(x100461,f879(f879(f878(x100461,x100461),a867),a867)),x100461),f328(f8(f878(x100461,x100461),f879(f879(f878(x100461,x100461),a867),a867),x100461),f330(f878(x100461,x100461)))),f263(x100461,x100461)))),x100462),x100463,x100464)+~P1(f328(f328(f330(f878(f873(x100461),f873(x100461))),f328(f328(f263(f873(x100461),f873(x100461)),x100463),x100464)),f155(x100461,x100462))) % 167.75/167.50 [10050]P55(x100501,f328(f328(f7(x100501,f879(f878(x100501,x100501),a867),f879(x100501,a867)),f328(f328(f8(f879(x100501,f879(f879(f878(x100501,x100501),a867),a867)),f879(f879(f878(x100501,x100501),a867),f879(x100501,a867)),x100501),f7(x100501,f879(f878(x100501,x100501),a867),a867)),f328(f328(f8(f879(x100501,f878(x100501,x100501)),f879(x100501,f879(f879(f878(x100501,x100501),a867),a867)),x100501),f328(f8(f878(x100501,x100501),f879(f879(f878(x100501,x100501),a867),a867),x100501),f330(f878(x100501,x100501)))),f263(x100501,x100501)))),x100502),x100503,x100504)+~P1(f328(f328(f330(f878(f879(x100501,a867),f879(x100501,a867))),f328(f328(f263(f879(x100501,a867),f879(x100501,a867)),x100503),x100504)),f320(x100501,x100502))) % 167.75/167.50 [10079]E(x100791,x100792)+~E(f328(f328(f7(x100793,f879(f878(x100793,x100794),a867),f879(x100794,a867)),f328(f328(f8(f879(x100794,f879(f879(f878(x100793,x100794),a867),a867)),f879(f879(f878(x100793,x100794),a867),f879(x100794,a867)),x100793),f7(x100794,f879(f878(x100793,x100794),a867),a867)),f328(f328(f8(f879(x100794,f878(x100793,x100794)),f879(x100794,f879(f879(f878(x100793,x100794),a867),a867)),x100793),f328(f8(f878(x100793,x100794),f879(f879(f878(x100793,x100794),a867),a867),x100794),f330(f878(x100793,x100794)))),f263(x100793,x100794)))),x100791),f328(f328(f7(x100793,f879(f878(x100793,x100794),a867),f879(x100794,a867)),f328(f328(f8(f879(x100794,f879(f879(f878(x100793,x100794),a867),a867)),f879(f879(f878(x100793,x100794),a867),f879(x100794,a867)),x100793),f7(x100794,f879(f878(x100793,x100794),a867),a867)),f328(f328(f8(f879(x100794,f878(x100793,x100794)),f879(x100794,f879(f879(f878(x100793,x100794),a867),a867)),x100793),f328(f8(f878(x100793,x100794),f879(f879(f878(x100793,x100794),a867),a867),x100794),f330(f878(x100793,x100794)))),f263(x100793,x100794)))),x100792)) % 167.75/167.50 [10083]~P33(x100831,f328(f328(f7(x100831,f879(f878(x100831,x100831),a867),f879(x100831,a867)),f328(f328(f8(f879(x100831,f879(f879(f878(x100831,x100831),a867),a867)),f879(f879(f878(x100831,x100831),a867),f879(x100831,a867)),x100831),f7(x100831,f879(f878(x100831,x100831),a867),a867)),f328(f328(f8(f879(x100831,f878(x100831,x100831)),f879(x100831,f879(f879(f878(x100831,x100831),a867),a867)),x100831),f328(f8(f878(x100831,x100831),f879(f879(f878(x100831,x100831),a867),a867),x100831),f330(f878(x100831,x100831)))),f263(x100831,x100831)))),x100834),x100832,x100833)+P1(f328(f328(f330(f878(f873(x100831),f873(x100831))),f328(f328(f263(f873(x100831),f873(x100831)),x100832),x100833)),f155(x100831,x100834))) % 167.75/167.50 [10084]~P55(x100841,f328(f328(f7(x100841,f879(f878(x100841,x100841),a867),f879(x100841,a867)),f328(f328(f8(f879(x100841,f879(f879(f878(x100841,x100841),a867),a867)),f879(f879(f878(x100841,x100841),a867),f879(x100841,a867)),x100841),f7(x100841,f879(f878(x100841,x100841),a867),a867)),f328(f328(f8(f879(x100841,f878(x100841,x100841)),f879(x100841,f879(f879(f878(x100841,x100841),a867),a867)),x100841),f328(f8(f878(x100841,x100841),f879(f879(f878(x100841,x100841),a867),a867),x100841),f330(f878(x100841,x100841)))),f263(x100841,x100841)))),x100844),x100842,x100843)+P1(f328(f328(f330(f878(f879(x100841,a867),f879(x100841,a867))),f328(f328(f263(f879(x100841,a867),f879(x100841,a867)),x100842),x100843)),f320(x100841,x100844))) % 167.75/167.50 [7452]~P91(x74521)+E(f328(f328(f80(x74521),f328(f107(x74521),x74522)),f328(f328(f22(x74521),f328(f107(x74521),x74523)),x74524)),f328(f328(f22(x74521),f328(f107(x74521),f328(f328(f80(a1),x74522),x74523))),x74524)) % 167.75/167.50 [7453]~P91(x74531)+E(f328(f328(f80(x74531),f328(f107(x74531),x74532)),f328(f328(f80(x74531),f328(f107(x74531),x74533)),x74534)),f328(f328(f80(x74531),f328(f107(x74531),f328(f328(f80(a1),x74532),x74533))),x74534)) % 167.75/167.50 [7454]~P91(x74541)+E(f328(f328(f81(x74541),f328(f107(x74541),x74542)),f328(f328(f81(x74541),f328(f107(x74541),x74543)),x74544)),f328(f328(f81(x74541),f328(f107(x74541),f328(f328(f81(a1),x74542),x74543))),x74544)) % 167.75/167.50 [7499]~P142(x74991)+E(f328(f163(x74991),f328(f328(f151(x74992,x74991),f328(f16(x74991,x74992),x74993)),x74994)),f328(f328(f81(x74991),f328(f104(x74991),f328(f193(f873(x74992)),x74994))),x74993)) % 167.75/167.50 [7736]E(f328(f274(x77361,f328(f328(f148(f878(a103,x77361)),x77362),x77363)),x77364),f328(f266(a103,x77361),x77362))+~P1(f328(f328(f243(a103),x77364),f328(f262(a103,x77361),x77362))) % 167.75/167.50 [7782]~P91(x77821)+E(f328(f328(f80(x77821),f328(f107(x77821),x77822)),f328(f328(f22(x77821),x77823),f328(f107(x77821),x77824))),f328(f328(f80(x77821),f328(f107(x77821),f328(f328(f80(a1),x77822),f328(f79(a1),x77824)))),x77823)) % 167.75/167.50 [7915]E(f328(f274(x79151,x79152),f328(f328(f22(a103),x79153),f328(f262(a103,x79151),x79154))),f328(f274(x79151,f328(f328(f148(f878(a103,x79151)),x79154),x79152)),x79153))+P1(f328(f328(f243(a103),x79153),f328(f262(a103,x79151),x79154))) % 167.75/167.50 [8360]~P1(f328(f328(f330(x83601),x83602),f328(f170(x83601),f118(x83601,x83604))))+P1(f328(f328(f330(x83601),x83602),f328(f170(x83601),f118(x83601,f328(f328(f125(x83601),x83603),x83604))))) % 167.75/167.50 [8361]~P1(f328(f328(f330(x83611),x83612),f328(f170(x83611),f118(x83611,x83613))))+P1(f328(f328(f330(x83611),x83612),f328(f170(x83611),f118(x83611,f328(f328(f125(x83611),x83613),x83614))))) % 167.75/167.50 [8378]E(f328(f328(f114(f879(x83781,a867)),f328(f328(f105(f879(x83781,a867)),x83782),x83783)),x83784),f328(f328(f105(f879(x83781,a867)),x83782),f328(f328(f114(f879(x83781,a867)),x83783),x83784)))+~P1(f328(f328(f242(f879(x83781,a867)),x83784),x83782)) % 167.75/167.50 [8688]~E(f328(f328(f114(f879(x86881,a867)),f328(f328(f105(f879(x86881,a867)),x86883),x86884)),x86882),f328(f328(f105(f879(x86881,a867)),x86883),f328(f328(f114(f879(x86881,a867)),x86884),x86882)))+P1(f328(f328(f242(f879(x86881,a867)),x86882),x86883)) % 167.75/167.50 [8972]~P1(f328(f328(f242(f879(x89721,a867)),x89722),f328(f328(f114(f879(x89721,a867)),x89723),x89724)))+P1(f328(f328(f242(f879(x89721,a867)),f328(f328(f22(f879(x89721,a867)),x89722),x89723)),x89724)) % 167.75/167.50 [9030]~P1(f328(f328(f328(f328(a200,f328(a26,x90301)),x90302),f328(a116,x90303)),x90304))+P1(f328(f328(f328(f328(a200,f328(f239(a869),f328(a28,x90301))),x90302),x90303),x90304)) % 167.75/167.50 [9092]P1(f328(f328(f242(f879(x90921,a867)),x90922),f328(f328(f114(f879(x90921,a867)),x90923),x90924)))+~P1(f328(f328(f242(f879(x90921,a867)),f328(f328(f22(f879(x90921,a867)),x90922),x90923)),x90924)) % 167.75/167.50 [9145]P1(f328(f328(f328(f328(a200,f328(a26,x91451)),x91452),f328(a116,x91453)),x91454))+~P1(f328(f328(f328(f328(a200,f328(f239(a869),f328(a28,x91451))),x91452),x91453),x91454)) % 167.75/167.50 [9177]~P84(x91771)+E(f328(f75(x91771),f328(f328(f6(x91772,x91771),f328(f328(f8(x91771,x91771,x91772),f75(x91771)),x91773)),x91774)),f328(f328(f6(x91772,x91771),f328(f328(f8(x91771,x91771,x91772),f75(x91771)),x91773)),x91774)) % 167.75/167.50 [9347]~P84(x93471)+P1(f328(f328(f242(x93471),f2(x93471)),f328(f328(f6(x93472,x93471),f328(f328(f8(x93471,x93471,x93472),f75(x93471)),x93473)),x93474))) % 167.75/167.50 [9352]~P66(x93521)+E(f328(f163(x93521),f328(f328(f151(x93522,x93521),f328(f73(x93521,x93521,x93522,f79(x93521)),x93523)),x93524)),f328(f79(x93521),f328(f163(x93521),f328(f328(f151(x93522,x93521),x93523),x93524)))) % 167.75/167.50 [9486]~P84(x94861)+P1(f328(f328(f242(x94861),f328(f75(x94861),f328(f328(f6(x94862,x94861),x94863),x94864))),f328(f328(f6(x94862,x94861),f328(f328(f8(x94861,x94861,x94862),f75(x94861)),x94863)),x94864))) % 167.75/167.50 [9518]~E(f328(f328(f80(a872),x95181),x95184),f328(f328(f80(a872),x95183),x95182))+P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),f328(f328(f263(a872,a872),x95181),x95182)),f328(f328(f263(a872,a872),x95183),x95184))),a112)) % 167.75/167.50 [9519]~P1(f328(f328(f243(a872),x95191),x95193))+P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),f328(f328(f263(a872,a872),x95191),x95192)),f328(f328(f263(a872,a872),x95193),x95194))),a35)) % 167.75/167.50 [9520]~P1(f328(f328(f243(a872),x95201),x95203))+P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),f328(f328(f263(a872,a872),x95201),x95202)),f328(f328(f263(a872,a872),x95203),x95204))),a70)) % 167.75/167.50 [9669]E(f328(f328(f80(a872),x96691),x96692),f328(f328(f80(a872),x96693),x96694))+~P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),f328(f328(f263(a872,a872),x96691),x96694)),f328(f328(f263(a872,a872),x96693),x96692))),a112)) % 167.75/167.50 [9696]E(f328(f328(f162(x96961),f328(f328(f135(x96961),f328(f193(f873(x96961)),f175(x96961,x96962,x96963))),x96963)),x96964),f328(f328(f162(x96961),x96963),f328(f328(f80(a872),x96964),f328(f193(f873(x96961)),f175(x96961,x96962,x96963)))))+~P1(f328(f328(f243(a872),x96964),f328(f193(f873(x96961)),f328(f328(f135(x96961),f328(f193(f873(x96961)),f175(x96961,x96962,x96963))),x96963)))) % 167.75/167.50 [9713]~P1(f328(f328(f330(x97132),x97134),f328(f328(f43(x97131,f879(x97132,a867)),f251(f879(x97131,a867))),x97133)))+P1(f328(f328(f328(f43(x97131,f879(x97132,a867)),f251(f879(x97131,a867))),f328(f328(f8(f879(x97132,a867),f879(x97132,a867),x97131),f328(f7(x97132,f879(x97132,a867),a867),f330(x97132))),x97133)),x97134)) % 167.75/167.50 [9714]~P1(f328(f328(f330(x97142),x97144),f328(f328(f44(x97141,f879(x97142,a867)),f251(f879(x97141,a867))),x97143)))+P1(f328(f328(f328(f44(x97141,f879(x97142,a867)),f251(f879(x97141,a867))),f328(f328(f8(f879(x97142,a867),f879(x97142,a867),x97141),f328(f7(x97142,f879(x97142,a867),a867),f330(x97142))),x97143)),x97144)) % 167.75/167.50 [9795]~P1(f328(f50(x97951,x97952),f328(f328(f263(a1,a1),x97954),x97953)))+P1(f328(f50(f328(f79(a1),x97951),x97952),f328(f328(f263(a1,a1),f328(f328(f328(f100(a1),f328(f328(a325,x97953),f2(a1))),f328(f79(a1),x97954)),f328(f328(f22(a1),f328(f79(a1),x97954)),f78(a1)))),f328(f328(f328(f100(a1),f328(f328(a325,x97953),f2(a1))),f2(a1)),f328(f328(f22(a1),x97952),x97953))))) % 167.75/167.50 [9804]P1(f328(f328(f330(x98041),x98042),f328(f328(f43(x98043,f879(x98041,a867)),f251(f879(x98043,a867))),x98044)))+~P1(f328(f328(f328(f43(x98043,f879(x98041,a867)),f251(f879(x98043,a867))),f328(f328(f8(f879(x98041,a867),f879(x98041,a867),x98043),f328(f7(x98041,f879(x98041,a867),a867),f330(x98041))),x98044)),x98042)) % 167.75/167.50 [9805]P1(f328(f328(f330(x98051),x98052),f328(f328(f44(x98053,f879(x98051,a867)),f251(f879(x98053,a867))),x98054)))+~P1(f328(f328(f328(f44(x98053,f879(x98051,a867)),f251(f879(x98053,a867))),f328(f328(f8(f879(x98051,a867),f879(x98051,a867),x98053),f328(f7(x98051,f879(x98051,a867),a867),f330(x98051))),x98054)),x98052)) % 167.75/167.50 [9817]E(f328(f328(f44(a872,f879(x98171,a867)),f251(f879(a872,a867))),x98172),f328(f328(f44(a872,f879(x98171,a867)),f251(f879(a872,a867))),x98173))+~E(f328(f328(f44(a872,f879(x98171,a867)),f328(f298(a872,f2(a872)),f375(x98172,x98174,x98173,x98171))),x98173),f328(f328(f44(a872,f879(x98171,a867)),f328(f298(a872,f2(a872)),f328(f328(f80(a872),f375(x98172,x98174,x98173,x98171)),x98174))),x98172)) % 167.75/167.50 [10137]~P1(f328(f328(f242(f879(f878(x101371,x101372),a867)),x101373),x101374))+P1(f328(f328(f242(f879(x101371,f879(x101372,a867))),f328(f328(f7(x101371,f879(f878(x101371,x101372),a867),f879(x101372,a867)),f328(f328(f8(f879(x101372,f879(f879(f878(x101371,x101372),a867),a867)),f879(f879(f878(x101371,x101372),a867),f879(x101372,a867)),x101371),f7(x101372,f879(f878(x101371,x101372),a867),a867)),f328(f328(f8(f879(x101372,f878(x101371,x101372)),f879(x101372,f879(f879(f878(x101371,x101372),a867),a867)),x101371),f328(f8(f878(x101371,x101372),f879(f879(f878(x101371,x101372),a867),a867),x101372),f330(f878(x101371,x101372)))),f263(x101371,x101372)))),x101373)),f328(f328(f7(x101371,f879(f878(x101371,x101372),a867),f879(x101372,a867)),f328(f328(f8(f879(x101372,f879(f879(f878(x101371,x101372),a867),a867)),f879(f879(f878(x101371,x101372),a867),f879(x101372,a867)),x101371),f7(x101372,f879(f878(x101371,x101372),a867),a867)),f328(f328(f8(f879(x101372,f878(x101371,x101372)),f879(x101372,f879(f879(f878(x101371,x101372),a867),a867)),x101371),f328(f8(f878(x101371,x101372),f879(f879(f878(x101371,x101372),a867),a867),x101372),f330(f878(x101371,x101372)))),f263(x101371,x101372)))),x101374))) % 167.75/167.50 [10154]P1(f328(f328(f242(f879(f878(x101541,x101542),a867)),x101543),x101544))+~P1(f328(f328(f242(f879(x101541,f879(x101542,a867))),f328(f328(f7(x101541,f879(f878(x101541,x101542),a867),f879(x101542,a867)),f328(f328(f8(f879(x101542,f879(f879(f878(x101541,x101542),a867),a867)),f879(f879(f878(x101541,x101542),a867),f879(x101542,a867)),x101541),f7(x101542,f879(f878(x101541,x101542),a867),a867)),f328(f328(f8(f879(x101542,f878(x101541,x101542)),f879(x101542,f879(f879(f878(x101541,x101542),a867),a867)),x101541),f328(f8(f878(x101541,x101542),f879(f879(f878(x101541,x101542),a867),a867),x101542),f330(f878(x101541,x101542)))),f263(x101541,x101542)))),x101543)),f328(f328(f7(x101541,f879(f878(x101541,x101542),a867),f879(x101542,a867)),f328(f328(f8(f879(x101542,f879(f879(f878(x101541,x101542),a867),a867)),f879(f879(f878(x101541,x101542),a867),f879(x101542,a867)),x101541),f7(x101542,f879(f878(x101541,x101542),a867),a867)),f328(f328(f8(f879(x101542,f878(x101541,x101542)),f879(x101542,f879(f879(f878(x101541,x101542),a867),a867)),x101541),f328(f8(f878(x101541,x101542),f879(f879(f878(x101541,x101542),a867),a867),x101542),f330(f878(x101541,x101542)))),f263(x101541,x101542)))),x101544))) % 167.75/167.50 [9226]~P1(f328(f328(f330(f878(x92261,x92261)),x92262),f304(x92261,x92264)))+P1(f328(f328(f330(f878(x92261,x92261)),x92262),f304(x92261,f328(f328(f114(f879(f878(x92261,x92261),a867)),x92263),x92264)))) % 167.75/167.50 [9227]~P1(f328(f328(f330(f878(x92271,x92271)),x92272),f304(x92271,x92273)))+P1(f328(f328(f330(f878(x92271,x92271)),x92272),f304(x92271,f328(f328(f114(f879(f878(x92271,x92271),a867)),x92273),x92274)))) % 167.75/167.50 [9586]~E(f328(f170(x95861),x95864),f182(x95861,x95862,x95863))+E(f328(f176(x95861,x95862),f328(f328(f151(x95861,f878(x95861,x95862)),f328(f328(f18(x95861,x95862,f878(x95861,x95862)),f263(x95861,x95862)),f328(f328(f8(f876(x95862),x95862,x95861),f239(x95862)),x95863))),x95864)),x95863) % 167.75/167.50 [9911]~P1(f328(f328(f243(a872),f328(f328(f80(a872),x99111),x99114)),f328(f328(f80(a872),x99113),x99112)))+P1(f328(f328(f243(a1),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x99111),x99112)),f192(f879(f878(a872,a872),a867)))))),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x99113),x99114)),f192(f879(f878(a872,a872),a867))))))) % 167.75/167.50 [9912]~P1(f328(f328(f242(a872),f328(f328(f80(a872),x99121),x99124)),f328(f328(f80(a872),x99123),x99122)))+P1(f328(f328(f242(a1),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x99121),x99122)),f192(f879(f878(a872,a872),a867)))))),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x99123),x99124)),f192(f879(f878(a872,a872),a867))))))) % 167.75/167.50 [9989]P1(f328(f328(f243(a872),f328(f328(f80(a872),x99891),x99892)),f328(f328(f80(a872),x99893),x99894)))+~P1(f328(f328(f243(a1),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x99891),x99894)),f192(f879(f878(a872,a872),a867)))))),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x99893),x99892)),f192(f879(f878(a872,a872),a867))))))) % 167.75/167.50 [9990]P1(f328(f328(f242(a872),f328(f328(f80(a872),x99901),x99902)),f328(f328(f80(a872),x99903),x99904)))+~P1(f328(f328(f242(a1),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x99901),x99904)),f192(f879(f878(a872,a872),a867)))))),f328(a89,f328(f282(f878(a872,a872),f878(a872,a872),a112),f328(f328(f306(f878(a872,a872)),f328(f328(f263(a872,a872),x99903),x99902)),f192(f879(f878(a872,a872),a867))))))) % 167.75/167.50 [10031]P1(f328(f328(f242(f879(x100311,a867)),f328(f328(f44(a872,f879(x100311,a867)),f251(f879(a872,a867))),x100312)),f328(f328(f44(a872,f879(x100311,a867)),f251(f879(a872,a867))),x100313)))+~P1(f328(f328(f242(f879(x100311,a867)),f328(f328(f44(a872,f879(x100311,a867)),f328(f298(a872,f2(a872)),f376(x100313,x100314,x100312,x100311))),x100312)),f328(f328(f44(a872,f879(x100311,a867)),f328(f298(a872,f2(a872)),f328(f328(f80(a872),f376(x100313,x100314,x100312,x100311)),x100314))),x100313))) % 167.75/167.50 [10128]~P1(f328(f328(f330(x101282),x101284),f328(f259(x101281,x101282),x101283)))+P1(f328(f258(x101281,x101282,f328(f328(f7(x101281,f879(f878(x101281,x101282),a867),f879(x101282,a867)),f328(f328(f8(f879(x101282,f879(f879(f878(x101281,x101282),a867),a867)),f879(f879(f878(x101281,x101282),a867),f879(x101282,a867)),x101281),f7(x101282,f879(f878(x101281,x101282),a867),a867)),f328(f328(f8(f879(x101282,f878(x101281,x101282)),f879(x101282,f879(f879(f878(x101281,x101282),a867),a867)),x101281),f328(f8(f878(x101281,x101282),f879(f879(f878(x101281,x101282),a867),a867),x101282),f330(f878(x101281,x101282)))),f263(x101281,x101282)))),x101283)),x101284)) % 167.75/167.50 [10129]~P1(f328(f328(f330(x101291),x101294),f328(f261(x101291,x101292),x101293)))+P1(f328(f257(x101291,x101292,f328(f328(f7(x101291,f879(f878(x101291,x101292),a867),f879(x101292,a867)),f328(f328(f8(f879(x101292,f879(f879(f878(x101291,x101292),a867),a867)),f879(f879(f878(x101291,x101292),a867),f879(x101292,a867)),x101291),f7(x101292,f879(f878(x101291,x101292),a867),a867)),f328(f328(f8(f879(x101292,f878(x101291,x101292)),f879(x101292,f879(f879(f878(x101291,x101292),a867),a867)),x101291),f328(f8(f878(x101291,x101292),f879(f879(f878(x101291,x101292),a867),a867),x101292),f330(f878(x101291,x101292)))),f263(x101291,x101292)))),x101293)),x101294)) % 167.75/167.50 [10140]P1(f328(f328(f330(x101401),x101402),f328(f259(x101403,x101401),x101404)))+~P1(f328(f258(x101403,x101401,f328(f328(f7(x101403,f879(f878(x101403,x101401),a867),f879(x101401,a867)),f328(f328(f8(f879(x101401,f879(f879(f878(x101403,x101401),a867),a867)),f879(f879(f878(x101403,x101401),a867),f879(x101401,a867)),x101403),f7(x101401,f879(f878(x101403,x101401),a867),a867)),f328(f328(f8(f879(x101401,f878(x101403,x101401)),f879(x101401,f879(f879(f878(x101403,x101401),a867),a867)),x101403),f328(f8(f878(x101403,x101401),f879(f879(f878(x101403,x101401),a867),a867),x101401),f330(f878(x101403,x101401)))),f263(x101403,x101401)))),x101404)),x101402)) % 167.75/167.50 [10141]P1(f328(f328(f330(x101411),x101412),f328(f261(x101411,x101413),x101414)))+~P1(f328(f257(x101411,x101413,f328(f328(f7(x101411,f879(f878(x101411,x101413),a867),f879(x101413,a867)),f328(f328(f8(f879(x101413,f879(f879(f878(x101411,x101413),a867),a867)),f879(f879(f878(x101411,x101413),a867),f879(x101413,a867)),x101411),f7(x101413,f879(f878(x101411,x101413),a867),a867)),f328(f328(f8(f879(x101413,f878(x101411,x101413)),f879(x101413,f879(f879(f878(x101411,x101413),a867),a867)),x101411),f328(f8(f878(x101411,x101413),f879(f879(f878(x101411,x101413),a867),a867),x101413),f330(f878(x101411,x101413)))),f263(x101411,x101413)))),x101414)),x101412)) % 167.75/167.50 [9827]P1(f328(f157(x98271,x98272),x98273))+~P1(f328(f157(x98271,f328(f328(f18(x98271,a867,a867),f328(f328(f8(a867,f879(a867,a867),x98271),a326),x98274)),x98272)),x98273)) % 167.75/167.50 [9828]P1(f328(f157(x98281,x98282),x98283))+~P1(f328(f157(x98281,f328(f328(f18(x98281,a867,a867),f328(f328(f8(a867,f879(a867,a867),x98281),a326),x98282)),x98284)),x98283)) % 167.75/167.50 [9913]~P111(x99131)+E(f328(f328(f81(x99131),f328(f328(f80(x99131),f78(x99131)),f78(x99131))),f328(f328(f6(a872,x99131),f328(f328(f8(x99131,x99131,a872),f328(f80(x99131),x99132)),f328(f328(f7(a872,x99131,x99131),f328(f328(f8(x99131,f879(x99131,x99131),a872),f81(x99131)),f104(x99131))),x99133))),f328(f249(a872),x99134))),f328(f328(f81(x99131),f328(f104(x99131),x99134)),f328(f328(f80(x99131),x99132),f328(f328(f80(x99131),x99132),f328(f328(f81(x99131),f328(f104(x99131),f328(f328(f22(a872),x99134),f78(a872)))),x99133))))) % 167.75/167.50 [10053]P1(f328(x100531,f556(x100532,x100533,x100534,x100531)))+P38(x100532,f328(f248(f878(x100532,x100532)),f328(f267(x100532,x100532,a867),f328(f328(f8(f879(x100532,a867),f879(x100532,a867),x100532),f328(f18(x100532,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100532),a326),x100531))),f328(f328(f7(x100532,f879(x100532,x100532),f879(x100532,a867)),f328(f328(f8(f879(x100532,a867),f879(f879(x100532,x100532),f879(x100532,a867)),x100532),f8(x100532,a867,x100532)),a325)),x100533))))) % 167.75/167.50 [10067]~P1(f328(f328(f243(a872),f328(x100674,f328(x100673,f556(x100671,x100673,x100674,x100672)))),f328(x100674,f556(x100671,x100673,x100674,x100672))))+P38(x100671,f328(f248(f878(x100671,x100671)),f328(f267(x100671,x100671,a867),f328(f328(f8(f879(x100671,a867),f879(x100671,a867),x100671),f328(f18(x100671,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100671),a326),x100672))),f328(f328(f7(x100671,f879(x100671,x100671),f879(x100671,a867)),f328(f328(f8(f879(x100671,a867),f879(f879(x100671,x100671),f879(x100671,a867)),x100671),f8(x100671,a867,x100671)),a325)),x100673))))) % 167.75/167.50 [10167]~P1(f328(f328(f330(f878(x101671,x101671)),f328(f328(f263(x101671,x101671),x101673),x101674)),f328(f328(f114(f879(f878(x101671,x101671),a867)),x101672),f304(x101671,f192(f879(f878(x101671,x101671),a867))))))+P1(f328(f328(f328(f328(f114(f879(x101671,f879(x101671,a867))),f328(f328(f7(x101671,f879(f878(x101671,x101671),a867),f879(x101671,a867)),f328(f328(f8(f879(x101671,f879(f879(f878(x101671,x101671),a867),a867)),f879(f879(f878(x101671,x101671),a867),f879(x101671,a867)),x101671),f7(x101671,f879(f878(x101671,x101671),a867),a867)),f328(f328(f8(f879(x101671,f878(x101671,x101671)),f879(x101671,f879(f879(f878(x101671,x101671),a867),a867)),x101671),f328(f8(f878(x101671,x101671),f879(f879(f878(x101671,x101671),a867),a867),x101671),f330(f878(x101671,x101671)))),f263(x101671,x101671)))),x101672)),a325),x101673),x101674)) % 167.75/167.50 [10177]P1(f328(f328(f330(f878(x101771,x101771)),f328(f328(f263(x101771,x101771),x101772),x101773)),f328(f328(f114(f879(f878(x101771,x101771),a867)),x101774),f304(x101771,f192(f879(f878(x101771,x101771),a867))))))+~P1(f328(f328(f328(f328(f114(f879(x101771,f879(x101771,a867))),f328(f328(f7(x101771,f879(f878(x101771,x101771),a867),f879(x101771,a867)),f328(f328(f8(f879(x101771,f879(f879(f878(x101771,x101771),a867),a867)),f879(f879(f878(x101771,x101771),a867),f879(x101771,a867)),x101771),f7(x101771,f879(f878(x101771,x101771),a867),a867)),f328(f328(f8(f879(x101771,f878(x101771,x101771)),f879(x101771,f879(f879(f878(x101771,x101771),a867),a867)),x101771),f328(f8(f878(x101771,x101771),f879(f879(f878(x101771,x101771),a867),a867),x101771),f330(f878(x101771,x101771)))),f263(x101771,x101771)))),x101774)),a325),x101772),x101773)) % 167.75/167.50 [10039]~P108(x100393)+E(f90(x100391,f328(f328(f18(x100391,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100391),a326),x100392)),f328(f328(f8(f879(x100391,a867),a867,x100391),f88(x100391)),f328(f328(f8(f879(x100391,a867),f879(x100391,a867),x100391),f328(f18(x100391,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100391),a331),x100392))),f328(f328(f8(x100393,f879(x100391,a867),x100391),f328(f7(x100391,x100393,a867),f328(f328(f8(x100393,f879(x100393,a867),x100391),f242(x100393)),x100394))),x100394))))),f328(f93(x100391,x100393,x100394),x100392)) % 167.75/167.50 [10082]~P108(x100823)+E(f90(x100821,f328(f328(f18(x100821,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100821),a326),x100822)),f328(f328(f8(f879(x100821,a867),a867,x100821),f88(x100821)),f328(f328(f8(f879(x100821,a867),f879(x100821,a867),x100821),f328(f18(x100821,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100821),a331),x100822))),f328(f328(f7(x100821,f879(x100821,x100823),f879(x100821,a867)),f328(f328(f8(f879(x100823,a867),f879(f879(x100821,x100823),f879(x100821,a867)),x100821),f8(x100823,a867,x100821)),f328(f328(f8(x100823,f879(x100823,a867),x100821),f242(x100823)),x100824))),x100824))))),f96(x100821,x100823,x100824,x100822)) % 167.75/167.50 [10126]E(f328(f328(f148(f873(x101261)),f328(f328(f148(x101261),x101262),f328(f139(f873(x101261),f873(x101261),f125(x101261),f117(x101261)),f328(f328(f151(f873(x101261),f873(x101261)),f153(f873(x101261),x101261,f117(x101261),f328(f328(f8(f873(x101261),f879(f873(x101261),f873(x101261)),x101261),f16(f873(x101261),f873(x101261))),f328(f328(f7(x101261,f873(x101261),f873(x101261)),f148(x101261)),f117(x101261))))),x101263)))),f178(x101261,f328(f328(f148(f873(x101261)),x101264),f328(f139(f873(f873(x101261)),f873(f873(x101261)),f125(f873(x101261)),f117(f873(x101261))),f328(f328(f151(f873(x101261),f873(f873(x101261))),f153(f873(f873(x101261)),x101261,f117(f873(x101261)),f328(f16(f879(f873(x101261),f873(f873(x101261))),x101261),f328(f328(f7(f873(x101261),f873(f873(x101261)),f873(f873(x101261))),f148(f873(x101261))),f117(f873(x101261)))))),x101263))))),f178(x101261,f328(f328(f148(f873(x101261)),f328(f328(f148(x101261),x101262),x101264)),x101263)))+~P1(f328(f316(f873(f873(x101261)),f179(x101261)),f328(f328(f148(f873(x101261)),f328(f328(f148(x101261),x101262),x101264)),x101263))) % 167.75/167.50 [10166]~P1(f328(f38(x101662),f328(f248(x101662),x101664)))+P1(f328(f38(x101661),f328(f248(x101661),f328(f328(f8(f879(x101662,a867),a867,x101661),f87(x101662)),f328(f328(f7(x101661,f879(x101662,a867),f879(x101662,a867)),f328(f328(f8(f879(x101662,f879(a867,a867)),f879(f879(x101662,a867),f879(x101662,a867)),x101661),f18(x101662,a867,a867)),f328(f328(f8(f879(x101662,a867),f879(x101662,f879(a867,a867)),x101661),f328(f8(a867,f879(a867,a867),x101662),a326)),f328(f328(f7(x101661,f879(x101662,x101661),f879(x101662,a867)),f328(f328(f8(f879(x101661,a867),f879(f879(x101662,x101661),f879(x101662,a867)),x101661),f8(x101661,a867,x101662)),a325)),x101663)))),x101664))))) % 167.75/167.50 [5244]E(x52441,x52442)+~E(f127(x52443,x52444,x52441),f127(x52443,x52445,x52442)) % 167.75/167.50 [5245]E(x52451,x52452)+~E(f127(x52453,x52451,x52454),f127(x52453,x52452,x52455)) % 167.75/167.50 [5246]E(x52461,x52462)+~E(f168(x52463,x52461,x52464),f168(x52463,x52462,x52465)) % 167.75/167.50 [5623]E(f328(f328(f306(x56231),x56232),f182(x56231,x56233,x56234)),f182(x56231,x56233,x56234))+~E(f328(x56234,x56232),f328(f235(x56233),x56235)) % 167.75/167.50 [6028]P1(f328(f258(x60281,x60282,x60283),x60284))+~P1(f328(f328(x60283,x60285),x60284)) % 167.75/167.50 [6030]P1(f328(f257(x60301,x60302,x60303),x60304))+~P1(f328(f328(x60303,x60304),x60305)) % 167.75/167.50 [6033]~E(f328(x60334,x60332),f328(f235(x60333),x60335))+P1(f328(f328(f330(x60331),x60332),f182(x60331,x60333,x60334))) % 167.75/167.50 [6034]~E(f328(x60344,x60345),f328(f235(x60341),x60342))+P1(f328(f328(f330(x60341),x60342),f184(x60343,x60341,x60344))) % 167.75/167.50 [6501]~E(x65015,f2(a103))+E(f328(f204(x65011,x65012,x65013,x65014),x65015),f119(x65012)) % 167.75/167.50 [6502]~E(x65025,f2(a103))+E(f328(f202(x65021,x65022,x65023,x65024),x65025),f128(x65022)) % 167.75/167.50 [6638]~E(x66383,f2(a103))+E(f328(f277(x66381,x66382,x66383,x66384),x66385),f328(f263(x66381,x66382),x66385)) % 167.75/167.50 [6710]~E(f328(x67104,x67105),f205(x67102))+E(f328(f237(f876(x67101),x67102,f205(x67101),x67103),f328(x67104,x67105)),f205(x67101)) % 167.75/167.50 [7334]E(f328(x73341,x73342),f205(x73343))+~E(f328(f183(x73344,x73343,x73345,x73341),x73342),f205(x73343)) % 167.75/167.50 [7335]E(f328(x73351,x73352),f205(x73353))+~E(f328(f183(x73354,x73353,x73351,x73355),x73352),f205(x73353)) % 167.75/167.50 [7371]E(f328(f183(x73711,x73712,x73713,x73714),x73715),f328(x73713,x73715))+P1(f328(f328(f330(x73711),x73715),f182(x73711,x73712,x73714))) % 167.75/167.50 [7372]E(f328(f183(x73721,x73722,x73723,x73724),x73725),f328(x73724,x73725))+P1(f328(f328(f330(x73721),x73725),f182(x73721,x73722,x73723))) % 167.75/167.50 [7694]~P21(x76944,x76941,x76942,x76945)+E(f328(f73(x76941,x76941,x76941,f328(x76942,x76943)),f328(x76942,x76943)),f328(x76942,x76943)) % 167.75/167.50 [7738]E(f328(f183(x77381,x77382,x77383,x77384),x77385),f328(x77384,x77385))+~P1(f328(f328(f330(x77381),x77385),f182(x77381,x77382,x77384))) % 167.75/167.50 [8084]~P17(x80845,x80841,x80842)+E(f328(f73(x80841,x80841,x80841,f328(x80842,x80843)),f328(x80842,x80844)),f328(f73(x80841,x80841,x80841,f328(x80842,x80844)),f328(x80842,x80843))) % 167.75/167.50 [8422]P1(f328(f328(f330(f878(x84221,x84221)),f328(f328(f263(x84221,x84221),x84222),x84223)),f322(x84221,x84224,x84225)))+~P1(f328(f328(f243(a872),f328(x84224,x84222)),f328(x84224,x84223))) % 167.75/167.50 [8514]~P1(f328(f328(f330(x85144),x85143),f295(x85144,x85141,x85142,x85145)))+P1(f328(f328(x85141,x85142),x85143)) % 167.75/167.50 [8515]~P1(f328(f328(f330(x85154),x85153),f292(x85154,x85151,x85152,x85155)))+P1(f328(f328(x85151,x85152),x85153)) % 167.75/167.50 [8516]~P1(f328(f328(f330(x85164),x85162),f295(x85164,x85161,x85165,x85163)))+P1(f328(f328(x85161,x85162),x85163)) % 167.75/167.50 [8517]~P1(f328(f328(f330(x85174),x85172),f292(x85174,x85171,x85175,x85173)))+P1(f328(f328(x85171,x85172),x85173)) % 167.75/167.50 [8665]~P53(x86652,x86651,x86655,x86653,x86654)+E(f328(f307(x86651,x86652,x86653),x86654),f251(f879(x86652,a867))) % 167.75/167.50 [9103]~P35(x91031,x91032,x91033,x91034,x91035)+P35(x91031,x91032,x91033,f328(f166(x91031),x91034),f328(f166(x91032),x91035)) % 167.75/167.50 [9105]~P35(x91051,x91052,x91053,f328(f166(x91051),x91054),x91055)+P35(x91051,x91052,x91053,x91054,f328(f166(x91052),x91055)) % 167.75/167.50 [9106]~P35(x91061,x91062,x91063,x91064,f328(f166(x91062),x91065))+P35(x91061,x91062,x91063,f328(f166(x91061),x91064),x91065) % 167.75/167.50 [9112]P35(x91121,x91122,x91123,x91124,x91125)+~P35(x91121,x91122,x91123,f328(f166(x91121),x91124),f328(f166(x91122),x91125)) % 167.75/167.50 [9509]P1(f328(f328(f330(f878(f873(x95091),f873(x95091))),f328(f328(f263(f873(x95091),f873(x95091)),f328(f328(f148(x95091),x95092),x95093)),f328(f328(f148(x95091),x95092),x95094))),f154(x95091,x95095)))+~P1(f328(f328(f330(f878(f873(x95091),f873(x95091))),f328(f328(f263(f873(x95091),f873(x95091)),x95093),x95094)),f154(x95091,x95095))) % 167.75/167.50 [9510]P1(f328(f328(f330(f878(f873(x95101),f873(x95101))),f328(f328(f263(f873(x95101),f873(x95101)),f328(f328(f125(x95101),x95102),x95103)),f328(f328(f125(x95101),x95102),x95104))),f144(x95101,x95105)))+~P1(f328(f328(f330(f878(f873(x95101),f873(x95101))),f328(f328(f263(f873(x95101),f873(x95101)),x95103),x95104)),f144(x95101,x95105))) % 167.77/167.50 [9703]E(f328(f328(f148(x97031),f665(x97032,x97033,x97034,x97035,x97031)),f668(x97032,x97033,x97034,x97035,x97031)),x97035)+~P1(f328(f328(f330(f878(f873(x97031),f873(x97031))),f328(f328(f263(f873(x97031),f873(x97031)),x97035),f328(f328(f148(x97031),x97034),x97033))),f155(x97031,x97032))) % 167.77/167.50 [9725]E(f328(f328(f148(x97251),f669(x97252,x97253,x97254,x97255,x97251)),f670(x97252,x97253,x97254,x97255,x97251)),x97253)+~P1(f328(f328(f330(f878(f873(x97251),f873(x97251))),f328(f328(f263(f873(x97251),f873(x97251)),f328(f328(f148(x97251),x97255),x97254)),x97253)),f155(x97251,x97252))) % 167.77/167.50 [9887]~P1(f328(f328(f330(f878(f873(x98871),f873(x98871))),f328(f328(f263(f873(x98871),f873(x98871)),f328(f328(f148(x98871),x98875),x98872)),x98874)),f155(x98871,x98873)))+P1(f328(f328(f330(f878(f873(x98871),f873(x98871))),f328(f328(f263(f873(x98871),f873(x98871)),x98872),f670(x98873,x98874,x98872,x98875,x98871))),f155(x98871,x98873))) % 167.77/167.50 [9957]~P1(f328(f328(f330(f878(f873(x99571),f873(x99571))),f328(f328(f263(f873(x99571),f873(x99571)),x99575),f328(f328(f148(x99571),x99574),x99573))),f155(x99571,x99572)))+P1(f328(f328(f330(f878(f873(x99571),f873(x99571))),f328(f328(f263(f873(x99571),f873(x99571)),f668(x99572,x99573,x99574,x99575,x99571)),x99573)),f155(x99571,x99572))) % 167.77/167.50 [10121]P1(f328(f328(f330(f878(x101211,x101211)),f328(f328(f263(x101211,x101211),f328(x101212,f328(f328(f80(a872),x101213),x101214))),f328(x101212,x101213))),f304(x101211,x101215)))+~P1(f328(f328(f330(f878(x101211,x101211)),f328(f328(f263(x101211,x101211),f328(x101212,f328(a116,f623(x101214,x101213,x101215,x101212,x101211)))),f328(x101212,f623(x101214,x101213,x101215,x101212,x101211)))),f304(x101211,x101215))) % 167.77/167.50 [5210]E(x52101,x52102)+~E(f328(f328(f148(x52103),x52104),x52101),f328(f328(f148(x52103),x52105),x52102)) % 167.77/167.50 [5211]E(x52111,x52112)+~E(f328(f328(f148(x52113),x52111),x52114),f328(f328(f148(x52113),x52112),x52115)) % 167.77/167.50 [5262]P1(f328(x52621,x52622))+~E(f328(f133(x52623,x52621),x52624),f328(f328(f148(x52623),x52622),x52625)) % 167.77/167.50 [5263]P1(f328(x52631,x52632))+~E(f328(f328(f148(x52633),x52632),x52634),f328(f133(x52633,x52631),x52635)) % 167.77/167.50 [5420]~E(f328(f328(f135(x54201),x54203),x54202),f328(f328(f148(x54201),x54204),x54205))+E(f328(f328(f162(x54201),x54202),x54203),x54204) % 167.77/167.50 [5552]~P16(x55524,x55525,x55521)+E(f328(f328(x55521,x55522),f328(f328(x55521,x55522),x55523)),f328(f328(x55521,x55522),x55523)) % 167.77/167.50 [6086]~E(x60864,f2(a103))+E(f328(f328(f121(x60861,x60862,x60863),x60864),x60865),f328(f328(f263(f873(x60862),x60861),f117(x60862)),x60865)) % 167.77/167.50 [6160]~P105(x61602)+~E(f328(f328(f145(x61601,x61602,x61603),x61604),x61605),f117(x61601)) % 167.77/167.50 [6538]E(x65381,x65382)+~E(f328(f328(f125(x65383),x65384),f328(f328(f148(x65383),x65381),f117(x65383))),f328(f328(f125(x65383),x65385),f328(f328(f148(x65383),x65382),f117(x65383)))) % 167.77/167.50 [6539]E(x65391,x65392)+~E(f328(f328(f125(x65393),x65391),f328(f328(f148(x65393),x65394),f117(x65393))),f328(f328(f125(x65393),x65392),f328(f328(f148(x65393),x65395),f117(x65393)))) % 167.77/167.50 [6794]E(f328(f186(x67941,x67942,x67943,x67944),x67945),f205(x67942))+P1(f328(f328(f330(x67941),x67945),x67944)) % 167.77/167.50 [6857]E(f328(f328(f306(x68571),f328(x68572,x68573)),f328(f307(x68574,x68571,x68572),x68575)),f328(f307(x68574,x68571,x68572),x68575))+~P1(f328(f328(f330(x68574),x68573),x68575)) % 167.77/167.50 [6864]~P1(f328(x68644,f328(x68643,x68645)))+P1(f328(f328(f308(x68641,x68642,x68643),x68644),x68645)) % 167.77/167.50 [6867]~P1(f328(f328(x68673,x68675),x68674))+P1(f328(f328(f252(x68671,x68672,x68673),x68674),x68675)) % 167.77/167.50 [6960]~E(f328(f307(x69601,x69602,x69603),x69604),x69605)+E(f328(f307(f879(x69601,a867),f879(x69602,a867),f307(x69601,x69602,x69603)),f328(f305(x69601),x69604)),f328(f305(x69602),x69605)) % 167.77/167.50 [6990]E(f328(f186(x69901,x69902,x69903,x69904),x69905),f328(x69903,x69905))+~P1(f328(f328(f330(x69901),x69905),x69904)) % 167.77/167.50 [7291]P26(x72911,x72912,x72913,x72914)+~P26(x72911,x72912,x72913,f328(f328(f306(x72911),x72915),x72914)) % 167.77/167.50 [7361]P1(f328(x73611,x73612))+~P1(f328(f328(f95(x73613,x73614,x73611),x73615),x73612)) % 167.77/167.50 [7405]~P1(f328(f328(f330(x74054),x74053),x74055))+P1(f328(f328(f330(x74051),f328(x74052,x74053)),f328(f307(x74054,x74051,x74052),x74055))) % 167.77/167.50 [7428]~P105(x74282)+E(f147(x74281,x74282,x74283,f328(f133(x74281,x74284),x74285)),f328(f133(x74281,x74284),f147(x74281,x74282,x74283,x74285))) % 167.77/167.50 [7461]P1(f328(x74611,f328(x74612,x74613)))+~P1(f328(f328(f308(x74614,x74615,x74612),x74611),x74613)) % 167.77/167.50 [7464]P1(f328(f328(x74641,x74642),x74643))+~P1(f328(f328(f252(x74644,x74645,x74641),x74643),x74642)) % 167.77/167.50 [7465]P1(f328(f328(x74651,x74652),x74653))+~P1(f328(f328(f95(x74654,x74651,x74655),x74652),x74653)) % 167.77/167.50 [7528]~P1(f328(f328(f330(x75283),f328(x75284,x75282)),x75285))+P1(f328(f328(f330(x75281),x75282),f328(f308(x75281,x75283,x75284),x75285))) % 167.77/167.50 [7929]~P1(f328(f328(f330(x79295),x79293),f328(f308(x79295,x79291,x79292),x79294)))+P1(f328(f328(f330(x79291),f328(x79292,x79293)),x79294)) % 167.77/167.50 [8151]~E(x81513,f328(f328(f328(f72(x81511,f876(x81512)),f328(f16(f876(x81512),x81511),f205(x81512))),x81514),f328(f235(x81512),x81515)))+E(f182(x81511,x81512,x81513),f328(f328(f306(x81511),x81514),f192(f879(x81511,a867)))) % 167.77/167.50 [8240]~P17(x82402,x82401,x82403)+E(f328(f139(x82401,x82402,f328(f7(x82402,x82401,x82401),x82403),x82404),f149(x82402,x82405)),f328(f328(f65(x82402,x82401,x82403),x82404),f328(f170(x82402),x82405))) % 167.77/167.50 [8259]E(f328(x82591,f351(x82592,x82591,x82593,x82594)),x82594)+~P1(f328(f328(f330(x82595),x82594),f328(f307(x82593,x82595,x82591),x82592))) % 167.77/167.50 [8567]~E(x85672,f328(f328(f148(x85671),x85674),x85675))+P1(f328(f328(f330(f878(f873(x85671),f873(x85671))),f328(f328(f263(f873(x85671),f873(x85671)),f117(x85671)),x85672)),f144(x85671,x85673))) % 167.77/167.50 [8620]~P35(x86201,x86203,x86205,x86202,x86204)+E(f328(f193(f873(x86201)),x86202),f328(f193(f873(x86203)),x86204)) % 167.77/167.50 [8633]P1(f328(f328(f242(f879(x86331,a867)),f328(f328(f43(x86332,f879(x86331,a867)),x86333),x86334)),f328(x86334,x86335)))+~P1(f328(f328(f330(x86332),x86335),x86333)) % 167.77/167.50 [8681]~P53(x86811,x86812,x86813,x86815,x86814)+E(f328(f307(x86811,x86812,x86813),f251(f879(x86811,a867))),x86814) % 167.77/167.50 [8884]E(f328(f328(f328(f72(x88841,f876(x88842)),f186(x88841,x88842,x88843,x88844)),x88845),f205(x88842)),f186(x88841,x88842,x88843,x88844))+P1(f328(f328(f330(x88841),x88845),x88844)) % 167.77/167.50 [8889]E(f328(f133(x88891,x88892),f782(x88893,x88894,x88895,x88892,x88891)),x88893)+~E(f328(f133(x88891,x88892),x88895),f328(f328(f148(x88891),x88894),x88893)) % 167.77/167.50 [8890]E(f328(f133(x88901,x88902),f785(x88903,x88902,x88904,x88905,x88901)),x88904)+~E(f328(f328(f148(x88901),x88905),x88904),f328(f133(x88901,x88902),x88903)) % 167.77/167.50 [8891]E(f328(x88911,f709(x88912,x88913,x88911,x88914,x88915)),x88912)+~E(f328(f328(f206(x88915,x88914),x88911),x88913),f328(f235(x88914),x88912)) % 167.77/167.50 [8895]E(f328(f235(x88951),f709(x88952,x88953,x88954,x88955,x88951)),x88953)+~E(f328(f328(f206(x88951,x88955),x88954),x88953),f328(f235(x88955),x88952)) % 167.77/167.50 [8993]E(f328(f193(f873(x89931)),x89932),x89933)+~P1(f328(f328(f330(f878(f873(x89931),f873(x89931))),f328(f328(f263(f873(x89931),f873(x89931)),x89934),x89932)),f328(f140(x89931,x89935),x89933))) % 167.77/167.50 [8994]E(f328(f193(f873(x89941)),x89942),x89943)+~P1(f328(f328(f330(f878(f873(x89941),f873(x89941))),f328(f328(f263(f873(x89941),f873(x89941)),x89942),x89944)),f328(f140(x89941,x89945),x89943))) % 167.77/167.50 [9062]P1(f328(f328(f330(x90621),f351(x90622,x90623,x90621,x90624)),x90622))+~P1(f328(f328(f330(x90625),x90624),f328(f307(x90621,x90625,x90623),x90622))) % 167.77/167.50 [9224]E(f328(f307(x92241,x92242,x92243),f343(x92244,x92243,x92241,x92245,x92242)),x92245)+~P1(f328(f328(f242(f879(x92242,a867)),x92245),f328(f307(x92241,x92242,x92243),x92244))) % 167.77/167.50 [9477]E(f328(x94771,f769(x94772,x94771,x94773,x94774,x94775)),f328(f235(x94775),x94774))+~P1(f328(f328(f330(x94775),x94774),f184(x94773,x94775,f186(x94773,x94775,x94771,x94772)))) % 167.77/167.50 [9526]P1(f328(f328(f330(f878(f873(x95261),f873(x95261))),f328(f328(f263(f873(x95261),f873(x95261)),f328(f328(f148(x95261),x95262),x95263)),f328(f328(f148(x95261),x95262),x95264))),f304(f873(x95261),f154(x95261,x95265))))+~P1(f328(f328(f330(f878(f873(x95261),f873(x95261))),f328(f328(f263(f873(x95261),f873(x95261)),x95263),x95264)),f304(f873(x95261),f154(x95261,x95265)))) % 167.77/167.50 [9557]~E(f328(x95573,f711(x95575,x95574,x95573,x95572,x95571)),f328(x95575,f711(x95575,x95574,x95573,x95572,x95571)))+E(f328(f328(f151(x95571,x95572),x95573),x95574),f328(f328(f151(x95571,x95572),x95575),x95574)) % 167.77/167.50 [9635]~E(f328(f133(x96351,x96355),x96354),f328(f328(f148(x96351),x96353),x96352))+E(f328(f328(f125(x96351),f783(x96352,x96353,x96354,x96355,x96351)),f328(f328(f148(x96351),x96353),f782(x96352,x96353,x96354,x96355,x96351))),x96354) % 167.77/167.50 [9636]~E(f328(f328(f148(x96361),x96365),x96364),f328(f133(x96361,x96363),x96362))+E(f328(f328(f125(x96361),f786(x96362,x96363,x96364,x96365,x96361)),f328(f328(f148(x96361),x96365),f785(x96362,x96363,x96364,x96365,x96361))),x96362) % 167.77/167.50 [9640]E(f328(f328(f151(x96401,x96402),x96403),x96404),f328(f328(f151(x96401,x96402),x96405),x96404))+P1(f328(f328(f330(x96401),f711(x96403,x96404,x96405,x96402,x96401)),f328(f170(x96401),x96404))) % 167.77/167.50 [9670]~P1(f328(f328(f330(x96705),x96704),f328(f282(x96701,x96705,x96703),x96702)))+P1(f328(f328(f330(x96701),f519(x96702,x96703,x96701,x96704,x96705)),x96702)) % 167.77/167.50 [9671]~P1(f328(f328(f330(x96715),x96714),f328(f282(x96711,x96715,x96713),x96712)))+P1(f328(f328(f330(x96711),f526(x96712,x96713,x96711,x96714,x96715)),x96712)) % 167.77/167.50 [9697]~P1(f328(f328(f242(f879(x96975,a867)),x96974),f328(f307(x96971,x96975,x96973),x96972)))+P1(f328(f328(f242(f879(x96971,a867)),f343(x96972,x96973,x96971,x96974,x96975)),x96972)) % 167.77/167.50 [9748]~P1(f328(f328(f330(x97485),x97484),f184(x97481,x97485,f186(x97481,x97485,x97483,x97482))))+P1(f328(f328(f330(x97481),f769(x97482,x97483,x97481,x97484,x97485)),x97482)) % 167.77/167.50 [10143]E(x101431,f2(a103))+E(f328(f237(f878(f873(x101432),x101433),f878(x101432,x101433),f328(f328(f263(f873(x101432),x101433),f117(x101432)),x101434),f328(f267(x101432,x101433,f878(f873(x101432),x101433)),f328(f328(f7(x101432,f879(x101433,f878(f873(x101432),x101433)),f879(x101433,f878(f873(x101432),x101433))),f328(f328(f8(f879(f878(f873(x101432),x101433),f878(f873(x101432),x101433)),f879(f879(x101433,f878(f873(x101432),x101433)),f879(x101433,f878(f873(x101432),x101433))),x101432),f8(f878(f873(x101432),x101433),f878(f873(x101432),x101433),x101433)),f328(f328(f8(f879(f873(x101432),f879(x101433,f878(f873(x101432),x101433))),f879(f878(f873(x101432),x101433),f878(f873(x101432),x101433)),x101432),f267(f873(x101432),x101433,f878(f873(x101432),x101433))),f328(f328(f8(f879(f873(x101432),f873(x101432)),f879(f873(x101432),f879(x101433,f878(f873(x101432),x101433))),x101432),f328(f8(f873(x101432),f879(x101433,f878(f873(x101432),x101433)),f873(x101432)),f263(f873(x101432),x101433))),f148(x101432))))),f328(f121(x101433,x101432,x101435),f328(f328(f22(a103),x101431),f78(a103)))))),f328(x101435,x101434)),f328(f328(f121(x101433,x101432,x101435),x101431),x101434)) % 167.77/167.50 [5433]~E(f328(x54333,x54334),x54335)+E(f328(f328(f328(f72(x54331,x54332),x54333),x54334),x54335),x54333) % 167.77/167.50 [5876]E(f328(x58761,x58762),x58763)+~E(f328(f328(f328(f72(x58764,x58765),x58761),x58762),x58763),x58761) % 167.77/167.50 [5968]E(x59681,x59682)+~E(f328(f266(x59683,x59684),f328(f328(f263(x59683,x59684),x59685),x59681)),x59682) % 167.77/167.50 [5969]E(x59691,x59692)+~E(f328(f262(x59693,x59694),f328(f328(f263(x59693,x59694),x59691),x59695)),x59692) % 167.77/167.50 [6236]~E(x62363,f328(f328(f125(x62361),x62364),f328(f328(f148(x62361),x62362),x62365)))+P1(f328(f328(f330(x62361),x62362),f328(f170(x62361),x62363))) % 167.77/167.50 [6624]E(f328(f307(x66241,x66242,f328(f16(x66242,x66241),x66243)),x66244),f328(f328(f306(x66242),x66243),f192(f879(x66242,a867))))+~P1(f328(f328(f330(x66241),x66245),x66244)) % 167.77/167.50 [6695]E(f328(f328(f114(f879(x66951,a867)),f328(f170(x66951),x66952)),f328(f170(x66951),x66953)),f328(f170(x66951),x66954))+~E(f164(x66951,x66955,x66954),f328(f328(f263(f873(x66951),f873(x66951)),x66952),x66953)) % 167.77/167.50 [6798]~P105(x67982)+E(f328(f193(f873(x67981)),f328(f328(f145(x67981,x67982,x67983),x67984),x67985)),f328(a116,f328(f193(f873(x67981)),x67985))) % 167.77/167.50 [6810]~P105(x68102)+E(f328(f170(x68101),f328(f328(f145(x68101,x68102,x68103),x68104),x68105)),f328(f328(f306(x68101),x68104),f328(f170(x68101),x68105))) % 167.77/167.50 [7081]~P111(x70811)+E(f328(f328(f80(x70811),f328(f328(f80(x70811),x70812),x70813)),f328(f328(f80(x70811),x70814),x70815)),f328(f328(f80(x70811),f328(f328(f80(x70811),x70812),x70814)),f328(f328(f80(x70811),x70813),x70815))) % 167.77/167.50 [7082]~P111(x70821)+E(f328(f328(f81(x70821),f328(f328(f81(x70821),x70822),x70823)),f328(f328(f81(x70821),x70824),x70825)),f328(f328(f81(x70821),f328(f328(f81(x70821),x70822),x70824)),f328(f328(f81(x70821),x70823),x70825))) % 167.77/167.50 [7083]~P60(x70831)+E(f328(f328(f286(x70831),f328(f328(f81(x70831),x70832),x70833)),f328(f328(f81(x70831),x70834),x70835)),f328(f328(f81(x70831),f328(f328(f286(x70831),x70832),x70834)),f328(f328(f286(x70831),x70833),x70835))) % 167.77/167.50 [7097]~P105(x70971)+E(f302(x70971,f328(f328(f241(x70971),x70972),x70973),f328(f328(f240(x70971),x70974),x70975)),f328(f328(f105(f879(x70971,a867)),f302(x70971,x70972,x70974)),f302(x70971,x70973,x70975))) % 167.77/167.50 [7098]~P105(x70981)+E(f301(x70981,f328(f328(f241(x70981),x70982),x70983),f328(f328(f240(x70981),x70984),x70985)),f328(f328(f105(f879(x70981,a867)),f301(x70981,x70982,x70984)),f301(x70981,x70983,x70985))) % 167.77/167.50 [7099]~P105(x70991)+E(f299(x70991,f328(f328(f241(x70991),x70992),x70993),f328(f328(f240(x70991),x70994),x70995)),f328(f328(f105(f879(x70991,a867)),f299(x70991,x70992,x70994)),f299(x70991,x70993,x70995))) % 167.77/167.50 [7100]~P105(x71001)+E(f328(f328(f105(f879(x71001,a867)),f328(f298(x71001,x71002),x71003)),f328(f298(x71001,x71004),x71005)),f328(f298(x71001,f328(f328(f241(x71001),x71002),x71004)),f328(f328(f240(x71001),x71003),x71005))) % 167.77/167.50 [7217]~P1(f328(x72171,f500(x72173,x72172,x72171)))+P1(f328(x72171,f328(f328(f263(x72172,x72173),x72174),x72175))) % 167.77/167.50 [7304]~E(f328(x73043,x73044),f205(x73042))+E(f184(x73041,x73042,f328(f328(f328(f72(x73041,f876(x73042)),x73043),x73044),f328(f235(x73042),x73045))),f328(f328(f306(x73042),x73045),f184(x73041,x73042,x73043))) % 167.77/167.50 [7325]~E(x73252,f328(x73254,x73255))+P1(f328(f328(f330(x73251),x73252),f328(f307(x73253,x73251,x73254),f251(f879(x73253,a867))))) % 167.77/167.50 [7383]~E(f328(x73833,x73834),f205(x73832))+E(f328(f328(f22(f879(x73831,a867)),f182(x73831,x73832,x73833)),f328(f328(f306(x73831),x73834),x73835)),f328(f328(f22(f879(x73831,a867)),f182(x73831,x73832,x73833)),x73835)) % 167.77/167.50 [7402]~P16(x74023,x74022,x74024)+P16(x74021,x74022,f328(f328(f8(x74023,f879(x74022,x74022),x74021),x74024),x74025)) % 167.77/167.50 [7403]~P17(x74033,x74032,x74034)+P17(x74031,x74032,f328(f328(f8(x74033,f879(x74032,x74032),x74031),x74034),x74035)) % 167.77/167.50 [7544]~P26(x75441,x75442,x75443,x75444)+P26(x75441,x75442,x75443,f328(f328(f22(f879(x75441,a867)),x75444),x75445)) % 167.77/167.50 [7703]~P1(f328(f328(x77033,x77034),x77035))+P1(f328(f328(f267(x77031,x77032,a867),x77033),f328(f328(f263(x77031,x77032),x77034),x77035))) % 167.77/167.50 [7818]~P1(f328(x78182,x78184))+~E(f328(f328(f135(x78181),f328(f193(f873(x78181)),f175(x78181,x78182,x78183))),x78183),f328(f328(f148(x78181),x78184),x78185)) % 167.77/167.50 [7838]P26(x78381,x78382,x78383,x78384)+~P26(x78381,x78382,x78383,f328(f328(f114(f879(x78381,a867)),x78385),x78384)) % 167.77/167.50 [7839]P26(x78391,x78392,x78393,x78394)+~P26(x78391,x78392,x78393,f328(f328(f114(f879(x78391,a867)),x78394),x78395)) % 167.77/167.50 [7886]~P105(x78862)+E(f328(f328(f145(x78861,x78862,x78863),x78864),f147(x78861,x78862,x78863,x78865)),f147(x78861,x78862,x78863,f328(f328(f148(x78861),x78864),x78865))) % 167.77/167.50 [8042]~P28(x80421,f328(a116,x80422),f328(f328(f328(f92(x80421),x80423),f328(a26,x80424)),x80425))+P28(x80421,x80422,f328(f328(f328(f92(x80421),x80423),f328(f239(a869),f328(a28,x80424))),x80425)) % 167.77/167.50 [8181]P28(x81811,f328(a116,x81812),f328(f328(f328(f92(x81811),x81813),f328(a26,x81814)),x81815))+~P28(x81811,x81812,f328(f328(f328(f92(x81811),x81813),f328(f239(a869),f328(a28,x81814))),x81815)) % 167.77/167.50 [8215]~P16(x82152,x82151,x82153)+E(f328(f139(x82151,x82152,f328(f7(x82152,x82151,x82151),x82153),x82154),x82155),f328(f328(f65(x82152,x82151,x82153),x82154),f328(f170(x82152),x82155))) % 167.77/167.50 [8245]~E(f328(f328(f135(x82451),f328(f193(f873(x82451)),f175(x82451,x82452,x82453))),x82453),f328(f328(f148(x82451),x82454),x82455))+E(f328(f328(f125(x82451),f175(x82451,x82452,x82453)),f328(f328(f148(x82451),x82454),x82455)),x82453) % 167.77/167.50 [8269]P1(f328(f328(x82691,x82692),x82693))+~P1(f328(f328(f267(x82694,x82695,a867),x82691),f328(f328(f263(x82694,x82695),x82692),x82693))) % 167.77/167.50 [8331]~E(f328(f328(f176(x83311,x83312),x83315),x83313),f328(f235(x83312),x83314))+P1(f328(f328(f330(f878(x83311,x83312)),f328(f328(f263(x83311,x83312),x83313),x83314)),f328(f170(f878(x83311,x83312)),x83315))) % 167.77/167.50 [8736]P1(f328(f328(f242(f879(x87361,a867)),f328(f307(x87362,x87361,x87363),x87364)),f328(f307(x87362,x87361,x87363),x87365)))+~P1(f328(f328(f242(f879(x87362,a867)),x87364),x87365)) % 167.77/167.50 [8737]P1(f328(f328(f242(f879(x87371,a867)),f328(f308(x87371,x87372,x87373),x87374)),f328(f308(x87371,x87372,x87373),x87375)))+~P1(f328(f328(f242(f879(x87372,a867)),x87374),x87375)) % 167.77/167.50 [8812]E(x88121,f2(a103))+E(f328(f328(f269(x88122,x88123,x88122,f878(x88123,x88122)),f328(x88124,x88125)),f277(x88123,x88122,f328(f328(f22(a103),x88121),f78(a103)),x88124)),f328(f277(x88123,x88122,x88121,x88124),x88125)) % 167.77/167.50 [9133]P28(x91331,x91332,f328(f328(f328(f92(x91331),x91333),x91334),x91335))+P1(f328(f328(x91333,f491(x91335,x91334,x91333,x91332)),f502(x91335,x91334,x91333,x91332))) % 167.77/167.50 [9333]E(f328(f235(x93331),f713(x93332,x93333,x93334,x93331,x93335)),f328(f328(f176(x93335,x93331),x93332),x93334))+~P1(f328(f328(f330(f878(x93335,x93331)),f328(f328(f263(x93335,x93331),x93334),x93333)),f328(f170(f878(x93335,x93331)),x93332))) % 167.77/167.50 [9377]P28(x93771,x93772,f328(f328(f328(f92(x93771),x93773),x93774),x93775))+~P1(f328(f328(x93775,f491(x93775,x93774,x93773,x93772)),f512(x93775,x93774,x93773,x93772))) % 167.77/167.50 [9437]P28(x94371,x94372,f328(f328(f328(f92(x94371),x94373),x94374),x94375))+P1(f328(f328(f328(f328(a200,x94374),f502(x94375,x94374,x94373,x94372)),x94372),f512(x94375,x94374,x94373,x94372))) % 167.77/167.50 [9440]~P25(x94401,x94402,f328(f328(f306(f871(x94401)),f328(f328(f328(f92(x94401),x94403),f328(f239(a869),f328(a28,x94404))),x94405)),f192(f879(f871(x94401),a867))))+P25(x94401,x94402,f328(f328(f306(f871(x94401)),f328(f328(f328(f92(x94401),x94403),f328(a26,x94404)),x94405)),f192(f879(f871(x94401),a867)))) % 167.77/167.50 [9468]~P1(f328(f38(x94683),f328(f307(x94682,x94683,x94685),f251(f879(x94682,a867)))))+P1(f328(f38(x94681),f328(f307(x94682,x94681,f328(f328(f8(x94683,x94681,x94682),x94684),x94685)),f251(f879(x94682,a867))))) % 167.77/167.50 [9492]P1(f328(f328(f242(f879(f879(x94921,a867),a867)),f328(f307(f879(x94922,a867),f879(x94921,a867),f307(x94922,x94921,x94923)),f328(f305(x94922),x94924))),f328(f305(x94921),x94925)))+~P1(f328(f328(f242(f879(x94921,a867)),f328(f307(x94922,x94921,x94923),x94924)),x94925)) % 167.77/167.50 [9505]~P1(f328(f38(f876(x95051)),f328(f307(x95052,f876(x95051),x95053),f251(f879(x95052,a867)))))+P1(f328(f38(f876(x95051)),f328(f307(x95052,f876(x95051),f328(f328(f328(f72(x95052,f876(x95051)),x95053),x95054),f328(f235(x95051),x95055))),f251(f879(x95052,a867))))) % 167.77/167.50 [9566]E(x95661,x95662)+~P1(f328(f67(x95663,x95664,x95665,x95661,f192(f879(x95663,a867))),x95662)) % 167.77/167.50 [9581]E(f328(f328(f263(x95811,x95812),f568(x95813,x95814,x95815,x95812,x95811)),f570(x95813,x95814,x95815,x95812,x95811)),x95815)+~P1(f328(f328(f330(f878(x95811,x95812)),x95815),f328(f328(f265(x95811,x95812),x95814),x95813))) % 167.77/167.50 [9676]P1(f328(f328(f330(x96761),f568(x96762,x96763,x96764,x96765,x96761)),x96763))+~P1(f328(f328(f330(f878(x96761,x96765)),x96764),f328(f328(f265(x96761,x96765),x96763),x96762))) % 167.77/167.50 [9784]P25(x97845,x97844,f328(f328(f306(f871(x97845)),f328(f328(f328(f92(x97845),x97841),x97843),x97842)),f192(f879(f871(x97845),a867))))+P1(f328(f328(x97841,f371(x97842,x97843,x97844,x97845,x97841)),f381(x97842,x97843,x97844,x97845,x97841))) % 167.77/167.50 [9835]P1(f328(f328(f330(x98351),f570(x98352,x98353,x98354,x98351,x98355)),f328(x98352,f568(x98352,x98353,x98354,x98351,x98355))))+~P1(f328(f328(f330(f878(x98355,x98351)),x98354),f328(f328(f265(x98355,x98351),x98353),x98352))) % 167.77/167.50 [9863]P1(f328(f328(f330(f878(x98631,x98631)),f328(f328(f263(x98631,x98631),x98632),f642(x98633,x98634,x98635,x98632,x98631))),x98633))+~P1(f328(f328(f330(f878(x98631,x98631)),f328(f328(f263(x98631,x98631),x98632),x98635)),f328(f328(f187(f878(x98631,x98631),a867),f328(a116,x98634)),x98633))) % 167.77/167.50 [9864]P1(f328(f328(f330(f878(x98641,x98641)),f328(f328(f263(x98641,x98641),x98642),f644(x98643,x98644,x98645,x98642,x98641))),x98643))+~P1(f328(f328(f330(f878(x98641,x98641)),f328(f328(f263(x98641,x98641),x98642),x98645)),f328(f328(f187(f878(x98641,x98641),a867),f328(a116,x98644)),x98643))) % 167.77/167.50 [9882]~P1(f328(f328(f330(f878(f873(x98821),f873(x98821))),f328(f328(f263(f873(x98821),f873(x98821)),f328(f328(f148(x98821),x98822),x98825)),x98824)),f155(x98821,x98823)))+P1(f328(f328(f330(f878(x98821,x98821)),f328(f328(f263(x98821,x98821),x98822),f669(x98823,x98824,x98825,x98822,x98821))),x98823)) % 167.77/167.50 [9884]~P25(x98841,x98842,f328(f328(f306(f871(x98841)),f328(f328(f328(f92(x98841),f95(x98841,x98843,x98844)),x98845),x98843)),f192(f879(f871(x98841),a867))))+P25(x98841,x98842,f328(f328(f306(f871(x98841)),f328(f328(f328(f92(x98841),x98843),f32(x98844,x98845)),f95(x98841,x98843,f328(f73(a867,a867,a868,a323),x98844)))),f192(f879(f871(x98841),a867)))) % 167.77/167.50 [9885]~P29(x98851,x98852,f328(f328(f306(f871(x98851)),f328(f328(f328(f92(x98851),f95(x98851,x98853,x98854)),x98855),x98853)),f192(f879(f871(x98851),a867))))+P29(x98851,x98852,f328(f328(f306(f871(x98851)),f328(f328(f328(f92(x98851),x98853),f32(x98854,x98855)),f95(x98851,x98853,f328(f73(a867,a867,a868,a323),x98854)))),f192(f879(f871(x98851),a867)))) % 167.77/167.50 [10144]P25(x101441,x101442,f328(f328(f306(f871(x101441)),f328(f328(f328(f92(x101441),x101443),x101444),x101445)),f192(f879(f871(x101441),a867))))+~P25(x101441,x101442,f328(f328(f306(f871(x101441)),f328(f328(f328(f92(x101441),f328(f16(f879(a868,a867),x101441),f328(f328(f7(a868,a868,a867),a325),f381(x101445,x101444,x101442,x101441,x101443)))),x101444),f328(f16(f879(a868,a867),x101441),f328(x101445,f371(x101445,x101444,x101442,x101441,x101443))))),f192(f879(f871(x101441),a867)))) % 167.77/167.50 [6310]P1(f328(x63102,x63104))+E(f175(x63101,x63102,f328(f328(f125(x63101),x63103),f328(f328(f148(x63101),x63104),x63105))),f175(x63101,x63102,x63103)) % 167.77/167.50 [6357]~P2(x63572)+E(f328(f328(f328(f114(f879(x63571,x63572)),x63573),x63574),x63575),f328(f328(f114(x63572),f328(x63573,x63575)),f328(x63574,x63575))) % 167.77/167.50 [6359]~P65(x63592)+E(f328(f328(f328(f22(f879(x63591,x63592)),x63593),x63594),x63595),f328(f328(f22(x63592),f328(x63593,x63595)),f328(x63594,x63595))) % 167.77/167.50 [6361]~P2(x63612)+E(f328(f328(f328(f105(f879(x63611,x63612)),x63613),x63614),x63615),f328(f328(f105(x63612),f328(x63613,x63615)),f328(x63614,x63615))) % 167.77/167.50 [6379]E(x63791,x63792)+E(f328(f328(f162(x63793),f328(f328(f156(x63793,x63794),x63791),x63795)),x63792),f328(f328(f162(x63793),x63794),x63792)) % 167.77/167.50 [6643]~E(x66434,f192(f879(x66433,a867)))+E(f328(f328(f114(f879(x66431,a867)),x66432),f328(f328(f44(x66433,f879(x66431,a867)),x66434),x66435)),x66432) % 167.77/167.50 [6644]~E(x66444,f192(f879(x66443,a867)))+E(f328(f328(f22(f879(x66441,a867)),x66442),f328(f328(f44(x66443,f879(x66441,a867)),x66444),x66445)),x66442) % 167.77/167.50 [6645]~E(x66454,f192(f879(x66453,a867)))+E(f328(f328(f105(f879(x66451,a867)),x66452),f328(f328(f43(x66453,f879(x66451,a867)),x66454),x66455)),x66452) % 167.77/167.50 [6659]~E(x66594,f192(f879(x66593,a867)))+E(f328(f328(f306(x66591),x66592),f328(f328(f44(x66593,f879(x66591,a867)),x66594),x66595)),f328(f328(f306(x66591),x66592),f192(f879(x66591,a867)))) % 167.77/167.50 [7450]E(f328(f328(f162(x74501),f328(f328(f151(x74502,x74501),x74503),x74504)),x74505),f328(x74503,f328(f328(f162(x74502),x74504),x74505)))+~P1(f328(f328(f243(a872),x74505),f328(f193(f873(x74502)),x74504))) % 167.77/167.50 [7516]E(f328(f328(f114(f879(x75161,a867)),f328(x75162,x75163)),f328(f328(f44(x75164,f879(x75161,a867)),x75165),x75162)),f328(f328(f44(x75164,f879(x75161,a867)),x75165),x75162))+~P1(f328(f328(f330(x75164),x75163),x75165)) % 167.77/167.50 [7517]E(f328(f328(f105(f879(x75171,a867)),f328(x75172,x75173)),f328(f328(f43(x75174,f879(x75171,a867)),x75175),x75172)),f328(f328(f43(x75174,f879(x75171,a867)),x75175),x75172))+~P1(f328(f328(f330(x75174),x75173),x75175)) % 167.77/167.50 [8122]~E(x81223,f192(f879(x81221,a867)))+E(f328(f328(f44(x81221,f879(x81222,a867)),x81223),f328(f328(f8(f879(x81222,a867),f879(x81222,a867),x81221),f328(f306(x81222),x81224)),x81225)),f192(f879(x81222,a867))) % 167.77/167.50 [8127]~P1(f328(f328(f330(x81274),x81273),x81275))+P1(f328(f328(f242(f879(x81271,a867)),f328(x81272,x81273)),f328(f328(f44(x81274,f879(x81271,a867)),x81275),x81272))) % 167.77/167.50 [8268]~E(f328(x82684,x82682),x82685)+P1(f328(f328(f330(x82681),x82682),f328(f308(x82681,x82683,x82684),f328(f328(f306(x82683),x82685),f192(f879(x82683,a867)))))) % 167.77/167.50 [8313]~P51(x83131,x83132,f328(f283(x83132,x83131),x83133))+E(f328(f328(f105(f879(x83131,a867)),f328(f282(x83132,x83131,x83133),x83134)),f328(f282(x83132,x83131,x83133),x83135)),f328(f282(x83132,x83131,x83133),f328(f328(f105(f879(x83132,a867)),x83134),x83135))) % 167.77/167.50 [8389]E(x83891,f2(a103))+E(f328(f120(x83892,x83893,f328(x83894,f328(f328(f22(a103),x83891),f78(a103)))),f328(f328(f7(x83892,a103,f874(x83893)),x83895),x83891)),f328(f204(x83892,x83893,x83894,x83895),x83891)) % 167.77/167.50 [8429]E(x84291,f192(f879(x84292,a867)))+E(f328(f328(f44(x84292,f879(x84293,a867)),x84291),f328(f328(f8(f879(x84293,a867),f879(x84293,a867),x84292),f328(f306(x84293),x84294)),x84295)),f328(f328(f306(x84293),x84294),f328(f328(f44(x84292,f879(x84293,a867)),x84291),x84295))) % 167.77/167.50 [8479]~P26(x84792,x84791,x84793,f251(f879(x84792,a867)))+E(f328(f328(f22(f879(x84791,a867)),f328(f307(x84792,x84791,x84793),x84794)),f328(f307(x84792,x84791,x84793),x84795)),f328(f307(x84792,x84791,x84793),f328(f328(f22(f879(x84792,a867)),x84794),x84795))) % 167.77/167.50 [8480]~P26(x84802,x84801,x84803,f251(f879(x84802,a867)))+E(f328(f328(f105(f879(x84801,a867)),f328(f307(x84802,x84801,x84803),x84804)),f328(f307(x84802,x84801,x84803),x84805)),f328(f307(x84802,x84801,x84803),f328(f328(f105(f879(x84802,a867)),x84804),x84805))) % 167.77/167.50 [8553]~P1(f328(f328(f68(x85531,x85532,x85535),x85533),x85534))+P1(f328(f328(f330(f878(x85531,x85532)),f328(f328(f263(x85531,x85532),x85533),x85534)),x85535)) % 167.77/167.50 [8585]P1(f328(f328(f330(x85851),x85852),f328(f259(x85853,x85851),x85854)))+~P1(f328(f328(f330(f878(x85853,x85851)),f328(f328(f263(x85853,x85851),x85855),x85852)),x85854)) % 167.77/167.50 [8587]P1(f328(f328(f330(x85871),x85872),f328(f261(x85871,x85873),x85874)))+~P1(f328(f328(f330(f878(x85871,x85873)),f328(f328(f263(x85871,x85873),x85872),x85875)),x85874)) % 167.77/167.50 [8723]P1(f328(f328(f68(x87231,x87232,x87233),x87234),x87235))+~P1(f328(f328(f330(f878(x87231,x87232)),f328(f328(f263(x87231,x87232),x87234),x87235)),x87233)) % 167.77/167.50 [8758]E(f328(x87581,x87582),x87583)+~P1(f328(f328(f330(x87584),x87582),f328(f308(x87584,x87585,x87581),f328(f328(f306(x87585),x87583),f192(f879(x87585,a867)))))) % 167.77/167.50 [8990]P1(f328(f328(f330(f878(x89901,x89902)),f328(f328(f263(x89901,x89902),x89903),x89904)),f328(f283(x89902,x89901),x89905)))+~P1(f328(f328(f330(f878(x89902,x89901)),f328(f328(f263(x89902,x89901),x89904),x89903)),x89905)) % 167.77/167.50 [9008]~P1(f328(f328(x90081,x90085),x90084))+P1(f328(f328(x90081,f328(f266(x90082,x90083),f328(f328(f263(x90082,x90083),x90084),x90085))),f328(f262(x90082,x90083),f328(f328(f263(x90082,x90083),x90084),x90085)))) % 167.77/167.50 [9038]~P1(f328(f328(f330(f878(x90382,x90381)),f328(f328(f263(x90382,x90381),x90384),x90383)),f328(f283(x90381,x90382),x90385)))+P1(f328(f328(f330(f878(x90381,x90382)),f328(f328(f263(x90381,x90382),x90383),x90384)),x90385)) % 167.77/167.50 [9070]~P1(f328(f328(f330(f878(x90703,x90701)),f328(f328(f263(x90703,x90701),x90705),x90702)),x90704))+P1(f328(f328(f330(x90701),x90702),f328(f282(x90703,x90701,x90704),f328(f328(f306(x90703),x90705),f192(f879(x90703,a867)))))) % 167.77/167.50 [9115]P1(f328(f328(f330(f878(x91151,x91152)),f328(f328(f263(x91151,x91152),x91153),x91154)),x91155))+~P1(f328(f328(f330(x91152),x91154),f328(f282(x91151,x91152,x91155),f328(f328(f306(x91151),x91153),f192(f879(x91151,a867)))))) % 167.77/167.50 [9136]E(f328(f328(f328(f72(x91361,f876(x91362)),f186(x91361,x91362,x91363,x91364)),x91365),f205(x91362)),f186(x91361,x91362,x91363,f328(f328(f22(f879(x91361,a867)),x91364),f328(f328(f306(x91361),x91365),f192(f879(x91361,a867))))))+~P1(f328(f328(f330(x91361),x91365),x91364)) % 167.77/167.50 [9204]~P67(x92041)+E(f328(f328(f6(a872,x92041),x92042),f299(a872,f328(f328(f80(a872),x92043),x92044),f328(f328(f80(a872),x92045),x92044))),f328(f328(f6(a872,x92041),f328(f328(f8(a872,x92041,a872),x92042),f328(f328(f7(a872,a872,a872),f80(a872)),x92044))),f299(a872,x92043,x92045))) % 167.77/167.50 [9228]~P67(x92281)+E(f328(f328(f6(a872,x92281),x92282),f328(f298(a872,f328(f328(f80(a872),x92283),x92284)),f328(f328(f80(a872),x92285),x92284))),f328(f328(f6(a872,x92281),f328(f328(f8(a872,x92281,a872),x92282),f328(f328(f7(a872,a872,a872),f80(a872)),x92284))),f328(f298(a872,x92283),x92285))) % 167.77/167.50 [9281]~P26(x92811,x92812,x92813,f251(f879(x92811,a867)))+E(f328(f328(f151(x92811,x92812),x92813),f328(f133(x92811,f328(f328(f8(a867,a867,x92811),a323),f328(a325,x92814))),x92815)),f328(f133(x92812,f328(f328(f8(a867,a867,x92812),a323),f328(a325,f328(x92813,x92814)))),f328(f328(f151(x92811,x92812),x92813),x92815))) % 167.77/167.50 [9299]~P26(x92991,x92992,x92993,f328(f328(f306(x92991),x92994),f328(f170(x92991),x92995)))+E(f328(f328(f151(x92991,x92992),x92993),f328(f133(x92991,f328(f328(f8(a867,a867,x92991),a323),f328(a325,x92994))),x92995)),f328(f133(x92992,f328(f328(f8(a867,a867,x92992),a323),f328(a325,f328(x92993,x92994)))),f328(f328(f151(x92991,x92992),x92993),x92995))) % 167.77/167.50 [9455]P1(f328(f328(f330(f878(f873(x94551),f873(x94551))),f328(f328(f263(f873(x94551),f873(x94551)),f328(f328(f148(x94551),x94552),x94553)),f328(f328(f148(x94551),x94554),x94553))),f154(x94551,x94555)))+~P1(f328(f328(f330(f878(x94551,x94551)),f328(f328(f263(x94551,x94551),x94552),x94554)),x94555)) % 167.77/167.50 [9493]P1(f328(f328(f328(f328(a200,x94931),x94932),x94933),f622(x94934,x94933,x94932,x94935,x94931)))+~P1(f328(f328(f328(f328(a200,f33(x94931,x94935)),x94932),x94933),x94934)) % 167.77/167.50 [9564]P25(x95641,x95642,f328(f328(f306(f871(x95641)),f328(f328(f328(f92(x95641),x95643),f328(a26,x95644)),x95645)),f192(f879(f871(x95641),a867))))+~P25(x95641,f328(f328(f306(f871(x95641)),f328(f328(f328(f92(x95641),x95643),f328(a26,x95644)),x95645)),x95642),f328(f328(f306(f871(x95641)),f328(f328(f328(f92(x95641),x95643),f328(f239(a869),f328(a28,x95644))),x95645)),f192(f879(f871(x95641),a867)))) % 167.77/167.50 [9576]E(f328(f328(f306(x95761),f863(x95762,x95763,x95764,x95765,x95761)),f864(x95762,x95763,x95764,x95765,x95761)),f328(f328(f306(x95761),x95764),x95763))+~P1(f328(f63(x95761,x95765,f328(f328(f306(x95761),x95764),x95763)),x95762)) % 167.77/167.50 [9577]E(f328(f328(f306(x95771),f865(x95772,x95773,x95774,x95775,x95771)),f866(x95772,x95773,x95774,x95775,x95771)),f328(f328(f306(x95771),x95774),x95773))+~P1(f328(f63(x95771,x95775,f328(f328(f306(x95771),x95774),x95773)),x95772)) % 167.77/167.50 [9661]P1(f328(f328(f330(x96611),f765(x96612,x96613,x96614,x96615,x96611)),x96614))+P1(f328(f328(f328(f43(x96611,f879(x96615,a867)),x96614),x96613),x96612)) % 167.77/167.50 [9666]P1(f328(f328(f330(x96661),f821(x96662,x96663,x96661,x96664,x96665)),x96663))+P1(f328(f328(f330(x96665),x96664),f328(f328(f43(x96661,f879(x96665,a867)),x96663),x96662))) % 167.77/167.50 [9674]P1(f328(f328(f330(x96741),f355(x96742,x96743,x96741,x96744,x96745)),x96743))+P1(f328(f328(f242(f879(x96745,a867)),x96744),f328(f328(f43(x96741,f879(x96745,a867)),x96743),x96742))) % 167.77/167.50 [9677]P1(f328(f328(x96771,f780(x96772,x96771,x96773,x96774,x96775)),x96772))+~P1(f328(f328(f328(f44(x96775,f879(x96774,a867)),x96773),x96771),x96772)) % 167.77/167.50 [9680]P1(f328(f328(f330(x96801),f780(x96802,x96803,x96804,x96805,x96801)),x96804))+~P1(f328(f328(f328(f44(x96801,f879(x96805,a867)),x96804),x96803),x96802)) % 167.77/167.50 [9690]P1(f328(f328(f330(x96901),f812(x96902,x96903,x96901,x96904,x96905)),x96903))+~P1(f328(f328(f330(x96905),x96904),f328(f328(f44(x96901,f879(x96905,a867)),x96903),x96902))) % 167.77/167.50 [9695]P1(f328(f328(f330(x96951),x96952),f328(x96953,f812(x96953,x96954,x96955,x96952,x96951))))+~P1(f328(f328(f330(x96951),x96952),f328(f328(f44(x96955,f879(x96951,a867)),x96954),x96953))) % 167.77/167.50 [9789]~P1(f328(f328(x97894,f765(x97895,x97894,x97893,x97892,x97891)),x97895))+P1(f328(f328(f328(f43(x97891,f879(x97892,a867)),x97893),x97894),x97895)) % 167.77/167.50 [9792]~P1(f328(f328(f330(x97921),x97922),f328(x97925,f821(x97925,x97924,x97923,x97922,x97921))))+P1(f328(f328(f330(x97921),x97922),f328(f328(f43(x97923,f879(x97921,a867)),x97924),x97925))) % 167.77/167.50 [9796]~P1(f328(f328(f242(f879(x97961,a867)),x97962),f328(x97965,f355(x97965,x97964,x97963,x97962,x97961))))+P1(f328(f328(f242(f879(x97961,a867)),x97962),f328(f328(f43(x97963,f879(x97961,a867)),x97964),x97965))) % 167.77/167.50 [9841]P1(f328(f328(f328(f328(a200,x98411),f622(x98412,x98413,x98414,x98411,x98415)),x98413),x98412))+~P1(f328(f328(f328(f328(a200,f33(x98415,x98411)),x98414),x98413),x98412)) % 167.77/167.50 [9867]~P1(f328(f328(f330(x98671),f863(x98675,x98674,x98673,x98672,x98671)),f864(x98675,x98674,x98673,x98672,x98671)))+~P1(f328(f63(x98671,x98672,f328(f328(f306(x98671),x98673),x98674)),x98675)) % 167.77/167.50 [9868]~P1(f328(f328(f330(x98681),f865(x98685,x98684,x98683,x98682,x98681)),f866(x98685,x98684,x98683,x98682,x98681)))+~P1(f328(f63(x98681,x98682,f328(f328(f306(x98681),x98683),x98684)),x98685)) % 167.77/167.50 [9869]~P1(f328(f328(f330(f878(x98691,x98691)),f328(f328(f263(x98691,x98691),x98692),x98695)),f328(f328(f187(f878(x98691,x98691),a867),f328(a116,x98694)),x98693)))+P1(f328(f328(f330(f878(x98691,x98691)),f328(f328(f263(x98691,x98691),x98692),f643(x98693,x98694,x98695,x98692,x98691))),f328(f328(f187(f878(x98691,x98691),a867),x98694),x98693))) % 167.77/167.50 [9876]P1(f328(f67(x98761,x98761,x98762,f863(x98763,x98764,x98765,x98762,x98761),f864(x98763,x98764,x98765,x98762,x98761)),x98763))+~P1(f328(f63(x98761,x98762,f328(f328(f306(x98761),x98765),x98764)),x98763)) % 167.77/167.50 [9877]P1(f328(f67(x98771,x98771,x98772,f865(x98773,x98774,x98775,x98772,x98771),f866(x98773,x98774,x98775,x98772,x98771)),x98773))+~P1(f328(f63(x98771,x98772,f328(f328(f306(x98771),x98775),x98774)),x98773)) % 167.77/167.50 [9889]~P105(x98891)+P15(x98891,f328(f328(f151(x98892,x98891),x98893),f328(f133(x98892,f328(f328(f7(x98892,x98891,a867),f328(f328(f8(x98891,f879(x98891,a867),x98892),a325),x98893)),f328(x98894,x98895))),x98895))) % 167.77/167.50 [9929]~P1(f328(f328(f330(x99292),x99295),f328(f282(x99291,x99292,x99294),x99293)))+P1(f328(f328(f330(f878(x99291,x99292)),f328(f328(f263(x99291,x99292),f519(x99293,x99294,x99291,x99295,x99292)),x99295)),x99294)) % 167.77/167.50 [9930]~P1(f328(f328(f330(x99302),x99305),f328(f282(x99301,x99302,x99304),x99303)))+P1(f328(f328(f330(f878(x99301,x99302)),f328(f328(f263(x99301,x99302),f526(x99303,x99304,x99301,x99305,x99302)),x99305)),x99304)) % 167.77/167.50 [9950]~P1(f328(f328(f330(f878(x99501,x99501)),f328(f328(f263(x99501,x99501),x99505),x99504)),f328(f328(f187(f878(x99501,x99501),a867),f328(a116,x99503)),x99502)))+P1(f328(f328(f330(f878(x99501,x99501)),f328(f328(f263(x99501,x99501),f643(x99502,x99503,x99504,x99505,x99501)),x99504)),x99502)) % 167.77/167.50 [9953]~P1(f328(f328(f330(f878(x99531,x99531)),f328(f328(f263(x99531,x99531),x99535),x99534)),f328(f328(f187(f878(x99531,x99531),a867),f328(a116,x99533)),x99532)))+P1(f328(f328(f330(f878(x99531,x99531)),f328(f328(f263(x99531,x99531),f642(x99532,x99533,x99534,x99535,x99531)),x99534)),f328(f328(f187(f878(x99531,x99531),a867),x99533),x99532))) % 167.77/167.50 [9954]~P1(f328(f328(f330(f878(x99541,x99541)),f328(f328(f263(x99541,x99541),x99545),x99544)),f328(f328(f187(f878(x99541,x99541),a867),f328(a116,x99543)),x99542)))+P1(f328(f328(f330(f878(x99541,x99541)),f328(f328(f263(x99541,x99541),f644(x99542,x99543,x99544,x99545,x99541)),x99544)),f328(f328(f187(f878(x99541,x99541),a867),x99543),x99542))) % 167.77/167.50 [9955]~P1(f328(f328(f330(f878(f873(x99551),f873(x99551))),f328(f328(f263(f873(x99551),f873(x99551)),x99555),f328(f328(f148(x99551),x99554),x99553))),f155(x99551,x99552)))+P1(f328(f328(f330(f878(x99551,x99551)),f328(f328(f263(x99551,x99551),f665(x99552,x99553,x99554,x99555,x99551)),x99554)),x99552)) % 167.77/167.50 [7043]E(x70431,f205(x70432))+E(f182(x70433,x70432,f328(f328(f328(f72(x70433,f876(x70432)),x70434),x70435),x70431)),f328(f328(f306(x70433),x70435),f182(x70433,x70432,x70434))) % 167.77/167.50 [7537]~E(x75373,f192(f879(x75372,a867)))+E(f328(f328(f114(f879(x75371,a867)),f328(f328(f44(x75372,f879(x75371,a867)),x75373),x75374)),x75375),x75375) % 167.77/167.50 [7538]~E(x75383,f192(f879(x75382,a867)))+E(f328(f328(f105(f879(x75381,a867)),f328(f328(f43(x75382,f879(x75381,a867)),x75383),x75384)),x75385),x75385) % 167.77/167.50 [7901]~E(x79015,f205(x79012))+E(f182(x79011,x79012,f328(f328(f328(f72(x79011,f876(x79012)),x79013),x79014),x79015)),f328(f328(f22(f879(x79011,a867)),f182(x79011,x79012,x79013)),f328(f328(f306(x79011),x79014),f192(f879(x79011,a867))))) % 167.77/167.50 [7967]~E(x79673,f192(f879(x79672,a867)))+E(f328(f328(f22(f879(x79671,a867)),f328(f328(f43(x79672,f879(x79671,a867)),x79673),x79674)),x79675),f328(f328(f22(f879(x79671,a867)),f251(f879(x79671,a867))),x79675)) % 167.77/167.50 [8094]E(f328(f328(f156(x80941,f328(f328(f125(x80941),x80942),x80943)),x80944),x80945),f328(f328(f125(x80941),f328(f328(f156(x80941,x80942),x80944),x80945)),x80943))+~P1(f328(f328(f243(a872),x80944),f328(f193(f873(x80941)),x80942))) % 167.77/167.50 [8219]P1(f328(f328(f330(x82191),x82195),f328(f170(x82191),x82193)))+E(f328(f328(f176(x82191,x82192),f328(f328(f180(x82191,x82192),x82193),f328(f328(f151(x82191,x82192),x82194),x82193))),x82195),f205(x82192)) % 167.77/167.50 [8340]~P1(f328(f328(f330(x83401),x83405),f328(f170(x83401),x83403)))+E(f328(f328(f176(x83401,x83402),f328(f328(f180(x83401,x83402),x83403),f328(f328(f151(x83401,x83402),x83404),x83403))),x83405),f328(f235(x83402),f328(x83404,x83405))) % 167.77/167.50 [8377]E(f328(f328(f162(x83771),f328(f328(f151(a872,x83771),x83772),f136(a872,f328(f298(a872,x83773),x83774)))),x83775),f328(x83772,f328(f328(f80(a872),x83773),x83775)))+~P1(f328(f328(f243(a872),x83775),f328(f328(f22(a872),x83774),x83773))) % 167.77/167.50 [8394]E(x83941,f2(a103))+E(f123(x83942,x83943,f328(x83944,f328(f328(f22(a103),x83941),f78(a103))),f328(f328(f7(x83942,a103,f874(f876(x83943))),x83945),x83941)),f328(f202(x83942,x83943,x83944,x83945),x83941)) % 167.77/167.50 [8419]~E(x84193,f192(f879(x84191,a867)))+E(f328(f328(f43(x84191,f879(x84192,a867)),x84193),f328(f328(f8(f879(x84192,a867),f879(x84192,a867),x84191),f328(f22(f879(x84192,a867)),x84194)),x84195)),f251(f879(x84192,a867))) % 167.77/167.50 [8420]~E(x84203,f192(f879(x84201,a867)))+E(f328(f328(f43(x84201,f879(x84202,a867)),x84203),f328(f328(f8(f879(x84202,a867),f879(x84202,a867),x84201),f328(f105(f879(x84202,a867)),x84204)),x84205)),f251(f879(x84202,a867))) % 167.77/167.50 [8421]~E(x84213,f192(f879(x84211,a867)))+E(f328(f328(f44(x84211,f879(x84212,a867)),x84213),f328(f328(f8(f879(x84212,a867),f879(x84212,a867),x84211),f328(f114(f879(x84212,a867)),x84214)),x84215)),f192(f879(x84212,a867))) % 167.77/167.50 [8423]~P135(x84232)+E(f328(f328(f6(x84231,x84232),f328(f328(f8(x84232,x84232,x84231),f328(f81(x84232),x84233)),x84234)),x84235),f328(f328(f81(x84232),x84233),f328(f328(f6(x84231,x84232),x84234),x84235))) % 167.77/167.50 [8708]E(x87081,f192(f879(x87082,a867)))+E(f328(f328(f43(x87082,f879(x87083,a867)),x87081),f328(f328(f8(f879(x87083,a867),f879(x87083,a867),x87082),f328(f22(f879(x87083,a867)),x87084)),x87085)),f328(f328(f22(f879(x87083,a867)),x87084),f328(f328(f44(x87082,f879(x87083,a867)),x87081),x87085))) % 167.77/167.50 [8709]E(x87091,f192(f879(x87092,a867)))+E(f328(f328(f43(x87092,f879(x87093,a867)),x87091),f328(f328(f8(f879(x87093,a867),f879(x87093,a867),x87092),f328(f105(f879(x87093,a867)),x87094)),x87095)),f328(f328(f105(f879(x87093,a867)),x87094),f328(f328(f43(x87092,f879(x87093,a867)),x87091),x87095))) % 167.77/167.50 [8710]E(x87101,f192(f879(x87102,a867)))+E(f328(f328(f44(x87102,f879(x87103,a867)),x87101),f328(f328(f8(f879(x87103,a867),f879(x87103,a867),x87102),f328(f114(f879(x87103,a867)),x87104)),x87105)),f328(f328(f114(f879(x87103,a867)),x87104),f328(f328(f44(x87102,f879(x87103,a867)),x87101),x87105))) % 167.77/167.50 [8904]~P1(f328(f328(f243(a872),f328(x89044,x89042)),f328(x89044,x89043)))+P1(f328(f328(f330(f878(x89041,x89041)),f328(f328(f263(x89041,x89041),x89042),x89043)),f150(x89041,f328(f328(f148(f879(x89041,a872)),x89044),x89045)))) % 167.77/167.50 [9171]~P26(x91712,x91711,x91713,f328(f328(f114(f879(x91712,a867)),x91714),x91715))+E(f328(f328(f105(f879(x91711,a867)),f328(f307(x91712,x91711,x91713),f328(f328(f22(f879(x91712,a867)),x91714),x91715))),f328(f307(x91712,x91711,x91713),f328(f328(f22(f879(x91712,a867)),x91715),x91714))),f192(f879(x91711,a867))) % 167.77/167.50 [9451]~P1(f328(f328(f242(f879(x94513,a867)),f328(f282(x94511,x94513,x94514),x94512)),x94515))+P1(f328(f328(f242(f879(x94511,a867)),x94512),f328(f79(f879(x94511,a867)),f328(f282(x94513,x94511,f328(f283(x94511,x94513),x94514)),f328(f79(f879(x94513,a867)),x94515))))) % 167.77/167.50 [9476]~P26(x94761,x94762,x94763,f328(f328(f306(x94761),x94764),x94765))+~P1(f328(f328(f330(x94762),f328(x94763,x94764)),f328(f307(x94761,x94762,x94763),f328(f328(f22(f879(x94761,a867)),x94765),f328(f328(f306(x94761),x94764),f192(f879(x94761,a867))))))) % 167.77/167.50 [9530]P1(f328(f328(f242(f879(x95301,a867)),f328(f282(x95302,x95301,x95303),x95304)),x95305))+~P1(f328(f328(f242(f879(x95302,a867)),x95304),f328(f79(f879(x95302,a867)),f328(f282(x95301,x95302,f328(f283(x95302,x95301),x95303)),f328(f79(f879(x95301,a867)),x95305))))) % 167.77/167.50 [9604]~P84(x96041)+P1(f328(f328(f242(x96041),f328(f75(x96041),f328(f328(f22(x96041),f328(f328(f80(x96041),x96042),x96043)),f328(f328(f80(x96041),x96044),x96045)))),f328(f328(f80(x96041),f328(f75(x96041),f328(f328(f22(x96041),x96042),x96044))),f328(f75(x96041),f328(f328(f22(x96041),x96043),x96045))))) % 167.77/167.50 [9710]P1(f328(f328(f330(x97101),f354(x97102,x97103,x97104,x97101,x97105)),x97104))+P1(f328(f328(f242(f879(x97105,a867)),f328(f328(f44(x97101,f879(x97105,a867)),x97104),x97103)),x97102)) % 167.77/167.50 [9907]~P1(f328(f328(f242(f879(x99071,a867)),f328(x99074,f354(x99075,x99074,x99073,x99072,x99071))),x99075))+P1(f328(f328(f242(f879(x99071,a867)),f328(f328(f44(x99072,f879(x99071,a867)),x99073),x99074)),x99075)) % 167.77/167.50 [8528]E(f328(f328(f125(x85281),x85282),f328(f328(f156(x85281,x85283),f328(f328(f22(a872),x85284),f328(f193(f873(x85281)),x85282))),x85285)),f328(f328(f156(x85281,f328(f328(f125(x85281),x85282),x85283)),x85284),x85285))+P1(f328(f328(f243(a872),x85284),f328(f193(f873(x85281)),x85282))) % 167.77/167.50 [8561]~P136(x85611)+E(f328(f328(f80(x85611),f328(f328(f81(x85611),x85612),x85613)),f328(f328(f80(x85611),f328(f328(f81(x85611),x85614),x85613)),x85615)),f328(f328(f80(x85611),f328(f328(f81(x85611),f328(f328(f80(x85611),x85612),x85614)),x85613)),x85615)) % 167.77/167.50 [9125]~P135(x91251)+E(f328(f163(x91251),f328(f328(f151(x91252,x91251),f328(f328(f8(x91251,x91251,x91252),f328(f81(x91251),x91253)),x91254)),x91255)),f328(f328(f81(x91251),x91253),f328(f163(x91251),f328(f328(f151(x91252,x91251),x91254),x91255)))) % 167.77/167.50 [9298]E(f328(f193(f873(x92981)),f328(f328(f173(x92981),f328(f328(f240(a872),f328(f193(f873(x92981)),x92982)),f328(f193(f873(x92983)),x92984))),x92982)),f328(f193(f873(x92983)),f328(f328(f173(x92983),f328(f328(f240(a872),f328(f193(f873(x92981)),x92982)),f328(f193(f873(x92983)),x92984))),x92984)))+P1(f328(x92985,f328(f328(f180(x92981,x92983),x92982),x92984))) % 167.77/167.50 [9541]~P135(x95412)+E(f328(f328(f6(x95411,x95412),f328(f328(f7(x95411,x95412,x95412),f328(f328(f8(x95412,f879(x95412,x95412),x95411),f81(x95412)),x95413)),x95414)),x95415),f328(f328(f81(x95412),f328(f328(f6(x95411,x95412),x95413),x95415)),x95414)) % 167.77/167.50 [9542]~P61(x95422)+E(f328(f328(f6(x95421,x95422),f328(f328(f7(x95421,x95422,x95422),f328(f328(f8(x95422,f879(x95422,x95422),x95421),f286(x95422)),x95423)),x95424)),x95425),f328(f328(f286(x95422),f328(f328(f6(x95421,x95422),x95423),x95425)),x95424)) % 167.77/167.50 [9549]~P66(x95492)+E(f328(f328(f6(x95491,x95492),f328(f328(f18(x95491,x95492,x95492),f328(f328(f8(x95492,f879(x95492,x95492),x95491),f22(x95492)),x95493)),x95494)),x95495),f328(f328(f22(x95492),f328(f328(f6(x95491,x95492),x95493),x95495)),f328(f328(f6(x95491,x95492),x95494),x95495))) % 167.77/167.50 [9550]~P67(x95502)+E(f328(f328(f6(x95501,x95502),f328(f328(f18(x95501,x95502,x95502),f328(f328(f8(x95502,f879(x95502,x95502),x95501),f80(x95502)),x95503)),x95504)),x95505),f328(f328(f80(x95502),f328(f328(f6(x95501,x95502),x95503),x95505)),f328(f328(f6(x95501,x95502),x95504),x95505))) % 167.77/167.50 [9551]~P73(x95512)+E(f328(f328(f9(x95511,x95512),f328(f328(f18(x95511,x95512,x95512),f328(f328(f8(x95512,f879(x95512,x95512),x95511),f81(x95512)),x95513)),x95514)),x95515),f328(f328(f81(x95512),f328(f328(f9(x95511,x95512),x95513),x95515)),f328(f328(f9(x95511,x95512),x95514),x95515))) % 167.77/167.50 [9589]~E(x95893,f192(f879(x95891,a867)))+E(f328(f328(f43(x95891,f879(x95892,a867)),x95893),f328(f328(f7(x95891,f879(x95892,a867),f879(x95892,a867)),f328(f328(f8(f879(x95892,a867),f879(f879(x95892,a867),f879(x95892,a867)),x95891),f22(f879(x95892,a867))),x95894)),x95895)),f251(f879(x95892,a867))) % 167.77/167.50 [9590]~E(x95903,f192(f879(x95901,a867)))+E(f328(f328(f43(x95901,f879(x95902,a867)),x95903),f328(f328(f7(x95901,f879(x95902,a867),f879(x95902,a867)),f328(f328(f8(f879(x95902,a867),f879(f879(x95902,a867),f879(x95902,a867)),x95901),f105(f879(x95902,a867))),x95904)),x95905)),f251(f879(x95902,a867))) % 167.77/167.50 [9591]~E(x95913,f192(f879(x95911,a867)))+E(f328(f328(f44(x95911,f879(x95912,a867)),x95913),f328(f328(f7(x95911,f879(x95912,a867),f879(x95912,a867)),f328(f328(f8(f879(x95912,a867),f879(f879(x95912,a867),f879(x95912,a867)),x95911),f114(f879(x95912,a867))),x95914)),x95915)),f192(f879(x95912,a867))) % 167.77/167.50 [9612]E(x96121,f192(f879(x96122,a867)))+E(f328(f328(f43(x96122,f879(x96123,a867)),x96121),f328(f328(f7(x96122,f879(x96123,a867),f879(x96123,a867)),f328(f328(f8(f879(x96123,a867),f879(f879(x96123,a867),f879(x96123,a867)),x96122),f22(f879(x96123,a867))),x96124)),x96125)),f328(f328(f22(f879(x96123,a867)),f328(f328(f43(x96122,f879(x96123,a867)),x96121),x96124)),x96125)) % 167.77/167.50 [9613]E(x96131,f192(f879(x96132,a867)))+E(f328(f328(f43(x96132,f879(x96133,a867)),x96131),f328(f328(f7(x96132,f879(x96133,a867),f879(x96133,a867)),f328(f328(f8(f879(x96133,a867),f879(f879(x96133,a867),f879(x96133,a867)),x96132),f105(f879(x96133,a867))),x96134)),x96135)),f328(f328(f105(f879(x96133,a867)),f328(f328(f43(x96132,f879(x96133,a867)),x96131),x96134)),x96135)) % 167.77/167.50 [9614]E(x96141,f192(f879(x96142,a867)))+E(f328(f328(f44(x96142,f879(x96143,a867)),x96141),f328(f328(f7(x96142,f879(x96143,a867),f879(x96143,a867)),f328(f328(f8(f879(x96143,a867),f879(f879(x96143,a867),f879(x96143,a867)),x96142),f114(f879(x96143,a867))),x96144)),x96145)),f328(f328(f114(f879(x96143,a867)),f328(f328(f44(x96142,f879(x96143,a867)),x96141),x96144)),x96145)) % 167.77/167.50 [9178]~P1(f328(f328(f242(a872),x91781),x91784))+E(f328(f328(f22(a872),f328(f328(f80(a872),f328(f328(f81(a872),x91781),x91782)),x91783)),f328(f328(f80(a872),f328(f328(f81(a872),x91784),x91782)),x91785)),f328(f328(f22(a872),x91783),f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x91784),x91781)),x91782)),x91785))) % 167.77/167.50 [9770]~P135(x97701)+E(f328(f163(x97701),f328(f328(f151(x97702,x97701),f328(f328(f7(x97702,x97701,x97701),f328(f328(f8(x97701,f879(x97701,x97701),x97702),f81(x97701)),x97703)),x97704)),x97705)),f328(f328(f81(x97701),f328(f163(x97701),f328(f328(f151(x97702,x97701),x97703),x97705))),x97704)) % 167.77/167.50 [9776]~P66(x97761)+E(f328(f163(x97761),f328(f328(f151(x97762,x97761),f328(f328(f18(x97762,x97761,x97761),f328(f328(f8(x97761,f879(x97761,x97761),x97762),f22(x97761)),x97763)),x97764)),x97765)),f328(f328(f22(x97761),f328(f163(x97761),f328(f328(f151(x97762,x97761),x97763),x97765))),f328(f163(x97761),f328(f328(f151(x97762,x97761),x97764),x97765)))) % 167.77/167.50 [9777]~P67(x97771)+E(f328(f163(x97771),f328(f328(f151(x97772,x97771),f328(f328(f18(x97772,x97771,x97771),f328(f328(f8(x97771,f879(x97771,x97771),x97772),f80(x97771)),x97773)),x97774)),x97775)),f328(f328(f80(x97771),f328(f163(x97771),f328(f328(f151(x97772,x97771),x97773),x97775))),f328(f163(x97771),f328(f328(f151(x97772,x97771),x97774),x97775)))) % 167.77/167.50 [9920]P1(f328(x99201,f328(f328(f180(x99202,x99203),x99204),x99205)))+~P1(f328(x99201,f328(f328(f180(x99202,x99203),f328(f328(f173(x99202),f328(f328(f240(a872),f328(f193(f873(x99202)),x99204)),f328(f193(f873(x99203)),x99205))),x99204)),f328(f328(f173(x99203),f328(f328(f240(a872),f328(f193(f873(x99202)),x99204)),f328(f193(f873(x99203)),x99205))),x99205)))) % 167.77/167.50 [10153]~P1(f328(f328(f330(f878(x101532,x101531)),f328(f328(f263(x101532,x101531),x101534),x101535)),f328(f283(x101531,x101532),x101533)))+P1(f328(f328(f252(x101531,x101532,f328(f328(f7(x101531,f879(f878(x101531,x101532),a867),f879(x101532,a867)),f328(f328(f8(f879(x101532,f879(f879(f878(x101531,x101532),a867),a867)),f879(f879(f878(x101531,x101532),a867),f879(x101532,a867)),x101531),f7(x101532,f879(f878(x101531,x101532),a867),a867)),f328(f328(f8(f879(x101532,f878(x101531,x101532)),f879(x101532,f879(f879(f878(x101531,x101532),a867),a867)),x101531),f328(f8(f878(x101531,x101532),f879(f879(f878(x101531,x101532),a867),a867),x101532),f330(f878(x101531,x101532)))),f263(x101531,x101532)))),x101533)),x101534),x101535)) % 167.77/167.50 [10162]P1(f328(f328(f330(f878(x101621,x101622)),f328(f328(f263(x101621,x101622),x101623),x101624)),f328(f283(x101622,x101621),x101625)))+~P1(f328(f328(f252(x101622,x101621,f328(f328(f7(x101622,f879(f878(x101622,x101621),a867),f879(x101621,a867)),f328(f328(f8(f879(x101621,f879(f879(f878(x101622,x101621),a867),a867)),f879(f879(f878(x101622,x101621),a867),f879(x101621,a867)),x101622),f7(x101621,f879(f878(x101622,x101621),a867),a867)),f328(f328(f8(f879(x101621,f878(x101622,x101621)),f879(x101621,f879(f879(f878(x101622,x101621),a867),a867)),x101622),f328(f8(f878(x101622,x101621),f879(f879(f878(x101622,x101621),a867),a867),x101621),f330(f878(x101622,x101621)))),f263(x101622,x101621)))),x101625)),x101623),x101624)) % 167.77/167.50 [9419]~P1(f328(f328(f242(a872),x94194),x94191))+E(f328(f328(f22(a872),f328(f328(f80(a872),f328(f328(f81(a872),x94191),x94192)),x94193)),f328(f328(f80(a872),f328(f328(f81(a872),x94194),x94192)),x94195)),f328(f328(f22(a872),f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x94191),x94194)),x94192)),x94193)),x94195)) % 167.77/167.50 [10171]P25(x101711,x101712,f328(f307(a870,f871(x101711),f328(f328(f18(a870,f879(x101711,f879(a868,a867)),f871(x101711)),f328(f328(f18(a870,a869,f879(f879(x101711,f879(a868,a867)),f871(x101711))),f328(f328(f8(f879(x101711,f879(a868,a867)),f879(a869,f879(f879(x101711,f879(a868,a867)),f871(x101711))),a870),f92(x101711)),x101713)),a26)),x101714)),x101715))+~P25(x101711,f328(f328(f114(f879(f871(x101711),a867)),x101712),f328(f307(a870,f871(x101711),f328(f328(f18(a870,f879(x101711,f879(a868,a867)),f871(x101711)),f328(f328(f18(a870,a869,f879(f879(x101711,f879(a868,a867)),f871(x101711))),f328(f328(f8(f879(x101711,f879(a868,a867)),f879(a869,f879(f879(x101711,f879(a868,a867)),f871(x101711))),a870),f92(x101711)),x101713)),a26)),x101714)),x101715)),f328(f307(a870,f871(x101711),f328(f328(f18(a870,f879(x101711,f879(a868,a867)),f871(x101711)),f328(f328(f18(a870,a869,f879(f879(x101711,f879(a868,a867)),f871(x101711))),f328(f328(f8(f879(x101711,f879(a868,a867)),f879(a869,f879(f879(x101711,f879(a868,a867)),f871(x101711))),a870),f92(x101711)),x101713)),f328(f328(f8(f876(a869),a869,a870),f239(a869)),a28))),x101714)),x101715)) % 167.77/167.50 [10172]P29(x101721,x101722,f328(f307(a870,f871(x101721),f328(f328(f18(a870,f879(x101721,f879(a868,a867)),f871(x101721)),f328(f328(f18(a870,a869,f879(f879(x101721,f879(a868,a867)),f871(x101721))),f328(f328(f8(f879(x101721,f879(a868,a867)),f879(a869,f879(f879(x101721,f879(a868,a867)),f871(x101721))),a870),f92(x101721)),x101723)),a26)),x101724)),x101725))+~P29(x101721,f328(f328(f114(f879(f871(x101721),a867)),x101722),f328(f307(a870,f871(x101721),f328(f328(f18(a870,f879(x101721,f879(a868,a867)),f871(x101721)),f328(f328(f18(a870,a869,f879(f879(x101721,f879(a868,a867)),f871(x101721))),f328(f328(f8(f879(x101721,f879(a868,a867)),f879(a869,f879(f879(x101721,f879(a868,a867)),f871(x101721))),a870),f92(x101721)),x101723)),a26)),x101724)),x101725)),f328(f307(a870,f871(x101721),f328(f328(f18(a870,f879(x101721,f879(a868,a867)),f871(x101721)),f328(f328(f18(a870,a869,f879(f879(x101721,f879(a868,a867)),f871(x101721))),f328(f328(f8(f879(x101721,f879(a868,a867)),f879(a869,f879(f879(x101721,f879(a868,a867)),f871(x101721))),a870),f92(x101721)),x101723)),f328(f328(f8(f876(a869),a869,a870),f239(a869)),a28))),x101724)),x101725)) % 167.77/167.50 [5238]E(x52381,x52382)+~E(f30(x52383,x52384,x52381),f30(x52385,x52386,x52382)) % 167.77/167.50 [5239]E(x52391,x52392)+~E(f30(x52393,x52391,x52394),f30(x52395,x52392,x52396)) % 167.77/167.50 [5240]E(x52401,x52402)+~E(f30(x52401,x52403,x52404),f30(x52402,x52405,x52406)) % 167.77/167.50 [5241]E(x52411,x52412)+~E(f29(x52413,x52414,x52411),f29(x52415,x52416,x52412)) % 167.77/167.50 [5242]E(x52421,x52422)+~E(f29(x52423,x52421,x52424),f29(x52425,x52422,x52426)) % 167.77/167.50 [5243]E(x52431,x52432)+~E(f29(x52431,x52433,x52434),f29(x52432,x52435,x52436)) % 167.77/167.50 [6686]E(f328(f183(x66861,x66862,x66863,x66864),x66865),f328(f235(x66862),x66866))+~E(f328(x66864,x66865),f328(f235(x66862),x66866)) % 167.77/167.50 [6830]E(f328(f237(f876(x68301),x68302,f205(x68301),x68303),f328(x68304,x68305)),f328(x68303,x68306))+~E(f328(x68304,x68305),f328(f235(x68302),x68306)) % 167.77/167.50 [8363]~P20(x83635,x83631,x83632,x83636)+E(f328(f73(x83631,x83631,x83631,f328(x83632,x83633)),f328(x83632,x83634)),f328(f73(x83631,x83631,x83631,f328(x83632,x83634)),f328(x83632,x83633))) % 167.77/167.50 [8602]~P53(x86024,x86025,x86022,x86021,x86026)+E(f328(x86021,f328(x86022,x86023)),x86023) % 167.77/167.50 [8756]P26(x87561,x87562,x87563,x87564)+~P26(x87561,x87565,f328(f73(x87562,x87565,x87561,x87566),x87563),x87564) % 167.77/167.50 [8839]~P26(x88394,x88392,f328(f73(x88391,x88392,x88394,x88393),x88395),x88396)+P26(x88391,x88392,x88393,f328(f307(x88394,x88391,x88395),x88396)) % 167.77/167.50 [9489]P50(x94891,x94892,x94893,x94894,x94895,x94896)+~P1(f328(f328(x94893,f328(x94894,x94895)),f328(x94894,x94896))) % 167.77/167.50 [9552]P1(f328(f38(x95521),x95522))+~P1(f328(f67(x95521,x95523,x95524,x95525,x95522),x95526)) % 167.77/167.50 [9560]~P1(f328(f328(f330(x95604),x95603),f296(x95604,x95605,x95601,x95602,x95606)))+P1(f328(f328(x95601,x95602),x95603)) % 167.77/167.50 [9561]~P1(f328(f328(f330(x95614),x95613),f293(x95614,x95611,x95615,x95612,x95616)))+P1(f328(f328(x95611,x95612),x95613)) % 167.77/167.50 [9562]~P1(f328(f328(f330(x95624),x95622),f296(x95624,x95621,x95625,x95626,x95623)))+P1(f328(f328(x95621,x95622),x95623)) % 167.77/167.50 [9563]~P1(f328(f328(f330(x95634),x95632),f293(x95634,x95635,x95631,x95636,x95633)))+P1(f328(f328(x95631,x95632),x95633)) % 167.77/167.50 [9626]~P50(x96265,x96266,x96261,x96262,x96263,x96264)+P1(f328(f328(x96261,f328(x96262,x96263)),f328(x96262,x96264))) % 167.77/167.50 [5744]E(x57441,x57442)+~E(f328(f328(f263(x57443,x57444),x57445),x57441),f328(f328(f263(x57443,x57444),x57446),x57442)) % 167.77/167.50 [5746]E(x57461,x57462)+~E(f328(f328(f263(x57463,x57464),x57461),x57465),f328(f328(f263(x57463,x57464),x57462),x57466)) % 167.77/167.50 [5870]~P17(x58705,x58706,x58701)+E(f328(f328(x58701,x58702),f328(f328(x58701,x58703),x58704)),f328(f328(x58701,x58703),f328(f328(x58701,x58702),x58704))) % 167.77/167.50 [7285]~P33(x72854,x72851,f328(f328(f148(x72854),x72852),x72855),f328(f328(f148(x72854),x72853),x72856))+P1(f328(f328(x72851,x72852),x72853)) % 167.77/167.50 [7653]P33(x76531,x76532,x76533,x76534)+~P33(x76531,x76532,f328(f328(f148(x76531),x76535),x76533),f328(f328(f148(x76531),x76536),x76534)) % 167.77/167.50 [8699]~P53(x86995,x86991,x86992,x86996,x86994)+P1(f328(f328(f330(x86991),f328(x86992,x86993)),x86994)) % 167.77/167.50 [8867]E(f328(f76(x88671,x88672,x88673,x88674,x88675),x88676),f328(x88673,x88676))+P1(f328(f328(f330(x88671),x88676),x88675)) % 167.77/167.50 [8887]~E(x88873,f328(f328(f148(x88871),x88875),x88876))+P1(f328(f328(f330(f878(f873(x88871),f873(x88871))),f328(f328(f263(f873(x88871),f873(x88871)),x88872),f328(f328(f125(x88871),x88872),x88873))),f144(x88871,x88874))) % 167.77/167.50 [8894]E(f328(f76(x88941,x88942,x88943,x88944,x88945),x88946),f328(x88944,x88946))+~P1(f328(f328(f330(x88941),x88946),x88945)) % 167.77/167.50 [8899]E(f328(f185(x88991,x88992,x88993,x88994,x88995),x88996),f328(x88993,x88996))+P1(f328(f328(f330(x88991),x88996),f328(f170(x88991),x88994))) % 167.77/167.50 [9129]~P35(x91291,x91292,x91293,x91295,x91296)+P35(x91291,x91292,x91293,f328(f328(f173(x91291),x91294),x91295),f328(f328(f173(x91292),x91294),x91296)) % 167.77/167.50 [9130]~P35(x91301,x91302,x91303,x91305,x91306)+P35(x91301,x91302,x91303,f328(f328(f135(x91301),x91304),x91305),f328(f328(f135(x91302),x91304),x91306)) % 167.77/167.50 [9624]~P24(x96244,x96242,x96245,x96243,x96246,x96241)+E(f328(x96241,f192(f879(x96242,a867))),x96243) % 167.77/167.50 [9870]~E(f328(x98704,f328(f262(x98701,x98703),x98705)),f328(x98706,f328(f262(x98701,x98703),x98705)))+E(f328(f268(x98701,x98702,x98703,x98703,x98704,f34(x98703)),x98705),f328(f268(x98701,x98702,x98703,x98703,x98706,f34(x98703)),x98705)) % 167.77/167.50 [9871]~E(f328(x98714,f328(f266(x98711,x98712),x98715)),f328(x98716,f328(f266(x98711,x98712),x98715)))+E(f328(f268(x98711,x98711,x98712,x98713,f34(x98711),x98714),x98715),f328(f268(x98711,x98711,x98712,x98713,f34(x98711),x98716),x98715)) % 167.77/167.50 [9916]~E(f328(f268(x99162,x99166,x99163,x99163,x99161,f34(x99163)),x99164),f328(f268(x99162,x99166,x99163,x99163,x99165,f34(x99163)),x99164))+E(f328(x99161,f328(f262(x99162,x99163),x99164)),f328(x99165,f328(f262(x99162,x99163),x99164))) % 167.77/167.50 [9917]~E(f328(f268(x99172,x99172,x99173,x99176,f34(x99172),x99171),x99174),f328(f268(x99172,x99172,x99173,x99176,f34(x99172),x99175),x99174))+E(f328(x99171,f328(f266(x99172,x99173),x99174)),f328(x99175,f328(f266(x99172,x99173),x99174))) % 167.77/167.50 [8795]P1(f328(f328(f330(x87951),x87952),x87953))+~P1(f328(f328(f330(f878(x87951,x87954)),f328(f328(f263(x87951,x87954),x87952),x87955)),f328(f328(f265(x87951,x87954),x87953),x87956))) % 167.77/167.50 [8809]P1(f328(f328(f330(x88091),x88092),f328(x88093,x88094)))+~P1(f328(f328(f330(f878(x88095,x88091)),f328(f328(f263(x88095,x88091),x88094),x88092)),f328(f328(f265(x88095,x88091),x88096),x88093))) % 167.77/167.50 [8896]~E(f328(f193(f873(x88961)),x88964),f328(f193(f873(x88962)),x88965))+E(f185(x88961,x88962,x88963,x88964,f328(f328(f125(x88962),x88965),x88966)),f185(x88961,x88962,x88963,x88964,x88965)) % 167.77/167.50 [8897]~E(f328(f193(f873(x88971)),x88974),f328(f193(f873(x88972)),x88976))+E(f185(x88971,x88972,x88973,f328(f328(f125(x88971),x88974),x88975),x88976),f185(x88971,x88972,x88973,x88974,x88976)) % 167.77/167.50 [9150]P1(f328(f328(f330(x91501),x91504),f182(x91501,x91502,x91506)))+E(f183(x91501,x91502,f328(f328(f328(f72(x91501,f876(x91502)),x91503),x91504),f328(f235(x91502),x91505)),x91506),f328(f328(f328(f72(x91501,f876(x91502)),f183(x91501,x91502,x91503,x91506)),x91504),f328(f235(x91502),x91505))) % 167.77/167.50 [9249]P1(f328(f328(f330(f878(x92491,x92491)),f328(f328(f263(x92491,x92491),f328(x92492,x92493)),f328(x92492,x92494))),x92495))+~P1(f328(f328(f330(f878(x92496,x92496)),f328(f328(f263(x92496,x92496),x92493),x92494)),f328(f328(f284(x92491,x92496),x92495),x92492))) % 167.77/167.50 [9269]~P1(f328(f328(f330(f878(x92694,x92694)),f328(f328(f263(x92694,x92694),f328(x92696,x92692)),f328(x92696,x92693))),x92695))+P1(f328(f328(f330(f878(x92691,x92691)),f328(f328(f263(x92691,x92691),x92692),x92693)),f328(f328(f284(x92694,x92691),x92695),x92696))) % 167.77/167.50 [9919]E(f328(f328(f263(x99191,x99192),f659(x99193,x99194,x99195,x99196,x99192,x99191)),f660(x99193,x99194,x99195,x99196,x99192,x99191)),x99196)+~P1(f328(f328(f330(f878(x99191,x99192)),x99196),f328(f328(f285(x99191,x99195,x99192),x99194),x99193))) % 167.77/167.50 [10119]~P1(f328(f328(f330(f878(x101191,x101196)),x101195),f328(f328(f285(x101191,x101192,x101196),x101194),x101193)))+P1(f328(f328(f330(f878(x101191,x101192)),f328(f328(f263(x101191,x101192),f659(x101193,x101194,x101192,x101195,x101196,x101191)),f661(x101193,x101194,x101192,x101195,x101196,x101191))),x101194)) % 167.77/167.50 [10120]~P1(f328(f328(f330(f878(x101206,x101202)),x101205),f328(f328(f285(x101206,x101201,x101202),x101204),x101203)))+P1(f328(f328(f330(f878(x101201,x101202)),f328(f328(f263(x101201,x101202),f661(x101203,x101204,x101201,x101205,x101202,x101206)),f660(x101203,x101204,x101201,x101205,x101202,x101206))),x101203)) % 167.77/167.50 [6147]~E(x61476,x61474)+E(f328(f328(f328(f328(f72(x61471,x61472),x61473),x61474),x61475),x61476),x61475) % 167.77/167.50 [6199]E(x61991,x61992)+E(f328(f328(f328(f328(f72(x61993,x61994),x61995),x61992),x61996),x61991),f328(x61995,x61991)) % 167.77/167.50 [7724]~P4(x77242)+E(f328(f328(f43(x77241,x77242),x77243),f328(f328(f7(x77241,x77244,x77242),x77245),x77246)),f328(f328(f328(f43(x77241,f879(x77244,x77242)),x77243),x77245),x77246)) % 167.77/167.50 [7725]~P4(x77252)+E(f328(f328(f44(x77251,x77252),x77253),f328(f328(f7(x77251,x77254,x77252),x77255),x77256)),f328(f328(f328(f44(x77251,f879(x77254,x77252)),x77253),x77255),x77256)) % 167.77/167.50 [8510]E(f328(f328(f44(x85101,f879(x85102,a867)),x85103),f328(f328(f8(f879(x85102,a867),f879(x85102,a867),x85101),f328(f306(x85102),x85104)),x85105)),f328(f328(f306(x85102),x85104),f328(f328(f44(x85101,f879(x85102,a867)),x85103),x85105)))+~P1(f328(f328(f330(x85101),x85106),x85103)) % 167.77/167.50 [8951]~P4(x89512)+E(f328(f328(f43(x89511,x89512),x89513),f328(f328(f8(f879(x89514,x89512),x89512,x89511),f328(f43(x89514,x89512),x89515)),f328(f7(x89514,x89511,x89512),x89516))),f328(f328(f43(x89514,x89512),x89515),f328(f328(f8(f879(x89511,x89512),x89512,x89514),f328(f43(x89511,x89512),x89513)),x89516))) % 167.77/167.50 [8952]~P4(x89522)+E(f328(f328(f44(x89521,x89522),x89523),f328(f328(f8(f879(x89524,x89522),x89522,x89521),f328(f44(x89524,x89522),x89525)),f328(f7(x89524,x89521,x89522),x89526))),f328(f328(f44(x89524,x89522),x89525),f328(f328(f8(f879(x89521,x89522),x89522,x89524),f328(f44(x89521,x89522),x89523)),x89526))) % 167.77/167.50 [9159]P1(f328(f328(f330(x91591),x91592),f328(f170(x91591),x91593)))+~P1(f328(f328(f330(f878(x91594,x91591)),f328(f328(f263(x91594,x91591),x91595),x91592)),f328(f170(f878(x91594,x91591)),f328(f328(f180(x91594,x91591),x91596),x91593)))) % 167.77/167.50 [9160]P1(f328(f328(f330(x91601),x91602),f328(f170(x91601),x91603)))+~P1(f328(f328(f330(f878(x91601,x91604)),f328(f328(f263(x91601,x91604),x91602),x91605)),f328(f170(f878(x91601,x91604)),f328(f328(f180(x91601,x91604),x91603),x91606)))) % 167.77/167.50 [9263]P1(f328(f328(f242(f879(x92631,a867)),f328(f282(x92632,x92631,x92633),x92634)),x92635))+~P1(f328(f328(f242(f879(f878(x92632,x92631),a867)),x92633),f328(f328(f265(x92632,x92631),x92636),f328(f16(f879(x92631,a867),x92632),x92635)))) % 167.77/167.50 [9454]P1(f328(f328(f330(f878(f873(x94541),f873(x94541))),f328(f328(f263(f873(x94541),f873(x94541)),f328(f328(f148(x94541),x94542),x94543)),f328(f328(f148(x94541),x94544),x94545))),f144(x94541,x94546)))+~P1(f328(f328(f330(f878(x94541,x94541)),f328(f328(f263(x94541,x94541),x94542),x94544)),x94546)) % 167.77/167.50 [9915]E(f328(f328(f263(x99151,x99152),f602(x99153,x99154,x99155,x99152,x99151,x99156)),f603(x99153,x99154,x99155,x99152,x99151,x99156)),x99156)+P1(f328(f328(f330(x99155),x99154),f328(f328(f267(x99151,x99152,f879(x99155,a867)),x99153),x99156))) % 167.77/167.50 [9921]E(f328(f328(f263(x99211,x99212),f604(x99213,x99214,x99212,x99211,x99215,x99216)),f605(x99213,x99214,x99212,x99211,x99215,x99216)),x99213)+~P1(f328(f328(f330(x99216),x99215),f328(f328(f267(x99211,x99212,f879(x99216,a867)),x99214),x99213))) % 167.77/167.50 [10078]P1(f328(f328(f330(x100781),x100782),f328(f328(x100783,f604(x100784,x100783,x100785,x100786,x100782,x100781)),f605(x100784,x100783,x100785,x100786,x100782,x100781))))+~P1(f328(f328(f330(x100781),x100782),f328(f328(f267(x100786,x100785,f879(x100781,a867)),x100783),x100784))) % 167.77/167.50 [10097]~P1(f328(f328(f330(x100971),x100972),f328(f328(x100975,f602(x100975,x100972,x100971,x100974,x100973,x100976)),f603(x100975,x100972,x100971,x100974,x100973,x100976))))+P1(f328(f328(f330(x100971),x100972),f328(f328(f267(x100973,x100974,f879(x100971,a867)),x100975),x100976))) % 167.77/167.50 [7847]P1(f328(f328(f330(x78471),x78474),x78476))+E(f186(x78471,x78472,f328(f328(f328(f72(x78471,f876(x78472)),x78473),x78474),x78475),x78476),f186(x78471,x78472,x78473,x78476)) % 167.77/167.50 [7924]P1(f328(f328(f330(x79241),x79244),x79246))+E(f328(f307(x79241,x79242,f328(f328(f328(f72(x79241,x79242),x79243),x79244),x79245)),x79246),f328(f307(x79241,x79242,x79243),x79246)) % 167.77/167.50 [7951]P1(f328(f328(f330(x79511),x79514),f328(f170(x79511),x79516)))+E(f328(f328(f151(x79511,x79512),f328(f328(f328(f72(x79511,x79512),x79513),x79514),x79515)),x79516),f328(f328(f151(x79511,x79512),x79513),x79516)) % 167.77/167.50 [8411]E(x84111,x84112)+E(f328(f328(f156(x84113,f328(f328(f156(x84113,x84114),x84111),x84115)),x84112),x84116),f328(f328(f156(x84113,f328(f328(f156(x84113,x84114),x84112),x84116)),x84111),x84115)) % 167.77/167.50 [8958]~P1(f328(f328(f330(x89583),x89586),x89585))+E(f328(f328(f306(x89581),x89582),f328(f307(x89583,x89581,x89584),f328(f328(f22(f879(x89583,a867)),x89585),f328(f328(f306(x89583),x89586),f192(f879(x89583,a867)))))),f328(f307(x89583,x89581,f328(f328(f328(f72(x89583,x89581),x89584),x89586),x89582)),x89585)) % 167.77/167.50 [9732]E(f185(x97321,x97322,x97323,f328(f328(f125(x97321),x97324),f328(f328(f148(x97321),x97325),f117(x97321))),x97326),f328(f328(f328(f72(x97321,f876(x97322)),f185(x97321,x97322,x97323,x97324,x97326)),x97325),f328(f235(x97322),f328(f328(f162(x97322),x97326),f328(f193(f873(x97321)),x97324)))))+~P1(f328(f328(f243(a872),f328(f193(f873(x97321)),x97324)),f328(f193(f873(x97322)),x97326))) % 167.77/167.50 [8738]~E(x87383,x87386)+E(f328(f328(f176(x87381,x87382),f328(f328(f148(f878(x87381,x87382)),f328(f328(f263(x87381,x87382),x87383),x87384)),x87385)),x87386),f328(f235(x87382),x87384)) % 167.77/167.50 [8765]E(x87651,x87652)+E(f328(f328(f176(x87653,x87654),f328(f328(f148(f878(x87653,x87654)),f328(f328(f263(x87653,x87654),x87651),x87655)),x87656)),x87652),f328(f328(f176(x87653,x87654),x87656),x87652)) % 167.77/167.50 [9032]~P1(f328(f328(x90324,x90325),x90326))+P1(f328(f328(f328(f328(f114(f879(x90321,f879(x90322,a867))),x90323),x90324),x90325),x90326)) % 167.77/167.50 [9034]~P1(f328(f328(x90343,x90345),x90346))+P1(f328(f328(f328(f328(f114(f879(x90341,f879(x90342,a867))),x90343),x90344),x90345),x90346)) % 167.77/167.50 [9320]P1(f328(f328(x93201,x93202),x93203))+~P1(f328(f328(f328(f328(f105(f879(x93204,f879(x93205,a867))),x93206),x93201),x93202),x93203)) % 167.77/167.50 [9321]P1(f328(f328(x93211,x93212),x93213))+~P1(f328(f328(f328(f328(f105(f879(x93214,f879(x93215,a867))),x93211),x93216),x93212),x93213)) % 167.77/167.50 [9754]~P67(x97542)+E(f328(f328(f6(x97541,x97542),f328(f328(f7(x97541,f879(x97543,a867),x97542),f328(f328(f8(f879(x97543,x97542),f879(f879(x97543,a867),x97542),x97541),f6(x97543,x97542)),x97544)),x97545)),x97546),f328(f328(f6(f878(x97541,x97543),x97542),f328(f267(x97541,x97543,x97542),x97544)),f328(f328(f265(x97541,x97543),x97546),f328(f16(f879(x97543,a867),x97541),x97545)))) % 167.77/167.50 [9755]~P73(x97552)+E(f328(f328(f9(x97551,x97552),f328(f328(f7(x97551,f879(x97553,a867),x97552),f328(f328(f8(f879(x97553,x97552),f879(f879(x97553,a867),x97552),x97551),f9(x97553,x97552)),x97554)),x97555)),x97556),f328(f328(f9(f878(x97551,x97553),x97552),f328(f267(x97551,x97553,x97552),x97554)),f328(f328(f265(x97551,x97553),x97556),f328(f16(f879(x97553,a867),x97551),x97555)))) % 167.77/167.50 [9898]~P67(x98982)+E(f328(f328(f6(x98981,x98982),f328(f328(f7(x98981,f879(x98983,a867),x98982),f328(f328(f8(f879(x98983,x98982),f879(f879(x98983,a867),x98982),x98981),f6(x98983,x98982)),f328(f7(x98983,x98981,x98982),x98984))),x98985)),x98986),f328(f328(f6(x98983,x98982),f328(f328(f7(x98983,f879(x98981,a867),x98982),f328(f328(f8(f879(x98981,x98982),f879(f879(x98981,a867),x98982),x98983),f6(x98981,x98982)),x98984)),x98986)),x98985)) % 167.77/167.50 [9593]~P1(f328(f328(f330(x95931),x95935),x95934))+E(f328(f328(f328(f72(x95931,f876(x95932)),f186(x95931,x95932,x95933,f328(f328(f22(f879(x95931,a867)),x95934),f328(f328(f306(x95931),x95935),f192(f879(x95931,a867)))))),x95935),x95936),f186(x95931,x95932,f328(f328(f328(f72(x95931,f876(x95932)),x95933),x95935),x95936),x95934)) % 167.77/167.50 [10175]~P1(f328(f328(f330(f878(x101751,x101752)),f328(f328(f263(x101751,x101752),x101755),x101756)),f328(f328(f114(f879(f878(x101751,x101752),a867)),x101753),x101754)))+P1(f328(f328(f328(f328(f114(f879(x101751,f879(x101752,a867))),f328(f328(f7(x101751,f879(f878(x101751,x101752),a867),f879(x101752,a867)),f328(f328(f8(f879(x101752,f879(f879(f878(x101751,x101752),a867),a867)),f879(f879(f878(x101751,x101752),a867),f879(x101752,a867)),x101751),f7(x101752,f879(f878(x101751,x101752),a867),a867)),f328(f328(f8(f879(x101752,f878(x101751,x101752)),f879(x101752,f879(f879(f878(x101751,x101752),a867),a867)),x101751),f328(f8(f878(x101751,x101752),f879(f879(f878(x101751,x101752),a867),a867),x101752),f330(f878(x101751,x101752)))),f263(x101751,x101752)))),x101753)),f328(f328(f7(x101751,f879(f878(x101751,x101752),a867),f879(x101752,a867)),f328(f328(f8(f879(x101752,f879(f879(f878(x101751,x101752),a867),a867)),f879(f879(f878(x101751,x101752),a867),f879(x101752,a867)),x101751),f7(x101752,f879(f878(x101751,x101752),a867),a867)),f328(f328(f8(f879(x101752,f878(x101751,x101752)),f879(x101752,f879(f879(f878(x101751,x101752),a867),a867)),x101751),f328(f8(f878(x101751,x101752),f879(f879(f878(x101751,x101752),a867),a867),x101752),f330(f878(x101751,x101752)))),f263(x101751,x101752)))),x101754)),x101755),x101756)) % 167.77/167.50 [10176]~P1(f328(f328(f330(f878(x101761,x101762)),f328(f328(f263(x101761,x101762),x101765),x101766)),f328(f328(f105(f879(f878(x101761,x101762),a867)),x101763),x101764)))+P1(f328(f328(f328(f328(f105(f879(x101761,f879(x101762,a867))),f328(f328(f7(x101761,f879(f878(x101761,x101762),a867),f879(x101762,a867)),f328(f328(f8(f879(x101762,f879(f879(f878(x101761,x101762),a867),a867)),f879(f879(f878(x101761,x101762),a867),f879(x101762,a867)),x101761),f7(x101762,f879(f878(x101761,x101762),a867),a867)),f328(f328(f8(f879(x101762,f878(x101761,x101762)),f879(x101762,f879(f879(f878(x101761,x101762),a867),a867)),x101761),f328(f8(f878(x101761,x101762),f879(f879(f878(x101761,x101762),a867),a867),x101762),f330(f878(x101761,x101762)))),f263(x101761,x101762)))),x101763)),f328(f328(f7(x101761,f879(f878(x101761,x101762),a867),f879(x101762,a867)),f328(f328(f8(f879(x101762,f879(f879(f878(x101761,x101762),a867),a867)),f879(f879(f878(x101761,x101762),a867),f879(x101762,a867)),x101761),f7(x101762,f879(f878(x101761,x101762),a867),a867)),f328(f328(f8(f879(x101762,f878(x101761,x101762)),f879(x101762,f879(f879(f878(x101761,x101762),a867),a867)),x101761),f328(f8(f878(x101761,x101762),f879(f879(f878(x101761,x101762),a867),a867),x101762),f330(f878(x101761,x101762)))),f263(x101761,x101762)))),x101764)),x101765),x101766)) % 167.77/167.50 [10182]P1(f328(f328(f330(f878(x101821,x101822)),f328(f328(f263(x101821,x101822),x101823),x101824)),f328(f328(f114(f879(f878(x101821,x101822),a867)),x101825),x101826)))+~P1(f328(f328(f328(f328(f114(f879(x101821,f879(x101822,a867))),f328(f328(f7(x101821,f879(f878(x101821,x101822),a867),f879(x101822,a867)),f328(f328(f8(f879(x101822,f879(f879(f878(x101821,x101822),a867),a867)),f879(f879(f878(x101821,x101822),a867),f879(x101822,a867)),x101821),f7(x101822,f879(f878(x101821,x101822),a867),a867)),f328(f328(f8(f879(x101822,f878(x101821,x101822)),f879(x101822,f879(f879(f878(x101821,x101822),a867),a867)),x101821),f328(f8(f878(x101821,x101822),f879(f879(f878(x101821,x101822),a867),a867),x101822),f330(f878(x101821,x101822)))),f263(x101821,x101822)))),x101825)),f328(f328(f7(x101821,f879(f878(x101821,x101822),a867),f879(x101822,a867)),f328(f328(f8(f879(x101822,f879(f879(f878(x101821,x101822),a867),a867)),f879(f879(f878(x101821,x101822),a867),f879(x101822,a867)),x101821),f7(x101822,f879(f878(x101821,x101822),a867),a867)),f328(f328(f8(f879(x101822,f878(x101821,x101822)),f879(x101822,f879(f879(f878(x101821,x101822),a867),a867)),x101821),f328(f8(f878(x101821,x101822),f879(f879(f878(x101821,x101822),a867),a867),x101822),f330(f878(x101821,x101822)))),f263(x101821,x101822)))),x101826)),x101823),x101824)) % 167.77/167.50 [10183]P1(f328(f328(f330(f878(x101831,x101832)),f328(f328(f263(x101831,x101832),x101833),x101834)),f328(f328(f105(f879(f878(x101831,x101832),a867)),x101835),x101836)))+~P1(f328(f328(f328(f328(f105(f879(x101831,f879(x101832,a867))),f328(f328(f7(x101831,f879(f878(x101831,x101832),a867),f879(x101832,a867)),f328(f328(f8(f879(x101832,f879(f879(f878(x101831,x101832),a867),a867)),f879(f879(f878(x101831,x101832),a867),f879(x101832,a867)),x101831),f7(x101832,f879(f878(x101831,x101832),a867),a867)),f328(f328(f8(f879(x101832,f878(x101831,x101832)),f879(x101832,f879(f879(f878(x101831,x101832),a867),a867)),x101831),f328(f8(f878(x101831,x101832),f879(f879(f878(x101831,x101832),a867),a867),x101832),f330(f878(x101831,x101832)))),f263(x101831,x101832)))),x101835)),f328(f328(f7(x101831,f879(f878(x101831,x101832),a867),f879(x101832,a867)),f328(f328(f8(f879(x101832,f879(f879(f878(x101831,x101832),a867),a867)),f879(f879(f878(x101831,x101832),a867),f879(x101832,a867)),x101831),f7(x101832,f879(f878(x101831,x101832),a867),a867)),f328(f328(f8(f879(x101832,f878(x101831,x101832)),f879(x101832,f879(f879(f878(x101831,x101832),a867),a867)),x101831),f328(f8(f878(x101831,x101832),f879(f879(f878(x101831,x101832),a867),a867),x101832),f330(f878(x101831,x101832)))),f263(x101831,x101832)))),x101836)),x101833),x101834)) % 167.77/167.50 [10169]~P1(f328(f328(f330(f878(x101692,x101693)),f328(f328(f263(x101692,x101693),x101695),x101696)),f328(f328(f43(x101691,f879(f878(x101692,x101693),a867)),f251(f879(x101691,a867))),x101694)))+P1(f328(f328(f328(f328(f43(x101691,f879(x101692,f879(x101693,a867))),f251(f879(x101691,a867))),f328(f328(f8(f879(f878(x101692,x101693),a867),f879(x101692,f879(x101693,a867)),x101691),f328(f7(x101692,f879(f878(x101692,x101693),a867),f879(x101693,a867)),f328(f328(f8(f879(x101693,f879(f879(f878(x101692,x101693),a867),a867)),f879(f879(f878(x101692,x101693),a867),f879(x101693,a867)),x101692),f7(x101693,f879(f878(x101692,x101693),a867),a867)),f328(f328(f8(f879(x101693,f878(x101692,x101693)),f879(x101693,f879(f879(f878(x101692,x101693),a867),a867)),x101692),f328(f8(f878(x101692,x101693),f879(f879(f878(x101692,x101693),a867),a867),x101693),f330(f878(x101692,x101693)))),f263(x101692,x101693))))),x101694)),x101695),x101696)) % 167.77/167.50 [10170]~P1(f328(f328(f330(f878(x101702,x101703)),f328(f328(f263(x101702,x101703),x101705),x101706)),f328(f328(f44(x101701,f879(f878(x101702,x101703),a867)),f251(f879(x101701,a867))),x101704)))+P1(f328(f328(f328(f328(f44(x101701,f879(x101702,f879(x101703,a867))),f251(f879(x101701,a867))),f328(f328(f8(f879(f878(x101702,x101703),a867),f879(x101702,f879(x101703,a867)),x101701),f328(f7(x101702,f879(f878(x101702,x101703),a867),f879(x101703,a867)),f328(f328(f8(f879(x101703,f879(f879(f878(x101702,x101703),a867),a867)),f879(f879(f878(x101702,x101703),a867),f879(x101703,a867)),x101702),f7(x101703,f879(f878(x101702,x101703),a867),a867)),f328(f328(f8(f879(x101703,f878(x101702,x101703)),f879(x101703,f879(f879(f878(x101702,x101703),a867),a867)),x101702),f328(f8(f878(x101702,x101703),f879(f879(f878(x101702,x101703),a867),a867),x101703),f330(f878(x101702,x101703)))),f263(x101702,x101703))))),x101704)),x101705),x101706)) % 167.77/167.50 [10179]P1(f328(f328(f330(f878(x101791,x101792)),f328(f328(f263(x101791,x101792),x101793),x101794)),f328(f328(f43(x101795,f879(f878(x101791,x101792),a867)),f251(f879(x101795,a867))),x101796)))+~P1(f328(f328(f328(f328(f43(x101795,f879(x101791,f879(x101792,a867))),f251(f879(x101795,a867))),f328(f328(f8(f879(f878(x101791,x101792),a867),f879(x101791,f879(x101792,a867)),x101795),f328(f7(x101791,f879(f878(x101791,x101792),a867),f879(x101792,a867)),f328(f328(f8(f879(x101792,f879(f879(f878(x101791,x101792),a867),a867)),f879(f879(f878(x101791,x101792),a867),f879(x101792,a867)),x101791),f7(x101792,f879(f878(x101791,x101792),a867),a867)),f328(f328(f8(f879(x101792,f878(x101791,x101792)),f879(x101792,f879(f879(f878(x101791,x101792),a867),a867)),x101791),f328(f8(f878(x101791,x101792),f879(f879(f878(x101791,x101792),a867),a867),x101792),f330(f878(x101791,x101792)))),f263(x101791,x101792))))),x101796)),x101793),x101794)) % 167.77/167.50 [10180]P1(f328(f328(f330(f878(x101801,x101802)),f328(f328(f263(x101801,x101802),x101803),x101804)),f328(f328(f44(x101805,f879(f878(x101801,x101802),a867)),f251(f879(x101805,a867))),x101806)))+~P1(f328(f328(f328(f328(f44(x101805,f879(x101801,f879(x101802,a867))),f251(f879(x101805,a867))),f328(f328(f8(f879(f878(x101801,x101802),a867),f879(x101801,f879(x101802,a867)),x101805),f328(f7(x101801,f879(f878(x101801,x101802),a867),f879(x101802,a867)),f328(f328(f8(f879(x101802,f879(f879(f878(x101801,x101802),a867),a867)),f879(f879(f878(x101801,x101802),a867),f879(x101802,a867)),x101801),f7(x101802,f879(f878(x101801,x101802),a867),a867)),f328(f328(f8(f879(x101802,f878(x101801,x101802)),f879(x101802,f879(f879(f878(x101801,x101802),a867),a867)),x101801),f328(f8(f878(x101801,x101802),f879(f879(f878(x101801,x101802),a867),a867),x101802),f330(f878(x101801,x101802)))),f263(x101801,x101802))))),x101806)),x101803),x101804)) % 167.77/167.50 [7398]E(f328(x73981,f328(x73982,x73983)),f328(x73984,x73983))+~E(f328(f73(x73985,x73986,x73987,x73981),x73982),x73984) % 167.77/167.50 [9623]~P23(x96233,x96234,x96231,x96235,x96236,x96237)+E(f328(f328(x96231,x96232),x96232),x96232) % 167.77/167.50 [9995]~E(f328(f237(f876(x99957),x99951,f205(x99957),x99955),f328(x99954,x99953)),f328(f235(x99957),x99952))+E(f328(f235(x99951),f767(x99952,x99953,x99954,x99955,x99956,x99957,x99951)),f328(x99954,x99953)) % 167.77/167.50 [9996]~E(f328(f237(f876(x99966),x99967,f205(x99966),x99961),f328(x99964,x99963)),f328(f235(x99966),x99962))+E(f328(x99961,f767(x99962,x99963,x99964,x99961,x99965,x99966,x99967)),f328(f235(x99966),x99962)) % 167.77/167.50 [5970]~E(f328(f328(f151(x59701,x59705),x59706),x59702),f328(f328(f151(x59703,x59705),x59707),x59704))+E(f328(f193(f873(x59701)),x59702),f328(f193(f873(x59703)),x59704)) % 167.77/167.50 [7475]E(x74751,x74752)+~E(f328(f328(f328(f72(x74753,f876(x74754)),x74755),x74756),f328(f235(x74754),x74751)),f328(f328(f328(f72(x74753,f876(x74754)),x74757),x74756),f328(f235(x74754),x74752))) % 167.77/167.50 [8444]E(f328(x84441,f328(x84442,x84443)),f328(x84444,x84443))+~E(f328(f73(x84445,x84446,x84447,x84441),x84442),f328(f73(x84446,x84446,x84447,f34(x84446)),x84444)) % 167.77/167.50 [8784]~P35(x87844,x87845,x87841,f328(f328(f148(x87844),x87842),x87846),f328(f328(f148(x87845),x87843),x87847))+P1(f328(f328(x87841,x87842),x87843)) % 167.77/167.50 [9166]P35(x91661,x91662,x91663,x91664,x91665)+~P35(x91661,x91662,x91663,f328(f328(f148(x91661),x91666),x91664),f328(f328(f148(x91662),x91667),x91665)) % 167.77/167.50 [9793]P1(f328(f328(x97931,x97932),f549(x97933,x97932,x97934,x97931)))+~P1(f328(f328(f264(x97935,x97936,x97937,x97931,x97934),x97932),x97933)) % 167.77/167.50 [9814]P1(f328(f328(x98141,f549(x98142,x98143,x98141,x98144)),x98142))+~P1(f328(f328(f264(x98145,x98146,x98147,x98144,x98141),x98143),x98142)) % 167.77/167.50 [6013]E(x60131,x60132)+~E(f328(f328(f328(f92(x60133),x60134),x60135),x60131),f328(f328(f328(f92(x60133),x60136),x60137),x60132)) % 167.77/167.50 [6014]E(x60141,x60142)+~E(f328(f328(f328(f92(x60143),x60144),x60141),x60145),f328(f328(f328(f92(x60143),x60146),x60142),x60147)) % 167.77/167.50 [6015]E(x60151,x60152)+~E(f328(f328(f328(f92(x60153),x60151),x60154),x60155),f328(f328(f328(f92(x60153),x60152),x60156),x60157)) % 167.77/167.50 [8902]~P21(x89026,x89021,x89023,x89027)+E(f328(f73(x89021,x89021,x89022,f328(x89023,x89024)),f328(f73(x89021,x89021,x89022,f328(x89023,x89024)),x89025)),f328(f73(x89021,x89021,x89022,f328(x89023,x89024)),x89025)) % 167.77/167.50 [9272]~P35(x92723,x92722,x92724,f328(f328(f151(x92721,x92723),x92725),x92726),x92727)+P35(x92721,x92722,f328(f328(f8(x92723,f879(x92722,a867),x92721),x92724),x92725),x92726,x92727) % 167.77/167.50 [9295]P35(x92951,x92952,x92953,f328(f328(f151(x92954,x92951),x92955),x92956),x92957)+~P35(x92954,x92952,f328(f328(f8(x92951,f879(x92952,a867),x92954),x92953),x92955),x92956,x92957) % 167.77/167.50 [9712]E(f185(x97121,x97122,f328(f328(f328(f72(x97121,f876(x97122)),x97123),x97124),f328(f235(x97122),x97125)),x97126,x97127),f328(f328(f328(f72(x97121,f876(x97122)),f185(x97121,x97122,x97123,x97126,x97127)),x97124),f328(f235(x97122),x97125)))+P1(f328(f328(f330(x97121),x97124),f328(f170(x97121),x97126))) % 167.77/167.50 [8901]~P1(f328(f328(f330(x89011),x89012),f328(f328(x89015,x89016),x89017)))+P1(f328(f328(f330(x89011),x89012),f328(f328(f267(x89013,x89014,f879(x89011,a867)),x89015),f328(f328(f263(x89013,x89014),x89016),x89017)))) % 167.77/167.50 [9192]P1(f328(f328(f328(x91921,x91922),x91923),x91924))+~P1(f328(f328(f328(f267(x91925,x91926,f879(x91927,a867)),x91921),f328(f328(f263(x91925,x91926),x91922),x91923)),x91924)) % 167.77/167.50 [9334]P1(f328(f328(f330(x93341),f328(f328(x93342,x93343),x93344)),f328(f307(f878(x93345,x93346),x93341,f328(f267(x93345,x93346,x93341),x93342)),x93347)))+~P1(f328(f328(f330(f878(x93345,x93346)),f328(f328(f263(x93345,x93346),x93343),x93344)),x93347)) % 167.77/167.50 [9672]P1(f328(f328(f330(f878(f873(x96721),f873(x96721))),f328(f328(f263(f873(x96721),f873(x96721)),f328(f328(f125(x96721),x96722),f328(f328(f148(x96721),x96723),x96724))),f328(f328(f125(x96721),x96722),f328(f328(f148(x96721),x96725),x96726)))),f144(x96721,x96727)))+~P1(f328(f328(f330(f878(x96721,x96721)),f328(f328(f263(x96721,x96721),x96723),x96725)),x96727)) % 167.77/167.50 [9734]~P35(x97341,x97343,x97344,x97346,f328(f328(f151(x97342,x97343),x97345),x97347))+P35(x97341,x97342,f328(f328(f7(x97341,f879(x97342,x97343),f879(x97342,a867)),f328(f328(f8(f879(x97343,a867),f879(f879(x97342,x97343),f879(x97342,a867)),x97341),f8(x97343,a867,x97342)),x97344)),x97345),x97346,x97347) % 167.77/167.50 [9818]P35(x98181,x98182,x98183,x98184,f328(f328(f151(x98185,x98182),x98186),x98187))+~P35(x98181,x98185,f328(f328(f7(x98181,f879(x98185,x98182),f879(x98185,a867)),f328(f328(f8(f879(x98182,a867),f879(f879(x98185,x98182),f879(x98185,a867)),x98181),f8(x98182,a867,x98185)),x98183)),x98186),x98184,x98187) % 167.77/167.50 [9184]E(x91841,x91842)+E(f328(f328(f328(f72(x91843,x91844),f328(f328(f328(f72(x91843,x91844),x91845),x91841),x91846)),x91842),x91847),f328(f328(f328(f72(x91843,x91844),f328(f328(f328(f72(x91843,x91844),x91845),x91842),x91847)),x91841),x91846)) % 167.77/167.50 [9428]E(f185(x94281,x94282,f328(f328(f328(f72(x94281,f876(x94282)),x94283),x94284),f328(f235(x94282),x94285)),x94286,x94287),f185(x94281,x94282,x94283,x94286,x94287))+~P1(f328(f328(f330(x94281),x94284),f328(f170(x94281),f328(f328(f173(x94281),f328(f193(f873(x94282)),x94287)),x94286)))) % 167.77/167.50 [9745]E(f185(x97451,x97452,f328(f328(f328(f72(x97451,f876(x97452)),x97453),x97454),f328(f235(x97452),x97455)),x97456,x97457),f328(f328(f328(f72(x97451,f876(x97452)),f185(x97451,x97452,x97453,x97456,x97457)),x97454),f328(f235(x97452),x97455)))+P1(f328(f328(f330(x97451),x97454),f328(f170(x97451),f328(f328(f173(x97451),f328(f193(f873(x97452)),x97457)),x97456)))) % 167.77/167.50 [10108]P1(f328(f328(f330(x101081),f790(x101082,x101083,x101084,x101085,x101086,x101087,x101081)),x101085))+P1(f328(f328(f328(f328(f43(x101081,f879(x101087,f879(x101086,a867))),x101085),x101084),x101083),x101082)) % 167.77/167.50 [10109]P1(f328(f328(f330(x101091),f800(x101092,x101093,x101094,x101095,x101096,x101097,x101091)),x101095))+~P1(f328(f328(f328(f328(f44(x101091,f879(x101097,f879(x101096,a867))),x101095),x101094),x101093),x101092)) % 167.77/167.50 [10134]P1(f328(f328(f328(x101341,f800(x101342,x101343,x101341,x101344,x101345,x101346,x101347)),x101343),x101342))+~P1(f328(f328(f328(f328(f44(x101347,f879(x101346,f879(x101345,a867))),x101344),x101341),x101343),x101342)) % 167.77/167.50 [10151]~P1(f328(f328(f328(x101515,f790(x101517,x101516,x101515,x101514,x101513,x101512,x101511)),x101516),x101517))+P1(f328(f328(f328(f328(f43(x101511,f879(x101512,f879(x101513,a867))),x101514),x101515),x101516),x101517)) % 167.77/167.50 [10168]~P1(f328(f328(f330(f878(x101681,x101683)),f328(f328(f263(x101681,x101683),x101686),x101687)),f328(f328(f285(x101681,x101682,x101683),x101684),x101685)))+P1(f328(f328(f264(x101681,x101682,x101683,f328(f328(f7(x101681,f879(f878(x101681,x101682),a867),f879(x101682,a867)),f328(f328(f8(f879(x101682,f879(f879(f878(x101681,x101682),a867),a867)),f879(f879(f878(x101681,x101682),a867),f879(x101682,a867)),x101681),f7(x101682,f879(f878(x101681,x101682),a867),a867)),f328(f328(f8(f879(x101682,f878(x101681,x101682)),f879(x101682,f879(f879(f878(x101681,x101682),a867),a867)),x101681),f328(f8(f878(x101681,x101682),f879(f879(f878(x101681,x101682),a867),a867),x101682),f330(f878(x101681,x101682)))),f263(x101681,x101682)))),x101684),f328(f328(f7(x101682,f879(f878(x101682,x101683),a867),f879(x101683,a867)),f328(f328(f8(f879(x101683,f879(f879(f878(x101682,x101683),a867),a867)),f879(f879(f878(x101682,x101683),a867),f879(x101683,a867)),x101682),f7(x101683,f879(f878(x101682,x101683),a867),a867)),f328(f328(f8(f879(x101683,f878(x101682,x101683)),f879(x101683,f879(f879(f878(x101682,x101683),a867),a867)),x101682),f328(f8(f878(x101682,x101683),f879(f879(f878(x101682,x101683),a867),a867),x101683),f330(f878(x101682,x101683)))),f263(x101682,x101683)))),x101685)),x101686),x101687)) % 167.77/167.50 [10178]P1(f328(f328(f330(f878(x101781,x101782)),f328(f328(f263(x101781,x101782),x101783),x101784)),f328(f328(f285(x101781,x101785,x101782),x101786),x101787)))+~P1(f328(f328(f264(x101781,x101785,x101782,f328(f328(f7(x101781,f879(f878(x101781,x101785),a867),f879(x101785,a867)),f328(f328(f8(f879(x101785,f879(f879(f878(x101781,x101785),a867),a867)),f879(f879(f878(x101781,x101785),a867),f879(x101785,a867)),x101781),f7(x101785,f879(f878(x101781,x101785),a867),a867)),f328(f328(f8(f879(x101785,f878(x101781,x101785)),f879(x101785,f879(f879(f878(x101781,x101785),a867),a867)),x101781),f328(f8(f878(x101781,x101785),f879(f879(f878(x101781,x101785),a867),a867),x101785),f330(f878(x101781,x101785)))),f263(x101781,x101785)))),x101786),f328(f328(f7(x101785,f879(f878(x101785,x101782),a867),f879(x101782,a867)),f328(f328(f8(f879(x101782,f879(f879(f878(x101785,x101782),a867),a867)),f879(f879(f878(x101785,x101782),a867),f879(x101782,a867)),x101785),f7(x101782,f879(f878(x101785,x101782),a867),a867)),f328(f328(f8(f879(x101782,f878(x101785,x101782)),f879(x101782,f879(f879(f878(x101785,x101782),a867),a867)),x101785),f328(f8(f878(x101785,x101782),f879(f879(f878(x101785,x101782),a867),a867),x101782),f330(f878(x101785,x101782)))),f263(x101785,x101782)))),x101787)),x101783),x101784)) % 167.77/167.50 [10118]~P135(x101182)+E(f328(f328(f6(x101181,x101182),f328(f328(f7(x101181,f879(x101183,a867),x101182),f328(f328(f8(f879(x101183,x101182),f879(f879(x101183,a867),x101182),x101181),f6(x101183,x101182)),f328(f328(f7(x101181,f879(x101183,x101182),f879(x101183,x101182)),f328(f328(f8(f879(x101182,x101182),f879(f879(x101183,x101182),f879(x101183,x101182)),x101181),f8(x101182,x101182,x101183)),f328(f328(f8(x101182,f879(x101182,x101182),x101181),f81(x101182)),x101184))),x101185))),x101186)),x101187),f328(f328(f81(x101182),f328(f328(f6(x101181,x101182),x101184),x101187)),f328(f328(f6(x101183,x101182),x101185),x101186))) % 167.77/167.50 [9225]~P20(x92257,x92251,x92253,x92258)+E(f328(f73(x92251,x92251,x92252,f328(x92253,x92254)),f328(f73(x92251,x92251,x92252,f328(x92253,x92255)),x92256)),f328(f73(x92251,x92251,x92252,f328(x92253,x92255)),f328(f73(x92251,x92251,x92252,f328(x92253,x92254)),x92256))) % 167.77/167.50 [10173]E(f328(f328(f263(x101731,x101732),f328(x101733,f575(x101734,x101735,x101733,x101736,x101737,x101738,x101732,x101731))),f328(x101735,f576(x101734,x101735,x101733,x101736,x101737,x101738,x101732,x101731))),x101738)+~P1(f328(f328(f330(f878(x101731,x101732)),x101738),f328(f307(f878(x101737,x101736),f878(x101731,x101732),f268(x101737,x101731,x101736,x101732,x101733,x101735)),x101734))) % 167.77/167.50 [10189]~P1(f328(f328(f330(f878(x101898,x101897)),x101896),f328(f307(f878(x101891,x101892),f878(x101898,x101897),f268(x101891,x101898,x101892,x101897,x101895,x101894)),x101893)))+P1(f328(f328(f330(f878(x101891,x101892)),f328(f328(f263(x101891,x101892),f575(x101893,x101894,x101895,x101892,x101891,x101896,x101897,x101898)),f576(x101893,x101894,x101895,x101892,x101891,x101896,x101897,x101898))),x101893)) % 167.77/167.50 [9662]P1(f328(f328(f330(f878(f878(x96621,x96622),f878(x96621,x96622))),f328(f328(f263(f878(x96621,x96622),f878(x96621,x96622)),f328(f328(f263(x96621,x96622),x96623),x96624)),f328(f328(f263(x96621,x96622),x96625),x96626))),f321(x96621,x96622,x96627,x96628)))+~P1(f328(f328(f330(f878(x96621,x96621)),f328(f328(f263(x96621,x96621),x96623),x96625)),x96627)) % 167.77/167.50 [10161]E(f328(f139(x101611,x101612,f328(f7(x101612,x101611,x101611),x101613),f328(x101614,x101615)),x101616),f328(x101614,f328(f139(x101617,x101612,f328(f7(x101612,x101617,x101617),x101618),x101615),x101616)))+P1(f328(f328(f330(x101612),f770(x101615,x101618,x101614,x101613,x101617,x101611,x101616,x101612)),f328(f170(x101612),x101616))) % 167.77/167.50 [10181]~E(f328(f73(x101811,x101811,x101817,f328(x101813,f770(x101815,x101818,x101814,x101813,x101817,x101811,x101816,x101812))),x101814),f328(f73(x101817,x101811,x101817,x101814),f328(x101818,f770(x101815,x101818,x101814,x101813,x101817,x101811,x101816,x101812))))+E(f328(f139(x101811,x101812,f328(f7(x101812,x101811,x101811),x101813),f328(x101814,x101815)),x101816),f328(x101814,f328(f139(x101817,x101812,f328(f7(x101812,x101817,x101817),x101818),x101815),x101816))) % 167.77/167.50 [8450]E(f328(x84501,f328(x84502,x84503)),f328(x84504,f328(x84505,x84503)))+~E(f328(f73(x84506,x84507,x84508,x84501),x84502),f328(f73(x84509,x84507,x84508,x84504),x84505)) % 167.77/167.50 [10047]P1(f328(f328(f330(f878(x100471,x100472)),f328(f328(f263(x100471,x100472),f328(x100473,x100474)),f328(x100475,x100476))),f328(f307(f878(x100477,x100478),f878(x100471,x100472),f268(x100477,x100471,x100478,x100472,x100473,x100475)),x100479)))+~P1(f328(f328(f330(f878(x100477,x100478)),f328(f328(f263(x100477,x100478),x100474),x100476)),x100479)) % 167.77/167.50 [8732]~E(f328(x87324,f328(x87325,x87326)),f328(x87329,f328(x873210,x873211)))+E(f328(f328(f73(x87321,x87322,x87323,x87324),x87325),x87326),f328(f328(f73(x87327,x87322,x87328,x87329),x873210),x873211)) % 167.77/167.50 [4568]~P100(x45681)+~P105(x45681)+E(f105(x45681),f240(x45681)) % 167.77/167.50 [4569]~P99(x45691)+~P105(x45691)+E(f114(x45691),f241(x45691)) % 167.77/167.50 [4811]~P117(x48111)+~P91(x48111)+E(f328(f75(x48111),f328(f107(x48111),a101)),f78(x48111)) % 167.77/167.50 [5089]E(x50891,f2(a1))+E(f82(a1,x50891),f328(f79(a1),f78(a1)))+P1(f328(f328(f243(a1),f2(a1)),x50891)) % 167.77/167.50 [5304]E(x53041,f2(a1))+E(f82(a1,x53041),f78(a1))+~P1(f328(f328(f243(a1),f2(a1)),x53041)) % 167.77/167.50 [7289]~P39(x72891)+P1(f328(f38(a1),x72891))+~P1(f328(f38(a872),f328(f307(a1,a872,a108),x72891))) % 167.77/167.50 [8558]~P8(a5000)+~P1(f328(f328(f330(f878(a870,a869)),x85581),f328(f170(f878(a870,a869)),a27)))+P1(f328(f328(f267(a870,a869,a867),f328(f16(f879(a869,a867),a870),a25)),x85581)) % 167.77/167.50 [9622]E(x96221,f192(f879(f878(a872,a872),a867)))+~P1(f328(f38(f878(a872,a872)),x96221))+P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),f192(f879(f878(a872,a872),a867))),x96221)),a37)) % 167.77/167.50 [9794]E(x97941,f2(a872))+E(x97941,f328(a116,f2(a872)))+~P1(f328(f328(f243(a872),x97941),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.77/167.50 [10075]E(x100751,f2(a103))+E(f328(f328(f80(a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(a20,f328(f328(f40(a103),x100751),f328(f107(a103),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))),f78(a1)),f328(a20,x100751))+E(f46(a103,x100751,f328(f107(a103),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f2(a103)) % 167.77/167.50 [9926]E(x99261,f2(a103))+~E(f46(a103,x99261,f328(f107(a103),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f2(a103))+E(f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(a20,f328(f328(f40(a103),x99261),f328(f107(a103),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f328(a20,x99261)) % 167.77/167.50 [4641]~P54(x46411,x46412)+P44(x46411,x46412)+~P45(a867) % 167.77/167.50 [4578]~P142(x45781)+P31(x45781,x45782)+~E(x45782,f2(x45781)) % 167.77/167.50 [4579]~P105(x45791)+P15(x45791,x45792)+~E(x45792,f117(x45791)) % 167.77/167.50 [4588]~P117(x45881)+~E(x45882,f2(x45881))+E(f82(x45881,x45882),f2(x45881)) % 167.77/167.50 [4589]~P88(x45891)+~E(x45892,f2(x45891))+E(f82(x45891,x45892),f2(x45891)) % 167.77/167.50 [4597]~P142(x45972)+~P31(x45972,x45971)+E(x45971,f2(x45972)) % 167.77/167.50 [4631]~P117(x46312)+~E(f82(x46312,x46311),f2(x46312))+E(x46311,f2(x46312)) % 167.77/167.50 [4648]~P3(x46482)+~P3(x46481)+P3(f879(x46481,x46482)) % 167.77/167.50 [4649]~P3(x46492)+~P3(x46491)+P3(f877(x46491,x46492)) % 167.77/167.50 [4650]~P3(x46502)+~P3(x46501)+P3(f878(x46501,x46502)) % 167.77/167.50 [4651]~P5(x46512)+~P5(x46511)+P5(f199(x46511,x46512)) % 167.77/167.50 [4652]~P143(x46522)+~P143(x46521)+P143(f878(x46521,x46522)) % 167.77/167.50 [4653]~P59(x46532)+~P59(x46531)+P59(f879(x46531,x46532)) % 167.77/167.50 [4654]~P59(x46542)+~P59(x46541)+P59(f877(x46541,x46542)) % 167.77/167.50 [4655]~P59(x46552)+~P59(x46551)+P59(f878(x46551,x46552)) % 167.77/167.50 [4656]~P59(x46561)+~P93(x46562)+P93(f879(x46561,x46562)) % 167.77/167.50 [4782]~P105(x47821)+~P15(x47821,x47822)+P15(x47821,f149(x47821,x47822)) % 167.77/167.50 [5020]~P5(x50202)+~P5(x50201)+P5(f46(a1,x50201,x50202)) % 167.77/167.50 [4599]~P75(x45991)+~E(x45992,f2(x45991))+E(f328(f79(x45991),x45992),x45992) % 167.77/167.50 [4603]~P138(x46031)+~E(x46032,f2(a1))+E(f328(f106(x46031),x46032),f2(x46031)) % 167.77/167.50 [4604]~P90(x46041)+~E(x46042,f2(a1))+E(f328(f106(x46041),x46042),f2(x46041)) % 167.77/167.50 [4628]~P74(x46281)+~E(f2(x46281),x46282)+E(f328(f79(x46281),x46282),f2(x46281)) % 167.77/167.50 [4629]~P84(x46291)+~E(x46292,f2(x46291))+E(f328(f75(x46291),x46292),f2(x46291)) % 167.77/167.50 [4630]~P74(x46301)+~E(x46302,f2(x46301))+E(f328(f79(x46301),x46302),f2(x46301)) % 167.77/167.50 [4658]~P75(x46582)+E(x46581,f2(x46582))+~E(f328(f79(x46582),x46581),x46581) % 167.77/167.50 [4664]E(x46641,f328(a108,x46642))+~E(x46641,f2(a872))+~E(x46642,f328(f104(a1),x46641)) % 167.77/167.50 [4665]E(f328(a108,x46651),x46652)+~E(x46652,f2(a872))+~E(x46651,f328(f104(a1),x46652)) % 167.77/167.50 [4669]~P90(x46692)+E(x46691,f2(a1))+~E(f328(f106(x46692),x46691),f2(x46692)) % 167.77/167.50 [4674]~P84(x46742)+E(x46741,f2(x46742))+~E(f328(f75(x46742),x46741),f2(x46742)) % 167.77/167.50 [4675]~P74(x46752)+E(x46751,f2(x46752))+~E(f328(f79(x46752),x46751),f2(x46752)) % 167.77/167.50 [4676]~P74(x46761)+E(f2(x46761),x46762)+~E(f328(f79(x46761),x46762),f2(x46761)) % 167.77/167.50 [4816]~P8(a5000)+~E(f328(a28,x48162),f328(f235(a869),x48161))+P1(f328(a25,x48161)) % 167.77/167.50 [4858]~P105(x48581)+~P15(x48581,x48582)+P15(x48581,f328(f169(x48581),x48582)) % 167.77/167.50 [4884]~P1(x48842)+~P1(x48841)+P1(f328(f328(a326,x48841),x48842)) % 167.77/167.50 [4916]~E(f78(a872),f2(a872))+E(f328(f39(x49161),x49162),f2(a872))+~P1(f328(f38(x49161),x49162)) % 167.77/167.50 [4949]~P135(x49491)+~P113(x49491)+E(f328(f328(f253(x49491),f2(x49491)),f328(a116,x49492)),f2(x49491)) % 167.77/167.50 [4987]~P105(x49871)+P15(x49871,f136(x49871,x49872))+~P1(f328(f38(x49871),x49872)) % 167.77/167.50 [4988]~P105(x49881)+P15(x49881,f758(x49882,x49881))+~P1(f328(f38(x49881),x49882)) % 167.77/167.50 [5010]~P105(x50101)+E(f328(f170(x50101),f136(x50101,x50102)),x50102)+~P1(f328(f38(x50101),x50102)) % 167.77/167.50 [5011]~P105(x50111)+E(f328(f170(x50111),f758(x50112,x50111)),x50112)+~P1(f328(f38(x50111),x50112)) % 167.77/167.50 [5041]P1(x50411)+P1(x50412)+~P1(f328(f328(a327,x50412),x50411)) % 167.77/167.50 [5053]E(x50531,f192(f879(x50532,a867)))+~E(f328(f39(x50532),x50531),f2(a872))+~P1(f328(f38(x50532),x50531)) % 167.77/167.50 [5058]P1(x50581)+~P1(x50582)+~P1(f328(f328(a331,x50582),x50581)) % 167.77/167.50 [5107]~P72(x51071)+E(f328(f75(x51071),x51072),x51072)+P1(f328(f328(f243(x51071),x51072),f2(x51071))) % 167.77/167.50 [5177]~P59(x51772)+~P1(f328(f59(x51772),x51771))+P1(f328(x51771,f716(x51771,x51772))) % 167.77/167.50 [5178]~P59(x51782)+~P1(f328(f59(x51782),x51781))+P1(f328(x51781,f726(x51781,x51782))) % 167.77/167.50 [5205]~P1(f328(a25,x52052))+~P1(f328(a25,x52051))+P1(f328(a25,f33(x52051,x52052))) % 167.77/167.50 [5214]E(x52141,f117(x52142))+P1(f328(f134(x52142),f118(x52142,x52141)))+~P1(f328(f134(x52142),x52141)) % 167.77/167.50 [5219]~P105(x52191)+~P1(f328(f38(x52191),x52192))+P1(f328(f134(x52191),f136(x52191,x52192))) % 167.77/167.50 [5220]~P105(x52201)+~P1(f328(f38(x52201),x52202))+P1(f328(f134(x52201),f758(x52202,x52201))) % 167.77/167.50 [5226]~P138(x52261)+E(f328(f104(x52261),f328(a108,x52262)),f328(f106(x52261),x52262))+P1(f328(f328(f243(a1),x52262),f2(a1))) % 167.77/167.50 [5254]P6(x52542,x52541)+E(f328(x52541,f524(x52541)),f328(x52541,f527(x52541)))+P1(f328(f328(x52541,f524(x52541)),f527(x52541))) % 167.77/167.50 [5269]E(f328(f104(a1),f380(x52691,x52692)),x52691)+P1(f328(x52692,f328(a108,x52691)))+~P1(f328(x52692,f2(a872))) % 167.77/167.50 [5281]~P59(x52811)+~P1(f328(x52812,f717(x52812,x52811)))+P1(f328(f60(x52811),x52812)) % 167.77/167.50 [5282]~P59(x52821)+~P1(f328(x52822,f727(x52822,x52821)))+P1(f328(f60(x52821),x52822)) % 167.77/167.50 [5297]~P59(x52972)+~P36(x52972,x52971,f57(x52972))+P1(f328(x52971,f774(x52971,x52972))) % 167.77/167.50 [5313]~P117(x53131)+~E(f82(x53131,x53132),f328(f79(x53131),f78(x53131)))+P1(f328(f328(f243(x53131),x53132),f2(x53131))) % 167.77/167.50 [5389]~E(x53892,f2(a1))+E(f222(x53891,x53892),f328(f328(f263(a1,a1),f2(a1)),f78(a1)))+P1(f328(f328(f243(a1),x53892),f2(a1))) % 167.77/167.50 [5390]~E(x53901,f2(a1))+E(f222(x53901,x53902),f328(f328(f263(a1,a1),f2(a1)),f78(a1)))+P1(f328(f328(f243(a1),x53902),f2(a1))) % 167.77/167.50 [5442]E(f328(f104(a1),f380(x54421,x54422)),x54421)+P1(f328(x54422,f328(a108,x54421)))+P1(f328(f328(f243(a1),x54421),f2(a1))) % 167.77/167.50 [5505]~P117(x55051)+E(f82(x55051,x55052),f328(f79(x55051),f78(x55051)))+~P1(f328(f328(f243(x55051),x55052),f2(x55051))) % 167.77/167.50 [5506]~P84(x55061)+E(f328(f75(x55061),x55062),f328(f79(x55061),x55062))+~P1(f328(f328(f243(x55061),x55062),f2(x55061))) % 167.77/167.50 [5507]~P84(x55071)+E(f328(f75(x55071),x55072),f328(f79(x55071),x55072))+~P1(f328(f328(f242(x55071),x55072),f2(x55071))) % 167.77/167.50 [5508]~P72(x55081)+E(f328(f75(x55081),x55082),f328(f79(x55081),x55082))+~P1(f328(f328(f243(x55081),x55082),f2(x55081))) % 167.77/167.50 [5604]~P1(f328(x56041,f380(x56042,x56041)))+P1(f328(x56041,f328(a108,x56042)))+~P1(f328(x56041,f2(a872))) % 167.77/167.50 [5611]E(x56111,f2(a872))+E(f328(a116,f848(x56112,x56111)),x56111)+~P1(f328(f328(f243(a872),x56111),f328(a116,x56112))) % 167.77/167.50 [5615]P6(x56151,x56152)+~E(f328(x56152,f524(x56152)),f328(x56152,f527(x56152)))+~P1(f328(f328(x56152,f524(x56152)),f527(x56152))) % 167.77/167.50 [5635]~P105(x56351)+P15(x56351,x56352)+P1(f328(f328(f242(a872),f741(x56352,x56351)),f742(x56352,x56351))) % 167.77/167.50 [5636]~P105(x56361)+P15(x56361,x56362)+P1(f328(f328(f242(a872),f749(x56362,x56361)),f754(x56362,x56361))) % 167.77/167.50 [5724]~P84(x57241)+~E(x57242,f2(x57241))+P1(f328(f328(f242(x57241),f328(f75(x57241),x57242)),f2(x57241))) % 167.77/167.50 [5803]~P59(x58032)+~P59(x58031)+E(f61(x58031,x58032,f57(x58031),f57(x58032)),f57(f878(x58031,x58032))) % 167.77/167.50 [5807]~P1(f328(x58071,f380(x58072,x58071)))+P1(f328(x58071,f328(a108,x58072)))+P1(f328(f328(f243(a1),x58072),f2(a1))) % 167.77/167.50 [5830]~P1(f328(x58301,f328(a108,x58302)))+P1(f328(x58301,f2(a872)))+~P1(f328(f328(f243(a1),x58302),f2(a1))) % 167.77/167.50 [6171]~P117(x61711)+~P1(f328(f328(f243(x61711),x61712),f2(x61711)))+P1(f328(f328(f243(x61711),f82(x61711,x61712)),f2(x61711))) % 167.77/167.50 [6285]~P117(x62851)+P1(f328(f328(f243(x62851),f328(f106(x62851),x62852)),f2(x62851)))+~P1(f328(f328(f243(a1),x62852),f2(a1))) % 167.77/167.50 [6286]~P117(x62861)+P1(f328(f328(f242(x62861),f328(f106(x62861),x62862)),f2(x62861)))+~P1(f328(f328(f242(a1),x62862),f2(a1))) % 167.77/167.50 [6293]~P84(x62932)+E(x62931,f2(x62932))+~P1(f328(f328(f242(x62932),f328(f75(x62932),x62931)),f2(x62932))) % 167.77/167.50 [6368]~P138(x63681)+~P1(f328(f328(f330(x63681),x63682),f113(x63681)))+P1(f328(f328(f330(x63681),f328(f79(x63681),x63682)),f113(x63681))) % 167.77/167.50 [6400]~P117(x64001)+~P1(f328(f328(f243(x64001),f82(x64001,x64002)),f2(x64001)))+P1(f328(f328(f243(x64001),x64002),f2(x64001))) % 167.77/167.50 [6569]~P117(x65692)+~P1(f328(f328(f243(x65692),f328(f106(x65692),x65691)),f2(x65692)))+P1(f328(f328(f243(a1),x65691),f2(a1))) % 167.77/167.50 [6570]~P117(x65702)+~P1(f328(f328(f242(x65702),f328(f106(x65702),x65701)),f2(x65702)))+P1(f328(f328(f242(a1),x65701),f2(a1))) % 167.77/167.50 [7074]~P117(x70741)+~P1(f328(f328(f243(x70741),x70742),f2(x70741)))+P1(f328(f328(f243(x70741),f328(f328(f80(x70741),x70742),x70742)),f2(x70741))) % 167.77/167.50 [7075]~P75(x70751)+~P1(f328(f328(f243(x70751),x70752),f2(x70751)))+P1(f328(f328(f243(x70751),f328(f328(f80(x70751),x70752),x70752)),f2(x70751))) % 167.77/167.50 [7076]~P75(x70761)+~P1(f328(f328(f242(x70761),x70762),f2(x70761)))+P1(f328(f328(f242(x70761),f328(f328(f80(x70761),x70762),x70762)),f2(x70761))) % 167.77/167.50 [7647]~P117(x76471)+~P1(f328(f328(f243(x76471),f328(f328(f80(x76471),x76472),x76472)),f2(x76471)))+P1(f328(f328(f243(x76471),x76472),f2(x76471))) % 167.77/167.50 [7648]~P75(x76481)+~P1(f328(f328(f243(x76481),f328(f328(f80(x76481),x76482),x76482)),f2(x76481)))+P1(f328(f328(f243(x76481),x76482),f2(x76481))) % 167.77/167.50 [7649]~P75(x76491)+~P1(f328(f328(f242(x76491),f328(f328(f80(x76491),x76492),x76492)),f2(x76491)))+P1(f328(f328(f242(x76491),x76492),f2(x76491))) % 167.77/167.50 [4714]~E(x47142,f2(a872))+~E(x47141,f2(a872))+E(f328(f328(f80(a872),x47141),x47142),f2(a872)) % 167.77/167.50 [4715]~E(x47152,f78(a872))+~E(x47151,f78(a872))+E(f328(f328(f81(a872),x47151),x47152),f78(a872)) % 167.77/167.50 [4716]~E(x47162,f78(a1))+~E(x47161,f78(a1))+E(f328(f328(f81(a1),x47161),x47162),f78(a1)) % 167.77/167.50 [4768]~P57(x47682)+E(x47681,f2(x47682))+E(f328(f328(f40(x47682),x47681),x47681),f78(x47682)) % 167.77/167.50 [4769]~P120(x47692)+E(x47691,f2(x47692))+E(f328(f328(f286(x47692),x47691),x47691),f78(x47692)) % 167.77/167.50 [4770]~P121(x47702)+E(x47701,f2(x47702))+E(f328(f328(f286(x47702),x47701),x47701),f78(x47702)) % 167.77/167.50 [4787]~P75(x47871)+~E(x47872,f2(x47871))+E(f328(f328(f80(x47871),x47872),x47872),f2(x47871)) % 167.77/167.50 [4790]~P139(x47901)+~E(x47902,f78(x47901))+E(f328(f328(f81(x47901),x47902),x47902),f78(x47901)) % 167.77/167.50 [4791]~P121(x47911)+~E(x47912,f2(x47911))+E(f328(f328(f286(x47911),x47912),x47912),f2(x47911)) % 167.77/167.50 [4837]~E(x48372,f2(a872))+~E(x48371,f2(a872))+E(f328(f79(a1),f328(f104(a1),x48371)),f328(f104(a1),x48372)) % 167.77/167.50 [4855]E(x48551,f78(a872))+E(x48552,f2(a872))+~E(f328(f328(f81(a872),x48552),x48551),x48552) % 167.77/167.50 [4865]E(x48651,f2(a872))+E(x48652,f2(a872))+~E(f328(f328(f81(a872),x48652),x48651),f2(a872)) % 167.77/167.50 [4893]~E(x48932,f2(a872))+~E(x48931,f328(a116,f2(a872)))+E(f328(f328(f80(a872),x48931),x48932),f328(a116,f2(a872))) % 167.77/167.50 [4894]~E(x48941,f2(a872))+~E(x48942,f328(a116,f2(a872)))+E(f328(f328(f80(a872),x48941),x48942),f328(a116,f2(a872))) % 167.77/167.50 [4899]E(x48991,f78(a1))+E(x48992,f328(f107(a1),a101))+~E(f328(f328(f81(a1),x48991),x48992),f78(a1)) % 167.77/167.50 [4900]E(x49001,f78(a1))+E(x49002,f328(f107(a1),a101))+~E(f328(f328(f81(a1),x49002),x49001),f78(a1)) % 167.77/167.50 [4901]E(x49011,f78(a1))+E(x49011,f328(f107(a1),a101))+~E(f328(f328(f81(a1),x49012),x49011),f78(a1)) % 167.77/167.50 [4903]E(x49031,f78(a1))+E(x49031,f328(f107(a1),a101))+~E(f328(f328(f81(a1),x49031),x49032),f78(a1)) % 167.77/167.50 [4920]~P75(x49202)+E(x49201,f2(x49202))+~E(f328(f328(f80(x49202),x49201),x49201),f2(x49202)) % 167.77/167.50 [4926]~E(x49261,f328(f107(a1),a101))+~E(x49262,f328(f107(a1),a101))+E(f328(f328(f81(a1),x49261),x49262),f78(a1)) % 167.77/167.50 [4938]E(x49381,f2(a872))+E(x49382,f2(a872))+~E(f328(f328(f80(a872),x49382),x49381),f328(a116,f2(a872))) % 167.77/167.50 [4948]~P60(x49481)+~P91(x49481)+E(f328(f328(f286(x49481),x49482),f328(f107(x49481),a83)),f2(x49481)) % 167.77/167.50 [4954]~P139(x49541)+~E(x49542,f328(f79(x49541),f78(x49541)))+E(f328(f328(f81(x49541),x49542),x49542),f78(x49541)) % 167.77/167.50 [4959]~P5(x49592)+~P5(x49591)+P5(f328(f328(f80(a1),x49591),x49592)) % 167.77/167.50 [4960]~P5(x49602)+~P5(x49601)+P5(f328(f328(f81(a1),x49601),x49602)) % 167.77/167.50 [4961]~P5(x49612)+~P5(x49611)+P5(f328(f328(f40(a1),x49611),x49612)) % 167.77/167.50 [4963]~E(x49632,f2(a1))+E(x49631,f2(a1))+E(f47(x49631,x49632),f328(f328(f263(a1,a1),f2(a1)),x49631)) % 167.77/167.50 [4985]~E(x49852,f328(a116,f2(a872)))+~E(x49851,f328(a116,f2(a872)))+E(f328(f328(f81(a872),x49851),x49852),f328(a116,f2(a872))) % 167.77/167.50 [5000]E(x50001,f2(a872))+E(x50002,f328(a116,f2(a872)))+~E(f328(f328(f253(a872),x50002),x50001),f328(a116,f2(a872))) % 167.77/167.50 [5001]E(x50011,f2(a872))+E(x50011,f328(a116,f2(a872)))+~E(f328(f328(f80(a872),x50012),x50011),f328(a116,f2(a872))) % 167.77/167.50 [5002]E(x50021,f2(a872))+E(x50021,f328(a116,f2(a872)))+~E(f328(f328(f80(a872),x50021),x50022),f328(a116,f2(a872))) % 167.77/167.50 [5012]~P60(x50121)+~P91(x50121)+E(f328(f328(f286(x50121),x50122),f328(f107(x50121),a101)),f328(f79(x50121),x50122)) % 167.77/167.50 [5033]E(x50331,f328(a108,x50332))+~E(x50331,f2(a872))+P1(f328(f328(f242(a1),f2(a1)),x50332)) % 167.77/167.50 [5034]E(f328(a108,x50341),x50342)+~E(x50342,f2(a872))+P1(f328(f328(f242(a1),f2(a1)),x50341)) % 167.77/167.50 [5049]E(x50491,f328(a116,f2(a872)))+E(x50492,f328(a116,f2(a872)))+~E(f328(f328(f80(a872),x50491),x50492),f328(a116,f2(a872))) % 167.77/167.50 [5060]~E(x50601,f328(a108,x50602))+E(x50601,f2(a872))+P1(f328(f328(f242(a1),f2(a1)),x50602)) % 167.77/167.50 [5061]~E(f328(a108,x50612),x50611)+E(x50611,f2(a872))+P1(f328(f328(f242(a1),f2(a1)),x50612)) % 167.77/167.50 [5083]~P2(x50831)+E(f328(f64(x50831,f114(x50831)),x50832),f13(x50831,x50832))+~P1(f328(f38(x50831),x50832)) % 167.77/167.50 [5084]~P2(x50841)+E(f328(f64(x50841,f105(x50841)),x50842),f10(x50841,x50842))+~P1(f328(f38(x50841),x50842)) % 167.77/167.50 [5085]~P105(x50851)+E(f328(f64(x50851,f240(x50851)),x50852),f14(x50851,x50852))+~P1(f328(f38(x50851),x50852)) % 167.77/167.50 [5086]~P105(x50861)+E(f328(f64(x50861,f241(x50861)),x50862),f15(x50861,x50862))+~P1(f328(f38(x50861),x50862)) % 167.77/167.50 [5088]~P59(x50881)+~P1(f328(x50882,f205(x50881)))+P1(f328(f59(f876(x50881)),x50882)) % 167.77/167.50 [5170]~P59(x51702)+P1(f328(x51701,f205(x51702)))+~P1(f328(f60(f876(x51702)),x51701)) % 167.77/167.50 [5171]E(x51711,x51712)+~E(f328(f328(f22(a872),x51712),x51711),f2(a872))+~E(f328(f328(f22(a872),x51711),x51712),f2(a872)) % 167.77/167.50 [5185]P5(x51851)+~P39(x51852)+~P1(f328(f328(f330(a1),x51851),x51852)) % 167.77/167.50 [5215]~P117(x52151)+~E(f82(x52151,x52152),f78(x52151))+P1(f328(f328(f243(x52151),f2(x52151)),x52152)) % 167.77/167.50 [5227]~P91(x52271)+E(f328(f104(x52271),f328(f107(a872),x52272)),f328(f107(x52271),x52272))+P1(f328(a197,f328(f107(a1),x52272))) % 167.77/167.50 [5233]~P44(x52331,x52332)+P45(a867)+P1(f328(f38(f878(x52331,x52331)),x52332)) % 167.77/167.50 [5306]~P105(x53061)+E(f328(f64(x53061,f240(x53061)),x53062),f11(x53061,f240(x53061),x53062))+~P1(f328(f38(x53061),x53062)) % 167.77/167.50 [5307]~P105(x53071)+E(f328(f64(x53071,f241(x53071)),x53072),f12(x53071,f241(x53071),x53072))+~P1(f328(f38(x53071),x53072)) % 167.77/167.50 [5320]E(x53201,x53202)+P1(f328(f328(f243(a872),x53202),x53201))+P1(f328(f328(f243(a872),x53201),x53202)) % 167.77/167.50 [5321]E(x53211,x53212)+P1(f328(f328(f243(a1),x53212),x53211))+P1(f328(f328(f243(a1),x53211),x53212)) % 167.77/167.50 [5376]~P91(x53761)+E(f328(f104(x53761),f328(f107(a872),x53762)),f2(x53761))+~P1(f328(a197,f328(f107(a1),x53762))) % 167.77/167.50 [5379]~E(x53792,f328(a108,x53791))+E(x53791,f328(f104(a1),x53792))+~P1(f328(f328(f242(a1),f2(a1)),x53791)) % 167.77/167.50 [5380]~E(f328(a108,x53801),x53802)+E(x53801,f328(f104(a1),x53802))+~P1(f328(f328(f242(a1),f2(a1)),x53801)) % 167.77/167.50 [5381]~E(x53811,f328(a108,x53812))+E(f328(f104(a1),x53811),x53812)+~P1(f328(f328(f242(a1),f2(a1)),x53812)) % 167.77/167.50 [5391]E(x53911,f328(a108,x53912))+~E(x53912,f328(f104(a1),x53911))+~P1(f328(f328(f242(a1),f2(a1)),x53912)) % 167.77/167.50 [5392]E(f328(a108,x53921),x53922)+~E(x53921,f328(f104(a1),x53922))+~P1(f328(f328(f242(a1),f2(a1)),x53921)) % 167.77/167.50 [5431]~P84(x54312)+E(x54311,f2(x54312))+P1(f328(f328(f243(x54312),f2(x54312)),f328(f75(x54312),x54311))) % 167.77/167.50 [5498]~P117(x54981)+E(f82(x54981,x54982),f78(x54981))+~P1(f328(f328(f243(x54981),f2(x54981)),x54982)) % 167.77/167.50 [5502]~P91(x55021)+E(f328(f104(x55021),f328(f107(a872),x55022)),f2(x55021))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x55022))) % 167.77/167.50 [5509]~P84(x55091)+E(f328(f75(x55091),x55092),x55092)+~P1(f328(f328(f243(x55091),f2(x55091)),x55092)) % 167.77/167.50 [5510]~P84(x55101)+E(f328(f75(x55101),x55102),x55102)+~P1(f328(f328(f242(x55101),f2(x55101)),x55102)) % 167.77/167.50 [5517]E(x55171,f2(a872))+~E(f136(a872,f328(f298(a872,x55172),x55171)),f117(a872))+P1(f328(f328(f242(a872),x55171),x55172)) % 167.77/167.50 [5527]~P67(x55271)+E(f328(f328(f6(x55271,x55271),f5(x55271)),f328(f170(x55271),x55272)),f328(f163(x55271),x55272))+~P1(f328(f134(x55271),x55272)) % 167.77/167.50 [5530]~P138(x55301)+E(f328(f104(x55301),f328(a108,x55302)),f328(f106(x55301),x55302))+~P1(f328(f328(f242(a1),f2(a1)),x55302)) % 167.77/167.50 [5557]E(x55571,x55572)+P1(f328(f328(f243(a872),x55571),x55572))+~P1(f328(f328(f242(a872),x55571),x55572)) % 167.77/167.50 [5558]E(x55581,x55582)+P1(f328(f328(f243(a1),x55581),x55582))+~P1(f328(f328(f242(a1),x55581),x55582)) % 167.77/167.50 [5561]E(x55611,f78(a1))+~E(f328(f328(f81(a1),x55612),x55611),f78(a1))+~P1(f328(f328(f243(a1),f2(a1)),x55612)) % 167.77/167.50 [5562]E(x55621,f78(a1))+~E(f328(f328(f81(a1),x55621),x55622),f78(a1))+~P1(f328(f328(f243(a1),f2(a1)),x55621)) % 167.77/167.50 [5601]~P39(x56012)+P1(f328(f328(f242(a1),f2(a1)),x56011))+~P1(f328(f328(f330(a1),x56011),x56012)) % 167.77/167.50 [5620]~P54(x56201,x56202)+P38(x56201,x56202)+~P1(f328(f38(f878(x56201,x56201)),x56202)) % 167.77/167.50 [5622]~P54(x56221,x56222)+P44(x56221,x56222)+~P1(f328(f38(f878(x56221,x56221)),x56222)) % 167.77/167.50 [5666]E(x56661,f192(f879(x56662,a867)))+~P1(f328(f38(x56662),x56661))+P1(f328(f328(f243(a872),f2(a872)),f328(f39(x56662),x56661))) % 167.77/167.50 [5693]~P1(f328(x56931,x56932))+P1(f328(x56931,f2(a872)))+P1(f328(f328(f243(a872),f394(x56932,x56931)),x56932)) % 167.77/167.50 [5718]E(x57181,f2(a872))+~E(f328(f163(a872),x57182),f2(a872))+~P1(f328(f328(f330(a872),x57181),f328(f170(a872),x57182))) % 167.77/167.50 [5784]E(x57841,x57842)+~P1(f328(f328(f242(a872),x57842),x57841))+~P1(f328(f328(f242(a872),x57841),x57842)) % 167.77/167.50 [5785]E(x57851,x57852)+~P1(f328(f328(f242(a1),x57852),x57851))+~P1(f328(f328(f242(a1),x57851),x57852)) % 167.77/167.50 [5786]E(f328(f39(x57861),x57862),f2(a872))+~P1(f328(f38(x57861),x57862))+P1(f328(f328(f330(x57861),f464(x57862,x57861)),x57862)) % 167.77/167.50 [5795]E(f51(x57951,x57952),f47(x57951,x57952))+P1(f328(f328(f242(a1),f2(a1)),x57951))+~P1(f328(f328(f243(a1),f2(a1)),x57952)) % 167.77/167.50 [5819]~P1(f328(x58191,f378(x58191)))+P1(f328(x58191,f328(a108,x58192)))+~P1(f328(f328(f242(a1),f2(a1)),x58192)) % 167.77/167.50 [5821]P1(f328(f328(f243(a872),x58211),f346(x58212)))+~P1(f328(f38(a872),x58212))+~P1(f328(f328(f330(a872),x58211),x58212)) % 167.77/167.50 [5822]P1(f328(f328(f242(a872),x58221),f342(x58222)))+~P1(f328(f38(a872),x58222))+~P1(f328(f328(f330(a872),x58221),x58222)) % 167.77/167.50 [5851]E(x58511,x58512)+~P1(f328(f328(f243(a872),x58511),f328(a116,x58512)))+P1(f328(f328(f243(a872),x58511),x58512)) % 167.77/167.50 [5885]E(x58851,f328(a116,x58852))+~P1(f328(f328(f242(a872),x58851),f328(a116,x58852)))+P1(f328(f328(f242(a872),x58851),x58852)) % 167.77/167.50 [5898]P1(f328(x58981,f379(x58981)))+~P1(f328(x58981,f328(a108,x58982)))+~P1(f328(f328(f242(a1),f2(a1)),x58982)) % 167.77/167.50 [5912]~P1(f328(x59121,x59122))+~P1(f328(f328(f242(a1),f2(a1)),x59122))+P1(f328(x59121,f328(f104(a1),f366(x59121)))) % 167.77/167.50 [5926]~P84(x59262)+~E(x59261,f2(x59262))+~P1(f328(f328(f243(x59262),f2(x59262)),f328(f75(x59262),x59261))) % 167.77/167.50 [5951]~P54(x59511,x59512)+P38(x59511,f328(f283(x59511,x59511),x59512))+~P1(f328(f38(f878(x59511,x59511)),x59512)) % 167.77/167.50 [5959]~P91(x59591)+E(f328(f104(x59591),f328(f107(a872),x59592)),f328(f107(x59591),x59592))+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x59592))) % 167.77/167.50 [5962]E(f328(a116,x59621),x59622)+~P1(f328(f328(f243(a872),x59621),x59622))+P1(f328(f328(f243(a872),f328(a116,x59621)),x59622)) % 167.77/167.50 [5975]E(f328(f328(f40(a1),x59751),x59752),f2(a1))+~P1(f328(f328(f242(a1),x59751),f2(a1)))+~P1(f328(f328(f243(a1),x59752),x59751)) % 167.77/167.50 [5986]E(f46(a1,x59861,x59862),x59861)+~P1(f328(f328(f242(a1),x59861),f2(a1)))+~P1(f328(f328(f243(a1),x59862),x59861)) % 167.77/167.50 [5999]E(f48(x59991,x59992),f47(x59991,x59992))+~P1(f328(f328(f242(a1),f2(a1)),x59991))+~P1(f328(f328(f242(a1),f2(a1)),x59992)) % 167.77/167.50 [6007]E(f328(f328(f40(a1),x60071),x60072),f2(a1))+~P1(f328(f328(f242(a1),f2(a1)),x60071))+~P1(f328(f328(f243(a1),x60071),x60072)) % 167.77/167.50 [6019]E(f46(a872,f328(f107(a872),x60191),f328(f107(a872),x60192)),f328(f107(a872),x60191))+P1(f328(a197,f328(f107(a1),x60191)))+~P1(f328(a197,f328(f107(a1),x60192))) % 167.77/167.50 [6021]E(f46(a1,x60211,x60212),x60211)+~P1(f328(f328(f242(a1),f2(a1)),x60211))+~P1(f328(f328(f243(a1),x60211),x60212)) % 167.77/167.50 [6022]E(x60221,x60222)+~P1(f328(f328(f243(a872),x60221),f328(a116,x60222)))+~P1(f328(f328(f242(a872),x60222),x60221)) % 167.77/167.50 [6039]~P117(x60391)+~P1(f328(f328(f243(x60391),x60392),f2(x60391)))+P1(f328(f328(f243(x60391),x60392),f328(f79(x60391),x60392))) % 167.77/167.50 [6040]~P75(x60401)+~P1(f328(f328(f242(x60401),x60402),f2(x60401)))+P1(f328(f328(f242(x60401),x60402),f328(f79(x60401),x60402))) % 167.77/167.50 [6050]~P4(x60501)+E(f328(f328(f65(x60501,x60501,f105(x60501)),f251(x60501)),x60502),f42(x60501,x60502))+~P1(f328(f38(x60501),x60502)) % 167.77/167.50 [6051]~P4(x60511)+E(f328(f328(f65(x60511,x60511,f114(x60511)),f192(x60511)),x60512),f41(x60511,x60512))+~P1(f328(f38(x60511),x60512)) % 167.77/167.50 [6065]~P116(x60651)+~P1(f328(f328(f243(a872),f2(a872)),x60652))+P1(f328(f328(f243(x60651),f2(x60651)),f328(f104(x60651),x60652))) % 167.77/167.50 [6066]~P117(x60661)+~P1(f328(f328(f243(a1),f2(a1)),x60662))+P1(f328(f328(f243(x60661),f2(x60661)),f328(f106(x60661),x60662))) % 167.77/167.50 [6067]~P117(x60671)+~P1(f328(f328(f242(a1),f2(a1)),x60672))+P1(f328(f328(f242(x60671),f2(x60671)),f328(f106(x60671),x60672))) % 167.77/167.50 [6070]~P5(x60702)+~P5(x60701)+E(f328(f307(a872,a1,f104(a1)),f299(a872,f328(a108,x60701),f328(a108,x60702))),f299(a1,x60701,x60702)) % 167.77/167.50 [6076]P1(f328(x60761,x60762))+~P1(f328(f328(f242(a1),f2(a1)),x60762))+~P1(f328(x60761,f328(f104(a1),f369(x60761)))) % 167.77/167.50 [6101]E(f328(f328(f80(a872),f328(f107(a872),x61011)),f328(f107(a872),x61012)),f328(f107(a872),x61011))+P1(f328(f328(f243(a1),x61011),a83))+~P1(f328(f328(f243(a1),x61012),a83)) % 167.77/167.50 [6105]~P117(x61051)+P1(f328(f328(f243(x61051),f2(x61051)),f82(x61051,x61052)))+~P1(f328(f328(f243(x61051),f2(x61051)),x61052)) % 167.77/167.50 [6116]~P77(x61161)+~P1(f328(f328(f243(x61161),x61162),f2(x61161)))+P1(f328(f328(f243(x61161),f2(x61161)),f328(f79(x61161),x61162))) % 167.77/167.50 [6117]~P77(x61171)+~P1(f328(f328(f242(x61171),x61172),f2(x61171)))+P1(f328(f328(f242(x61171),f2(x61171)),f328(f79(x61171),x61172))) % 167.77/167.50 [6120]E(x61201,f251(f879(x61202,a867)))+~E(f328(f39(x61202),x61201),f328(f39(x61202),f251(f879(x61202,a867))))+~P1(f328(f38(x61202),f251(f879(x61202,a867)))) % 167.77/167.50 [6162]~P117(x61621)+P1(f328(f328(f243(x61621),x61622),f2(x61621)))+~P1(f328(f328(f243(x61621),x61622),f328(f79(x61621),x61622))) % 167.77/167.50 [6163]~P75(x61631)+P1(f328(f328(f242(x61631),x61632),f2(x61631)))+~P1(f328(f328(f242(x61631),x61632),f328(f79(x61631),x61632))) % 167.77/167.50 [6173]~P91(x61731)+P1(f328(f328(f330(x61731),f328(f107(x61731),x61732)),f190(x61731)))+~P1(f328(f328(f242(a1),a83),x61732)) % 167.77/167.50 [6204]E(x62041,f2(a872))+~P1(f328(f328(f243(a872),x62041),f328(a116,x62042)))+P1(f328(f328(f243(a872),f848(x62042,x62041)),x62042)) % 167.77/167.50 [6226]~P117(x62261)+~P1(f328(f328(f243(x62261),f2(x62261)),f82(x62261,x62262)))+P1(f328(f328(f243(x62261),f2(x62261)),x62262)) % 167.77/167.50 [6228]~E(f328(f107(a872),x62282),f328(f107(a872),x62281))+P1(f328(f328(f242(a1),f328(f107(a1),x62281)),f2(a1)))+~P1(f328(a197,f328(f107(a1),x62282))) % 167.77/167.50 [6258]E(f328(f262(a1,a1),f51(x62581,x62582)),f328(f328(f40(a1),x62581),x62582))+~P1(f328(f328(f243(a1),x62581),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x62582)) % 167.77/167.50 [6291]E(f328(f266(a1,a1),f51(x62911,x62912)),f46(a1,x62911,x62912))+~P1(f328(f328(f243(a1),x62911),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x62912)) % 167.77/167.50 [6294]~P116(x62942)+~P1(f328(f328(f243(x62942),f2(x62942)),f328(f104(x62942),x62941)))+P1(f328(f328(f243(a872),f2(a872)),x62941)) % 167.77/167.50 [6295]~P117(x62952)+~P1(f328(f328(f243(x62952),f2(x62952)),f328(f106(x62952),x62951)))+P1(f328(f328(f243(a1),f2(a1)),x62951)) % 167.77/167.50 [6296]~P117(x62962)+~P1(f328(f328(f242(x62962),f2(x62962)),f328(f106(x62962),x62961)))+P1(f328(f328(f242(a1),f2(a1)),x62961)) % 167.77/167.50 [6299]E(f328(f262(a1,a1),f48(x62991,x62992)),f328(f328(f40(a1),x62991),x62992))+~P1(f328(f328(f243(a1),f2(a1)),x62991))+~P1(f328(f328(f242(a1),f2(a1)),x62992)) % 167.77/167.50 [6314]E(f328(f266(a1,a1),f48(x63141,x63142)),f46(a1,x63141,x63142))+~P1(f328(f328(f243(a1),f2(a1)),x63141))+~P1(f328(f328(f242(a1),f2(a1)),x63142)) % 167.77/167.50 [6329]~P77(x63291)+P1(f328(f328(f243(x63291),x63292),f2(x63291)))+~P1(f328(f328(f243(x63291),f2(x63291)),f328(f79(x63291),x63292))) % 167.77/167.50 [6330]~P77(x63301)+P1(f328(f328(f242(x63301),x63302),f2(x63301)))+~P1(f328(f328(f242(x63301),f2(x63301)),f328(f79(x63301),x63302))) % 167.77/167.50 [6355]P1(f328(f50(x63551,x63552),f51(x63551,x63552)))+~P1(f328(f328(f243(a1),x63551),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x63552)) % 167.77/167.50 [6380]P1(f328(f50(x63801,x63802),f48(x63801,x63802)))+~P1(f328(f328(f243(a1),f2(a1)),x63802))+~P1(f328(f328(f242(a1),f2(a1)),x63801)) % 167.77/167.50 [6423]~P77(x64231)+P1(f328(f328(f243(x64231),f328(f79(x64231),x64232)),f2(x64231)))+~P1(f328(f328(f243(x64231),f2(x64231)),x64232)) % 167.77/167.50 [6424]~P77(x64241)+P1(f328(f328(f242(x64241),f328(f79(x64241),x64242)),f2(x64241)))+~P1(f328(f328(f242(x64241),f2(x64241)),x64242)) % 167.77/167.50 [6441]E(f328(f328(f22(a872),f328(a108,x64411)),f328(a108,x64412)),f328(a108,f199(x64411,x64412)))+~P1(f328(f328(f242(a1),f2(a1)),x64412))+~P1(f328(f328(f242(a1),f2(a1)),x64411)) % 167.77/167.50 [6458]P1(f328(f328(f242(a1),f2(a1)),f199(x64581,x64582)))+~P1(f328(f328(f242(a1),f2(a1)),x64582))+~P1(f328(f328(f242(a1),f2(a1)),x64581)) % 167.77/167.50 [6495]~P1(f328(x64951,x64952))+P1(f328(x64951,f2(a872)))+P1(f328(x64951,f328(f328(f80(a872),f394(x64952,x64951)),f78(a872)))) % 167.77/167.50 [6576]E(f328(f107(a872),x65761),f328(f107(a872),x65762))+~P1(f328(f328(f242(a1),f328(f107(a1),x65762)),f2(a1)))+~P1(f328(a197,f328(f107(a1),x65761))) % 167.77/167.50 [6586]~E(x65861,f2(a872))+~E(f704(x65862,x65861),f2(a872))+E(f328(f139(a872,a872,f80(a872),x65861),x65862),f2(a872)) % 167.77/167.50 [6612]~P1(f328(f38(x66121),f861(x66122,x66121)))+~P1(f328(f38(f879(x66121,a867)),x66122))+P1(f328(f38(x66121),f41(f879(x66121,a867),x66122))) % 167.77/167.50 [6618]E(x66181,x66182)+P1(f328(f328(f243(a1),x66181),x66182))+~P1(f328(f328(f243(a1),x66181),f328(f328(f80(a1),x66182),f78(a1)))) % 167.77/167.50 [6620]P1(f328(f328(f243(a872),f328(a108,x66201)),f328(a108,x66202)))+~P1(f328(f328(f243(a1),f2(a1)),x66202))+~P1(f328(f328(f243(a1),x66201),x66202)) % 167.77/167.50 [6621]P1(f328(f328(f243(a872),f328(a108,x66211)),f328(a108,x66212)))+~P1(f328(f328(f242(a1),f2(a1)),x66211))+~P1(f328(f328(f243(a1),x66211),x66212)) % 167.77/167.50 [6622]P1(f328(f328(f242(a872),f328(a108,x66221)),f328(a108,x66222)))+~P1(f328(f328(f243(a1),f2(a1)),x66221))+~P1(f328(f328(f242(a1),x66221),x66222)) % 167.77/167.50 [6623]P1(f328(f328(f242(a872),f328(a108,x66231)),f328(a108,x66232)))+~P1(f328(f328(f242(a1),f2(a1)),x66232))+~P1(f328(f328(f242(a1),x66231),x66232)) % 167.77/167.50 [6635]E(f46(a872,f328(a108,x66351),f328(a108,x66352)),f328(a108,f46(a1,x66351,x66352)))+~P1(f328(f328(f242(a1),f2(a1)),x66352))+~P1(f328(f328(f242(a1),f2(a1)),x66351)) % 167.77/167.50 [6657]~P77(x66571)+~P1(f328(f328(f243(x66571),f328(f79(x66571),x66572)),f2(x66571)))+P1(f328(f328(f243(x66571),f2(x66571)),x66572)) % 167.77/167.50 [6658]~P77(x66581)+~P1(f328(f328(f242(x66581),f328(f79(x66581),x66582)),f2(x66581)))+P1(f328(f328(f242(x66581),f2(x66581)),x66582)) % 167.77/167.50 [6673]~P1(f328(f328(f243(a1),a83),x66732))+~P1(f328(f328(f243(a1),x66731),x66732))+P1(f328(f328(f243(a872),f328(f107(a872),x66731)),f328(f107(a872),x66732))) % 167.77/167.50 [6764]~P1(f328(f328(f242(a1),f2(a1)),x67641))+P1(f328(f328(f243(a872),f328(a108,x67641)),x67642))+~P1(f328(f328(f243(a1),x67641),f328(f104(a1),x67642))) % 167.77/167.50 [6781]E(x67811,f2(a1))+E(f46(a1,x67812,x67811),f2(a1))+E(f328(f328(f22(a1),f328(f79(a1),f328(f328(f40(a1),x67812),x67811))),f78(a1)),f328(f328(f40(a1),x67812),f328(f79(a1),x67811))) % 167.77/167.50 [6797]~P1(f328(f328(f242(a1),f2(a1)),x67971))+~P1(f328(f328(f243(a872),f328(a108,x67971)),x67972))+P1(f328(f328(f243(a1),x67971),f328(f104(a1),x67972))) % 167.77/167.50 [6834]~P1(f328(f328(f242(a872),f328(a108,x68341)),f328(a108,x68342)))+~P1(f328(f328(f243(a1),f2(a1)),x68341))+P1(f328(f328(f242(a1),x68341),x68342)) % 167.77/167.50 [6835]~P1(f328(f328(f242(a872),f328(a108,x68351)),f328(a108,x68352)))+~P1(f328(f328(f242(a1),f2(a1)),x68352))+P1(f328(f328(f242(a1),x68351),x68352)) % 167.77/167.50 [6862]P1(f328(f328(f242(a1),x68621),x68622))+~P1(f328(f328(f242(a872),f328(f107(a872),x68621)),f328(f107(a872),x68622)))+P1(f328(f328(f242(a1),x68621),a83)) % 167.77/167.50 [6887]P1(f328(f328(f242(a1),f2(a1)),f46(a1,x68871,x68872)))+~P1(f328(f328(f242(a1),f2(a1)),x68872))+~P1(f328(f328(f242(a1),f2(a1)),x68871)) % 167.77/167.50 [6985]P1(f328(f328(f243(a1),a83),x69851))+~P1(f328(f328(f243(a1),x69852),x69851))+~P1(f328(f328(f243(a872),f328(f107(a872),x69852)),f328(f107(a872),x69851))) % 167.77/167.50 [7036]E(f328(f328(f263(a1,a1),f328(f328(f40(a1),x70361),x70362)),f46(a1,x70361,x70362)),f51(x70361,x70362))+~P1(f328(f328(f243(a1),x70361),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x70362)) % 167.77/167.50 [7057]E(f328(f328(f263(a1,a1),f328(f328(f40(a1),x70571),x70572)),f46(a1,x70571,x70572)),f48(x70571,x70572))+~P1(f328(f328(f242(a1),f2(a1)),x70572))+~P1(f328(f328(f242(a1),f2(a1)),x70571)) % 167.77/167.50 [7108]~P95(x71082)+E(x71081,f117(x71082))+E(f328(f139(x71082,x71082,f81(x71082),f328(f138(x71082),x71081)),f328(f169(x71082),x71081)),f328(f64(x71082,f81(x71082)),f328(f170(x71082),x71081))) % 167.77/167.50 [7222]~E(x72221,f2(a872))+E(f328(f139(a872,a872,f80(a872),x72221),x72222),f2(a872))+P1(f328(f328(f330(a872),f704(x72222,x72221)),f328(f170(a872),x72222))) % 167.77/167.50 [7269]~P1(f328(f328(f243(a1),x72692),f2(a1)))+P1(f328(f328(f243(a1),f328(f328(f40(a1),x72691),x72692)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x72691)) % 167.77/167.50 [7271]~P1(f328(f328(f243(a1),x72711),f2(a1)))+P1(f328(f328(f243(a1),f328(f328(f40(a1),x72711),x72712)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x72712)) % 167.77/167.50 [7272]~P1(f328(f328(f243(a1),x72722),f2(a1)))+P1(f328(f328(f242(a1),f328(f328(f40(a1),x72721),x72722)),f2(a1)))+~P1(f328(f328(f242(a1),f2(a1)),x72721)) % 167.77/167.50 [7273]~P1(f328(f328(f242(a1),x72731),f2(a1)))+P1(f328(f328(f242(a1),f328(f328(f40(a1),x72731),x72732)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x72732)) % 167.77/167.50 [7279]P1(f328(f328(f330(f879(x72791,a867)),f861(x72792,x72791)),x72792))+~P1(f328(f38(f879(x72791,a867)),x72792))+P1(f328(f38(x72791),f41(f879(x72791,a867),x72792))) % 167.77/167.50 [7376]P26(x73761,x73761,x73762,f251(f879(x73761,a867)))+~E(f328(f307(x73761,x73761,x73762),f251(f879(x73761,a867))),f251(f879(x73761,a867)))+~P1(f328(f38(x73761),f251(f879(x73761,a867)))) % 167.77/167.50 [7503]~P26(x75031,x75031,x75032,f251(f879(x75031,a867)))+E(f328(f307(x75031,x75031,x75032),f251(f879(x75031,a867))),f251(f879(x75031,a867)))+~P1(f328(f38(x75031),f251(f879(x75031,a867)))) % 167.77/167.50 [7641]E(f328(f328(f40(a1),x76411),x76412),f328(f107(a1),a101))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x76411),x76412)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x76411)) % 167.77/167.50 [7700]~P1(f328(f328(f243(a1),x77002),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f40(a1),x77001),x77002)),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x77001)) % 167.77/167.50 [7705]E(f328(f328(f80(a1),x77051),x77052),f46(a1,x77051,x77052))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x77051),x77052)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x77051)) % 167.77/167.50 [7708]P1(f328(f328(f243(a1),x77081),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f40(a1),x77081),x77082)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x77082)) % 167.77/167.50 [8097]~P59(x80971)+~P1(f328(f60(f876(x80971)),x80972))+P1(f328(f60(x80971),f328(f328(f8(f876(x80971),a867,x80971),x80972),f235(x80971)))) % 167.77/167.50 [8416]~P105(x84161)+P15(x84161,x84162)+~P1(f328(f328(f242(x84161),f328(f328(f162(x84161),x84162),f741(x84162,x84161))),f328(f328(f162(x84161),x84162),f742(x84162,x84161)))) % 167.77/167.50 [8417]~P105(x84171)+P15(x84171,x84172)+~P1(f328(f328(f242(x84171),f328(f328(f162(x84171),x84172),f749(x84172,x84171))),f328(f328(f162(x84171),x84172),f754(x84172,x84171)))) % 167.77/167.50 [8572]~P59(x85721)+P1(f328(f59(f876(x85721)),x85722))+~P1(f328(f59(x85721),f328(f328(f8(f876(x85721),a867,x85721),x85722),f235(x85721)))) % 167.77/167.50 [9742]~P59(x97421)+~P59(x97422)+E(f328(f328(f151(f873(x97421),f879(x97422,x97421)),f328(f328(f8(f879(x97422,f876(x97421)),f879(x97422,x97421),f873(x97421)),f73(f876(x97421),x97421,x97422,f239(x97421))),f328(f328(f8(f873(f878(x97422,x97421)),f879(x97422,f876(x97421)),f873(x97421)),f176(x97422,x97421)),f328(f180(x97422,x97421),f57(x97422))))),f56(x97421,f328(f193(f873(x97422)),f57(x97422)),f57(x97421))),f57(f879(x97422,x97421))) % 167.77/167.50 [5659]E(x56591,f2(a1))+~E(f46(a1,x56592,x56591),f2(a1))+E(f328(f328(f40(a1),x56592),f328(f79(a1),x56591)),f328(f79(a1),f328(f328(f40(a1),x56592),x56591))) % 167.77/167.50 [5677]~P39(x56772)+~P39(x56771)+P39(f328(f328(f114(f879(a1,a867)),x56771),x56772)) % 167.77/167.50 [5678]~P39(x56782)+~P39(x56781)+P39(f328(f328(f105(f879(a1,a867)),x56781),x56782)) % 167.77/167.50 [5696]~P60(x56961)+~P91(x56961)+E(f328(f79(x56961),f328(f328(f286(x56961),f78(x56961)),x56962)),f328(f328(f286(x56961),f328(f107(x56961),a101)),x56962)) % 167.77/167.50 [5811]E(x58111,f2(a1))+~E(f46(a1,x58112,x58111),f2(a1))+E(f328(f328(f40(a1),f328(f79(a1),x58112)),x58111),f328(f79(a1),f328(f328(f40(a1),x58112),x58111))) % 167.77/167.50 [5945]~P105(x59451)+P15(x59451,x59452)+P1(f328(f328(f243(a872),f742(x59452,x59451)),f328(f193(f873(x59451)),x59452))) % 167.77/167.50 [5946]~P105(x59461)+P15(x59461,x59462)+P1(f328(f328(f243(a872),f754(x59462,x59461)),f328(f193(f873(x59461)),x59462))) % 167.77/167.50 [6097]~P91(x60971)+~E(f328(f107(x60971),x60972),f2(x60971))+P31(x60971,f328(f107(x60971),f328(f328(f80(a1),x60972),f328(f79(a1),a83)))) % 167.77/167.50 [6098]~P91(x60981)+~E(f328(f107(x60981),x60982),f2(x60981))+P31(x60981,f328(f107(x60981),f328(f328(f80(a1),a83),f328(f79(a1),x60982)))) % 167.77/167.50 [6100]E(f328(a52,f48(f328(f79(a1),x61001),f328(f79(a1),x61002))),f47(x61001,x61002))+P1(f328(f328(f243(a1),f2(a1)),x61002))+P1(f328(f328(f242(a1),f2(a1)),x61001)) % 167.77/167.50 [6234]~E(x62342,f2(a872))+~E(x62341,f2(a872))+P1(f328(f328(f242(a1),f328(f104(a1),x62341)),f328(f79(a1),f328(f104(a1),x62342)))) % 167.77/167.50 [6262]E(f328(f328(f80(a872),f328(f107(a872),x62621)),f328(f107(a872),x62622)),f328(f107(a872),f328(f328(f80(a1),x62621),x62622)))+P1(f328(f328(f243(a1),x62621),a83))+P1(f328(f328(f243(a1),x62622),a83)) % 167.77/167.50 [6389]~P75(x63891)+~P1(f328(f328(f243(x63891),f2(x63891)),x63892))+P1(f328(f328(f243(x63891),f328(f79(x63891),x63892)),x63892)) % 167.77/167.50 [6390]~P75(x63901)+~P1(f328(f328(f242(x63901),f2(x63901)),x63902))+P1(f328(f328(f242(x63901),f328(f79(x63901),x63902)),x63902)) % 167.77/167.50 [6562]E(f328(f328(f22(a872),f328(a108,x65621)),f328(a108,x65622)),f328(a108,f328(f328(f22(a1),x65621),x65622)))+~P1(f328(f328(f242(a1),f2(a1)),x65622))+~P1(f328(f328(f242(a1),x65622),x65621)) % 167.77/167.50 [6595]E(f328(a108,f46(a1,f328(f107(a1),x65951),f328(f107(a1),x65952))),f46(a872,f328(f107(a872),x65951),f328(f107(a872),x65952)))+P1(f328(a197,f328(f107(a1),x65951)))+P1(f328(a197,f328(f107(a1),x65952))) % 167.77/167.50 [6613]~P75(x66131)+P1(f328(f328(f243(x66131),f2(x66131)),x66132))+~P1(f328(f328(f243(x66131),f328(f79(x66131),x66132)),x66132)) % 167.77/167.50 [6614]~P75(x66141)+P1(f328(f328(f242(x66141),f2(x66141)),x66142))+~P1(f328(f328(f242(x66141),f328(f79(x66141),x66142)),x66142)) % 167.77/167.50 [6626]~P75(x66261)+~P1(f328(f328(f243(x66261),f2(x66261)),x66262))+P1(f328(f328(f243(x66261),f2(x66261)),f328(f328(f80(x66261),x66262),x66262))) % 167.77/167.50 [6629]~P75(x66291)+~P1(f328(f328(f242(x66291),f2(x66291)),x66292))+P1(f328(f328(f242(x66291),f2(x66291)),f328(f328(f80(x66291),x66292),x66292))) % 167.77/167.50 [6640]E(f328(f328(f80(a872),f328(a108,x66401)),f328(a108,x66402)),f328(a108,f328(f328(f80(a1),x66401),x66402)))+~P1(f328(f328(f242(a1),f2(a1)),x66402))+~P1(f328(f328(f242(a1),f2(a1)),x66401)) % 167.77/167.50 [6652]E(x66521,f2(a872))+P1(f328(f328(f243(a872),f2(a872)),x66522))+~P1(f328(f328(f243(a872),f2(a872)),f328(f328(f253(a872),x66522),x66521))) % 167.77/167.50 [6682]~P91(x66821)+E(f328(f107(x66821),x66822),f2(x66821))+~P31(x66821,f328(f107(x66821),f328(f328(f80(a1),a83),f328(f79(a1),x66822)))) % 167.77/167.50 [6683]~P91(x66831)+E(f328(f107(x66831),x66832),f2(x66831))+~P31(x66831,f328(f107(x66831),f328(f328(f80(a1),x66832),f328(f79(a1),a83)))) % 167.77/167.50 [6742]~P1(f328(f38(x67421),x67422))+~P1(f328(f38(x67421),f251(f879(x67421,a867))))+P1(f328(f38(x67421),f328(f79(f879(x67421,a867)),x67422))) % 167.77/167.50 [6765]~P1(f328(f328(f243(a1),f2(a1)),x67652))+~P1(f328(f328(f242(a1),x67652),x67651))+P1(f328(f328(f243(a1),f2(a1)),f328(f328(f40(a1),x67651),x67652))) % 167.77/167.50 [6766]~P1(f328(f328(f243(a1),x67662),f2(a1)))+~P1(f328(f328(f242(a1),x67661),f2(a1)))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f40(a1),x67661),x67662))) % 167.77/167.50 [6805]~P1(f328(f328(f243(a872),f2(a872)),x68052))+~P1(f328(f328(f243(a872),f2(a872)),x68051))+P1(f328(f328(f243(a872),f2(a872)),f328(f328(f81(a872),x68051),x68052))) % 167.77/167.50 [6806]~P1(f328(f328(f242(a1),f2(a1)),x68062))+~P1(f328(f328(f242(a1),f2(a1)),x68061))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),x68061),x68062))) % 167.77/167.50 [6807]~P1(f328(f328(f242(a1),f2(a1)),x68072))+~P1(f328(f328(f242(a1),f2(a1)),x68071))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f81(a1),x68071),x68072))) % 167.77/167.50 [6808]~P1(f328(f328(f243(a1),f2(a1)),x68082))+~P1(f328(f328(f242(a1),f2(a1)),x68081))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f40(a1),x68081),x68082))) % 167.77/167.50 [6809]~P1(f328(f328(f242(a1),f2(a1)),x68092))+~P1(f328(f328(f242(a1),f2(a1)),x68091))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f40(a1),x68091),x68092))) % 167.77/167.50 [6875]E(x68751,f2(a1))+E(f46(a1,x68752,x68751),f2(a1))+E(f328(f328(f22(a1),f328(f79(a1),f328(f328(f40(a1),x68752),x68751))),f78(a1)),f328(f328(f40(a1),f328(f79(a1),x68752)),x68751)) % 167.77/167.50 [6928]P1(f328(f328(f243(a872),f2(a872)),x69281))+P1(f328(f328(f243(a872),f2(a872)),x69282))+~P1(f328(f328(f243(a872),f2(a872)),f328(f328(f80(a872),x69282),x69281))) % 167.77/167.50 [6932]~P75(x69321)+P1(f328(f328(f243(x69321),f2(x69321)),x69322))+~P1(f328(f328(f243(x69321),f2(x69321)),f328(f328(f80(x69321),x69322),x69322))) % 167.77/167.50 [6933]~P75(x69331)+P1(f328(f328(f242(x69331),f2(x69331)),x69332))+~P1(f328(f328(f242(x69331),f2(x69331)),f328(f328(f80(x69331),x69332),x69332))) % 167.77/167.50 [6986]~P1(f328(f38(x69861),x69862))+P1(f328(f38(x69861),f251(f879(x69861,a867))))+~P1(f328(f38(x69861),f328(f79(f879(x69861,a867)),x69862))) % 167.77/167.50 [7049]P1(f328(f328(f242(a1),x70491),f2(a1)))+~P1(f328(f328(f243(a1),x70492),f2(a1)))+~P1(f328(f328(f242(a1),f2(a1)),f328(f328(f40(a1),x70491),x70492))) % 167.77/167.50 [7055]~P1(f328(f328(f243(a1),f2(a1)),x70551))+P1(f328(f328(f242(a1),x70551),x70552))+~P1(f328(f328(f243(a1),f2(a1)),f328(f328(f40(a1),x70552),x70551))) % 167.77/167.50 [7056]~P1(f328(f328(f242(a1),f2(a1)),x70562))+P1(f328(f328(f242(a1),x70561),x70562))+~P1(f328(f328(f243(a1),f2(a1)),f328(f328(f40(a1),x70562),x70561))) % 167.77/167.50 [7085]P1(f328(f328(f243(a1),f2(a1)),x70851))+~P1(f328(f328(f242(a1),f2(a1)),x70852))+~P1(f328(f328(f243(a1),f2(a1)),f328(f328(f40(a1),x70852),x70851))) % 167.77/167.50 [7086]P1(f328(f328(f242(a1),f2(a1)),x70861))+~P1(f328(f328(f243(a1),f2(a1)),x70862))+~P1(f328(f328(f242(a1),f2(a1)),f328(f328(f40(a1),x70861),x70862))) % 167.77/167.50 [7533]~P1(f328(f38(x75332),f251(f879(x75332,a867))))+~P1(f328(f38(x75331),f251(f879(x75331,a867))))+P1(f328(f38(f877(x75331,x75332)),f251(f879(f877(x75331,x75332),a867)))) % 167.77/167.50 [7534]~P1(f328(f38(x75342),f251(f879(x75342,a867))))+~P1(f328(f38(x75341),f251(f879(x75341,a867))))+P1(f328(f38(f878(x75341,x75342)),f251(f879(f878(x75341,x75342),a867)))) % 167.77/167.50 [7605]~P1(f328(f328(f243(a872),f328(a116,f2(a872))),x76051))+~P1(f328(f328(f243(a872),f328(a116,f2(a872))),x76052))+P1(f328(f328(f243(a872),x76051),f328(f328(f81(a872),x76052),x76051))) % 167.77/167.50 [7606]~P1(f328(f328(f243(a872),f328(a116,f2(a872))),x76061))+~P1(f328(f328(f243(a872),f328(a116,f2(a872))),x76062))+P1(f328(f328(f243(a872),x76061),f328(f328(f81(a872),x76061),x76062))) % 167.77/167.50 [7640]E(f328(f39(x76401),f251(f879(x76401,a867))),f328(a116,f2(a872)))+P1(f328(f38(x76402),f251(f879(x76402,a867))))+~P1(f328(f38(f879(x76402,x76401)),f251(f879(f879(x76402,x76401),a867)))) % 167.77/167.50 [7770]~P1(f328(f328(f243(a872),f328(a116,f2(a872))),x77702))+~P1(f328(f328(f243(a872),f328(a116,f2(a872))),x77701))+P1(f328(f328(f243(a872),f328(a116,f2(a872))),f328(f328(f81(a872),x77701),x77702))) % 167.77/167.50 [7771]~P1(f328(f328(f242(a872),f328(a116,f2(a872))),x77711))+~P1(f328(f328(f242(a872),f328(a116,f2(a872))),x77712))+P1(f328(f328(f242(a872),f328(a116,f2(a872))),f328(f328(f81(a872),x77711),x77712))) % 167.77/167.50 [8461]E(x84611,f117(x84612))+~P1(f328(f134(x84612),x84611))+E(f175(x84612,f328(f328(f8(a867,a867,x84612),a323),f328(f328(f7(x84612,x84612,a867),a325),f141(x84612,x84611))),x84611),f118(x84612,x84611)) % 167.77/167.50 [8563]~P39(x85632)+~P39(x85631)+E(f328(f307(a872,a1,f104(a1)),f328(f328(f114(f879(a872,a867)),f328(f307(a1,a872,a108),x85631)),f328(f307(a1,a872,a108),x85632))),f328(f328(f114(f879(a1,a867)),x85631),x85632)) % 167.77/167.50 [8564]~P39(x85642)+~P39(x85641)+E(f328(f307(a872,a1,f104(a1)),f328(f328(f105(f879(a872,a867)),f328(f307(a1,a872,a108),x85641)),f328(f307(a1,a872,a108),x85642))),f328(f328(f105(f879(a1,a867)),x85641),x85642)) % 167.77/167.50 [9219]~P91(x92191)+~E(f328(f107(x92191),x92192),f78(x92191))+P31(x92191,f328(f107(x92191),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f79(a1),x92192)))) % 167.77/167.50 [9452]~P91(x94521)+E(f328(f107(x94521),x94522),f78(x94521))+~P31(x94521,f328(f107(x94521),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f79(a1),x94522)))) % 167.77/167.50 [10186]E(x101861,f2(a1))+E(x101862,f2(a1))+E(f328(f268(a1,a1,a1,a1,f34(a1),f328(f81(a1),f82(a1,x101862))),f328(f328(f328(f100(f878(a1,a1)),f328(f328(a325,f82(a1,x101861)),f82(a1,x101862))),f54(x101861,x101862)),f328(f328(f267(a1,a1,f878(a1,a1)),f328(f328(f18(a1,f879(a1,f878(a1,a1)),f879(a1,f878(a1,a1))),f328(f328(f8(f879(a1,f879(f878(a1,a1),f878(a1,a1))),f879(f879(a1,f878(a1,a1)),f879(a1,f878(a1,a1))),a1),f18(a1,f878(a1,a1),f878(a1,a1))),f328(f328(f8(f878(a1,a1),f879(a1,f879(f878(a1,a1),f878(a1,a1))),a1),f328(f7(a1,f878(a1,a1),f879(f878(a1,a1),f878(a1,a1))),f328(f328(f8(a867,f879(f878(a1,a1),f879(f878(a1,a1),f878(a1,a1))),a1),f100(f878(a1,a1))),f328(f328(f7(a1,a1,a867),a325),f2(a1))))),f328(f328(f7(a1,a1,f878(a1,a1)),f328(f328(f8(a1,f879(a1,f878(a1,a1)),a1),f263(a1,a1)),f79(a1))),f2(a1))))),f328(f328(f7(a1,f879(a1,a1),f879(a1,f878(a1,a1))),f328(f328(f8(f879(a1,f878(a1,a1)),f879(f879(a1,a1),f879(a1,f878(a1,a1))),a1),f8(a1,f878(a1,a1),a1)),f328(f328(f8(a1,f879(a1,f878(a1,a1)),a1),f263(a1,a1)),f328(f328(f7(a1,a1,a1),f328(f328(f8(a1,f879(a1,a1),a1),f22(a1)),f79(a1))),f78(a1))))),f328(f22(a1),f328(f75(a1),x101862))))),f54(x101861,x101862)))),f47(x101861,x101862)) % 167.77/167.50 [10187]E(x101871,f2(a1))+E(x101872,f2(a1))+E(f328(f268(a1,a1,a1,a1,f34(a1),f328(f81(a1),f82(a1,x101872))),f328(f328(f328(f100(f878(a1,a1)),f328(f328(a327,f328(f328(a326,f328(f328(f243(a1),f2(a1)),x101872)),f328(f328(f242(a1),f2(a1)),x101871))),f328(f328(a326,f328(f328(f243(a1),x101872),f2(a1))),f328(f328(f243(a1),x101871),f2(a1))))),f54(x101871,x101872)),f328(f328(f267(a1,a1,f878(a1,a1)),f328(f328(f18(a1,f879(a1,f878(a1,a1)),f879(a1,f878(a1,a1))),f328(f328(f8(f879(a1,f879(f878(a1,a1),f878(a1,a1))),f879(f879(a1,f878(a1,a1)),f879(a1,f878(a1,a1))),a1),f18(a1,f878(a1,a1),f878(a1,a1))),f328(f328(f8(f878(a1,a1),f879(a1,f879(f878(a1,a1),f878(a1,a1))),a1),f328(f7(a1,f878(a1,a1),f879(f878(a1,a1),f878(a1,a1))),f328(f328(f8(a867,f879(f878(a1,a1),f879(f878(a1,a1),f878(a1,a1))),a1),f100(f878(a1,a1))),f328(f328(f7(a1,a1,a867),a325),f2(a1))))),f328(f328(f7(a1,a1,f878(a1,a1)),f328(f328(f8(a1,f879(a1,f878(a1,a1)),a1),f263(a1,a1)),f79(a1))),f2(a1))))),f328(f328(f7(a1,f879(a1,a1),f879(a1,f878(a1,a1))),f328(f328(f8(f879(a1,f878(a1,a1)),f879(f879(a1,a1),f879(a1,f878(a1,a1))),a1),f8(a1,f878(a1,a1),a1)),f328(f328(f8(a1,f879(a1,f878(a1,a1)),a1),f263(a1,a1)),f328(f328(f7(a1,a1,a1),f328(f328(f8(a1,f879(a1,a1),a1),f22(a1)),f79(a1))),f78(a1))))),f328(f22(a1),f328(f75(a1),x101872))))),f54(x101871,x101872)))),f47(x101871,x101872)) % 167.77/167.50 [10188]~P30(a5000)+P25(a868,x101881,f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),a325),x101882),f328(a198,x101882))),f192(f879(f871(a868),a867))))+~P25(a868,x101881,f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),f328(f328(f8(f879(a868,f879(a868,a867)),f879(a868,a867),a868),f328(f8(f879(a868,a867),a867,a868),f88(a868))),f328(f328(f8(f879(a868,a867),f879(a868,f879(a868,a867)),a868),f328(f7(a868,f879(a868,a867),f879(a868,a867)),f328(f328(f8(f879(a868,f879(a867,a867)),f879(f879(a868,a867),f879(a868,a867)),a868),f18(a868,a867,a867)),f328(f328(f8(f879(a868,a867),f879(a868,f879(a867,a867)),a868),f328(f8(a867,f879(a867,a867),a868),a331)),f328(a198,x101882))))),a325))),x101882),a325)),f192(f879(f871(a868),a867)))) % 167.77/167.50 [5685]~P117(x56851)+~P91(x56851)+E(f328(f75(x56851),f328(f328(f253(x56851),f328(f107(x56851),a101)),x56852)),f78(x56851)) % 167.77/167.50 [6174]~P138(x61741)+~P1(f328(f328(f243(a1),x61742),f2(a1)))+E(f328(f79(x61741),f328(f104(x61741),f328(a108,f328(f79(a1),x61742)))),f328(f106(x61741),x61742)) % 167.77/167.50 [6373]P1(f328(f328(f242(a103),x63731),f78(a103)))+E(f328(f328(f80(a103),f78(a103)),f276(x63731,f328(f328(f40(a103),x63732),x63731))),f276(x63731,x63732))+P1(f328(f328(f243(a103),x63732),x63731)) % 167.77/167.50 [6973]~P90(x69731)+~P1(f328(f328(f330(x69731),x69732),f113(x69731)))+~E(f328(f328(f80(x69731),f328(f328(f80(x69731),f78(x69731)),x69732)),x69732),f2(x69731)) % 167.77/167.50 [7087]~P1(f328(f328(f243(a1),x70871),f2(a1)))+~P1(f328(f328(f242(a1),x70872),f2(a1)))+E(f328(f262(a1,a1),f328(a52,f48(f328(f79(a1),x70871),f328(f79(a1),x70872)))),f328(f328(f40(a1),x70871),x70872)) % 167.77/167.50 [7104]~P1(f328(f328(f243(a1),x71041),f2(a1)))+~P1(f328(f328(f242(a1),x71042),f2(a1)))+E(f328(f266(a1,a1),f328(a52,f48(f328(f79(a1),x71041),f328(f79(a1),x71042)))),f46(a1,x71041,x71042)) % 167.77/167.50 [7110]~P1(f328(f328(f243(a1),x71102),f2(a1)))+E(f328(f262(a1,a1),f328(a52,f51(f328(f79(a1),x71101),f328(f79(a1),x71102)))),f328(f328(f40(a1),x71101),x71102))+~P1(f328(f328(f243(a1),f2(a1)),x71101)) % 167.77/167.50 [7128]~P1(f328(f328(f243(a1),x71282),f2(a1)))+E(f328(f266(a1,a1),f328(a52,f51(f328(f79(a1),x71281),f328(f79(a1),x71282)))),f46(a1,x71281,x71282))+~P1(f328(f328(f243(a1),f2(a1)),x71281)) % 167.77/167.50 [7183]E(f328(f328(f40(a1),f328(f328(f253(a1),x71831),x71832)),x71831),f328(f328(f253(a1),x71831),f328(f328(f22(a872),x71832),f328(a116,f2(a872)))))+~P1(f328(f328(f243(a872),f2(a872)),x71832))+~P1(f328(f328(f243(a1),f2(a1)),x71831)) % 167.77/167.50 [7276]~P1(f328(f328(f243(a872),f2(a872)),x72761))+~P1(f328(f328(f243(a872),f2(a872)),x72762))+P1(f328(f328(f243(a872),f328(f328(f22(a872),x72761),x72762)),x72761)) % 167.77/167.50 [7277]~P1(f328(f328(f243(a872),f2(a872)),x72771))+~P1(f328(f328(f243(a872),f78(a872)),x72772))+P1(f328(f328(f243(a872),f328(f328(f40(a872),x72771),x72772)),x72771)) % 167.77/167.50 [7278]~P1(f328(f328(f243(a1),f2(a1)),x72781))+~P1(f328(f328(f243(a1),f78(a1)),x72782))+P1(f328(f328(f243(a1),f328(f328(f40(a1),x72781),x72782)),x72781)) % 167.77/167.50 [7425]E(x74251,f2(a872))+~E(x74252,f2(a1))+~P1(f328(f328(f243(a1),f2(a1)),f328(f328(f253(a1),f328(f75(a1),x74252)),x74251))) % 167.77/167.50 [7850]~E(x78502,f117(f873(x78501)))+E(f328(f193(f873(f873(x78501))),f178(x78501,x78502)),f2(a872))+~P15(a872,f328(f166(a872),f328(f328(f151(f873(x78501),a872),f193(f873(x78501))),x78502))) % 167.77/167.50 [8096]P1(f328(x80961,x80962))+~P1(f328(x80961,f328(a110,f573(x80961,x80962))))+~P1(f328(f328(f330(f879(f878(a872,a872),a867)),x80962),a102)) % 167.77/167.50 [8115]E(x81151,f117(f873(x81152)))+E(f328(f193(f873(x81152)),f328(f328(f162(f873(x81152)),x81151),f2(a872))),f328(f193(f873(f873(x81152))),f178(x81152,x81151)))+~P15(a872,f328(f166(a872),f328(f328(f151(f873(x81152),a872),f193(f873(x81152))),x81151))) % 167.77/167.50 [8827]~P1(f328(f38(x88271),f328(f248(x88271),x88272)))+~P1(f328(f38(x88271),f251(f879(x88271,a867))))+P1(f328(f38(x88271),f328(f248(x88271),f328(f328(f8(a867,a867,x88271),a323),x88272)))) % 167.77/167.50 [8888]E(f328(f328(f263(a872,a872),f328(a116,f328(f328(f40(a872),f328(f328(f22(a872),x88881),x88882)),x88882))),f46(a872,f328(f328(f22(a872),x88881),x88882),x88882)),f85(f878(a872,a872),f49(x88881,x88882)))+~P1(f328(f328(f243(a872),f2(a872)),x88882))+~P1(f328(f328(f242(a872),x88882),x88881)) % 167.77/167.50 [9182]~P1(f328(f38(x91821),f328(f248(x91821),x91822)))+P1(f328(f38(x91821),f251(f879(x91821,a867))))+~P1(f328(f38(x91821),f328(f248(x91821),f328(f328(f8(a867,a867,x91821),a323),x91822)))) % 167.77/167.50 [9909]P27(x99091,x99092)+~P38(x99091,f328(f262(f879(f878(x99091,x99091),a867),f879(f878(x99091,x99091),a867)),x99092))+~P1(f328(f328(f242(f879(f878(x99091,x99091),a867)),f328(f328(f285(x99091,x99091,x99091),f328(f262(f879(f878(x99091,x99091),a867),f879(f878(x99091,x99091),a867)),x99092)),f328(f266(f879(f878(x99091,x99091),a867),f879(f878(x99091,x99091),a867)),x99092))),f328(f262(f879(f878(x99091,x99091),a867),f879(f878(x99091,x99091),a867)),x99092))) % 167.77/167.50 [7209]~P1(f328(f328(f243(a872),f2(a872)),x72092))+P1(f328(f328(f243(a872),x72091),x72092))+E(f328(a116,f328(f328(f40(a872),f328(f328(f22(a872),x72091),x72092)),x72092)),f328(f328(f40(a872),x72091),x72092)) % 167.77/167.50 [7346]~P1(f328(f328(f243(a872),f2(a872)),x73462))+~P1(f328(f328(f242(a872),x73462),x73461))+E(f328(a116,f328(f328(f40(a872),f328(f328(f22(a872),x73461),x73462)),x73462)),f328(f328(f40(a872),x73461),x73462)) % 167.77/167.50 [8333]~P91(x83331)+~P90(x83331)+~P31(x83331,f328(f107(x83331),f328(f328(f22(a1),f328(f328(f80(a1),x83332),x83332)),a101))) % 167.77/167.50 [9089]E(x90891,f2(a872))+E(f328(f328(f267(a872,a872,f878(a872,a872)),f328(f328(f8(a872,f879(a872,f878(a872,a872)),a872),f263(a872,a872)),a116)),f85(f878(a872,a872),f49(f328(f328(f22(a872),x90892),x90891),x90891))),f85(f878(a872,a872),f49(x90892,x90891)))+P1(f328(f328(f243(a872),x90892),x90891)) % 167.77/167.50 [9517]P1(f328(x95172,f652(x95172,x95171)))+P1(f328(x95171,f652(x95172,x95171)))+E(f328(f248(a1),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),f2(a1)))),x95171)),f328(f248(a1),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),f2(a1)))),x95172))) % 167.77/167.50 [9521]~P1(f328(x95212,f652(x95212,x95211)))+~P1(f328(x95211,f652(x95212,x95211)))+E(f328(f248(a1),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),f2(a1)))),x95211)),f328(f248(a1),f328(f328(f18(a1,a867,a867),f328(f328(f8(a867,f879(a867,a867),a1),a326),f328(f242(a1),f2(a1)))),x95212))) % 167.77/167.50 [7561]~P61(x75611)+~P91(x75611)+E(f328(f328(f286(x75611),x75612),f328(f107(x75611),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),x75612) % 167.77/167.50 [9218]~P91(x92181)+~E(f328(f107(x92181),x92182),f78(x92181))+P31(x92181,f328(f107(x92181),f328(f328(f80(a1),x92182),f328(f79(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.77/167.50 [9395]~P139(x93951)+~E(x93952,f78(x93951))+E(f328(f328(f253(x93951),x93952),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(x93951)) % 167.77/167.50 [9396]~P139(x93961)+~E(x93962,f2(x93961))+E(f328(f328(f253(x93961),x93962),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f2(x93961)) % 167.77/167.50 [9409]~P139(x94091)+~E(x94092,f328(f79(x94091),f78(x94091)))+E(f328(f328(f253(x94091),x94092),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(x94091)) % 167.77/167.50 [9453]~P91(x94531)+E(f328(f107(x94531),x94532),f78(x94531))+~P31(x94531,f328(f107(x94531),f328(f328(f80(a1),x94532),f328(f79(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.77/167.50 [9843]~P117(x98432)+E(x98431,f2(x98432))+P1(f328(f328(f243(x98432),f2(x98432)),f328(f328(f253(x98432),x98431),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 167.77/167.50 [9908]~P117(x99082)+~E(x99081,f2(x99082))+~P1(f328(f328(f243(x99082),f2(x99082)),f328(f328(f253(x99082),x99081),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 167.77/167.50 [9934]P1(f328(f328(f242(a1),x99341),f2(a1)))+P1(f328(f328(f243(a1),x99342),x99341))+E(f328(f45(x99341),f48(x99342,f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99341))),f48(x99342,x99341)) % 167.77/167.50 [9935]~P1(f328(f328(f243(a1),f2(a1)),x99351))+P1(f328(f328(f243(a1),x99352),x99351))+E(f328(f45(x99351),f48(x99352,f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99351))),f48(x99352,x99351)) % 167.77/167.50 [9936]P1(f328(f328(f242(a1),x99361),f2(a1)))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),x99362),x99361)))+E(f328(f45(x99361),f51(x99362,f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99361))),f51(x99362,x99361)) % 167.77/167.50 [9937]~P1(f328(f328(f243(a1),f2(a1)),x99371))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),x99372),x99371)))+E(f328(f45(x99371),f51(x99372,f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99371))),f51(x99372,x99371)) % 167.77/167.50 [9938]~P142(x99381)+~P1(f328(f328(f242(a1),f2(a1)),x99382))+E(f328(f104(x99381),f328(a108,f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99382))),f328(f328(f80(x99381),f328(f104(x99381),f328(a108,x99382))),f328(f104(x99381),f328(a108,x99382)))) % 167.77/167.50 [5021]~P144(x50211,x50212,x50213)+~E(x50213,f2(a1))+P1(f328(x50211,x50212)) % 167.77/167.50 [5143]~P105(x51431)+~P15(x51431,x51433)+P15(x51431,f167(x51431,x51432,x51433)) % 167.77/167.50 [5144]~P105(x51441)+~P15(x51441,x51443)+P15(x51441,f175(x51441,x51442,x51443)) % 167.77/167.50 [4725]~P74(x47252)+~E(x47253,f328(f79(x47252),x47251))+E(x47251,f328(f79(x47252),x47253)) % 167.77/167.50 [4727]~P74(x47271)+~E(f328(f79(x47271),x47273),x47272)+E(f328(f79(x47271),x47272),x47273) % 167.77/167.50 [4801]~P105(x48013)+E(x48011,x48012)+~E(f328(f249(x48013),x48011),f328(f249(x48013),x48012)) % 167.77/167.50 [4802]~P102(x48023)+E(x48021,x48022)+~E(f328(f104(x48023),x48021),f328(f104(x48023),x48022)) % 167.77/167.50 [4803]~P105(x48033)+E(x48031,x48032)+~E(f328(f300(x48033),x48031),f328(f300(x48033),x48032)) % 167.77/167.50 [4804]~P105(x48043)+E(x48041,x48042)+~E(f328(f250(x48043),x48041),f328(f250(x48043),x48042)) % 167.77/167.50 [4805]~P105(x48053)+E(x48051,x48052)+~E(f328(f297(x48053),x48051),f328(f297(x48053),x48052)) % 167.77/167.50 [4806]~P74(x48063)+E(x48061,x48062)+~E(f328(f79(x48063),x48061),f328(f79(x48063),x48062)) % 167.77/167.50 [4807]~P94(x48073)+E(x48071,x48072)+~E(f328(f79(x48073),x48071),f328(f79(x48073),x48072)) % 167.77/167.50 [4808]~P90(x48083)+E(x48081,x48082)+~E(f328(f106(x48083),x48081),f328(f106(x48083),x48082)) % 167.77/167.50 [4907]~P59(x49071)+~P1(f328(x49072,x49073))+P1(f328(f59(x49071),x49072)) % 167.77/167.50 [4940]~P59(x49403)+P1(f328(x49401,x49402))+~P1(f328(f60(x49403),x49401)) % 167.77/167.50 [5040]~P145(x50401,x50403,x50402)+~E(x50402,f2(a1))+P1(f328(x50401,f2(a1))) % 167.77/167.50 [5078]~E(x50781,f2(a872))+E(f773(x50781,x50782,x50783),f192(f879(x50783,a867)))+~E(f328(f39(x50783),x50782),f328(a116,x50781)) % 167.77/167.50 [5232]~E(x52322,f2(a872))+E(f328(f262(a872,a872),x52321),f2(a872))+~P1(f328(f49(x52323,x52322),x52321)) % 167.77/167.50 [5278]P1(f328(x52781,x52782))+~E(x52783,f328(f104(a1),x52782))+~P1(f328(x52781,f328(a108,x52783))) % 167.77/167.50 [5750]~E(x57503,f2(a872))+~P1(f328(x57501,x57502))+P1(f328(x57501,f46(a872,x57502,x57503))) % 167.77/167.50 [5881]~P1(f328(a25,x58813))+~P1(f328(a25,x58812))+P1(f328(a25,f30(x58811,x58812,x58813))) % 167.77/167.50 [5913]~P59(x59133)+~P11(x59133,x59131,x59132)+P1(f328(x59131,f718(x59132,x59131,x59133))) % 167.77/167.50 [6154]~E(x61543,f2(a872))+P1(f328(x61541,x61542))+~P1(f328(x61541,f46(a872,x61542,x61543))) % 167.77/167.50 [6305]~P59(x63051)+P12(x63051,x63052,x63053)+~P1(f328(x63052,f719(x63053,x63052,x63051))) % 167.77/167.50 [6831]E(x68311,f2(a872))+~P1(f328(x68312,f457(x68311,x68313,x68312)))+P1(f328(x68312,f46(a872,x68313,x68311))) % 167.77/167.50 [6938]~P4(x69381)+~P1(f328(f328(f242(x69381),x69382),f348(x69383,x69382,x69381)))+P1(f328(f328(f242(x69381),x69382),f42(x69381,x69383))) % 167.77/167.50 [6940]~P1(f328(x69401,x69402))+~P1(f328(x69401,f457(x69403,x69402,x69401)))+P1(f328(x69401,f46(a872,x69402,x69403))) % 167.77/167.50 [7042]E(x70421,f117(x70422))+E(f328(f328(f148(x70422),f705(x70423,x70421,x70422)),f708(x70423,x70421,x70422)),x70421)+~P1(f328(f328(f330(f873(x70422)),x70421),f158(x70422,x70423))) % 167.77/167.50 [7073]~P138(x70731)+~P1(f328(f328(f330(x70731),x70732),f113(x70731)))+P1(f328(f328(f330(x70731),f328(f328(f253(x70731),x70732),x70733)),f113(x70731))) % 167.77/167.50 [7395]P38(x73951,x73952)+~P1(f328(f328(f330(x73951),x73953),f627(x73952,x73951)))+P1(f328(f328(f330(x73951),f651(x73952,x73951,x73953)),f627(x73952,x73951))) % 167.77/167.50 [7667]E(x76671,f117(x76672))+~P1(f328(f328(f330(f873(x76672)),x76671),f158(x76672,x76673)))+P1(f328(f328(f330(f873(x76672)),f708(x76673,x76671,x76672)),f158(x76672,x76673))) % 167.77/167.50 [7720]E(x77201,f2(a872))+E(f328(f328(f80(a872),f328(f328(f81(a872),x77201),f458(x77201,x77202,x77203))),f457(x77201,x77202,x77203)),x77202)+P1(f328(x77203,f46(a872,x77202,x77201))) % 167.77/167.50 [7765]~P1(f328(x77653,x77652))+E(f328(f328(f80(a872),f328(f328(f81(a872),x77651),f458(x77651,x77652,x77653))),f457(x77651,x77652,x77653)),x77652)+P1(f328(x77653,f46(a872,x77652,x77651))) % 167.77/167.50 [7906]P1(f328(f328(f243(a1),x79061),f439(x79062,x79063,x79061)))+P1(f328(f328(x79063,f328(f328(f40(a1),x79062),x79061)),f46(a1,x79062,x79061)))+~P1(f328(f328(f243(a1),x79061),f2(a1))) % 167.77/167.50 [8180]P1(f328(f328(x81802,f328(f328(f40(a1),x81801),x81803)),f46(a1,x81801,x81803)))+~P1(f328(f328(f243(a1),x81803),f2(a1)))+P1(f328(f328(f242(a1),f439(x81801,x81802,x81803)),f2(a1))) % 167.77/167.50 [8366]E(f328(f328(f80(a1),f328(f328(f81(a1),x83661),f443(x83662,x83663,x83661))),f439(x83662,x83663,x83661)),x83662)+P1(f328(f328(x83663,f328(f328(f40(a1),x83662),x83661)),f46(a1,x83662,x83661)))+~P1(f328(f328(f243(a1),x83661),f2(a1))) % 167.77/167.50 [8609]~P1(f328(f328(x86091,f443(x86092,x86091,x86093)),f439(x86092,x86091,x86093)))+P1(f328(f328(x86091,f328(f328(f40(a1),x86092),x86093)),f46(a1,x86092,x86093)))+~P1(f328(f328(f243(a1),x86093),f2(a1))) % 167.77/167.50 [8837]~P105(x88371)+~P15(x88371,x88373)+P15(x88371,f146(x88371,x88371,f5(x88371),x88372,x88373)) % 167.77/167.50 [9344]~P123(x93442)+E(x93441,f2(x93442))+~P1(f328(f328(f242(x93442),f328(f328(f80(x93442),f328(f328(f81(x93442),x93443),x93443)),f328(f328(f81(x93442),x93441),x93441))),f2(x93442))) % 167.77/167.50 [9345]~P123(x93452)+E(x93451,f2(x93452))+~P1(f328(f328(f242(x93452),f328(f328(f80(x93452),f328(f328(f81(x93452),x93451),x93451)),f328(f328(f81(x93452),x93453),x93453))),f2(x93452))) % 167.77/167.50 [10124]~P117(x101241)+~P1(f328(f328(f243(x101241),x101242),f2(x101241)))+P1(f328(f328(f243(x101241),f328(f328(f253(x101241),x101242),f328(a116,f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x101243)))),f2(x101241))) % 167.77/167.50 [10132]~P117(x101322)+E(x101321,f2(x101322))+~P1(f328(f328(f242(x101322),f328(f328(f80(x101322),f328(f328(f253(x101322),x101323),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x101322),x101321),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f2(x101322))) % 167.77/167.50 [10133]~P117(x101332)+E(x101331,f2(x101332))+~P1(f328(f328(f242(x101332),f328(f328(f80(x101332),f328(f328(f253(x101332),x101331),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x101332),x101333),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f2(x101332))) % 167.77/167.50 [4757]~E(x47572,x47573)+~P66(x47571)+E(f328(f328(f22(x47571),x47572),x47573),f2(x47571)) % 167.77/167.50 [4758]~E(x47582,x47583)+~P74(x47581)+E(f328(f328(f22(x47581),x47582),x47583),f2(x47581)) % 167.77/167.50 [4771]~P140(x47711)+~E(x47713,f2(x47711))+E(f328(f328(f80(x47711),x47712),x47713),x47712) % 167.77/167.50 [4788]~P137(x47881)+~E(x47883,f2(x47881))+E(f328(f328(f81(x47881),x47882),x47883),f2(x47881)) % 167.77/167.50 [4789]~P137(x47891)+~E(x47892,f2(x47891))+E(f328(f328(f81(x47891),x47892),x47893),f2(x47891)) % 167.77/167.50 [4810]~E(x48103,f117(x48101))+~E(x48102,f117(x48101))+E(f328(f328(f125(x48101),x48102),x48103),f117(x48101)) % 167.77/167.50 [4897]~P140(x48972)+E(x48971,f2(x48972))+~E(f328(f328(f80(x48972),x48973),x48971),x48973) % 167.77/167.50 [4898]~P74(x48981)+~E(x48982,f328(f79(x48981),x48983))+E(f328(f328(f80(x48981),x48982),x48983),f2(x48981)) % 167.77/167.50 [4905]E(x49051,f117(x49052))+E(x49053,f2(a872))+~E(f328(f328(f173(x49052),x49053),x49051),f117(x49052)) % 167.77/167.50 [4911]~P66(x49113)+E(x49111,x49112)+~E(f328(f328(f22(x49113),x49111),x49112),f2(x49113)) % 167.77/167.50 [4912]~P74(x49123)+E(x49121,x49122)+~E(f328(f328(f22(x49123),x49121),x49122),f2(x49123)) % 167.77/167.50 [4921]~P139(x49212)+E(x49211,f2(x49212))+~E(f328(f328(f253(x49212),x49211),x49213),f2(x49212)) % 167.77/167.50 [4922]~P64(x49222)+E(x49221,f192(x49222))+~E(f328(f328(f114(x49222),x49223),x49221),f192(x49222)) % 167.77/167.50 [4923]~P64(x49232)+E(x49231,f192(x49232))+~E(f328(f328(f114(x49232),x49231),x49233),f192(x49232)) % 167.77/167.50 [4924]~P97(x49242)+E(x49241,f251(x49242))+~E(f328(f328(f105(x49242),x49243),x49241),f251(x49242)) % 167.77/167.50 [4925]~P97(x49252)+E(x49251,f251(x49252))+~E(f328(f328(f105(x49252),x49251),x49253),f251(x49252)) % 167.77/167.50 [4991]~P74(x49912)+E(x49911,f328(f79(x49912),x49913))+~E(f328(f328(f80(x49912),x49911),x49913),f2(x49912)) % 167.77/167.50 [4992]~P74(x49921)+E(f328(f79(x49921),x49922),x49923)+~E(f328(f328(f80(x49921),x49922),x49923),f2(x49921)) % 167.77/167.50 [4994]~E(x49942,x49943)+~P106(x49941)+P1(f328(f328(f242(x49941),x49942),x49943)) % 167.77/167.50 [4996]~E(x49962,x49963)+~P107(x49961)+P1(f328(f328(f242(x49961),x49962),x49963)) % 167.77/167.50 [4997]~E(x49972,x49973)+~P93(x49971)+P1(f328(f328(f91(x49971),x49972),x49973)) % 167.77/167.50 [5094]~P119(x50941)+~E(x50942,f328(f79(x50941),x50943))+E(f328(f328(f81(x50941),x50942),x50942),f328(f328(f81(x50941),x50943),x50943)) % 167.77/167.50 [5102]~P105(x51021)+~P15(x51021,x51023)+P15(x51021,f328(f328(f173(x51021),x51022),x51023)) % 167.77/167.50 [5103]~P105(x51031)+~P15(x51031,x51033)+P15(x51031,f328(f328(f135(x51031),x51032),x51033)) % 167.77/167.50 [5141]E(x51411,x51412)+E(x51413,f2(a872))+~E(f328(f328(f81(a872),x51413),x51411),f328(f328(f81(a872),x51413),x51412)) % 167.77/167.50 [5142]E(x51421,x51422)+E(x51423,f2(a872))+~E(f328(f328(f81(a872),x51421),x51423),f328(f328(f81(a872),x51422),x51423)) % 167.77/167.50 [5223]~E(x52232,x52233)+~P107(x52231)+E(f299(x52231,x52232,x52233),f328(f328(f306(x52231),x52232),f192(f879(x52231,a867)))) % 167.77/167.50 [5265]E(x52651,x52652)+~P93(x52653)+~P1(f328(f328(f91(x52653),x52651),x52652)) % 167.77/167.50 [5276]~E(x52761,x52762)+~P105(x52763)+~P1(f328(f328(f243(x52763),x52761),x52762)) % 167.77/167.50 [5277]~E(x52771,x52772)+~P107(x52773)+~P1(f328(f328(f243(x52773),x52771),x52772)) % 167.77/167.50 [5287]~P107(x52871)+E(f328(f298(x52871,x52872),x52873),f192(f879(x52871,a867)))+P1(f328(f328(f243(x52871),x52872),x52873)) % 167.77/167.50 [5334]~P107(x53341)+E(f301(x53341,x53342,x53343),f192(f879(x53341,a867)))+P1(f328(f328(f243(x53341),x53342),x53343)) % 167.77/167.50 [5335]~P107(x53351)+E(f299(x53351,x53352,x53353),f192(f879(x53351,a867)))+P1(f328(f328(f242(x53351),x53352),x53353)) % 167.77/167.50 [5336]~P107(x53361)+E(f192(f879(x53361,a867)),f301(x53361,x53362,x53363))+P1(f328(f328(f243(x53361),x53362),x53363)) % 167.77/167.50 [5337]~P107(x53371)+E(f192(f879(x53371,a867)),f299(x53371,x53372,x53373))+P1(f328(f328(f242(x53371),x53372),x53373)) % 167.77/167.50 [5345]~P99(x53451)+~E(f328(f328(f114(x53451),x53452),x53453),x53453)+P1(f328(f328(f242(x53451),x53452),x53453)) % 167.77/167.50 [5346]~P100(x53461)+~E(f328(f328(f105(x53461),x53462),x53463),x53462)+P1(f328(f328(f242(x53461),x53462),x53463)) % 167.77/167.50 [5347]~P105(x53471)+~E(f328(f328(f240(x53471),x53472),x53473),x53472)+P1(f328(f328(f242(x53471),x53472),x53473)) % 167.77/167.50 [5348]~P105(x53481)+~E(f328(f328(f241(x53481),x53482),x53483),x53483)+P1(f328(f328(f242(x53481),x53482),x53483)) % 167.77/167.50 [5368]~P105(x53681)+P15(x53681,x53682)+~P15(x53681,f328(f328(f148(x53681),x53683),x53682)) % 167.77/167.50 [5369]~P105(x53691)+P15(x53691,x53692)+~P15(x53691,f328(f328(f125(x53691),x53693),x53692)) % 167.77/167.50 [5370]~P105(x53701)+P15(x53701,x53702)+~P15(x53701,f328(f328(f125(x53701),x53702),x53703)) % 167.77/167.50 [5438]~P105(x54381)+P1(f328(f328(f242(x54381),x54383),x54382))+P1(f328(f328(f243(x54381),x54382),x54383)) % 167.77/167.50 [5440]~P105(x54401)+P1(f328(f328(f242(x54401),x54403),x54402))+P1(f328(f328(f242(x54401),x54402),x54403)) % 167.77/167.50 [5478]~P99(x54781)+E(f328(f328(f114(x54781),x54782),x54783),x54782)+~P1(f328(f328(f242(x54781),x54783),x54782)) % 167.77/167.50 [5480]~P99(x54801)+E(f328(f328(f114(x54801),x54802),x54803),x54803)+~P1(f328(f328(f242(x54801),x54802),x54803)) % 167.77/167.50 [5481]~P100(x54811)+E(f328(f328(f105(x54811),x54812),x54813),x54813)+~P1(f328(f328(f242(x54811),x54813),x54812)) % 167.77/167.50 [5483]~P100(x54831)+E(f328(f328(f105(x54831),x54832),x54833),x54832)+~P1(f328(f328(f242(x54831),x54832),x54833)) % 167.77/167.50 [5484]~P105(x54841)+E(f328(f328(f240(x54841),x54842),x54843),x54843)+~P1(f328(f328(f242(x54841),x54843),x54842)) % 167.77/167.50 [5486]~P105(x54861)+E(f328(f328(f240(x54861),x54862),x54863),x54862)+~P1(f328(f328(f242(x54861),x54862),x54863)) % 167.77/167.50 [5487]~P105(x54871)+E(f328(f328(f241(x54871),x54872),x54873),x54872)+~P1(f328(f328(f242(x54871),x54873),x54872)) % 167.77/167.50 [5489]~P105(x54891)+E(f328(f328(f241(x54891),x54892),x54893),x54893)+~P1(f328(f328(f242(x54891),x54892),x54893)) % 167.77/167.50 [5496]~P120(x54962)+E(x54961,f2(x54962))+E(f328(f328(f286(x54962),f328(f79(x54962),x54963)),f328(f79(x54962),x54961)),f328(f328(f286(x54962),x54963),x54961)) % 167.77/167.50 [5541]~P107(x55411)+E(f328(f298(x55411,x55412),x55413),f192(f879(x55411,a867)))+~P1(f328(f328(f242(x55411),x55413),x55412)) % 167.77/167.50 [5574]~P107(x55741)+E(f302(x55741,x55742,x55743),f192(f879(x55741,a867)))+~P1(f328(f328(f242(x55741),x55743),x55742)) % 167.77/167.50 [5575]~P107(x55751)+E(f301(x55751,x55752,x55753),f192(f879(x55751,a867)))+~P1(f328(f328(f242(x55751),x55753),x55752)) % 167.77/167.50 [5576]~P107(x55761)+E(f299(x55761,x55762,x55763),f192(f879(x55761,a867)))+~P1(f328(f328(f243(x55761),x55763),x55762)) % 167.77/167.50 [5627]~E(f328(f328(f22(a872),x56271),x56273),x56272)+E(x56271,f328(f328(f80(a872),x56272),x56273))+~P1(f328(f328(f242(a872),x56273),x56271)) % 167.77/167.50 [5628]~E(x56281,f328(f328(f80(a872),x56283),x56282))+E(f328(f328(f22(a872),x56281),x56282),x56283)+~P1(f328(f328(f242(a872),x56282),x56281)) % 167.77/167.50 [5674]~P1(f328(x56741,x56743))+P1(f328(x56741,f367(x56741,x56742)))+~P1(f328(f328(f243(a872),x56743),x56742)) % 167.77/167.50 [5675]~P1(f328(x56751,x56753))+P1(f328(x56751,f388(x56751,x56752)))+~P1(f328(f328(f242(a872),x56753),x56752)) % 167.77/167.50 [5683]~P107(x56831)+~E(f328(f298(x56831,x56832),x56833),f192(f879(x56831,a867)))+~P1(f328(f328(f243(x56831),x56832),x56833)) % 167.77/167.50 [5688]~P106(x56881)+~P1(f328(f328(f243(x56881),x56882),x56883))+P1(f328(f328(f242(x56881),x56882),x56883)) % 167.77/167.50 [5690]~P107(x56901)+~P1(f328(f328(f243(x56901),x56902),x56903))+P1(f328(f328(f242(x56901),x56902),x56903)) % 167.77/167.50 [5798]~P107(x57981)+~E(f301(x57981,x57982,x57983),f192(f879(x57981,a867)))+~P1(f328(f328(f243(x57981),x57982),x57983)) % 167.77/167.50 [5799]~P107(x57991)+~E(f299(x57991,x57992,x57993),f192(f879(x57991,a867)))+~P1(f328(f328(f242(x57991),x57992),x57993)) % 167.77/167.50 [5800]~P107(x58001)+~E(f192(f879(x58001,a867)),f301(x58001,x58002,x58003))+~P1(f328(f328(f243(x58001),x58002),x58003)) % 167.77/167.50 [5801]~P107(x58011)+~E(f192(f879(x58011,a867)),f299(x58011,x58012,x58013))+~P1(f328(f328(f242(x58011),x58012),x58013)) % 167.77/167.50 [5809]P1(f328(x58091,x58092))+~P1(f328(x58091,f368(x58091,x58093)))+~P1(f328(f328(f243(a872),x58092),x58093)) % 167.77/167.50 [5810]P1(f328(x58101,x58102))+~P1(f328(x58101,f395(x58101,x58103)))+~P1(f328(f328(f242(a872),x58102),x58103)) % 167.77/167.50 [5818]~E(x58181,f328(a116,x58183))+P1(f328(f328(f243(a872),x58181),f328(a116,x58182)))+~P1(f328(f328(f243(a872),x58183),x58182)) % 167.77/167.50 [5834]E(x58341,x58342)+~E(f328(f328(f81(a872),x58343),x58341),f328(f328(f81(a872),x58343),x58342))+~P1(f328(f328(f243(a872),f2(a872)),x58343)) % 167.77/167.50 [5892]E(f328(x58921,f849(x58921,x58922,x58923)),f78(a872))+~E(f328(f328(f6(x58923,a872),x58921),x58922),f78(a872))+~P1(f328(f38(x58923),x58922)) % 167.77/167.50 [5904]~P4(x59041)+P1(f328(f328(f242(x59041),x59042),f41(x59041,x59043)))+~P1(f328(f328(f330(x59041),x59042),x59043)) % 167.77/167.50 [5930]~P105(x59301)+~P1(f328(f328(f243(x59301),x59303),x59302))+~P1(f328(f328(f243(x59301),x59302),x59303)) % 167.77/167.50 [5933]~P105(x59331)+~P1(f328(f328(f242(x59331),x59333),x59332))+~P1(f328(f328(f243(x59331),x59332),x59333)) % 167.77/167.50 [5937]~P106(x59371)+~P1(f328(f328(f243(x59371),x59373),x59372))+~P1(f328(f328(f243(x59371),x59372),x59373)) % 167.77/167.50 [5938]~P106(x59381)+~P1(f328(f328(f242(x59381),x59383),x59382))+~P1(f328(f328(f243(x59381),x59382),x59383)) % 167.77/167.50 [5939]~P107(x59391)+~P1(f328(f328(f243(x59391),x59393),x59392))+~P1(f328(f328(f243(x59391),x59392),x59393)) % 167.77/167.50 [5965]~E(f328(x59652,f850(x59652,x59653,x59651)),f2(a872))+E(f328(f328(f6(x59651,a872),x59652),x59653),f2(a872))+~P1(f328(f38(x59651),x59653)) % 167.77/167.50 [5966]~E(f328(x59662,f347(x59662,x59663,x59661)),f78(a872))+E(f328(f328(f9(x59661,a872),x59662),x59663),f78(a872))+~P1(f328(f38(x59661),x59663)) % 167.77/167.50 [5979]~P108(x59791)+~P1(f328(f328(f243(x59791),x59793),x59792))+P1(f328(f328(f330(x59791),x59792),f328(f300(x59791),x59793))) % 167.77/167.50 [5980]~P108(x59801)+~P1(f328(f328(f242(x59801),x59803),x59802))+P1(f328(f328(f330(x59801),x59802),f328(f250(x59801),x59803))) % 167.77/167.50 [5981]~P108(x59811)+~P1(f328(f328(f243(x59811),x59812),x59813))+P1(f328(f328(f330(x59811),x59812),f328(f249(x59811),x59813))) % 167.77/167.50 [5982]~P108(x59821)+~P1(f328(f328(f242(x59821),x59822),x59823))+P1(f328(f328(f330(x59821),x59822),f328(f297(x59821),x59823))) % 167.77/167.50 [5994]E(f328(x59941,f851(x59941,x59942,x59943)),f328(a116,f2(a872)))+~E(f328(f328(f6(x59943,a872),x59941),x59942),f328(a116,f2(a872)))+~P1(f328(f38(x59943),x59942)) % 167.77/167.50 [6077]~P4(x60771)+~P1(f328(f328(f330(x60771),x60773),x60772))+P1(f328(f328(f242(x60771),f42(x60771,x60772)),x60773)) % 167.77/167.50 [6094]~P1(f328(f328(f242(a872),x60941),x60943))+P1(f328(f328(f242(a872),x60941),x60942))+~P1(f328(f328(f242(a872),x60943),x60942)) % 167.77/167.50 [6095]~P1(f328(f328(f242(a1),x60951),x60953))+P1(f328(f328(f242(a1),x60951),x60952))+~P1(f328(f328(f242(a1),x60953),x60952)) % 167.77/167.50 [6112]~P108(x61121)+~P1(f328(f328(f330(x61121),x61123),f328(f300(x61121),x61122)))+P1(f328(f328(f243(x61121),x61122),x61123)) % 167.77/167.50 [6113]~P108(x61131)+~P1(f328(f328(f330(x61131),x61132),f328(f249(x61131),x61133)))+P1(f328(f328(f243(x61131),x61132),x61133)) % 167.77/167.50 [6114]~P108(x61141)+~P1(f328(f328(f330(x61141),x61143),f328(f250(x61141),x61142)))+P1(f328(f328(f242(x61141),x61142),x61143)) % 167.77/167.50 [6115]~P108(x61151)+~P1(f328(f328(f330(x61151),x61152),f328(f297(x61151),x61153)))+P1(f328(f328(f242(x61151),x61152),x61153)) % 167.77/167.50 [6240]P1(f328(x62401,x62402))+~P1(f328(x62401,f588(x62401)))+~P1(f328(f328(f330(x62403),x62402),f251(f879(x62403,a867)))) % 167.77/167.50 [6339]~P62(x63391)+P1(f328(f328(f243(x63391),f2(x63391)),f433(x63393,x63392,x63391)))+P1(f328(f328(f242(x63391),x63392),x63393)) % 167.77/167.50 [6406]~P77(x64061)+~P1(f328(f328(f243(x64061),x64063),f328(f79(x64061),x64062)))+P1(f328(f328(f243(x64061),x64062),f328(f79(x64061),x64063))) % 167.77/167.50 [6408]~P77(x64081)+~P1(f328(f328(f242(x64081),x64083),f328(f79(x64081),x64082)))+P1(f328(f328(f242(x64081),x64082),f328(f79(x64081),x64083))) % 167.77/167.50 [6420]~P1(f328(f328(f243(a872),x64201),x64203))+~P1(f328(f328(f243(a872),x64203),x64202))+P1(f328(f328(f243(a872),f328(a116,x64201)),x64202)) % 167.77/167.50 [6447]~P117(x64471)+P1(f328(f328(f243(x64471),f328(f106(x64471),x64472)),f328(f106(x64471),x64473)))+~P1(f328(f328(f243(a1),x64472),x64473)) % 167.77/167.50 [6448]~P116(x64481)+P1(f328(f328(f243(x64481),f328(f104(x64481),x64482)),f328(f104(x64481),x64483)))+~P1(f328(f328(f243(a872),x64482),x64483)) % 167.77/167.50 [6449]~P116(x64491)+P1(f328(f328(f242(x64491),f328(f104(x64491),x64492)),f328(f104(x64491),x64493)))+~P1(f328(f328(f242(a872),x64492),x64493)) % 167.77/167.50 [6450]~P117(x64501)+P1(f328(f328(f242(x64501),f328(f106(x64501),x64502)),f328(f106(x64501),x64503)))+~P1(f328(f328(f242(a1),x64502),x64503)) % 167.77/167.50 [6456]~P105(x64561)+E(f328(f328(f114(f879(x64561,a867)),f328(f249(x64561),x64562)),f328(f298(x64561,x64562),x64563)),f328(f249(x64561),x64563))+~P1(f328(f328(f242(x64561),x64562),x64563)) % 167.77/167.50 [6485]~P77(x64851)+~P1(f328(f328(f243(x64851),x64853),x64852))+P1(f328(f328(f243(x64851),f328(f79(x64851),x64852)),f328(f79(x64851),x64853))) % 167.77/167.50 [6487]~P77(x64871)+~P1(f328(f328(f242(x64871),x64873),x64872))+P1(f328(f328(f242(x64871),f328(f79(x64871),x64872)),f328(f79(x64871),x64873))) % 167.77/167.50 [6489]~P94(x64891)+~P1(f328(f328(f242(x64891),x64893),x64892))+P1(f328(f328(f242(x64891),f328(f79(x64891),x64892)),f328(f79(x64891),x64893))) % 167.77/167.50 [6521]~P105(x65211)+E(f328(f328(f114(f879(x65211,a867)),f328(f249(x65211),x65212)),f299(x65211,x65212,x65213)),f328(f297(x65211),x65213))+~P1(f328(f328(f242(x65211),x65212),x65213)) % 167.77/167.50 [6522]~P105(x65221)+E(f328(f328(f114(f879(x65221,a867)),f328(f297(x65221),x65222)),f302(x65221,x65222,x65223)),f328(f249(x65221),x65223))+~P1(f328(f328(f243(x65221),x65222),x65223)) % 167.77/167.50 [6523]~P105(x65231)+E(f328(f328(f114(f879(x65231,a867)),f328(f297(x65231),x65232)),f301(x65231,x65232,x65233)),f328(f297(x65231),x65233))+~P1(f328(f328(f242(x65231),x65232),x65233)) % 167.77/167.50 [6557]~P105(x65571)+E(f328(f328(f114(f879(x65571,a867)),f328(f298(x65571,x65572),x65573)),f328(f250(x65571),x65573)),f328(f250(x65571),x65572))+~P1(f328(f328(f242(x65571),x65572),x65573)) % 167.77/167.50 [6713]~P105(x67131)+E(f328(f328(f114(f879(x67131,a867)),f302(x67131,x67132,x67133)),f328(f250(x67131),x67133)),f328(f300(x67131),x67132))+~P1(f328(f328(f243(x67131),x67132),x67133)) % 167.77/167.50 [6714]~P105(x67141)+E(f328(f328(f114(f879(x67141,a867)),f301(x67141,x67142,x67143)),f328(f300(x67141),x67143)),f328(f300(x67141),x67142))+~P1(f328(f328(f242(x67141),x67142),x67143)) % 167.77/167.50 [6715]~P105(x67151)+E(f328(f328(f114(f879(x67151,a867)),f299(x67151,x67152,x67153)),f328(f300(x67151),x67153)),f328(f250(x67151),x67152))+~P1(f328(f328(f242(x67151),x67152),x67153)) % 167.77/167.50 [6733]P1(f328(x67331,x67332))+~P1(f328(f328(f242(a872),x67332),x67333))+P1(f328(f328(f330(a872),f395(x67331,x67333)),f299(a872,f2(a872),x67333))) % 167.77/167.50 [6767]E(x67671,x67672)+~E(f328(f328(f162(x67673),x67671),f654(x67673,x67672,x67671)),f328(f328(f162(x67673),x67672),f654(x67673,x67672,x67671)))+~E(f328(f193(f873(x67673)),x67671),f328(f193(f873(x67673)),x67672)) % 167.77/167.50 [6772]~E(x67723,f328(f328(f40(a872),x67721),x67722))+~P1(f328(f328(f243(a872),f2(a872)),x67722))+P1(f328(f328(f243(a872),x67721),f328(f328(f81(a872),x67722),f328(a116,x67723)))) % 167.77/167.50 [6789]~P1(f328(x67891,x67893))+~P1(f328(f328(f242(a872),x67893),x67892))+P1(f328(f328(f330(a872),f388(x67891,x67892)),f299(a872,f2(a872),x67892))) % 167.77/167.50 [6828]~P1(f328(x68281,x68283))+P1(f328(x68281,f396(x68281,x68282)))+~P1(f328(f328(f330(a872),x68283),f299(a872,f2(a872),x68282))) % 167.77/167.50 [6848]~P116(x68483)+~P1(f328(f328(f243(x68483),f328(f104(x68483),x68481)),f328(f104(x68483),x68482)))+P1(f328(f328(f243(a872),x68481),x68482)) % 167.77/167.50 [6849]~P117(x68493)+~P1(f328(f328(f243(x68493),f328(f106(x68493),x68491)),f328(f106(x68493),x68492)))+P1(f328(f328(f243(a1),x68491),x68492)) % 167.77/167.50 [6850]~P116(x68503)+~P1(f328(f328(f242(x68503),f328(f104(x68503),x68501)),f328(f104(x68503),x68502)))+P1(f328(f328(f242(a872),x68501),x68502)) % 167.77/167.50 [6851]~P117(x68513)+~P1(f328(f328(f242(x68513),f328(f106(x68513),x68511)),f328(f106(x68513),x68512)))+P1(f328(f328(f242(a1),x68511),x68512)) % 167.77/167.50 [6869]~P116(x68691)+~P1(f328(f328(f243(x68691),f78(x68691)),x68692))+P1(f328(f328(f243(x68691),f78(x68691)),f328(f328(f253(x68691),x68692),f328(a116,x68693)))) % 167.77/167.50 [6871]~P77(x68711)+~P1(f328(f328(f243(x68711),f328(f79(x68711),x68713)),f328(f79(x68711),x68712)))+P1(f328(f328(f243(x68711),x68712),x68713)) % 167.77/167.50 [6872]~P77(x68721)+~P1(f328(f328(f242(x68721),f328(f79(x68721),x68723)),f328(f79(x68721),x68722)))+P1(f328(f328(f242(x68721),x68722),x68723)) % 167.77/167.50 [6873]~P94(x68731)+~P1(f328(f328(f242(x68731),f328(f79(x68731),x68733)),f328(f79(x68731),x68732)))+P1(f328(f328(f242(x68731),x68732),x68733)) % 167.77/167.50 [6897]P1(f328(x68971,x68972))+~P1(f328(x68971,f397(x68971,x68973)))+~P1(f328(f328(f330(a872),x68972),f299(a872,f2(a872),x68973))) % 167.77/167.50 [6916]~P62(x69161)+P1(f328(f328(f243(x69161),f433(x69163,x69162,x69161)),f78(x69161)))+P1(f328(f328(f242(x69161),x69162),x69163)) % 167.77/167.50 [6935]~E(f46(a872,x69353,x69352),f46(a872,x69351,x69352))+E(f328(f328(f80(a872),x69351),f328(f328(f81(a872),x69352),f465(x69351,x69352,x69353))),x69353)+~P1(f328(f328(f242(a872),x69351),x69353)) % 167.77/167.50 [6954]E(f328(x69541,f760(x69541,x69542,x69543)),f205(x69542))+~P1(f328(f38(x69543),f182(x69543,x69542,x69541)))+P1(f328(f38(x69543),f251(f879(x69543,a867)))) % 167.77/167.50 [6993]E(f328(f328(f6(x69931,a872),x69932),x69933),f2(a872))+~P1(f328(f38(x69931),x69933))+P1(f328(f328(f330(x69931),f850(x69932,x69933,x69931)),x69933)) % 167.77/167.50 [6994]E(f328(f328(f9(x69941,a872),x69942),x69943),f78(a872))+~P1(f328(f38(x69941),x69943))+P1(f328(f328(f330(x69941),f347(x69942,x69943,x69941)),x69943)) % 167.77/167.50 [7016]~P105(x70161)+~P1(f328(f328(f243(x70161),x70162),x70163))+P1(f328(f328(f243(f879(x70161,a867)),f328(f249(x70161),x70162)),f328(f249(x70161),x70163))) % 167.77/167.50 [7017]~P105(x70171)+~P1(f328(f328(f242(x70171),x70172),x70173))+P1(f328(f328(f242(f879(x70171,a867)),f328(f249(x70171),x70172)),f328(f249(x70171),x70173))) % 167.77/167.50 [7018]~P105(x70181)+~P1(f328(f328(f242(x70181),x70183),x70182))+P1(f328(f328(f242(f879(x70181,a867)),f328(f300(x70181),x70182)),f328(f300(x70181),x70183))) % 167.77/167.50 [7019]~P107(x70191)+~P1(f328(f328(f242(x70191),x70193),x70192))+P1(f328(f328(f242(f879(x70191,a867)),f328(f250(x70191),x70192)),f328(f250(x70191),x70193))) % 167.77/167.50 [7020]~P107(x70201)+~P1(f328(f328(f242(x70201),x70202),x70203))+P1(f328(f328(f242(f879(x70201,a867)),f328(f297(x70201),x70202)),f328(f297(x70201),x70203))) % 167.77/167.50 [7028]~P4(x70281)+P1(f328(f328(f242(x70281),x70282),f42(x70281,x70283)))+P1(f328(f328(f330(x70281),f348(x70283,x70282,x70281)),x70283)) % 167.77/167.50 [7034]~P77(x70341)+P1(f328(f328(f243(x70341),f328(f328(f22(x70341),x70342),x70343)),f2(x70341)))+~P1(f328(f328(f243(x70341),x70342),x70343)) % 167.77/167.50 [7035]~P77(x70351)+P1(f328(f328(f242(x70351),f328(f328(f22(x70351),x70352),x70353)),f2(x70351)))+~P1(f328(f328(f242(x70351),x70352),x70353)) % 167.77/167.50 [7077]P1(f328(x70771,x70772))+P1(f328(f328(f242(a872),f397(x70771,x70773)),x70773))+~P1(f328(f328(f330(a872),x70772),f299(a872,f2(a872),x70773))) % 167.77/167.50 [7117]~E(f328(f328(f6(x71171,a872),x71172),x71173),f78(a872))+~P1(f328(f38(x71171),x71173))+P1(f328(f328(f330(x71171),f849(x71172,x71173,x71171)),x71173)) % 167.77/167.50 [7118]~P1(f328(x71181,x71183))+P1(f328(f328(f242(a872),f396(x71181,x71182)),x71182))+~P1(f328(f328(f330(a872),x71183),f299(a872,f2(a872),x71182))) % 167.77/167.50 [7158]~P4(x71581)+P1(f328(f328(f330(x71581),f349(x71583,x71582,x71581)),x71582))+P1(f328(f328(f242(x71581),f41(x71581,x71582)),x71583)) % 167.77/167.50 [7191]~E(f328(f328(f6(x71911,a872),x71912),x71913),f328(a116,f2(a872)))+~P1(f328(f38(x71911),x71913))+P1(f328(f328(f330(x71911),f851(x71912,x71913,x71911)),x71913)) % 167.77/167.50 [7202]E(x72021,f2(a872))+P1(f328(x72022,f46(a872,x72023,x72021)))+P1(f328(f328(f243(a872),f457(x72021,x72023,x72022)),x72021)) % 167.77/167.50 [7307]~P1(f328(x73071,x73072))+P1(f328(x73071,f46(a872,x73072,x73073)))+P1(f328(f328(f243(a872),f457(x73073,x73072,x73071)),x73073)) % 167.77/167.50 [7429]E(x74291,f117(x74292))+~P1(f328(f328(f330(f873(x74292)),x74291),f158(x74292,x74293)))+P1(f328(f328(f330(x74292),f705(x74293,x74291,x74292)),x74293)) % 167.77/167.50 [7451]~P105(x74511)+E(f328(f328(f114(f879(x74511,a867)),f328(f328(f306(x74511),x74512),f192(f879(x74511,a867)))),f302(x74511,x74512,x74513)),f328(f298(x74511,x74512),x74513))+~P1(f328(f328(f243(x74511),x74512),x74513)) % 167.77/167.50 [7477]~P105(x74771)+E(f328(f328(f114(f879(x74771,a867)),f328(f328(f306(x74771),x74772),f192(f879(x74771,a867)))),f301(x74771,x74772,x74773)),f299(x74771,x74772,x74773))+~P1(f328(f328(f242(x74771),x74772),x74773)) % 167.77/167.50 [7585]~P105(x75851)+P1(f328(f328(f243(x75851),x75852),x75853))+~P1(f328(f328(f243(f879(x75851,a867)),f328(f249(x75851),x75852)),f328(f249(x75851),x75853))) % 167.77/167.50 [7586]~P105(x75861)+P1(f328(f328(f242(x75861),x75862),x75863))+~P1(f328(f328(f242(f879(x75861,a867)),f328(f300(x75861),x75863)),f328(f300(x75861),x75862))) % 167.77/167.50 [7587]~P107(x75871)+P1(f328(f328(f242(x75871),x75872),x75873))+~P1(f328(f328(f242(f879(x75871,a867)),f328(f250(x75871),x75873)),f328(f250(x75871),x75872))) % 167.77/167.50 [7588]~P105(x75881)+P1(f328(f328(f242(x75881),x75882),x75883))+~P1(f328(f328(f242(f879(x75881,a867)),f328(f249(x75881),x75882)),f328(f249(x75881),x75883))) % 167.77/167.50 [7589]~P107(x75891)+P1(f328(f328(f242(x75891),x75892),x75893))+~P1(f328(f328(f242(f879(x75891,a867)),f328(f297(x75891),x75892)),f328(f297(x75891),x75893))) % 167.77/167.50 [7612]~P77(x76121)+~P1(f328(f328(f243(x76121),f328(f328(f22(x76121),x76122),x76123)),f2(x76121)))+P1(f328(f328(f243(x76121),x76122),x76123)) % 167.77/167.50 [7613]~P77(x76131)+~P1(f328(f328(f242(x76131),f328(f328(f22(x76131),x76132),x76133)),f2(x76131)))+P1(f328(f328(f242(x76131),x76132),x76133)) % 167.77/167.50 [7772]E(x77721,f2(a872))+~E(f328(f139(a872,a872,f80(a872),x77722),x77723),f2(a872))+~P1(f328(f328(f330(a872),x77721),f328(f170(a872),x77723))) % 167.77/167.50 [7776]~P4(x77761)+~P1(f328(f328(f242(x77761),f349(x77763,x77762,x77761)),x77763))+P1(f328(f328(f242(x77761),f41(x77761,x77762)),x77763)) % 167.77/167.50 [7932]P1(f328(f328(f242(a1),f2(a1)),f449(x79321,x79322,x79323)))+P1(f328(f328(x79322,f328(f328(f40(a1),x79321),x79323)),f46(a1,x79321,x79323)))+~P1(f328(f328(f243(a1),f2(a1)),x79323)) % 167.77/167.50 [8018]E(x80181,x80182)+~E(f328(f193(f873(x80183)),x80181),f328(f193(f873(x80183)),x80182))+~P1(f328(f328(f267(x80183,x80183,a867),a325),f679(x80183,x80181,x80182))) % 167.77/167.50 [8087]~P38(x80872,x80873)+E(x80871,f192(f879(x80872,a867)))+~P1(f328(f328(f242(f879(x80872,a867)),x80871),f328(f282(x80872,x80872,x80873),x80871))) % 167.77/167.50 [8158]P40(x81581,x81582,x81583)+P1(f328(f328(f330(x81581),f579(x81583,x81582,x81581)),x81582))+P1(f328(f328(f330(f878(x81581,x81581)),f580(x81583,x81582,x81581)),x81583)) % 167.77/167.50 [8184]P1(f328(f328(x81842,f328(f328(f40(a1),x81841),x81843)),f46(a1,x81841,x81843)))+~P1(f328(f328(f243(a1),f2(a1)),x81843))+P1(f328(f328(f243(a1),f449(x81841,x81842,x81843)),x81843)) % 167.77/167.50 [8213]E(f328(f307(a872,a872,f328(f328(f7(a872,a872,a872),f22(a872)),x82131)),f328(f298(a872,x82132),x82133)),f192(f879(a872,a867)))+P1(f328(f328(f243(a872),x82131),x82133))+P1(f328(f328(f243(a872),x82132),x82133)) % 167.77/167.50 [8319]E(f328(f307(a872,a872,f328(f328(f7(a872,a872,a872),f22(a872)),x83191)),f328(f298(a872,x83192),x83193)),f328(f328(f306(a872),f2(a872)),f192(f879(a872,a867))))+P1(f328(f328(f243(a872),x83191),x83193))+~P1(f328(f328(f243(a872),x83192),x83193)) % 167.77/167.50 [8336]~P105(x83361)+E(f146(x83361,x83361,f5(x83361),x83362,x83363),x83363)+~P1(f328(f328(f330(x83361),x83362),f328(f170(x83361),x83363))) % 167.77/167.50 [8350]P26(x83501,x83501,x83502,x83503)+~P1(f328(f38(x83501),x83503))+~P1(f328(f328(f242(f879(x83501,a867)),x83503),f328(f307(x83501,x83501,x83502),x83503))) % 167.77/167.50 [8373]E(f328(f328(f80(a1),f328(f328(f81(a1),x83731),f445(x83732,x83733,x83731))),f449(x83732,x83733,x83731)),x83732)+P1(f328(f328(x83733,f328(f328(f40(a1),x83732),x83731)),f46(a1,x83732,x83731)))+~P1(f328(f328(f243(a1),f2(a1)),x83731)) % 167.77/167.50 [8615]~P1(f328(f328(x86151,f445(x86152,x86151,x86153)),f449(x86152,x86151,x86153)))+P1(f328(f328(x86151,f328(f328(f40(a1),x86152),x86153)),f46(a1,x86152,x86153)))+~P1(f328(f328(f243(a1),f2(a1)),x86153)) % 167.77/167.50 [9482]~P1(f328(f38(x94821),x94822))+~P1(f328(f328(f330(x94821),x94823),x94822))+P1(f328(f328(f243(a872),f328(f39(x94821),f328(f328(f22(f879(x94821,a867)),x94822),f328(f328(f306(x94821),x94823),f192(f879(x94821,a867)))))),f328(f39(x94821),x94822))) % 167.77/167.50 [10085]P40(x100851,x100852,x100853)+~P1(f328(f328(f267(x100851,x100851,a867),f328(f328(f7(x100851,f879(x100851,a867),f879(x100851,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x100851,a867),f879(x100851,a867)),x100851),f8(a867,a867,x100851)),f328(f328(f8(a867,f879(a867,a867),x100851),a326),f328(f328(f7(x100851,f879(x100851,a867),a867),f330(x100851)),x100852)))),f328(f328(f7(x100851,f879(x100851,a867),a867),f330(x100851)),x100852))),f580(x100853,x100852,x100851)))+P1(f328(f328(f330(x100851),f579(x100853,x100852,x100851)),x100852)) % 167.77/167.50 [5457]~P120(x54572)+E(x54571,f2(x54572))+E(f328(f328(f286(x54572),x54573),f328(f79(x54572),x54571)),f328(f79(x54572),f328(f328(f286(x54572),x54573),x54571))) % 167.77/167.50 [5590]~E(x55903,f192(f879(x55901,a867)))+~E(x55902,f192(f879(x55901,a867)))+E(f328(f328(f114(f879(x55901,a867)),x55902),x55903),f192(f879(x55901,a867))) % 167.77/167.50 [5648]~E(x56483,f2(a872))+~P1(f328(x56481,f2(a872)))+P1(f328(x56481,f328(f328(f40(a872),x56482),x56483))) % 167.77/167.50 [5790]~P63(x57902)+E(x57901,f2(x57902))+E(f328(f328(f286(x57902),f328(f75(x57902),x57903)),f328(f75(x57902),x57901)),f328(f75(x57902),f328(f328(f286(x57902),x57903),x57901))) % 167.77/167.50 [5955]~P1(f328(f38(x59551),x59553))+E(f328(f39(x59551),f328(f328(f306(x59551),x59552),x59553)),f328(a116,f328(f39(x59551),x59553)))+P1(f328(f328(f330(x59551),x59552),x59553)) % 167.77/167.50 [6026]~E(x60262,f2(a872))+P1(f328(x60261,f2(a872)))+~P1(f328(x60261,f328(f328(f40(a872),x60263),x60262))) % 167.77/167.50 [6045]~P1(f328(f38(x60451),x60453))+E(f328(f39(x60451),f328(f328(f306(x60451),x60452),x60453)),f328(f39(x60451),x60453))+~P1(f328(f328(f330(x60451),x60452),x60453)) % 167.77/167.50 [6079]~P1(f328(f38(x60791),x60793))+E(f328(f39(x60791),f328(f328(f306(x60791),x60792),x60793)),f328(f328(f80(a872),f78(a872)),f328(f39(x60791),x60793)))+P1(f328(f328(f330(x60791),x60792),x60793)) % 167.77/167.50 [6202]E(f328(f328(f80(a872),x62021),f852(x62021,x62022,x62023)),x62022)+~P1(f328(x62023,f2(a872)))+P1(f328(x62023,f328(f328(f22(a872),x62022),x62021))) % 167.77/167.50 [6203]E(f328(f328(f80(a872),x62031),f853(x62031,x62032,x62033)),x62032)+~P1(f328(x62033,f2(a872)))+P1(f328(x62033,f328(f328(f22(a872),x62032),x62031))) % 167.77/167.50 [6250]~P4(x62501)+~P1(f328(f38(x62501),x62503))+E(f328(f328(f65(x62501,x62501,f114(x62501)),x62502),x62503),f328(f328(f114(x62501),x62502),f41(x62501,x62503))) % 167.77/167.50 [6251]~P4(x62511)+~P1(f328(f38(x62511),x62513))+E(f328(f328(f65(x62511,x62511,f105(x62511)),x62512),x62513),f328(f328(f105(x62511),x62512),f42(x62511,x62513))) % 167.77/167.50 [6257]~P91(x62571)+~E(f328(f107(x62571),x62572),f328(f107(x62571),x62573))+P31(x62571,f328(f107(x62571),f328(f328(f80(a1),x62572),f328(f79(a1),x62573)))) % 167.77/167.50 [6264]~P138(x62641)+E(f328(f328(f22(x62641),f328(f104(x62641),x62642)),f328(f104(x62641),x62643)),f328(f104(x62641),f328(f328(f22(a872),x62642),x62643)))+~P1(f328(f328(f242(a872),x62643),x62642)) % 167.77/167.50 [6349]E(f328(f328(f80(a872),x63491),f852(x63491,x63492,x63493)),x63492)+P1(f328(f328(f243(a872),x63492),x63491))+P1(f328(x63493,f328(f328(f22(a872),x63492),x63491))) % 167.77/167.50 [6350]E(f328(f328(f80(a872),x63501),f853(x63501,x63502,x63503)),x63502)+P1(f328(f328(f243(a872),x63502),x63501))+P1(f328(x63503,f328(f328(f22(a872),x63502),x63501))) % 167.77/167.50 [6365]~P117(x63651)+E(f328(f328(f81(x63651),f328(f75(x63651),x63652)),x63653),f328(f75(x63651),f328(f328(f81(x63651),x63652),x63653)))+~P1(f328(f328(f242(x63651),f2(x63651)),x63653)) % 167.77/167.50 [6366]~P62(x63661)+E(f328(f328(f286(x63661),f328(f75(x63661),x63662)),x63663),f328(f75(x63661),f328(f328(f286(x63661),x63662),x63663)))+~P1(f328(f328(f243(x63661),f2(x63661)),x63663)) % 167.77/167.50 [6374]~P2(x63741)+~P1(f328(f38(x63741),x63743))+E(f328(f328(f65(x63741,x63741,f114(x63741)),x63742),x63743),f13(x63741,f328(f328(f306(x63741),x63742),x63743))) % 167.77/167.50 [6375]~P2(x63751)+~P1(f328(f38(x63751),x63753))+E(f328(f328(f65(x63751,x63751,f105(x63751)),x63752),x63753),f10(x63751,f328(f328(f306(x63751),x63752),x63753))) % 167.77/167.50 [6376]~P105(x63761)+~P1(f328(f38(x63761),x63763))+E(f328(f328(f65(x63761,x63761,f240(x63761)),x63762),x63763),f14(x63761,f328(f328(f306(x63761),x63762),x63763))) % 167.77/167.50 [6377]~P105(x63771)+~P1(f328(f38(x63771),x63773))+E(f328(f328(f65(x63771,x63771,f241(x63771)),x63772),x63773),f15(x63771,f328(f328(f306(x63771),x63772),x63773))) % 167.77/167.50 [6422]E(x64221,f117(x64222))+~E(f178(x64222,x64223),f117(f873(x64222)))+~P1(f328(f328(f330(f873(x64222)),x64221),f328(f170(f873(x64222)),x64223))) % 167.77/167.50 [6464]~P1(f328(f134(x64641),x64643))+P1(f328(f328(f330(x64641),x64642),f328(f170(x64641),x64643)))+P1(f328(f134(x64641),f328(f328(f148(x64641),x64642),x64643))) % 167.77/167.50 [6475]~P95(x64751)+~P1(f328(f38(x64751),x64753))+E(f328(f64(x64751,f81(x64751)),f328(f328(f306(x64751),x64752),x64753)),f328(f328(f65(x64751,x64751,f81(x64751)),x64752),x64753)) % 167.77/167.50 [6497]~P105(x64971)+~P1(f328(f38(x64971),x64973))+E(f11(x64971,f240(x64971),f328(f328(f306(x64971),x64972),x64973)),f328(f328(f65(x64971,x64971,f240(x64971)),x64972),x64973)) % 167.77/167.50 [6498]~P105(x64981)+~P1(f328(f38(x64981),x64983))+E(f12(x64981,f241(x64981),f328(f328(f306(x64981),x64982),x64983)),f328(f328(f65(x64981,x64981,f241(x64981)),x64982),x64983)) % 167.77/167.50 [6500]P1(f328(x65001,f2(a872)))+~P1(f328(f328(f243(a872),x65002),x65003))+~P1(f328(x65001,f328(f328(f22(a872),x65002),x65003))) % 167.77/167.50 [6518]~P117(x65181)+P1(f328(f328(f243(x65181),x65182),x65183))+~P1(f328(f328(f243(x65181),f328(f75(x65181),x65182)),x65183)) % 167.77/167.50 [6520]~P84(x65201)+P1(f328(f328(f242(x65201),x65202),x65203))+~P1(f328(f328(f242(x65201),f328(f75(x65201),x65202)),x65203)) % 167.77/167.50 [6537]E(x65371,f117(x65372))+E(f328(f138(x65372),f328(f328(f135(x65372),x65373),x65371)),f328(f328(f162(x65372),x65371),x65373))+~P1(f328(f328(f243(a872),x65373),f328(f193(f873(x65372)),x65371))) % 167.77/167.50 [6588]~P1(f328(x65881,x65883))+P1(f328(x65881,f372(x65881,x65882)))+~P1(f328(f328(f330(a872),x65883),f328(f298(a872,f2(a872)),x65882))) % 167.77/167.50 [6610]P1(f328(x66101,x66102))+~P1(f328(f328(f243(a872),x66102),x66103))+P1(f328(f328(f330(a872),f368(x66101,x66103)),f328(f298(a872,f2(a872)),x66103))) % 167.77/167.50 [6627]~P116(x66271)+~P1(f328(f328(f243(x66271),f2(x66271)),x66272))+P1(f328(f328(f243(x66271),f2(x66271)),f328(f328(f253(x66271),x66272),x66273))) % 167.77/167.50 [6628]~P116(x66281)+~P1(f328(f328(f242(x66281),f78(x66281)),x66282))+P1(f328(f328(f242(x66281),f78(x66281)),f328(f328(f253(x66281),x66282),x66283))) % 167.77/167.50 [6630]~P116(x66301)+~P1(f328(f328(f242(x66301),f2(x66301)),x66302))+P1(f328(f328(f242(x66301),f2(x66301)),f328(f328(f253(x66301),x66302),x66303))) % 167.77/167.50 [6654]~P1(f328(x66541,x66543))+~P1(f328(f328(f243(a872),x66543),x66542))+P1(f328(f328(f330(a872),f367(x66541,x66542)),f328(f298(a872,f2(a872)),x66542))) % 167.77/167.50 [6661]P1(f328(f38(x66611),x66612))+~P1(f328(f38(x66611),x66613))+~P1(f328(f328(f242(f879(x66611,a867)),x66612),x66613)) % 167.77/167.50 [6669]P1(f328(x66691,x66692))+~P1(f328(x66691,f370(x66691,x66693)))+~P1(f328(f328(f330(a872),x66692),f328(f298(a872,f2(a872)),x66693))) % 167.77/167.50 [6680]E(x66801,f2(a872))+P1(f328(x66802,f382(x66801,x66803,x66802)))+~P1(f328(x66802,f328(f328(f40(a872),x66803),x66801))) % 167.77/167.50 [6688]~P123(x66882)+E(x66881,f2(x66882))+~E(f328(f328(f80(x66882),f328(f328(f81(x66882),x66883),x66883)),f328(f328(f81(x66882),x66881),x66881)),f2(x66882)) % 167.77/167.50 [6689]~P123(x66892)+E(x66891,f2(x66892))+~E(f328(f328(f80(x66892),f328(f328(f81(x66892),x66891),x66891)),f328(f328(f81(x66892),x66893),x66893)),f2(x66892)) % 167.77/167.50 [6734]E(x67341,f2(a872))+~P1(f328(x67342,f383(x67341,x67343,x67342)))+P1(f328(x67342,f328(f328(f40(a872),x67343),x67341))) % 167.77/167.50 [6739]~P105(x67391)+~P15(x67391,x67393)+P15(x67391,f328(f328(f145(x67391,x67391,f5(x67391)),x67392),x67393)) % 167.77/167.50 [6782]P1(f328(x67821,f382(x67822,x67823,x67821)))+P1(f328(x67821,f2(a872)))+~P1(f328(x67821,f328(f328(f40(a872),x67823),x67822))) % 167.77/167.50 [6788]~P91(x67881)+E(f328(f107(x67881),x67882),f328(f107(x67881),x67883))+~P31(x67881,f328(f107(x67881),f328(f328(f80(a1),x67882),f328(f79(a1),x67883)))) % 167.77/167.50 [6854]E(x68541,f2(a1))+E(x68542,f2(a1))+~P1(f328(f50(x68542,x68542),f328(f328(f263(a1,a1),x68543),x68541))) % 167.77/167.50 [6855]E(x68551,f78(a1))+E(x68552,f2(a1))+~P1(f328(f50(x68552,x68552),f328(f328(f263(a1,a1),x68551),x68553))) % 167.77/167.50 [6870]P1(f328(x68701,x68702))+P1(f328(f328(f243(a872),f370(x68701,x68703)),x68703))+~P1(f328(f328(f330(a872),x68702),f328(f298(a872,f2(a872)),x68703))) % 167.77/167.50 [6892]~P1(f328(x68921,f852(x68923,x68922,x68921)))+~P1(f328(x68921,f2(a872)))+P1(f328(x68921,f328(f328(f22(a872),x68922),x68923))) % 167.77/167.50 [6893]~P1(f328(x68931,f853(x68933,x68932,x68931)))+~P1(f328(x68931,f2(a872)))+P1(f328(x68931,f328(f328(f22(a872),x68932),x68933))) % 167.77/167.50 [6894]~P1(f328(x68941,f383(x68943,x68942,x68941)))+~P1(f328(x68941,f2(a872)))+P1(f328(x68941,f328(f328(f40(a872),x68942),x68943))) % 167.77/167.50 [6912]~P1(f328(x69121,x69123))+P1(f328(f328(f243(a872),f372(x69121,x69122)),x69122))+~P1(f328(f328(f330(a872),x69123),f328(f298(a872,f2(a872)),x69122))) % 167.77/167.50 [6913]E(f328(f328(f22(a872),f328(f328(f22(a872),x69131),x69132)),f328(f328(f22(a872),x69133),x69132)),f328(f328(f22(a872),x69131),x69133))+~P1(f328(f328(f242(a872),x69132),x69131))+~P1(f328(f328(f242(a872),x69132),x69133)) % 167.77/167.50 [6948]~P77(x69481)+~P1(f328(f328(f243(x69481),f328(f79(x69481),x69483)),x69482))+P1(f328(f328(f243(x69481),f328(f79(x69481),x69482)),x69483)) % 167.77/167.50 [6949]~P117(x69491)+~P1(f328(f328(f243(x69491),f328(f75(x69491),x69492)),x69493))+P1(f328(f328(f243(x69491),f328(f79(x69491),x69492)),x69493)) % 167.77/167.50 [6951]~P77(x69511)+~P1(f328(f328(f242(x69511),f328(f79(x69511),x69513)),x69512))+P1(f328(f328(f242(x69511),f328(f79(x69511),x69512)),x69513)) % 167.77/167.50 [6953]~P84(x69531)+~P1(f328(f328(f242(x69531),f328(f75(x69531),x69532)),x69533))+P1(f328(f328(f242(x69531),f328(f79(x69531),x69532)),x69533)) % 167.77/167.50 [6987]~P1(f328(x69873,f852(x69872,x69871,x69873)))+P1(f328(f328(f243(a872),x69871),x69872))+P1(f328(x69873,f328(f328(f22(a872),x69871),x69872))) % 167.77/167.50 [6988]~P1(f328(x69883,f853(x69882,x69881,x69883)))+P1(f328(f328(f243(a872),x69881),x69882))+P1(f328(x69883,f328(f328(f22(a872),x69881),x69882))) % 167.77/167.50 [7038]~E(f835(x70383,x70382,x70381),f836(x70383,x70382,x70381))+E(f328(f328(f105(f879(x70381,a867)),x70382),f41(f879(x70381,a867),x70383)),f192(f879(x70381,a867)))+P1(f328(f328(f330(f879(x70381,a867)),x70382),x70383)) % 167.77/167.50 [7047]~P1(f328(f38(x70471),x70473))+P1(f328(f38(x70471),f42(f879(x70471,a867),x70472)))+~P1(f328(f328(f330(f879(x70471,a867)),x70473),x70472)) % 167.77/167.50 [7106]~P105(x71061)+E(f328(f328(f114(f879(x71061,a867)),f328(f298(x71061,x71062),x71063)),f328(f328(f306(x71061),x71063),f192(f879(x71061,a867)))),f299(x71061,x71062,x71063))+~P1(f328(f328(f242(x71061),x71062),x71063)) % 167.77/167.50 [7107]E(x71071,f2(a872))+P1(f328(f328(f243(a872),f384(x71071,x71073,x71072)),x71071))+P1(f328(x71072,f328(f328(f40(a872),x71073),x71071))) % 167.77/167.50 [7142]E(x71421,x71422)+~P1(f328(f328(f242(f879(x71423,a867)),x71421),x71422))+P1(f328(f328(f243(f879(x71423,a867)),x71421),x71422)) % 167.77/167.50 [7155]E(x71551,x71552)+~E(f328(f193(f873(x71553)),x71551),f328(f193(f873(x71553)),x71552))+P1(f328(f328(f243(a872),f654(x71553,x71551,x71552)),f328(f193(f873(x71553)),x71552))) % 167.77/167.50 [7203]P7(x72031,x72032,x72033)+~E(f328(f261(x72031,x72031),x72033),x72032)+~E(f328(f328(f285(x72031,x72031,x72031),f328(f283(x72031,x72031),x72033)),x72033),x72033) % 167.77/167.50 [7275]~P1(f328(x72751,f2(a872)))+P1(f328(f328(f243(a872),f384(x72753,x72752,x72751)),x72753))+P1(f328(x72751,f328(f328(f40(a872),x72752),x72753))) % 167.77/167.50 [7284]~P105(x72841)+E(f328(f328(f114(f879(x72841,a867)),f302(x72841,x72842,x72843)),f328(f328(f306(x72841),x72843),f192(f879(x72841,a867)))),f301(x72841,x72842,x72843))+~P1(f328(f328(f243(x72841),x72842),x72843)) % 167.77/167.50 [7384]~P1(f328(f38(x73841),x73843))+P1(f328(f328(f243(a872),f328(f39(x73841),x73842)),f328(f39(x73841),x73843)))+~P1(f328(f328(f243(f879(x73841,a867)),x73842),x73843)) % 167.77/167.50 [7385]~P1(f328(f38(x73851),x73853))+P1(f328(f328(f242(a872),f328(f39(x73851),x73852)),f328(f39(x73851),x73853)))+~P1(f328(f328(f242(f879(x73851,a867)),x73852),x73853)) % 167.77/167.50 [7521]E(x75211,x75212)+~P1(f328(f328(f242(f879(x75213,a867)),x75212),x75211))+~P1(f328(f328(f242(f879(x75213,a867)),x75211),x75212)) % 167.77/167.50 [7524]~P105(x75241)+P15(x75241,x75242)+~P15(x75241,f328(f328(f145(x75241,x75241,f5(x75241)),x75243),x75242)) % 167.77/167.50 [7592]~P1(f328(f328(f243(a872),x75923),x75922))+~P1(f328(f328(f243(a872),x75923),x75921))+P1(f328(f328(f243(a872),f328(f328(f22(a872),x75921),x75922)),f328(f328(f22(a872),x75921),x75923))) % 167.77/167.50 [7593]~P1(f328(f328(f243(a872),x75931),x75933))+~P1(f328(f328(f242(a872),x75932),x75931))+P1(f328(f328(f243(a872),f328(f328(f22(a872),x75931),x75932)),f328(f328(f22(a872),x75933),x75932))) % 167.77/167.50 [7610]~P1(f328(f328(f243(a1),x76102),f2(a1)))+~P1(f328(f328(f242(a1),x76103),x76101))+P1(f328(f328(f242(a1),f328(f328(f40(a1),x76101),x76102)),f328(f328(f40(a1),x76103),x76102))) % 167.77/167.50 [7630]~P1(f328(f328(f243(a872),f2(a872)),x76302))+~P1(f328(f328(f243(a872),x76301),x76303))+P1(f328(f328(f243(a872),f328(f328(f81(a872),x76301),x76302)),f328(f328(f81(a872),x76303),x76302))) % 167.77/167.50 [7631]~P1(f328(f328(f243(a872),f2(a872)),x76311))+~P1(f328(f328(f243(a872),x76312),x76313))+P1(f328(f328(f243(a872),f328(f328(f81(a872),x76311),x76312)),f328(f328(f81(a872),x76311),x76313))) % 167.77/167.50 [7632]~P1(f328(f328(f243(a1),f2(a1)),x76321))+~P1(f328(f328(f243(a1),x76322),x76323))+P1(f328(f328(f243(a1),f328(f328(f81(a1),x76321),x76322)),f328(f328(f81(a1),x76321),x76323))) % 167.77/167.50 [7634]~P1(f328(f328(f243(a872),f2(a872)),x76343))+~P1(f328(f328(f242(a872),x76343),x76342))+P1(f328(f328(f242(a872),f328(f328(f40(a872),x76341),x76342)),f328(f328(f40(a872),x76341),x76343))) % 167.77/167.50 [7635]~P1(f328(f328(f243(a1),f2(a1)),x76352))+~P1(f328(f328(f242(a1),x76351),x76353))+P1(f328(f328(f242(a1),f328(f328(f40(a1),x76351),x76352)),f328(f328(f40(a1),x76353),x76352))) % 167.77/167.50 [7685]E(x76851,f2(a872))+E(f328(f328(f80(a872),f328(f328(f81(a872),x76851),f383(x76851,x76852,x76853))),f384(x76851,x76852,x76853)),x76852)+P1(f328(x76853,f328(f328(f40(a872),x76852),x76851))) % 167.77/167.50 [7743]E(f328(f328(f80(a872),f328(f328(f81(a872),x77431),f383(x77431,x77432,x77433))),f384(x77431,x77432,x77433)),x77432)+~P1(f328(x77433,f2(a872)))+P1(f328(x77433,f328(f328(f40(a872),x77432),x77431))) % 167.77/167.50 [7752]~P1(f328(x77523,x77522))+P1(f328(f328(f328(a198,x77521),x77522),f609(x77522,x77521,x77523)))+~P1(f328(f328(f328(a198,f32(x77523,x77521)),x77522),x77522)) % 167.77/167.50 [7763]~P1(f328(f38(x77631),x77633))+P1(f328(f328(f330(x77631),f356(x77632,x77633,x77631)),x77633))+P1(f328(f328(f243(a872),f2(a872)),f328(f328(f9(x77631,a872),x77632),x77633))) % 167.77/167.50 [7764]~P1(f328(f38(x77641),x77643))+P1(f328(f328(f330(x77641),f450(x77642,x77643,x77641)),x77643))+P1(f328(f328(f243(a872),f2(a872)),f328(f328(f9(x77641,a872),x77642),x77643))) % 167.77/167.50 [8051]E(x80511,f192(f879(x80512,a867)))+E(x80511,f328(f328(f306(x80512),x80513),f192(f879(x80512,a867))))+~P1(f328(f328(f242(f879(x80512,a867)),x80511),f328(f328(f306(x80512),x80513),f192(f879(x80512,a867))))) % 167.77/167.50 [8069]~P59(x80691)+P12(x80691,x80692,x80693)+P1(f328(f328(f330(f873(x80691)),f719(x80693,x80692,x80691)),f328(f170(f873(x80691)),f56(x80691,x80693,f57(x80691))))) % 167.77/167.50 [8089]~P1(f328(f328(f243(a872),f2(a872)),x80893))+P1(f328(f328(f243(a872),x80891),x80892))+~P1(f328(f328(f243(a872),f328(f328(f253(a872),x80893),x80891)),f328(f328(f253(a872),x80893),x80892))) % 167.77/167.50 [8091]~P1(f328(f328(f243(a872),f2(a872)),x80913))+P1(f328(f328(f242(a872),x80911),x80912))+~P1(f328(f328(f242(a872),f328(f328(f81(a872),x80913),x80911)),f328(f328(f81(a872),x80913),x80912))) % 167.77/167.50 [8092]~P1(f328(f328(f243(a872),f2(a872)),x80923))+P1(f328(f328(f242(a872),x80921),x80922))+~P1(f328(f328(f242(a872),f328(f328(f81(a872),x80921),x80923)),f328(f328(f81(a872),x80922),x80923))) % 167.77/167.50 [8118]~P59(x81181)+~P11(x81181,x81183,x81182)+P1(f328(f328(f330(f873(x81181)),f718(x81182,x81183,x81181)),f328(f170(f873(x81181)),f56(x81181,x81182,f57(x81181))))) % 167.77/167.50 [8136]~E(f328(f328(f105(f879(x81361,a867)),f836(x81363,x81362,x81361)),f835(x81363,x81362,x81361)),f192(f879(x81361,a867)))+E(f328(f328(f105(f879(x81361,a867)),x81362),f41(f879(x81361,a867),x81363)),f192(f879(x81361,a867)))+P1(f328(f328(f330(f879(x81361,a867)),x81362),x81363)) % 167.77/167.50 [8153]E(x81531,f117(x81532))+~E(f328(f139(f873(x81532),f873(x81532),f125(x81532),f117(x81532)),x81533),f117(x81532))+~P1(f328(f328(f330(f873(x81532)),x81531),f328(f170(f873(x81532)),x81533))) % 167.77/167.50 [8218]E(x82181,f192(f879(f879(x82182,a867),a867)))+P1(f328(f328(f330(f879(x82182,a867)),f453(x82183,x82181,x82182)),x82181))+P1(f328(f328(f242(f879(x82182,a867)),f42(f879(x82182,a867),x82181)),x82183)) % 167.77/167.50 [8226]~P67(x82261)+~P73(x82261)+E(f328(f328(f6(a1,x82261),f328(f328(f8(a872,x82261,a1),x82262),a108)),f328(f307(a872,a1,f104(a1)),x82263)),f328(f328(f6(a872,x82261),x82262),x82263)) % 167.77/167.50 [8227]~P67(x82271)+~P73(x82271)+E(f328(f328(f9(a1,x82271),f328(f328(f8(a872,x82271,a1),x82272),a108)),f328(f307(a872,a1,f104(a1)),x82273)),f328(f328(f9(a872,x82271),x82272),x82273)) % 167.77/167.50 [8266]~P1(f328(f38(x82661),x82663))+~P1(f328(f328(f243(a872),f2(a872)),f328(x82662,f356(x82662,x82663,x82661))))+P1(f328(f328(f243(a872),f2(a872)),f328(f328(f9(x82661,a872),x82662),x82663))) % 167.77/167.50 [8267]~P1(f328(f38(x82671),x82673))+~P1(f328(f328(f243(a872),f2(a872)),f328(x82672,f450(x82672,x82673,x82671))))+P1(f328(f328(f243(a872),f2(a872)),f328(f328(f9(x82671,a872),x82672),x82673))) % 167.77/167.50 [8297]~P1(f328(x82971,x82973))+P1(f328(f328(f328(a198,f32(x82971,x82972)),f609(x82973,x82972,x82971)),x82973))+~P1(f328(f328(f328(a198,f32(x82971,x82972)),x82973),x82973)) % 167.77/167.50 [8301]~P61(x83012)+E(x83011,f78(x83012))+E(f328(f328(f286(x83012),f328(f328(f22(x83012),f328(f328(f253(x83012),x83011),x83013)),f78(x83012))),f328(f328(f22(x83012),x83011),f78(x83012))),f328(f328(f6(a872,x83012),f328(f253(x83012),x83011)),f328(f298(a872,f2(a872)),x83013))) % 167.77/167.50 [8359]E(x83591,f2(a872))+~P1(f328(x83593,f328(f328(f40(a872),x83592),x83591)))+P1(f328(f328(f243(a872),x83592),f328(f328(f81(a872),x83591),f328(a116,f382(x83591,x83592,x83593))))) % 167.77/167.50 [8376]P1(f328(x83761,f2(a872)))+~P1(f328(x83761,f328(f328(f40(a872),x83762),x83763)))+P1(f328(f328(f243(a872),x83762),f328(f328(f81(a872),x83763),f328(a116,f382(x83763,x83762,x83761))))) % 167.77/167.50 [8418]E(x84181,f2(a872))+~P1(f328(x84183,f328(f328(f40(a872),x84182),x84181)))+P1(f328(f328(f242(a872),f328(f328(f81(a872),x84181),f382(x84181,x84182,x84183))),x84182)) % 167.77/167.50 [8452]P1(f328(x84521,f2(a872)))+~P1(f328(x84521,f328(f328(f40(a872),x84523),x84522)))+P1(f328(f328(f242(a872),f328(f328(f81(a872),x84522),f382(x84522,x84523,x84521))),x84523)) % 167.77/167.50 [8455]~P105(x84551)+E(f328(f328(f145(x84551,x84551,f5(x84551)),x84552),x84553),f146(x84551,x84551,f5(x84551),x84552,x84553))+P1(f328(f328(f330(x84551),x84552),f328(f170(x84551),x84553))) % 167.77/167.50 [8491]~E(f328(x84913,f594(x84912,x84913,x84911)),f328(x84913,f596(x84912,x84913,x84911)))+~P56(x84911,f328(x84913,f595(x84912,x84913,x84911)))+P56(x84911,f328(f328(f44(x84912,f879(x84911,f879(x84911,a867))),f251(f879(x84912,a867))),x84913)) % 167.77/167.50 [8501]E(x85011,f192(f879(f879(x85012,a867),a867)))+~P1(f328(f328(f242(f879(x85012,a867)),f453(x85013,x85011,x85012)),x85013))+P1(f328(f328(f242(f879(x85012,a867)),f42(f879(x85012,a867),x85011)),x85013)) % 167.77/167.50 [8566]~P63(x85661)+~P1(f328(f328(f243(x85661),x85662),x85663))+P1(f328(f328(f243(x85661),x85662),f328(f328(f286(x85661),f328(f328(f80(x85661),x85662),x85663)),f328(f328(f80(x85661),f78(x85661)),f78(x85661))))) % 167.77/167.50 [8621]~P1(f328(f328(x86211,f505(x86211,x86213,x86212)),f509(x86211,x86213,x86212)))+P1(f328(f328(x86211,x86212),x86213))+~P1(f328(f316(f878(a1,a1),a53),f328(f328(f263(a1,a1),x86212),x86213))) % 167.77/167.50 [8622]~P1(f328(f328(x86221,f510(x86221,x86223,x86222)),f511(x86221,x86223,x86222)))+P1(f328(f328(x86221,x86222),x86223))+~P1(f328(f316(f878(a1,a1),a58),f328(f328(f263(a1,a1),x86222),x86223))) % 167.77/167.50 [8623]~P1(f328(f328(x86231,f513(x86231,x86233,x86232)),f514(x86231,x86233,x86232)))+P1(f328(f328(x86231,x86232),x86233))+~P1(f328(f316(f878(a1,a1),a231),f328(f328(f263(a1,a1),x86232),x86233))) % 167.77/167.50 [8624]~P1(f328(f328(x86241,f517(x86241,x86243,x86242)),f518(x86241,x86243,x86242)))+P1(f328(f328(x86241,x86242),x86243))+~P1(f328(f316(f878(a872,a872),a226),f328(f328(f263(a872,a872),x86242),x86243))) % 167.77/167.50 [8625]~P1(f328(f328(x86251,f690(x86251,x86253,x86252)),f692(x86251,x86253,x86252)))+P1(f328(f328(x86251,x86252),x86253))+~P1(f328(f316(f878(a1,a1),a181),f328(f328(f263(a1,a1),x86252),x86253))) % 167.77/167.50 [8878]P1(f328(f328(x88781,x88782),x88783))+P1(f328(f316(f878(a872,a872),a226),f328(f328(f263(a872,a872),f517(x88781,x88783,x88782)),f518(x88781,x88783,x88782))))+~P1(f328(f316(f878(a872,a872),a226),f328(f328(f263(a872,a872),x88782),x88783))) % 167.77/167.50 [8879]P1(f328(f328(x88791,x88792),x88793))+P1(f328(f316(f878(a1,a1),a53),f328(f328(f263(a1,a1),f505(x88791,x88793,x88792)),f509(x88791,x88793,x88792))))+~P1(f328(f316(f878(a1,a1),a53),f328(f328(f263(a1,a1),x88792),x88793))) % 167.77/167.50 [8880]P1(f328(f328(x88801,x88802),x88803))+P1(f328(f316(f878(a1,a1),a58),f328(f328(f263(a1,a1),f510(x88801,x88803,x88802)),f511(x88801,x88803,x88802))))+~P1(f328(f316(f878(a1,a1),a58),f328(f328(f263(a1,a1),x88802),x88803))) % 167.77/167.50 [8881]P1(f328(f328(x88811,x88812),x88813))+P1(f328(f316(f878(a1,a1),a231),f328(f328(f263(a1,a1),f513(x88811,x88813,x88812)),f514(x88811,x88813,x88812))))+~P1(f328(f316(f878(a1,a1),a231),f328(f328(f263(a1,a1),x88812),x88813))) % 167.77/167.50 [8882]P1(f328(f328(x88821,x88822),x88823))+P1(f328(f316(f878(a1,a1),a181),f328(f328(f263(a1,a1),f690(x88821,x88823,x88822)),f692(x88821,x88823,x88822))))+~P1(f328(f316(f878(a1,a1),a181),f328(f328(f263(a1,a1),x88822),x88823))) % 167.77/167.50 [9229]~P1(f328(f38(x92291),x92293))+P1(f328(f328(f330(f878(f879(x92291,a867),f879(x92291,a867))),f328(f328(f263(f879(x92291,a867),f879(x92291,a867)),x92292),x92293)),f303(x92291)))+~P1(f328(f328(f243(f879(x92291,a867)),x92292),x92293)) % 167.77/167.50 [9300]~P56(x93001,f328(x93003,f595(x93002,x93003,x93001)))+P56(x93001,f328(f328(f44(x93002,f879(x93001,f879(x93001,a867))),f251(f879(x93002,a867))),x93003))+~E(f328(f328(f105(f879(x93001,a867)),f257(x93001,x93001,f328(x93003,f594(x93002,x93003,x93001)))),f258(x93001,x93001,f328(x93003,f596(x93002,x93003,x93001)))),f192(f879(x93001,a867))) % 167.77/167.50 [9389]~P29(a868,f192(f879(f871(a868),a867)),f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),x93891),x93892),x93893)),f192(f879(f871(a868),a867))))+P25(a868,f192(f879(f871(a868),a867)),f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),x93891),x93892),x93893)),f192(f879(f871(a868),a867))))+~P25(a868,f192(f879(f871(a868),a867)),f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),a325),x93892),f328(a198,x93892))),f192(f879(f871(a868),a867)))) % 167.77/167.50 [9499]P40(x94991,x94992,x94993)+P1(f328(f328(f330(f878(x94991,x94991)),f580(x94993,x94992,x94991)),x94993))+~P1(f328(f328(f330(f878(x94991,x94991)),f328(f328(f263(x94991,x94991),f579(x94993,x94992,x94991)),f579(x94993,x94992,x94991))),x94993)) % 167.77/167.50 [10086]P40(x100861,x100862,x100863)+~P1(f328(f328(f267(x100861,x100861,a867),f328(f328(f7(x100861,f879(x100861,a867),f879(x100861,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x100861,a867),f879(x100861,a867)),x100861),f8(a867,a867,x100861)),f328(f328(f8(a867,f879(a867,a867),x100861),a326),f328(f328(f7(x100861,f879(x100861,a867),a867),f330(x100861)),x100862)))),f328(f328(f7(x100861,f879(x100861,a867),a867),f330(x100861)),x100862))),f580(x100863,x100862,x100861)))+~P1(f328(f328(f330(f878(x100861,x100861)),f328(f328(f263(x100861,x100861),f579(x100863,x100862,x100861)),f579(x100863,x100862,x100861))),x100863)) % 167.77/167.50 [5629]~P57(x56292)+E(x56291,f2(x56292))+E(f328(f328(f40(x56292),f328(f328(f81(x56292),x56293),x56291)),x56291),x56293) % 167.77/167.50 [5630]~P57(x56302)+E(x56301,f2(x56302))+E(f328(f328(f40(x56302),f328(f328(f81(x56302),x56301),x56303)),x56301),x56303) % 167.77/167.50 [6421]~P67(x64211)+~E(f328(x64212,f2(a872)),f2(x64211))+E(f328(f328(f6(a872,x64211),x64212),f328(f298(a872,f328(a116,f2(a872))),x64213)),f328(f328(f6(a872,x64211),x64212),f328(f298(a872,f2(a872)),x64213))) % 167.77/167.50 [6549]~P57(x65492)+E(x65491,f2(x65492))+E(f328(f328(f40(x65492),f328(f328(f80(x65492),x65493),x65491)),x65491),f328(f328(f80(x65492),f328(f328(f40(x65492),x65493),x65491)),f78(x65492))) % 167.77/167.50 [6550]~P57(x65502)+E(x65501,f2(x65502))+E(f328(f328(f40(x65502),f328(f328(f80(x65502),x65501),x65503)),x65501),f328(f328(f80(x65502),f328(f328(f40(x65502),x65503),x65501)),f78(x65502))) % 167.77/167.50 [6770]~P1(f328(x67703,f2(a1)))+P1(f328(f328(f242(a872),x67701),x67702))+P1(f328(x67703,f328(f104(a1),f328(f328(f22(a872),x67702),x67701)))) % 167.77/167.50 [6876]P1(f328(f328(f242(a872),x68762),x68761))+P1(f328(f328(f243(a872),x68761),x68762))+P1(f328(x68763,f328(f104(a1),f328(f328(f22(a872),x68761),x68762)))) % 167.77/167.50 [6946]E(f328(f328(f80(a872),f328(f107(a872),x69461)),f328(f328(f80(a872),f328(f107(a872),x69462)),x69463)),f328(f328(f80(a872),f328(f107(a872),x69461)),x69463))+P1(f328(a197,f328(f107(a1),x69461)))+~P1(f328(a197,f328(f107(a1),x69462))) % 167.77/167.50 [7025]~E(x70252,f328(f328(f40(a872),x70253),x70251))+~P1(f328(f328(f243(a872),f2(a872)),x70251))+P1(f328(f328(f242(a872),f328(f328(f81(a872),x70251),x70252)),x70253)) % 167.77/167.50 [7139]~P1(f328(f38(x71391),x71393))+~P1(f328(f38(x71391),x71392))+P1(f328(f38(x71391),f328(f328(f114(f879(x71391,a867)),x71392),x71393))) % 167.77/167.50 [7435]~P105(x74351)+~P1(f328(f38(x74351),x74352))+E(f136(x74351,f328(f328(f22(f879(x74351,a867)),x74352),f328(f328(f306(x74351),x74353),f192(f879(x74351,a867))))),f167(x74351,x74353,f136(x74351,x74352))) % 167.77/167.50 [7501]P1(f328(x75011,f2(a1)))+~P1(f328(f328(f243(a872),x75012),x75013))+~P1(f328(x75011,f328(f104(a1),f328(f328(f22(a872),x75012),x75013)))) % 167.77/167.50 [7518]~P1(f328(f38(x75181),x75182))+E(f328(f39(x75181),f328(f328(f22(f879(x75181,a867)),x75182),f328(f328(f306(x75181),x75183),f192(f879(x75181,a867))))),f328(f39(x75181),x75182))+P1(f328(f328(f330(x75181),x75183),x75182)) % 167.77/167.50 [7650]~P116(x76501)+~P1(f328(f328(f243(x76501),f78(x76501)),x76502))+P1(f328(f328(f243(x76501),f78(x76501)),f328(f328(f81(x76501),x76502),f328(f328(f253(x76501),x76502),x76503)))) % 167.77/167.50 [7695]~P1(f328(f38(x76951),x76953))+E(f328(f328(f22(a872),f328(f39(x76951),x76952)),f328(f39(x76951),x76953)),f328(f39(x76951),f328(f328(f22(f879(x76951,a867)),x76952),x76953)))+~P1(f328(f328(f242(f879(x76951,a867)),x76953),x76952)) % 167.77/167.50 [7753]~P1(f328(f328(f242(a872),x77532),x77533))+~P1(f328(f328(f242(a872),x77531),f328(f328(f22(a872),x77533),x77532)))+P1(f328(f328(f242(a872),f328(f328(f80(a872),x77531),x77532)),x77533)) % 167.77/167.50 [7808]P1(f328(f38(x78081),x78082))+~P1(f328(f38(x78081),x78083))+~P1(f328(f38(x78081),f328(f328(f22(f879(x78081,a867)),x78082),x78083))) % 167.77/167.50 [7814]~P1(f328(f38(x78141),x78142))+E(f328(f39(x78141),f328(f328(f22(f879(x78141,a867)),x78142),f328(f328(f306(x78141),x78143),f192(f879(x78141,a867))))),f328(f328(f22(a872),f328(f39(x78141),x78142)),f78(a872)))+~P1(f328(f328(f330(x78141),x78143),x78142)) % 167.77/167.50 [7890]P56(x78901,x78902)+~P56(x78901,x78903)+~P1(f328(f328(f242(f879(x78901,f879(x78901,a867))),x78902),x78903)) % 167.77/167.50 [7931]~P1(f328(f328(f242(a872),x79313),x79312))+P1(f328(f328(f242(a872),x79311),f328(f328(f22(a872),x79312),x79313)))+~P1(f328(f328(f242(a872),f328(f328(f80(a872),x79311),x79313)),x79312)) % 167.77/167.50 [7949]P38(x79491,x79492)+~P38(x79491,x79493)+~P1(f328(f328(f242(f879(f878(x79491,x79491),a867)),x79492),x79493)) % 167.77/167.50 [7950]P54(x79501,x79502)+~P54(x79501,x79503)+~P1(f328(f328(f242(f879(f878(x79501,x79501),a867)),x79502),x79503)) % 167.77/167.50 [8191]~P116(x81911)+~P1(f328(f328(f243(x81911),f78(x81911)),x81912))+P1(f328(f328(f243(x81911),f328(f328(f253(x81911),x81912),x81913)),f328(f328(f81(x81911),x81912),f328(f328(f253(x81911),x81912),x81913)))) % 167.77/167.50 [8284]~P1(f328(x82841,f2(a1)))+~P1(f328(x82841,f328(f328(f22(a1),f328(f104(a1),x82842)),f328(f104(a1),x82843))))+P1(f328(x82841,f328(f104(a1),f328(f328(f22(a872),x82842),x82843)))) % 167.77/167.50 [8298]~P1(f328(f328(f242(a872),x82983),x82982))+P1(f328(x82981,f328(f328(f22(a1),f328(f104(a1),x82982)),f328(f104(a1),x82983))))+~P1(f328(x82981,f328(f104(a1),f328(f328(f22(a872),x82982),x82983)))) % 167.77/167.50 [8316]P1(f328(f328(f243(a872),x83161),x83162))+~P1(f328(x83163,f328(f328(f22(a1),f328(f104(a1),x83161)),f328(f104(a1),x83162))))+P1(f328(x83163,f328(f104(a1),f328(f328(f22(a872),x83161),x83162)))) % 167.77/167.50 [8370]~P123(x83702)+E(x83701,f2(x83702))+P1(f328(f328(f243(x83702),f2(x83702)),f328(f328(f80(x83702),f328(f328(f81(x83702),x83703),x83703)),f328(f328(f81(x83702),x83701),x83701)))) % 167.77/167.50 [8371]~P123(x83712)+E(x83711,f2(x83712))+P1(f328(f328(f243(x83712),f2(x83712)),f328(f328(f80(x83712),f328(f328(f81(x83712),x83711),x83711)),f328(f328(f81(x83712),x83713),x83713)))) % 167.77/167.50 [8474]~P1(f328(f328(f243(a872),f2(a872)),x84741))+~P1(f328(f328(f243(a1),x84742),x84743))+P1(f328(f328(f243(a1),f328(f328(f81(a1),f328(f104(a1),x84741)),x84742)),f328(f328(f81(a1),f328(f104(a1),x84741)),x84743))) % 167.77/167.50 [8530]E(f328(f328(f105(f879(x85301,a867)),x85302),f41(f879(x85301,a867),x85303)),f192(f879(x85301,a867)))+P1(f328(f328(f330(f879(x85301,a867)),x85302),x85303))+P1(f328(f328(f330(f879(x85301,a867)),f836(x85303,x85302,x85301)),f328(f328(f306(f879(x85301,a867)),x85302),x85303))) % 167.77/167.50 [8531]E(f328(f328(f105(f879(x85311,a867)),x85312),f41(f879(x85311,a867),x85313)),f192(f879(x85311,a867)))+P1(f328(f328(f330(f879(x85311,a867)),x85312),x85313))+P1(f328(f328(f330(f879(x85311,a867)),f835(x85313,x85312,x85311)),f328(f328(f306(f879(x85311,a867)),x85312),x85313))) % 167.77/167.50 [8565]E(x85651,x85652)+~E(f328(f193(f873(x85653)),x85651),f328(f193(f873(x85653)),x85652))+P1(f328(f328(f330(f878(x85653,x85653)),f679(x85653,x85651,x85652)),f328(f170(f878(x85653,x85653)),f328(f328(f180(x85653,x85653),x85652),x85651)))) % 167.77/167.50 [8798]E(f304(x87981,x87982),f304(x87981,x87983))+~P1(f328(f328(f242(f879(f878(x87981,x87981),a867)),x87983),f304(x87981,x87982)))+~P1(f328(f328(f242(f879(f878(x87981,x87981),a867)),x87982),x87983)) % 167.77/167.50 [8858]~P40(x88581,f251(f879(x88581,a867)),x88583)+P1(f328(f328(f242(f879(f878(f873(x88581),f873(x88581)),a867)),f154(x88581,x88582)),f155(x88581,x88583)))+~P1(f328(f328(f242(f879(f878(x88581,x88581),a867)),x88582),x88583)) % 167.77/167.50 [9065]P38(x90651,x90652)+~P1(f328(f328(f330(x90651),x90653),f627(x90652,x90651)))+P1(f328(f328(f330(f878(x90651,x90651)),f328(f328(f263(x90651,x90651),f651(x90652,x90651,x90653)),x90653)),x90652)) % 167.77/167.50 [9099]~P1(f328(f38(x90991),x90992))+P1(f328(f38(f879(x90991,a867)),f328(f328(f62(x90991),x90992),x90993)))+~P1(f328(f328(f242(f879(f878(x90991,x90991),a867)),x90993),f328(f328(f265(x90991,x90991),x90992),f328(f16(f879(x90991,a867),x90991),x90992)))) % 167.77/167.50 [9134]P40(x91341,x91342,x91343)+P1(f328(f328(f330(x91341),f574(x91343,x91342,x91341)),x91342))+~P1(f328(f328(f242(f879(f878(x91341,x91341),a867)),x91343),f328(f328(f265(x91341,x91341),x91342),f328(f16(f879(x91341,a867),x91341),x91342)))) % 167.77/167.50 [9135]P40(x91351,x91352,x91353)+P1(f328(f328(f330(x91351),f578(x91352,x91353,x91351)),x91352))+~P1(f328(f328(f242(f879(f878(x91351,x91351),a867)),x91353),f328(f328(f265(x91351,x91351),x91352),f328(f16(f879(x91351,a867),x91351),x91352)))) % 167.77/167.50 [9170]~P63(x91701)+~P1(f328(f328(f243(x91701),x91702),x91703))+P1(f328(f328(f243(x91701),f328(f328(f286(x91701),f328(f328(f80(x91701),x91702),x91703)),f328(f328(f80(x91701),f78(x91701)),f78(x91701)))),x91703)) % 167.77/167.50 [9199]~P62(x91991)+P1(f328(f328(f242(x91991),x91992),x91993))+~P1(f328(f328(f242(x91991),f328(f328(f81(x91991),f433(x91993,x91992,x91991)),x91992)),x91993)) % 167.77/167.50 [9335]E(f328(f193(f873(f873(x93351))),f328(f133(f873(x93351),f328(f328(f8(a872,a867,f873(x93351)),f328(f243(a872),x93352)),f193(f873(x93351)))),f178(x93351,x93353))),f328(f193(f873(x93351)),f328(f328(f162(f873(x93351)),x93353),x93352)))+~P15(a872,f328(f166(a872),f328(f328(f151(f873(x93351),a872),f193(f873(x93351))),x93353)))+~P1(f328(f328(f243(a872),x93352),f328(f193(f873(f873(x93351))),x93353))) % 167.77/167.50 [9443]~P38(x94431,x94432)+P27(x94431,f328(f328(f263(f879(f878(x94431,x94431),a867),f879(f878(x94431,x94431),a867)),x94432),x94433))+~P1(f328(f328(f242(f879(f878(x94431,x94431),a867)),f328(f328(f285(x94431,x94431,x94431),x94432),x94433)),x94432)) % 167.77/167.50 [9450]E(f328(f328(f151(f873(x94501),x94501),f328(f328(f7(f873(x94501),a872,x94501),f162(x94501)),x94502)),f328(f133(f873(x94501),f328(f328(f8(a872,a867,f873(x94501)),f328(f243(a872),x94502)),f193(f873(x94501)))),f178(x94501,x94503))),f328(f328(f162(f873(x94501)),x94503),x94502))+~P15(a872,f328(f166(a872),f328(f328(f151(f873(x94501),a872),f193(f873(x94501))),x94503)))+~P1(f328(f328(f243(a872),x94502),f328(f193(f873(f873(x94501))),x94503))) % 167.77/167.50 [9587]P40(x95871,x95872,x95873)+~P1(f328(f328(f330(f878(x95871,x95871)),f328(f328(f263(x95871,x95871),f574(x95873,x95872,x95871)),f574(x95873,x95872,x95871))),x95873))+~P1(f328(f328(f242(f879(f878(x95871,x95871),a867)),x95873),f328(f328(f265(x95871,x95871),x95872),f328(f16(f879(x95871,a867),x95871),x95872)))) % 167.77/167.50 [9588]P40(x95881,x95882,x95883)+~P1(f328(f328(f330(f878(x95881,x95881)),f328(f328(f263(x95881,x95881),f578(x95882,x95883,x95881)),f578(x95882,x95883,x95881))),x95883))+~P1(f328(f328(f242(f879(f878(x95881,x95881),a867)),x95883),f328(f328(f265(x95881,x95881),x95882),f328(f16(f879(x95881,a867),x95881),x95882)))) % 167.77/167.50 [9765]~P138(x97651)+~P122(x97651)+E(f328(f328(f286(x97651),f328(f106(x97651),f328(f328(f73(f878(a1,a1),a1,x97652,f262(a1,a1)),f219(x97652)),x97653))),f328(f106(x97651),f328(f328(f73(f878(a1,a1),a1,x97652,f266(a1,a1)),f219(x97652)),x97653))),f232(x97652,x97651,x97653)) % 167.77/167.50 [9966]~E(x99663,f2(a872))+~E(f328(f193(f873(x99661)),f328(f328(f162(f873(x99661)),x99662),f745(x99663,x99661,x99662))),x99663)+E(f328(f328(f151(a872,f873(x99661)),f328(f328(f7(a872,f873(a872),f873(x99661)),f328(f328(f8(f879(a872,x99661),f879(f873(a872),f873(x99661)),a872),f151(a872,x99661)),f328(f7(a872,a872,x99661),f328(f328(f8(f873(x99661),f879(a872,x99661),a872),f162(x99661)),f328(f162(f873(x99661)),x99662))))),f136(a872,f328(f298(a872,f2(a872)),f328(f193(f873(f873(x99661))),x99662))))),f136(a872,f328(f298(a872,f2(a872)),x99663))),f178(x99661,x99662)) % 167.77/167.50 [9967]E(x99671,f117(f873(x99672)))+~E(f328(f193(f873(x99672)),f328(f328(f162(f873(x99672)),x99671),f745(x99673,x99672,x99671))),x99673)+E(f328(f328(f151(a872,f873(x99672)),f328(f328(f7(a872,f873(a872),f873(x99672)),f328(f328(f8(f879(a872,x99672),f879(f873(a872),f873(x99672)),a872),f151(a872,x99672)),f328(f7(a872,a872,x99672),f328(f328(f8(f873(x99672),f879(a872,x99672),a872),f162(x99672)),f328(f162(f873(x99672)),x99671))))),f136(a872,f328(f298(a872,f2(a872)),f328(f193(f873(f873(x99672))),x99671))))),f136(a872,f328(f298(a872,f2(a872)),x99673))),f178(x99672,x99671)) % 167.77/167.50 [9968]~E(x99683,f2(a872))+E(f328(f328(f151(a872,f873(x99681)),f328(f328(f7(a872,f873(a872),f873(x99681)),f328(f328(f8(f879(a872,x99681),f879(f873(a872),f873(x99681)),a872),f151(a872,x99681)),f328(f7(a872,a872,x99681),f328(f328(f8(f873(x99681),f879(a872,x99681),a872),f162(x99681)),f328(f162(f873(x99681)),x99682))))),f136(a872,f328(f298(a872,f2(a872)),f328(f193(f873(f873(x99681))),x99682))))),f136(a872,f328(f298(a872,f2(a872)),x99683))),f178(x99681,x99682))+P1(f328(f328(f243(a872),f745(x99683,x99681,x99682)),f328(f193(f873(f873(x99681))),x99682))) % 167.77/167.50 [9969]E(x99691,f117(f873(x99692)))+E(f328(f328(f151(a872,f873(x99692)),f328(f328(f7(a872,f873(a872),f873(x99692)),f328(f328(f8(f879(a872,x99692),f879(f873(a872),f873(x99692)),a872),f151(a872,x99692)),f328(f7(a872,a872,x99692),f328(f328(f8(f873(x99692),f879(a872,x99692),a872),f162(x99692)),f328(f162(f873(x99692)),x99691))))),f136(a872,f328(f298(a872,f2(a872)),f328(f193(f873(f873(x99692))),x99691))))),f136(a872,f328(f298(a872,f2(a872)),x99693))),f178(x99692,x99691))+P1(f328(f328(f243(a872),f745(x99693,x99692,x99691)),f328(f193(f873(f873(x99692))),x99691))) % 167.77/167.50 [7692]E(f328(f328(f80(a872),f328(f107(a872),x76921)),f328(f328(f80(a872),f328(f107(a872),x76922)),x76923)),f328(f328(f80(a872),f328(f107(a872),f328(f328(f80(a1),x76921),x76922))),x76923))+P1(f328(a197,f328(f107(a1),x76921)))+P1(f328(a197,f328(f107(a1),x76922))) % 167.77/167.50 [8464]~P1(f328(f38(x84641),x84642))+~P1(f328(f328(f330(x84641),x84643),x84642))+E(f328(a116,f328(f39(x84641),f328(f328(f22(f879(x84641,a867)),x84642),f328(f328(f306(x84641),x84643),f192(f879(x84641,a867)))))),f328(f39(x84641),x84642)) % 167.77/167.50 [8481]~P1(f328(f38(x84811),x84812))+~P1(f328(f328(f330(x84811),x84813),x84812))+E(f328(f328(f80(a872),f78(a872)),f328(f39(x84811),f328(f328(f22(f879(x84811,a867)),x84812),f328(f328(f306(x84811),x84813),f192(f879(x84811,a867)))))),f328(f39(x84811),x84812)) % 167.77/167.50 [8574]~P105(x85741)+~P1(f328(f38(x85741),x85743))+E(f328(f328(f145(x85741,x85741,f5(x85741)),x85742),f136(x85741,f328(f328(f22(f879(x85741,a867)),x85743),f328(f328(f306(x85741),x85742),f192(f879(x85741,a867)))))),f136(x85741,f328(f328(f306(x85741),x85742),x85743))) % 167.77/167.50 [8728]~P1(f328(f38(x87281),x87283))+~P1(f328(f38(x87281),x87282))+E(f328(f328(f80(a872),f328(f39(x87281),f328(f328(f114(f879(x87281,a867)),x87282),x87283))),f328(f39(x87281),f328(f328(f105(f879(x87281,a867)),x87282),x87283))),f328(f328(f80(a872),f328(f39(x87281),x87282)),f328(f39(x87281),x87283))) % 167.77/167.50 [9914]~P26(x99141,f879(f879(x99141,a867),a867),f328(f328(f7(x99141,f879(f878(x99141,x99141),a867),f879(f879(x99141,a867),a867)),f328(f328(f8(f879(x99141,a867),f879(f879(f878(x99141,x99141),a867),f879(f879(x99141,a867),a867)),x99141),f62(x99141)),f328(f328(f7(x99141,f879(x99141,a867),f879(x99141,a867)),f306(x99141)),f192(f879(x99141,a867))))),x99143),x99142)+~P1(f328(f38(x99141),x99142))+E(f328(f39(f879(x99141,a867)),f328(f328(f62(x99141),x99142),x99143)),f328(f39(x99141),x99142)) % 167.77/167.50 [7962]~P91(x79621)+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x79623)))+E(f328(f328(f253(x79621),x79622),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),x79623),x79623)),a101))),f78(x79621)) % 167.77/167.50 [9426]~P91(x94261)+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x94263)))+E(f328(f328(f253(x94261),x94262),f328(f107(a872),f328(f328(f22(a1),f328(f328(f80(a1),x94263),x94263)),a101))),f328(f328(f86(x94261,x94261),f328(f328(f253(x94261),x94262),f328(f107(a872),x94263))),f328(f328(f18(x94261,x94261,x94261),f328(f328(f8(x94261,f879(x94261,x94261),x94261),f81(x94261)),f328(f81(x94261),x94262))),f5(x94261)))) % 167.77/167.50 [9824]~P1(f328(f134(x98241),x98243))+~P1(f328(f328(f330(x98241),x98242),f328(f170(x98241),x98243)))+E(f328(f328(f135(x98241),f328(f193(f873(x98241)),f175(x98241,f328(f328(f8(a867,a867,x98241),a323),f328(f328(f7(x98241,x98241,a867),a325),x98242)),f328(f166(x98241),x98243)))),f328(f166(x98241),x98243)),f328(f328(f148(x98241),x98242),f328(f166(x98241),f175(x98241,f328(f328(f8(a867,a867,x98241),a323),f328(f328(f7(x98241,x98241,a867),a325),x98242)),x98243)))) % 167.77/167.50 [9895]P1(f328(f328(f242(f879(f878(x98951,x98951),a867)),f304(x98951,x98952)),x98953))+~P1(f328(f328(f242(f879(f878(x98951,x98951),a867)),f304(x98951,f192(f879(f878(x98951,x98951),a867)))),x98953))+~P1(f328(f328(f242(f879(f878(x98951,x98951),a867)),f328(f328(f285(x98951,x98951,x98951),f328(f328(f105(f879(f878(x98951,x98951),a867)),f304(x98951,x98952)),x98953)),x98952)),x98953)) % 167.77/167.50 [9736]~P1(f328(f38(x97361),f328(f248(x97361),x97363)))+~P1(f328(f38(x97361),f328(f248(x97361),x97362)))+P1(f328(f38(x97361),f328(f248(x97361),f328(f328(f18(x97361,a867,a867),f328(f328(f8(a867,f879(a867,a867),x97361),a327),x97362)),x97363)))) % 167.77/167.50 [10028]P1(f328(f328(f242(f879(f878(x100281,x100281),a867)),f328(f328(f285(x100281,x100281,x100281),x100282),f304(x100281,x100282))),x100283))+~P1(f328(f328(f242(f879(f878(x100281,x100281),a867)),x100282),x100283))+~P1(f328(f328(f242(f879(f878(x100281,x100281),a867)),f328(f328(f285(x100281,x100281,x100281),f328(f328(f105(f879(f878(x100281,x100281),a867)),f328(f328(f285(x100281,x100281,x100281),x100282),f304(x100281,x100282))),x100283)),x100282)),x100283)) % 167.77/167.50 [9982]~P117(x99822)+E(x99821,f2(x99822))+~E(f328(f328(f80(x99822),f328(f328(f253(x99822),x99823),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x99822),x99821),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f2(x99822)) % 167.77/167.50 [9983]~P117(x99832)+E(x99831,f2(x99832))+~E(f328(f328(f80(x99832),f328(f328(f253(x99832),x99831),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x99832),x99833),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f2(x99832)) % 167.77/167.50 [9988]~P1(f328(f134(x99881),x99883))+~P1(f328(f328(f330(x99881),x99882),f328(f170(x99881),x99883)))+E(f328(f166(x99881),f328(f169(x99881),f328(f328(f135(x99881),f328(f193(f873(x99881)),f175(x99881,f328(f328(f8(a867,a867,x99881),a323),f328(f328(f7(x99881,x99881,a867),a325),x99882)),x99883))),x99883))),f175(x99881,f328(f328(f8(a867,a867,x99881),a323),f328(f328(f7(x99881,x99881,a867),a325),x99882)),f328(f166(x99881),x99883))) % 167.77/167.50 [10073]~P117(x100732)+E(x100731,f2(x100732))+P1(f328(f328(f243(x100732),f2(x100732)),f328(f328(f80(x100732),f328(f328(f253(x100732),x100733),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100732),x100731),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))) % 167.77/167.50 [10074]~P117(x100742)+E(x100741,f2(x100742))+P1(f328(f328(f243(x100742),f2(x100742)),f328(f328(f80(x100742),f328(f328(f253(x100742),x100741),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100742),x100743),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))) % 167.77/167.50 [10116]~P117(x101161)+P1(f328(f328(f242(x101161),f2(x101161)),x101162))+~P1(f328(f328(f242(x101161),f2(x101161)),f328(f328(f253(x101161),x101162),f328(a116,f328(f328(f81(a872),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x101163))))) % 167.77/167.50 [5470]~P25(x54701,x54704,x54703)+P25(x54701,x54702,x54703)+~P25(x54701,x54702,x54704) % 167.77/167.50 [4931]~E(x49312,f90(x49313,x49311))+P1(f328(x49311,x49312))+~P1(f328(x49311,x49314)) % 167.77/167.50 [6681]~P38(x66812,x66814)+~P38(x66811,x66813)+P38(f878(x66811,x66812),f321(x66811,x66812,x66813,x66814)) % 167.77/167.50 [5113]~P6(x51134,x51131)+~E(f328(x51131,x51132),f328(x51131,x51133))+P1(f328(f328(x51131,x51132),x51133)) % 167.77/167.50 [5285]~P6(x52854,x52851)+E(f328(x52851,x52852),f328(x52851,x52853))+~P1(f328(f328(x52851,x52852),x52853)) % 167.77/167.50 [5377]~P19(x53773,x53774,x53771)+E(f328(x53771,x53772),f328(f64(x53773,x53774),x53772))+~P1(f328(f38(x53773),x53772)) % 167.77/167.50 [5378]~P9(x53783,x53784,x53781)+E(f328(x53781,x53782),f328(f64(x53783,x53784),x53782))+~P1(f328(f38(x53783),x53782)) % 167.77/167.50 [5503]~P6(x55034,x55031)+~P1(f328(f328(x55031,x55033),x55032))+P1(f328(f328(x55031,x55032),x55033)) % 167.77/167.50 [5571]E(x55711,x55712)+~E(f328(f262(x55713,x55714),x55711),f328(f262(x55713,x55714),x55712))+~E(f328(f266(x55713,x55714),x55711),f328(f266(x55713,x55714),x55712)) % 167.77/167.50 [5597]E(x55971,x55972)+~P1(f328(f49(x55973,x55974),x55972))+~P1(f328(f49(x55973,x55974),x55971)) % 167.77/167.50 [5789]~P67(x57892)+E(f233(x57891,x57892,x57893,x57894),f2(x57892))+P1(f328(f38(x57891),x57894)) % 167.77/167.50 [5925]~P1(f328(f316(x59251,x59252),x59254))+P1(f328(f316(x59251,x59252),x59253))+~P1(f328(f328(x59252,x59253),x59254)) % 167.77/167.50 [7802]E(x78021,f2(a872))+~P1(f328(x78022,x78023))+P1(f328(x78022,f810(x78022,x78023,x78021,x78024))) % 167.77/167.50 [7885]~P105(x78852)+~P1(f328(f134(x78851),x78854))+P1(f328(f134(x78851),f147(x78851,x78852,x78853,x78854))) % 167.77/167.50 [8106]~P1(f328(f38(x81062),x81064))+~P1(f328(f38(x81061),x81063))+P1(f328(f38(f877(x81061,x81062)),f315(x81061,x81062,x81063,x81064))) % 167.77/167.50 [8107]~P1(f328(f134(x81072),x81074))+~P1(f328(f134(x81071),x81073))+P1(f328(f134(f878(x81071,x81072)),f61(x81071,x81072,x81073,x81074))) % 167.77/167.50 [8111]P1(f328(f328(f330(f873(x81111)),f328(f328(f125(x81111),x81112),x81113)),f158(x81111,x81114)))+~P1(f328(f328(f330(f873(x81111)),x81113),f158(x81111,x81114)))+~P1(f328(f328(f330(f873(x81111)),x81112),f158(x81111,x81114))) % 167.77/167.50 [8403]E(x84031,f2(a872))+P1(f328(x84032,x84033))+~P1(f328(x84032,f811(x84032,x84033,x84031,x84034))) % 167.77/167.50 [8443]~P105(x84433)+~P1(f328(f134(x84431),f147(x84431,x84433,x84434,x84432)))+P1(f328(f134(x84431),x84432)) % 167.77/167.50 [8719]~P1(f328(f328(f330(f878(x87191,x87191)),f328(f328(f263(x87191,x87191),x87192),x87194)),f304(x87191,x87193)))+P1(f328(f328(f330(x87191),x87192),f317(x87191,x87193)))+~P1(f328(f328(f330(x87191),x87194),f317(x87191,x87193))) % 167.77/167.50 [5097]~P67(x50972)+E(f328(f328(f6(x50971,x50972),x50973),x50974),f2(x50972))+P1(f328(f38(x50971),x50974)) % 167.77/167.50 [5100]~P73(x51002)+E(f328(f328(f9(x51001,x51002),x51003),x51004),f78(x51002))+P1(f328(f38(x51001),x51004)) % 167.77/167.50 [5248]~P70(x52483)+E(x52481,x52482)+~E(f328(f328(f80(x52483),x52484),x52481),f328(f328(f80(x52483),x52484),x52482)) % 167.77/167.50 [5249]~P71(x52493)+E(x52491,x52492)+~E(f328(f328(f80(x52493),x52494),x52491),f328(f328(f80(x52493),x52494),x52492)) % 167.77/167.50 [5251]~P70(x52513)+E(x52511,x52512)+~E(f328(f328(f80(x52513),x52511),x52514),f328(f328(f80(x52513),x52512),x52514)) % 167.77/167.50 [5373]~P4(x53733)+E(x53731,f192(f879(x53732,a867)))+E(f328(f328(f43(x53732,x53733),x53731),f328(f16(x53733,x53732),x53734)),x53734) % 167.77/167.50 [5374]~P4(x53743)+E(x53741,f192(f879(x53742,a867)))+E(f328(f328(f44(x53742,x53743),x53741),f328(f16(x53743,x53742),x53744)),x53744) % 167.77/167.50 [5585]~P107(x55853)+E(x55851,x55852)+~E(f299(x55853,x55854,x55851),f328(f328(f306(x55853),x55852),f192(f879(x55853,a867)))) % 167.77/167.50 [5586]~P107(x55863)+E(x55861,x55862)+~E(f299(x55863,x55861,x55862),f328(f328(f306(x55863),x55864),f192(f879(x55863,a867)))) % 167.77/167.50 [5646]~P36(x56463,x56461,x56464)+P36(x56463,x56461,f328(f328(f148(x56463),x56462),x56464))+P1(f328(x56461,x56462)) % 167.77/167.50 [5749]~P32(x57491,x57492,x57494)+~P1(f328(x57492,x57493))+P32(x57491,x57492,f328(f328(f148(x57491),x57493),x57494)) % 167.77/167.50 [5882]P1(f328(x58821,x58822))+~P1(f328(f256(x58823,x58821),x58824))+~P1(f328(f328(f330(x58823),x58822),x58824)) % 167.77/167.50 [5891]~P32(x58911,x58912,x58914)+~P32(x58911,x58912,x58913)+P32(x58911,x58912,f328(f328(f125(x58911),x58913),x58914)) % 167.77/167.50 [5901]P34(x59011,x59012,x59013)+~P34(x59011,x59012,f328(f328(f148(x59011),x59014),x59013))+P1(f328(x59012,x59014)) % 167.77/167.50 [5902]P36(x59021,x59022,x59023)+~P36(x59021,x59022,f328(f328(f148(x59021),x59024),x59023))+P1(f328(x59022,x59024)) % 167.77/167.50 [5976]P34(x59761,x59762,x59763)+P34(x59761,x59762,x59764)+~P34(x59761,x59762,f328(f328(f125(x59761),x59764),x59763)) % 167.77/167.50 [5995]~P67(x59951)+E(f328(f328(f6(a872,x59951),x59952),f328(f298(a872,x59953),f328(a116,x59954))),f2(x59951))+~P1(f328(f328(f243(a872),x59954),x59953)) % 167.77/167.50 [6000]~P58(x60001)+~E(f46(x60001,x60002,x60003),f46(x60001,x60004,x60003))+E(f46(x60001,f328(f79(x60001),x60002),x60003),f46(x60001,f328(f79(x60001),x60004),x60003)) % 167.77/167.50 [6068]P1(f328(x60681,x60682))+~E(f328(f133(x60683,x60681),x60684),x60684)+~P1(f328(f328(f330(x60683),x60682),f328(f170(x60683),x60684))) % 167.77/167.50 [6087]~E(f328(f328(f80(a872),x60873),x60872),f328(f328(f80(a872),x60871),x60874))+~P1(f328(f328(f243(a872),x60873),x60874))+P1(f328(f328(f243(a872),x60871),x60872)) % 167.77/167.50 [6091]P34(x60911,x60912,x60913)+~P1(f328(x60912,x60914))+~P1(f328(f328(f330(x60911),x60914),f328(f170(x60911),x60913))) % 167.77/167.50 [6127]~P32(x61273,x61271,x61274)+P1(f328(x61271,x61272))+~P1(f328(f328(f330(x61273),x61272),f328(f170(x61273),x61274))) % 167.77/167.50 [6129]~E(f328(f133(x61291,x61292),x61293),f117(x61291))+~P1(f328(x61292,x61294))+~P1(f328(f328(f330(x61291),x61294),f328(f170(x61291),x61293))) % 167.77/167.50 [6130]~E(f175(x61303,x61301,x61304),x61304)+P1(f328(x61301,x61302))+~P1(f328(f328(f330(x61303),x61302),f328(f170(x61303),x61304))) % 167.77/167.50 [6166]~E(x61664,f192(f879(x61662,a867)))+~E(x61663,f192(f879(x61661,a867)))+E(f315(x61661,x61662,x61663,x61664),f192(f879(f877(x61661,x61662),a867))) % 167.77/167.50 [6312]P1(f328(x63121,x63122))+~P1(f328(f157(x63123,x63121),x63124))+~P1(f328(f328(f330(x63123),x63122),f328(f170(x63123),x63124))) % 167.77/167.50 [6578]~P67(x65781)+E(f328(f328(f6(a872,x65781),x65782),f299(a872,x65783,f328(a116,x65784))),f2(x65781))+~P1(f328(f328(f243(a872),f328(a116,x65784)),x65783)) % 167.77/167.50 [6625]E(x66251,x66252)+~P1(f328(f328(f328(a198,x66253),x66254),x66251))+~P1(f328(f328(f328(a198,x66253),x66254),x66252)) % 167.77/167.50 [6720]~P105(x67201)+E(f328(f328(f22(f879(x67201,a867)),f328(f298(x67201,x67202),x67203)),f328(f298(x67201,x67202),x67204)),f328(f298(x67201,x67204),x67203))+~P1(f328(f328(f242(x67201),x67202),x67204)) % 167.77/167.50 [6792]~E(x67923,x67924)+E(x67921,f2(a872))+P1(f328(f328(f330(x67922),x67923),f328(f170(x67922),f168(x67922,x67921,x67924)))) % 167.77/167.50 [7071]~P1(f328(f328(f330(f873(x70711)),x70714),f158(x70711,x70713)))+P1(f328(f328(f330(x70711),x70712),x70713))+~P1(f328(f328(f330(x70711),x70712),f328(f170(x70711),x70714))) % 167.77/167.50 [7078]~P38(x70781,x70782)+P1(f328(f328(f330(x70781),f628(x70782,x70781,x70783)),x70783))+~P1(f328(f328(f330(x70781),x70784),x70783)) % 167.77/167.50 [7134]~P67(x71341)+E(f328(f328(f328(f66(x71341,x71342,f80(x71341)),x71343),f2(x71341)),x71344),f328(f328(f6(x71342,x71341),x71343),x71344))+~P1(f328(f38(x71342),x71344)) % 167.77/167.50 [7136]~P73(x71361)+E(f328(f328(f328(f66(x71361,x71362,f81(x71361)),x71363),f78(x71361)),x71364),f328(f328(f9(x71362,x71361),x71363),x71364))+~P1(f328(f38(x71362),x71364)) % 167.77/167.50 [7166]P26(x71661,x71662,x71663,x71664)+~E(f328(f39(x71662),f328(f307(x71661,x71662,x71663),x71664)),f328(f39(x71661),x71664))+~P1(f328(f38(x71661),x71664)) % 167.77/167.50 [7352]~P67(x73521)+E(f328(f328(f80(x73521),f328(x73522,x73523)),f328(f328(f6(a872,x73521),x73522),f301(a872,x73523,x73524))),f328(f328(f6(a872,x73521),x73522),f299(a872,x73523,x73524)))+~P1(f328(f328(f242(a872),x73523),x73524)) % 167.77/167.50 [7362]~P67(x73621)+~P26(x73622,x73621,x73623,x73624)+E(f328(f328(f6(x73621,x73621),f34(x73621)),f328(f307(x73622,x73621,x73623),x73624)),f328(f328(f6(x73622,x73621),x73623),x73624)) % 167.77/167.50 [7363]~P73(x73631)+~P26(x73632,x73631,x73633,x73634)+E(f328(f328(f9(x73631,x73631),f34(x73631)),f328(f307(x73632,x73631,x73633),x73634)),f328(f328(f9(x73632,x73631),x73633),x73634)) % 167.77/167.50 [7416]E(f328(f39(f877(x74161,x74162)),f315(x74161,x74162,x74163,x74164)),f328(f328(f80(a872),f328(f39(x74161),x74163)),f328(f39(x74162),x74164)))+~P1(f328(f38(x74162),x74164))+~P1(f328(f38(x74161),x74163)) % 167.77/167.50 [7502]E(x75021,x75022)+P1(f328(f328(f330(x75023),x75021),f328(f170(x75023),f167(x75023,x75022,x75024))))+~P1(f328(f328(f330(x75023),x75021),f328(f170(x75023),x75024))) % 167.77/167.50 [7729]~P67(x77291)+E(f328(f328(f80(x77291),f328(f328(f6(a872,x77291),x77292),f328(f298(a872,x77293),x77294))),f328(x77292,x77294)),f328(f328(f6(a872,x77291),x77292),f328(f298(a872,x77293),f328(a116,x77294))))+P1(f328(f328(f243(a872),x77294),x77293)) % 167.77/167.50 [7784]~P26(x77841,x77842,x77843,f251(f879(x77841,a867)))+~P1(f328(f38(x77842),x77844))+P1(f328(f38(x77841),f328(f308(x77841,x77842,x77843),x77844))) % 167.77/167.50 [7898]P1(f328(f328(f330(f873(x78981)),f328(f328(f148(x78981),x78982),x78983)),f158(x78981,x78984)))+~P1(f328(f328(f330(f873(x78981)),x78983),f158(x78981,x78984)))+~P1(f328(f328(f330(x78981),x78982),x78984)) % 167.77/167.50 [7986]~E(f328(f307(x79863,x79861,x79864),f251(f879(x79863,a867))),f251(f879(x79861,a867)))+P1(f328(f38(x79861),x79862))+~P1(f328(f38(x79863),f328(f308(x79863,x79861,x79864),x79862))) % 167.77/167.50 [8077]~P26(x80771,x80773,x80774,x80772)+P1(f328(f38(x80771),x80772))+~P1(f328(f38(x80773),f328(f307(x80771,x80773,x80774),x80772))) % 167.77/167.50 [8099]~E(x80992,x80993)+P1(f328(f328(f330(f878(x80991,x80991)),f328(f328(f263(x80991,x80991),x80992),x80993)),f260(x80991,x80994)))+~P1(f328(f328(f330(x80991),x80992),x80994)) % 167.77/167.50 [8138]~P67(x81381)+E(f328(f328(f80(x81381),f328(f328(f6(a872,x81381),x81382),f299(a872,x81383,x81384))),f328(x81382,f328(a116,x81384))),f328(f328(f6(a872,x81381),x81382),f299(a872,x81383,f328(a116,x81384))))+P1(f328(f328(f243(a872),f328(a116,x81384)),x81383)) % 167.77/167.50 [8210]P1(f328(x82101,x82102))+~P1(f328(x82101,f328(f328(f162(x82103),x82104),f676(x82101,x82104,x82103))))+~P1(f328(f328(f330(x82103),x82102),f328(f170(x82103),x82104))) % 167.77/167.51 [8349]~P1(f328(f328(f330(x83491),x83492),f317(x83491,x83494)))+P1(f328(f328(f330(f873(x83491)),f328(f328(f148(x83491),x83492),x83493)),f317(f873(x83491),f154(x83491,x83494))))+~P1(f328(f328(f330(f873(x83491)),x83493),f317(f873(x83491),f154(x83491,x83494)))) % 167.77/167.51 [8362]~P26(x83622,x83623,x83624,f557(x83624,x83623,x83622,x83621))+P26(x83622,x83623,x83624,f42(f879(x83622,a867),x83621))+E(x83621,f192(f879(f879(x83622,a867),a867))) % 167.77/167.51 [8638]E(x86381,x86382)+~P1(f328(f328(f330(f878(x86383,x86383)),f328(f328(f263(x86383,x86383),x86381),x86382)),f304(x86383,x86384)))+P1(f328(f328(f330(x86383),x86381),f328(f261(x86383,x86383),x86384))) % 167.77/167.51 [8900]E(x89001,f2(a872))+P1(f328(x89002,x89003))+P1(f328(f328(f330(x89004),f811(x89002,x89003,x89001,x89004)),f328(f170(x89004),f168(x89004,x89001,x89003)))) % 167.77/167.51 [8910]E(x89101,f2(a872))+~P1(f328(x89103,x89104))+P1(f328(f328(f330(x89102),f810(x89103,x89104,x89101,x89102)),f328(f170(x89102),f168(x89102,x89101,x89104)))) % 167.77/167.51 [8918]P26(x89182,x89183,x89184,f42(f879(x89182,a867),x89181))+E(x89181,f192(f879(f879(x89182,a867),a867)))+P1(f328(f328(f330(f879(x89182,a867)),f557(x89184,x89183,x89182,x89181)),x89181)) % 167.77/167.51 [9054]P1(f328(f38(x90541),x90542))+~P1(f328(f38(x90544),f328(f307(x90541,x90544,x90543),x90542)))+P1(f328(f328(f330(x90541),f490(x90543,x90544,x90542,x90541)),x90542)) % 167.77/167.51 [9148]~P4(x91482)+E(f328(f328(f65(x91481,x91482,f328(f328(f8(x91482,f879(x91482,x91482),x91481),f105(x91482)),x91483)),f251(x91482)),x91484),f328(f328(f43(x91481,x91482),x91484),x91483))+~P1(f328(f38(x91481),x91484)) % 167.77/167.51 [9149]~P4(x91492)+E(f328(f328(f65(x91491,x91492,f328(f328(f8(x91492,f879(x91492,x91492),x91491),f114(x91492)),x91493)),f192(x91492)),x91494),f328(f328(f44(x91491,x91492),x91494),x91493))+~P1(f328(f38(x91491),x91494)) % 167.77/167.51 [9232]P1(f328(x92321,x92322))+~P1(f328(x92321,f328(f328(f162(x92323),x92324),f732(x92322,x92321,x92324,x92323))))+~P1(f328(f328(f330(x92323),x92322),f328(f170(x92323),x92324))) % 167.77/167.51 [9252]E(x92521,x92522)+~P1(f328(f328(f330(f878(x92523,x92523)),f328(f328(f263(x92523,x92523),x92521),x92522)),f304(x92523,x92524)))+P1(f328(f328(f330(f878(x92523,x92523)),f328(f328(f263(x92523,x92523),x92521),x92522)),f328(f328(f285(x92523,x92523,x92523),x92524),f304(x92523,x92524)))) % 167.77/167.51 [9301]~E(f328(f193(f873(x93011)),x93012),f328(f193(f873(x93011)),x93013))+~P1(f328(f328(f330(f878(f873(x93011),f873(x93011))),f328(f328(f263(f873(x93011),f873(x93011)),x93012),x93013)),f144(x93011,x93014)))+P1(f328(f328(f330(f878(f873(x93011),f873(x93011))),f328(f328(f263(f873(x93011),f873(x93011)),x93012),x93013)),f142(x93011,x93014))) % 167.77/167.51 [9534]P32(x95341,f328(f328(f18(x95341,a867,a867),f328(f328(f8(a867,f879(a867,a867),x95341),a327),f328(f328(f8(a867,a867,x95341),a323),x95342))),f328(a325,x95343)),x95344)+~P1(f328(x95342,x95343))+~P36(x95341,x95342,f328(f328(f148(x95341),x95343),x95344)) % 167.77/167.51 [9698]~P32(x96981,f328(f328(f18(x96981,a867,a867),f328(f328(f8(a867,f879(a867,a867),x96981),a327),f328(f328(f8(a867,a867,x96981),a323),x96982))),f328(a325,x96983)),x96984)+~P1(f328(x96982,x96983))+P36(x96981,x96982,f328(f328(f148(x96981),x96983),x96984)) % 167.77/167.51 [9702]~P36(x97021,x97022,x97024)+~P32(x97021,f328(f328(f18(x97021,a867,a867),f328(f328(f8(a867,f879(a867,a867),x97021),a327),f328(f328(f8(a867,a867,x97021),a323),x97022))),f328(a325,x97023)),x97024)+P36(x97021,x97022,f328(f328(f148(x97021),x97023),x97024)) % 167.77/167.51 [9739]~P66(x97391)+E(f328(f328(f6(a872,x97391),f328(f328(f18(a872,x97391,x97391),f328(f328(f8(x97391,f879(x97391,x97391),a872),f22(x97391)),x97392)),f328(f328(f8(a872,x97391,a872),x97392),f328(f328(f7(a872,a872,a872),f80(a872)),f78(a872))))),f299(a872,x97393,x97394)),f2(x97391))+P1(f328(f328(f242(a872),x97393),x97394)) % 167.77/167.51 [9981]~P38(x99812,x99814)+~P26(x99812,x99811,x99813,f251(f879(x99812,a867)))+P38(x99811,f328(f307(f878(x99812,x99812),f878(x99811,x99811),f268(x99812,x99811,x99812,x99811,x99813,x99813)),x99814)) % 167.77/167.51 [10142]~E(f328(f193(f873(x101421)),x101423),f328(f193(f873(x101421)),x101422))+P1(f328(f328(f330(f878(f873(x101421),f873(x101421))),f328(f328(f263(f873(x101421),f873(x101421)),x101422),x101423)),f155(x101421,x101424)))+~P1(f328(f328(f267(x101421,x101421,a867),f328(f328(f7(x101421,f879(f878(x101421,x101421),a867),f879(x101421,a867)),f328(f328(f8(f879(x101421,f879(f879(f878(x101421,x101421),a867),a867)),f879(f879(f878(x101421,x101421),a867),f879(x101421,a867)),x101421),f7(x101421,f879(f878(x101421,x101421),a867),a867)),f328(f328(f8(f879(x101421,f878(x101421,x101421)),f879(x101421,f879(f879(f878(x101421,x101421),a867),a867)),x101421),f328(f8(f878(x101421,x101421),f879(f879(f878(x101421,x101421),a867),a867),x101421),f330(f878(x101421,x101421)))),f263(x101421,x101421)))),x101424)),f680(x101424,x101423,x101422,x101421))) % 167.77/167.51 [6052]~P57(x60521)+~E(x60522,f2(x60521))+E(f328(f328(f40(x60521),f328(f328(f81(x60521),x60522),x60523)),f328(f328(f81(x60521),x60522),x60524)),f2(x60521)) % 167.77/167.51 [6090]E(x60901,f117(x60902))+E(x60903,f328(f328(f22(a872),f328(f193(f873(x60902)),x60901)),f78(a872)))+E(f141(x60902,f328(f328(f156(x60902,x60901),x60903),x60904)),f141(x60902,x60901)) % 167.77/167.51 [6118]E(x61181,x61182)+P1(f328(x61183,x61182))+~P1(f328(f328(f328(f306(x61184),x61181),x61183),x61182)) % 167.77/167.51 [6134]~P67(x61341)+~P1(f328(f134(x61342),x61344))+E(f328(f163(x61341),f328(f328(f151(x61342,x61341),x61343),x61344)),f328(f328(f6(x61342,x61341),x61343),f328(f170(x61342),x61344))) % 167.77/167.51 [6159]~P73(x61592)+~P1(f328(f38(x61591),x61594))+E(f328(f328(f9(x61591,x61592),f328(f16(x61592,x61591),x61593)),x61594),f328(f328(f253(x61592),x61593),f328(f39(x61591),x61594))) % 167.77/167.51 [6167]~E(x61674,x61672)+P1(f328(x61671,x61672))+P1(f328(f328(f328(a198,f32(x61671,x61673)),x61672),x61674)) % 167.77/167.51 [6215]~P57(x62152)+E(x62151,f2(x62152))+E(f328(f328(f40(x62152),f328(f328(f81(x62152),x62153),x62151)),f328(f328(f81(x62152),x62154),x62151)),f328(f328(f40(x62152),x62153),x62154)) % 167.77/167.51 [6217]~P60(x62172)+E(x62171,f2(x62172))+E(f328(f328(f286(x62172),f328(f328(f81(x62172),x62173),x62171)),f328(f328(f81(x62172),x62174),x62171)),f328(f328(f286(x62172),x62173),x62174)) % 167.77/167.51 [6218]~P60(x62182)+E(x62181,f2(x62182))+E(f328(f328(f286(x62182),f328(f328(f81(x62182),x62181),x62183)),f328(f328(f81(x62182),x62181),x62184)),f328(f328(f286(x62182),x62183),x62184)) % 167.77/167.51 [6219]~P57(x62192)+E(x62191,f2(x62192))+E(f328(f328(f40(x62192),f328(f328(f81(x62192),x62191),x62193)),f328(f328(f81(x62192),x62191),x62194)),f328(f328(f40(x62192),x62193),x62194)) % 167.77/167.51 [6282]P1(f328(x62821,x62822))+~E(x62823,f328(f328(f80(a872),x62824),x62822))+~P1(f328(x62821,f328(f328(f22(a872),x62823),x62824))) % 167.77/167.51 [6362]P29(x63621,x63622,x63623)+P28(x63621,f591(x63623,x63622,x63621),x63624)+~P1(f328(f328(f330(f871(x63621)),x63624),x63622)) % 167.77/167.51 [6364]~P1(f328(x63642,x63643))+~P1(f328(f157(x63641,x63642),x63644))+P1(f328(f157(x63641,x63642),f328(f328(f148(x63641),x63643),x63644))) % 167.77/167.51 [6404]E(x64041,f117(x64042))+~E(x64043,f328(f328(f22(a872),f328(f193(f873(x64042)),x64041)),f78(a872)))+E(f141(x64042,f328(f328(f156(x64042,x64041),x64043),x64044)),x64044) % 167.77/167.51 [6427]~P99(x64271)+~P1(f328(f328(f243(x64271),x64272),x64274))+P1(f328(f328(f243(x64271),x64272),f328(f328(f114(x64271),x64273),x64274))) % 167.77/167.51 [6428]~P99(x64281)+~P1(f328(f328(f243(x64281),x64282),x64283))+P1(f328(f328(f243(x64281),x64282),f328(f328(f114(x64281),x64283),x64284))) % 167.77/167.51 [6430]~P105(x64301)+~P1(f328(f328(f243(x64301),x64302),x64304))+P1(f328(f328(f243(x64301),x64302),f328(f328(f241(x64301),x64303),x64304))) % 167.77/167.51 [6432]~P105(x64321)+~P1(f328(f328(f243(x64321),x64322),x64323))+P1(f328(f328(f243(x64321),x64322),f328(f328(f241(x64321),x64323),x64324))) % 167.77/167.51 [6433]~P99(x64331)+~P1(f328(f328(f242(x64331),x64332),x64334))+P1(f328(f328(f242(x64331),x64332),f328(f328(f114(x64331),x64333),x64334))) % 167.77/167.51 [6434]~P99(x64341)+~P1(f328(f328(f242(x64341),x64342),x64343))+P1(f328(f328(f242(x64341),x64342),f328(f328(f114(x64341),x64343),x64344))) % 167.77/167.51 [6436]~P105(x64361)+~P1(f328(f328(f242(x64361),x64362),x64364))+P1(f328(f328(f242(x64361),x64362),f328(f328(f241(x64361),x64363),x64364))) % 167.77/167.51 [6438]~P105(x64381)+~P1(f328(f328(f242(x64381),x64382),x64383))+P1(f328(f328(f242(x64381),x64382),f328(f328(f241(x64381),x64383),x64384))) % 167.77/167.51 [6524]~E(f328(f328(f162(x65241),x65242),x65243),x65244)+E(f328(f328(f156(x65241,x65242),x65243),x65244),x65242)+~P1(f328(f328(f243(a872),x65243),f328(f193(f873(x65241)),x65242))) % 167.77/167.51 [6564]P1(f328(x65641,x65642))+~P1(f328(x65643,x65642))+~P1(f328(f328(f242(f879(x65644,a867)),x65643),x65641)) % 167.77/167.51 [6596]~E(f328(f328(f156(x65961,x65962),x65963),x65964),x65962)+E(f328(f328(f162(x65961),x65962),x65963),x65964)+~P1(f328(f328(f243(a872),x65963),f328(f193(f873(x65961)),x65962))) % 167.77/167.51 [6611]~P1(f328(f157(x66111,x66112),x66114))+~P1(f328(f157(x66111,x66112),x66113))+P1(f328(f157(x66111,x66112),f328(f328(f125(x66111),x66113),x66114))) % 167.77/167.51 [6708]P28(x67081,x67082,x67083)+~P28(x67081,f328(a116,x67082),f592(x67082,x67084,x67081))+~P1(f328(f328(f330(f871(x67081)),x67083),x67084)) % 167.77/167.51 [6717]E(x67171,f192(f879(x67172,a867)))+E(x67173,f192(f879(x67174,a867)))+~E(f328(f328(f265(x67174,x67172),x67173),f328(f16(f879(x67172,a867),x67174),x67171)),f192(f879(f878(x67174,x67172),a867))) % 167.77/167.51 [6736]E(x67361,x67362)+P1(f328(f328(f330(x67363),x67361),x67364))+~P1(f328(f328(f330(x67363),x67361),f328(f328(f306(x67363),x67362),x67364))) % 167.77/167.51 [6752]~P105(x67521)+P1(f328(f328(f243(x67521),x67522),x67523))+~P1(f328(f328(f243(x67521),x67522),f328(f328(f240(x67521),x67524),x67523))) % 167.77/167.51 [6753]~P105(x67531)+P1(f328(f328(f243(x67531),x67532),x67533))+~P1(f328(f328(f243(x67531),x67532),f328(f328(f240(x67531),x67533),x67534))) % 167.77/167.51 [6755]~P100(x67551)+P1(f328(f328(f242(x67551),x67552),x67553))+~P1(f328(f328(f242(x67551),x67552),f328(f328(f105(x67551),x67554),x67553))) % 167.77/167.51 [6757]~P100(x67571)+P1(f328(f328(f242(x67571),x67572),x67573))+~P1(f328(f328(f242(x67571),x67572),f328(f328(f105(x67571),x67573),x67574))) % 167.77/167.51 [6759]~P105(x67591)+P1(f328(f328(f242(x67591),x67592),x67593))+~P1(f328(f328(f242(x67591),x67592),f328(f328(f240(x67591),x67594),x67593))) % 167.77/167.51 [6761]~P105(x67611)+P1(f328(f328(f242(x67611),x67612),x67613))+~P1(f328(f328(f242(x67611),x67612),f328(f328(f240(x67611),x67613),x67614))) % 167.77/167.51 [6783]~E(f328(f328(f162(x67831),x67833),x67834),x67832)+P1(f328(f328(f330(x67831),x67832),f328(f170(x67831),x67833)))+~P1(f328(f328(f243(a872),x67834),f328(f193(f873(x67831)),x67833))) % 167.77/167.51 [6795]~P105(x67951)+~P15(x67951,f328(f328(f148(x67951),x67952),f328(f328(f148(x67951),x67953),x67954)))+P1(f328(f328(f242(x67951),x67952),x67953)) % 167.77/167.51 [6856]E(x68561,x68562)+P1(f328(x68563,x68561))+~P1(f328(f328(f328(a198,f32(x68563,x68564)),x68561),x68562)) % 167.77/167.51 [6936]~P32(x69362,x69361,x69363)+P1(f328(x69361,f328(f328(f162(x69362),x69363),x69364)))+~P1(f328(f328(f243(a872),x69364),f328(f193(f873(x69362)),x69363))) % 167.77/167.51 [6955]E(x69551,f2(a1))+E(f328(f328(f40(a1),x69552),x69551),x69553)+~P1(f328(f50(x69552,x69551),f328(f328(f263(a1,a1),x69553),x69554))) % 167.77/167.51 [6976]E(f46(a1,x69762,x69761),x69763)+E(x69761,f2(a1))+~P1(f328(f50(x69762,x69761),f328(f328(f263(a1,a1),x69764),x69763))) % 167.77/167.51 [7092]P1(f328(f328(f330(x70921),x70922),x70923))+~P1(f328(f328(f330(x70921),x70922),x70924))+~P1(f328(f328(f243(f879(x70921,a867)),x70924),x70923)) % 167.77/167.51 [7096]P1(f328(f328(f330(x70961),x70962),x70963))+~P1(f328(f328(f330(x70961),x70962),x70964))+~P1(f328(f328(f242(f879(x70961,a867)),x70964),x70963)) % 167.77/167.51 [7206]P34(x72061,x72062,x72063)+~P1(f328(x72062,f328(f328(f162(x72061),x72063),x72064)))+~P1(f328(f328(f243(a872),x72064),f328(f193(f873(x72061)),x72063))) % 167.77/167.51 [7317]~P108(x73172)+~P1(f328(f328(f243(f879(x73171,x73172)),x73173),x73174))+P1(f328(f328(f242(f879(x73171,x73172)),x73173),x73174)) % 167.77/167.51 [7404]~P25(x74041,x74042,x74044)+P25(x74041,x74042,f328(f328(f306(f871(x74041)),x74043),x74044))+~P25(x74041,x74042,f328(f328(f306(f871(x74041)),x74043),f192(f879(f871(x74041),a867)))) % 167.77/167.51 [7448]~P1(f328(f328(f330(x74481),x74482),x74484))+P1(f328(f328(f330(x74481),x74482),f41(f879(x74481,a867),x74483)))+~P1(f328(f328(f330(f879(x74481,a867)),x74484),x74483)) % 167.77/167.51 [7460]P28(x74601,x74602,x74603)+P1(f328(f328(f330(f871(x74601)),f592(x74602,x74604,x74601)),x74604))+~P1(f328(f328(f330(f871(x74601)),x74603),x74604)) % 167.77/167.51 [7480]~P81(x74801)+~P1(f328(f328(f243(x74801),x74803),x74804))+P1(f328(f328(f243(x74801),f328(f328(f80(x74801),x74802),x74803)),f328(f328(f80(x74801),x74802),x74804))) % 167.77/167.51 [7481]~P82(x74811)+~P1(f328(f328(f243(x74811),x74813),x74814))+P1(f328(f328(f243(x74811),f328(f328(f80(x74811),x74812),x74813)),f328(f328(f80(x74811),x74812),x74814))) % 167.77/167.51 [7482]~P81(x74821)+~P1(f328(f328(f243(x74821),x74822),x74824))+P1(f328(f328(f243(x74821),f328(f328(f80(x74821),x74822),x74823)),f328(f328(f80(x74821),x74824),x74823))) % 167.77/167.51 [7483]~P82(x74831)+~P1(f328(f328(f243(x74831),x74832),x74834))+P1(f328(f328(f243(x74831),f328(f328(f80(x74831),x74832),x74833)),f328(f328(f80(x74831),x74834),x74833))) % 167.77/167.51 [7484]~P82(x74841)+~P1(f328(f328(f242(x74841),x74843),x74844))+P1(f328(f328(f242(x74841),f328(f328(f80(x74841),x74842),x74843)),f328(f328(f80(x74841),x74842),x74844))) % 167.77/167.51 [7485]~P83(x74851)+~P1(f328(f328(f242(x74851),x74853),x74854))+P1(f328(f328(f242(x74851),f328(f328(f80(x74851),x74852),x74853)),f328(f328(f80(x74851),x74852),x74854))) % 167.77/167.51 [7486]~P82(x74861)+~P1(f328(f328(f242(x74861),x74862),x74864))+P1(f328(f328(f242(x74861),f328(f328(f80(x74861),x74862),x74863)),f328(f328(f80(x74861),x74864),x74863))) % 167.77/167.51 [7487]~P83(x74871)+~P1(f328(f328(f242(x74871),x74872),x74874))+P1(f328(f328(f242(x74871),f328(f328(f80(x74871),x74872),x74873)),f328(f328(f80(x74871),x74874),x74873))) % 167.77/167.51 [7496]~P109(x74961)+~P92(x74961)+E(f328(f328(f22(x74961),f328(f328(f81(x74961),x74962),f328(f107(x74961),x74963))),f328(f328(f81(x74961),x74964),f328(f107(x74961),x74963))),f328(f328(f81(x74961),f328(f328(f22(x74961),x74962),x74964)),f328(f107(x74961),x74963))) % 167.77/167.51 [7497]~P136(x74971)+~P92(x74971)+E(f328(f328(f80(x74971),f328(f328(f81(x74971),x74972),f328(f107(x74971),x74973))),f328(f328(f81(x74971),x74974),f328(f107(x74971),x74973))),f328(f328(f81(x74971),f328(f328(f80(x74971),x74972),x74974)),f328(f107(x74971),x74973))) % 167.77/167.51 [7532]~P67(x75321)+E(f328(f328(f80(x75321),f328(x75322,x75323)),f328(f328(f6(a872,x75321),x75322),f299(a872,f328(a116,x75323),x75324))),f328(f328(f6(a872,x75321),x75322),f299(a872,x75323,x75324)))+~P1(f328(f328(f242(a872),x75323),x75324)) % 167.77/167.51 [7543]~P26(x75432,x75431,x75433,f328(f170(x75432),x75434))+~P1(f328(f134(x75432),x75434))+P1(f328(f134(x75431),f328(f328(f151(x75432,x75431),x75433),x75434))) % 167.77/167.51 [7594]~P1(f328(f328(f243(a872),x75942),x75944))+~P1(f328(f328(f243(a872),x75941),x75943))+P1(f328(f328(f243(a872),f328(f328(f80(a872),x75941),x75942)),f328(f328(f80(a872),x75943),x75944))) % 167.77/167.51 [7595]~P1(f328(f328(f243(a1),x75951),x75953))+~P1(f328(f328(f242(a1),x75952),x75954))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x75951),x75952)),f328(f328(f80(a1),x75953),x75954))) % 167.77/167.51 [7596]~P1(f328(f328(f242(a872),x75962),x75964))+~P1(f328(f328(f242(a872),x75961),x75963))+P1(f328(f328(f242(a872),f328(f328(f80(a872),x75961),x75962)),f328(f328(f80(a872),x75963),x75964))) % 167.77/167.51 [7597]~P1(f328(f328(f242(a872),x75972),x75974))+~P1(f328(f328(f242(a872),x75971),x75973))+P1(f328(f328(f242(a872),f328(f328(f81(a872),x75971),x75972)),f328(f328(f81(a872),x75973),x75974))) % 167.77/167.51 [7645]P1(f328(f328(f330(x76451),x76452),x76453))+~P1(f328(f328(f330(x76451),x76452),f42(f879(x76451,a867),x76454)))+~P1(f328(f328(f330(f879(x76451,a867)),x76453),x76454)) % 167.77/167.51 [7661]~P1(f328(x76611,f674(x76611,x76613,x76612)))+P1(f328(x76611,f328(f328(f162(x76612),x76613),x76614)))+~P1(f328(f328(f243(a872),x76614),f328(f193(f873(x76612)),x76613))) % 167.77/167.51 [7666]P1(f328(x76661,x76662))+~P1(f328(f328(f330(x76664),x76662),f328(f170(x76664),x76663)))+P1(f328(f328(f243(a872),f676(x76661,x76663,x76664)),f328(f193(f873(x76664)),x76663))) % 167.77/167.51 [7714]~P108(x77141)+~P1(f328(f328(f242(f879(x77142,x77141)),x77144),x77143))+~P1(f328(f328(f243(f879(x77142,x77141)),x77143),x77144)) % 167.77/167.51 [7761]~P1(f328(x77614,x77612))+~P1(f328(f328(f330(x77611),x77612),x77613))+P1(f328(f328(f330(x77611),x77612),f328(f328(f105(f879(x77611,a867)),x77613),f328(f248(x77611),x77614)))) % 167.77/167.51 [7907]~P1(f328(f328(f330(x79071),x79073),x79074))+~P1(f328(f328(f243(f879(x79071,a867)),x79072),x79074))+P1(f328(f328(f243(f879(x79071,a867)),x79072),f328(f328(f306(x79071),x79073),x79074))) % 167.77/167.51 [7909]E(f328(f328(f105(f879(x79091,a867)),x79092),x79093),f192(f879(x79091,a867)))+~E(f328(f328(f105(f879(x79091,a867)),f41(f879(x79091,a867),x79094)),x79093),f192(f879(x79091,a867)))+~P1(f328(f328(f330(f879(x79091,a867)),x79092),x79094)) % 167.77/167.51 [7982]P1(f328(f328(f330(x79821),x79822),x79823))+~P1(f328(f328(f242(f879(x79821,a867)),x79823),f328(f328(f306(x79821),x79822),x79824)))+P1(f328(f328(f242(f879(x79821,a867)),x79823),x79824)) % 167.77/167.51 [7999]P1(f328(f328(f330(x79992),f674(x79991,x79993,x79992)),f328(f170(x79992),x79993)))+P1(f328(x79991,f328(f328(f162(x79992),x79993),x79994)))+~P1(f328(f328(f243(a872),x79994),f328(f193(f873(x79992)),x79993))) % 167.77/167.51 [8007]~P1(f328(f328(f243(f879(x80071,a867)),x80072),x80074))+P1(f328(f328(f243(f879(x80071,a867)),x80072),x80073))+~P1(f328(f328(f243(f879(x80071,a867)),x80074),x80073)) % 167.77/167.51 [8008]~P1(f328(f328(f242(f879(x80081,a867)),x80082),x80084))+P1(f328(f328(f243(f879(x80081,a867)),x80082),x80083))+~P1(f328(f328(f243(f879(x80081,a867)),x80084),x80083)) % 167.77/167.51 [8009]~P1(f328(f328(f242(f879(x80091,a867)),x80094),x80093))+~P1(f328(f328(f243(f879(x80091,a867)),x80092),x80094))+P1(f328(f328(f243(f879(x80091,a867)),x80092),x80093)) % 167.77/167.51 [8010]~P1(f328(f328(f242(f879(x80101,a867)),x80102),x80104))+P1(f328(f328(f242(f879(x80101,a867)),x80102),x80103))+~P1(f328(f328(f242(f879(x80101,a867)),x80104),x80103)) % 167.77/167.51 [8050]~P1(f328(f328(f330(x80501),x80504),x80503))+~P1(f328(f328(f243(f879(x80501,a867)),x80502),f328(f328(f306(x80501),x80504),x80503)))+P1(f328(f328(f243(f879(x80501,a867)),x80502),x80503)) % 167.77/167.51 [8062]~P82(x80621)+P1(f328(f328(f243(x80621),x80622),x80623))+~P1(f328(f328(f243(x80621),f328(f328(f80(x80621),x80624),x80622)),f328(f328(f80(x80621),x80624),x80623))) % 167.77/167.51 [8064]~P82(x80641)+P1(f328(f328(f243(x80641),x80642),x80643))+~P1(f328(f328(f243(x80641),f328(f328(f80(x80641),x80642),x80644)),f328(f328(f80(x80641),x80643),x80644))) % 167.77/167.51 [8066]~P82(x80661)+P1(f328(f328(f242(x80661),x80662),x80663))+~P1(f328(f328(f242(x80661),f328(f328(f80(x80661),x80664),x80662)),f328(f328(f80(x80661),x80664),x80663))) % 167.77/167.51 [8068]~P82(x80681)+P1(f328(f328(f242(x80681),x80682),x80683))+~P1(f328(f328(f242(x80681),f328(f328(f80(x80681),x80682),x80684)),f328(f328(f80(x80681),x80683),x80684))) % 167.77/167.51 [8082]~P1(f328(f328(f328(a198,x80822),x80823),x80824))+~P1(f328(f328(f328(a198,f32(x80821,x80822)),x80824),x80823))+P1(f328(f328(f328(a198,f32(x80821,x80822)),x80823),x80823)) % 167.77/167.51 [8117]P1(f328(x81171,x81172))+~E(f328(f328(f135(x81173),f328(f193(f873(x81173)),f175(x81173,x81171,x81174))),x81174),f117(x81173))+~P1(f328(f328(f330(x81173),x81172),f328(f170(x81173),x81174))) % 167.77/167.51 [8253]P1(f328(x82531,x82532))+~P1(f328(f328(f330(x82533),x82532),f328(f170(x82533),x82534)))+P1(f328(f328(f243(a872),f328(f193(f873(x82533)),f328(f133(x82533,x82531),x82534))),f328(f193(f873(x82533)),x82534))) % 167.77/167.51 [8494]E(x84941,x84942)+P1(f328(f328(f328(a198,x84943),x84941),f599(x84942,x84941,x84943,x84944)))+~P1(f328(f328(f328(a198,f32(x84944,x84943)),x84941),x84942)) % 167.77/167.51 [8523]~P1(f328(x85234,x85232))+P1(f328(f328(f328(a198,x85231),x85232),f599(x85233,x85232,x85231,x85234)))+~P1(f328(f328(f328(a198,f32(x85234,x85231)),x85232),x85233)) % 167.77/167.51 [8730]~P1(f328(x87301,f781(x87301,x87303,x87302,x87304)))+P1(f328(x87301,f328(f328(f162(x87302),x87303),x87304)))+~P1(f328(f328(f243(a872),x87304),f328(f193(f873(x87302)),x87303))) % 167.77/167.51 [8753]~P26(x87534,x87533,x87531,f251(f879(x87534,a867)))+E(f328(x87531,f540(x87532,x87531,x87533,x87534)),x87532)+~P1(f328(f328(f330(x87533),x87532),f328(f307(x87534,x87533,x87531),f251(f879(x87534,a867))))) % 167.77/167.51 [8818]E(f175(x88181,x88182,x88183),f328(f328(f173(x88181),x88184),x88183))+P1(f328(f328(f243(a872),f756(x88182,x88183,x88181,x88184)),x88184))+P1(f328(f328(f243(a872),x88184),f328(f193(f873(x88181)),x88183))) % 167.77/167.51 [8821]E(f175(x88211,x88212,x88213),f328(f328(f173(x88211),x88214),x88213))+P1(f328(f328(f243(a872),f756(x88212,x88213,x88211,x88214)),x88214))+P1(f328(x88212,f328(f328(f162(x88211),x88213),x88214))) % 167.77/167.51 [8850]P1(f328(x88501,x88502))+~P1(f328(f328(f330(x88504),x88502),f328(f170(x88504),x88503)))+P1(f328(f328(f243(a872),f732(x88502,x88501,x88503,x88504)),f328(f193(f873(x88504)),x88503))) % 167.77/167.51 [8853]E(f175(x88531,x88532,x88533),f328(f328(f173(x88531),x88534),x88533))+P1(f328(f328(f243(a872),x88534),f328(f193(f873(x88531)),x88533)))+P1(f328(f328(f243(a872),f756(x88532,x88533,x88531,x88534)),f328(f193(f873(x88531)),x88533))) % 167.77/167.51 [8860]E(f175(x88601,x88602,x88603),f328(f328(f173(x88601),x88604),x88603))+P1(f328(x88602,f328(f328(f162(x88601),x88603),x88604)))+P1(f328(f328(f243(a872),f756(x88602,x88603,x88601,x88604)),f328(f193(f873(x88601)),x88603))) % 167.77/167.51 [8885]~P116(x88854)+P1(f328(f328(f330(x88851),f658(x88852,x88853,x88851,x88854)),x88853))+P1(f328(f328(f243(x88854),f2(x88854)),f328(f328(f9(x88851,x88854),x88852),x88853))) % 167.77/167.51 [8886]~P116(x88864)+P1(f328(f328(f330(x88861),f662(x88862,x88863,x88861,x88864)),x88863))+P1(f328(f328(f242(x88864),f2(x88864)),f328(f328(f9(x88861,x88864),x88862),x88863))) % 167.77/167.51 [8920]~P1(f328(f38(x89201),x89204))+P1(f328(f328(f330(x89201),f561(x89202,x89203,x89204,x89201)),x89204))+P1(f328(f38(f878(x89201,x89203)),f328(f328(f265(x89201,x89203),x89204),x89202))) % 167.77/167.51 [8954]P1(f328(f328(f330(x89542),f781(x89541,x89543,x89542,x89544)),f328(f170(x89542),x89543)))+P1(f328(x89541,f328(f328(f162(x89542),x89543),x89544)))+~P1(f328(f328(f243(a872),x89544),f328(f193(f873(x89542)),x89543))) % 167.77/167.51 [9059]E(x90591,x90592)+P1(f328(f328(f328(a198,f32(x90593,x90594)),f599(x90591,x90592,x90594,x90593)),x90591))+~P1(f328(f328(f328(a198,f32(x90593,x90594)),x90592),x90591)) % 167.77/167.51 [9063]~P1(f328(x90631,x90634))+P1(f328(f328(f328(a198,f32(x90631,x90632)),f599(x90633,x90634,x90632,x90631)),x90633))+~P1(f328(f328(f328(a198,f32(x90631,x90632)),x90634),x90633)) % 167.77/167.51 [9085]P1(f328(f328(f242(a872),x90854),f328(f193(f873(x90852)),f175(x90852,x90853,x90851))))+P1(f328(f328(f243(a872),f757(x90851,x90852,x90853,x90854)),x90854))+~P1(f328(f328(f242(a872),x90854),f328(f193(f873(x90852)),x90851))) % 167.77/167.51 [9189]~E(f328(f328(f176(x91891,x91892),x91893),f768(x91894,x91893,x91892,x91891)),f328(f328(f176(x91891,x91892),x91894),f768(x91894,x91893,x91892,x91891)))+E(f328(f176(x91891,x91892),x91893),f328(f176(x91891,x91892),x91894))+~E(f328(f170(x91891),f328(f328(f151(f878(x91891,x91892),x91891),f262(x91891,x91892)),x91893)),f328(f170(x91891),f328(f328(f151(f878(x91891,x91892),x91891),f262(x91891,x91892)),x91894))) % 167.77/167.51 [9235]E(f175(x92351,x92352,x92353),f328(f328(f173(x92351),x92354),x92353))+~P1(f328(x92352,f328(f328(f162(x92351),x92353),f756(x92352,x92353,x92351,x92354))))+P1(f328(f328(f243(a872),x92354),f328(f193(f873(x92351)),x92353))) % 167.77/167.51 [9239]E(f175(x92391,x92392,x92393),f328(f328(f173(x92391),x92394),x92393))+~P1(f328(x92392,f328(f328(f162(x92391),x92393),f756(x92392,x92393,x92391,x92394))))+P1(f328(x92392,f328(f328(f162(x92391),x92393),x92394))) % 167.77/167.51 [9246]~P1(f328(f38(x92461),x92463))+~P1(f328(f38(x92462),f328(x92464,f561(x92464,x92462,x92463,x92461))))+P1(f328(f38(f878(x92461,x92462)),f328(f328(f265(x92461,x92462),x92463),x92464))) % 167.77/167.51 [9254]~P116(x92541)+~P1(f328(f328(f243(x92541),f2(x92541)),f328(x92543,f658(x92543,x92544,x92542,x92541))))+P1(f328(f328(f243(x92541),f2(x92541)),f328(f328(f9(x92542,x92541),x92543),x92544))) % 167.77/167.51 [9255]~P116(x92551)+~P1(f328(f328(f242(x92551),f2(x92551)),f328(x92553,f662(x92553,x92554,x92552,x92551))))+P1(f328(f328(f242(x92551),f2(x92551)),f328(f328(f9(x92552,x92551),x92553),x92554))) % 167.77/167.51 [9261]~E(f328(f193(f873(x92614)),x92612),f328(f193(f873(x92614)),x92613))+P1(f328(f328(f330(f878(f873(x92614),f873(x92614))),f328(f328(f263(f873(x92614),f873(x92614)),x92613),x92612)),f155(x92614,x92611)))+P1(f328(f328(f243(a872),f666(x92611,x92612,x92613,x92614)),f328(f193(f873(x92614)),x92613))) % 167.77/167.51 [9315]~P1(f328(x93153,f328(f328(f162(x93152),x93154),f757(x93154,x93152,x93153,x93151))))+P1(f328(f328(f242(a872),x93151),f328(f193(f873(x93152)),f175(x93152,x93153,x93154))))+~P1(f328(f328(f242(a872),x93151),f328(f193(f873(x93152)),x93154))) % 167.77/167.51 [9392]E(f328(f328(f173(x93921),f675(x93922,x93923,x93924,x93921)),x93923),f328(f328(f173(x93921),f675(x93922,x93923,x93924,x93921)),x93924))+~P1(f328(f328(f330(f878(f873(x93921),f873(x93921))),f328(f328(f263(f873(x93921),f873(x93921)),x93924),x93923)),f144(x93921,x93922)))+P1(f328(f328(f243(a872),f328(f193(f873(x93921)),x93924)),f328(f193(f873(x93921)),x93923))) % 167.77/167.51 [9446]~P1(f328(f328(f243(a872),f2(a872)),x94463))+~P1(f328(f328(f243(a872),x94464),x94461))+P1(f328(f328(f243(a872),f328(f328(f80(a872),f328(f328(f81(a872),x94461),f46(a872,x94462,x94463))),x94464)),f328(f328(f81(a872),x94461),x94463))) % 167.77/167.51 [9642]~P108(x96422)+~P1(f328(f328(f242(x96422),f328(x96423,f344(x96424,x96423,x96421,x96422))),f328(x96424,f344(x96424,x96423,x96421,x96422))))+P1(f328(f328(f242(f879(x96421,x96422)),x96423),x96424)) % 167.77/167.51 [9746]~P66(x97461)+E(f328(f328(f6(a872,x97461),f328(f328(f18(a872,x97461,x97461),f328(f328(f8(x97461,f879(x97461,x97461),a872),f22(x97461)),x97462)),f328(f328(f8(a872,x97461,a872),x97462),f328(f328(f7(a872,a872,a872),f80(a872)),f78(a872))))),f299(a872,x97463,x97464)),f328(f328(f22(x97461),f328(x97462,x97463)),f328(x97462,f328(f328(f80(a872),x97464),f78(a872)))))+~P1(f328(f328(f242(a872),x97463),x97464)) % 167.77/167.51 [6787]E(f328(f328(f125(x67871),x67872),x67873),x67874)+~E(x67873,f328(f328(f135(x67871),f328(f193(f873(x67871)),x67872)),x67874))+~E(f328(f328(f173(x67871),f328(f193(f873(x67871)),x67872)),x67874),x67872) % 167.77/167.51 [6843]~P61(x68432)+E(x68431,f2(x68432))+E(f328(f328(f286(x68432),f328(f328(f253(x68432),x68433),x68434)),f328(f328(f253(x68432),x68431),x68434)),f328(f328(f253(x68432),f328(f328(f286(x68432),x68433),x68431)),x68434)) % 167.77/167.51 [6978]~E(f328(f193(f873(x69781)),x69783),f328(f193(f873(x69782)),x69784))+~P1(f328(f134(x69781),x69783))+E(f182(x69781,x69782,f328(f176(x69781,x69782),f328(f328(f180(x69781,x69782),x69783),x69784))),f328(f170(x69781),x69783)) % 167.77/167.51 [6995]~P100(x69951)+~P1(f328(f328(f243(x69951),x69953),x69954))+P1(f328(f328(f243(x69951),f328(f328(f105(x69951),x69952),x69953)),x69954)) % 167.77/167.51 [6996]~P100(x69961)+~P1(f328(f328(f243(x69961),x69962),x69964))+P1(f328(f328(f243(x69961),f328(f328(f105(x69961),x69962),x69963)),x69964)) % 167.77/167.51 [6998]~P105(x69981)+~P1(f328(f328(f243(x69981),x69983),x69984))+P1(f328(f328(f243(x69981),f328(f328(f240(x69981),x69982),x69983)),x69984)) % 167.77/167.51 [7000]~P105(x70001)+~P1(f328(f328(f243(x70001),x70002),x70004))+P1(f328(f328(f243(x70001),f328(f328(f240(x70001),x70002),x70003)),x70004)) % 167.77/167.51 [7001]~P100(x70011)+~P1(f328(f328(f242(x70011),x70013),x70014))+P1(f328(f328(f242(x70011),f328(f328(f105(x70011),x70012),x70013)),x70014)) % 167.77/167.51 [7002]~P100(x70021)+~P1(f328(f328(f242(x70021),x70022),x70024))+P1(f328(f328(f242(x70021),f328(f328(f105(x70021),x70022),x70023)),x70024)) % 167.77/167.51 [7004]~P105(x70041)+~P1(f328(f328(f242(x70041),x70043),x70044))+P1(f328(f328(f242(x70041),f328(f328(f240(x70041),x70042),x70043)),x70044)) % 167.77/167.51 [7006]~P105(x70061)+~P1(f328(f328(f242(x70061),x70062),x70064))+P1(f328(f328(f242(x70061),f328(f328(f240(x70061),x70062),x70063)),x70064)) % 167.77/167.51 [7026]~P1(f328(x70263,x70264))+~P1(f328(x70262,x70264))+P1(f328(f328(f328(f105(f879(x70261,a867)),x70262),x70263),x70264)) % 167.77/167.51 [7150]P25(x71501,x71502,x71503)+~P25(x71501,x71504,x71503)+~P1(f328(f328(f242(f879(f871(x71501),a867)),x71504),x71502)) % 167.77/167.51 [7151]P25(x71511,x71512,x71513)+~P25(x71511,x71512,x71514)+~P1(f328(f328(f242(f879(f871(x71511),a867)),x71513),x71514)) % 167.77/167.51 [7522]~P67(x75221)+E(f328(f328(f80(x75221),f328(x75222,x75223)),f328(f328(f6(a872,x75221),x75222),f328(f298(a872,f328(a116,x75223)),x75224))),f328(f328(f6(a872,x75221),x75222),f328(f298(a872,x75223),x75224)))+~P1(f328(f328(f243(a872),x75223),x75224)) % 167.77/167.51 [7550]~P105(x75501)+P1(f328(f328(f243(x75501),x75502),x75503))+~P1(f328(f328(f243(x75501),f328(f328(f241(x75501),x75504),x75502)),x75503)) % 167.77/167.51 [7551]~P105(x75511)+P1(f328(f328(f243(x75511),x75512),x75513))+~P1(f328(f328(f243(x75511),f328(f328(f241(x75511),x75512),x75514)),x75513)) % 167.77/167.51 [7553]~P99(x75531)+P1(f328(f328(f242(x75531),x75532),x75533))+~P1(f328(f328(f242(x75531),f328(f328(f114(x75531),x75534),x75532)),x75533)) % 167.77/167.51 [7555]~P99(x75551)+P1(f328(f328(f242(x75551),x75552),x75553))+~P1(f328(f328(f242(x75551),f328(f328(f114(x75551),x75552),x75554)),x75553)) % 167.77/167.51 [7557]~P105(x75571)+P1(f328(f328(f242(x75571),x75572),x75573))+~P1(f328(f328(f242(x75571),f328(f328(f241(x75571),x75574),x75572)),x75573)) % 167.77/167.51 [7559]~P105(x75591)+P1(f328(f328(f242(x75591),x75592),x75593))+~P1(f328(f328(f242(x75591),f328(f328(f241(x75591),x75592),x75594)),x75593)) % 167.77/167.51 [7637]~P1(f328(f328(f330(x76371),x76372),x76374))+P1(f328(f328(f330(x76371),x76372),x76373))+P1(f328(f328(f330(x76371),x76372),f328(f328(f22(f879(x76371,a867)),x76374),x76373))) % 167.77/167.51 [7721]P1(f328(x77211,x77212))+P1(f328(x77213,x77212))+~P1(f328(f328(f328(f114(f879(x77214,a867)),x77213),x77211),x77212)) % 167.77/167.51 [7732]~P1(f328(f328(f330(x77321),x77322),x77324))+~P1(f328(f328(f330(x77321),x77322),x77323))+P1(f328(f328(f330(x77321),x77322),f328(f328(f105(f879(x77321,a867)),x77323),x77324))) % 167.77/167.51 [7785]~P99(x77851)+~P1(f328(f38(x77851),x77854))+E(f328(f328(f65(x77851,x77851,f114(x77851)),x77852),f328(f328(f306(x77851),x77853),x77854)),f328(f328(f114(x77851),x77853),f328(f328(f65(x77851,x77851,f114(x77851)),x77852),x77854))) % 167.77/167.51 [7786]~P100(x77861)+~P1(f328(f38(x77861),x77864))+E(f328(f328(f65(x77861,x77861,f105(x77861)),x77862),f328(f328(f306(x77861),x77863),x77864)),f328(f328(f105(x77861),x77863),f328(f328(f65(x77861,x77861,f105(x77861)),x77862),x77864))) % 167.77/167.51 [7787]~P105(x77871)+~P1(f328(f38(x77871),x77874))+E(f328(f328(f65(x77871,x77871,f240(x77871)),x77872),f328(f328(f306(x77871),x77873),x77874)),f328(f328(f240(x77871),x77873),f328(f328(f65(x77871,x77871,f240(x77871)),x77872),x77874))) % 167.77/167.51 [7788]~P105(x77881)+~P1(f328(f38(x77881),x77884))+E(f328(f328(f65(x77881,x77881,f241(x77881)),x77882),f328(f328(f306(x77881),x77883),x77884)),f328(f328(f241(x77881),x77883),f328(f328(f65(x77881,x77881,f241(x77881)),x77882),x77884))) % 167.77/167.51 [7789]~P109(x77891)+~P92(x77891)+E(f328(f328(f22(x77891),f328(f328(f81(x77891),f328(f107(x77891),x77892)),x77893)),f328(f328(f81(x77891),f328(f107(x77891),x77892)),x77894)),f328(f328(f81(x77891),f328(f107(x77891),x77892)),f328(f328(f22(x77891),x77893),x77894))) % 167.77/167.51 [7790]~P136(x77901)+~P92(x77901)+E(f328(f328(f80(x77901),f328(f328(f81(x77901),f328(f107(x77901),x77902)),x77903)),f328(f328(f81(x77901),f328(f107(x77901),x77902)),x77904)),f328(f328(f81(x77901),f328(f107(x77901),x77902)),f328(f328(f80(x77901),x77903),x77904))) % 167.77/167.51 [7905]E(x79051,x79052)+P1(f328(f328(f330(x79053),x79051),f328(f170(x79053),x79054)))+~P1(f328(f328(f330(x79053),x79051),f328(f170(x79053),f328(f328(f148(x79053),x79052),x79054)))) % 167.77/167.51 [7930]~P59(x79301)+~E(f328(f193(f873(x79302)),x79303),f328(f193(f873(x79301)),f57(x79301)))+E(f328(f328(f176(x79301,x79302),f328(f328(f180(x79301,x79302),f57(x79301)),x79303)),x79304),f328(f235(x79302),f731(x79304,x79303,x79302,x79301))) % 167.77/167.51 [8075]P51(x80751,x80752,x80753)+~P51(x80751,x80752,x80754)+~P1(f328(f328(f242(f879(f878(x80751,x80752),a867)),x80753),x80754)) % 167.77/167.51 [8120]P1(f328(f328(f330(x81201),x81202),x81203))+P1(f328(f328(f330(x81201),x81202),x81204))+~P1(f328(f328(f330(x81201),x81202),f328(f328(f114(f879(x81201,a867)),x81204),x81203))) % 167.77/167.51 [8130]~P40(x81301,x81304,x81303)+~P1(f328(f328(f330(x81301),x81302),x81304))+P1(f328(f328(f330(f878(x81301,x81301)),f328(f328(f263(x81301,x81301),x81302),x81302)),x81303)) % 167.77/167.51 [8147]~P1(f328(f38(x81472),x81474))+~P1(f328(f38(x81471),x81473))+P1(f328(f38(f878(x81471,x81472)),f328(f328(f265(x81471,x81472),x81473),f328(f16(f879(x81472,a867),x81471),x81474)))) % 167.77/167.51 [8148]~P1(f328(f328(f330(x81481),x81482),x81484))+~P1(f328(f328(f242(f879(x81481,a867)),x81483),x81484))+P1(f328(f328(f242(f879(x81481,a867)),f328(f328(f306(x81481),x81482),x81483)),x81484)) % 167.77/167.51 [8156]~P73(x81562)+~P142(x81562)+E(f328(f328(f9(x81561,x81562),f328(f328(f8(a872,x81562,x81561),f104(x81562)),x81563)),x81564),f328(f104(x81562),f328(f328(f9(x81561,a872),x81563),x81564))) % 167.77/167.51 [8157]~P73(x81572)+~P138(x81572)+E(f328(f328(f9(x81571,x81572),f328(f328(f8(a1,x81572,x81571),f106(x81572)),x81573)),x81574),f328(f106(x81572),f328(f328(f9(x81571,a1),x81573),x81574))) % 167.77/167.51 [8186]E(f328(f328(f22(f879(x81861,a867)),x81862),f328(f328(f22(f879(x81861,a867)),x81863),x81864)),x81864)+~P1(f328(f328(f242(f879(x81861,a867)),x81862),x81863))+~P1(f328(f328(f242(f879(x81861,a867)),x81864),x81862)) % 167.77/167.51 [8285]~P1(f328(f38(x82851),x82854))+E(f328(f328(f22(a872),f328(f328(f6(x82851,a872),x82852),x82853)),f328(f328(f6(x82851,a872),x82852),x82854)),f328(f328(f6(x82851,a872),x82852),f328(f328(f22(f879(x82851,a867)),x82853),x82854)))+~P1(f328(f328(f242(f879(x82851,a867)),x82854),x82853)) % 167.77/167.51 [8439]~P7(x84391,x84394,x84393)+~P1(f328(f328(f330(x84391),x84392),x84394))+P1(f328(f328(f330(x84391),x84392),f328(f282(x84391,x84391,x84393),f328(f328(f306(x84391),x84392),f192(f879(x84391,a867)))))) % 167.77/167.51 [8499]~P1(f328(f328(f242(f879(x84991,a867)),x84992),x84993))+~P1(f328(f328(f242(f879(x84991,a867)),x84992),x84994))+P1(f328(f328(f242(f879(x84991,a867)),x84992),f328(f328(f105(f879(x84991,a867)),x84993),x84994))) % 167.77/167.51 [8603]E(x86031,f192(f879(x86032,a867)))+P1(f328(f38(x86033),x86034))+~P1(f328(f38(f878(x86033,x86032)),f328(f328(f265(x86033,x86032),x86034),f328(f16(f879(x86032,a867),x86033),x86031)))) % 167.77/167.51 [8604]E(x86041,f192(f879(x86042,a867)))+P1(f328(f38(x86043),x86044))+~P1(f328(f38(f878(x86042,x86043)),f328(f328(f265(x86042,x86043),x86041),f328(f16(f879(x86043,a867),x86042),x86044)))) % 167.77/167.51 [8673]P1(f328(f328(f330(x86731),x86732),f317(x86731,x86733)))+~P1(f328(f328(f330(x86731),x86734),f317(x86731,x86733)))+~P1(f328(f328(f330(f878(x86731,x86731)),f328(f328(f263(x86731,x86731),x86732),x86734)),x86733)) % 167.77/167.51 [8725]~P38(x87251,x87254)+P1(f328(f328(f330(f878(x87251,x87251)),f328(f328(f263(x87251,x87251),x87253),x87252)),f304(x87251,x87254)))+P38(x87251,f328(f328(f306(f878(x87251,x87251)),f328(f328(f263(x87251,x87251),x87252),x87253)),x87254)) % 167.77/167.51 [8726]~P54(x87261,x87264)+P1(f328(f328(f330(f878(x87261,x87261)),f328(f328(f263(x87261,x87261),x87263),x87262)),f304(x87261,x87264)))+P54(x87261,f328(f328(f306(f878(x87261,x87261)),f328(f328(f263(x87261,x87261),x87262),x87263)),x87264)) % 167.77/167.51 [8803]~E(x88032,x88033)+~P1(f328(f328(f330(x88031),x88032),f328(f170(x88031),x88034)))+P1(f328(f328(f330(f878(x88031,x88031)),f328(f328(f263(x88031,x88031),x88032),x88033)),f328(f170(f878(x88031,x88031)),f328(f328(f180(x88031,x88031),x88034),x88034)))) % 167.77/167.51 [8883]~E(x88833,x88834)+P1(f328(f328(f267(x88831,x88831,a867),a325),x88832))+~P1(f328(f328(f330(f878(x88831,x88831)),x88832),f328(f170(f878(x88831,x88831)),f328(f328(f180(x88831,x88831),x88833),x88834)))) % 167.77/167.51 [8911]~P1(f328(x89114,x89112))+P1(f328(f328(f328(f328(a200,x89111),x89112),x89113),f590(x89113,x89112,x89111,x89114)))+~P1(f328(f328(f328(f328(a200,f32(x89114,x89111)),x89112),x89113),x89112)) % 167.77/167.51 [8938]P1(f328(f328(f330(f878(f873(x89381),f873(x89381))),f328(f328(f263(f873(x89381),f873(x89381)),x89382),x89383)),f144(x89381,x89384)))+~E(f328(f328(f173(x89381),f328(f193(f873(x89381)),x89382)),x89383),x89382)+~P1(f328(f328(f243(a872),f328(f193(f873(x89381)),x89382)),f328(f193(f873(x89381)),x89383))) % 167.77/167.51 [9035]~P1(f328(f38(x90351),x90354))+P1(f328(f328(f330(x90351),f722(x90352,x90353,x90354,x90351)),x90354))+P1(f328(f38(x90353),f328(f328(f44(x90351,f879(x90353,a867)),x90354),x90352))) % 167.77/167.51 [9036]~P1(f328(f38(x90361),x90364))+P1(f328(f328(f330(x90361),f846(x90362,x90363,x90364,x90361)),x90364))+P1(f328(f38(x90363),f328(f328(f44(x90361,f879(x90363,a867)),x90364),x90362))) % 167.77/167.51 [9119]P1(f328(f328(f330(f878(x91191,x91191)),x91192),f328(f328(f285(x91191,x91191,x91191),x91193),f304(x91191,x91193))))+~P1(f328(f328(f243(a872),f2(a872)),x91194))+~P1(f328(f328(f330(f878(x91191,x91191)),x91192),f328(f328(f187(f878(x91191,x91191),a867),x91194),x91193))) % 167.77/167.51 [9127]~P38(x91271,x91272)+~P1(f328(f328(f330(f878(x91271,x91271)),f328(f328(f263(x91271,x91271),x91274),x91273)),x91272))+~P1(f328(f328(f330(f878(x91271,x91271)),f328(f328(f263(x91271,x91271),x91273),x91274)),x91272)) % 167.77/167.51 [9253]~P1(f328(f38(x92531),x92534))+E(f328(f328(f6(x92531,a872),f328(f328(f8(f879(x92532,a867),a872,x92531),f39(x92532)),x92533)),x92534),f328(f39(f878(x92531,x92532)),f328(f328(f265(x92531,x92532),x92534),x92533)))+P1(f328(f328(f330(x92531),f563(x92533,x92532,x92534,x92531)),x92534)) % 167.77/167.51 [9257]~P1(f328(f134(x92571),x92572))+P1(f328(f134(x92571),f328(f328(f156(x92571,x92572),x92573),x92574)))+P1(f328(f328(f330(x92571),x92574),f328(f328(f22(f879(x92571,a867)),f328(f170(x92571),x92572)),f328(f328(f306(x92571),f328(f328(f162(x92571),x92572),x92573)),f192(f879(x92571,a867)))))) % 167.77/167.51 [9273]~P1(f328(f38(x92732),x92733))+~P1(f328(f38(x92731),f328(x92734,f722(x92734,x92731,x92733,x92732))))+P1(f328(f38(x92731),f328(f328(f44(x92732,f879(x92731,a867)),x92733),x92734))) % 167.77/167.51 [9274]~P1(f328(f38(x92742),x92743))+~P1(f328(f38(x92741),f328(x92744,f846(x92744,x92741,x92743,x92742))))+P1(f328(f38(x92741),f328(f328(f44(x92742,f879(x92741,a867)),x92743),x92744))) % 167.77/167.51 [9353]~P1(f328(f328(f330(f878(x93531,x93531)),x93532),f328(f328(f285(x93531,x93531,x93531),x93534),f304(x93531,x93534))))+P1(f328(f328(f330(f878(x93531,x93531)),x93532),f328(f328(f285(x93531,x93531,x93531),x93533),f304(x93531,x93533))))+~P1(f328(f328(f242(f879(f878(x93531,x93531),a867)),x93534),x93533)) % 167.77/167.51 [9360]E(f328(f328(f173(x93601),f675(x93604,x93603,x93602,x93601)),x93603),f328(f328(f173(x93601),f675(x93604,x93603,x93602,x93601)),x93602))+~P1(f328(f328(f330(f878(f873(x93601),f873(x93601))),f328(f328(f263(f873(x93601),f873(x93601)),x93602),x93603)),f144(x93601,x93604)))+E(f328(f328(f173(x93601),f328(f193(f873(x93601)),x93602)),x93603),x93602) % 167.77/167.51 [9376]~P1(f328(f38(x93761),x93764))+E(f328(f328(f6(x93761,a872),f328(f328(f8(f879(x93762,a867),a872,x93761),f39(x93762)),x93763)),x93764),f328(f39(f878(x93761,x93762)),f328(f328(f265(x93761,x93762),x93764),x93763)))+~P1(f328(f38(x93762),f328(x93763,f563(x93763,x93762,x93764,x93761)))) % 167.77/167.51 [9380]~E(f328(f193(f873(x93801)),x93803),f328(f193(f873(x93801)),x93802))+P1(f328(f328(f330(f878(f873(x93801),f873(x93801))),f328(f328(f263(f873(x93801),f873(x93801)),x93802),x93803)),f155(x93801,x93804)))+P1(f328(f328(f330(f878(x93801,x93801)),f680(x93804,x93803,x93802,x93801)),f328(f170(f878(x93801,x93801)),f328(f328(f180(x93801,x93801),x93802),x93803)))) % 167.77/167.51 [9458]~P1(f328(f328(f330(f878(f873(x94581),f873(x94581))),f328(f328(f263(f873(x94581),f873(x94581)),x94582),x94583)),f144(x94581,x94584)))+E(f328(f328(f173(x94581),f328(f193(f873(x94581)),x94582)),x94583),x94582)+P1(f328(f328(f243(a872),f675(x94584,x94583,x94582,x94581)),f328(f328(f240(a872),f328(f193(f873(x94581)),x94582)),f328(f193(f873(x94581)),x94583)))) % 167.77/167.51 [9459]E(f328(f176(x94591,x94592),x94593),f328(f176(x94591,x94592),x94594))+~E(f328(f170(x94591),f328(f328(f151(f878(x94591,x94592),x94591),f262(x94591,x94592)),x94593)),f328(f170(x94591),f328(f328(f151(f878(x94591,x94592),x94591),f262(x94591,x94592)),x94594)))+P1(f328(f328(f330(x94591),f768(x94593,x94594,x94592,x94591)),f328(f170(x94591),f328(f328(f151(f878(x94591,x94592),x94591),f262(x94591,x94592)),x94594)))) % 167.77/167.51 [9475]~P1(f328(x94751,x94754))+P1(f328(f328(f328(f328(a200,f32(x94751,x94752)),f590(x94753,x94754,x94752,x94751)),x94753),x94754))+~P1(f328(f328(f328(f328(a200,f32(x94751,x94752)),x94754),x94753),x94754)) % 167.77/167.51 [9480]~P1(f328(f328(f330(f878(f873(x94801),f873(x94801))),f328(f328(f263(f873(x94801),f873(x94801)),x94802),x94803)),f144(x94801,x94804)))+P1(f328(f328(f243(a872),f328(f193(f873(x94801)),x94802)),f328(f193(f873(x94801)),x94803)))+P1(f328(f328(f243(a872),f675(x94804,x94803,x94802,x94801)),f328(f328(f240(a872),f328(f193(f873(x94801)),x94802)),f328(f193(f873(x94801)),x94803)))) % 167.77/167.51 [9783]~P1(f328(f328(f328(x97831,f723(x97831,x97834,x97833,x97832)),f724(x97831,x97834,x97833,x97832)),f725(x97831,x97834,x97833,x97832)))+P1(f328(f328(f328(x97831,x97832),x97833),x97834))+~P1(f328(f316(f878(f879(a1,f876(f873(a324))),f878(a1,a1)),a314),f328(f328(f263(f879(a1,f876(f873(a324))),f878(a1,a1)),x97832),f328(f328(f263(a1,a1),x97833),x97834)))) % 167.77/167.51 [9862]P1(f328(f328(f328(x98621,x98622),x98623),x98624))+P1(f328(f316(f878(f879(a1,f876(f873(a324))),f878(a1,a1)),a314),f328(f328(f263(f879(a1,f876(f873(a324))),f878(a1,a1)),f723(x98621,x98624,x98623,x98622)),f328(f328(f263(a1,a1),f724(x98621,x98624,x98623,x98622)),f725(x98621,x98624,x98623,x98622)))))+~P1(f328(f316(f878(f879(a1,f876(f873(a324))),f878(a1,a1)),a314),f328(f328(f263(f879(a1,f876(f873(a324))),f878(a1,a1)),x98622),f328(f328(f263(a1,a1),x98623),x98624)))) % 167.77/167.51 [9901]~P1(f328(f328(f330(f878(f873(x99011),f873(x99011))),f328(f328(f263(f873(x99011),f873(x99011)),x99012),x99013)),f144(x99011,x99014)))+E(f328(f328(f173(x99011),f328(f193(f873(x99011)),x99012)),x99013),x99012)+P1(f328(f328(f330(f878(x99011,x99011)),f328(f328(f263(x99011,x99011),f328(f328(f162(x99011),x99012),f675(x99014,x99013,x99012,x99011))),f328(f328(f162(x99011),x99013),f675(x99014,x99013,x99012,x99011)))),x99014)) % 167.77/167.51 [9902]~P1(f328(f328(f330(f878(f873(x99021),f873(x99021))),f328(f328(f263(f873(x99021),f873(x99021)),x99022),x99023)),f144(x99021,x99024)))+P1(f328(f328(f243(a872),f328(f193(f873(x99021)),x99022)),f328(f193(f873(x99021)),x99023)))+P1(f328(f328(f330(f878(x99021,x99021)),f328(f328(f263(x99021,x99021),f328(f328(f162(x99021),x99022),f675(x99024,x99023,x99022,x99021))),f328(f328(f162(x99021),x99023),f675(x99024,x99023,x99022,x99021)))),x99024)) % 167.77/167.51 [9959]~E(f328(f193(f873(x99591)),x99592),f328(f193(f873(x99591)),x99593))+P1(f328(f328(f330(f878(f873(x99591),f873(x99591))),f328(f328(f263(f873(x99591),f873(x99591)),x99592),x99593)),f155(x99591,x99594)))+~P1(f328(f328(f330(f878(x99591,x99591)),f328(f328(f263(x99591,x99591),f328(f328(f162(x99591),x99592),f666(x99594,x99593,x99592,x99591))),f328(f328(f162(x99591),x99593),f666(x99594,x99593,x99592,x99591)))),x99594)) % 167.77/167.51 [10094]~P67(x100941)+~P1(f328(f38(x100942),x100944))+E(f328(f163(x100941),f328(f328(f151(x100942,x100941),x100943),f90(f873(x100942),f328(f328(f18(f873(x100942),a867,a867),f328(f328(f8(a867,f879(a867,a867),f873(x100942)),a326),f328(f328(f7(f873(x100942),f879(x100942,a867),a867),f328(f328(f8(f879(x100942,a867),f879(f879(x100942,a867),a867),f873(x100942)),a325),f170(x100942))),x100944))),f134(x100942))))),f233(x100942,x100941,x100943,x100944)) % 167.77/167.51 [7364]~P60(x73642)+E(x73641,f2(x73642))+E(f328(f328(f286(x73642),f328(f328(f80(x73642),x73643),f328(f328(f81(x73642),x73644),x73641))),x73641),f328(f328(f80(x73642),x73644),f328(f328(f286(x73642),x73643),x73641))) % 167.77/167.51 [7365]~P57(x73652)+E(x73651,f2(x73652))+E(f328(f328(f40(x73652),f328(f328(f80(x73652),x73653),f328(f328(f81(x73652),x73654),x73651))),x73651),f328(f328(f80(x73652),x73654),f328(f328(f40(x73652),x73653),x73651))) % 167.77/167.51 [7366]~P57(x73662)+E(x73661,f2(x73662))+E(f328(f328(f40(x73662),f328(f328(f80(x73662),x73663),f328(f328(f81(x73662),x73661),x73664))),x73661),f328(f328(f80(x73662),x73664),f328(f328(f40(x73662),x73663),x73661))) % 167.77/167.51 [7600]~P61(x76002)+E(x76001,f2(x76002))+E(f328(f328(f286(x76002),f328(f328(f22(x76002),x76003),f328(f328(f81(x76002),x76001),x76004))),x76001),f328(f328(f22(x76002),f328(f328(f286(x76002),x76003),x76001)),x76004)) % 167.77/167.51 [7601]~P60(x76012)+E(x76011,f2(x76012))+E(f328(f328(f286(x76012),f328(f328(f80(x76012),x76013),f328(f328(f81(x76012),x76014),x76011))),x76011),f328(f328(f80(x76012),f328(f328(f286(x76012),x76013),x76011)),x76014)) % 167.77/167.51 [7602]~P61(x76022)+E(x76021,f2(x76022))+E(f328(f328(f286(x76022),f328(f328(f80(x76022),x76023),f328(f328(f81(x76022),x76021),x76024))),x76021),f328(f328(f80(x76022),f328(f328(f286(x76022),x76023),x76021)),x76024)) % 167.77/167.51 [8314]~P1(f328(f157(x83141,x83143),x83144))+~P1(f328(f157(x83141,x83142),x83144))+P1(f328(f157(x83141,f328(f328(f105(f879(x83141,a867)),x83142),x83143)),x83144)) % 167.77/167.51 [8687]~E(f328(f328(f285(x86871,x86871,x86871),x86872),x86874),f192(f879(f878(x86871,x86871),a867)))+~E(f328(f328(f285(x86871,x86871,x86871),x86872),x86873),f192(f879(f878(x86871,x86871),a867)))+E(f328(f328(f285(x86871,x86871,x86871),x86872),f328(f328(f114(f879(f878(x86871,x86871),a867)),x86873),x86874)),f192(f879(f878(x86871,x86871),a867))) % 167.77/167.51 [8804]~P1(f328(f328(f242(f879(x88041,a867)),x88043),x88044))+~P1(f328(f328(f242(f879(x88041,a867)),x88042),x88044))+P1(f328(f328(f242(f879(x88041,a867)),f328(f328(f114(f879(x88041,a867)),x88042),x88043)),x88044)) % 167.77/167.51 [9183]~P1(f328(f38(x91831),x91834))+~P1(f328(f38(x91831),x91833))+E(f328(f328(f22(a872),f328(f328(f80(a872),f328(f328(f6(x91831,a872),x91832),x91833)),f328(f328(f6(x91831,a872),x91832),x91834))),f328(f328(f6(x91831,a872),x91832),f328(f328(f105(f879(x91831,a867)),x91833),x91834))),f328(f328(f6(x91831,a872),x91832),f328(f328(f114(f879(x91831,a867)),x91833),x91834))) % 167.77/167.51 [9270]~P1(f328(f328(f330(x92701),x92703),x92702))+~P1(f328(f328(f242(f879(x92701,a867)),x92702),f328(f328(f306(x92701),x92703),x92704)))+P1(f328(f328(f242(f879(x92701,a867)),f328(f328(f22(f879(x92701,a867)),x92702),f328(f328(f306(x92701),x92703),f192(f879(x92701,a867))))),x92704)) % 167.77/167.51 [9430]~P1(f328(f328(f330(x94301),x94303),x94302))+P1(f328(f328(f242(f879(x94301,a867)),x94302),f328(f328(f306(x94301),x94303),x94304)))+~P1(f328(f328(f242(f879(x94301,a867)),f328(f328(f22(f879(x94301,a867)),x94302),f328(f328(f306(x94301),x94303),f192(f879(x94301,a867))))),x94304)) % 167.77/167.51 [9522]~P1(f328(f328(f243(a872),x95222),x95224))+~P1(f328(f328(f242(a872),x95221),x95223))+P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),f328(f328(f263(a872,a872),x95221),x95222)),f328(f328(f263(a872,a872),x95223),x95224))),a35)) % 167.77/167.51 [9523]~P1(f328(f328(f242(a872),x95232),x95234))+~P1(f328(f328(f242(a872),x95231),x95233))+P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),f328(f328(f263(a872,a872),x95231),x95232)),f328(f328(f263(a872,a872),x95233),x95234))),a70)) % 167.77/167.51 [9822]~P1(f328(f328(f330(f873(x98221)),x98224),f158(x98221,x98223)))+~P1(f328(f328(f330(f873(x98221)),x98224),f158(x98221,x98222)))+P1(f328(f157(x98221,f328(f328(f105(f879(x98221,a867)),f328(f328(f7(x98221,f879(x98221,a867),a867),f330(x98221)),x98222)),f328(f328(f7(x98221,f879(x98221,a867),a867),f330(x98221)),x98223))),x98224)) % 167.77/167.51 [9924]~P26(x99241,f879(f879(x99241,a867),a867),f328(f328(f7(x99241,f879(f878(x99241,x99241),a867),f879(f879(x99241,a867),a867)),f328(f328(f8(f879(x99241,a867),f879(f879(f878(x99241,x99241),a867),f879(f879(x99241,a867),a867)),x99241),f62(x99241)),f328(f328(f7(x99241,f879(x99241,a867),f879(x99241,a867)),f306(x99241)),f192(f879(x99241,a867))))),x99243),x99242)+~P1(f328(f328(f330(x99241),x99244),x99242))+E(f328(f328(f22(f879(f879(x99241,a867),a867)),f328(f328(f62(x99241),x99242),x99243)),f328(f328(f62(x99241),f328(f328(f306(x99241),x99244),f192(f879(x99241,a867)))),x99243)),f328(f328(f62(x99241),f328(f328(f22(f879(x99241,a867)),x99242),f328(f328(f306(x99241),x99244),f192(f879(x99241,a867))))),x99243)) % 167.77/167.51 [10058]~P40(x100581,x100582,x100584)+~P1(f328(f328(f330(f878(x100581,x100581)),x100583),x100584))+P1(f328(f328(f267(x100581,x100581,a867),f328(f328(f7(x100581,f879(x100581,a867),f879(x100581,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x100581,a867),f879(x100581,a867)),x100581),f8(a867,a867,x100581)),f328(f328(f8(a867,f879(a867,a867),x100581),a326),f328(f328(f7(x100581,f879(x100581,a867),a867),f330(x100581)),x100582)))),f328(f328(f7(x100581,f879(x100581,a867),a867),f330(x100581)),x100582))),x100583)) % 167.77/167.51 [10070]P1(f328(f38(x100701),x100702))+~P1(f328(f38(x100703),f328(f307(x100701,x100703,x100704),x100702)))+~P1(f328(f38(x100701),f328(f248(x100701),f328(f328(f18(x100701,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100701),a326),f328(f328(f7(x100701,f879(x100701,a867),a867),f330(x100701)),x100702))),f328(f328(f7(x100701,x100703,a867),f328(f328(f8(x100703,f879(x100703,a867),x100701),a325),x100704)),f328(x100704,f490(x100704,x100703,x100702,x100701))))))) % 167.77/167.51 [8057]~P61(x80572)+E(x80571,f2(x80572))+E(f328(f328(f286(x80572),f328(f328(f22(x80572),f328(f328(f81(x80572),x80571),x80573)),x80574)),x80571),f328(f328(f22(x80572),x80573),f328(f328(f286(x80572),x80574),x80571))) % 167.77/167.51 [8058]~P61(x80582)+E(x80581,f2(x80582))+E(f328(f328(f286(x80582),f328(f328(f80(x80582),f328(f328(f81(x80582),x80581),x80583)),x80584)),x80581),f328(f328(f80(x80582),x80583),f328(f328(f286(x80582),x80584),x80581))) % 167.77/167.51 [8969]~E(f328(f328(f285(x89691,x89691,x89691),x89693),x89694),f192(f879(f878(x89691,x89691),a867)))+~E(f328(f328(f285(x89691,x89691,x89691),x89692),x89694),f192(f879(f878(x89691,x89691),a867)))+E(f328(f328(f285(x89691,x89691,x89691),f328(f328(f114(f879(f878(x89691,x89691),a867)),x89692),x89693)),x89694),f192(f879(f878(x89691,x89691),a867))) % 167.77/167.51 [10001]~P143(x100011)+~P143(x100012)+E(f328(f328(f313(x100011),f328(f328(f7(x100011,a103,f876(f873(a324))),f328(f328(f8(f879(x100012,f876(f873(a324))),f879(a103,f876(f873(a324))),x100011),f313(x100012)),f328(f328(f8(f879(x100012,f878(x100011,x100012)),f879(x100012,f876(f873(a324))),x100011),f328(f8(f878(x100011,x100012),f876(f873(a324)),x100012),x100013)),f263(x100011,x100012)))),x100014)),x100014),f328(f328(f313(f878(x100011,x100012)),x100013),x100014)) % 167.77/167.51 [9731]~P1(f328(f157(x97311,x97313),x97314))+~P1(f328(f157(x97311,x97312),x97314))+P1(f328(f157(x97311,f328(f328(f18(x97311,a867,a867),f328(f328(f8(a867,f879(a867,a867),x97311),a326),x97312)),x97313)),x97314)) % 167.77/167.51 [9993]P1(f328(x99931,f461(x99932,x99933,x99931,x99934)))+~P1(f328(f38(x99934),f328(f248(x99934),x99931)))+P1(f328(f38(x99933),f328(f248(x99933),f328(f328(f8(f879(x99934,a867),a867,x99933),f87(x99934)),f328(f328(f8(f879(x99934,a867),f879(x99934,a867),x99933),f328(f18(x99934,a867,a867),f328(f328(f8(a867,f879(a867,a867),x99934),a326),x99931))),x99932))))) % 167.77/167.51 [10014]~P1(f328(f38(x100142),f328(f248(x100142),x100143)))+~P1(f328(f38(x100141),f328(f248(x100141),f328(f328(f7(x100141,x100142,a867),x100144),f461(x100144,x100141,x100143,x100142)))))+P1(f328(f38(x100141),f328(f248(x100141),f328(f328(f8(f879(x100142,a867),a867,x100141),f87(x100142)),f328(f328(f8(f879(x100142,a867),f879(x100142,a867),x100141),f328(f18(x100142,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100142),a326),x100143))),x100144))))) % 167.77/167.51 [5006]~E(x50062,x50064)+E(f168(x50061,x50062,x50063),f168(x50061,x50064,x50065))+~E(x50062,f2(a872)) % 167.77/167.51 [5268]E(x52681,x52682)+~E(f168(x52684,x52683,x52681),f168(x52684,x52685,x52682))+E(x52683,f2(a872)) % 167.77/167.51 [6505]E(x65051,x65052)+~E(f328(x65053,x65051),f328(x65053,x65052))+~P26(x65054,x65055,x65053,f251(f879(x65054,a867))) % 167.77/167.51 [6665]~E(f328(x66653,x66655),f205(x66652))+~E(f328(x66654,x66655),f205(x66652))+E(f328(f183(x66651,x66652,x66653,x66654),x66655),f205(x66652)) % 167.77/167.51 [7399]E(x73991,x73992)+~P26(x73993,x73994,x73995,f251(f879(x73993,a867)))+~E(f328(f307(x73993,x73994,x73995),x73991),f328(f307(x73993,x73994,x73995),x73992)) % 167.77/167.51 [7654]P26(x76542,x76543,f530(x76544,x76543,x76542,x76541),x76541)+~E(f328(f307(x76543,x76542,x76545),x76544),x76541)+E(x76541,f192(f879(x76542,a867))) % 167.77/167.51 [8200]~P1(f328(f328(x82003,x82002),x82005))+~P1(f328(f328(x82003,x82004),x82002))+P1(f328(f328(f330(x82001),x82002),f295(x82001,x82003,x82004,x82005))) % 167.77/167.51 [8201]~P1(f328(f328(x82013,x82012),x82015))+~P1(f328(f328(x82013,x82014),x82012))+P1(f328(f328(f330(x82011),x82012),f292(x82011,x82013,x82014,x82015))) % 167.77/167.51 [8762]~P26(x87621,x87623,x87625,f251(f879(x87621,a867)))+~P26(x87623,x87622,x87624,f251(f879(x87623,a867)))+P26(x87621,x87622,f328(f73(x87623,x87622,x87621,x87624),x87625),f251(f879(x87621,a867))) % 167.77/167.51 [9329]P1(f328(f328(f330(f878(x93291,x93291)),f328(f328(f263(x93291,x93291),x93292),x93293)),f304(x93291,x93294)))+~P1(f328(f328(f330(f878(x93291,x93291)),f328(f328(f263(x93291,x93291),x93292),x93295)),f304(x93291,x93294)))+~P1(f328(f328(f330(f878(x93291,x93291)),f328(f328(f263(x93291,x93291),x93295),x93293)),f304(x93291,x93294))) % 167.77/167.51 [9367]~P105(x93672)+~P1(f328(f134(x93671),x93675))+P1(f328(f134(x93671),f146(x93671,x93672,x93673,x93674,x93675))) % 167.77/167.51 [5339]~E(x53392,f117(x53391))+E(f328(f328(f125(x53391),x53392),x53393),f328(f328(f148(x53391),x53394),x53395))+~E(x53393,f328(f328(f148(x53391),x53394),x53395)) % 167.77/167.51 [5340]~E(x53402,f117(x53401))+E(f328(f328(f125(x53401),x53402),x53403),f328(f328(f148(x53401),x53404),x53405))+~E(f328(f328(f148(x53401),x53404),x53405),x53403) % 167.77/167.51 [6462]~E(f328(f193(f873(x64621)),x64625),f328(f193(f873(x64622)),x64624))+E(f328(f328(f151(f878(x64621,x64622),x64622),f266(x64621,x64622)),x64623),x64624)+~E(f328(f328(f180(x64621,x64622),x64625),x64624),x64623) % 167.77/167.51 [6463]~E(f328(f193(f873(x64631)),x64634),f328(f193(f873(x64632)),x64635))+E(f328(f328(f151(f878(x64631,x64632),x64631),f262(x64631,x64632)),x64633),x64634)+~E(f328(f328(f180(x64631,x64632),x64634),x64635),x64633) % 167.77/167.51 [6937]~P105(x69371)+~P15(x69371,f328(f328(f151(x69372,x69371),x69373),x69375))+P15(x69371,f328(f328(f151(x69372,x69371),x69373),f328(f133(x69372,x69374),x69375))) % 167.77/167.51 [6982]~P1(f328(x69823,x69825))+~P1(f328(f328(x69822,x69824),x69825))+P1(f328(f328(f95(x69821,x69822,x69823),x69824),x69825)) % 167.77/167.51 [7079]~P105(x70791)+P15(x70791,f328(f328(f151(x70792,x70791),x70793),f167(x70792,x70794,x70795)))+~P15(x70791,f328(f328(f151(x70792,x70791),x70793),x70795)) % 167.77/167.51 [7102]~P51(x71023,x71022,x71025)+~P51(x71021,x71023,x71024)+P51(x71021,x71022,f328(f328(f285(x71021,x71023,x71022),x71024),x71025)) % 167.77/167.51 [7196]E(x71961,x71962)+~P26(x71963,x71964,x71965,f251(f879(x71963,a867)))+~E(f328(f328(f151(x71963,x71964),x71965),x71961),f328(f328(f151(x71963,x71964),x71965),x71962)) % 167.77/167.51 [7350]~P1(f328(f328(f243(a872),x73501),f328(x73503,x73505)))+P1(f328(f328(f243(a872),x73501),f152(x73502,x73503,x73504)))+~P1(f328(f328(f330(x73502),x73505),f328(f170(x73502),x73504))) % 167.77/167.51 [7351]~P1(f328(f328(f242(a872),x73511),f328(x73513,x73515)))+P1(f328(f328(f242(a872),x73511),f152(x73512,x73513,x73514)))+~P1(f328(f328(f330(x73512),x73515),f328(f170(x73512),x73514))) % 167.77/167.51 [7754]P1(f328(x77541,x77542))+~P1(f328(x77541,x77543))+~P1(f328(f328(f330(x77544),x77542),f328(f170(x77544),f168(x77544,x77545,x77543)))) % 167.77/167.51 [7755]P1(f328(x77551,x77552))+~P1(f328(x77551,x77553))+~P1(f328(f328(f330(x77554),x77553),f328(f170(x77554),f168(x77554,x77555,x77552)))) % 167.77/167.51 [7760]~P107(x77601)+P1(f328(f328(f242(f879(x77601,a867)),f299(x77601,x77602,x77603)),f299(x77601,x77604,x77605)))+P1(f328(f328(f242(x77601),x77602),x77603)) % 167.77/167.51 [7783]~P4(x77831)+P1(f328(f328(f242(x77831),f328(f328(f43(x77832,x77831),x77833),x77834)),f328(x77834,x77835)))+~P1(f328(f328(f330(x77832),x77835),x77833)) % 167.77/167.51 [7851]~P26(x78511,x78512,x78514,x78513)+E(f328(f77(x78511,x78512,x78513,x78514),f328(x78514,x78515)),x78515)+~P1(f328(f328(f330(x78511),x78515),x78513)) % 167.77/167.51 [8045]~P1(f328(x80451,x80455))+P1(f328(x80451,f845(x80451,x80452,x80453,x80454)))+~P1(f328(f328(f330(x80454),x80455),x80453)) % 167.77/167.51 [8046]~P1(f328(x80461,x80465))+P1(f328(x80461,f845(x80461,x80462,x80463,x80464)))+~P1(f328(f328(f330(x80464),x80465),x80462)) % 167.77/167.51 [8145]P1(f328(f38(x81451),x81452))+~P1(f328(f38(x81453),x81454))+~P1(f328(f328(f242(f879(x81451,a867)),x81452),f328(f307(x81453,x81451,x81455),x81454))) % 167.77/167.51 [8318]E(x83181,x83182)+~P26(x83183,x83184,x83185,f328(f328(f114(f879(x83183,a867)),f328(f170(x83183),x83181)),f328(f170(x83183),x83182)))+~E(f328(f328(f151(x83183,x83184),x83185),x83181),f328(f328(f151(x83183,x83184),x83185),x83182)) % 167.77/167.51 [8372]~P107(x83721)+~P1(f328(f328(f243(f879(x83721,a867)),f299(x83721,x83724,x83725)),f299(x83721,x83722,x83723)))+P1(f328(f328(f242(x83721),x83722),x83723)) % 167.77/167.51 [8437]~P26(x84371,x84374,x84375,f251(f879(x84371,a867)))+~P1(f328(f328(f330(x84374),f328(x84375,x84372)),f328(f307(x84371,x84374,x84375),x84373)))+P1(f328(f328(f330(x84371),x84372),x84373)) % 167.77/167.51 [8512]P1(f328(x85121,x85122))+~P1(f328(x85121,f551(x85121,x85123,x85124,x85125)))+~P1(f328(f328(f330(x85125),x85122),x85124)) % 167.77/167.51 [8513]P1(f328(x85131,x85132))+~P1(f328(x85131,f551(x85131,x85133,x85134,x85135)))+~P1(f328(f328(f330(x85135),x85132),x85133)) % 167.77/167.51 [8801]~P26(x88012,x88013,x88011,x88014)+E(f328(x88011,f328(f77(x88012,x88013,x88014,x88011),x88015)),x88015)+~P1(f328(f328(f330(x88013),x88015),f328(f307(x88012,x88013,x88011),x88014))) % 167.77/167.51 [8905]E(x89051,f117(x89052))+E(f328(f328(f148(x89052),x89053),f693(x89054,x89053,x89055,x89051,x89052)),x89051)+~E(f328(f328(f125(x89052),x89051),x89055),f328(f328(f148(x89052),x89053),x89054)) % 167.77/167.51 [8906]E(x89061,f117(x89062))+E(f328(f328(f148(x89062),x89063),f694(x89064,x89061,x89065,x89063,x89062)),x89061)+~E(f328(f328(f125(x89062),x89061),x89064),f328(f328(f148(x89062),x89063),x89065)) % 167.77/167.51 [8924]E(f328(f328(f148(x89242),x89243),f693(x89244,x89243,x89241,x89245,x89242)),x89245)+~E(f328(f328(f125(x89242),x89245),x89241),f328(f328(f148(x89242),x89243),x89244))+E(x89241,f328(f328(f148(x89242),x89243),x89244)) % 167.77/167.51 [8925]E(f328(f328(f148(x89251),x89252),f694(x89254,x89255,x89253,x89252,x89251)),x89255)+~E(f328(f328(f125(x89251),x89255),x89254),f328(f328(f148(x89251),x89252),x89253))+E(f328(f328(f148(x89251),x89252),x89253),x89254) % 167.77/167.51 [9005]~E(f328(f307(x90053,x90052,x90054),f251(f879(x90053,a867))),f251(f879(x90052,a867)))+~E(f328(f307(x90051,x90053,x90055),f251(f879(x90051,a867))),f251(f879(x90053,a867)))+E(f328(f307(x90051,x90052,f328(f73(x90053,x90052,x90051,x90054),x90055)),f251(f879(x90051,a867))),f251(f879(x90052,a867))) % 167.77/167.51 [9373]E(x93731,f117(x93732))+~E(f328(f328(f125(x93732),x93731),x93733),f328(f328(f148(x93732),x93735),x93734))+E(f328(f328(f125(x93732),f694(x93733,x93731,x93734,x93735,x93732)),x93733),x93734) % 167.77/167.51 [9374]E(x93741,f117(x93742))+~E(f328(f328(f125(x93742),x93741),x93745),f328(f328(f148(x93742),x93744),x93743))+E(f328(f328(f125(x93742),f693(x93743,x93744,x93745,x93741,x93742)),x93745),x93743) % 167.77/167.51 [9381]E(f328(f328(f125(x93812),f693(x93814,x93813,x93811,x93815,x93812)),x93811),x93814)+~E(f328(f328(f125(x93812),x93815),x93811),f328(f328(f148(x93812),x93813),x93814))+E(x93811,f328(f328(f148(x93812),x93813),x93814)) % 167.77/167.51 [9382]~E(f328(f328(f125(x93821),x93825),x93824),f328(f328(f148(x93821),x93822),x93823))+E(f328(f328(f125(x93821),f694(x93824,x93825,x93823,x93822,x93821)),x93824),x93823)+E(f328(f328(f148(x93821),x93822),x93823),x93824) % 167.77/167.51 [9383]E(f328(f328(f125(x93831),x93835),f696(x93833,x93832,x93834,x93835,x93831)),x93832)+E(f328(f328(f125(x93831),x93832),f695(x93833,x93832,x93834,x93835,x93831)),x93835)+~E(f328(f328(f125(x93831),x93835),x93834),f328(f328(f125(x93831),x93832),x93833)) % 167.77/167.51 [9416]~P105(x94161)+P15(x94161,f328(f328(f151(x94162,x94161),x94163),f146(x94162,x94161,x94163,x94164,x94165)))+~P15(x94161,f328(f328(f151(x94162,x94161),x94163),x94165)) % 167.77/167.51 [9427]~P55(x94275,x94271,x94274,x94273)+P1(f328(f328(x94271,x94272),f548(x94273,x94274,x94271,x94275,x94272)))+~P1(f328(f328(f330(x94275),x94272),x94274)) % 167.77/167.51 [9535]~P1(f328(f328(f330(f878(x95351,x95351)),f328(f328(f263(x95351,x95351),x95355),x95353)),f304(x95351,x95354)))+P1(f328(f328(f330(f878(x95351,x95351)),f328(f328(f263(x95351,x95351),x95352),x95353)),f328(f328(f285(x95351,x95351,x95351),x95354),f304(x95351,x95354))))+~P1(f328(f328(f330(f878(x95351,x95351)),f328(f328(f263(x95351,x95351),x95352),x95355)),f328(f328(f285(x95351,x95351,x95351),x95354),f304(x95351,x95354)))) % 167.77/167.51 [9536]~P1(f328(f328(f330(f878(x95361,x95361)),f328(f328(f263(x95361,x95361),x95362),x95365)),f304(x95361,x95364)))+P1(f328(f328(f330(f878(x95361,x95361)),f328(f328(f263(x95361,x95361),x95362),x95363)),f328(f328(f285(x95361,x95361,x95361),x95364),f304(x95361,x95364))))+~P1(f328(f328(f330(f878(x95361,x95361)),f328(f328(f263(x95361,x95361),x95365),x95363)),f328(f328(f285(x95361,x95361,x95361),x95364),f304(x95361,x95364)))) % 167.77/167.51 [9539]P1(f328(f328(f330(f878(f873(x95391),f873(x95391))),f328(f328(f263(f873(x95391),f873(x95391)),x95392),x95393)),f155(x95391,f304(x95391,x95394))))+~P1(f328(f328(f330(f878(f873(x95391),f873(x95391))),f328(f328(f263(f873(x95391),f873(x95391)),x95392),x95395)),f155(x95391,f304(x95391,x95394))))+~P1(f328(f328(f330(f878(f873(x95391),f873(x95391))),f328(f328(f263(f873(x95391),f873(x95391)),x95395),x95393)),f155(x95391,f304(x95391,x95394)))) % 167.77/167.51 [9543]E(f328(f328(f125(x95431),x95432),f695(x95433,x95432,x95434,x95435,x95431)),x95435)+E(f328(f328(f125(x95431),f696(x95433,x95432,x95434,x95435,x95431)),x95433),x95434)+~E(f328(f328(f125(x95431),x95432),x95433),f328(f328(f125(x95431),x95435),x95434)) % 167.77/167.51 [9544]E(f328(f328(f125(x95441),x95442),f696(x95443,x95444,x95445,x95442,x95441)),x95444)+E(f328(f328(f125(x95441),f695(x95443,x95444,x95445,x95442,x95441)),x95445),x95443)+~E(f328(f328(f125(x95441),x95442),x95445),f328(f328(f125(x95441),x95444),x95443)) % 167.77/167.51 [9598]P1(f328(f328(f330(f878(x95981,x95981)),f328(f328(f263(x95981,x95981),x95982),x95983)),f328(f328(f285(x95981,x95981,x95981),x95984),f304(x95981,x95984))))+~P1(f328(f328(f330(f878(x95981,x95981)),f328(f328(f263(x95981,x95981),x95982),x95985)),f328(f328(f285(x95981,x95981,x95981),x95984),f304(x95981,x95984))))+~P1(f328(f328(f330(f878(x95981,x95981)),f328(f328(f263(x95981,x95981),x95985),x95983)),f328(f328(f285(x95981,x95981,x95981),x95984),f304(x95981,x95984)))) % 167.77/167.51 [9627]P35(x96271,x96272,x96273,x96274,x96275)+~E(f328(f193(f873(x96271)),x96274),f328(f193(f873(x96272)),x96275))+~P1(f328(f328(f267(x96271,x96272,a867),x96273),f734(x96275,x96274,x96273,x96272,x96271))) % 167.77/167.51 [9628]P35(x96281,x96282,x96283,x96284,x96285)+~E(f328(f193(f873(x96281)),x96284),f328(f193(f873(x96282)),x96285))+~P1(f328(f328(f267(x96281,x96282,a867),x96283),f735(x96283,x96285,x96284,x96282,x96281))) % 167.77/167.51 [9633]E(f328(f328(f125(x96331),f695(x96332,x96333,x96334,x96335,x96331)),x96334),x96332)+~E(f328(f328(f125(x96331),x96333),x96332),f328(f328(f125(x96331),x96335),x96334))+E(f328(f328(f125(x96331),f696(x96332,x96333,x96334,x96335,x96331)),x96332),x96334) % 167.77/167.51 [9648]~P105(x96482)+E(f328(f328(f145(x96481,x96482,x96483),x96484),x96485),f328(f328(f148(x96481),x96484),x96485))+P1(f328(f328(f330(x96481),f784(x96484,x96483,x96485,x96481,x96482)),f328(f170(x96481),x96485))) % 167.77/167.51 [9653]~P55(x96531,x96534,x96533,x96532)+~P1(f328(f328(f330(x96531),x96535),x96533))+P1(f328(f328(f330(x96531),f548(x96532,x96533,x96534,x96531,x96535)),x96532)) % 167.77/167.51 [9774]~P1(f328(f328(f330(f878(f879(x97741,a867),f879(x97741,a867))),f328(f328(f263(f879(x97741,a867),f879(x97741,a867)),x97744),x97743)),f320(x97741,x97742)))+~P1(f328(f328(f330(x97741),x97745),x97744))+P1(f328(f328(f330(x97741),f616(x97742,x97743,x97744,x97741,x97745)),x97743)) % 167.77/167.51 [9786]~P105(x97862)+E(f328(f328(f145(x97861,x97862,x97863),x97864),x97865),f328(f328(f148(x97861),x97864),x97865))+~P1(f328(f328(f242(x97862),f328(x97863,x97864)),f328(x97863,f784(x97864,x97863,x97865,x97861,x97862)))) % 167.77/167.51 [9976]P35(x99761,x99762,x99763,x99764,x99765)+~E(f328(f193(f873(x99761)),x99764),f328(f193(f873(x99762)),x99765))+~P1(f328(f328(x99763,f328(f328(f162(x99761),x99764),f736(x99765,x99764,x99763,x99762,x99761))),f328(f328(f162(x99762),x99765),f736(x99765,x99764,x99763,x99762,x99761)))) % 167.77/167.51 [9977]P35(x99771,x99772,x99773,x99774,x99775)+~E(f328(f193(f873(x99771)),x99774),f328(f193(f873(x99772)),x99775))+~P1(f328(f328(x99773,f328(f328(f162(x99771),x99774),f772(x99773,x99775,x99772,x99774,x99771))),f328(f328(f162(x99772),x99775),f772(x99773,x99775,x99772,x99774,x99771)))) % 167.77/167.51 [6533]~P18(x65332,x65335,x65331)+~P1(f328(f38(x65332),x65334))+E(f328(x65331,f328(f328(f306(x65332),x65333),x65334)),f328(f328(f65(x65332,x65332,x65335),x65333),x65334)) % 167.77/167.51 [6534]~E(x65343,x65344)+~E(x65342,x65345)+E(f328(f328(f306(x65341),x65342),f328(f328(f306(x65341),x65343),f192(f879(x65341,a867)))),f328(f328(f306(x65341),x65344),f328(f328(f306(x65341),x65345),f192(f879(x65341,a867))))) % 167.77/167.51 [6544]P1(f328(x65442,x65445))+E(f175(x65441,x65442,f328(f328(f125(x65441),x65443),x65444)),f175(x65441,x65442,x65443))+~P1(f328(f328(f330(x65441),x65445),f328(f170(x65441),x65443))) % 167.77/167.51 [6581]E(f328(x65811,x65812),f192(f879(x65813,a867)))+~E(f328(f328(f44(x65814,f879(x65813,a867)),x65815),x65811),f192(f879(x65813,a867)))+~P1(f328(f328(f330(x65814),x65812),x65815)) % 167.77/167.51 [6582]E(f328(x65821,x65822),f251(f879(x65823,a867)))+~E(f328(f328(f43(x65824,f879(x65823,a867)),x65825),x65821),f251(f879(x65823,a867)))+~P1(f328(f328(f330(x65824),x65822),x65825)) % 167.77/167.51 [7089]~E(x70892,x70894)+~P140(x70891)+E(f328(f328(f80(x70891),f328(f328(f81(x70891),x70892),x70893)),f328(f328(f81(x70891),x70894),x70895)),f328(f328(f80(x70891),f328(f328(f81(x70891),x70892),x70895)),f328(f328(f81(x70891),x70894),x70893))) % 167.77/167.51 [7149]~P4(x71491)+~P1(f328(f328(f330(x71494),x71493),x71495))+P1(f328(f328(f242(x71491),f328(x71492,x71493)),f328(f328(f44(x71494,x71491),x71495),x71492))) % 167.77/167.51 [7201]~P108(x72011)+P1(f328(f328(f242(x72011),f328(x72012,x72013)),f328(x72014,x72013)))+~P1(f328(f328(f242(f879(x72015,x72011)),x72012),x72014)) % 167.77/167.51 [7318]E(x73181,x73182)+E(x73183,x73181)+~E(f328(f328(f306(x73184),x73181),f328(f328(f306(x73184),x73185),f192(f879(x73184,a867)))),f328(f328(f306(x73184),x73182),f328(f328(f306(x73184),x73183),f192(f879(x73184,a867))))) % 167.77/167.51 [7319]E(x73191,x73192)+E(x73193,x73191)+~E(f328(f328(f306(x73194),x73193),f328(f328(f306(x73194),x73192),f192(f879(x73194,a867)))),f328(f328(f306(x73194),x73195),f328(f328(f306(x73194),x73191),f192(f879(x73194,a867))))) % 167.77/167.51 [7320]E(x73201,x73202)+E(x73201,x73203)+~E(f328(f328(f306(x73204),x73203),f328(f328(f306(x73204),x73202),f192(f879(x73204,a867)))),f328(f328(f306(x73204),x73205),f328(f328(f306(x73204),x73201),f192(f879(x73204,a867))))) % 167.77/167.51 [7321]E(x73211,x73212)+E(x73211,x73213)+~E(f328(f328(f306(x73214),x73211),f328(f328(f306(x73214),x73215),f192(f879(x73214,a867)))),f328(f328(f306(x73214),x73212),f328(f328(f306(x73214),x73213),f192(f879(x73214,a867))))) % 167.77/167.51 [7565]~P1(f328(f328(f328(a198,x75651),x75653),x75655))+~P1(f328(f328(f328(a198,x75652),x75655),x75654))+P1(f328(f328(f328(a198,f33(x75651,x75652)),x75653),x75654)) % 167.77/167.51 [7861]P26(x78611,x78612,x78613,x78614)+~P26(x78611,x78612,x78613,x78615)+~P1(f328(f328(f242(f879(x78611,a867)),x78614),x78615)) % 167.77/167.51 [7868]~P1(f328(f328(f242(a872),x78685),x78683))+~P1(f328(f328(f328(f328(a200,x78681),x78682),x78685),x78684))+P1(f328(f328(f328(f328(a200,x78681),x78682),x78683),x78684)) % 167.77/167.51 [8035]E(x80351,x80352)+~E(f328(f307(x80353,x80354,x80355),x80351),f328(f307(x80353,x80354,x80355),x80352))+~P26(x80353,x80354,x80355,f328(f328(f114(f879(x80353,a867)),x80351),x80352)) % 167.77/167.51 [8110]P1(f328(x81102,x81104))+E(f328(f328(f135(x81101),f328(f193(f873(x81101)),f175(x81101,x81102,x81103))),x81103),f328(f328(f148(x81101),x81104),x81105))+~E(f328(f328(f125(x81101),f175(x81101,x81102,x81103)),f328(f328(f148(x81101),x81104),x81105)),x81103) % 167.77/167.51 [8142]~P26(x81421,x81422,x81423,x81425)+~P26(x81421,x81422,x81423,x81424)+P26(x81421,x81422,x81423,f328(f328(f105(f879(x81421,a867)),x81424),x81425)) % 167.77/167.51 [8161]P1(f328(x81611,x81612))+~P1(f328(f328(f328(a198,x81614),x81612),x81615))+P1(f328(f328(f328(a198,f30(x81611,x81613,x81614)),x81612),x81615)) % 167.77/167.51 [8198]~P1(f328(x81981,x81984))+~P1(f328(f328(f328(a198,x81982),x81984),x81985))+P1(f328(f328(f328(a198,f30(x81981,x81982,x81983)),x81984),x81985)) % 167.77/167.51 [8260]~P67(x82601)+E(f328(f328(f80(x82601),f328(x82602,x82603)),f328(f163(x82601),f328(f328(f151(x82604,x82601),x82602),f167(x82604,x82603,x82605)))),f328(f163(x82601),f328(f328(f151(x82604,x82601),x82602),x82605)))+~P1(f328(f328(f330(x82604),x82603),f328(f170(x82604),x82605))) % 167.77/167.51 [8348]~P105(x83481)+~P15(x83481,f328(f328(f151(x83482,x83481),x83483),x83485))+P15(x83481,f328(f328(f151(x83482,x83481),x83483),f328(f328(f145(x83482,x83481,x83483),x83484),x83485))) % 167.77/167.51 [8433]~P4(x84331)+P1(f328(f328(f242(x84331),f328(f328(f43(x84332,x84331),x84333),x84334)),f328(f328(f43(x84332,x84331),x84335),x84334)))+~P1(f328(f328(f242(f879(x84332,a867)),x84335),x84333)) % 167.77/167.51 [8434]~P4(x84341)+P1(f328(f328(f242(x84341),f328(f328(f44(x84342,x84341),x84343),x84344)),f328(f328(f44(x84342,x84341),x84345),x84344)))+~P1(f328(f328(f242(f879(x84342,a867)),x84343),x84345)) % 167.77/167.51 [8466]~P105(x84663)+P1(f328(f134(x84661),x84662))+~P1(f328(f134(x84661),f328(f328(f145(x84661,x84663,x84664),x84665),x84662))) % 167.77/167.51 [8534]P1(f328(x85341,x85342))+P1(f328(f328(f328(a198,x85343),x85342),x85344))+~P1(f328(f328(f328(a198,f30(x85341,x85345,x85343)),x85342),x85344)) % 167.77/167.51 [8552]~P1(f328(x85524,x85522))+P1(f328(f328(f328(a198,x85521),x85522),x85523))+~P1(f328(f328(f328(a198,f30(x85524,x85521,x85525)),x85522),x85523)) % 167.77/167.51 [8614]~P105(x86141)+~P1(f328(f328(f330(x86142),x86143),f328(f170(x86142),x86144)))+~P1(f328(f134(x86142),f328(f328(f145(x86142,x86141,x86145),x86143),x86144))) % 167.77/167.51 [8631]P1(f328(f328(f328(a198,x86311),x86312),x86313))+P1(f328(f328(f328(a198,x86314),x86312),x86313))+~P1(f328(f328(f328(a198,f30(x86315,x86311,x86314)),x86312),x86313)) % 167.77/167.51 [8697]~P105(x86971)+P15(x86971,f328(f328(f151(x86972,x86971),x86973),x86974))+~P15(x86971,f328(f328(f151(x86972,x86971),x86973),f328(f328(f145(x86972,x86971,x86973),x86975),x86974))) % 167.77/167.51 [8789]~P105(x87892)+E(f328(f328(f145(x87891,x87892,x87893),x87894),x87895),f146(x87891,x87892,x87893,x87894,x87895))+P1(f328(f328(f330(x87892),f328(x87893,x87894)),f328(f307(x87891,x87892,x87893),f328(f170(x87891),x87895)))) % 167.77/167.51 [8863]~P105(x88632)+E(f146(x88631,x88632,x88633,x88634,x88635),x88635)+~P1(f328(f328(f330(x88632),f328(x88633,x88634)),f328(f307(x88631,x88632,x88633),f328(f170(x88631),x88635)))) % 167.77/167.51 [8877]~P26(x88772,x88771,x88773,x88775)+P1(f328(f328(f243(f879(x88771,a867)),f328(f307(x88772,x88771,x88773),x88774)),f328(f307(x88772,x88771,x88773),x88775)))+~P1(f328(f328(f243(f879(x88772,a867)),x88774),x88775)) % 167.77/167.51 [9047]~P26(x90471,x90472,x90473,f251(f879(x90471,a867)))+~P1(f328(f328(f242(f879(x90472,a867)),x90474),f328(f307(x90471,x90472,x90473),x90475)))+P1(f328(f328(f242(f879(x90471,a867)),f328(f308(x90471,x90472,x90473),x90474)),x90475)) % 167.77/167.51 [9069]~E(f328(f307(x90693,x90691,x90694),f251(f879(x90693,a867))),f251(f879(x90691,a867)))+P1(f328(f328(f242(f879(x90691,a867)),x90692),f328(f307(x90693,x90691,x90694),x90695)))+~P1(f328(f328(f242(f879(x90693,a867)),f328(f308(x90693,x90691,x90694),x90692)),x90695)) % 167.77/167.51 [9093]~E(f328(f235(x90932),x90934),f328(f328(f176(x90931,x90932),x90935),x90933))+~P1(f328(f134(x90931),f328(f328(f151(f878(x90931,x90932),x90931),f262(x90931,x90932)),x90935)))+P1(f328(f328(f330(f878(x90931,x90932)),f328(f328(f263(x90931,x90932),x90933),x90934)),f328(f170(f878(x90931,x90932)),x90935))) % 167.77/167.51 [9175]~P26(x91751,x91754,x91755,f251(f879(x91751,a867)))+~P1(f328(f328(f242(f879(x91754,a867)),f328(f307(x91751,x91754,x91755),x91752)),f328(f307(x91751,x91754,x91755),x91753)))+P1(f328(f328(f242(f879(x91751,a867)),x91752),x91753)) % 167.77/167.51 [9240]E(f328(f235(x92401),x92402),f328(f328(f176(x92403,x92401),x92404),x92405))+~P1(f328(f134(x92403),f328(f328(f151(f878(x92403,x92401),x92403),f262(x92403,x92401)),x92404)))+~P1(f328(f328(f330(f878(x92403,x92401)),f328(f328(f263(x92403,x92401),x92405),x92402)),f328(f170(f878(x92403,x92401)),x92404))) % 167.77/167.51 [9242]E(f328(f328(f176(x92421,x92422),x92423),x92424),f328(f235(x92422),x92425))+~P1(f328(f134(x92421),f328(f328(f151(f878(x92421,x92422),x92421),f262(x92421,x92422)),x92423)))+~P1(f328(f328(f330(f878(x92421,x92422)),f328(f328(f263(x92421,x92422),x92424),x92425)),f328(f170(f878(x92421,x92422)),x92423))) % 167.77/167.51 [9297]~P79(x92971)+~E(f328(x92973,f752(x92973,x92974,x92975,x92972,x92971)),f2(x92971))+E(f328(f163(x92971),f328(f328(f151(x92972,x92971),x92973),f328(f133(x92972,x92974),x92975))),f328(f163(x92971),f328(f328(f151(x92972,x92971),x92973),x92975))) % 167.77/167.51 [9474]~P17(x94741,x94742,x94743)+~P1(f328(f38(x94741),x94745))+P1(f328(f67(x94741,x94742,x94743,x94744,x94745),f328(f328(f65(x94741,x94742,x94743),x94744),x94745))) % 167.77/167.51 [9556]P1(f328(x95561,f653(x95562,x95561,x95563,x95564,x95565)))+~P1(f328(f328(f242(f879(x95565,a867)),x95564),x95563))+P1(f328(f328(f242(f879(x95565,a867)),f328(f328(f105(f879(x95565,a867)),x95564),f328(f248(x95565),x95561))),f328(f328(f105(f879(x95565,a867)),x95563),f328(f248(x95565),x95562)))) % 167.77/167.51 [9570]~P79(x95701)+~P1(f328(x95704,f752(x95703,x95704,x95705,x95702,x95701)))+E(f328(f163(x95701),f328(f328(f151(x95702,x95701),x95703),f328(f133(x95702,x95704),x95705))),f328(f163(x95701),f328(f328(f151(x95702,x95701),x95703),x95705))) % 167.77/167.51 [9651]~P4(x96515)+P1(f328(f328(f330(x96511),f352(x96512,x96513,x96511,x96514,x96515)),x96513))+P1(f328(f328(f242(x96515),x96514),f328(f328(f43(x96511,x96515),x96513),x96512))) % 167.77/167.51 [9654]~P79(x96541)+E(f328(f163(x96541),f328(f328(f151(x96542,x96541),x96543),f328(f133(x96542,x96544),x96545))),f328(f163(x96541),f328(f328(f151(x96542,x96541),x96543),x96545)))+P1(f328(f328(f330(x96542),f752(x96543,x96544,x96545,x96542,x96541)),f328(f170(x96542),x96545))) % 167.77/167.51 [9664]~P1(f328(x96645,f653(x96645,x96643,x96644,x96642,x96641)))+~P1(f328(f328(f242(f879(x96641,a867)),x96642),x96644))+P1(f328(f328(f242(f879(x96641,a867)),f328(f328(f105(f879(x96641,a867)),x96642),f328(f248(x96641),x96643))),f328(f328(f105(f879(x96641,a867)),x96644),f328(f248(x96641),x96645)))) % 167.77/167.51 [9699]P35(x96991,x96992,x96993,x96994,x96995)+~E(f328(f193(f873(x96992)),x96995),f328(f193(f873(x96991)),x96994))+P1(f328(f328(f243(a872),f736(x96995,x96994,x96993,x96992,x96991)),f328(f193(f873(x96991)),x96994))) % 167.77/167.51 [9700]P35(x97001,x97002,x97003,x97004,x97005)+~E(f328(f193(f873(x97002)),x97005),f328(f193(f873(x97001)),x97004))+P1(f328(f328(f243(a872),f772(x97003,x97005,x97002,x97004,x97001)),f328(f193(f873(x97001)),x97004))) % 167.77/167.51 [9733]P1(f328(f328(f330(x97331),f653(x97332,x97333,x97334,x97335,x97331)),x97335))+~P1(f328(f328(f242(f879(x97331,a867)),x97335),x97334))+P1(f328(f328(f242(f879(x97331,a867)),f328(f328(f105(f879(x97331,a867)),x97335),f328(f248(x97331),x97333))),f328(f328(f105(f879(x97331,a867)),x97334),f328(f248(x97331),x97332)))) % 167.77/167.51 [9787]~P4(x97871)+~P1(f328(f328(f242(x97871),x97872),f328(x97875,f352(x97875,x97874,x97873,x97872,x97871))))+P1(f328(f328(f242(x97871),x97872),f328(f328(f43(x97873,x97871),x97874),x97875))) % 167.77/167.51 [9820]~P73(x98201)+~P1(f328(f38(x98202),x98205))+E(f328(f328(f328(f66(x98201,x98202,f81(x98201)),f328(f328(f18(x98202,x98201,x98201),f328(f328(f8(x98201,f879(x98201,x98201),x98202),f81(x98201)),x98203)),x98204)),f78(x98201)),x98205),f328(f328(f81(x98201),f328(f328(f328(f66(x98201,x98202,f81(x98201)),x98203),f78(x98201)),x98205)),f328(f328(f328(f66(x98201,x98202,f81(x98201)),x98204),f78(x98201)),x98205))) % 167.77/167.51 [9883]~P1(f328(f328(f330(f878(f879(x98831,a867),f879(x98831,a867))),f328(f328(f263(f879(x98831,a867),f879(x98831,a867)),x98835),x98834)),f320(x98831,x98833)))+~P1(f328(f328(f330(x98831),x98832),x98835))+P1(f328(f328(f330(f878(x98831,x98831)),f328(f328(f263(x98831,x98831),x98832),f616(x98833,x98834,x98835,x98831,x98832))),x98833)) % 167.77/167.51 [10011]~P1(f328(f328(f330(f878(f873(x100111),f873(x100111))),f328(f328(f263(f873(x100111),f873(x100111)),f328(f328(f125(x100111),x100115),x100112)),f328(f328(f125(x100111),x100115),x100113))),f144(x100111,x100114)))+P1(f328(f328(f330(f878(f873(x100111),f873(x100111))),f328(f328(f263(f873(x100111),f873(x100111)),x100112),x100113)),f144(x100111,x100114)))+P1(f328(f328(f330(f878(x100111,x100111)),f328(f328(f263(x100111,x100111),f701(x100114,x100113,x100112,x100115,x100111)),f701(x100114,x100113,x100112,x100115,x100111))),x100114)) % 167.77/167.51 [7129]~E(f328(f193(f873(x71291)),x71293),f328(f193(f873(x71292)),x71294))+E(f328(f328(f176(x71291,x71292),f328(f328(f180(x71291,x71292),x71293),x71294)),x71295),f205(x71292))+P1(f328(f328(f330(x71291),x71295),f328(f170(x71291),x71293))) % 167.77/167.51 [7204]~E(x72043,x72045)+E(f328(f328(f162(x72041),f328(f328(f156(x72041,x72042),x72043),x72044)),x72045),x72044)+~P1(f328(f328(f243(a872),x72043),f328(f193(f873(x72041)),x72042))) % 167.77/167.51 [7313]~E(f328(f328(f125(x73131),x73132),x73134),f328(f328(f125(x73131),x73133),x73135))+E(f328(f328(f173(x73131),f328(f193(f873(x73131)),x73132)),x73133),x73132)+P1(f328(f328(f242(a872),f328(f193(f873(x73131)),x73133)),f328(f193(f873(x73131)),x73132))) % 167.77/167.51 [7330]~E(x73305,x73302)+P1(f328(x73301,x73302))+P1(f328(f328(f328(f328(a200,f32(x73301,x73303)),x73302),x73304),x73305)) % 167.77/167.51 [7822]~E(f328(f328(f125(x78221),x78222),x78224),f328(f328(f125(x78221),x78223),x78225))+E(f328(f328(f173(x78221),f328(f193(f873(x78221)),x78222)),x78223),x78222)+~P1(f328(f328(f242(a872),f328(f193(f873(x78221)),x78222)),f328(f193(f873(x78221)),x78223))) % 167.77/167.51 [7846]~P1(f328(f38(x78461),f328(x78464,x78465)))+~P1(f328(f328(f330(x78462),x78465),x78463))+P1(f328(f38(x78461),f328(f328(f43(x78462,f879(x78461,a867)),x78463),x78464))) % 167.77/167.51 [7899]~E(f328(f193(f873(x78991)),x78992),f328(f193(f873(x78993)),x78994))+~E(f328(f328(f176(x78991,x78993),f328(f328(f180(x78991,x78993),x78992),x78994)),x78995),f205(x78993))+~P1(f328(f328(f330(x78991),x78995),f328(f170(x78991),x78992))) % 167.77/167.51 [8020]~P40(x80201,x80203,x80205)+~P40(x80201,x80202,x80204)+P40(x80201,f328(f328(f114(f879(x80201,a867)),x80202),x80203),f328(f328(f114(f879(f878(x80201,x80201),a867)),x80204),x80205)) % 167.77/167.51 [8021]~P40(x80211,x80213,x80215)+~P40(x80211,x80212,x80214)+P40(x80211,f328(f328(f105(f879(x80211,a867)),x80212),x80213),f328(f328(f105(f879(f878(x80211,x80211),a867)),x80214),x80215)) % 167.77/167.51 [8104]E(x81041,x81042)+P1(f328(x81043,x81041))+~P1(f328(f328(f328(f328(a200,f32(x81043,x81044)),x81041),x81045),x81042)) % 167.77/167.51 [8384]E(f328(f328(f263(x83841,x83842),f328(f328(f162(x83841),x83843),x83844)),f328(f328(f162(x83842),x83845),x83844)),f328(f328(f162(f878(x83841,x83842)),f328(f328(f180(x83841,x83842),x83843),x83845)),x83844))+~P1(f328(f328(f243(a872),x83844),f328(f193(f873(x83841)),x83843)))+~P1(f328(f328(f243(a872),x83844),f328(f193(f873(x83842)),x83845))) % 167.77/167.51 [8544]~P40(x85441,x85443,x85444)+P1(f328(f328(f330(x85441),x85442),x85443))+~P1(f328(f328(f330(f878(x85441,x85441)),f328(f328(f263(x85441,x85441),x85445),x85442)),x85444)) % 167.77/167.51 [8545]~P40(x85451,x85453,x85454)+P1(f328(f328(f330(x85451),x85452),x85453))+~P1(f328(f328(f330(f878(x85451,x85451)),f328(f328(f263(x85451,x85451),x85452),x85455)),x85454)) % 167.77/167.51 [8546]~P7(x85461,x85463,x85464)+P1(f328(f328(f330(x85461),x85462),x85463))+~P1(f328(f328(f330(f878(x85461,x85461)),f328(f328(f263(x85461,x85461),x85465),x85462)),x85464)) % 167.77/167.51 [8547]~P7(x85471,x85473,x85474)+P1(f328(f328(f330(x85471),x85472),x85473))+~P1(f328(f328(f330(f878(x85471,x85471)),f328(f328(f263(x85471,x85471),x85472),x85475)),x85474)) % 167.77/167.51 [8811]~P7(x88111,x88115,x88112)+E(f328(f282(x88111,x88111,x88112),f328(f328(f306(x88111),x88113),f192(f879(x88111,a867)))),f328(f282(x88111,x88111,x88112),f328(f328(f306(x88111),x88114),f192(f879(x88111,a867)))))+~P1(f328(f328(f330(f878(x88111,x88111)),f328(f328(f263(x88111,x88111),x88113),x88114)),x88112)) % 167.77/167.51 [8892]~P1(f328(f328(f328(f328(a200,x88922),x88923),x88924),x88925))+~P1(f328(f328(f328(f328(a200,f32(x88921,x88922)),x88925),x88924),x88923))+P1(f328(f328(f328(f328(a200,f32(x88921,x88922)),x88923),x88924),x88923)) % 167.77/167.51 [9002]P1(f328(x90021,x90022))+~P1(f328(f328(f330(x90023),x90022),x90025))+P1(f328(f328(f330(x90023),f551(x90021,x90024,x90025,x90023)),f328(f328(f114(f879(x90023,a867)),x90025),x90024))) % 167.77/167.51 [9003]P1(f328(x90031,x90032))+~P1(f328(f328(f330(x90033),x90032),x90034))+P1(f328(f328(f330(x90033),f551(x90031,x90034,x90035,x90033)),f328(f328(f114(f879(x90033,a867)),x90035),x90034))) % 167.77/167.51 [9011]~P1(f328(x90112,x90115))+~P1(f328(f328(f330(x90111),x90115),x90114))+P1(f328(f328(f330(x90111),f845(x90112,x90113,x90114,x90111)),f328(f328(f114(f879(x90111,a867)),x90114),x90113))) % 167.77/167.51 [9012]~P1(f328(x90122,x90125))+~P1(f328(f328(f330(x90121),x90125),x90123))+P1(f328(f328(f330(x90121),f845(x90122,x90123,x90124,x90121)),f328(f328(f114(f879(x90121,a867)),x90124),x90123))) % 167.77/167.51 [9027]~P1(f328(f328(f242(f879(x90271,a867)),x90273),x90275))+~P1(f328(f328(f242(f879(x90271,a867)),x90272),x90274))+P1(f328(f328(f242(f879(x90271,a867)),f328(f328(f114(f879(x90271,a867)),x90272),x90273)),f328(f328(f114(f879(x90271,a867)),x90274),x90275))) % 167.77/167.51 [9028]~P1(f328(f328(f242(f879(x90281,a867)),x90285),x90283))+~P1(f328(f328(f242(f879(x90281,a867)),x90282),x90284))+P1(f328(f328(f242(f879(x90281,a867)),f328(f328(f22(f879(x90281,a867)),x90282),x90283)),f328(f328(f22(f879(x90281,a867)),x90284),x90285))) % 167.77/167.51 [9029]~P1(f328(f328(f242(f879(x90291,a867)),x90293),x90295))+~P1(f328(f328(f242(f879(x90291,a867)),x90292),x90294))+P1(f328(f328(f242(f879(x90291,a867)),f328(f328(f105(f879(x90291,a867)),x90292),x90293)),f328(f328(f105(f879(x90291,a867)),x90294),x90295))) % 167.77/167.51 [9118]~E(f328(f193(f873(x91181)),x91183),f328(f193(f873(x91182)),x91184))+E(f328(f328(f176(x91181,x91182),f328(f328(f180(x91181,x91182),x91183),x91184)),x91185),f328(f235(x91182),f710(x91185,x91184,x91182,x91183,x91181)))+~P1(f328(f328(f330(x91181),x91185),f328(f170(x91181),x91183))) % 167.77/167.51 [9122]P1(f328(f328(f330(f878(x91221,x91221)),f328(f328(f263(x91221,x91221),x91222),x91223)),f322(x91221,x91224,x91225)))+~P1(f328(f328(f242(a872),f328(x91224,x91222)),f328(x91224,x91223)))+~P1(f328(f328(f330(f878(x91221,x91221)),f328(f328(f263(x91221,x91221),x91222),x91223)),x91225)) % 167.77/167.51 [9307]P1(f328(f328(f330(f878(x93071,x93071)),f328(f328(f263(x93071,x93071),x93072),x93073)),f304(x93071,x93074)))+~P1(f328(f328(f330(f878(x93071,x93071)),f328(f328(f263(x93071,x93071),x93072),x93075)),f304(x93071,x93074)))+~P1(f328(f328(f330(f878(x93071,x93071)),f328(f328(f263(x93071,x93071),x93075),x93073)),x93074)) % 167.77/167.51 [9308]P1(f328(f328(f330(f878(x93081,x93081)),f328(f328(f263(x93081,x93081),x93082),x93083)),f304(x93081,x93084)))+~P1(f328(f328(f330(f878(x93081,x93081)),f328(f328(f263(x93081,x93081),x93085),x93083)),f304(x93081,x93084)))+~P1(f328(f328(f330(f878(x93081,x93081)),f328(f328(f263(x93081,x93081),x93082),x93085)),x93084)) % 167.77/167.51 [9405]E(x94051,x94052)+E(f328(a116,f635(x94053,x94054,x94051,x94052,x94055)),x94054)+~P1(f328(f328(f330(f878(x94055,x94055)),f328(f328(f263(x94055,x94055),x94052),x94051)),f328(f328(f187(f878(x94055,x94055),a867),x94054),x94053))) % 167.77/167.51 [9406]E(x94061,x94062)+E(f328(a116,f636(x94063,x94064,x94061,x94062,x94065)),x94064)+~P1(f328(f328(f330(f878(x94065,x94065)),f328(f328(f263(x94065,x94065),x94062),x94061)),f328(f328(f187(f878(x94065,x94065),a867),x94064),x94063))) % 167.77/167.51 [9407]E(x94071,f2(a872))+E(f328(a116,f635(x94072,x94071,x94073,x94074,x94075)),x94071)+~P1(f328(f328(f330(f878(x94075,x94075)),f328(f328(f263(x94075,x94075),x94074),x94073)),f328(f328(f187(f878(x94075,x94075),a867),x94071),x94072))) % 167.77/167.51 [9408]E(x94081,f2(a872))+E(f328(a116,f636(x94082,x94081,x94083,x94084,x94085)),x94081)+~P1(f328(f328(f330(f878(x94085,x94085)),f328(f328(f263(x94085,x94085),x94084),x94083)),f328(f328(f187(f878(x94085,x94085),a867),x94081),x94082))) % 167.77/167.51 [9424]P1(f328(f328(f330(f878(x94241,x94241)),f328(f328(f263(x94241,x94241),x94242),x94243)),f328(f328(f285(x94241,x94241,x94241),x94244),f304(x94241,x94244))))+~P1(f328(f328(f330(f878(x94241,x94241)),f328(f328(f263(x94241,x94241),x94242),x94245)),x94244))+~P1(f328(f328(f330(f878(x94241,x94241)),f328(f328(f263(x94241,x94241),x94245),x94243)),x94244)) % 167.77/167.51 [9431]~P1(f328(f328(f330(f878(x94311,x94311)),f328(f328(f263(x94311,x94311),x94312),x94315)),f304(x94311,x94314)))+P1(f328(f328(f330(f878(x94311,x94311)),f328(f328(f263(x94311,x94311),x94312),x94313)),f328(f328(f285(x94311,x94311,x94311),x94314),f304(x94311,x94314))))+~P1(f328(f328(f330(f878(x94311,x94311)),f328(f328(f263(x94311,x94311),x94315),x94313)),x94314)) % 167.77/167.51 [9470]~P7(x94701,x94705,x94702)+~P1(f328(f328(f330(f878(x94701,x94701)),f328(f328(f263(x94701,x94701),x94703),x94704)),x94702))+P1(f328(f328(f242(f879(x94701,a867)),f328(f282(x94701,x94701,x94702),f328(f328(f306(x94701),x94703),f192(f879(x94701,a867))))),f328(f282(x94701,x94701,x94702),f328(f328(f306(x94701),x94704),f192(f879(x94701,a867)))))) % 167.77/167.51 [9494]E(x94941,x94942)+P1(f328(f328(f328(f328(a200,x94943),x94941),x94944),f577(x94942,x94944,x94941,x94943,x94945)))+~P1(f328(f328(f328(f328(a200,f32(x94945,x94943)),x94941),x94944),x94942)) % 167.77/167.51 [9498]~P1(f328(x94985,x94982))+P1(f328(f328(f328(f328(a200,x94981),x94982),x94983),f577(x94984,x94983,x94982,x94981,x94985)))+~P1(f328(f328(f328(f328(a200,f32(x94985,x94981)),x94982),x94983),x94984)) % 167.77/167.51 [9528]P1(f328(f328(f330(f878(x95281,x95281)),f328(f328(f263(x95281,x95281),x95282),x95283)),f328(f328(f285(x95281,x95281,x95281),x95284),f304(x95281,x95284))))+~P1(f328(f328(f330(f878(x95281,x95281)),f328(f328(f263(x95281,x95281),x95282),x95285)),f328(f328(f285(x95281,x95281,x95281),x95284),f304(x95281,x95284))))+~P1(f328(f328(f330(f878(x95281,x95281)),f328(f328(f263(x95281,x95281),x95285),x95283)),x95284)) % 167.77/167.51 [9529]P1(f328(f328(f330(f878(x95291,x95291)),f328(f328(f263(x95291,x95291),x95292),x95293)),f328(f328(f285(x95291,x95291,x95291),x95294),f304(x95291,x95294))))+~P1(f328(f328(f330(f878(x95291,x95291)),f328(f328(f263(x95291,x95291),x95295),x95293)),f328(f328(f285(x95291,x95291,x95291),x95294),f304(x95291,x95294))))+~P1(f328(f328(f330(f878(x95291,x95291)),f328(f328(f263(x95291,x95291),x95292),x95295)),x95294)) % 167.77/167.51 [9579]~P1(f328(f67(x95791,x95791,x95794,x95792,x95793),x95795))+P1(f328(f328(f330(x95791),x95792),x95793))+P1(f328(f63(x95791,x95794,f328(f328(f306(x95791),x95792),x95793)),x95795)) % 167.77/167.51 [9618]~E(f328(f307(x96183,x96182,x96185),x96184),x96181)+E(x96181,f192(f879(x96182,a867)))+P1(f328(f328(f242(f879(x96183,a867)),f328(f307(x96182,x96183,f530(x96184,x96183,x96182,x96181)),x96181)),x96184)) % 167.77/167.51 [9667]~P4(x96675)+P1(f328(f328(f330(x96671),f353(x96672,x96673,x96674,x96671,x96675)),x96674))+P1(f328(f328(f242(x96675),f328(f328(f44(x96671,x96675),x96674),x96673)),x96672)) % 167.77/167.51 [9719]P35(x97191,x97192,x97193,x97194,x97195)+~E(f328(f193(f873(x97191)),x97194),f328(f193(f873(x97192)),x97195))+P1(f328(f328(f330(f878(x97191,x97192)),f734(x97195,x97194,x97193,x97192,x97191)),f328(f170(f878(x97191,x97192)),f328(f328(f180(x97191,x97192),x97194),x97195)))) % 167.77/167.51 [9720]P35(x97201,x97202,x97203,x97204,x97205)+~E(f328(f193(f873(x97201)),x97204),f328(f193(f873(x97202)),x97205))+P1(f328(f328(f330(f878(x97201,x97202)),f735(x97203,x97205,x97204,x97202,x97201)),f328(f170(f878(x97201,x97202)),f328(f328(f180(x97201,x97202),x97204),x97205)))) % 167.77/167.51 [9850]E(x98501,x98502)+P1(f328(f328(f328(f328(a200,f32(x98503,x98504)),f577(x98501,x98505,x98502,x98504,x98503)),x98505),x98501))+~P1(f328(f328(f328(f328(a200,f32(x98503,x98504)),x98502),x98505),x98501)) % 167.77/167.51 [9852]~P1(f328(x98521,x98525))+P1(f328(f328(f328(f328(a200,f32(x98521,x98522)),f577(x98523,x98524,x98525,x98522,x98521)),x98524),x98523))+~P1(f328(f328(f328(f328(a200,f32(x98521,x98522)),x98525),x98524),x98523)) % 167.77/167.51 [9860]E(x98601,x98602)+P1(f328(f328(f330(f878(x98603,x98603)),f328(f328(f263(x98603,x98603),x98601),f637(x98604,x98605,x98602,x98601,x98603))),x98604))+~P1(f328(f328(f330(f878(x98603,x98603)),f328(f328(f263(x98603,x98603),x98601),x98602)),f328(f328(f187(f878(x98603,x98603),a867),x98605),x98604))) % 167.77/167.51 [9861]E(x98611,f2(a872))+P1(f328(f328(f330(f878(x98612,x98612)),f328(f328(f263(x98612,x98612),x98613),f637(x98614,x98611,x98615,x98613,x98612))),x98614))+~P1(f328(f328(f330(f878(x98612,x98612)),f328(f328(f263(x98612,x98612),x98613),x98615)),f328(f328(f187(f878(x98612,x98612),a867),x98611),x98614))) % 167.77/167.51 [9904]~P4(x99041)+~P1(f328(f328(f242(x99041),f328(x99044,f353(x99045,x99044,x99043,x99042,x99041))),x99045))+P1(f328(f328(f242(x99041),f328(f328(f44(x99042,x99041),x99043),x99044)),x99045)) % 167.77/167.51 [9946]E(x99461,x99462)+P1(f328(f328(f330(f878(x99463,x99463)),f328(f328(f263(x99463,x99463),f634(x99464,x99465,x99461,x99462,x99463)),x99461)),x99464))+~P1(f328(f328(f330(f878(x99463,x99463)),f328(f328(f263(x99463,x99463),x99462),x99461)),f328(f328(f187(f878(x99463,x99463),a867),x99465),x99464))) % 167.77/167.51 [9947]E(x99471,f2(a872))+P1(f328(f328(f330(f878(x99472,x99472)),f328(f328(f263(x99472,x99472),f634(x99473,x99471,x99474,x99475,x99472)),x99474)),x99473))+~P1(f328(f328(f330(f878(x99472,x99472)),f328(f328(f263(x99472,x99472),x99475),x99474)),f328(f328(f187(f878(x99472,x99472),a867),x99471),x99473))) % 167.77/167.51 [9951]E(x99511,x99512)+P1(f328(f328(f330(f878(x99513,x99513)),f328(f328(f263(x99513,x99513),x99511),f634(x99514,x99515,x99512,x99511,x99513))),f328(f328(f187(f878(x99513,x99513),a867),f635(x99514,x99515,x99512,x99511,x99513)),x99514)))+~P1(f328(f328(f330(f878(x99513,x99513)),f328(f328(f263(x99513,x99513),x99511),x99512)),f328(f328(f187(f878(x99513,x99513),a867),x99515),x99514))) % 167.77/167.51 [9952]E(x99521,f2(a872))+P1(f328(f328(f330(f878(x99522,x99522)),f328(f328(f263(x99522,x99522),x99523),f634(x99524,x99521,x99525,x99523,x99522))),f328(f328(f187(f878(x99522,x99522),a867),f635(x99524,x99521,x99525,x99523,x99522)),x99524)))+~P1(f328(f328(f330(f878(x99522,x99522)),f328(f328(f263(x99522,x99522),x99523),x99525)),f328(f328(f187(f878(x99522,x99522),a867),x99521),x99524))) % 167.77/167.51 [10002]E(x100021,x100022)+P1(f328(f328(f330(f878(x100023,x100023)),f328(f328(f263(x100023,x100023),f637(x100024,x100025,x100021,x100022,x100023)),x100021)),f328(f328(f187(f878(x100023,x100023),a867),f636(x100024,x100025,x100021,x100022,x100023)),x100024)))+~P1(f328(f328(f330(f878(x100023,x100023)),f328(f328(f263(x100023,x100023),x100022),x100021)),f328(f328(f187(f878(x100023,x100023),a867),x100025),x100024))) % 167.77/167.51 [10003]E(x100031,f2(a872))+P1(f328(f328(f330(f878(x100032,x100032)),f328(f328(f263(x100032,x100032),f637(x100033,x100031,x100034,x100035,x100032)),x100034)),f328(f328(f187(f878(x100032,x100032),a867),f636(x100033,x100031,x100034,x100035,x100032)),x100033)))+~P1(f328(f328(f330(f878(x100032,x100032)),f328(f328(f263(x100032,x100032),x100035),x100034)),f328(f328(f187(f878(x100032,x100032),a867),x100031),x100033))) % 167.77/167.51 [10036]~P67(x100362)+~P1(f328(f38(x100361),x100365))+E(f328(f328(f6(x100361,x100362),f328(f328(f7(x100361,x100362,x100362),f328(f328(f18(x100361,x100362,f879(x100362,x100362)),f328(f328(f8(a867,f879(x100362,f879(x100362,x100362)),x100361),f100(x100362)),f328(f328(f7(x100361,f879(x100361,a867),a867),f330(x100361)),x100363))),x100364)),f2(x100362))),x100365),f328(f328(f6(x100361,x100362),x100364),f328(f328(f105(f879(x100361,a867)),x100365),x100363))) % 167.77/167.51 [8611]~P67(x86111)+~P1(f328(f38(x86114),x86115))+E(f328(f328(f80(x86111),f328(x86112,x86113)),f328(f328(f6(x86114,x86111),x86112),f328(f328(f22(f879(x86114,a867)),x86115),f328(f328(f306(x86114),x86113),f192(f879(x86114,a867)))))),f328(f328(f6(x86114,x86111),x86112),f328(f328(f306(x86114),x86113),x86115))) % 167.77/167.51 [8612]~P73(x86121)+~P1(f328(f38(x86124),x86125))+E(f328(f328(f81(x86121),f328(x86122,x86123)),f328(f328(f9(x86124,x86121),x86122),f328(f328(f22(f879(x86124,a867)),x86125),f328(f328(f306(x86124),x86123),f192(f879(x86124,a867)))))),f328(f328(f9(x86124,x86121),x86122),f328(f328(f306(x86124),x86123),x86125))) % 167.77/167.51 [8933]~P105(x89332)+~P15(x89332,f328(f166(x89332),f328(f328(f151(x89331,x89332),x89334),x89335)))+E(f328(f133(x89331,f328(f328(f8(x89332,a867,x89331),f328(f243(x89332),x89333)),x89334)),x89335),f175(x89331,f328(f328(f8(x89332,a867,x89331),f328(f243(x89332),x89333)),x89334),x89335)) % 167.77/167.51 [8959]~P67(x89591)+E(f328(f328(f80(x89591),f328(f328(f6(a872,x89591),x89592),f299(a872,x89593,x89594))),f328(f328(f6(a872,x89591),x89592),f299(a872,f328(f328(f80(a872),x89594),f78(a872)),f328(f328(f80(a872),x89594),x89595)))),f328(f328(f6(a872,x89591),x89592),f299(a872,x89593,f328(f328(f80(a872),x89594),x89595))))+~P1(f328(f328(f242(a872),x89593),f328(f328(f80(a872),x89594),f78(a872)))) % 167.77/167.51 [8960]~P1(f328(f328(f330(x89601),x89604),x89605))+~P1(f328(f328(f242(f879(x89601,a867)),f328(f170(x89601),x89602)),x89605))+P1(f328(f328(f242(f879(x89601,a867)),f328(f170(x89601),f328(f328(f156(x89601,x89602),x89603),x89604))),x89605)) % 167.77/167.51 [9185]~P4(x91852)+~P1(f328(f38(x91851),x91855))+E(f328(f328(f65(x91851,x91852,f328(f328(f8(x91852,f879(x91852,x91852),x91851),f114(x91852)),x91853)),x91854),x91855),f328(f328(f114(x91852),x91854),f328(f328(f44(x91851,x91852),x91855),x91853))) % 167.77/167.51 [9186]~P4(x91862)+~P1(f328(f38(x91861),x91865))+E(f328(f328(f65(x91861,x91862,f328(f328(f8(x91862,f879(x91862,x91862),x91861),f105(x91862)),x91863)),x91864),x91865),f328(f328(f105(x91862),x91864),f328(f328(f43(x91861,x91862),x91865),x91863))) % 167.77/167.51 [9233]E(f328(x92331,x92332),f328(x92331,x92333))+P1(f328(f328(f243(a872),f328(x92331,x92332)),f328(x92331,x92333)))+~P1(f328(f328(f330(f878(x92334,x92334)),f328(f328(f263(x92334,x92334),x92332),x92333)),f150(x92334,f328(f328(f148(f879(x92334,a872)),x92331),x92335)))) % 167.77/167.51 [9264]~E(f328(x92644,x92642),f328(x92644,x92643))+~P1(f328(f328(f330(f878(x92641,x92641)),f328(f328(f263(x92641,x92641),x92642),x92643)),f150(x92641,x92645)))+P1(f328(f328(f330(f878(x92641,x92641)),f328(f328(f263(x92641,x92641),x92642),x92643)),f150(x92641,f328(f328(f148(f879(x92641,a872)),x92644),x92645)))) % 167.77/167.51 [9286]~P26(x92861,x92862,x92863,x92865)+P26(x92861,x92862,x92863,f328(f328(f306(x92861),x92864),x92865))+P1(f328(f328(f330(x92862),f328(x92863,x92864)),f328(f307(x92861,x92862,x92863),f328(f328(f22(f879(x92861,a867)),x92865),f328(f328(f306(x92861),x92864),f192(f879(x92861,a867))))))) % 167.77/167.51 [9290]P1(f328(x92902,x92905))+~P1(f328(f328(f330(x92901),x92905),f328(f170(x92901),x92903)))+E(f328(f328(f135(x92901),f328(f193(f873(x92901)),f175(x92901,x92902,f328(f328(f125(x92901),x92903),x92904)))),f328(f328(f125(x92901),x92903),x92904)),f328(f328(f125(x92901),f328(f328(f135(x92901),f328(f193(f873(x92901)),f175(x92901,x92902,x92903))),x92903)),x92904)) % 167.77/167.51 [9293]~P1(f328(f328(f330(f878(x92931,x92931)),f328(f328(f263(x92931,x92931),x92932),x92933)),f150(x92931,x92935)))+~P1(f328(f328(f242(a872),f328(x92934,x92932)),f328(x92934,x92933)))+P1(f328(f328(f330(f878(x92931,x92931)),f328(f328(f263(x92931,x92931),x92932),x92933)),f150(x92931,f328(f328(f148(f879(x92931,a872)),x92934),x92935)))) % 167.77/167.51 [9358]P1(f328(f328(f330(f878(x93584,x93584)),f328(f328(f263(x93584,x93584),x93582),x93583)),f150(x93584,x93585)))+P1(f328(f328(f243(a872),f328(x93581,x93582)),f328(x93581,x93583)))+~P1(f328(f328(f330(f878(x93584,x93584)),f328(f328(f263(x93584,x93584),x93582),x93583)),f150(x93584,f328(f328(f148(f879(x93584,a872)),x93581),x93585)))) % 167.77/167.51 [9501]~P1(f328(f328(f330(f878(f873(x95011),f873(x95011))),f328(f328(f263(f873(x95011),f873(x95011)),x95012),x95014)),f155(x95011,x95015)))+~P1(f328(f328(f243(a872),x95013),f328(f193(f873(x95011)),x95012)))+P1(f328(f328(f330(f878(x95011,x95011)),f328(f328(f263(x95011,x95011),f328(f328(f162(x95011),x95012),x95013)),f328(f328(f162(x95011),x95014),x95013))),x95015)) % 167.77/167.51 [9747]E(x97471,f2(a1))+~P1(f328(f50(x97473,x97471),f328(f328(f263(a1,a1),x97474),x97475)))+P1(f328(f50(f328(f328(f81(a1),x97472),x97473),x97471),f328(f328(f263(a1,a1),f328(f328(f80(a1),f328(f328(f81(a1),x97472),x97474)),f328(f328(f40(a1),f328(f328(f81(a1),x97472),x97475)),x97471))),f46(a1,f328(f328(f81(a1),x97472),x97475),x97471)))) % 167.77/167.51 [9749]~P1(f328(f328(f243(a872),f2(a872)),x97493))+~P1(f328(f49(x97492,x97493),f328(f328(f263(a872,a872),x97494),x97495)))+P1(f328(f49(f328(f328(f81(a872),x97491),x97492),x97493),f328(f328(f263(a872,a872),f328(f328(f80(a872),f328(f328(f81(a872),x97491),x97494)),f328(f328(f40(a872),f328(f328(f81(a872),x97491),x97495)),x97493))),f46(a872,f328(f328(f81(a872),x97491),x97495),x97493)))) % 167.77/167.51 [10059]~P67(x100592)+~P1(f328(f38(x100591),x100594))+E(f328(f328(f6(x100591,x100592),x100593),f328(f248(x100591),f328(f328(f18(x100591,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100591),a326),f328(f328(f7(x100591,f879(x100591,a867),a867),f330(x100591)),x100594))),f328(f328(f7(x100591,f879(x100591,a867),a867),f330(x100591)),x100595)))),f328(f328(f6(x100591,x100592),f328(f328(f7(x100591,x100592,x100592),f328(f328(f18(x100591,x100592,f879(x100592,x100592)),f328(f328(f8(a867,f879(x100592,f879(x100592,x100592)),x100591),f100(x100592)),f328(f328(f7(x100591,f879(x100591,a867),a867),f330(x100591)),x100595))),x100593)),f2(x100592))),x100594)) % 167.77/167.51 [8242]~E(f328(f328(f125(x82421),x82422),x82425),f328(f328(f125(x82421),x82423),x82424))+E(f328(f328(f125(x82421),f328(f328(f135(x82421),f328(f193(f873(x82421)),x82422)),x82423)),x82424),x82425)+P1(f328(f328(f242(a872),f328(f193(f873(x82421)),x82423)),f328(f193(f873(x82421)),x82422))) % 167.77/167.51 [8436]~E(f328(f328(f125(x84362),x84363),x84361),f328(f328(f125(x84362),x84364),x84365))+E(x84361,f328(f328(f125(x84362),f328(f328(f135(x84362),f328(f193(f873(x84362)),x84363)),x84364)),x84365))+~P1(f328(f328(f242(a872),f328(f193(f873(x84362)),x84363)),f328(f193(f873(x84362)),x84364))) % 167.77/167.51 [8524]~E(f328(f328(f80(a872),f328(f328(f81(a872),x85243),x85244)),x85241),f328(f328(f80(a872),f328(f328(f81(a872),x85242),x85244)),x85245))+~P1(f328(f328(f242(a872),x85243),x85242))+E(x85241,f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x85242),x85243)),x85244)),x85245)) % 167.77/167.51 [8525]~E(f328(f328(f80(a872),f328(f328(f81(a872),x85251),x85253)),x85254),f328(f328(f80(a872),f328(f328(f81(a872),x85252),x85253)),x85255))+~P1(f328(f328(f242(a872),x85252),x85251))+E(f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x85251),x85252)),x85253)),x85254),x85255) % 167.77/167.51 [8690]E(f328(f328(f80(a872),f328(f328(f81(a872),x86901),x86902)),x86903),f328(f328(f80(a872),f328(f328(f81(a872),x86904),x86902)),x86905))+~P1(f328(f328(f242(a872),x86904),x86901))+~E(x86905,f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x86901),x86904)),x86902)),x86903)) % 167.77/167.51 [8691]E(f328(f328(f80(a872),f328(f328(f81(a872),x86911),x86912)),x86913),f328(f328(f80(a872),f328(f328(f81(a872),x86914),x86912)),x86915))+~P1(f328(f328(f242(a872),x86914),x86911))+~E(f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x86911),x86914)),x86912)),x86913),x86915) % 167.77/167.51 [9555]~P60(x95552)+~P1(f328(f38(x95551),x95555))+E(f328(f328(f9(x95551,x95552),f328(f328(f18(x95551,x95552,x95552),f328(f328(f8(x95552,f879(x95552,x95552),x95551),f286(x95552)),x95553)),x95554)),x95555),f328(f328(f286(x95552),f328(f328(f9(x95551,x95552),x95553),x95555)),f328(f328(f9(x95551,x95552),x95554),x95555))) % 167.77/167.51 [9683]~E(f638(x96835,x96834,x96833,x96832,x96831),f639(x96835,x96834,x96833,x96832,x96831))+P1(f328(f328(f330(f878(x96831,x96831)),f328(f328(f263(x96831,x96831),x96832),x96833)),f304(x96831,x96834)))+~P1(f328(f328(f330(f878(x96831,x96831)),f328(f328(f263(x96831,x96831),x96832),x96833)),f304(x96831,f328(f328(f114(f879(f878(x96831,x96831),a867)),x96834),x96835)))) % 167.77/167.51 [9684]~E(f640(x96845,x96844,x96843,x96842,x96841),f641(x96845,x96844,x96843,x96842,x96841))+P1(f328(f328(f330(f878(x96841,x96841)),f328(f328(f263(x96841,x96841),x96842),x96843)),f304(x96841,x96844)))+~P1(f328(f328(f330(f878(x96841,x96841)),f328(f328(f263(x96841,x96841),x96842),x96843)),f304(x96841,f328(f328(f114(f879(f878(x96841,x96841),a867)),x96844),x96845)))) % 167.77/167.51 [9894]P1(f328(f328(f330(f878(x98941,x98941)),f328(f328(f263(x98941,x98941),x98942),f641(x98945,x98944,x98943,x98942,x98941))),f304(x98941,x98944)))+P1(f328(f328(f330(f878(x98941,x98941)),f328(f328(f263(x98941,x98941),x98942),x98943)),f304(x98941,x98944)))+~P1(f328(f328(f330(f878(x98941,x98941)),f328(f328(f263(x98941,x98941),x98942),x98943)),f304(x98941,f328(f328(f114(f879(f878(x98941,x98941),a867)),x98944),x98945)))) % 167.77/167.51 [9973]P1(f328(f328(f330(f878(x99731,x99731)),f328(f328(f263(x99731,x99731),f639(x99735,x99734,x99733,x99732,x99731)),x99733)),f304(x99731,x99734)))+P1(f328(f328(f330(f878(x99731,x99731)),f328(f328(f263(x99731,x99731),x99732),x99733)),f304(x99731,x99734)))+~P1(f328(f328(f330(f878(x99731,x99731)),f328(f328(f263(x99731,x99731),x99732),x99733)),f304(x99731,f328(f328(f114(f879(f878(x99731,x99731),a867)),x99734),x99735)))) % 167.77/167.51 [10009]P1(f328(f328(f330(f878(x100091,x100091)),f328(f328(f263(x100091,x100091),x100092),x100093)),f304(x100091,x100094)))+P1(f328(f328(f330(f878(x100091,x100091)),f328(f328(f263(x100091,x100091),f638(x100095,x100094,x100093,x100092,x100091)),f639(x100095,x100094,x100093,x100092,x100091))),x100095))+~P1(f328(f328(f330(f878(x100091,x100091)),f328(f328(f263(x100091,x100091),x100092),x100093)),f304(x100091,f328(f328(f114(f879(f878(x100091,x100091),a867)),x100094),x100095)))) % 167.77/167.51 [10010]P1(f328(f328(f330(f878(x100101,x100101)),f328(f328(f263(x100101,x100101),x100102),x100103)),f304(x100101,x100104)))+P1(f328(f328(f330(f878(x100101,x100101)),f328(f328(f263(x100101,x100101),f641(x100105,x100104,x100103,x100102,x100101)),f640(x100105,x100104,x100103,x100102,x100101))),x100105))+~P1(f328(f328(f330(f878(x100101,x100101)),f328(f328(f263(x100101,x100101),x100102),x100103)),f304(x100101,f328(f328(f114(f879(f878(x100101,x100101),a867)),x100104),x100105)))) % 167.77/167.51 [10130]~P1(f328(f328(f330(f878(f873(x101301),f873(x101301))),f328(f328(f263(f873(x101301),f873(x101301)),x101304),x101305)),f155(x101301,x101302)))+~P1(f328(f328(f330(f878(x101301,x101301)),x101303),f328(f170(f878(x101301,x101301)),f328(f328(f180(x101301,x101301),x101304),x101305))))+P1(f328(f328(f267(x101301,x101301,a867),f328(f328(f7(x101301,f879(f878(x101301,x101301),a867),f879(x101301,a867)),f328(f328(f8(f879(x101301,f879(f879(f878(x101301,x101301),a867),a867)),f879(f879(f878(x101301,x101301),a867),f879(x101301,a867)),x101301),f7(x101301,f879(f878(x101301,x101301),a867),a867)),f328(f328(f8(f879(x101301,f878(x101301,x101301)),f879(x101301,f879(f879(f878(x101301,x101301),a867),a867)),x101301),f328(f8(f878(x101301,x101301),f879(f879(f878(x101301,x101301),a867),a867),x101301),f330(f878(x101301,x101301)))),f263(x101301,x101301)))),x101302)),x101303)) % 167.77/167.51 [9583]~P1(f328(f328(f242(a872),x95833),x95832))+~P1(f328(f328(f243(a872),f328(f328(f80(a872),f328(f328(f81(a872),x95833),x95834)),x95831)),f328(f328(f80(a872),f328(f328(f81(a872),x95832),x95834)),x95835)))+P1(f328(f328(f243(a872),x95831),f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x95832),x95833)),x95834)),x95835))) % 167.77/167.51 [9584]~P1(f328(f328(f242(a872),x95843),x95842))+~P1(f328(f328(f242(a872),f328(f328(f80(a872),f328(f328(f81(a872),x95843),x95844)),x95841)),f328(f328(f80(a872),f328(f328(f81(a872),x95842),x95844)),x95845)))+P1(f328(f328(f242(a872),x95841),f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x95842),x95843)),x95844)),x95845))) % 167.77/167.51 [9602]~P1(f328(f328(f242(a872),x96021),x96024))+P1(f328(f328(f243(a872),f328(f328(f80(a872),f328(f328(f81(a872),x96021),x96022)),x96023)),f328(f328(f80(a872),f328(f328(f81(a872),x96024),x96022)),x96025)))+~P1(f328(f328(f243(a872),x96023),f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x96024),x96021)),x96022)),x96025))) % 167.77/167.51 [9603]~P1(f328(f328(f242(a872),x96031),x96034))+P1(f328(f328(f242(a872),f328(f328(f80(a872),f328(f328(f81(a872),x96031),x96032)),x96033)),f328(f328(f80(a872),f328(f328(f81(a872),x96034),x96032)),x96035)))+~P1(f328(f328(f242(a872),x96033),f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x96034),x96031)),x96032)),x96035))) % 167.77/167.51 [9717]~P1(f328(f328(f242(a872),x97172),x97171))+~P1(f328(f328(f243(a872),f328(f328(f80(a872),f328(f328(f81(a872),x97171),x97173)),x97174)),f328(f328(f80(a872),f328(f328(f81(a872),x97172),x97173)),x97175)))+P1(f328(f328(f243(a872),f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x97171),x97172)),x97173)),x97174)),x97175)) % 167.77/167.51 [9718]~P1(f328(f328(f242(a872),x97182),x97181))+~P1(f328(f328(f242(a872),f328(f328(f80(a872),f328(f328(f81(a872),x97181),x97183)),x97184)),f328(f328(f80(a872),f328(f328(f81(a872),x97182),x97183)),x97185)))+P1(f328(f328(f242(a872),f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x97181),x97182)),x97183)),x97184)),x97185)) % 167.77/167.51 [9771]~P1(f328(f328(f242(a872),x97714),x97711))+P1(f328(f328(f243(a872),f328(f328(f80(a872),f328(f328(f81(a872),x97711),x97712)),x97713)),f328(f328(f80(a872),f328(f328(f81(a872),x97714),x97712)),x97715)))+~P1(f328(f328(f243(a872),f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x97711),x97714)),x97712)),x97713)),x97715)) % 167.77/167.51 [9772]~P1(f328(f328(f242(a872),x97724),x97721))+P1(f328(f328(f242(a872),f328(f328(f80(a872),f328(f328(f81(a872),x97721),x97722)),x97723)),f328(f328(f80(a872),f328(f328(f81(a872),x97724),x97722)),x97725)))+~P1(f328(f328(f242(a872),f328(f328(f80(a872),f328(f328(f81(a872),f328(f328(f22(a872),x97721),x97724)),x97722)),x97723)),x97725)) % 167.77/167.51 [9994]~P13(x99941,x99942,x99945,x99943)+~P1(f328(f328(f330(f878(x99941,x99941)),x99944),x99945))+P1(f328(f328(f267(x99941,x99941,a867),f328(f328(f7(x99941,f879(x99941,x99942),f879(x99941,a867)),f328(f328(f8(f879(x99942,a867),f879(f879(x99941,x99942),f879(x99941,a867)),x99941),f8(x99942,a867,x99941)),f328(f328(f8(x99942,f879(x99942,a867),x99941),a325),x99943))),x99943)),x99944)) % 167.77/167.51 [6775]~E(f328(x67754,x67755),f205(x67752))+E(f328(f183(x67751,x67752,x67753,x67754),x67755),f328(f235(x67752),x67756))+~E(f328(x67753,x67755),f328(f235(x67752),x67756)) % 167.77/167.51 [6877]~E(f328(x68773,x68776),f205(x68771))+E(f328(f237(f876(x68771),x68772,f205(x68771),x68773),f328(x68774,x68775)),f205(x68771))+~E(f328(x68774,x68775),f328(f235(x68772),x68776)) % 167.77/167.51 [7459]E(f328(x74591,x74592),f205(x74593))+~E(f328(f183(x74595,x74593,x74596,x74591),x74592),f328(f235(x74593),x74594))+E(f328(x74591,x74592),f328(f235(x74593),x74594)) % 167.77/167.51 [7495]~E(f328(f183(x74956,x74953,x74955,x74951),x74952),f328(f235(x74953),x74954))+E(f328(x74951,x74952),f328(f235(x74953),x74954))+E(f328(x74955,x74952),f328(f235(x74953),x74954)) % 167.77/167.51 [8399]~P20(x83996,x83991,x83992,x83994)+E(f328(f73(x83991,x83991,x83991,f328(x83992,x83993)),f328(x83994,x83995)),f328(f73(x83991,x83991,x83991,f328(x83994,x83995)),f328(x83992,x83993)))+~P1(f328(f38(x83996),x83995)) % 167.77/167.51 [8823]~P26(x88231,x88233,x88235,x88236)+~P26(x88233,x88232,x88234,f328(f307(x88231,x88233,x88235),x88236))+P26(x88231,x88232,f328(f73(x88233,x88232,x88231,x88234),x88235),x88236) % 167.77/167.51 [9390]~P1(f328(f328(x93903,x93902),x93906))+~P1(f328(f328(x93904,x93905),x93902))+P1(f328(f328(f330(x93901),x93902),f296(x93901,x93903,x93904,x93905,x93906))) % 167.77/167.51 [9391]~P1(f328(f328(x93914,x93912),x93916))+~P1(f328(f328(x93913,x93915),x93912))+P1(f328(f328(f330(x93911),x93912),f293(x93911,x93913,x93914,x93915,x93916))) % 167.77/167.51 [9502]E(x95021,x95022)+E(x95023,x95024)+~P1(f328(f328(f330(f878(f873(x95025),f873(x95025))),f328(f328(f263(f873(x95025),f873(x95025)),f328(f328(f148(x95025),x95023),x95021)),f328(f328(f148(x95025),x95024),x95022))),f154(x95025,x95026))) % 167.77/167.51 [9511]~E(x95112,x95114)+P1(f328(f328(f330(f878(f873(x95111),f873(x95111))),f328(f328(f263(f873(x95111),f873(x95111)),f328(f328(f148(x95111),x95112),x95113)),f328(f328(f148(x95111),x95114),x95115))),f142(x95111,x95116)))+~P1(f328(f328(f330(f878(f873(x95111),f873(x95111))),f328(f328(f263(f873(x95111),f873(x95111)),x95113),x95115)),f142(x95111,x95116))) % 167.77/167.51 [9512]~E(x95122,x95124)+P1(f328(f328(f330(f878(f873(x95121),f873(x95121))),f328(f328(f263(f873(x95121),f873(x95121)),f328(f328(f148(x95121),x95122),x95123)),f328(f328(f148(x95121),x95124),x95125))),f144(x95121,x95126)))+~P1(f328(f328(f330(f878(f873(x95121),f873(x95121))),f328(f328(f263(f873(x95121),f873(x95121)),x95123),x95125)),f144(x95121,x95126))) % 167.77/167.51 [9513]~E(x95132,x95134)+P1(f328(f328(f330(f878(f873(x95131),f873(x95131))),f328(f328(f263(f873(x95131),f873(x95131)),f328(f328(f148(x95131),x95132),x95133)),f328(f328(f148(x95131),x95134),x95135))),f154(x95131,x95136)))+~P1(f328(f328(f330(f878(f873(x95131),f873(x95131))),f328(f328(f263(f873(x95131),f873(x95131)),x95133),x95135)),f154(x95131,x95136))) % 167.77/167.51 [9514]~E(x95142,x95144)+P1(f328(f328(f330(f878(f873(x95141),f873(x95141))),f328(f328(f263(f873(x95141),f873(x95141)),f328(f328(f125(x95141),x95142),x95143)),f328(f328(f125(x95141),x95144),x95145))),f154(x95141,x95146)))+~P1(f328(f328(f330(f878(f873(x95141),f873(x95141))),f328(f328(f263(f873(x95141),f873(x95141)),x95143),x95145)),f154(x95141,x95146))) % 167.77/167.51 [9515]~E(x95153,x95155)+P1(f328(f328(f330(f878(f873(x95151),f873(x95151))),f328(f328(f263(f873(x95151),f873(x95151)),f328(f328(f125(x95151),x95152),x95153)),f328(f328(f125(x95151),x95154),x95155))),f154(x95151,x95156)))+~P1(f328(f328(f330(f878(f873(x95151),f873(x95151))),f328(f328(f263(f873(x95151),f873(x95151)),x95152),x95154)),f154(x95151,x95156))) % 167.77/167.51 [9571]E(x95711,x95712)+P1(f328(f328(f330(f878(f873(x95713),f873(x95713))),f328(f328(f263(f873(x95713),f873(x95713)),x95711),x95712)),f154(x95713,x95714)))+~P1(f328(f328(f330(f878(f873(x95713),f873(x95713))),f328(f328(f263(f873(x95713),f873(x95713)),f328(f328(f148(x95713),x95715),x95711)),f328(f328(f148(x95713),x95716),x95712))),f154(x95713,x95714))) % 167.77/167.51 [9721]~E(x97213,x97215)+P1(f328(f328(f330(f878(f873(x97211),f873(x97211))),f328(f328(f263(f873(x97211),f873(x97211)),f328(f328(f125(x97211),x97212),f328(f328(f148(x97211),x97213),f117(x97211)))),f328(f328(f125(x97211),x97214),f328(f328(f148(x97211),x97215),f117(x97211))))),f154(x97211,x97216)))+~P1(f328(f328(f330(f878(f873(x97211),f873(x97211))),f328(f328(f263(f873(x97211),f873(x97211)),x97212),x97214)),f154(x97211,x97216))) % 167.77/167.51 [9737]E(f328(x97371,x97372),f205(x97373))+~E(f328(f237(f876(x97376),x97373,f205(x97376),x97374),f328(x97371,x97372)),f205(x97376))+E(f328(x97374,f766(x97372,x97371,x97374,x97375,x97376,x97373)),f205(x97376)) % 167.77/167.51 [9738]E(f328(x97381,x97382),f205(x97383))+~E(f328(f237(f876(x97386),x97383,f205(x97386),x97384),f328(x97381,x97382)),f205(x97386))+E(f328(f235(x97383),f766(x97382,x97381,x97384,x97385,x97386,x97383)),f328(x97381,x97382)) % 167.77/167.51 [9775]E(x97751,x97752)+E(x97753,x97754)+~P1(f328(f328(f330(f878(f873(x97755),f873(x97755))),f328(f328(f263(f873(x97755),f873(x97755)),f328(f328(f125(x97755),x97753),f328(f328(f148(x97755),x97751),f117(x97755)))),f328(f328(f125(x97755),x97754),f328(f328(f148(x97755),x97752),f117(x97755))))),f154(x97755,x97756))) % 167.77/167.51 [9800]E(x98001,x98002)+~P1(f328(f328(f330(f878(f873(x98003),f873(x98003))),f328(f328(f263(f873(x98003),f873(x98003)),f328(f328(f125(x98003),x98001),f328(f328(f148(x98003),x98005),f117(x98003)))),f328(f328(f125(x98003),x98002),f328(f328(f148(x98003),x98006),f117(x98003))))),f154(x98003,x98004)))+P1(f328(f328(f330(f878(f873(x98003),f873(x98003))),f328(f328(f263(f873(x98003),f873(x98003)),x98001),x98002)),f154(x98003,x98004))) % 167.77/167.51 [9836]~P1(f328(f328(f330(f878(f879(x98361,a867),f879(x98361,a867))),f328(f328(f263(f879(x98361,a867),f879(x98361,a867)),x98362),x98364)),f320(x98361,x98366)))+~P1(f328(f328(f330(f878(f879(x98361,a867),f879(x98361,a867))),f328(f328(f263(f879(x98361,a867),f879(x98361,a867)),x98363),x98365)),f320(x98361,x98366)))+P1(f328(f328(f330(f878(f879(x98361,a867),f879(x98361,a867))),f328(f328(f263(f879(x98361,a867),f879(x98361,a867)),f328(f328(f114(f879(x98361,a867)),x98362),x98363)),f328(f328(f114(f879(x98361,a867)),x98364),x98365))),f320(x98361,x98366))) % 167.77/167.51 [5224]~E(f328(x52243,x52246),x52245)+~E(x52244,f328(f235(x52241),x52246))+E(f328(f328(f206(x52241,x52242),x52243),x52244),f328(f235(x52242),x52245)) % 167.77/167.51 [5638]~E(f328(f328(f125(x56381),x56386),x56383),x56385)+E(f328(f328(f125(x56381),x56382),x56383),f328(f328(f148(x56381),x56384),x56385))+~E(x56382,f328(f328(f148(x56381),x56384),x56386)) % 167.77/167.51 [5639]~E(f328(f328(f125(x56391),x56396),x56393),x56395)+E(f328(f328(f125(x56391),x56392),x56393),f328(f328(f125(x56391),x56394),x56395))+~E(x56392,f328(f328(f125(x56391),x56394),x56396)) % 167.77/167.51 [5641]E(f328(f328(f125(x56411),x56412),x56413),f328(f328(f148(x56411),x56414),x56415))+~E(f328(f328(f148(x56411),x56414),x56416),x56412)+~E(x56415,f328(f328(f125(x56411),x56416),x56413)) % 167.77/167.51 [5643]~E(f328(f328(f125(x56431),x56432),x56436),x56434)+E(f328(f328(f125(x56431),x56432),x56433),f328(f328(f125(x56431),x56434),x56435))+~E(x56433,f328(f328(f125(x56431),x56436),x56435)) % 167.77/167.51 [6769]E(f328(x67691,x67692),f328(x67693,x67692))+~E(f328(f328(f151(x67694,x67695),x67691),x67696),f328(f328(f151(x67694,x67695),x67693),x67696))+~P1(f328(f328(f330(x67694),x67692),f328(f170(x67694),x67696))) % 167.77/167.51 [7152]~P20(x71524,x71525,x71526,x71521)+E(f328(f328(x71521,x71522),x71523),f328(f328(f65(x71524,x71525,x71526),x71523),x71522))+~P1(f328(f38(x71524),x71522)) % 167.77/167.51 [7220]~E(x72202,f328(x72204,x72206))+~P1(f328(f328(f330(x72203),x72206),x72205))+P1(f328(f328(f330(x72201),x72202),f328(f307(x72203,x72201,x72204),x72205))) % 167.77/167.51 [7221]~E(f328(x72214,x72212),x72216)+~P1(f328(f328(f330(x72213),x72216),x72215))+P1(f328(f328(f330(x72211),x72212),f328(f308(x72211,x72213,x72214),x72215))) % 167.77/167.51 [7676]~P33(x76761,x76762,x76764,x76766)+P33(x76761,x76762,f328(f328(f148(x76761),x76763),x76764),f328(f328(f148(x76761),x76765),x76766))+~P1(f328(f328(x76762,x76763),x76765)) % 167.77/167.51 [8698]~P53(x86984,x86985,x86981,x86982,x86986)+E(f328(x86981,f328(x86982,x86983)),x86983)+~P1(f328(f328(f330(x86985),x86983),x86986)) % 167.77/167.51 [9504]E(x95041,x95042)+E(f328(f193(f873(x95043)),x95044),f328(f193(f873(x95043)),x95045))+~P1(f328(f328(f330(f878(f873(x95043),f873(x95043))),f328(f328(f263(f873(x95043),f873(x95043)),f328(f328(f148(x95043),x95041),x95044)),f328(f328(f148(x95043),x95042),x95045))),f142(x95043,x95046))) % 167.77/167.51 [9567]~P17(x95671,x95672,x95673)+E(f328(f328(f65(x95671,x95672,x95673),x95674),x95675),x95676)+~P1(f328(f67(x95671,x95672,x95673,x95674,x95675),x95676)) % 167.77/167.51 [9574]E(f328(f193(f873(x95741)),x95742),f328(f193(f873(x95741)),x95743))+P1(f328(f328(f330(f878(f873(x95741),f873(x95741))),f328(f328(f263(f873(x95741),f873(x95741)),x95742),x95743)),f142(x95741,x95744)))+~P1(f328(f328(f330(f878(f873(x95741),f873(x95741))),f328(f328(f263(f873(x95741),f873(x95741)),f328(f328(f148(x95741),x95745),x95742)),f328(f328(f148(x95741),x95746),x95743))),f142(x95741,x95744))) % 167.77/167.51 [9596]~P1(f328(f328(f330(f878(x95961,x95961)),f328(f328(f263(x95961,x95961),x95962),x95964)),f304(x95961,x95966)))+P1(f328(f328(f330(f878(f873(x95961),f873(x95961))),f328(f328(f263(f873(x95961),f873(x95961)),f328(f328(f148(x95961),x95962),x95963)),f328(f328(f148(x95961),x95964),x95965))),f304(f873(x95961),f154(x95961,x95966))))+~P1(f328(f328(f330(f878(f873(x95961),f873(x95961))),f328(f328(f263(f873(x95961),f873(x95961)),x95963),x95965)),f304(f873(x95961),f154(x95961,x95966)))) % 167.77/167.51 [9781]~P1(f328(x97812,x97816))+~E(f328(f133(x97811,x97812),x97813),f328(f328(f148(x97811),x97814),x97815))+~P1(f328(f328(f330(x97811),x97816),f328(f170(x97811),f783(x97815,x97814,x97813,x97812,x97811)))) % 167.77/167.51 [9782]~P1(f328(x97824,x97826))+~E(f328(f328(f148(x97821),x97822),x97823),f328(f133(x97821,x97824),x97825))+~P1(f328(f328(f330(x97821),x97826),f328(f170(x97821),f786(x97825,x97824,x97823,x97822,x97821)))) % 167.77/167.51 [10087]~P67(x100872)+E(f328(f328(f6(x100871,x100872),f328(f328(f8(f879(x100873,a867),x100872,x100871),f328(f6(x100873,x100872),x100874)),f328(f328(f8(f879(x100873,a867),f879(x100873,a867),x100871),f248(x100873)),f328(f328(f8(f879(x100873,a867),f879(x100873,a867),x100871),f328(f18(x100873,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100873),a326),f328(f328(f7(x100873,f879(x100873,a867),a867),f330(x100873)),x100875)))),f328(f7(x100873,x100871,a867),f328(f328(f8(x100871,f879(x100871,a867),x100873),a325),x100876)))))),f328(f307(x100873,x100871,x100876),x100875)),f328(f328(f6(x100873,x100872),x100874),x100875))+~P1(f328(f38(x100873),x100875)) % 167.77/167.51 [6827]~P105(x68273)+P1(f328(x68272,x68275))+E(f328(f133(x68271,x68272),f328(f328(f145(x68271,x68273,x68274),x68275),x68276)),f328(f133(x68271,x68272),x68276)) % 167.77/167.51 [6829]P1(f328(x68291,x68292))+~E(f164(x68293,x68291,x68294),f328(f328(f263(f873(x68293),f873(x68293)),x68295),x68296))+~P1(f328(f328(f330(x68293),x68292),f328(f170(x68293),x68295))) % 167.77/167.51 [6874]~P1(f328(x68742,x68746))+~E(f164(x68741,x68742,x68743),f328(f328(f263(f873(x68741),f873(x68741)),x68744),x68745))+~P1(f328(f328(f330(x68741),x68746),f328(f170(x68741),x68745))) % 167.77/167.51 [7539]~P16(x75391,x75392,x75393)+~P1(f328(f38(x75391),x75396))+E(f328(f328(f65(x75391,x75392,x75393),x75394),f328(f328(f306(x75391),x75395),x75396)),f328(f328(f65(x75391,x75392,x75393),f328(f328(x75393,x75395),x75394)),x75396)) % 167.77/167.51 [7591]~P105(x75912)+~P1(f328(f328(f242(x75912),f328(x75913,x75914)),f328(x75913,x75915)))+E(f328(f328(f145(x75911,x75912,x75913),x75914),f328(f328(f148(x75911),x75915),x75916)),f328(f328(f148(x75911),x75914),f328(f328(f148(x75911),x75915),x75916))) % 167.77/167.51 [7706]E(x77061,x77062)+~E(f328(f328(f265(x77063,x77064),x77061),f328(f16(f879(x77064,a867),x77063),x77065)),f328(f328(f265(x77063,x77064),x77062),f328(f16(f879(x77064,a867),x77063),x77065)))+~P1(f328(f328(f330(x77064),x77066),x77065)) % 167.77/167.51 [7773]~P16(x77731,x77732,x77733)+~P1(f328(f38(x77731),x77736))+E(f328(f328(f65(x77731,x77732,x77733),x77734),f328(f328(f306(x77731),x77735),x77736)),f328(f328(x77733,x77735),f328(f328(f65(x77731,x77732,x77733),x77734),x77736))) % 167.77/167.51 [7891]~P17(x78911,x78912,x78913)+~P1(f328(f38(x78911),x78916))+E(f328(f328(f65(x78911,x78912,x78913),f328(f328(x78913,x78914),x78915)),x78916),f328(f328(x78913,x78914),f328(f328(f65(x78911,x78912,x78913),x78915),x78916))) % 167.77/167.51 [7960]~P21(x79602,x79605,x79606,x79601)+~P1(f328(f38(x79602),x79604))+E(f328(x79601,f328(f328(f306(x79602),x79603),x79604)),f328(f73(x79605,x79605,x79605,f328(x79601,x79604)),f328(x79606,x79603))) % 167.77/167.51 [7992]~P105(x79922)+P1(f328(f328(f242(x79922),f328(x79923,x79924)),f328(x79923,x79925)))+E(f328(f328(f145(x79921,x79922,x79923),x79924),f328(f328(f148(x79921),x79925),x79926)),f328(f328(f148(x79921),x79925),f328(f328(f145(x79921,x79922,x79923),x79924),x79926))) % 167.77/167.51 [8134]~E(f328(f193(f873(x81341)),x81345),f328(f193(f873(x81342)),x81346))+~E(f328(f193(f873(x81341)),x81343),f328(f193(f873(x81342)),x81344))+E(f328(f328(f125(f878(x81341,x81342)),f328(f328(f180(x81341,x81342),x81343),x81344)),f328(f328(f180(x81341,x81342),x81345),x81346)),f328(f328(f180(x81341,x81342),f328(f328(f125(x81341),x81343),x81345)),f328(f328(f125(x81342),x81344),x81346))) % 167.77/167.51 [8257]~E(x82572,f328(f307(x82573,x82571,x82574),x82576))+P1(f328(f328(f242(f879(x82571,a867)),x82572),f328(f307(x82573,x82571,x82574),x82575)))+~P1(f328(f328(f242(f879(x82573,a867)),x82576),x82575)) % 167.77/167.51 [8357]~P105(x83575)+E(f328(x83571,x83572),f328(x83571,x83573))+E(f328(f328(f145(x83574,x83575,x83571),x83572),f328(f328(f145(x83574,x83575,x83571),x83573),x83576)),f328(f328(f145(x83574,x83575,x83571),x83573),f328(f328(f145(x83574,x83575,x83571),x83572),x83576))) % 167.77/167.51 [8392]~P26(x83923,x83921,x83924,x83925)+P26(x83923,x83921,f328(f328(f328(f72(x83923,x83921),x83924),x83926),x83922),x83925)+P1(f328(f328(f330(x83921),x83922),f328(f307(x83923,x83921,x83924),x83925))) % 167.77/167.51 [8536]~P1(f328(f328(f330(x85362),x85364),f328(x85366,x85363)))+~P1(f328(f328(f330(x85361),x85363),x85365))+P1(f328(f328(f330(f878(x85361,x85362)),f328(f328(f263(x85361,x85362),x85363),x85364)),f328(f328(f265(x85361,x85362),x85365),x85366))) % 167.77/167.51 [9000]~P67(x90002)+~P26(x90004,x90001,x90005,x90006)+E(f328(f328(f6(x90001,x90002),x90003),f328(f307(x90004,x90001,x90005),x90006)),f328(f328(f6(x90004,x90002),f328(f73(x90001,x90002,x90004,x90003),x90005)),x90006)) % 167.77/167.51 [9001]~P73(x90012)+~P26(x90014,x90011,x90015,x90016)+E(f328(f328(f9(x90011,x90012),x90013),f328(f307(x90014,x90011,x90015),x90016)),f328(f328(f9(x90014,x90012),f328(f73(x90011,x90012,x90014,x90013),x90015)),x90016)) % 167.77/167.51 [9049]~P35(x90492,x90495,x90491,x90493,x90496)+P1(f328(f328(x90491,f328(f328(f162(x90492),x90493),x90494)),f328(f328(f162(x90495),x90496),x90494)))+~P1(f328(f328(f243(a872),x90494),f328(f193(f873(x90495)),x90496))) % 167.77/167.51 [9050]~P35(x90502,x90505,x90501,x90503,x90506)+P1(f328(f328(x90501,f328(f328(f162(x90502),x90503),x90504)),f328(f328(f162(x90505),x90506),x90504)))+~P1(f328(f328(f243(a872),x90504),f328(f193(f873(x90502)),x90503))) % 167.77/167.51 [9260]~P20(x92603,x92601,x92606,x92602)+~P1(f328(f38(x92603),x92604))+E(f328(f73(x92601,x92601,x92601,f328(x92602,f328(f328(f22(f879(x92603,a867)),x92604),f328(f328(f306(x92603),x92605),f192(f879(x92603,a867)))))),f328(x92606,x92605)),f328(x92602,f328(f328(f306(x92603),x92605),x92604))) % 167.77/167.51 [9874]~E(f328(f307(x98742,x98744,x98746),f251(f879(x98742,a867))),f251(f879(x98744,a867)))+~E(f328(f307(x98741,x98743,x98745),f251(f879(x98741,a867))),f251(f879(x98743,a867)))+E(f328(f307(f878(x98741,x98742),f878(x98743,x98744),f268(x98741,x98743,x98742,x98744,x98745,x98746)),f251(f879(f878(x98741,x98742),a867))),f251(f879(f878(x98743,x98744),a867))) % 167.77/167.51 [9922]~P26(x99223,x99224,x99225,f328(x99226,f581(x99226,x99225,x99224,x99223,x99222,x99221)))+P26(x99223,x99224,x99225,f328(f328(f43(x99222,f879(x99223,a867)),x99221),x99226))+E(x99221,f192(f879(x99222,a867))) % 167.77/167.51 [9980]P26(x99806,x99805,x99804,f328(f328(f43(x99802,f879(x99806,a867)),x99801),x99803))+E(x99801,f192(f879(x99802,a867)))+P1(f328(f328(f330(x99802),f581(x99803,x99804,x99805,x99806,x99802,x99801)),x99801)) % 167.77/167.51 [9985]P1(f328(f328(f330(x99851),f610(x99852,x99853,x99854,x99855,x99856,x99851)),x99856))+P1(f328(f328(f242(f879(f878(x99851,x99854),a867)),f328(f328(f265(x99851,x99854),x99856),x99853)),f328(f328(f265(x99851,x99854),x99855),x99852)))+~P1(f328(f328(f242(f879(x99851,a867)),x99856),x99855)) % 167.77/167.51 [10023]P25(x100236,x100235,f328(f328(f306(f871(x100236)),f328(f328(f328(f92(x100236),x100231),x100233),x100232)),f192(f879(f871(x100236),a867))))+~P25(x100236,x100235,f328(f328(f306(f871(x100236)),f328(f328(f328(f92(x100236),x100234),x100233),x100232)),f192(f879(f871(x100236),a867))))+P1(f328(f328(x100231,f416(x100231,x100232,x100233,x100234,x100235,x100236)),f426(x100231,x100232,x100233,x100234,x100235,x100236))) % 167.77/167.51 [10024]P25(x100246,x100245,f328(f328(f306(f871(x100246)),f328(f328(f328(f92(x100246),x100244),x100243),x100242)),f192(f879(f871(x100246),a867))))+~P25(x100246,x100245,f328(f328(f306(f871(x100246)),f328(f328(f328(f92(x100246),x100244),x100243),x100241)),f192(f879(f871(x100246),a867))))+P1(f328(f328(x100241,f438(x100242,x100241,x100243,x100244,x100245,x100246)),f446(x100242,x100241,x100243,x100244,x100245,x100246))) % 167.77/167.51 [10062]~P25(x100621,x100622,f328(f328(f306(f871(x100621)),f328(f328(f328(f92(x100621),x100623),x100624),x100626)),f192(f879(f871(x100621),a867))))+P25(x100621,x100622,f328(f328(f306(f871(x100621)),f328(f328(f328(f92(x100621),x100623),x100624),x100625)),f192(f879(f871(x100621),a867))))+~P1(f328(f328(x100625,f438(x100625,x100626,x100624,x100623,x100622,x100621)),f446(x100625,x100626,x100624,x100623,x100622,x100621))) % 167.77/167.51 [10063]~P25(x100631,x100632,f328(f328(f306(f871(x100631)),f328(f328(f328(f92(x100631),x100636),x100634),x100635)),f192(f879(f871(x100631),a867))))+P25(x100631,x100632,f328(f328(f306(f871(x100631)),f328(f328(f328(f92(x100631),x100633),x100634),x100635)),f192(f879(f871(x100631),a867))))+~P1(f328(f328(x100636,f416(x100633,x100635,x100634,x100636,x100632,x100631)),f426(x100633,x100635,x100634,x100636,x100632,x100631))) % 167.77/167.51 [10098]~P1(f328(f328(f242(f879(x100982,a867)),f328(x100984,f610(x100986,x100984,x100982,x100985,x100983,x100981))),f328(x100986,f610(x100986,x100984,x100982,x100985,x100983,x100981))))+~P1(f328(f328(f242(f879(x100981,a867)),x100983),x100985))+P1(f328(f328(f242(f879(f878(x100981,x100982),a867)),f328(f328(f265(x100981,x100982),x100983),x100984)),f328(f328(f265(x100981,x100982),x100985),x100986))) % 167.77/167.51 [7726]~P1(f328(x77261,x77265))+~P1(f328(x77266,x77264))+P1(f328(x77261,f328(f266(x77262,x77263),f328(f328(f263(x77262,x77263),x77264),x77265)))) % 167.77/167.51 [7727]~P1(f328(x77271,x77274))+~P1(f328(x77276,x77275))+P1(f328(x77271,f328(f262(x77272,x77273),f328(f328(f263(x77272,x77273),x77274),x77275)))) % 167.77/167.51 [7748]~E(f328(f193(f873(x77481)),x77483),f328(f193(f873(x77484)),x77485))+~E(f328(f328(f176(x77481,x77484),f328(f328(f180(x77481,x77484),x77483),x77485)),x77482),f328(f235(x77484),x77486))+P1(f328(f328(f330(x77481),x77482),f328(f170(x77481),x77483))) % 167.77/167.51 [7778]~P1(f328(f328(x77784,x77786),x77785))+~P1(f328(f328(f330(x77781),x77786),x77783))+P1(f328(f328(f328(f44(x77781,f879(x77782,a867)),x77783),x77784),x77785)) % 167.77/167.51 [8081]~P1(f328(f328(f330(x80811),x80812),f328(x80815,x80816)))+~P1(f328(f328(f330(x80813),x80816),x80814))+P1(f328(f328(f330(x80811),x80812),f328(f328(f44(x80813,f879(x80811,a867)),x80814),x80815))) % 167.77/167.51 [8125]P1(f328(f328(x81251,x81252),x81253))+~P1(f328(f328(x81254,x81252),x81253))+~P1(f328(f328(f242(f879(x81255,f879(x81256,a867))),x81254),x81251)) % 167.77/167.51 [8279]P1(f328(f328(x82791,x82792),x82793))+~P1(f328(f328(f330(x82794),x82792),x82795))+~P1(f328(f328(f328(f43(x82794,f879(x82796,a867)),x82795),x82791),x82793)) % 167.77/167.51 [8415]P1(f328(f328(f330(x84151),x84152),f328(x84153,x84154)))+~P1(f328(f328(f330(x84155),x84154),x84156))+~P1(f328(f328(f330(x84151),x84152),f328(f328(f43(x84155,f879(x84151,a867)),x84156),x84153))) % 167.77/167.51 [8608]~P1(f328(f328(f328(f328(a200,x86081),x86083),x86084),x86086))+~P1(f328(f328(f328(f328(a200,x86082),x86086),x86084),x86085))+P1(f328(f328(f328(f328(a200,f33(x86081,x86082)),x86083),x86084),x86085)) % 167.77/167.51 [8680]~P13(x86804,x86805,x86806,x86801)+E(f328(x86801,x86802),f328(x86801,x86803))+~P1(f328(f328(f330(f878(x86804,x86804)),f328(f328(f263(x86804,x86804),x86802),x86803)),x86806)) % 167.77/167.51 [8711]P1(f328(f328(f242(f879(x87111,a867)),x87112),f328(x87113,x87114)))+~P1(f328(f328(f330(x87115),x87114),x87116))+~P1(f328(f328(f242(f879(x87111,a867)),x87112),f328(f328(f43(x87115,f879(x87111,a867)),x87116),x87113))) % 167.77/167.51 [8739]~P51(x87393,x87394,f328(f283(x87394,x87393),x87395))+E(x87391,f192(f879(x87392,a867)))+E(f328(f328(f43(x87392,f879(x87393,a867)),x87391),f328(f328(f8(f879(x87394,a867),f879(x87393,a867),x87392),f282(x87394,x87393,x87395)),x87396)),f328(f282(x87394,x87393,x87395),f328(f328(f43(x87392,f879(x87394,a867)),x87391),x87396))) % 167.77/167.51 [8814]P1(f328(f328(f330(x88141),x88142),f328(f282(x88143,x88141,x88144),x88145)))+~P1(f328(f328(f330(x88143),x88146),x88145))+~P1(f328(f328(f330(f878(x88143,x88141)),f328(f328(f263(x88143,x88141),x88146),x88142)),x88144)) % 167.77/167.51 [8932]P1(f328(x89321,x89322))+~P1(f328(f328(f328(f328(a200,x89324),x89322),x89325),x89326))+P1(f328(f328(f328(f328(a200,f30(x89321,x89323,x89324)),x89322),x89325),x89326)) % 167.77/167.51 [8949]~P1(f328(x89491,x89494))+~P1(f328(f328(f328(f328(a200,x89492),x89494),x89495),x89496))+P1(f328(f328(f328(f328(a200,f30(x89491,x89492,x89493)),x89494),x89495),x89496)) % 167.77/167.51 [9124]P1(f328(f328(f242(f879(x91241,a867)),f328(f282(x91242,x91241,x91243),x91244)),f328(f282(x91242,x91241,x91245),x91246)))+~P1(f328(f328(f242(f879(x91242,a867)),x91244),x91246))+~P1(f328(f328(f242(f879(f878(x91242,x91241),a867)),x91243),x91245)) % 167.77/167.51 [9212]P1(f328(x92121,x92122))+P1(f328(f328(f328(f328(a200,x92123),x92122),x92124),x92125))+~P1(f328(f328(f328(f328(a200,f30(x92121,x92126,x92123)),x92122),x92124),x92125)) % 167.77/167.51 [9217]~P1(f328(x92175,x92172))+P1(f328(f328(f328(f328(a200,x92171),x92172),x92173),x92174))+~P1(f328(f328(f328(f328(a200,f30(x92175,x92171,x92176)),x92172),x92173),x92174)) % 167.77/167.51 [9267]P1(f328(f328(f328(f328(a200,x92671),x92672),x92673),x92674))+P1(f328(f328(f328(f328(a200,x92675),x92672),x92673),x92674))+~P1(f328(f328(f328(f328(a200,f30(x92676,x92671,x92675)),x92672),x92673),x92674)) % 167.77/167.51 [9309]~P1(f328(f328(f330(x93092),x93096),x93094))+~P1(f328(f328(f242(f879(x93091,a867)),x93093),x93095))+P1(f328(f328(f242(f879(f878(x93091,x93092),a867)),f328(f328(f265(x93091,x93092),x93093),f328(f16(f879(x93092,a867),x93091),x93094))),f328(f328(f265(x93091,x93092),x93095),f328(f16(f879(x93092,a867),x93091),x93094)))) % 167.77/167.51 [9322]~P35(x93221,x93222,x93223,x93225,x93226)+P1(f328(f328(f267(x93221,x93222,a867),x93223),x93224))+~P1(f328(f328(f330(f878(x93221,x93222)),x93224),f328(f170(f878(x93221,x93222)),f328(f328(f180(x93221,x93222),x93225),x93226)))) % 167.77/167.51 [9456]~E(x94563,x94565)+P1(f328(f328(f330(f878(f873(x94561),f873(x94561))),f328(f328(f263(f873(x94561),f873(x94561)),f328(f328(f148(x94561),x94562),x94563)),f328(f328(f148(x94561),x94564),x94565))),f154(x94561,x94566)))+~P1(f328(f328(f330(f878(x94561,x94561)),f328(f328(f263(x94561,x94561),x94562),x94564)),x94566)) % 167.77/167.51 [9462]~E(f328(f193(f873(x94621)),x94625),f328(f193(f873(x94622)),x94626))+E(f185(x94621,x94622,f186(x94621,x94622,x94623,f328(f328(f22(f879(x94621,a867)),x94624),f328(f170(x94621),x94625))),x94625,x94626),f186(x94621,x94622,f185(x94621,x94622,x94623,x94625,x94626),x94624))+~P1(f328(f328(f242(f879(x94621,a867)),f328(f170(x94621),x94625)),x94624)) % 167.77/167.51 [9463]~E(f328(f193(f873(x94631)),x94633),f328(f193(f873(x94631)),x94635))+P1(f328(f328(f330(f878(f873(x94631),f873(x94631))),f328(f328(f263(f873(x94631),f873(x94631)),f328(f328(f148(x94631),x94632),x94633)),f328(f328(f148(x94631),x94634),x94635))),f142(x94631,x94636)))+~P1(f328(f328(f330(f878(x94631,x94631)),f328(f328(f263(x94631,x94631),x94632),x94634)),x94636)) % 167.77/167.51 [9495]P1(f328(f328(f330(f878(x94951,x94951)),f328(f328(f263(x94951,x94951),x94952),x94953)),f328(f328(f187(f878(x94951,x94951),a867),f328(a116,x94954)),x94955)))+~P1(f328(f328(f330(f878(x94951,x94951)),f328(f328(f263(x94951,x94951),x94956),x94953)),x94955))+~P1(f328(f328(f330(f878(x94951,x94951)),f328(f328(f263(x94951,x94951),x94952),x94956)),f328(f328(f187(f878(x94951,x94951),a867),x94954),x94955))) % 167.77/167.51 [9496]P1(f328(f328(f330(f878(x94961,x94961)),f328(f328(f263(x94961,x94961),x94962),x94963)),f328(f328(f187(f878(x94961,x94961),a867),f328(a116,x94964)),x94965)))+~P1(f328(f328(f330(f878(x94961,x94961)),f328(f328(f263(x94961,x94961),x94962),x94966)),x94965))+~P1(f328(f328(f330(f878(x94961,x94961)),f328(f328(f263(x94961,x94961),x94966),x94963)),f328(f328(f187(f878(x94961,x94961),a867),x94964),x94965))) % 167.77/167.51 [9500]~P1(f328(f328(f330(x95004),x95005),x95006))+P1(f328(f328(f242(f879(x95001,a867)),x95002),x95003))+~P1(f328(f328(f242(f879(f878(x95001,x95004),a867)),f328(f328(f265(x95001,x95004),x95002),f328(f16(f879(x95004,a867),x95001),x95006))),f328(f328(f265(x95001,x95004),x95003),f328(f16(f879(x95004,a867),x95001),x95006)))) % 167.77/167.51 [9545]E(x95451,x95452)+~P1(f328(f328(f330(f878(f873(x95453),f873(x95453))),f328(f328(f263(f873(x95453),f873(x95453)),f328(f328(f148(x95453),x95451),x95455)),f328(f328(f148(x95453),x95452),x95456))),f142(x95453,x95454)))+P1(f328(f328(f330(f878(x95453,x95453)),f328(f328(f263(x95453,x95453),x95451),x95452)),x95454)) % 167.77/167.51 [9546]E(x95461,x95462)+~P1(f328(f328(f330(f878(f873(x95463),f873(x95463))),f328(f328(f263(f873(x95463),f873(x95463)),f328(f328(f148(x95463),x95461),x95465)),f328(f328(f148(x95463),x95462),x95466))),f144(x95463,x95464)))+P1(f328(f328(f330(f878(x95463,x95463)),f328(f328(f263(x95463,x95463),x95461),x95462)),x95464)) % 167.77/167.51 [9547]E(x95471,x95472)+~P1(f328(f328(f330(f878(f873(x95473),f873(x95473))),f328(f328(f263(f873(x95473),f873(x95473)),f328(f328(f148(x95473),x95471),x95475)),f328(f328(f148(x95473),x95472),x95476))),f154(x95473,x95474)))+P1(f328(f328(f330(f878(x95473,x95473)),f328(f328(f263(x95473,x95473),x95471),x95472)),x95474)) % 167.77/167.51 [9582]P1(f328(f328(f330(f878(f873(x95821),f873(x95821))),f328(f328(f263(f873(x95821),f873(x95821)),f328(f328(f148(x95821),x95822),x95823)),f328(f328(f148(x95821),x95824),x95825))),f155(x95821,x95826)))+~P1(f328(f328(f330(f878(f873(x95821),f873(x95821))),f328(f328(f263(f873(x95821),f873(x95821)),x95823),x95825)),f155(x95821,x95826)))+~P1(f328(f328(f330(f878(x95821,x95821)),f328(f328(f263(x95821,x95821),x95822),x95824)),x95826)) % 167.77/167.51 [9600]P1(f328(x96001,x96002))+~P1(f328(x96001,f753(x96001,x96003,x96004,x96005,x96006)))+~P1(f328(f328(f330(x96006),x96002),f328(f328(f44(x96005,f879(x96006,a867)),x96004),x96003))) % 167.77/167.51 [9605]~P1(f328(f328(f330(f878(f873(x96051),f873(x96051))),f328(f328(f263(f873(x96051),f873(x96051)),f328(f328(f148(x96051),x96052),x96055)),f328(f328(f148(x96051),x96053),x96056))),f142(x96051,x96054)))+P1(f328(f328(f330(f878(f873(x96051),f873(x96051))),f328(f328(f263(f873(x96051),f873(x96051)),x96055),x96056)),f142(x96051,x96054)))+P1(f328(f328(f330(f878(x96051,x96051)),f328(f328(f263(x96051,x96051),x96052),x96053)),x96054)) % 167.77/167.51 [9606]~P1(f328(f328(f330(f878(f873(x96061),f873(x96061))),f328(f328(f263(f873(x96061),f873(x96061)),f328(f328(f148(x96061),x96062),x96065)),f328(f328(f148(x96061),x96063),x96066))),f144(x96061,x96064)))+P1(f328(f328(f330(f878(f873(x96061),f873(x96061))),f328(f328(f263(f873(x96061),f873(x96061)),x96065),x96066)),f144(x96061,x96064)))+P1(f328(f328(f330(f878(x96061,x96061)),f328(f328(f263(x96061,x96061),x96062),x96063)),x96064)) % 167.77/167.51 [9607]~P1(f328(f328(f330(f878(f873(x96071),f873(x96071))),f328(f328(f263(f873(x96071),f873(x96071)),f328(f328(f148(x96071),x96072),x96075)),f328(f328(f148(x96071),x96073),x96076))),f154(x96071,x96074)))+P1(f328(f328(f330(f878(f873(x96071),f873(x96071))),f328(f328(f263(f873(x96071),f873(x96071)),x96075),x96076)),f154(x96071,x96074)))+P1(f328(f328(f330(f878(x96071,x96071)),f328(f328(f263(x96071,x96071),x96072),x96073)),x96074)) % 167.77/167.51 [9693]P1(f328(x96931,x96932))+P1(f328(f328(f330(x96933),f744(x96931,x96934,x96935,x96933,x96936)),x96935))+~P1(f328(f328(f330(x96936),x96932),f328(f328(f44(x96933,f879(x96936,a867)),x96935),x96934))) % 167.77/167.51 [9704]~E(x97042,x97044)+P1(f328(f328(f330(f878(f873(x97041),f873(x97041))),f328(f328(f263(f873(x97041),f873(x97041)),f328(f328(f125(x97041),x97042),f328(f328(f148(x97041),x97043),f117(x97041)))),f328(f328(f125(x97041),x97044),f328(f328(f148(x97041),x97045),f117(x97041))))),f154(x97041,x97046)))+~P1(f328(f328(f330(f878(x97041,x97041)),f328(f328(f263(x97041,x97041),x97043),x97045)),x97046)) % 167.77/167.51 [9791]E(x97911,x97912)+~P1(f328(f328(f330(f878(f873(x97913),f873(x97913))),f328(f328(f263(f873(x97913),f873(x97913)),f328(f328(f125(x97913),x97915),f328(f328(f148(x97913),x97911),f117(x97913)))),f328(f328(f125(x97913),x97916),f328(f328(f148(x97913),x97912),f117(x97913))))),f154(x97913,x97914)))+P1(f328(f328(f330(f878(x97913,x97913)),f328(f328(f263(x97913,x97913),x97911),x97912)),x97914)) % 167.77/167.51 [9819]~P1(f328(f328(f330(f878(f873(x98191),f873(x98191))),f328(f328(f263(f873(x98191),f873(x98191)),f328(f328(f125(x98191),x98195),f328(f328(f148(x98191),x98192),f117(x98191)))),f328(f328(f125(x98191),x98196),f328(f328(f148(x98191),x98193),f117(x98191))))),f154(x98191,x98194)))+P1(f328(f328(f330(f878(f873(x98191),f873(x98191))),f328(f328(f263(f873(x98191),f873(x98191)),x98195),x98196)),f154(x98191,x98194)))+P1(f328(f328(f330(f878(x98191,x98191)),f328(f328(f263(x98191,x98191),x98192),x98193)),x98194)) % 167.77/167.51 [9837]P1(f328(x98371,x98372))+P1(f328(f328(f330(x98373),f753(x98371,x98374,x98375,x98376,x98373)),f328(x98374,f744(x98371,x98374,x98375,x98376,x98373))))+~P1(f328(f328(f330(x98373),x98372),f328(f328(f44(x98376,f879(x98373,a867)),x98375),x98374))) % 167.77/167.51 [8829]~P17(x88293,x88294,x88291)+~P1(f328(f38(x88293),x88296))+E(f328(f328(x88291,x88292),f328(f328(f65(x88293,x88294,x88291),x88295),f328(f328(f22(f879(x88293,a867)),x88296),f328(f328(f306(x88293),x88292),f192(f879(x88293,a867)))))),f328(f328(f65(x88293,x88294,x88291),x88295),f328(f328(f306(x88293),x88292),x88296))) % 167.77/167.51 [8915]~E(f328(f328(f176(x89151,x89152),x89154),x89155),f328(f235(x89152),x89156))+~P1(f328(f328(x89153,x89155),x89156))+E(f328(f328(f176(x89151,x89152),f328(f133(f878(x89151,x89152),f328(f267(x89151,x89152,a867),x89153)),x89154)),x89155),f328(f235(x89152),x89156)) % 167.77/167.51 [9131]~P1(f328(f328(f330(x91315),x91313),x91316))+P1(f328(f328(f242(f879(x91311,a867)),f328(x91312,x91313)),x91314))+~P1(f328(f328(f242(f879(x91311,a867)),f328(f328(f44(x91315,f879(x91311,a867)),x91316),x91312)),x91314)) % 167.77/167.51 [9764]~P7(x97641,x97645,x97644)+P1(f328(f328(f330(f878(x97641,x97641)),f328(f328(f263(x97641,x97641),x97642),x97643)),x97644))+~P1(f328(f328(f330(x97641),x97646),f328(f328(f105(f879(x97641,a867)),f328(f282(x97641,x97641,x97644),f328(f328(f306(x97641),x97642),f192(f879(x97641,a867))))),f328(f282(x97641,x97641,x97644),f328(f328(f306(x97641),x97643),f192(f879(x97641,a867))))))) % 167.77/167.51 [8575]~P109(x85752)+~E(f328(f328(f80(x85752),f328(f328(f81(x85752),x85754),x85755)),x85751),f328(f328(f80(x85752),f328(f328(f81(x85752),x85753),x85755)),x85756))+E(x85751,f328(f328(f80(x85752),f328(f328(f81(x85752),f328(f328(f22(x85752),x85753),x85754)),x85755)),x85756)) % 167.77/167.51 [8576]~P109(x85761)+~E(f328(f328(f80(x85761),f328(f328(f81(x85761),x85762),x85764)),x85765),f328(f328(f80(x85761),f328(f328(f81(x85761),x85763),x85764)),x85766))+E(f328(f328(f80(x85761),f328(f328(f81(x85761),f328(f328(f22(x85761),x85762),x85763)),x85764)),x85765),x85766) % 167.77/167.51 [8742]~P109(x87421)+E(f328(f328(f80(x87421),f328(f328(f81(x87421),x87422),x87423)),x87424),f328(f328(f80(x87421),f328(f328(f81(x87421),x87425),x87423)),x87426))+~E(x87426,f328(f328(f80(x87421),f328(f328(f81(x87421),f328(f328(f22(x87421),x87422),x87425)),x87423)),x87424)) % 167.77/167.51 [8743]~P109(x87431)+E(f328(f328(f80(x87431),f328(f328(f81(x87431),x87432),x87433)),x87434),f328(f328(f80(x87431),f328(f328(f81(x87431),x87435),x87433)),x87436))+~E(f328(f328(f80(x87431),f328(f328(f81(x87431),f328(f328(f22(x87431),x87432),x87435)),x87433)),x87434),x87436) % 167.77/167.51 [9071]~P1(f328(f328(x90714,x90715),x90716))+~P1(f328(f328(x90713,x90715),x90716))+P1(f328(f328(f328(f328(f105(f879(x90711,f879(x90712,a867))),x90713),x90714),x90715),x90716)) % 167.77/167.51 [9330]P1(f328(f328(x93301,x93302),x93303))+P1(f328(f328(x93304,x93302),x93303))+~P1(f328(f328(f328(f328(f114(f879(x93305,f879(x93306,a867))),x93304),x93301),x93302),x93303)) % 167.77/167.51 [9620]~P110(x96201)+~P1(f328(f328(f243(x96201),f328(f328(f80(x96201),f328(f328(f81(x96201),x96204),x96205)),x96202)),f328(f328(f80(x96201),f328(f328(f81(x96201),x96203),x96205)),x96206)))+P1(f328(f328(f243(x96201),x96202),f328(f328(f80(x96201),f328(f328(f81(x96201),f328(f328(f22(x96201),x96203),x96204)),x96205)),x96206))) % 167.77/167.51 [9621]~P110(x96211)+~P1(f328(f328(f242(x96211),f328(f328(f80(x96211),f328(f328(f81(x96211),x96214),x96215)),x96212)),f328(f328(f80(x96211),f328(f328(f81(x96211),x96213),x96215)),x96216)))+P1(f328(f328(f242(x96211),x96212),f328(f328(f80(x96211),f328(f328(f81(x96211),f328(f328(f22(x96211),x96213),x96214)),x96215)),x96216))) % 167.77/167.51 [9646]~P110(x96461)+P1(f328(f328(f243(x96461),f328(f328(f80(x96461),f328(f328(f81(x96461),x96462),x96463)),x96464)),f328(f328(f80(x96461),f328(f328(f81(x96461),x96465),x96463)),x96466)))+~P1(f328(f328(f243(x96461),x96464),f328(f328(f80(x96461),f328(f328(f81(x96461),f328(f328(f22(x96461),x96465),x96462)),x96463)),x96466))) % 167.77/167.51 [9647]~P110(x96471)+P1(f328(f328(f242(x96471),f328(f328(f80(x96471),f328(f328(f81(x96471),x96472),x96473)),x96474)),f328(f328(f80(x96471),f328(f328(f81(x96471),x96475),x96473)),x96476)))+~P1(f328(f328(f242(x96471),x96474),f328(f328(f80(x96471),f328(f328(f81(x96471),f328(f328(f22(x96471),x96475),x96472)),x96473)),x96476))) % 167.77/167.51 [9752]~P110(x97521)+~P1(f328(f328(f243(x97521),f328(f328(f80(x97521),f328(f328(f81(x97521),x97522),x97524)),x97525)),f328(f328(f80(x97521),f328(f328(f81(x97521),x97523),x97524)),x97526)))+P1(f328(f328(f243(x97521),f328(f328(f80(x97521),f328(f328(f81(x97521),f328(f328(f22(x97521),x97522),x97523)),x97524)),x97525)),x97526)) % 167.77/167.51 [9753]~P110(x97531)+~P1(f328(f328(f242(x97531),f328(f328(f80(x97531),f328(f328(f81(x97531),x97532),x97534)),x97535)),f328(f328(f80(x97531),f328(f328(f81(x97531),x97533),x97534)),x97536)))+P1(f328(f328(f242(x97531),f328(f328(f80(x97531),f328(f328(f81(x97531),f328(f328(f22(x97531),x97532),x97533)),x97534)),x97535)),x97536)) % 167.77/167.51 [9802]~P110(x98021)+P1(f328(f328(f243(x98021),f328(f328(f80(x98021),f328(f328(f81(x98021),x98022),x98023)),x98024)),f328(f328(f80(x98021),f328(f328(f81(x98021),x98025),x98023)),x98026)))+~P1(f328(f328(f243(x98021),f328(f328(f80(x98021),f328(f328(f81(x98021),f328(f328(f22(x98021),x98022),x98025)),x98023)),x98024)),x98026)) % 167.77/167.51 [9803]~P110(x98031)+P1(f328(f328(f242(x98031),f328(f328(f80(x98031),f328(f328(f81(x98031),x98032),x98033)),x98034)),f328(f328(f80(x98031),f328(f328(f81(x98031),x98035),x98033)),x98036)))+~P1(f328(f328(f242(x98031),f328(f328(f80(x98031),f328(f328(f81(x98031),f328(f328(f22(x98031),x98032),x98035)),x98033)),x98034)),x98036)) % 167.77/167.51 [9974]~P67(x99742)+~P1(f328(f38(x99741),x99746))+E(f328(f328(f6(x99741,x99742),f328(f328(f18(x99741,x99742,x99742),f328(f328(f18(x99741,x99742,f879(x99742,x99742)),f328(f328(f8(a867,f879(x99742,f879(x99742,x99742)),x99741),f100(x99742)),x99743)),x99744)),x99745)),x99746),f328(f328(f80(x99742),f328(f328(f6(x99741,x99742),x99744),f328(f328(f105(f879(x99741,a867)),x99746),f328(f248(x99741),x99743)))),f328(f328(f6(x99741,x99742),x99745),f328(f328(f105(f879(x99741,a867)),x99746),f328(f79(f879(x99741,a867)),f328(f248(x99741),x99743)))))) % 167.77/167.51 [10032]P1(f328(f328(f330(x100322),x100324),x100326))+P1(f328(f328(f330(x100322),x100325),x100326))+E(f328(f308(x100321,x100322,f328(f328(f7(x100321,x100322,x100322),f328(f328(f7(x100321,x100322,f879(x100322,x100322)),f328(f328(f8(a867,f879(x100322,f879(x100322,x100322)),x100321),f100(x100322)),f328(f328(f7(x100321,f879(x100321,a867),a867),f330(x100321)),x100323))),x100324)),x100325)),x100326),f192(f879(x100321,a867))) % 167.77/167.51 [10033]P1(f328(f328(f330(x100332),x100335),x100336))+~P1(f328(f328(f330(x100332),x100334),x100336))+E(f328(f308(x100331,x100332,f328(f328(f7(x100331,x100332,x100332),f328(f328(f7(x100331,x100332,f879(x100332,x100332)),f328(f328(f8(a867,f879(x100332,f879(x100332,x100332)),x100331),f100(x100332)),f328(f328(f7(x100331,f879(x100331,a867),a867),f330(x100331)),x100333))),x100334)),x100335)),x100336),x100333) % 167.77/167.51 [10034]P1(f328(f328(f330(x100342),x100344),x100346))+~P1(f328(f328(f330(x100342),x100345),x100346))+E(f328(f308(x100341,x100342,f328(f328(f7(x100341,x100342,x100342),f328(f328(f7(x100341,x100342,f879(x100342,x100342)),f328(f328(f8(a867,f879(x100342,f879(x100342,x100342)),x100341),f100(x100342)),f328(f328(f7(x100341,f879(x100341,a867),a867),f330(x100341)),x100343))),x100344)),x100345)),x100346),f328(f79(f879(x100341,a867)),x100343)) % 167.77/167.51 [10035]~P1(f328(f328(f330(x100352),x100354),x100356))+~P1(f328(f328(f330(x100352),x100355),x100356))+E(f328(f308(x100351,x100352,f328(f328(f7(x100351,x100352,x100352),f328(f328(f7(x100351,x100352,f879(x100352,x100352)),f328(f328(f8(a867,f879(x100352,f879(x100352,x100352)),x100351),f100(x100352)),f328(f328(f7(x100351,f879(x100351,a867),a867),f330(x100351)),x100353))),x100354)),x100355)),x100356),f251(f879(x100351,a867))) % 167.77/167.51 [10164]P25(x101641,x101642,f328(f328(f306(f871(x101641)),f328(f328(f328(f92(x101641),f328(x101643,x101644)),f328(a26,x101644)),f328(x101645,x101644))),f192(f879(f871(x101641),a867))))+~P1(f328(f328(f330(a870),x101644),x101646))+~P25(x101641,f328(f328(f114(f879(f871(x101641),a867)),x101642),f328(f307(a870,f871(x101641),f328(f328(f18(a870,f879(x101641,f879(a868,a867)),f871(x101641)),f328(f328(f18(a870,a869,f879(f879(x101641,f879(a868,a867)),f871(x101641))),f328(f328(f8(f879(x101641,f879(a868,a867)),f879(a869,f879(f879(x101641,f879(a868,a867)),f871(x101641))),a870),f92(x101641)),x101643)),a26)),x101645)),x101646)),f328(f307(a870,f871(x101641),f328(f328(f18(a870,f879(x101641,f879(a868,a867)),f871(x101641)),f328(f328(f18(a870,a869,f879(f879(x101641,f879(a868,a867)),f871(x101641))),f328(f328(f8(f879(x101641,f879(a868,a867)),f879(a869,f879(f879(x101641,f879(a868,a867)),f871(x101641))),a870),f92(x101641)),x101643)),f328(f328(f8(f876(a869),a869,a870),f239(a869)),a28))),x101645)),x101646)) % 167.77/167.51 [8605]E(x86051,x86052)+~P53(x86054,x86055,x86053,x86056,x86057)+~E(f328(x86053,x86051),f328(x86053,x86052)) % 167.77/167.51 [6980]E(f328(f237(f876(x69801),x69802,f205(x69801),x69803),f328(x69804,x69805)),f328(f235(x69801),x69806))+~E(f328(x69804,x69805),f328(f235(x69802),x69807))+~E(f328(x69803,x69807),f328(f235(x69801),x69806)) % 167.77/167.51 [8636]~P10(x86366,x86365,x86367,x86364,x86361)+E(f328(f328(x86361,x86362),x86363),x86364)+P1(f328(f38(x86365),x86363)) % 167.77/167.51 [9483]P43(x94831,x94832,x94833,x94834,x94835,f328(f328(x94833,x94836),x94837))+~E(f328(f328(x94833,x94836),x94837),x94834)+~E(x94835,f192(f879(x94831,a867))) % 167.77/167.51 [9668]~P1(f328(x96686,x96683))+~P1(f328(f328(f330(f878(x96682,x96682)),f328(f328(f263(x96682,x96682),x96684),x96685)),f328(x96687,x96683)))+P1(f328(f328(f330(f878(f878(x96681,x96682),f878(x96681,x96682))),f328(f328(f263(f878(x96681,x96682),f878(x96681,x96682)),f328(f328(f263(x96681,x96682),x96683),x96684)),f328(f328(f263(x96681,x96682),x96683),x96685))),f280(x96681,x96682,x96686,x96687))) % 167.77/167.51 [10089]~P43(x100892,x100897,x100893,x100896,x100891,f328(f328(x100893,x100895),x100894))+E(f328(f328(x100893,f520(x100894,x100895,x100891,x100896,x100893,x100897,x100892)),f521(x100894,x100895,x100891,x100896,x100893,x100897,x100892)),f328(f328(x100893,x100895),x100894))+E(x100891,f192(f879(x100892,a867))) % 167.77/167.51 [10090]~P43(x100907,x100906,x100901,x100904,x100905,f328(f328(x100901,x100902),x100903))+E(f328(f328(x100901,f520(x100903,x100902,x100905,x100904,x100901,x100906,x100907)),f521(x100903,x100902,x100905,x100904,x100901,x100906,x100907)),f328(f328(x100901,x100902),x100903))+E(f328(f328(x100901,x100902),x100903),x100904) % 167.77/167.51 [9169]~P35(x91691,x91692,x91693,x91695,x91697)+P35(x91691,x91692,x91693,f328(f328(f148(x91691),x91694),x91695),f328(f328(f148(x91692),x91696),x91697))+~P1(f328(f328(x91693,x91694),x91696)) % 167.77/167.51 [9187]P35(x91871,x91872,x91873,x91874,x91875)+~P35(x91871,x91872,x91873,f328(f328(f125(x91871),x91876),x91874),f328(f328(f125(x91872),x91877),x91875))+~E(f328(f193(f873(x91871)),x91876),f328(f193(f873(x91872)),x91877)) % 167.77/167.51 [9188]P35(x91881,x91882,x91883,x91884,x91885)+~P35(x91881,x91882,x91883,f328(f328(f125(x91881),x91884),x91886),f328(f328(f125(x91882),x91885),x91887))+~E(f328(f193(f873(x91881)),x91884),f328(f193(f873(x91882)),x91885)) % 167.77/167.51 [9393]~P35(x93931,x93932,x93933,x93935,x93937)+~P35(x93931,x93932,x93933,x93934,x93936)+P35(x93931,x93932,x93933,f328(f328(f125(x93931),x93934),x93935),f328(f328(f125(x93932),x93936),x93937)) % 167.77/167.51 [9741]~P1(f328(f67(x97411,x97414,x97415,x97416,x97413),x97417))+P1(f328(f67(x97411,x97414,x97415,x97416,f328(f328(f306(x97411),x97412),x97413)),f328(f328(x97415,x97412),x97417)))+P1(f328(f328(f330(x97411),x97412),x97413)) % 167.77/167.51 [9872]~P26(x98723,x98721,x98724,f251(f879(x98723,a867)))+E(f328(f328(f176(x98721,x98722),f328(f328(f151(f878(x98723,x98722),f878(x98721,x98722)),f328(f267(x98723,x98722,f878(x98721,x98722)),f328(f328(f8(x98721,f879(x98722,f878(x98721,x98722)),x98723),f263(x98721,x98722)),x98724))),x98725)),f328(x98724,x98726)),f328(f235(x98722),x98727))+~E(f328(f328(f176(x98723,x98722),x98725),x98726),f328(f235(x98722),x98727)) % 167.77/167.51 [10110]~P43(x101102,x101107,x101106,x101105,x101101,f328(f328(x101106,x101104),x101103))+E(x101101,f192(f879(x101102,a867)))+P1(f328(f328(f330(x101102),f520(x101103,x101104,x101101,x101105,x101106,x101107,x101102)),x101101)) % 167.77/167.51 [10111]~P43(x101115,x101117,x101111,x101114,x101116,f328(f328(x101111,x101112),x101113))+E(f328(f328(x101111,x101112),x101113),x101114)+P1(f328(f328(f330(x101115),f520(x101113,x101112,x101116,x101114,x101111,x101117,x101115)),x101116)) % 167.77/167.51 [6768]~E(x67685,x67687)+~E(x67686,x67684)+E(f328(f328(f328(f328(f72(x67681,f876(x67682)),x67683),x67684),f328(f235(x67682),x67685)),x67686),f328(f235(x67682),x67687)) % 167.77/167.51 [6896]E(x68961,x68962)+~E(f328(x68965,x68961),f328(f235(x68964),x68967))+E(f328(f328(f328(f328(f72(x68963,f876(x68964)),x68965),x68962),f328(f235(x68964),x68966)),x68961),f328(f235(x68964),x68967)) % 167.77/167.51 [7616]E(x76161,x76162)+~E(x76163,x76164)+~E(f328(f328(f328(f328(f72(x76165,f876(x76166)),x76167),x76164),f328(f235(x76166),x76161)),x76163),f328(f235(x76166),x76162)) % 167.77/167.51 [7682]E(x76821,x76822)+E(f328(x76823,x76824),f328(f235(x76825),x76821))+~E(f328(f328(f328(f328(f72(x76826,f876(x76825)),x76823),x76827),f328(f235(x76825),x76822)),x76824),f328(f235(x76825),x76821)) % 167.77/167.51 [7683]E(x76831,x76832)+E(f328(x76833,x76831),f328(f235(x76834),x76835))+~E(f328(f328(f328(f328(f72(x76836,f876(x76834)),x76833),x76832),f328(f235(x76834),x76837)),x76831),f328(f235(x76834),x76835)) % 167.77/167.51 [8854]~P22(x88544,x88545,x88546,x88547,x88541)+~P1(f328(f38(x88545),x88543))+E(f328(f328(x88541,x88542),x88543),f328(f328(f328(f66(x88544,x88545,x88546),x88542),x88547),x88543)) % 167.77/167.51 [8855]~P10(x88554,x88555,x88556,x88557,x88551)+~P1(f328(f38(x88555),x88553))+E(f328(f328(x88551,x88552),x88553),f328(f328(f328(f66(x88554,x88555,x88556),x88552),x88557),x88553)) % 167.77/167.51 [9449]~P25(x94491,x94492,f328(f328(f306(f871(x94491)),f328(f328(f328(f92(x94491),x94493),x94494),x94497)),f192(f879(f871(x94491),a867))))+P25(x94491,x94492,f328(f328(f306(f871(x94491)),f328(f328(f328(f92(x94491),x94493),f33(x94494,x94495)),x94496)),f192(f879(f871(x94491),a867))))+~P25(x94491,x94492,f328(f328(f306(f871(x94491)),f328(f328(f328(f92(x94491),x94497),x94495),x94496)),f192(f879(f871(x94491),a867)))) % 167.77/167.51 [9641]~P24(x96413,x96414,x96415,x96417,x96416,x96411)+~P1(f328(f38(x96414),x96412))+E(f328(x96411,x96412),f328(f328(f328(f66(x96413,x96414,x96415),x96416),x96417),x96412)) % 167.77/167.51 [9797]P43(x97971,x97972,x97973,x97974,x97975,f328(f328(x97973,x97976),x97977))+~P43(x97971,x97972,x97973,x97974,f328(f328(f22(f879(x97971,a867)),x97975),f328(f328(f306(x97971),x97976),f192(f879(x97971,a867)))),x97977)+~P1(f328(f328(f330(x97971),x97976),x97975)) % 167.77/167.51 [10064]~P25(x100641,x100642,f328(f328(f306(f871(x100641)),f328(f328(f328(f92(x100641),f95(x100641,x100643,x100644)),x100645),x100647)),f192(f879(f871(x100641),a867))))+P25(x100641,x100642,f328(f328(f306(f871(x100641)),f328(f328(f328(f92(x100641),x100643),f30(x100644,x100645,x100646)),x100647)),f192(f879(f871(x100641),a867))))+~P25(x100641,x100642,f328(f328(f306(f871(x100641)),f328(f328(f328(f92(x100641),f95(x100641,x100643,f328(f73(a867,a867,a868,a323),x100644))),x100646),x100647)),f192(f879(f871(x100641),a867)))) % 167.77/167.51 [10135]~P43(x101352,x101353,x101354,x101355,x101351,f328(f328(x101354,x101357),x101356))+P43(x101352,x101353,x101354,x101355,f328(f328(f22(f879(x101352,a867)),x101351),f328(f328(f306(x101352),f520(x101356,x101357,x101351,x101355,x101354,x101353,x101352)),f192(f879(x101352,a867)))),f521(x101356,x101357,x101351,x101355,x101354,x101353,x101352))+E(x101351,f192(f879(x101352,a867))) % 167.77/167.51 [10136]~P43(x101365,x101366,x101361,x101364,x101367,f328(f328(x101361,x101362),x101363))+P43(x101365,x101366,x101361,x101364,f328(f328(f22(f879(x101365,a867)),x101367),f328(f328(f306(x101365),f520(x101363,x101362,x101367,x101364,x101361,x101366,x101365)),f192(f879(x101365,a867)))),f521(x101363,x101362,x101367,x101364,x101361,x101366,x101365))+E(f328(f328(x101361,x101362),x101363),x101364) % 167.77/167.51 [9176]E(f185(x91761,x91762,x91763,x91764,f328(f328(f156(x91762,x91765),x91766),x91767)),f185(x91761,x91762,x91763,x91764,x91765))+~P1(f328(f328(f243(a872),x91766),f328(f193(f873(x91762)),x91765)))+~P1(f328(f328(f242(a872),f328(f193(f873(x91761)),x91764)),x91766)) % 167.77/167.51 [9471]P1(f328(f328(f242(f879(f878(x94711,x94712),a867)),f328(f328(f285(x94711,x94713,x94712),x94714),x94715)),f328(f328(f285(x94711,x94713,x94712),x94716),x94717)))+~P1(f328(f328(f242(f879(f878(x94713,x94712),a867)),x94715),x94717))+~P1(f328(f328(f242(f879(f878(x94711,x94713),a867)),x94714),x94716)) % 167.77/167.51 [9808]~P1(f328(f328(f330(x98081),x98086),x98085))+P1(f328(f67(x98081,x98082,x98083,x98084,x98085),f328(f328(x98083,x98086),x98087)))+~P1(f328(f67(x98081,x98082,x98083,x98084,f328(f328(f22(f879(x98081,a867)),x98085),f328(f328(f306(x98081),x98086),f192(f879(x98081,a867))))),x98087)) % 167.77/167.51 [10195]~P135(x101951)+~P26(f878(x101952,x101953),x101951,f328(f267(x101952,x101953,x101951),f328(f328(f7(x101952,f879(x101953,x101951),f879(x101953,x101951)),f328(f328(f8(f879(x101951,x101951),f879(f879(x101953,x101951),f879(x101953,x101951)),x101952),f8(x101951,x101951,x101953)),f328(f328(f8(x101951,f879(x101951,x101951),x101952),f81(x101951)),x101954))),x101955)),f328(f328(f265(x101952,x101953),x101956),f328(f16(f879(x101953,a867),x101952),x101957)))+E(f328(f328(f6(x101951,x101951),f34(x101951)),f328(f248(x101951),f328(f328(f8(f879(x101952,a867),a867,x101951),f87(x101952)),f328(f328(f8(f879(x101952,f879(x101953,a867)),f879(x101952,a867),x101951),f328(f8(f879(x101953,a867),a867,x101952),f87(x101953))),f328(f328(f7(x101951,f879(x101952,f879(x101953,a867)),f879(x101952,f879(x101953,a867))),f328(f328(f8(f879(x101952,f879(f879(x101953,a867),f879(x101953,a867))),f879(f879(x101952,f879(x101953,a867)),f879(x101952,f879(x101953,a867))),x101951),f18(x101952,f879(x101953,a867),f879(x101953,a867))),f328(f328(f8(f879(x101952,f879(x101953,f879(a867,a867))),f879(x101952,f879(f879(x101953,a867),f879(x101953,a867))),x101951),f328(f8(f879(x101953,f879(a867,a867)),f879(f879(x101953,a867),f879(x101953,a867)),x101952),f18(x101953,a867,a867))),f328(f328(f8(f879(x101952,f879(x101953,a867)),f879(x101952,f879(x101953,f879(a867,a867))),x101951),f328(f8(f879(x101953,a867),f879(x101953,f879(a867,a867)),x101952),f328(f8(a867,f879(a867,a867),x101953),a326))),f328(f328(f7(x101951,f879(x101952,f879(x101953,x101951)),f879(x101952,f879(x101953,a867))),f328(f328(f8(f879(f879(x101953,x101951),f879(x101953,a867)),f879(f879(x101952,f879(x101953,x101951)),f879(x101952,f879(x101953,a867))),x101951),f8(f879(x101953,x101951),f879(x101953,a867),x101952)),f328(f328(f8(f879(x101951,a867),f879(f879(x101953,x101951),f879(x101953,a867)),x101951),f8(x101951,a867,x101953)),a325))),f328(f328(f7(x101952,f879(x101953,x101951),f879(x101953,x101951)),f328(f328(f8(f879(x101951,x101951),f879(f879(x101953,x101951),f879(x101953,x101951)),x101952),f8(x101951,x101951,x101953)),f328(f328(f8(x101951,f879(x101951,x101951),x101952),f81(x101951)),x101954))),x101955)))))),f328(f328(f7(x101952,f879(x101953,a867),f879(x101953,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x101953,a867),f879(x101953,a867)),x101952),f8(a867,a867,x101953)),f328(f328(f8(a867,f879(a867,a867),x101952),a326),f328(f328(f7(x101952,f879(x101952,a867),a867),f330(x101952)),x101956)))),f328(f328(f7(x101953,f879(x101953,a867),a867),f330(x101953)),x101957))))))),f328(f328(f81(x101951),f328(f328(f6(x101952,x101951),x101954),x101956)),f328(f328(f6(x101953,x101951),x101955),x101957))) % 167.77/167.51 [9639]~P1(f328(f328(x96394,x96396),x96398))+~P1(f328(f328(x96395,x96398),x96397))+P1(f328(f328(f264(x96391,x96392,x96393,x96394,x96395),x96396),x96397)) % 167.77/167.51 [9237]~P20(x92378,x92371,x92373,x92375)+~P1(f328(f38(x92378),x92376))+E(f328(f73(x92371,x92371,x92372,f328(x92373,x92374)),f328(f73(x92371,x92371,x92372,f328(x92375,x92376)),x92377)),f328(f73(x92371,x92371,x92372,f328(x92375,x92376)),f328(f73(x92371,x92371,x92372,f328(x92373,x92374)),x92377))) % 167.77/167.51 [9629]~P23(x96297,x96292,x96295,x96298,x96296,x96291)+~P1(f328(f38(x96292),x96294))+E(f328(x96291,f328(f328(f306(x96292),x96293),x96294)),f328(f328(x96295,f328(x96296,x96293)),f328(x96291,x96294))) % 167.77/167.51 [9750]~P26(x97502,x97504,x97506,x97508)+~P26(x97501,x97503,x97505,x97507)+P26(f878(x97501,x97502),f878(x97503,x97504),f268(x97501,x97503,x97502,x97504,x97505,x97506),f328(f328(f265(x97501,x97502),x97507),f328(f16(f879(x97502,a867),x97501),x97508))) % 167.77/167.51 [9417]P1(f328(f328(f330(f878(x94171,x94172)),f328(f328(f263(x94171,x94172),x94173),x94174)),f328(f328(f285(x94171,x94175,x94172),x94176),x94177)))+~P1(f328(f328(f330(f878(x94171,x94175)),f328(f328(f263(x94171,x94175),x94173),x94178)),x94176))+~P1(f328(f328(f330(f878(x94175,x94172)),f328(f328(f263(x94175,x94172),x94178),x94174)),x94177)) % 167.77/167.51 [9608]~P1(f328(f328(f242(f879(f878(x96083,x96082),a867)),x96085),f328(f328(f265(x96083,x96082),x96088),f328(f16(f879(x96082,a867),x96083),x96087))))+~P1(f328(f328(f242(f879(f878(x96081,x96083),a867)),x96084),f328(f328(f265(x96081,x96083),x96086),f328(f16(f879(x96083,a867),x96081),x96088))))+P1(f328(f328(f242(f879(f878(x96081,x96082),a867)),f328(f328(f285(x96081,x96083,x96082),x96084),x96085)),f328(f328(f265(x96081,x96082),x96086),f328(f16(f879(x96082,a867),x96081),x96087)))) % 167.77/167.51 [9663]~E(x96633,x96635)+P1(f328(f328(f330(f878(f878(x96631,x96632),f878(x96631,x96632))),f328(f328(f263(f878(x96631,x96632),f878(x96631,x96632)),f328(f328(f263(x96631,x96632),x96633),x96634)),f328(f328(f263(x96631,x96632),x96635),x96636))),f321(x96631,x96632,x96637,x96638)))+~P1(f328(f328(f330(f878(x96632,x96632)),f328(f328(f263(x96632,x96632),x96634),x96636)),x96638)) % 167.77/167.51 [9773]E(x97731,x97732)+~P1(f328(f328(f330(f878(f878(x97733,x97735),f878(x97733,x97735))),f328(f328(f263(f878(x97733,x97735),f878(x97733,x97735)),f328(f328(f263(x97733,x97735),x97731),x97736)),f328(f328(f263(x97733,x97735),x97732),x97737))),f321(x97733,x97735,x97734,x97738)))+P1(f328(f328(f330(f878(x97733,x97733)),f328(f328(f263(x97733,x97733),x97731),x97732)),x97734)) % 167.77/167.51 [9790]~P1(f328(f328(f330(f878(f878(x97901,x97905),f878(x97901,x97905))),f328(f328(f263(f878(x97901,x97905),f878(x97901,x97905)),f328(f328(f263(x97901,x97905),x97902),x97906)),f328(f328(f263(x97901,x97905),x97903),x97907))),f321(x97901,x97905,x97904,x97908)))+P1(f328(f328(f330(f878(x97901,x97901)),f328(f328(f263(x97901,x97901),x97902),x97903)),x97904))+P1(f328(f328(f330(f878(x97905,x97905)),f328(f328(f263(x97905,x97905),x97906),x97907)),x97908)) % 167.77/167.51 [9694]~P24(x96947,x96945,x96941,x96948,x96942,x96944)+~P1(f328(f38(x96945),x96946))+E(f328(f328(x96941,f328(x96942,x96943)),f328(x96944,f328(f328(f22(f879(x96945,a867)),x96946),f328(f328(f306(x96945),x96943),f192(f879(x96945,a867)))))),f328(x96944,f328(f328(f306(x96945),x96943),x96946))) % 167.77/167.51 [9195]~P1(f328(f328(f328(x91955,x91958),x91956),x91957))+~P1(f328(f328(f330(x91951),x91958),x91954))+P1(f328(f328(f328(f328(f44(x91951,f879(x91952,f879(x91953,a867))),x91954),x91955),x91956),x91957)) % 167.77/167.51 [9404]P1(f328(f328(f328(x94041,x94042),x94043),x94044))+~P1(f328(f328(f330(x94045),x94042),x94046))+~P1(f328(f328(f328(f328(f43(x94045,f879(x94047,f879(x94048,a867))),x94046),x94041),x94043),x94044)) % 167.77/167.51 [9601]~P22(x96013,x96012,x96014,x96018,x96011)+~P1(f328(f38(x96012),x96017))+E(f328(f328(x96011,f328(f328(f18(x96012,x96013,x96013),f328(f328(f8(x96013,f879(x96013,x96013),x96012),x96014),x96015)),x96016)),x96017),f328(f328(x96014,f328(f328(x96011,x96015),x96017)),f328(f328(x96011,x96016),x96017))) % 167.77/167.51 [9880]~E(f328(f307(x98802,x98804,x98806),x98808),x988010)+~E(f328(f307(x98801,x98803,x98805),x98807),x98809)+E(f328(f307(f878(x98801,x98802),f878(x98803,x98804),f268(x98801,x98803,x98802,x98804,x98805,x98806)),f328(f328(f265(x98801,x98802),x98807),f328(f16(f879(x98802,a867),x98801),x98808))),f328(f328(f265(x98803,x98804),x98809),f328(f16(f879(x98804,a867),x98803),x988010))) % 167.77/167.51 [8221]~P30(a5000)+~P8(a5000)+~P1(f328(a25,x82211))+P25(a868,f192(f879(f871(a868),a867)),f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),a325),x82211),f328(a198,x82211))),f192(f879(f871(a868),a867)))) % 167.77/167.51 [4817]~P105(x48172)+~P15(x48172,x48171)+P15(x48172,f118(x48172,x48171))+E(x48171,f117(x48172)) % 167.77/167.51 [4818]~P105(x48182)+~P15(x48182,x48181)+P15(x48182,f740(x48181,x48182))+E(x48181,f117(x48182)) % 167.77/167.51 [5051]~P4(x50512)+E(f10(x50512,x50511),f42(x50512,x50511))+E(x50511,f192(f879(x50512,a867)))+~P1(f328(f38(x50512),x50511)) % 167.77/167.51 [5052]~P4(x50522)+E(f13(x50522,x50521),f41(x50522,x50521))+E(x50521,f192(f879(x50522,a867)))+~P1(f328(f38(x50522),x50521)) % 167.77/167.51 [5212]~P105(x52122)+~P15(x52122,x52121)+E(x52121,f117(x52122))+E(f328(f328(f148(x52122),f759(x52121,x52122)),f740(x52121,x52122)),x52121) % 167.77/167.51 [6004]~P2(x60042)+E(x60041,f192(f879(x60042,a867)))+P1(f328(f328(f242(x60042),f10(x60042,x60041)),f13(x60042,x60041)))+~P1(f328(f38(x60042),x60041)) % 167.77/167.51 [6016]~P39(x60162)+~P39(x60161)+E(x60161,x60162)+~E(f328(f307(a1,a872,a108),x60161),f328(f307(a1,a872,a108),x60162)) % 167.77/167.51 [9051]~P117(x90511)+~P1(f328(f328(f330(x90511),x90512),f113(x90511)))+P1(f328(f328(f243(x90511),f328(f328(f80(x90511),f328(f328(f80(x90511),f78(x90511)),x90512)),x90512)),f2(x90511)))+~P1(f328(f328(f243(x90511),x90512),f2(x90511))) % 167.77/167.51 [9292]~P117(x92921)+~P1(f328(f328(f330(x92921),x92922),f113(x92921)))+~P1(f328(f328(f243(x92921),f328(f328(f80(x92921),f328(f328(f80(x92921),f78(x92921)),x92922)),x92922)),f2(x92921)))+P1(f328(f328(f243(x92921),x92922),f2(x92921))) % 167.77/167.51 [4873]~P135(x48732)+~P113(x48732)+E(x48731,f2(a872))+E(f328(f328(f253(x48732),f2(x48732)),x48731),f2(x48732)) % 167.77/167.51 [4877]~P135(x48771)+~P113(x48771)+~E(x48772,f2(a872))+E(f328(f328(f253(x48771),f2(x48771)),x48772),f78(x48771)) % 167.77/167.51 [5038]~P139(x50382)+E(x50381,f78(x50382))+E(x50381,f328(f79(x50382),f78(x50382)))+~E(f328(f328(f81(x50382),x50381),x50381),f78(x50382)) % 167.77/167.51 [5295]~P88(x52952)+E(x52951,f2(x52952))+E(f82(x52952,x52951),f328(f79(x52952),f78(x52952)))+P1(f328(f328(f243(x52952),f2(x52952)),x52951)) % 167.77/167.51 [5528]~P88(x55282)+E(f82(x55282,x55281),f78(x55282))+E(x55281,f2(x55282))+~P1(f328(f328(f243(x55282),f2(x55282)),x55281)) % 167.77/167.51 [5537]E(x55371,x55372)+~E(f328(f107(a872),x55371),f328(f107(a872),x55372))+P1(f328(a197,f328(f107(a1),x55372)))+P1(f328(a197,f328(f107(a1),x55371))) % 167.77/167.51 [5588]~P90(x55881)+~E(x55882,f2(x55881))+E(f328(f328(f80(x55881),x55882),x55882),f2(x55881))+~P1(f328(f328(f330(x55881),x55882),f113(x55881))) % 167.77/167.51 [5626]E(x56261,f2(a1))+~E(f328(f328(f40(a1),x56262),x56261),f2(a1))+P1(f328(f328(f243(a1),x56261),x56262))+P1(f328(f328(f243(a1),x56262),x56261)) % 167.77/167.51 [5657]E(x56571,f2(a1))+~E(f328(f328(f40(a1),x56572),x56571),f2(a1))+P1(f328(f328(f242(a1),x56572),f2(a1)))+P1(f328(f328(f243(a1),x56572),x56571)) % 167.77/167.51 [5691]E(x56911,f2(a1))+~E(f328(f328(f40(a1),x56912),x56911),f2(a1))+P1(f328(f328(f242(a1),f2(a1)),x56912))+P1(f328(f328(f243(a1),x56911),x56912)) % 167.77/167.51 [5727]~P90(x57272)+E(x57271,f2(x57272))+~E(f328(f328(f80(x57272),x57271),x57271),f2(x57272))+~P1(f328(f328(f330(x57272),x57271),f113(x57272))) % 167.77/167.51 [5787]E(f328(f107(a872),x57871),f328(f107(a872),x57872))+~E(f328(f107(a1),x57872),f2(a1))+P1(f328(a197,f328(f107(a1),x57872)))+~P1(f328(a197,f328(f107(a1),x57871))) % 167.77/167.51 [5814]~E(f328(f107(a872),x58142),f328(f107(a872),x58141))+E(f328(f107(a1),x58141),f2(a1))+P1(f328(a197,f328(f107(a1),x58141)))+~P1(f328(a197,f328(f107(a1),x58142))) % 167.77/167.51 [5823]~P105(x58232)+E(x58231,f192(f879(x58232,a867)))+~P1(f328(f38(x58232),x58231))+P1(f328(f328(f330(x58232),f14(x58232,x58231)),x58231)) % 167.77/167.51 [5824]~P105(x58242)+E(x58241,f192(f879(x58242,a867)))+~P1(f328(f38(x58242),x58241))+P1(f328(f328(f330(x58242),f15(x58242,x58241)),x58241)) % 167.77/167.51 [5984]~P117(x59841)+~P91(x59841)+P1(f328(f328(f243(x59841),f2(x59841)),f328(f107(x59841),x59842)))+~P1(f328(f328(f243(a1),a83),x59842)) % 167.77/167.51 [5985]~P117(x59851)+~P91(x59851)+P1(f328(f328(f242(x59851),f2(x59851)),f328(f107(x59851),x59852)))+~P1(f328(f328(f242(a1),a83),x59852)) % 167.77/167.51 [6003]~P117(x60031)+~P91(x60031)+E(f328(f75(x60031),f328(f107(x60031),x60032)),f328(f107(x60031),x60032))+P1(f328(f328(f243(x60031),f328(f107(x60031),x60032)),f2(x60031))) % 167.77/167.51 [6043]E(x60431,x60432)+~E(f328(a108,x60431),f328(a108,x60432))+~P1(f328(f328(f242(a1),f2(a1)),x60432))+~P1(f328(f328(f242(a1),f2(a1)),x60431)) % 167.77/167.51 [6242]~P91(x62422)+~P117(x62422)+~P1(f328(f328(f243(x62422),f2(x62422)),f328(f107(x62422),x62421)))+P1(f328(f328(f243(a1),a83),x62421)) % 167.77/167.51 [6243]~P91(x62432)+~P117(x62432)+~P1(f328(f328(f242(x62432),f2(x62432)),f328(f107(x62432),x62431)))+P1(f328(f328(f242(a1),a83),x62431)) % 167.77/167.51 [6248]~P117(x62481)+~P91(x62481)+P1(f328(f328(f243(x62481),f328(f107(x62481),x62482)),f2(x62481)))+~P1(f328(f328(f243(a1),x62482),a83)) % 167.77/167.51 [6249]~P117(x62491)+~P91(x62491)+P1(f328(f328(f242(x62491),f328(f107(x62491),x62492)),f2(x62491)))+~P1(f328(f328(f242(a1),x62492),a83)) % 167.77/167.51 [6555]~P91(x65552)+~P117(x65552)+~P1(f328(f328(f243(x65552),f328(f107(x65552),x65551)),f2(x65552)))+P1(f328(f328(f243(a1),x65551),a83)) % 167.77/167.51 [6556]~P91(x65562)+~P117(x65562)+~P1(f328(f328(f242(x65562),f328(f107(x65562),x65561)),f2(x65562)))+P1(f328(f328(f242(a1),x65561),a83)) % 167.77/167.51 [6648]~P117(x66481)+~P91(x66481)+E(f328(f75(x66481),f328(f107(x66481),x66482)),f328(f79(x66481),f328(f107(x66481),x66482)))+~P1(f328(f328(f243(x66481),f328(f107(x66481),x66482)),f2(x66481))) % 167.77/167.51 [6666]E(f328(f107(a872),x66661),f328(f107(a872),x66662))+~E(f328(f107(a1),x66662),f2(a1))+~P1(f328(f328(f242(a1),f328(f107(a1),x66661)),f2(a1)))+~P1(f328(a197,f328(f107(a1),x66661))) % 167.77/167.51 [7545]~P105(x75452)+E(x75451,f192(f879(x75452,a867)))+~P1(f328(f38(x75452),x75451))+P1(f328(f328(f242(x75452),f11(x75452,f240(x75452),x75451)),f12(x75452,f241(x75452),x75451))) % 167.77/167.51 [7867]~P39(x78672)+~P5(x78671)+P1(f328(f328(f330(a1),x78671),x78672))+~P1(f328(f328(f330(a872),f328(a108,x78671)),f328(f307(a1,a872,a108),x78672))) % 167.77/167.51 [8137]~P59(x81372)+P1(f328(x81371,f205(x81372)))+~P1(f328(f59(f876(x81372)),x81371))+P1(f328(f59(x81372),f328(f328(f8(f876(x81372),a867,x81372),x81371),f235(x81372)))) % 167.77/167.51 [8613]~P59(x86131)+~P1(f328(x86132,f205(x86131)))+P1(f328(f60(f876(x86131)),x86132))+~P1(f328(f60(x86131),f328(f328(f8(f876(x86131),a867,x86131),x86132),f235(x86131)))) % 167.77/167.51 [5820]~P138(x58202)+E(x58201,f2(a1))+E(f328(f79(x58202),f328(f106(x58202),f328(f79(a1),x58201))),f328(f106(x58202),x58201))+~P1(f328(f328(f243(a1),x58201),f2(a1))) % 167.77/167.51 [5893]~P90(x58931)+~P91(x58931)+~P31(x58931,f328(f107(x58931),x58932))+P31(x58931,f328(f107(x58931),f328(f328(f80(a1),x58932),x58932))) % 167.77/167.51 [6230]~P75(x62302)+E(x62301,f192(f879(x62302,a867)))+E(f15(x62302,f328(f307(x62302,x62302,f79(x62302)),x62301)),f328(f79(x62302),f14(x62302,x62301)))+~P1(f328(f38(x62302),x62301)) % 167.77/167.51 [6231]~P75(x62312)+E(x62311,f192(f879(x62312,a867)))+E(f14(x62312,f328(f307(x62312,x62312,f79(x62312)),x62311)),f328(f79(x62312),f15(x62312,x62311)))+~P1(f328(f38(x62312),x62311)) % 167.77/167.51 [6263]~P90(x62631)+~P91(x62631)+P31(x62631,f328(f107(x62631),x62632))+~P31(x62631,f328(f107(x62631),f328(f328(f80(a1),x62632),x62632))) % 167.77/167.51 [6351]E(x63511,f2(a1))+E(f328(a52,f51(f328(f79(a1),x63511),f328(f79(a1),x63512))),f47(x63511,x63512))+P1(f328(f328(f242(a1),f2(a1)),x63512))+~P1(f328(f328(f242(a1),f2(a1)),x63511)) % 167.77/167.51 [8467]~P30(a5000)+~P1(f328(a25,x84671))+P25(a868,x84672,f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),a325),x84671),f328(a198,x84671))),f192(f879(f871(a868),a867))))+P1(f328(f328(f330(a870),f655(x84671,x84672)),f182(a870,a869,a28))) % 167.77/167.51 [8659]~P39(x86592)+~P39(x86591)+P1(f328(f328(f243(f879(a872,a867)),f328(f307(a1,a872,a108),x86591)),f328(f307(a1,a872,a108),x86592)))+~P1(f328(f328(f243(f879(a1,a867)),x86591),x86592)) % 167.77/167.51 [8872]~E(f762(x88722,x88721),f763(x88722,x88721))+~P1(f328(f134(x88721),f764(x88722,x88721)))+~P1(f328(f134(f873(x88721)),x88722))+P1(f328(f134(x88721),f328(f139(f873(x88721),f873(x88721),f125(x88721),f117(x88721)),x88722))) % 167.77/167.51 [8970]~P39(x89702)+~P39(x89701)+~P1(f328(f328(f243(f879(a872,a867)),f328(f307(a1,a872,a108),x89701)),f328(f307(a1,a872,a108),x89702)))+P1(f328(f328(f243(f879(a1,a867)),x89701),x89702)) % 167.77/167.51 [8971]~P39(x89712)+~P39(x89711)+~P1(f328(f328(f242(f879(a872,a867)),f328(f307(a1,a872,a108),x89711)),f328(f307(a1,a872,a108),x89712)))+P1(f328(f328(f242(f879(a1,a867)),x89711),x89712)) % 167.77/167.51 [8977]~E(f762(x89772,x89771),f763(x89772,x89771))+~P1(f328(f134(f873(x89771)),x89772))+P1(f328(f134(x89771),f328(f139(f873(x89771),f873(x89771),f125(x89771),f117(x89771)),x89772)))+P1(f328(f328(f330(f873(x89771)),f764(x89772,x89771)),f328(f170(f873(x89771)),x89772))) % 167.77/167.51 [9018]~P1(f328(f134(x90181),f764(x90182,x90181)))+~P1(f328(f134(f873(x90181)),x90182))+P1(f328(f134(x90181),f328(f139(f873(x90181),f873(x90181),f125(x90181),f117(x90181)),x90182)))+P1(f328(f328(f330(f873(x90181)),f763(x90182,x90181)),f328(f170(f873(x90181)),x90182))) % 167.77/167.51 [9019]~P1(f328(f134(x90191),f764(x90192,x90191)))+~P1(f328(f134(f873(x90191)),x90192))+P1(f328(f134(x90191),f328(f139(f873(x90191),f873(x90191),f125(x90191),f117(x90191)),x90192)))+P1(f328(f328(f330(f873(x90191)),f762(x90192,x90191)),f328(f170(f873(x90191)),x90192))) % 167.77/167.51 [9096]~P1(f328(f134(f873(x90961)),x90962))+P1(f328(f134(x90961),f328(f139(f873(x90961),f873(x90961),f125(x90961),f117(x90961)),x90962)))+P1(f328(f328(f330(f873(x90961)),f763(x90962,x90961)),f328(f170(f873(x90961)),x90962)))+P1(f328(f328(f330(f873(x90961)),f764(x90962,x90961)),f328(f170(f873(x90961)),x90962))) % 167.77/167.51 [9097]~P1(f328(f134(f873(x90971)),x90972))+P1(f328(f134(x90971),f328(f139(f873(x90971),f873(x90971),f125(x90971),f117(x90971)),x90972)))+P1(f328(f328(f330(f873(x90971)),f762(x90972,x90971)),f328(f170(f873(x90971)),x90972)))+P1(f328(f328(f330(f873(x90971)),f764(x90972,x90971)),f328(f170(f873(x90971)),x90972))) % 167.77/167.51 [9110]~E(f328(f328(f105(f879(x91101,a867)),f328(f170(x91101),f763(x91102,x91101))),f328(f170(x91101),f762(x91102,x91101))),f192(f879(x91101,a867)))+~P1(f328(f134(x91101),f764(x91102,x91101)))+~P1(f328(f134(f873(x91101)),x91102))+P1(f328(f134(x91101),f328(f139(f873(x91101),f873(x91101),f125(x91101),f117(x91101)),x91102))) % 167.77/167.51 [9172]~E(f328(f328(f105(f879(x91721,a867)),f328(f170(x91721),f763(x91722,x91721))),f328(f170(x91721),f762(x91722,x91721))),f192(f879(x91721,a867)))+~P1(f328(f134(f873(x91721)),x91722))+P1(f328(f134(x91721),f328(f139(f873(x91721),f873(x91721),f125(x91721),f117(x91721)),x91722)))+P1(f328(f328(f330(f873(x91721)),f764(x91722,x91721)),f328(f170(f873(x91721)),x91722))) % 167.77/167.51 [9441]E(x94411,f2(a1))+E(x94412,f2(a1))+E(f328(f328(f86(a1,f878(a1,a1)),f328(f328(a224,x94412),x94411)),f328(f328(f18(a1,a1,f878(a1,a1)),f328(f328(f8(a1,f879(a1,f878(a1,a1)),a1),f263(a1,a1)),f328(f40(a1),x94412))),f328(f40(a1),x94411))),f222(x94412,x94411))+P1(f328(f328(f243(a1),x94411),f2(a1))) % 167.77/167.51 [9525]~P30(a5000)+~P1(f328(a25,x95252))+P25(a868,x95251,f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),a325),x95252),f328(a198,x95252))),f192(f879(f871(a868),a867))))+~P25(a868,x95251,f328(f328(f306(f871(a868)),f328(f328(f328(f92(a868),a325),f328(a26,f655(x95252,x95251))),f328(a198,f328(a26,f655(x95252,x95251))))),f192(f879(f871(a868),a867)))) % 167.77/167.51 [8204]~P91(x82042)+~P117(x82042)+~P1(f328(f328(f243(x82042),f328(f107(x82042),x82041)),f78(x82042)))+P1(f328(f328(f243(a1),x82041),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))) % 167.77/167.51 [8205]~P91(x82052)+~P117(x82052)+~P1(f328(f328(f242(x82052),f328(f107(x82052),x82051)),f78(x82052)))+P1(f328(f328(f242(a1),x82051),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))) % 167.77/167.51 [8476]~P117(x84761)+~P91(x84761)+P1(f328(f328(f243(x84761),f328(f107(x84761),x84762)),f78(x84761)))+~P1(f328(f328(f243(a1),x84762),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))) % 167.77/167.51 [8477]~P117(x84771)+~P91(x84771)+P1(f328(f328(f242(x84771),f328(f107(x84771),x84772)),f78(x84771)))+~P1(f328(f328(f242(a1),x84772),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))) % 167.77/167.51 [8685]~P91(x86852)+~P117(x86852)+~P1(f328(f328(f243(x86852),f78(x86852)),f328(f107(x86852),x86851)))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),x86851)) % 167.77/167.51 [8686]~P91(x86862)+~P117(x86862)+~P1(f328(f328(f242(x86862),f78(x86862)),f328(f107(x86862),x86861)))+P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),x86861)) % 167.77/167.51 [9057]~P117(x90571)+~P91(x90571)+P1(f328(f328(f243(x90571),f78(x90571)),f328(f107(x90571),x90572)))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),x90572)) % 167.77/167.51 [9058]~P117(x90581)+~P91(x90581)+P1(f328(f328(f242(x90581),f78(x90581)),f328(f107(x90581),x90582)))+~P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),x90582)) % 167.77/167.51 [9573]~P139(x95732)+E(x95731,f78(x95732))+E(x95731,f328(f79(x95732),f78(x95732)))+~E(f328(f328(f253(x95732),x95731),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(x95732)) % 167.77/167.51 [9848]~P62(x98481)+~P91(x98481)+~P1(f328(f328(f243(x98481),f2(x98481)),x98482))+P1(f328(f328(f243(x98481),f2(x98481)),f328(f328(f286(x98481),x98482),f328(f107(x98481),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 167.77/167.51 [9910]~P62(x99101)+~P91(x99101)+P1(f328(f328(f243(x99101),f2(x99101)),x99102))+~P1(f328(f328(f243(x99101),f2(x99101)),f328(f328(f286(x99101),x99102),f328(f107(x99101),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 167.77/167.51 [10163]~P138(x101632)+E(x101631,f2(a1))+P1(f328(f328(f243(a1),x101631),f2(a1)))+E(f328(f328(f267(a1,a1,x101632),f328(f328(f7(a1,f879(a1,f879(x101632,x101632)),f879(a1,x101632)),f328(f328(f8(f879(f879(x101632,x101632),x101632),f879(f879(a1,f879(x101632,x101632)),f879(a1,x101632)),a1),f8(f879(x101632,x101632),x101632,a1)),f328(f328(f8(x101632,f879(f879(x101632,x101632),x101632),a1),f86(x101632,x101632)),f106(x101632)))),f328(f328(f7(a1,f879(x101632,x101632),f879(x101632,x101632)),f328(f328(f8(f879(x101632,f879(x101632,x101632)),f879(f879(x101632,x101632),f879(x101632,x101632)),a1),f18(x101632,x101632,x101632)),f328(f328(f7(a1,f879(x101632,x101632),f879(x101632,f879(x101632,x101632))),f328(f328(f8(f879(x101632,f879(x101632,x101632)),f879(f879(x101632,x101632),f879(x101632,f879(x101632,x101632))),a1),f8(x101632,f879(x101632,x101632),x101632)),f328(f328(f8(a867,f879(x101632,f879(x101632,x101632)),a1),f100(x101632)),f328(f328(f7(a1,a1,a867),a325),f2(a1))))),f328(f328(f18(x101632,x101632,x101632),f80(x101632)),f5(x101632))))),f328(f328(f7(x101632,x101632,x101632),f328(f328(f8(x101632,f879(x101632,x101632),x101632),f80(x101632)),f328(f328(f18(x101632,x101632,x101632),f80(x101632)),f5(x101632)))),f78(x101632))))),f47(x101631,f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f106(x101632),x101631)) % 167.77/167.51 [5207]~P59(x52073)+~P36(x52073,x52072,f57(x52073))+E(x52071,f774(x52072,x52073))+~P1(f328(x52072,x52071)) % 167.77/167.51 [5365]~P59(x53651)+P36(x53651,x53652,f57(x53651))+~E(f775(x53652,x53651,x53653),x53653)+~P1(f328(x53652,x53653)) % 167.77/167.51 [4844]~P90(x48443)+~P91(x48443)+E(x48441,x48442)+~E(f328(f107(x48443),x48441),f328(f107(x48443),x48442)) % 167.77/167.51 [5983]~P59(x59831)+P36(x59831,x59832,f57(x59831))+~P1(f328(x59832,x59833))+P1(f328(x59832,f775(x59832,x59831,x59833))) % 167.77/167.51 [5993]~P1(f328(x59931,x59932))+~P1(f328(x59931,x59933))+~P1(f328(f328(f242(a872),x59933),f394(x59932,x59931)))+P1(f328(x59931,f2(a872))) % 167.77/167.51 [6414]P145(x64142,x64143,x64141)+E(x64141,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f807(x64141,x64143,x64142)))+P1(f328(f328(f243(a1),x64141),f2(a1))) % 167.77/167.51 [6415]P144(x64152,x64153,x64151)+E(x64151,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f815(x64151,x64153,x64152)))+P1(f328(f328(f243(a1),x64151),f2(a1))) % 167.77/167.51 [6535]P144(x65351,x65352,x65353)+~P1(f328(x65351,x65352))+P1(f328(f328(f242(a1),f2(a1)),f815(x65353,x65352,x65351)))+P1(f328(f328(f243(a1),x65353),f2(a1))) % 167.77/167.51 [6561]P145(x65611,x65612,x65613)+P1(f328(f328(f242(a1),f2(a1)),f807(x65613,x65612,x65611)))+~P1(f328(x65611,f2(a1)))+P1(f328(f328(f243(a1),x65613),f2(a1))) % 167.77/167.51 [6589]P145(x65892,x65893,x65891)+E(x65891,f2(a1))+~P1(f328(x65892,f808(x65891,x65893,x65892)))+P1(f328(f328(f243(a1),x65891),f2(a1))) % 167.77/167.51 [6590]P144(x65902,x65903,x65901)+E(x65901,f2(a1))+~P1(f328(x65902,f815(x65901,x65903,x65902)))+P1(f328(f328(f243(a1),x65901),f2(a1))) % 167.77/167.51 [6691]~P4(x66911)+~P105(x66911)+~P1(f328(f328(f243(x66911),x66912),f41(x66911,x66913)))+P1(f328(f328(f243(x66911),x66912),f832(x66913,x66912,x66911))) % 167.77/167.51 [6700]P144(x67001,x67002,x67003)+~P1(f328(x67001,x67002))+~P1(f328(x67001,f815(x67003,x67002,x67001)))+P1(f328(f328(f243(a1),x67003),f2(a1))) % 167.77/167.51 [6732]P145(x67321,x67322,x67323)+~P1(f328(x67321,f808(x67323,x67322,x67321)))+~P1(f328(x67321,f2(a1)))+P1(f328(f328(f243(a1),x67323),f2(a1))) % 167.77/167.51 [6983]P145(x69832,x69833,x69831)+E(x69831,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f807(x69831,x69833,x69832)))+P1(f328(f328(f243(a1),x69831),f806(x69831,x69833,x69832))) % 167.77/167.51 [6984]P144(x69842,x69843,x69841)+E(x69841,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f815(x69841,x69843,x69842)))+P1(f328(f328(f243(a1),x69841),f814(x69841,x69843,x69842))) % 167.77/167.51 [7101]P144(x71011,x71012,x71013)+~P1(f328(x71011,x71012))+P1(f328(f328(f242(a1),f2(a1)),f815(x71013,x71012,x71011)))+P1(f328(f328(f243(a1),x71013),f814(x71013,x71012,x71011))) % 167.77/167.51 [7120]P145(x71201,x71202,x71203)+P1(f328(f328(f242(a1),f2(a1)),f807(x71203,x71202,x71201)))+P1(f328(f328(f243(a1),x71203),f806(x71203,x71202,x71201)))+~P1(f328(x71201,f2(a1))) % 167.77/167.51 [7153]P145(x71532,x71533,x71531)+E(x71531,f2(a1))+~P1(f328(x71532,f808(x71531,x71533,x71532)))+P1(f328(f328(f243(a1),x71531),f806(x71531,x71533,x71532))) % 167.77/167.51 [7154]P144(x71542,x71543,x71541)+E(x71541,f2(a1))+~P1(f328(x71542,f815(x71541,x71543,x71542)))+P1(f328(f328(f243(a1),x71541),f814(x71541,x71543,x71542))) % 167.77/167.51 [7197]P145(x71972,x71973,x71971)+E(x71971,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f807(x71971,x71973,x71972)))+~P1(f328(x71972,f813(x71971,x71973,x71972))) % 167.77/167.51 [7198]P144(x71982,x71983,x71981)+E(x71981,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f815(x71981,x71983,x71982)))+~P1(f328(x71982,f814(x71981,x71983,x71982))) % 167.77/167.51 [7286]P144(x72861,x72862,x72863)+~P1(f328(x72861,x72862))+~P1(f328(x72861,f815(x72863,x72862,x72861)))+P1(f328(f328(f243(a1),x72863),f814(x72863,x72862,x72861))) % 167.77/167.51 [7302]P145(x73021,x73022,x73023)+~P1(f328(x73021,f808(x73023,x73022,x73021)))+P1(f328(f328(f243(a1),x73023),f806(x73023,x73022,x73021)))+~P1(f328(x73021,f2(a1))) % 167.77/167.51 [7306]P144(x73061,x73062,x73063)+~P1(f328(x73061,x73062))+P1(f328(f328(f242(a1),f2(a1)),f815(x73063,x73062,x73061)))+~P1(f328(x73061,f814(x73063,x73062,x73061))) % 167.77/167.51 [7324]P145(x73241,x73242,x73243)+P1(f328(f328(f242(a1),f2(a1)),f807(x73243,x73242,x73241)))+~P1(f328(x73241,f813(x73243,x73242,x73241)))+~P1(f328(x73241,f2(a1))) % 167.77/167.51 [7348]P145(x73482,x73483,x73481)+E(x73481,f2(a1))+~P1(f328(x73482,f808(x73481,x73483,x73482)))+~P1(f328(x73482,f813(x73481,x73483,x73482))) % 167.77/167.51 [7349]P144(x73492,x73493,x73491)+E(x73491,f2(a1))+~P1(f328(x73492,f815(x73491,x73493,x73492)))+~P1(f328(x73492,f814(x73491,x73493,x73492))) % 167.77/167.51 [7440]P144(x74401,x74402,x74403)+~P1(f328(x74401,x74402))+~P1(f328(x74401,f815(x74403,x74402,x74401)))+~P1(f328(x74401,f814(x74403,x74402,x74401))) % 167.77/167.51 [7457]P145(x74571,x74572,x74573)+~P1(f328(x74571,f808(x74573,x74572,x74571)))+~P1(f328(x74571,f813(x74573,x74572,x74571)))+~P1(f328(x74571,f2(a1))) % 167.77/167.51 [7505]P145(x75052,x75053,x75051)+E(x75051,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f807(x75051,x75053,x75052)))+P1(f328(f328(f242(a1),f806(x75051,x75053,x75052)),f2(a1))) % 167.77/167.51 [7506]P144(x75062,x75063,x75061)+E(x75061,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f815(x75061,x75063,x75062)))+P1(f328(f328(f242(a1),f814(x75061,x75063,x75062)),f2(a1))) % 167.77/167.51 [7507]~P138(x75071)+~P1(f328(f328(f330(x75071),x75073),f113(x75071)))+~P1(f328(f328(f330(x75071),x75072),f113(x75071)))+P1(f328(f328(f330(x75071),f328(f328(f22(x75071),x75072),x75073)),f113(x75071))) % 167.77/167.51 [7508]~P138(x75081)+~P1(f328(f328(f330(x75081),x75083),f113(x75081)))+~P1(f328(f328(f330(x75081),x75082),f113(x75081)))+P1(f328(f328(f330(x75081),f328(f328(f80(x75081),x75082),x75083)),f113(x75081))) % 167.77/167.51 [7509]~P142(x75091)+~P1(f328(f328(f330(x75091),x75093),f190(x75091)))+~P1(f328(f328(f330(x75091),x75092),f190(x75091)))+P1(f328(f328(f330(x75091),f328(f328(f80(x75091),x75092),x75093)),f190(x75091))) % 167.77/167.51 [7510]~P138(x75101)+~P1(f328(f328(f330(x75101),x75103),f113(x75101)))+~P1(f328(f328(f330(x75101),x75102),f113(x75101)))+P1(f328(f328(f330(x75101),f328(f328(f81(x75101),x75102),x75103)),f113(x75101))) % 167.77/167.51 [7511]~P142(x75111)+~P1(f328(f328(f330(x75111),x75113),f190(x75111)))+~P1(f328(f328(f330(x75111),x75112),f190(x75111)))+P1(f328(f328(f330(x75111),f328(f328(f81(x75111),x75112),x75113)),f190(x75111))) % 167.77/167.51 [7512]~P86(x75121)+~P1(f328(f328(f243(x75121),x75123),f2(x75121)))+~P1(f328(f328(f243(x75121),x75122),f2(x75121)))+P1(f328(f328(f243(x75121),f328(f328(f80(x75121),x75122),x75123)),f2(x75121))) % 167.77/167.51 [7513]~P86(x75131)+~P1(f328(f328(f242(x75131),x75132),f2(x75131)))+~P1(f328(f328(f243(x75131),x75133),f2(x75131)))+P1(f328(f328(f243(x75131),f328(f328(f80(x75131),x75132),x75133)),f2(x75131))) % 167.77/167.51 [7514]~P86(x75141)+~P1(f328(f328(f242(x75141),x75143),f2(x75141)))+~P1(f328(f328(f243(x75141),x75142),f2(x75141)))+P1(f328(f328(f243(x75141),f328(f328(f80(x75141),x75142),x75143)),f2(x75141))) % 167.77/167.51 [7515]~P86(x75151)+~P1(f328(f328(f242(x75151),x75153),f2(x75151)))+~P1(f328(f328(f242(x75151),x75152),f2(x75151)))+P1(f328(f328(f242(x75151),f328(f328(f80(x75151),x75152),x75153)),f2(x75151))) % 167.77/167.51 [7541]P145(x75413,x75412,x75411)+E(x75411,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x75411),f808(x75411,x75412,x75413))),f807(x75411,x75412,x75413)),x75412)+P1(f328(f328(f243(a1),x75411),f2(a1))) % 167.77/167.51 [7542]P144(x75423,x75422,x75421)+E(x75421,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x75421),f816(x75421,x75422,x75423))),f815(x75421,x75422,x75423)),x75422)+P1(f328(f328(f243(a1),x75421),f2(a1))) % 167.77/167.51 [7626]P144(x76261,x76262,x76263)+~P1(f328(x76261,x76262))+P1(f328(f328(f242(a1),f2(a1)),f815(x76263,x76262,x76261)))+P1(f328(f328(f242(a1),f814(x76263,x76262,x76261)),f2(a1))) % 167.77/167.51 [7655]P145(x76551,x76552,x76553)+P1(f328(f328(f242(a1),f2(a1)),f807(x76553,x76552,x76551)))+~P1(f328(x76551,f2(a1)))+P1(f328(f328(f242(a1),f806(x76553,x76552,x76551)),f2(a1))) % 167.77/167.51 [7664]P144(x76643,x76642,x76641)+~P1(f328(x76643,x76642))+E(f328(f328(f80(a1),f328(f328(f81(a1),x76641),f816(x76641,x76642,x76643))),f815(x76641,x76642,x76643)),x76642)+P1(f328(f328(f243(a1),x76641),f2(a1))) % 167.77/167.51 [7671]P145(x76712,x76713,x76711)+E(x76711,f2(a1))+~P1(f328(x76712,f808(x76711,x76713,x76712)))+P1(f328(f328(f242(a1),f806(x76711,x76713,x76712)),f2(a1))) % 167.77/167.51 [7672]P144(x76722,x76723,x76721)+E(x76721,f2(a1))+~P1(f328(x76722,f815(x76721,x76723,x76722)))+P1(f328(f328(f242(a1),f814(x76721,x76723,x76722)),f2(a1))) % 167.77/167.51 [7677]P145(x76773,x76772,x76771)+E(f328(f328(f80(a1),f328(f328(f81(a1),x76771),f808(x76771,x76772,x76773))),f807(x76771,x76772,x76773)),x76772)+~P1(f328(x76773,f2(a1)))+P1(f328(f328(f243(a1),x76771),f2(a1))) % 167.77/167.51 [7733]P144(x77331,x77332,x77333)+~P1(f328(x77331,x77332))+~P1(f328(x77331,f815(x77333,x77332,x77331)))+P1(f328(f328(f242(a1),f814(x77333,x77332,x77331)),f2(a1))) % 167.77/167.51 [7737]P145(x77371,x77372,x77373)+~P1(f328(x77371,f808(x77373,x77372,x77371)))+~P1(f328(x77371,f2(a1)))+P1(f328(f328(f242(a1),f806(x77373,x77372,x77371)),f2(a1))) % 167.77/167.51 [7809]~P62(x78091)+~P1(f328(f328(f243(x78091),f328(f328(f286(x78091),x78093),x78092)),f2(x78091)))+P1(f328(f328(f243(x78091),x78092),f2(x78091)))+P1(f328(f328(f243(x78091),x78093),f2(x78091))) % 167.77/167.51 [7810]~P123(x78101)+~P1(f328(f328(f242(x78101),f328(f328(f81(x78101),x78103),x78102)),f2(x78101)))+P1(f328(f328(f242(x78101),x78102),f2(x78101)))+P1(f328(f328(f242(x78101),x78103),f2(x78101))) % 167.77/167.51 [7811]~P62(x78111)+~P1(f328(f328(f242(x78111),f328(f328(f286(x78111),x78113),x78112)),f2(x78111)))+P1(f328(f328(f242(x78111),x78112),f2(x78111)))+P1(f328(f328(f242(x78111),x78113),f2(x78111))) % 167.77/167.51 [7925]P145(x79253,x79252,x79251)+E(x79251,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x79251),f808(x79251,x79252,x79253))),f807(x79251,x79252,x79253)),x79252)+P1(f328(f328(f243(a1),x79251),f806(x79251,x79252,x79253))) % 167.77/167.51 [7926]P144(x79263,x79262,x79261)+E(x79261,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x79261),f816(x79261,x79262,x79263))),f815(x79261,x79262,x79263)),x79262)+P1(f328(f328(f243(a1),x79261),f814(x79261,x79262,x79263))) % 167.77/167.51 [7938]P145(x79383,x79382,x79381)+E(x79381,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x79381),f813(x79381,x79382,x79383))),f806(x79381,x79382,x79383)),x79382)+P1(f328(f328(f242(a1),f2(a1)),f807(x79381,x79382,x79383))) % 167.77/167.51 [7939]P144(x79393,x79392,x79391)+E(x79391,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x79391),f817(x79391,x79392,x79393))),f814(x79391,x79392,x79393)),x79392)+P1(f328(f328(f242(a1),f2(a1)),f815(x79391,x79392,x79393))) % 167.77/167.51 [7980]P144(x79803,x79802,x79801)+~P1(f328(x79803,x79802))+E(f328(f328(f80(a1),f328(f328(f81(a1),x79801),f816(x79801,x79802,x79803))),f815(x79801,x79802,x79803)),x79802)+P1(f328(f328(f243(a1),x79801),f814(x79801,x79802,x79803))) % 167.77/167.51 [7989]P145(x79893,x79892,x79891)+E(f328(f328(f80(a1),f328(f328(f81(a1),x79891),f808(x79891,x79892,x79893))),f807(x79891,x79892,x79893)),x79892)+P1(f328(f328(f243(a1),x79891),f806(x79891,x79892,x79893)))+~P1(f328(x79893,f2(a1))) % 167.77/167.51 [7995]P144(x79953,x79952,x79951)+~P1(f328(x79953,x79952))+E(f328(f328(f80(a1),f328(f328(f81(a1),x79951),f817(x79951,x79952,x79953))),f814(x79951,x79952,x79953)),x79952)+P1(f328(f328(f242(a1),f2(a1)),f815(x79951,x79952,x79953))) % 167.77/167.51 [8001]P145(x80013,x80012,x80011)+E(f328(f328(f80(a1),f328(f328(f81(a1),x80011),f813(x80011,x80012,x80013))),f806(x80011,x80012,x80013)),x80012)+P1(f328(f328(f242(a1),f2(a1)),f807(x80011,x80012,x80013)))+~P1(f328(x80013,f2(a1))) % 167.77/167.51 [8012]P145(x80123,x80122,x80121)+E(x80121,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80121),f808(x80121,x80122,x80123))),f807(x80121,x80122,x80123)),x80122)+~P1(f328(x80123,f813(x80121,x80122,x80123))) % 167.77/167.51 [8013]P144(x80133,x80132,x80131)+E(x80131,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80131),f816(x80131,x80132,x80133))),f815(x80131,x80132,x80133)),x80132)+~P1(f328(x80133,f814(x80131,x80132,x80133))) % 167.77/167.51 [8014]P145(x80143,x80142,x80141)+E(x80141,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80141),f813(x80141,x80142,x80143))),f806(x80141,x80142,x80143)),x80142)+~P1(f328(x80143,f808(x80141,x80142,x80143))) % 167.77/167.51 [8015]P144(x80153,x80152,x80151)+E(x80151,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80151),f817(x80151,x80152,x80153))),f814(x80151,x80152,x80153)),x80152)+~P1(f328(x80153,f815(x80151,x80152,x80153))) % 167.77/167.51 [8073]P144(x80733,x80732,x80731)+~P1(f328(x80733,x80732))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80731),f816(x80731,x80732,x80733))),f815(x80731,x80732,x80733)),x80732)+~P1(f328(x80733,f814(x80731,x80732,x80733))) % 167.77/167.51 [8074]P144(x80743,x80742,x80741)+~P1(f328(x80743,x80742))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80741),f817(x80741,x80742,x80743))),f814(x80741,x80742,x80743)),x80742)+~P1(f328(x80743,f815(x80741,x80742,x80743))) % 167.77/167.51 [8085]P145(x80853,x80852,x80851)+E(f328(f328(f80(a1),f328(f328(f81(a1),x80851),f808(x80851,x80852,x80853))),f807(x80851,x80852,x80853)),x80852)+~P1(f328(x80853,f813(x80851,x80852,x80853)))+~P1(f328(x80853,f2(a1))) % 167.77/167.51 [8086]P145(x80863,x80862,x80861)+E(f328(f328(f80(a1),f328(f328(f81(a1),x80861),f813(x80861,x80862,x80863))),f806(x80861,x80862,x80863)),x80862)+~P1(f328(x80863,f808(x80861,x80862,x80863)))+~P1(f328(x80863,f2(a1))) % 167.77/167.51 [8194]P145(x81943,x81942,x81941)+E(x81941,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x81941),f808(x81941,x81942,x81943))),f807(x81941,x81942,x81943)),x81942)+P1(f328(f328(f242(a1),f806(x81941,x81942,x81943)),f2(a1))) % 167.77/167.51 [8195]P144(x81953,x81952,x81951)+E(x81951,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x81951),f816(x81951,x81952,x81953))),f815(x81951,x81952,x81953)),x81952)+P1(f328(f328(f242(a1),f814(x81951,x81952,x81953)),f2(a1))) % 167.77/167.51 [8241]P144(x82413,x82412,x82411)+~P1(f328(x82413,x82412))+E(f328(f328(f80(a1),f328(f328(f81(a1),x82411),f816(x82411,x82412,x82413))),f815(x82411,x82412,x82413)),x82412)+P1(f328(f328(f242(a1),f814(x82411,x82412,x82413)),f2(a1))) % 167.77/167.51 [8246]P145(x82463,x82462,x82461)+E(f328(f328(f80(a1),f328(f328(f81(a1),x82461),f808(x82461,x82462,x82463))),f807(x82461,x82462,x82463)),x82462)+~P1(f328(x82463,f2(a1)))+P1(f328(f328(f242(a1),f806(x82461,x82462,x82463)),f2(a1))) % 167.77/167.51 [8374]P145(x83743,x83742,x83741)+E(x83741,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x83741),f813(x83741,x83742,x83743))),f806(x83741,x83742,x83743)),x83742)+E(f328(f328(f80(a1),f328(f328(f81(a1),x83741),f808(x83741,x83742,x83743))),f807(x83741,x83742,x83743)),x83742) % 167.77/167.51 [8375]P144(x83753,x83752,x83751)+E(x83751,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x83751),f817(x83751,x83752,x83753))),f814(x83751,x83752,x83753)),x83752)+E(f328(f328(f80(a1),f328(f328(f81(a1),x83751),f816(x83751,x83752,x83753))),f815(x83751,x83752,x83753)),x83752) % 167.77/167.51 [8398]P144(x83983,x83982,x83981)+~P1(f328(x83983,x83982))+E(f328(f328(f80(a1),f328(f328(f81(a1),x83981),f817(x83981,x83982,x83983))),f814(x83981,x83982,x83983)),x83982)+E(f328(f328(f80(a1),f328(f328(f81(a1),x83981),f816(x83981,x83982,x83983))),f815(x83981,x83982,x83983)),x83982) % 167.77/167.51 [8410]P145(x84103,x84102,x84101)+E(f328(f328(f80(a1),f328(f328(f81(a1),x84101),f813(x84101,x84102,x84103))),f806(x84101,x84102,x84103)),x84102)+E(f328(f328(f80(a1),f328(f328(f81(a1),x84101),f808(x84101,x84102,x84103))),f807(x84101,x84102,x84103)),x84102)+~P1(f328(x84103,f2(a1))) % 167.77/167.51 [9064]~P123(x90641)+~E(x90643,f2(x90641))+~E(x90642,f2(x90641))+P1(f328(f328(f242(x90641),f328(f328(f80(x90641),f328(f328(f81(x90641),x90642),x90642)),f328(f328(f81(x90641),x90643),x90643))),f2(x90641))) % 167.77/167.51 [10113]~P117(x101131)+~E(x101133,f2(x101131))+~E(x101132,f2(x101131))+P1(f328(f328(f242(x101131),f328(f328(f80(x101131),f328(f328(f253(x101131),x101132),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x101131),x101133),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f2(x101131))) % 167.77/167.51 [4792]~E(x47923,x47921)+~P120(x47922)+E(x47921,f2(x47922))+E(f328(f328(f286(x47922),x47923),x47921),f78(x47922)) % 167.77/167.51 [4845]~P64(x48451)+~E(x48453,f192(x48451))+~E(x48452,f192(x48451))+E(f328(f328(f114(x48451),x48452),x48453),f192(x48451)) % 167.77/167.51 [4846]~P97(x48461)+~E(x48463,f251(x48461))+~E(x48462,f251(x48461))+E(f328(f328(f105(x48461),x48462),x48463),f251(x48461)) % 167.77/167.51 [4932]~P120(x49323)+E(x49321,x49322)+E(x49322,f2(x49323))+~E(f328(f328(f286(x49323),x49321),x49322),f78(x49323)) % 167.77/167.51 [4951]~P125(x49512)+E(x49511,f2(x49512))+E(x49513,f2(x49512))+~E(f328(f328(f81(x49512),x49513),x49511),f2(x49512)) % 167.77/167.51 [4952]~P137(x49522)+E(x49521,f2(x49522))+E(x49523,f2(x49522))+~E(f328(f328(f81(x49522),x49523),x49521),f2(x49522)) % 167.77/167.51 [5332]~P119(x53323)+E(x53321,x53322)+E(x53321,f328(f79(x53323),x53322))+~E(f328(f328(f81(x53323),x53321),x53321),f328(f328(f81(x53323),x53322),x53322)) % 167.77/167.51 [5372]~P94(x53721)+E(f328(f79(x53721),x53722),x53723)+~E(f328(f328(f114(x53721),x53722),x53723),f251(x53721))+~E(f328(f328(f105(x53721),x53722),x53723),f192(x53721)) % 167.77/167.51 [5451]~P117(x54513)+E(x54511,x54512)+P1(f328(f328(f243(x54513),x54512),x54511))+P1(f328(f328(f243(x54513),x54511),x54512)) % 167.77/167.51 [5452]~P105(x54523)+E(x54521,x54522)+P1(f328(f328(f243(x54523),x54522),x54521))+P1(f328(f328(f243(x54523),x54521),x54522)) % 167.77/167.51 [5453]~E(x54532,x54533)+~P105(x54531)+P1(f328(f328(f242(x54531),x54532),x54533))+P1(f328(f328(f243(x54531),x54532),x54533)) % 167.77/167.51 [5707]~P107(x57073)+E(x57071,x57072)+~P1(f328(f328(f242(x57073),x57072),x57071))+P1(f328(f328(f243(x57073),x57072),x57071)) % 167.77/167.51 [5709]~P105(x57093)+E(x57091,x57092)+~P1(f328(f328(f242(x57093),x57091),x57092))+P1(f328(f328(f243(x57093),x57091),x57092)) % 167.77/167.51 [5715]~P107(x57153)+E(x57151,x57152)+~P1(f328(f328(f242(x57153),x57151),x57152))+P1(f328(f328(f243(x57153),x57151),x57152)) % 167.77/167.51 [5817]P144(x58171,x58172,x58173)+~P1(f328(x58171,x58172))+P1(f328(f328(f243(a1),x58173),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x58173)) % 167.77/167.51 [5864]P145(x58641,x58642,x58643)+~P1(f328(x58641,f2(a1)))+P1(f328(f328(f243(a1),x58643),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x58643)) % 167.77/167.51 [5868]~P2(x58681)+E(f328(f328(f114(x58681),x58682),f10(x58681,x58683)),x58682)+~P1(f328(f38(x58681),x58683))+~P1(f328(f328(f330(x58681),x58682),x58683)) % 167.77/167.51 [5869]~P2(x58691)+E(f328(f328(f105(x58691),x58692),f13(x58691,x58693)),x58692)+~P1(f328(f38(x58691),x58693))+~P1(f328(f328(f330(x58691),x58692),x58693)) % 167.77/167.51 [5905]~P2(x59051)+E(f328(f328(f114(x59051),x59052),f13(x59051,x59053)),f13(x59051,x59053))+~P1(f328(f38(x59051),x59053))+~P1(f328(f328(f330(x59051),x59052),x59053)) % 167.77/167.51 [5906]~P2(x59061)+E(f328(f328(f105(x59061),x59062),f10(x59061,x59063)),f10(x59061,x59063))+~P1(f328(f38(x59061),x59063))+~P1(f328(f328(f330(x59061),x59062),x59063)) % 167.77/167.51 [5907]~P105(x59071)+E(f328(f328(f240(x59071),x59072),f14(x59071,x59073)),f14(x59071,x59073))+~P1(f328(f38(x59071),x59073))+~P1(f328(f328(f330(x59071),x59072),x59073)) % 167.77/167.51 [5908]~P105(x59081)+E(f328(f328(f241(x59081),x59082),f15(x59081,x59083)),f15(x59081,x59083))+~P1(f328(f38(x59081),x59083))+~P1(f328(f328(f330(x59081),x59082),x59083)) % 167.77/167.51 [5950]E(x59501,x59502)+~P107(x59503)+~P1(f328(f328(f242(x59503),x59502),x59501))+~P1(f328(f328(f242(x59503),x59501),x59502)) % 167.77/167.51 [6088]~P106(x60881)+P1(f328(f328(f242(x60881),x60883),x60882))+~P1(f328(f328(f242(x60881),x60882),x60883))+P1(f328(f328(f243(x60881),x60882),x60883)) % 167.77/167.51 [6109]~P105(x61091)+~P1(f328(f38(x61091),x61093))+P1(f328(f328(f242(x61091),x61092),f15(x61091,x61093)))+~P1(f328(f328(f330(x61091),x61092),x61093)) % 167.77/167.51 [6164]~P105(x61641)+E(f328(f328(f240(x61641),x61642),f12(x61641,f241(x61641),x61643)),x61642)+~P1(f328(f38(x61641),x61643))+~P1(f328(f328(f330(x61641),x61642),x61643)) % 167.77/167.51 [6165]~P105(x61651)+E(f328(f328(f241(x61651),x61652),f11(x61651,f240(x61651),x61653)),x61652)+~P1(f328(f38(x61651),x61653))+~P1(f328(f328(f330(x61651),x61652),x61653)) % 167.77/167.51 [6304]E(x63041,x63042)+~E(f328(f328(f22(a872),x63041),x63043),f328(f328(f22(a872),x63042),x63043))+~P1(f328(f328(f242(a872),x63043),x63041))+~P1(f328(f328(f242(a872),x63043),x63042)) % 167.77/167.51 [6331]~P105(x63311)+~P1(f328(f38(x63311),x63312))+~P1(f328(f328(f330(x63311),x63313),x63312))+P1(f328(f328(f242(x63311),f14(x63311,x63312)),x63313)) % 167.77/167.51 [6393]P145(x63932,x63933,x63931)+E(x63931,f2(a1))+P1(f328(f328(f243(a1),x63931),f806(x63931,x63933,x63932)))+P1(f328(f328(f243(a1),f2(a1)),x63931)) % 167.77/167.51 [6394]P144(x63942,x63943,x63941)+E(x63941,f2(a1))+P1(f328(f328(f243(a1),x63941),f814(x63941,x63943,x63942)))+P1(f328(f328(f243(a1),f2(a1)),x63941)) % 167.77/167.51 [6395]~P105(x63951)+E(f328(f328(f240(x63951),x63952),f11(x63951,f240(x63951),x63953)),f11(x63951,f240(x63951),x63953))+~P1(f328(f38(x63951),x63953))+~P1(f328(f328(f330(x63951),x63952),x63953)) % 167.77/167.51 [6396]~P105(x63961)+E(f328(f328(f241(x63961),x63962),f12(x63961,f241(x63961),x63963)),f12(x63961,f241(x63961),x63963))+~P1(f328(f38(x63961),x63963))+~P1(f328(f328(f330(x63961),x63962),x63963)) % 167.77/167.51 [6402]~P1(f328(x64021,x64022))+P1(f328(x64021,f493(x64022,x64021,x64023)))+P1(f328(x64021,f2(a872)))+~P1(f328(f328(f243(a872),x64022),x64023)) % 167.77/167.51 [6457]~P1(f328(x64571,x64572))+~P1(f328(f38(x64573),x64572))+P1(f328(x64571,f649(x64571,x64572,x64573)))+P1(f328(x64571,f192(f879(x64573,a867)))) % 167.77/167.51 [6470]~P117(x64701)+~P91(x64701)+P1(f328(f328(f243(x64701),f328(f107(x64701),x64702)),f328(f107(x64701),x64703)))+~P1(f328(f328(f243(a1),x64702),x64703)) % 167.77/167.51 [6471]~P117(x64711)+~P91(x64711)+P1(f328(f328(f242(x64711),f328(f107(x64711),x64712)),f328(f107(x64711),x64713)))+~P1(f328(f328(f242(a1),x64712),x64713)) % 167.77/167.51 [6474]~P1(f328(x64741,x64743))+~P1(f328(f38(x64742),x64743))+P1(f328(f38(x64742),f649(x64741,x64743,x64742)))+P1(f328(x64741,f192(f879(x64742,a867)))) % 167.77/167.51 [6507]P144(x65071,x65072,x65073)+~P1(f328(x65071,x65072))+P1(f328(f328(f243(a1),x65073),f814(x65073,x65072,x65071)))+P1(f328(f328(f243(a1),f2(a1)),x65073)) % 167.77/167.51 [6541]P145(x65411,x65412,x65413)+P1(f328(f328(f243(a1),x65413),f806(x65413,x65412,x65411)))+~P1(f328(x65411,f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x65413)) % 167.77/167.51 [6572]~P108(x65721)+~P92(x65721)+E(f328(f328(f240(x65721),f328(f107(x65721),x65722)),f328(f107(x65721),x65723)),f328(f107(x65721),x65723))+P1(f328(f328(f242(x65721),f328(f107(x65721),x65722)),f328(f107(x65721),x65723))) % 167.77/167.51 [6573]~P108(x65731)+~P92(x65731)+E(f328(f328(f241(x65731),f328(f107(x65731),x65732)),f328(f107(x65731),x65733)),f328(f107(x65731),x65732))+P1(f328(f328(f242(x65731),f328(f107(x65731),x65732)),f328(f107(x65731),x65733))) % 167.77/167.51 [6632]P145(x66322,x66323,x66321)+E(x66321,f2(a1))+~P1(f328(x66322,f813(x66321,x66323,x66322)))+P1(f328(f328(f243(a1),f2(a1)),x66321)) % 167.77/167.51 [6633]P144(x66332,x66333,x66331)+E(x66331,f2(a1))+~P1(f328(x66332,f814(x66331,x66333,x66332)))+P1(f328(f328(f243(a1),f2(a1)),x66331)) % 167.77/167.51 [6637]P1(f328(x66371,x66372))+~P1(f328(f38(x66373),x66372))+P1(f328(x66371,f687(x66371,x66372,x66373)))+~P1(f328(x66371,f192(f879(x66373,a867)))) % 167.77/167.51 [6656]P1(f328(x66561,x66562))+P1(f328(f38(x66563),f687(x66561,x66562,x66563)))+~P1(f328(f38(x66563),x66562))+~P1(f328(x66561,f192(f879(x66563,a867)))) % 167.77/167.51 [6721]P144(x67211,x67212,x67213)+~P1(f328(x67211,x67212))+~P1(f328(x67211,f814(x67213,x67212,x67211)))+P1(f328(f328(f243(a1),f2(a1)),x67213)) % 167.77/167.51 [6751]P145(x67511,x67512,x67513)+~P1(f328(x67511,f813(x67513,x67512,x67511)))+~P1(f328(x67511,f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x67513)) % 167.77/167.51 [6860]~P91(x68603)+~P117(x68603)+~P1(f328(f328(f243(x68603),f328(f107(x68603),x68601)),f328(f107(x68603),x68602)))+P1(f328(f328(f243(a1),x68601),x68602)) % 167.77/167.51 [6861]~P91(x68613)+~P117(x68613)+~P1(f328(f328(f242(x68613),f328(f107(x68613),x68611)),f328(f107(x68613),x68612)))+P1(f328(f328(f242(a1),x68611),x68612)) % 167.77/167.51 [6888]~P105(x68881)+~P15(x68881,x68883)+P15(x68881,f328(f328(f148(x68881),x68882),x68883))+~P1(f328(f328(f242(x68881),x68882),f743(x68883,x68882,x68881))) % 167.77/167.51 [6889]~P105(x68891)+~P15(x68891,x68893)+P15(x68891,f328(f328(f148(x68891),x68892),x68893))+~P1(f328(f328(f242(x68891),x68892),f746(x68893,x68892,x68891))) % 167.77/167.51 [6890]~P105(x68901)+~P15(x68901,x68903)+P15(x68901,f328(f328(f148(x68901),x68902),x68903))+~P1(f328(f328(f242(x68901),x68902),f777(x68902,x68903,x68901))) % 167.77/167.51 [6974]P145(x69742,x69743,x69741)+E(x69741,f2(a1))+P1(f328(f328(f243(a1),x69741),f2(a1)))+P1(f328(f328(f243(a1),f807(x69741,x69743,x69742)),x69741)) % 167.77/167.51 [6975]P144(x69752,x69753,x69751)+E(x69751,f2(a1))+P1(f328(f328(f243(a1),x69751),f2(a1)))+P1(f328(f328(f243(a1),f815(x69751,x69753,x69752)),x69751)) % 167.77/167.51 [7014]P145(x70142,x70143,x70141)+E(x70141,f2(a1))+P1(f328(f328(f242(a1),f806(x70141,x70143,x70142)),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x70141)) % 167.77/167.51 [7015]P144(x70152,x70153,x70151)+E(x70151,f2(a1))+P1(f328(f328(f242(a1),f814(x70151,x70153,x70152)),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x70151)) % 167.77/167.51 [7037]~P105(x70371)+~P15(x70371,x70373)+E(f328(f328(f145(x70371,x70371,f5(x70371)),x70372),f167(x70371,x70372,x70373)),x70373)+~P1(f328(f328(f330(x70371),x70372),f328(f170(x70371),x70373))) % 167.77/167.51 [7084]P144(x70841,x70842,x70843)+~P1(f328(x70841,x70842))+P1(f328(f328(f243(a1),x70843),f2(a1)))+P1(f328(f328(f243(a1),f815(x70843,x70842,x70841)),x70843)) % 167.77/167.51 [7090]~P108(x70901)+~P92(x70901)+E(f328(f328(f240(x70901),f328(f107(x70901),x70902)),f328(f107(x70901),x70903)),f328(f107(x70901),x70902))+~P1(f328(f328(f242(x70901),f328(f107(x70901),x70902)),f328(f107(x70901),x70903))) % 167.77/167.51 [7091]~P108(x70911)+~P92(x70911)+E(f328(f328(f241(x70911),f328(f107(x70911),x70912)),f328(f107(x70911),x70913)),f328(f107(x70911),x70913))+~P1(f328(f328(f242(x70911),f328(f107(x70911),x70912)),f328(f107(x70911),x70913))) % 167.77/167.51 [7105]P145(x71051,x71052,x71053)+~P1(f328(x71051,f2(a1)))+P1(f328(f328(f243(a1),x71053),f2(a1)))+P1(f328(f328(f243(a1),f807(x71053,x71052,x71051)),x71053)) % 167.77/167.51 [7113]P144(x71131,x71132,x71133)+~P1(f328(x71131,x71132))+P1(f328(f328(f242(a1),f814(x71133,x71132,x71131)),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x71133)) % 167.77/167.51 [7137]P145(x71371,x71372,x71373)+~P1(f328(x71371,f2(a1)))+P1(f328(f328(f242(a1),f806(x71373,x71372,x71371)),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x71373)) % 167.77/167.51 [7167]~P1(f328(x71671,x71672))+P1(f328(x71671,f2(a872)))+~P1(f328(f328(f243(a872),x71672),x71673))+P1(f328(f328(f243(a872),f493(x71672,x71671,x71673)),x71673)) % 167.77/167.51 [7184]~P105(x71841)+~P15(x71841,x71843)+P15(x71841,f328(f328(f148(x71841),x71842),x71843))+P1(f328(f328(f330(x71841),f743(x71843,x71842,x71841)),f328(f170(x71841),x71843))) % 167.77/167.51 [7185]~P105(x71851)+~P15(x71851,x71853)+P15(x71851,f328(f328(f148(x71851),x71852),x71853))+P1(f328(f328(f330(x71851),f746(x71853,x71852,x71851)),f328(f170(x71851),x71853))) % 167.77/167.51 [7186]~P105(x71861)+~P15(x71861,x71863)+P15(x71861,f328(f328(f148(x71861),x71862),x71863))+P1(f328(f328(f330(x71861),f777(x71862,x71863,x71861)),f328(f170(x71861),x71863))) % 167.77/167.51 [7290]~P4(x72901)+~P105(x72901)+~P1(f328(f328(f243(x72901),x72903),f41(x72901,x72902)))+P1(f328(f328(f330(x72901),f832(x72902,x72903,x72901)),x72902)) % 167.77/167.51 [7455]~P4(x74551)+~P105(x74551)+~P1(f328(f328(f243(x74551),f42(x74551,x74553)),x74552))+P1(f328(f328(f330(x74551),f818(x74552,x74553,x74551)),x74553)) % 167.77/167.51 [7456]~P4(x74561)+~P105(x74561)+~P1(f328(f328(f243(x74561),f42(x74561,x74563)),x74562))+P1(f328(f328(f243(x74561),f818(x74562,x74563,x74561)),x74562)) % 167.77/167.51 [7471]P145(x74712,x74713,x74711)+E(x74711,f2(a1))+P1(f328(f328(f243(a1),x74711),f806(x74711,x74713,x74712)))+P1(f328(f328(f243(a1),f807(x74711,x74713,x74712)),x74711)) % 167.77/167.51 [7472]P144(x74722,x74723,x74721)+E(x74721,f2(a1))+P1(f328(f328(f243(a1),x74721),f814(x74721,x74723,x74722)))+P1(f328(f328(f243(a1),f815(x74721,x74723,x74722)),x74721)) % 167.77/167.51 [7562]P145(x75623,x75622,x75621)+E(x75621,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x75621),f813(x75621,x75622,x75623))),f806(x75621,x75622,x75623)),x75622)+P1(f328(f328(f243(a1),f2(a1)),x75621)) % 167.77/167.51 [7563]P144(x75633,x75632,x75631)+E(x75631,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x75631),f817(x75631,x75632,x75633))),f814(x75631,x75632,x75633)),x75632)+P1(f328(f328(f243(a1),f2(a1)),x75631)) % 167.77/167.51 [7567]~P127(x75671)+~P1(f328(f328(f243(x75671),x75673),f2(x75671)))+P1(f328(f328(f243(x75671),f328(f328(f81(x75671),x75672),x75673)),f2(x75671)))+~P1(f328(f328(f243(x75671),f2(x75671)),x75672)) % 167.77/167.51 [7568]~P127(x75681)+~P1(f328(f328(f243(x75681),x75682),f2(x75681)))+P1(f328(f328(f243(x75681),f328(f328(f81(x75681),x75682),x75683)),f2(x75681)))+~P1(f328(f328(f243(x75681),f2(x75681)),x75683)) % 167.77/167.51 [7569]~P62(x75691)+~P1(f328(f328(f243(x75691),x75693),f2(x75691)))+P1(f328(f328(f243(x75691),f328(f328(f286(x75691),x75692),x75693)),f2(x75691)))+~P1(f328(f328(f243(x75691),f2(x75691)),x75692)) % 167.77/167.51 [7570]~P62(x75701)+~P1(f328(f328(f243(x75701),x75702),f2(x75701)))+P1(f328(f328(f243(x75701),f328(f328(f286(x75701),x75702),x75703)),f2(x75701)))+~P1(f328(f328(f243(x75701),f2(x75701)),x75703)) % 167.77/167.51 [7571]~P63(x75711)+~P1(f328(f328(f243(x75711),x75713),f2(x75711)))+P1(f328(f328(f243(x75711),f328(f328(f286(x75711),x75712),x75713)),f2(x75711)))+~P1(f328(f328(f243(x75711),f2(x75711)),x75712)) % 167.77/167.51 [7572]~P63(x75721)+~P1(f328(f328(f243(x75721),x75722),f2(x75721)))+P1(f328(f328(f243(x75721),f328(f328(f286(x75721),x75722),x75723)),f2(x75721)))+~P1(f328(f328(f243(x75721),f2(x75721)),x75723)) % 167.77/167.51 [7574]~P123(x75741)+~P1(f328(f328(f242(x75741),x75743),f2(x75741)))+P1(f328(f328(f242(x75741),f328(f328(f81(x75741),x75742),x75743)),f2(x75741)))+~P1(f328(f328(f242(x75741),f2(x75741)),x75742)) % 167.77/167.51 [7575]~P123(x75751)+~P1(f328(f328(f242(x75751),x75752),f2(x75751)))+P1(f328(f328(f242(x75751),f328(f328(f81(x75751),x75752),x75753)),f2(x75751)))+~P1(f328(f328(f242(x75751),f2(x75751)),x75753)) % 167.77/167.51 [7577]~P131(x75771)+~P1(f328(f328(f242(x75771),x75773),f2(x75771)))+P1(f328(f328(f242(x75771),f328(f328(f81(x75771),x75772),x75773)),f2(x75771)))+~P1(f328(f328(f242(x75771),f2(x75771)),x75772)) % 167.77/167.51 [7579]~P131(x75791)+~P1(f328(f328(f242(x75791),x75792),f2(x75791)))+P1(f328(f328(f242(x75791),f328(f328(f81(x75791),x75792),x75793)),f2(x75791)))+~P1(f328(f328(f242(x75791),f2(x75791)),x75793)) % 167.77/167.51 [7580]~P62(x75801)+~P1(f328(f328(f242(x75801),x75803),f2(x75801)))+P1(f328(f328(f242(x75801),f328(f328(f286(x75801),x75802),x75803)),f2(x75801)))+~P1(f328(f328(f242(x75801),f2(x75801)),x75802)) % 167.77/167.51 [7581]~P62(x75811)+~P1(f328(f328(f242(x75811),x75812),f2(x75811)))+P1(f328(f328(f242(x75811),f328(f328(f286(x75811),x75812),x75813)),f2(x75811)))+~P1(f328(f328(f242(x75811),f2(x75811)),x75813)) % 167.77/167.51 [7582]~P63(x75821)+~P1(f328(f328(f243(x75821),x75823),f2(x75821)))+P1(f328(f328(f242(x75821),f328(f328(f286(x75821),x75822),x75823)),f2(x75821)))+~P1(f328(f328(f242(x75821),f2(x75821)),x75822)) % 167.77/167.51 [7583]~P63(x75831)+~P1(f328(f328(f242(x75831),x75832),f2(x75831)))+P1(f328(f328(f242(x75831),f328(f328(f286(x75831),x75832),x75833)),f2(x75831)))+~P1(f328(f328(f243(x75831),f2(x75831)),x75833)) % 167.77/167.51 [7598]P144(x75981,x75982,x75983)+~P1(f328(x75981,x75982))+P1(f328(f328(f243(a1),x75983),f814(x75983,x75982,x75981)))+P1(f328(f328(f243(a1),f815(x75983,x75982,x75981)),x75983)) % 167.77/167.51 [7611]P145(x76111,x76112,x76113)+P1(f328(f328(f243(a1),x76113),f806(x76113,x76112,x76111)))+~P1(f328(x76111,f2(a1)))+P1(f328(f328(f243(a1),f807(x76113,x76112,x76111)),x76113)) % 167.77/167.51 [7662]P145(x76622,x76623,x76621)+E(x76621,f2(a1))+~P1(f328(x76622,f813(x76621,x76623,x76622)))+P1(f328(f328(f243(a1),f807(x76621,x76623,x76622)),x76621)) % 167.77/167.51 [7663]P144(x76632,x76633,x76631)+E(x76631,f2(a1))+~P1(f328(x76632,f814(x76631,x76633,x76632)))+P1(f328(f328(f243(a1),f815(x76631,x76633,x76632)),x76631)) % 167.77/167.51 [7674]P144(x76743,x76742,x76741)+~P1(f328(x76743,x76742))+E(f328(f328(f80(a1),f328(f328(f81(a1),x76741),f817(x76741,x76742,x76743))),f814(x76741,x76742,x76743)),x76742)+P1(f328(f328(f243(a1),f2(a1)),x76741)) % 167.77/167.51 [7691]P145(x76913,x76912,x76911)+E(f328(f328(f80(a1),f328(f328(f81(a1),x76911),f813(x76911,x76912,x76913))),f806(x76911,x76912,x76913)),x76912)+~P1(f328(x76913,f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x76911)) % 167.77/167.51 [7717]~P1(f328(x77171,x77173))+~P1(f328(f38(x77172),x77173))+P1(f328(f328(f330(x77172),f629(x77171,x77173,x77172)),f649(x77171,x77173,x77172)))+P1(f328(x77171,f192(f879(x77172,a867)))) % 167.77/167.51 [7728]P144(x77281,x77282,x77283)+~P1(f328(x77281,x77282))+~P1(f328(x77281,f814(x77283,x77282,x77281)))+P1(f328(f328(f243(a1),f815(x77283,x77282,x77281)),x77283)) % 167.77/167.51 [7734]P145(x77341,x77342,x77343)+~P1(f328(x77341,f813(x77343,x77342,x77341)))+~P1(f328(x77341,f2(a1)))+P1(f328(f328(f243(a1),f807(x77343,x77342,x77341)),x77343)) % 167.77/167.51 [7840]~P62(x78401)+~P1(f328(f328(f243(x78401),f328(f328(f286(x78401),x78403),x78402)),f2(x78401)))+P1(f328(f328(f243(x78401),x78402),f2(x78401)))+P1(f328(f328(f243(x78401),f2(x78401)),x78402)) % 167.77/167.51 [7841]~P62(x78411)+~P1(f328(f328(f243(x78411),f328(f328(f286(x78411),x78412),x78413)),f2(x78411)))+P1(f328(f328(f243(x78411),x78412),f2(x78411)))+P1(f328(f328(f243(x78411),f2(x78411)),x78412)) % 167.77/167.51 [7842]~P123(x78421)+~P1(f328(f328(f242(x78421),f328(f328(f81(x78421),x78423),x78422)),f2(x78421)))+P1(f328(f328(f242(x78421),x78422),f2(x78421)))+P1(f328(f328(f242(x78421),f2(x78421)),x78422)) % 167.77/167.51 [7843]~P123(x78431)+~P1(f328(f328(f242(x78431),f328(f328(f81(x78431),x78432),x78433)),f2(x78431)))+P1(f328(f328(f242(x78431),x78432),f2(x78431)))+P1(f328(f328(f242(x78431),f2(x78431)),x78432)) % 167.77/167.51 [7844]~P62(x78441)+~P1(f328(f328(f242(x78441),f328(f328(f286(x78441),x78443),x78442)),f2(x78441)))+P1(f328(f328(f242(x78441),x78442),f2(x78441)))+P1(f328(f328(f242(x78441),f2(x78441)),x78442)) % 167.77/167.51 [7845]~P62(x78451)+~P1(f328(f328(f242(x78451),f328(f328(f286(x78451),x78452),x78453)),f2(x78451)))+P1(f328(f328(f242(x78451),x78452),f2(x78451)))+P1(f328(f328(f242(x78451),f2(x78451)),x78452)) % 167.77/167.51 [7869]~P62(x78691)+~P1(f328(f328(f243(x78691),f328(f328(f286(x78691),x78692),x78693)),f2(x78691)))+P1(f328(f328(f243(x78691),f2(x78691)),x78692))+P1(f328(f328(f243(x78691),f2(x78691)),x78693)) % 167.77/167.51 [7870]~P123(x78701)+~P1(f328(f328(f242(x78701),f328(f328(f81(x78701),x78702),x78703)),f2(x78701)))+P1(f328(f328(f242(x78701),f2(x78701)),x78702))+P1(f328(f328(f242(x78701),f2(x78701)),x78703)) % 167.77/167.51 [7871]~P62(x78711)+~P1(f328(f328(f242(x78711),f328(f328(f286(x78711),x78712),x78713)),f2(x78711)))+P1(f328(f328(f242(x78711),f2(x78711)),x78712))+P1(f328(f328(f242(x78711),f2(x78711)),x78713)) % 167.77/167.51 [7892]P145(x78922,x78923,x78921)+E(x78921,f2(a1))+P1(f328(f328(f242(a1),f806(x78921,x78923,x78922)),f2(a1)))+P1(f328(f328(f243(a1),f807(x78921,x78923,x78922)),x78921)) % 167.77/167.51 [7893]P144(x78932,x78933,x78931)+E(x78931,f2(a1))+P1(f328(f328(f242(a1),f814(x78931,x78933,x78932)),f2(a1)))+P1(f328(f328(f243(a1),f815(x78931,x78933,x78932)),x78931)) % 167.77/167.51 [7900]~P116(x79001)+~P1(f328(f328(f243(x79001),x79002),f78(x79001)))+P1(f328(f328(f243(x79001),f328(f328(f253(x79001),x79002),f328(a116,x79003))),f78(x79001)))+~P1(f328(f328(f243(x79001),f2(x79001)),x79002)) % 167.77/167.51 [7955]~P105(x79551)+~E(x79553,f117(x79551))+~P15(x79551,f328(f166(x79551),x79553))+E(f328(f139(x79551,x79551,f328(f7(x79551,x79551,x79551),f241(x79551)),x79552),f328(f166(x79551),x79553)),x79552) % 167.77/167.51 [7957]P144(x79571,x79572,x79573)+~P1(f328(x79571,x79572))+P1(f328(f328(f242(a1),f814(x79573,x79572,x79571)),f2(a1)))+P1(f328(f328(f243(a1),f815(x79573,x79572,x79571)),x79573)) % 167.77/167.51 [7964]P145(x79641,x79642,x79643)+~P1(f328(x79641,f2(a1)))+P1(f328(f328(f242(a1),f806(x79643,x79642,x79641)),f2(a1)))+P1(f328(f328(f243(a1),f807(x79643,x79642,x79641)),x79643)) % 167.77/167.51 [8189]P145(x81893,x81892,x81891)+E(x81891,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x81891),f813(x81891,x81892,x81893))),f806(x81891,x81892,x81893)),x81892)+P1(f328(f328(f243(a1),f807(x81891,x81892,x81893)),x81891)) % 167.77/167.51 [8190]P144(x81903,x81902,x81901)+E(x81901,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x81901),f817(x81901,x81902,x81903))),f814(x81901,x81902,x81903)),x81902)+P1(f328(f328(f243(a1),f815(x81901,x81902,x81903)),x81901)) % 167.77/167.51 [8232]P144(x82323,x82322,x82321)+~P1(f328(x82323,x82322))+E(f328(f328(f80(a1),f328(f328(f81(a1),x82321),f817(x82321,x82322,x82323))),f814(x82321,x82322,x82323)),x82322)+P1(f328(f328(f243(a1),f815(x82321,x82322,x82323)),x82321)) % 167.77/167.51 [8233]~P67(x82331)+~P73(x82331)+~P39(x82333)+E(f328(f328(f6(a872,x82331),f328(f328(f8(a1,x82331,a872),x82332),f104(a1))),f328(f307(a1,a872,a108),x82333)),f328(f328(f6(a1,x82331),x82332),x82333)) % 167.77/167.51 [8234]~P67(x82341)+~P73(x82341)+~P39(x82343)+E(f328(f328(f9(a872,x82341),f328(f328(f8(a1,x82341,a872),x82342),f104(a1))),f328(f307(a1,a872,a108),x82343)),f328(f328(f9(a1,x82341),x82342),x82343)) % 167.77/167.51 [8243]P145(x82433,x82432,x82431)+E(f328(f328(f80(a1),f328(f328(f81(a1),x82431),f813(x82431,x82432,x82433))),f806(x82431,x82432,x82433)),x82432)+~P1(f328(x82433,f2(a1)))+P1(f328(f328(f243(a1),f807(x82431,x82432,x82433)),x82431)) % 167.77/167.51 [8262]~E(x82622,f2(a872))+~E(f328(f262(a872,a872),x82623),f2(a872))+~E(x82621,f328(f328(f80(a872),f328(f328(f81(a872),f328(f262(a872,a872),x82623)),x82622)),f328(f266(a872,a872),x82623)))+P1(f328(f49(x82621,x82622),x82623)) % 167.77/167.51 [8315]P1(f328(x83151,x83152))+~P1(f328(f328(f330(x83153),f677(x83151,x83152,x83153)),f687(x83151,x83152,x83153)))+~P1(f328(f38(x83153),x83152))+~P1(f328(x83151,f192(f879(x83153,a867)))) % 167.77/167.51 [8934]P1(f328(x89341,x89342))+~P1(f328(f38(x89343),x89342))+~P1(f328(x89341,f328(f328(f306(x89343),f677(x89341,x89342,x89343)),f687(x89341,x89342,x89343))))+~P1(f328(x89341,f192(f879(x89343,a867)))) % 167.77/167.51 [9168]P1(f328(f328(f242(a1),x91681),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),f328(f328(f81(a1),x91682),x91681)),x91683)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x91682))+~P1(f328(f328(f242(a1),f2(a1)),x91683)) % 167.77/167.51 [5778]~P2(x57782)+E(x57781,f192(f879(x57782,a867)))+~P1(f328(f38(x57782),x57781))+E(f13(x57782,f328(f328(f306(x57782),x57783),x57781)),f328(f328(f114(x57782),x57783),f13(x57782,x57781))) % 167.77/167.51 [5779]~P2(x57792)+E(x57791,f192(f879(x57792,a867)))+~P1(f328(f38(x57792),x57791))+E(f10(x57792,f328(f328(f306(x57792),x57793),x57791)),f328(f328(f105(x57792),x57793),f10(x57792,x57791))) % 167.77/167.51 [5780]~P105(x57802)+E(x57801,f192(f879(x57802,a867)))+~P1(f328(f38(x57802),x57801))+E(f14(x57802,f328(f328(f306(x57802),x57803),x57801)),f328(f328(f240(x57802),x57803),f14(x57802,x57801))) % 167.77/167.51 [5781]~P105(x57812)+E(x57811,f192(f879(x57812,a867)))+~P1(f328(f38(x57812),x57811))+E(f15(x57812,f328(f328(f306(x57812),x57813),x57811)),f328(f328(f241(x57812),x57813),f15(x57812,x57811))) % 167.77/167.51 [6085]~P123(x60851)+~E(x60853,f2(x60851))+~E(x60852,f2(x60851))+E(f328(f328(f80(x60851),f328(f328(f81(x60851),x60852),x60852)),f328(f328(f81(x60851),x60853),x60853)),f2(x60851)) % 167.77/167.51 [6156]~P95(x61562)+E(x61561,f192(f879(x61562,a867)))+~P1(f328(f38(x61562),x61561))+E(f328(f64(x61562,f81(x61562)),f328(f328(f306(x61562),x61563),x61561)),f328(f328(f81(x61562),x61563),f328(f64(x61562,f81(x61562)),x61561))) % 167.77/167.51 [6283]~P105(x62832)+E(x62831,f192(f879(x62832,a867)))+~P1(f328(f38(x62832),x62831))+E(f11(x62832,f240(x62832),f328(f328(f306(x62832),x62833),x62831)),f328(f328(f240(x62832),x62833),f11(x62832,f240(x62832),x62831))) % 167.77/167.51 [6284]~P105(x62842)+E(x62841,f192(f879(x62842,a867)))+~P1(f328(f38(x62842),x62841))+E(f12(x62842,f241(x62842),f328(f328(f306(x62842),x62843),x62841)),f328(f328(f241(x62842),x62843),f12(x62842,f241(x62842),x62841))) % 167.77/167.51 [6786]~P69(x67861)+~P1(f328(f38(x67861),x67863))+E(f328(f64(x67861,f81(x67861)),f328(f328(f306(x67861),x67862),x67863)),f328(f328(f65(x67861,x67861,f81(x67861)),x67862),x67863))+P1(f328(f328(f330(x67861),x67862),x67863)) % 167.77/167.51 [6868]~E(f328(f328(f80(a1),x68682),f328(f328(f81(a1),x68683),x68681)),x68683)+~P1(f328(f328(f243(a1),f2(a1)),x68683))+P1(f328(f328(f242(a1),f78(a1)),x68681))+~P1(f328(f328(f243(a1),x68682),x68683)) % 167.77/167.51 [6895]~E(f328(f328(f80(a1),x68952),f328(f328(f81(a1),x68953),x68951)),x68953)+P1(f328(f328(f242(a1),x68951),f78(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x68953))+~P1(f328(f328(f242(a1),f2(a1)),x68952)) % 167.77/167.51 [6911]E(x69111,f2(a872))+~P1(f328(f49(x69113,x69111),x69112))+~P1(f328(f328(f243(a872),f2(a872)),x69111))+P1(f328(f328(f243(a872),f328(f266(a872,a872),x69112)),x69111)) % 167.77/167.51 [6941]~P134(x69411)+~P1(f328(f328(f242(x69411),x69412),f2(x69411)))+~P1(f328(f328(f242(x69411),x69413),f2(x69411)))+E(f328(f328(f81(x69411),f328(f75(x69411),x69412)),f328(f75(x69411),x69413)),f328(f75(x69411),f328(f328(f81(x69411),x69412),x69413))) % 167.77/167.51 [6991]~P134(x69911)+~P1(f328(f328(f242(x69911),x69912),f2(x69911)))+E(f328(f328(f81(x69911),f328(f75(x69911),x69912)),f328(f75(x69911),x69913)),f328(f75(x69911),f328(f328(f81(x69911),x69912),x69913)))+~P1(f328(f328(f242(x69911),f2(x69911)),x69913)) % 167.77/167.51 [6992]~P134(x69921)+~P1(f328(f328(f242(x69921),x69923),f2(x69921)))+E(f328(f328(f81(x69921),f328(f75(x69921),x69922)),f328(f75(x69921),x69923)),f328(f75(x69921),f328(f328(f81(x69921),x69922),x69923)))+~P1(f328(f328(f242(x69921),f2(x69921)),x69922)) % 167.77/167.51 [7046]~P134(x70461)+E(f328(f328(f81(x70461),f328(f75(x70461),x70462)),f328(f75(x70461),x70463)),f328(f75(x70461),f328(f328(f81(x70461),x70462),x70463)))+~P1(f328(f328(f242(x70461),f2(x70461)),x70462))+~P1(f328(f328(f242(x70461),f2(x70461)),x70463)) % 167.77/167.51 [7062]~P123(x70621)+~P1(f328(f328(f243(x70621),x70623),f2(x70621)))+~P1(f328(f328(f243(x70621),x70622),f2(x70621)))+P1(f328(f328(f243(x70621),f2(x70621)),f328(f328(f81(x70621),x70622),x70623))) % 167.77/167.51 [7063]~P62(x70631)+~P1(f328(f328(f243(x70631),x70633),f2(x70631)))+~P1(f328(f328(f243(x70631),x70632),f2(x70631)))+P1(f328(f328(f243(x70631),f2(x70631)),f328(f328(f286(x70631),x70632),x70633))) % 167.77/167.51 [7064]~P63(x70641)+~P1(f328(f328(f243(x70641),x70643),f2(x70641)))+~P1(f328(f328(f243(x70641),x70642),f2(x70641)))+P1(f328(f328(f243(x70641),f2(x70641)),f328(f328(f286(x70641),x70642),x70643))) % 167.77/167.51 [7066]~P110(x70661)+~P1(f328(f328(f242(x70661),x70663),f2(x70661)))+~P1(f328(f328(f242(x70661),x70662),f2(x70661)))+P1(f328(f328(f242(x70661),f2(x70661)),f328(f328(f81(x70661),x70662),x70663))) % 167.77/167.51 [7067]~P123(x70671)+~P1(f328(f328(f242(x70671),x70673),f2(x70671)))+~P1(f328(f328(f242(x70671),x70672),f2(x70671)))+P1(f328(f328(f242(x70671),f2(x70671)),f328(f328(f81(x70671),x70672),x70673))) % 167.77/167.51 [7068]~P62(x70681)+~P1(f328(f328(f242(x70681),x70683),f2(x70681)))+~P1(f328(f328(f242(x70681),x70682),f2(x70681)))+P1(f328(f328(f242(x70681),f2(x70681)),f328(f328(f286(x70681),x70682),x70683))) % 167.77/167.51 [7069]~P63(x70691)+~P1(f328(f328(f243(x70691),x70693),f2(x70691)))+~P1(f328(f328(f242(x70691),x70692),f2(x70691)))+P1(f328(f328(f242(x70691),f2(x70691)),f328(f328(f286(x70691),x70692),x70693))) % 167.77/167.51 [7070]~P116(x70701)+~P1(f328(f328(f243(a872),f2(a872)),x70703))+~P1(f328(f328(f243(x70701),f78(x70701)),x70702))+P1(f328(f328(f243(x70701),f78(x70701)),f328(f328(f253(x70701),x70702),x70703))) % 167.77/167.51 [7168]~P116(x71681)+~P1(f328(f328(f243(x71681),f78(x71681)),x71683))+~P1(f328(f328(f243(x71681),f78(x71681)),x71682))+P1(f328(f328(f243(x71681),f78(x71681)),f328(f328(f81(x71681),x71682),x71683))) % 167.77/167.51 [7169]~P86(x71691)+~P1(f328(f328(f243(x71691),f2(x71691)),x71693))+~P1(f328(f328(f243(x71691),f2(x71691)),x71692))+P1(f328(f328(f243(x71691),f2(x71691)),f328(f328(f80(x71691),x71692),x71693))) % 167.77/167.51 [7172]~P127(x71721)+~P1(f328(f328(f243(x71721),f2(x71721)),x71723))+~P1(f328(f328(f243(x71721),f2(x71721)),x71722))+P1(f328(f328(f243(x71721),f2(x71721)),f328(f328(f81(x71721),x71722),x71723))) % 167.77/167.51 [7173]~P62(x71731)+~P1(f328(f328(f243(x71731),f2(x71731)),x71733))+~P1(f328(f328(f243(x71731),f2(x71731)),x71732))+P1(f328(f328(f243(x71731),f2(x71731)),f328(f328(f286(x71731),x71732),x71733))) % 167.77/167.51 [7174]~P63(x71741)+~P1(f328(f328(f243(x71741),f2(x71741)),x71743))+~P1(f328(f328(f243(x71741),f2(x71741)),x71742))+P1(f328(f328(f243(x71741),f2(x71741)),f328(f328(f286(x71741),x71742),x71743))) % 167.77/167.51 [7176]~P110(x71761)+~P1(f328(f328(f242(x71761),f2(x71761)),x71763))+~P1(f328(f328(f242(x71761),f2(x71761)),x71762))+P1(f328(f328(f242(x71761),f2(x71761)),f328(f328(f81(x71761),x71762),x71763))) % 167.77/167.51 [7177]~P123(x71771)+~P1(f328(f328(f242(x71771),f2(x71771)),x71773))+~P1(f328(f328(f242(x71771),f2(x71771)),x71772))+P1(f328(f328(f242(x71771),f2(x71771)),f328(f328(f81(x71771),x71772),x71773))) % 167.77/167.51 [7178]~P131(x71781)+~P1(f328(f328(f242(x71781),f2(x71781)),x71783))+~P1(f328(f328(f242(x71781),f2(x71781)),x71782))+P1(f328(f328(f242(x71781),f2(x71781)),f328(f328(f81(x71781),x71782),x71783))) % 167.77/167.51 [7179]~P62(x71791)+~P1(f328(f328(f242(x71791),f2(x71791)),x71793))+~P1(f328(f328(f242(x71791),f2(x71791)),x71792))+P1(f328(f328(f242(x71791),f2(x71791)),f328(f328(f286(x71791),x71792),x71793))) % 167.77/167.51 [7180]~P63(x71801)+~P1(f328(f328(f243(x71801),f2(x71801)),x71803))+~P1(f328(f328(f242(x71801),f2(x71801)),x71802))+P1(f328(f328(f242(x71801),f2(x71801)),f328(f328(f286(x71801),x71802),x71803))) % 167.77/167.51 [7251]~P2(x72511)+~P1(f328(f38(x72511),x72513))+E(f13(x72511,f328(f328(f306(x72511),x72512),x72513)),x72512)+~E(f328(f328(f22(f879(x72511,a867)),x72513),f328(f328(f306(x72511),x72512),f192(f879(x72511,a867)))),f192(f879(x72511,a867))) % 167.77/167.51 [7252]~P2(x72521)+~P1(f328(f38(x72521),x72523))+E(f10(x72521,f328(f328(f306(x72521),x72522),x72523)),x72522)+~E(f328(f328(f22(f879(x72521,a867)),x72523),f328(f328(f306(x72521),x72522),f192(f879(x72521,a867)))),f192(f879(x72521,a867))) % 167.77/167.51 [7253]~P105(x72531)+~P1(f328(f38(x72531),x72533))+E(f14(x72531,f328(f328(f306(x72531),x72532),x72533)),x72532)+~E(f328(f328(f22(f879(x72531,a867)),x72533),f328(f328(f306(x72531),x72532),f192(f879(x72531,a867)))),f192(f879(x72531,a867))) % 167.77/167.51 [7254]~P105(x72541)+~P1(f328(f38(x72541),x72543))+E(f15(x72541,f328(f328(f306(x72541),x72542),x72543)),x72542)+~E(f328(f328(f22(f879(x72541,a867)),x72543),f328(f328(f306(x72541),x72542),f192(f879(x72541,a867)))),f192(f879(x72541,a867))) % 167.77/167.51 [7255]~P62(x72551)+P1(f328(f328(f243(x72551),x72552),f2(x72551)))+P1(f328(f328(f243(x72551),f2(x72551)),x72553))+~P1(f328(f328(f243(x72551),f2(x72551)),f328(f328(f286(x72551),x72553),x72552))) % 167.77/167.51 [7256]~P62(x72561)+P1(f328(f328(f243(x72561),x72562),f2(x72561)))+P1(f328(f328(f243(x72561),f2(x72561)),x72563))+~P1(f328(f328(f243(x72561),f2(x72561)),f328(f328(f286(x72561),x72562),x72563))) % 167.77/167.51 [7257]~P62(x72571)+P1(f328(f328(f243(x72571),x72572),f2(x72571)))+P1(f328(f328(f243(x72571),f2(x72571)),x72572))+~P1(f328(f328(f243(x72571),f2(x72571)),f328(f328(f286(x72571),x72573),x72572))) % 167.77/167.51 [7258]~P62(x72581)+P1(f328(f328(f243(x72581),x72582),f2(x72581)))+P1(f328(f328(f243(x72581),f2(x72581)),x72582))+~P1(f328(f328(f243(x72581),f2(x72581)),f328(f328(f286(x72581),x72582),x72583))) % 167.77/167.51 [7259]~P123(x72591)+P1(f328(f328(f242(x72591),x72592),f2(x72591)))+P1(f328(f328(f242(x72591),f2(x72591)),x72593))+~P1(f328(f328(f242(x72591),f2(x72591)),f328(f328(f81(x72591),x72593),x72592))) % 167.77/167.51 [7260]~P123(x72601)+P1(f328(f328(f242(x72601),x72602),f2(x72601)))+P1(f328(f328(f242(x72601),f2(x72601)),x72603))+~P1(f328(f328(f242(x72601),f2(x72601)),f328(f328(f81(x72601),x72602),x72603))) % 167.77/167.51 [7261]~P62(x72611)+P1(f328(f328(f242(x72611),x72612),f2(x72611)))+P1(f328(f328(f242(x72611),f2(x72611)),x72613))+~P1(f328(f328(f242(x72611),f2(x72611)),f328(f328(f286(x72611),x72613),x72612))) % 167.77/167.51 [7262]~P62(x72621)+P1(f328(f328(f242(x72621),x72622),f2(x72621)))+P1(f328(f328(f242(x72621),f2(x72621)),x72623))+~P1(f328(f328(f242(x72621),f2(x72621)),f328(f328(f286(x72621),x72622),x72623))) % 167.77/167.51 [7263]~P123(x72631)+P1(f328(f328(f242(x72631),x72632),f2(x72631)))+P1(f328(f328(f242(x72631),f2(x72631)),x72632))+~P1(f328(f328(f242(x72631),f2(x72631)),f328(f328(f81(x72631),x72633),x72632))) % 167.77/167.51 [7264]~P123(x72641)+P1(f328(f328(f242(x72641),x72642),f2(x72641)))+P1(f328(f328(f242(x72641),f2(x72641)),x72642))+~P1(f328(f328(f242(x72641),f2(x72641)),f328(f328(f81(x72641),x72642),x72643))) % 167.77/167.51 [7265]~P62(x72651)+P1(f328(f328(f242(x72651),x72652),f2(x72651)))+P1(f328(f328(f242(x72651),f2(x72651)),x72652))+~P1(f328(f328(f242(x72651),f2(x72651)),f328(f328(f286(x72651),x72653),x72652))) % 167.77/167.51 [7266]~P62(x72661)+P1(f328(f328(f242(x72661),x72662),f2(x72661)))+P1(f328(f328(f242(x72661),f2(x72661)),x72662))+~P1(f328(f328(f242(x72661),f2(x72661)),f328(f328(f286(x72661),x72662),x72663))) % 167.77/167.51 [7356]~E(f328(f328(f105(f879(x73561,a867)),f328(f170(x73561),x73562)),f328(f170(x73561),x73563)),f192(f879(x73561,a867)))+~P1(f328(f134(x73561),x73563))+~P1(f328(f134(x73561),x73562))+P1(f328(f134(x73561),f328(f328(f125(x73561),x73562),x73563))) % 167.77/167.51 [7357]~P105(x73571)+~P1(f328(f38(x73571),x73573))+E(f11(x73571,f240(x73571),f328(f328(f306(x73571),x73572),x73573)),x73572)+~E(f328(f328(f22(f879(x73571,a867)),x73573),f328(f328(f306(x73571),x73572),f192(f879(x73571,a867)))),f192(f879(x73571,a867))) % 167.77/167.51 [7358]~P105(x73581)+~P1(f328(f38(x73581),x73583))+E(f12(x73581,f241(x73581),f328(f328(f306(x73581),x73582),x73583)),x73582)+~E(f328(f328(f22(f879(x73581,a867)),x73583),f328(f328(f306(x73581),x73582),f192(f879(x73581,a867)))),f192(f879(x73581,a867))) % 167.77/167.51 [7373]~P117(x73731)+~P1(f328(f328(f243(x73731),x73732),x73733))+~P1(f328(f328(f243(x73731),f328(f79(x73731),x73732)),x73733))+P1(f328(f328(f243(x73731),f328(f75(x73731),x73732)),x73733)) % 167.77/167.51 [7375]~P84(x73751)+~P1(f328(f328(f242(x73751),x73752),x73753))+~P1(f328(f328(f242(x73751),f328(f79(x73751),x73752)),x73753))+P1(f328(f328(f242(x73751),f328(f75(x73751),x73752)),x73753)) % 167.77/167.51 [7445]~P127(x74451)+P1(f328(f328(f243(x74451),f2(x74451)),x74452))+~P1(f328(f328(f243(x74451),f2(x74451)),x74453))+~P1(f328(f328(f243(x74451),f2(x74451)),f328(f328(f81(x74451),x74453),x74452))) % 167.77/167.51 [7446]~P127(x74461)+P1(f328(f328(f243(x74461),f2(x74461)),x74462))+~P1(f328(f328(f243(x74461),f2(x74461)),x74463))+~P1(f328(f328(f243(x74461),f2(x74461)),f328(f328(f81(x74461),x74462),x74463))) % 167.77/167.51 [7750]E(x77501,x77502)+~P1(f328(f38(x77503),x77501))+~P1(f328(f328(f242(a872),f328(f39(x77503),x77501)),f328(f39(x77503),x77502)))+~P1(f328(f328(f242(f879(x77503,a867)),x77502),x77501)) % 167.77/167.51 [7896]~P1(f328(f328(f243(a1),x78961),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x78962))+~P1(f328(f328(f242(a1),x78962),x78963))+P1(f328(f328(f242(a1),f328(f328(f40(a1),x78961),x78962)),f328(f328(f40(a1),x78961),x78963))) % 167.77/167.51 [7908]~P1(f328(f328(f243(a1),f2(a1)),x79083))+~P1(f328(f328(f242(a1),f2(a1)),x79081))+~P1(f328(f328(f242(a1),x79083),x79082))+P1(f328(f328(f242(a1),f328(f328(f40(a1),x79081),x79082)),f328(f328(f40(a1),x79081),x79083))) % 167.77/167.51 [8040]E(f328(x80401,f451(x80402,x80401,x80403)),x80402)+~P1(f328(f328(f242(a1),x80402),f328(x80401,x80403)))+P1(f328(f328(f243(a872),f452(x80402,x80401,x80403)),x80403))+~P1(f328(f328(f242(a1),f328(x80401,f2(a872))),x80402)) % 167.77/167.51 [8041]E(f328(x80411,f455(x80412,x80411,x80413)),x80412)+~P1(f328(f328(f242(a1),x80412),f328(x80411,x80413)))+P1(f328(f328(f243(a872),f456(x80412,x80411,x80413)),x80413))+~P1(f328(f328(f242(a1),f328(x80411,f2(a872))),x80412)) % 167.77/167.51 [8146]~P1(f328(f38(x81461),x81463))+~P1(f328(f328(f243(a872),f328(f39(x81461),x81462)),f328(f39(x81461),x81463)))+~P1(f328(f328(f242(f879(x81461,a867)),x81462),x81463))+P1(f328(f328(f243(f879(x81461,a867)),x81462),x81463)) % 167.77/167.51 [8178]E(f328(f328(f80(a1),f400(x81783,x81781,x81782)),f401(x81783,x81781,x81782)),x81781)+E(f328(f328(f22(a1),x81781),x81782),x81781)+~P1(f328(f328(f243(a1),f2(a1)),x81782))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x81781),f78(a1))),x81783)) % 167.77/167.51 [8179]E(f328(f328(f22(a1),f414(x81793,x81791,x81792)),f415(x81793,x81791,x81792)),x81791)+E(f328(f328(f80(a1),x81791),x81792),x81791)+~P1(f328(f328(f243(a1),f2(a1)),x81792))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x81791),f78(a1))),x81793)) % 167.77/167.51 [8238]~P1(f328(f328(f242(a872),x82383),x82381))+P1(f328(f328(f243(a872),x82381),x82382))+~P1(f328(f328(f242(a872),x82383),x82382))+~P1(f328(f328(f243(a872),f328(f328(f22(a872),x82381),x82383)),f328(f328(f22(a872),x82382),x82383))) % 167.77/167.51 [8239]~P1(f328(f328(f242(a872),x82393),x82391))+P1(f328(f328(f242(a872),x82391),x82392))+~P1(f328(f328(f242(a872),x82393),x82392))+~P1(f328(f328(f242(a872),f328(f328(f22(a872),x82391),x82393)),f328(f328(f22(a872),x82392),x82393))) % 167.77/167.51 [8255]~P105(x82552)+E(x82551,f117(x82552))+~P15(x82552,f328(f166(x82552),x82551))+E(f328(f139(x82552,x82552,f328(f7(x82552,x82552,x82552),f241(x82552)),x82553),f328(f166(x82552),x82551)),f328(f328(f241(x82552),f328(f328(f162(x82552),x82551),f2(a872))),x82553)) % 167.77/167.51 [8320]E(f328(f328(f22(a1),x83201),x83202),x83201)+~P1(f328(f328(f243(a1),f2(a1)),x83202))+P1(f328(f328(f330(a1),f400(x83203,x83201,x83202)),x83203))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x83201),f78(a1))),x83203)) % 167.77/167.51 [8321]E(f328(f328(f80(a1),x83211),x83212),x83211)+~P1(f328(f328(f243(a1),f2(a1)),x83212))+P1(f328(f328(f330(a1),f414(x83213,x83211,x83212)),x83213))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x83211),f78(a1))),x83213)) % 167.77/167.51 [8396]~P1(f328(f328(f242(a1),x83961),f328(x83962,x83963)))+P1(f328(f328(f242(a872),f451(x83961,x83962,x83963)),x83963))+P1(f328(f328(f243(a872),f452(x83961,x83962,x83963)),x83963))+~P1(f328(f328(f242(a1),f328(x83962,f2(a872))),x83961)) % 167.77/167.51 [8397]~P1(f328(f328(f242(a1),x83971),f328(x83972,x83973)))+P1(f328(f328(f242(a872),f455(x83971,x83972,x83973)),x83973))+P1(f328(f328(f243(a872),f456(x83971,x83972,x83973)),x83973))+~P1(f328(f328(f242(a1),f328(x83972,f2(a872))),x83971)) % 167.77/167.51 [8470]E(f328(f328(f22(a1),x84701),x84702),x84701)+~P1(f328(f328(f243(a1),f2(a1)),x84702))+P1(f328(f328(f330(a1),f401(x84703,x84701,x84702)),f299(a1,f78(a1),x84702)))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x84701),f78(a1))),x84703)) % 167.77/167.51 [8471]E(f328(f328(f80(a1),x84711),x84712),x84711)+~P1(f328(f328(f243(a1),f2(a1)),x84712))+P1(f328(f328(f330(a1),f415(x84713,x84711,x84712)),f299(a1,f78(a1),x84712)))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x84711),f78(a1))),x84713)) % 167.77/167.51 [8606]~P116(x86061)+~P1(f328(f328(f243(x86061),x86062),f78(x86061)))+~P1(f328(f328(f243(x86061),f2(x86061)),x86062))+P1(f328(f328(f243(x86061),f328(f328(f81(x86061),x86062),f328(f328(f253(x86061),x86062),x86063))),f328(f328(f253(x86061),x86062),x86063))) % 167.77/167.51 [8692]~P1(f328(x86921,x86922))+P1(f328(x86921,f2(a872)))+~P1(f328(f328(f243(a872),x86922),x86923))+~P1(f328(x86921,f46(a872,f328(a116,f493(x86922,x86921,x86923)),x86923))) % 167.77/167.51 [8830]E(f518(x88301,x88302,x88303),f2(a872))+P1(f328(f328(x88301,x88303),x88302))+P1(f328(f328(x88301,f518(x88301,x88302,x88303)),f46(a872,f517(x88301,x88302,x88303),f518(x88301,x88302,x88303))))+~P1(f328(f316(f878(a872,a872),a226),f328(f328(f263(a872,a872),x88303),x88302))) % 167.77/167.51 [8868]~P26(x88681,x88681,x88682,x88683)+E(f328(f307(x88681,x88681,x88682),x88683),x88683)+~P1(f328(f38(x88681),x88683))+~P1(f328(f328(f242(f879(x88681,a867)),f328(f307(x88681,x88681,x88682),x88683)),x88683)) % 167.77/167.51 [9109]P1(f328(f328(x91091,x91092),x91093))+~P1(f328(f328(f243(a1),f514(x91091,x91093,x91092)),f2(a1)))+P1(f328(f328(x91091,f328(f79(a1),f513(x91091,x91093,x91092))),f328(f79(a1),f514(x91091,x91093,x91092))))+~P1(f328(f316(f878(a1,a1),a231),f328(f328(f263(a1,a1),x91092),x91093))) % 167.77/167.51 [9296]P1(f328(f328(x92961,x92962),x92963))+P1(f328(f328(x92961,f328(f328(f80(a1),f690(x92961,x92963,x92962)),f78(a1))),f692(x92961,x92963,x92962)))+~P1(f328(f328(f242(a1),f690(x92961,x92963,x92962)),f692(x92961,x92963,x92962)))+~P1(f328(f316(f878(a1,a1),a181),f328(f328(f263(a1,a1),x92962),x92963))) % 167.77/167.51 [9726]~P59(x97262)+~P59(x97261)+~P1(f328(f60(f878(x97261,x97262)),x97263))+P1(f328(f60(x97261),f328(f328(f8(f879(x97262,a867),a867,x97261),f60(x97262)),f328(f328(f8(f879(x97262,f878(x97261,x97262)),f879(x97262,a867),x97261),f328(f8(f878(x97261,x97262),a867,x97262),x97263)),f263(x97261,x97262))))) % 167.77/167.51 [9727]~P59(x97272)+~P59(x97271)+~P1(f328(f59(f878(x97271,x97272)),x97273))+P1(f328(f59(x97271),f328(f328(f8(f879(x97272,a867),a867,x97271),f59(x97272)),f328(f328(f8(f879(x97272,f878(x97271,x97272)),f879(x97272,a867),x97271),f328(f8(f878(x97271,x97272),a867,x97272),x97273)),f263(x97271,x97272))))) % 167.77/167.51 [9829]~P59(x98292)+~P59(x98291)+P1(f328(f60(f878(x98291,x98292)),x98293))+~P1(f328(f60(x98291),f328(f328(f8(f879(x98292,a867),a867,x98291),f60(x98292)),f328(f328(f8(f879(x98292,f878(x98291,x98292)),f879(x98292,a867),x98291),f328(f8(f878(x98291,x98292),a867,x98292),x98293)),f263(x98291,x98292))))) % 167.77/167.51 [9830]~P59(x98302)+~P59(x98301)+P1(f328(f59(f878(x98301,x98302)),x98303))+~P1(f328(f59(x98301),f328(f328(f8(f879(x98302,a867),a867,x98301),f59(x98302)),f328(f328(f8(f879(x98302,f878(x98301,x98302)),f879(x98302,a867),x98301),f328(f8(f878(x98301,x98302),a867,x98302),x98303)),f263(x98301,x98302))))) % 167.77/167.51 [9999]E(f328(x99991,f451(x99992,x99991,x99993)),x99992)+~P1(f328(f328(f242(a1),x99992),f328(x99991,x99993)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x99991,f328(f328(f80(a872),f452(x99992,x99991,x99993)),f78(a872)))),f328(x99991,f452(x99992,x99991,x99993))))),f78(a1)))+~P1(f328(f328(f242(a1),f328(x99991,f2(a872))),x99992)) % 167.77/167.51 [10000]E(f328(x100001,f455(x100002,x100001,x100003)),x100002)+~P1(f328(f328(f242(a1),x100002),f328(x100001,x100003)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x100001,f328(f328(f80(a872),f456(x100002,x100001,x100003)),f78(a872)))),f328(x100001,f456(x100002,x100001,x100003))))),f78(a1)))+~P1(f328(f328(f242(a1),f328(x100001,f2(a872))),x100002)) % 167.77/167.51 [10004]~P1(f328(f328(f242(a1),x100041),f328(x100042,x100043)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x100042,f328(f328(f80(a872),f452(x100041,x100042,x100043)),f78(a872)))),f328(x100042,f452(x100041,x100042,x100043))))),f78(a1)))+P1(f328(f328(f242(a872),f451(x100041,x100042,x100043)),x100043))+~P1(f328(f328(f242(a1),f328(x100042,f2(a872))),x100041)) % 167.77/167.51 [10005]~P1(f328(f328(f242(a1),x100051),f328(x100052,x100053)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x100052,f328(f328(f80(a872),f456(x100051,x100052,x100053)),f78(a872)))),f328(x100052,f456(x100051,x100052,x100053))))),f78(a1)))+P1(f328(f328(f242(a872),f455(x100051,x100052,x100053)),x100053))+~P1(f328(f328(f242(a1),f328(x100052,f2(a872))),x100051)) % 167.77/167.51 [10060]E(x100601,x100602)+~E(f328(f139(f873(x100603),f873(x100603),f125(x100603),f117(x100603)),x100601),f328(f139(f873(x100603),f873(x100603),f125(x100603),f117(x100603)),x100602))+~E(f328(f193(f873(f873(x100603))),x100601),f328(f193(f873(f873(x100603))),x100602))+~P1(f328(f328(f267(f873(x100603),f873(x100603),a867),f328(f328(f7(f873(x100603),f879(f873(x100603),a872),f879(f873(x100603),a867)),f328(f328(f8(f879(a872,a867),f879(f879(f873(x100603),a872),f879(f873(x100603),a867)),f873(x100603)),f8(a872,a867,f873(x100603))),f328(f328(f8(a872,f879(a872,a867),f873(x100603)),a325),f193(f873(x100603))))),f193(f873(x100603)))),f738(x100602,x100601,x100603))) % 167.77/167.51 [10061]E(x100611,x100612)+~E(f328(f139(f873(x100613),f873(x100613),f125(x100613),f117(x100613)),x100611),f328(f139(f873(x100613),f873(x100613),f125(x100613),f117(x100613)),x100612))+~E(f328(f193(f873(f873(x100613))),x100611),f328(f193(f873(f873(x100613))),x100612))+~P1(f328(f328(f267(f873(x100613),f873(x100613),a867),f328(f328(f7(f873(x100613),f879(f873(x100613),a872),f879(f873(x100613),a867)),f328(f328(f8(f879(a872,a867),f879(f879(f873(x100613),a872),f879(f873(x100613),a867)),f873(x100613)),f8(a872,a867,f873(x100613))),f328(f328(f8(a872,f879(a872,a867),f873(x100613)),a325),f193(f873(x100613))))),f193(f873(x100613)))),f739(x100611,x100612,x100613))) % 167.77/167.51 [6773]~E(f78(a872),f2(a872))+~P1(f328(f38(x67731),x67733))+~P1(f328(f38(x67731),x67732))+E(f328(f328(f80(a872),f328(f39(x67731),x67732)),f328(f39(x67731),x67733)),f328(f39(x67731),f328(f328(f114(f879(x67731,a867)),x67732),x67733))) % 167.77/167.51 [7187]~P100(x71871)+~P1(f328(f38(x71871),x71872))+~P1(f328(f328(f330(x71871),x71873),x71872))+P1(f328(f328(f242(x71871),f328(f64(x71871,f105(x71871)),x71872)),x71873)) % 167.77/167.51 [7188]~P105(x71881)+~P1(f328(f38(x71881),x71882))+~P1(f328(f328(f330(x71881),x71883),x71882))+P1(f328(f328(f242(x71881),f328(f64(x71881,f240(x71881)),x71882)),x71883)) % 167.77/167.51 [7439]~P1(f328(f38(x74391),x74393))+~P1(f328(f38(x74391),x74392))+~E(f328(f328(f105(f879(x74391,a867)),x74392),x74393),f192(f879(x74391,a867)))+E(f328(f328(f80(a872),f328(f39(x74391),x74392)),f328(f39(x74391),x74393)),f328(f39(x74391),f328(f328(f114(f879(x74391,a867)),x74392),x74393))) % 167.77/167.51 [8244]~P38(x82441,x82443)+~P38(x82441,x82442)+~E(f328(f328(f105(f879(x82441,a867)),f328(f261(x82441,x82441),x82442)),f328(f259(x82441,x82441),x82443)),f192(f879(x82441,a867)))+P38(x82441,f328(f328(f114(f879(f878(x82441,x82441),a867)),x82442),x82443)) % 167.77/167.51 [8335]E(x83351,f328(f328(f40(a872),x83352),x83353))+~P1(f328(f328(f243(a872),f2(a872)),x83353))+~P1(f328(f328(f243(a872),x83352),f328(f328(f81(a872),x83353),f328(a116,x83351))))+~P1(f328(f328(f242(a872),f328(f328(f81(a872),x83353),x83351)),x83352)) % 167.77/167.51 [8468]~P1(f328(f38(x84681),x84682))+~P1(f328(f38(x84681),x84683))+E(f328(f328(f80(a872),f328(f39(x84681),x84682)),f328(f39(x84681),x84683)),f328(f39(x84681),f328(f328(f114(f879(x84681,a867)),x84682),x84683)))+P1(f328(f328(f330(x84681),f856(x84683,x84682,x84681)),f328(f328(f105(f879(x84681,a867)),x84682),x84683))) % 167.77/167.51 [8842]~P123(x88422)+~E(x88421,f2(x88422))+~E(x88423,f2(x88422))+~P1(f328(f328(f243(x88422),f2(x88422)),f328(f328(f80(x88422),f328(f328(f81(x88422),x88423),x88423)),f328(f328(f81(x88422),x88421),x88421)))) % 167.77/167.51 [9375]~P38(x93751,x93753)+~P38(x93751,x93752)+P38(x93751,f328(f328(f114(f879(f878(x93751,x93751),a867)),x93752),x93753))+~P1(f328(f328(f242(f879(f878(x93751,x93751),a867)),f328(f328(f285(x93751,x93751,x93751),x93752),x93753)),x93752)) % 167.77/167.51 [9503]~P1(f328(x95031,x95033))+~P1(f328(f38(x95032),x95033))+P1(f328(x95031,f192(f879(x95032,a867))))+~P1(f328(x95031,f328(f328(f22(f879(x95032,a867)),f649(x95031,x95033,x95032)),f328(f328(f306(x95032),f629(x95031,x95033,x95032)),f192(f879(x95032,a867)))))) % 167.77/167.51 [9756]~P59(x97561)+~P59(x97562)+P12(x97561,f328(f328(f8(f879(x97562,x97561),a867,f873(x97561)),x97563),f328(f328(f8(f879(x97562,f876(x97561)),f879(x97562,x97561),f873(x97561)),f73(f876(x97561),x97561,x97562,f239(x97561))),f328(f328(f8(f873(f878(x97562,x97561)),f879(x97562,f876(x97561)),f873(x97561)),f176(x97562,x97561)),f328(f180(x97562,x97561),f57(x97562))))),f328(f193(f873(x97562)),f57(x97562)))+~P1(f328(f60(f879(x97562,x97561)),x97563)) % 167.77/167.51 [9757]~P59(x97571)+~P59(x97572)+P11(x97571,f328(f328(f8(f879(x97572,x97571),a867,f873(x97571)),x97573),f328(f328(f8(f879(x97572,f876(x97571)),f879(x97572,x97571),f873(x97571)),f73(f876(x97571),x97571,x97572,f239(x97571))),f328(f328(f8(f873(f878(x97572,x97571)),f879(x97572,f876(x97571)),f873(x97571)),f176(x97572,x97571)),f328(f180(x97572,x97571),f57(x97572))))),f328(f193(f873(x97572)),f57(x97572)))+~P1(f328(f59(f879(x97572,x97571)),x97573)) % 167.77/167.51 [9853]~P59(x98531)+~P59(x98532)+~P12(x98532,f328(f328(f8(f879(x98531,x98532),a867,f873(x98532)),x98533),f328(f328(f8(f879(x98531,f876(x98532)),f879(x98531,x98532),f873(x98532)),f73(f876(x98532),x98532,x98531,f239(x98532))),f328(f328(f8(f873(f878(x98531,x98532)),f879(x98531,f876(x98532)),f873(x98532)),f176(x98531,x98532)),f328(f180(x98531,x98532),f57(x98531))))),f328(f193(f873(x98531)),f57(x98531)))+P1(f328(f60(f879(x98531,x98532)),x98533)) % 167.77/167.51 [9854]~P59(x98541)+~P59(x98542)+~P11(x98542,f328(f328(f8(f879(x98541,x98542),a867,f873(x98542)),x98543),f328(f328(f8(f879(x98541,f876(x98542)),f879(x98541,x98542),f873(x98542)),f73(f876(x98542),x98542,x98541,f239(x98542))),f328(f328(f8(f873(f878(x98541,x98542)),f879(x98541,f876(x98542)),f873(x98542)),f176(x98541,x98542)),f328(f180(x98541,x98542),f57(x98541))))),f328(f193(f873(x98541)),f57(x98541)))+P1(f328(f59(f879(x98541,x98542)),x98543)) % 167.77/167.51 [8644]~P1(f328(f328(f243(a1),f2(a1)),x86443))+P1(f328(f328(f242(a1),f2(a1)),x86441))+~P1(f328(f328(f243(a1),x86442),x86443))+~P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),f328(f328(f81(a1),x86443),x86441)),x86442))) % 167.77/167.51 [8666]~P2(x86661)+~P1(f328(f38(x86661),x86662))+E(f328(f328(f22(f879(x86661,a867)),x86662),f328(f328(f306(x86661),x86663),f192(f879(x86661,a867)))),f192(f879(x86661,a867)))+E(f328(f328(f114(x86661),x86663),f13(x86661,f328(f328(f22(f879(x86661,a867)),x86662),f328(f328(f306(x86661),x86663),f192(f879(x86661,a867)))))),f13(x86661,f328(f328(f306(x86661),x86663),x86662))) % 167.77/167.51 [8667]~P2(x86671)+~P1(f328(f38(x86671),x86672))+E(f328(f328(f22(f879(x86671,a867)),x86672),f328(f328(f306(x86671),x86673),f192(f879(x86671,a867)))),f192(f879(x86671,a867)))+E(f328(f328(f105(x86671),x86673),f10(x86671,f328(f328(f22(f879(x86671,a867)),x86672),f328(f328(f306(x86671),x86673),f192(f879(x86671,a867)))))),f10(x86671,f328(f328(f306(x86671),x86673),x86672))) % 167.77/167.51 [8668]~P105(x86681)+~P1(f328(f38(x86681),x86682))+E(f328(f328(f22(f879(x86681,a867)),x86682),f328(f328(f306(x86681),x86683),f192(f879(x86681,a867)))),f192(f879(x86681,a867)))+E(f328(f328(f240(x86681),x86683),f14(x86681,f328(f328(f22(f879(x86681,a867)),x86682),f328(f328(f306(x86681),x86683),f192(f879(x86681,a867)))))),f14(x86681,f328(f328(f306(x86681),x86683),x86682))) % 167.77/167.51 [8669]~P105(x86691)+~P1(f328(f38(x86691),x86692))+E(f328(f328(f22(f879(x86691,a867)),x86692),f328(f328(f306(x86691),x86693),f192(f879(x86691,a867)))),f192(f879(x86691,a867)))+E(f328(f328(f241(x86691),x86693),f15(x86691,f328(f328(f22(f879(x86691,a867)),x86692),f328(f328(f306(x86691),x86693),f192(f879(x86691,a867)))))),f15(x86691,f328(f328(f306(x86691),x86693),x86692))) % 167.77/167.51 [8733]~P105(x87331)+~P1(f328(f38(x87331),x87332))+E(f328(f328(f22(f879(x87331,a867)),x87332),f328(f328(f306(x87331),x87333),f192(f879(x87331,a867)))),f192(f879(x87331,a867)))+E(f328(f328(f240(x87331),x87333),f11(x87331,f240(x87331),f328(f328(f22(f879(x87331,a867)),x87332),f328(f328(f306(x87331),x87333),f192(f879(x87331,a867)))))),f11(x87331,f240(x87331),f328(f328(f306(x87331),x87333),x87332))) % 167.77/167.51 [8734]~P105(x87341)+~P1(f328(f38(x87341),x87342))+E(f328(f328(f22(f879(x87341,a867)),x87342),f328(f328(f306(x87341),x87343),f192(f879(x87341,a867)))),f192(f879(x87341,a867)))+E(f328(f328(f241(x87341),x87343),f12(x87341,f241(x87341),f328(f328(f22(f879(x87341,a867)),x87342),f328(f328(f306(x87341),x87343),f192(f879(x87341,a867)))))),f12(x87341,f241(x87341),f328(f328(f306(x87341),x87343),x87342))) % 167.77/167.51 [9316]E(x93161,x93162)+~E(f328(f139(f873(x93163),f873(x93163),f125(x93163),f117(x93163)),x93161),f328(f139(f873(x93163),f873(x93163),f125(x93163),f117(x93163)),x93162))+~E(f328(f193(f873(f873(x93163))),x93161),f328(f193(f873(f873(x93163))),x93162))+P1(f328(f328(f330(f878(f873(x93163),f873(x93163))),f738(x93162,x93161,x93163)),f328(f170(f878(f873(x93163),f873(x93163))),f328(f328(f180(f873(x93163),f873(x93163)),x93161),x93162)))) % 167.77/167.51 [9317]E(x93171,x93172)+~E(f328(f139(f873(x93173),f873(x93173),f125(x93173),f117(x93173)),x93171),f328(f139(f873(x93173),f873(x93173),f125(x93173),f117(x93173)),x93172))+~E(f328(f193(f873(f873(x93173))),x93171),f328(f193(f873(f873(x93173))),x93172))+P1(f328(f328(f330(f878(f873(x93173),f873(x93173))),f739(x93171,x93172,x93173)),f328(f170(f878(f873(x93173),f873(x93173))),f328(f328(f180(f873(x93173),f873(x93173)),x93172),x93171)))) % 167.77/167.51 [10145]~P98(x101452)+E(x101451,f192(f879(x101452,a867)))+~P1(f328(f38(x101452),x101451))+E(f10(x101452,f328(f248(x101452),f328(f328(f8(f879(x101452,a867),a867,x101452),f87(x101452)),f328(f328(f7(x101452,f879(x101452,a867),f879(x101452,a867)),f328(f328(f8(f879(x101452,f879(a867,a867)),f879(f879(x101452,a867),f879(x101452,a867)),x101452),f18(x101452,a867,a867)),f328(f328(f8(f879(x101452,a867),f879(x101452,f879(a867,a867)),x101452),f328(f8(a867,f879(a867,a867),x101452),a326)),f328(f328(f7(x101452,f879(x101452,x101452),f879(x101452,a867)),f328(f328(f8(f879(x101452,a867),f879(f879(x101452,x101452),f879(x101452,a867)),x101452),f8(x101452,a867,x101452)),a325)),f328(f114(x101452),x101453))))),f328(f328(f7(x101452,f879(x101452,a867),a867),f330(x101452)),x101451))))),f328(f328(f114(x101452),x101453),f10(x101452,x101451))) % 167.77/167.51 [10146]~P98(x101462)+E(x101461,f192(f879(x101462,a867)))+~P1(f328(f38(x101462),x101461))+E(f13(x101462,f328(f248(x101462),f328(f328(f8(f879(x101462,a867),a867,x101462),f87(x101462)),f328(f328(f7(x101462,f879(x101462,a867),f879(x101462,a867)),f328(f328(f8(f879(x101462,f879(a867,a867)),f879(f879(x101462,a867),f879(x101462,a867)),x101462),f18(x101462,a867,a867)),f328(f328(f8(f879(x101462,a867),f879(x101462,f879(a867,a867)),x101462),f328(f8(a867,f879(a867,a867),x101462),a326)),f328(f328(f7(x101462,f879(x101462,x101462),f879(x101462,a867)),f328(f328(f8(f879(x101462,a867),f879(f879(x101462,x101462),f879(x101462,a867)),x101462),f8(x101462,a867,x101462)),a325)),f328(f105(x101462),x101463))))),f328(f328(f7(x101462,f879(x101462,a867),a867),f330(x101462)),x101461))))),f328(f328(f105(x101462),x101463),f13(x101462,x101461))) % 167.77/167.51 [10147]~P76(x101472)+E(x101471,f192(f879(x101472,a867)))+~P1(f328(f38(x101472),x101471))+E(f14(x101472,f328(f248(x101472),f328(f328(f8(f879(x101472,a867),a867,x101472),f87(x101472)),f328(f328(f7(x101472,f879(x101472,a867),f879(x101472,a867)),f328(f328(f8(f879(x101472,f879(a867,a867)),f879(f879(x101472,a867),f879(x101472,a867)),x101472),f18(x101472,a867,a867)),f328(f328(f8(f879(x101472,a867),f879(x101472,f879(a867,a867)),x101472),f328(f8(a867,f879(a867,a867),x101472),a326)),f328(f328(f7(x101472,f879(x101472,x101472),f879(x101472,a867)),f328(f328(f8(f879(x101472,a867),f879(f879(x101472,x101472),f879(x101472,a867)),x101472),f8(x101472,a867,x101472)),a325)),f328(f80(x101472),x101473))))),f328(f328(f7(x101472,f879(x101472,a867),a867),f330(x101472)),x101471))))),f328(f328(f80(x101472),x101473),f14(x101472,x101471))) % 167.77/167.51 [10148]~P76(x101482)+E(x101481,f192(f879(x101482,a867)))+~P1(f328(f38(x101482),x101481))+E(f15(x101482,f328(f248(x101482),f328(f328(f8(f879(x101482,a867),a867,x101482),f87(x101482)),f328(f328(f7(x101482,f879(x101482,a867),f879(x101482,a867)),f328(f328(f8(f879(x101482,f879(a867,a867)),f879(f879(x101482,a867),f879(x101482,a867)),x101482),f18(x101482,a867,a867)),f328(f328(f8(f879(x101482,a867),f879(x101482,f879(a867,a867)),x101482),f328(f8(a867,f879(a867,a867),x101482),a326)),f328(f328(f7(x101482,f879(x101482,x101482),f879(x101482,a867)),f328(f328(f8(f879(x101482,a867),f879(f879(x101482,x101482),f879(x101482,a867)),x101482),f8(x101482,a867,x101482)),a325)),f328(f80(x101482),x101483))))),f328(f328(f7(x101482,f879(x101482,a867),a867),f330(x101482)),x101481))))),f328(f328(f80(x101482),x101483),f15(x101482,x101481))) % 167.77/167.51 [10149]~P105(x101492)+E(x101491,f192(f879(x101492,a867)))+~P1(f328(f38(x101492),x101491))+E(f12(x101492,f241(x101492),f328(f248(x101492),f328(f328(f8(f879(x101492,a867),a867,x101492),f87(x101492)),f328(f328(f7(x101492,f879(x101492,a867),f879(x101492,a867)),f328(f328(f8(f879(x101492,f879(a867,a867)),f879(f879(x101492,a867),f879(x101492,a867)),x101492),f18(x101492,a867,a867)),f328(f328(f8(f879(x101492,a867),f879(x101492,f879(a867,a867)),x101492),f328(f8(a867,f879(a867,a867),x101492),a326)),f328(f328(f7(x101492,f879(x101492,x101492),f879(x101492,a867)),f328(f328(f8(f879(x101492,a867),f879(f879(x101492,x101492),f879(x101492,a867)),x101492),f8(x101492,a867,x101492)),a325)),f328(f240(x101492),x101493))))),f328(f328(f7(x101492,f879(x101492,a867),a867),f330(x101492)),x101491))))),f328(f328(f240(x101492),x101493),f12(x101492,f241(x101492),x101491))) % 167.77/167.51 [10150]~P105(x101502)+E(x101501,f192(f879(x101502,a867)))+~P1(f328(f38(x101502),x101501))+E(f11(x101502,f240(x101502),f328(f248(x101502),f328(f328(f8(f879(x101502,a867),a867,x101502),f87(x101502)),f328(f328(f7(x101502,f879(x101502,a867),f879(x101502,a867)),f328(f328(f8(f879(x101502,f879(a867,a867)),f879(f879(x101502,a867),f879(x101502,a867)),x101502),f18(x101502,a867,a867)),f328(f328(f8(f879(x101502,a867),f879(x101502,f879(a867,a867)),x101502),f328(f8(a867,f879(a867,a867),x101502),a326)),f328(f328(f7(x101502,f879(x101502,x101502),f879(x101502,a867)),f328(f328(f8(f879(x101502,a867),f879(f879(x101502,x101502),f879(x101502,a867)),x101502),f8(x101502,a867,x101502)),a325)),f328(f241(x101502),x101503))))),f328(f328(f7(x101502,f879(x101502,a867),a867),f330(x101502)),x101501))))),f328(f328(f241(x101502),x101503),f11(x101502,f240(x101502),x101501))) % 167.77/167.51 [9903]~P117(x99031)+~E(x99033,f2(x99031))+~E(x99032,f2(x99031))+E(f328(f328(f80(x99031),f328(f328(f253(x99031),x99032),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x99031),x99033),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f2(x99031)) % 167.77/167.51 [10045]~P116(x100451)+~P1(f328(f328(f242(x100451),f2(x100451)),x100453))+P1(f328(f328(f242(x100451),x100452),x100453))+~P1(f328(f328(f242(x100451),f328(f328(f253(x100451),x100452),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100451),x100453),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 167.77/167.51 [10091]~P117(x100912)+~E(x100911,f2(x100912))+~E(x100913,f2(x100912))+~P1(f328(f328(f243(x100912),f2(x100912)),f328(f328(f80(x100912),f328(f328(f253(x100912),x100913),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100912),x100911),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))) % 167.77/167.51 [9278]E(x92781,x92782)+~E(f671(x92781,x92782,x92784,x92783),f672(x92781,x92782,x92784,x92783))+P1(f328(f328(f330(f878(f873(x92783),f873(x92783))),f328(f328(f263(f873(x92783),f873(x92783)),x92782),x92781)),f144(x92783,x92784)))+P1(f328(f328(f330(f878(f873(x92783),f873(x92783))),f328(f328(f263(f873(x92783),f873(x92783)),x92781),x92782)),f144(x92783,x92784))) % 167.77/167.51 [4831]~P60(x48312)+~E(x48314,f2(x48312))+~E(x48311,f2(x48312))+E(x48311,f328(f328(f286(x48312),x48313),x48314)) % 167.77/167.51 [4832]~P60(x48321)+~E(x48323,f2(x48321))+~E(x48324,f2(x48321))+E(f328(f328(f286(x48321),x48322),x48323),x48324) % 167.77/167.51 [4941]~P60(x49412)+E(x49411,f2(x49412))+~E(x49413,f2(x49412))+~E(x49411,f328(f328(f286(x49412),x49414),x49413)) % 167.77/167.51 [4942]~P60(x49422)+E(x49421,f2(x49422))+~E(x49423,f2(x49422))+~E(f328(f328(f286(x49422),x49424),x49423),x49421) % 167.77/167.51 [5120]~P120(x51202)+E(x51201,f2(x51202))+~E(f328(f328(f286(x51202),x51203),x51201),x51204)+E(x51203,f328(f328(f81(x51202),x51204),x51201)) % 167.77/167.51 [5122]~P120(x51222)+E(x51221,f2(x51222))+~E(f328(f328(f81(x51222),x51223),x51221),x51224)+E(x51223,f328(f328(f286(x51222),x51224),x51221)) % 167.77/167.51 [5123]~P60(x51232)+E(x51231,f2(x51232))+~E(f328(f328(f286(x51232),x51233),x51231),x51234)+E(x51233,f328(f328(f81(x51232),x51234),x51231)) % 167.77/167.51 [5124]~P60(x51242)+E(x51241,f2(x51242))+~E(f328(f328(f81(x51242),x51243),x51241),x51244)+E(x51243,f328(f328(f286(x51242),x51244),x51241)) % 167.77/167.51 [5125]~P120(x51252)+E(x51251,f2(x51252))+~E(x51253,f328(f328(f286(x51252),x51254),x51251))+E(f328(f328(f81(x51252),x51253),x51251),x51254) % 167.77/167.51 [5127]~P120(x51272)+E(x51271,f2(x51272))+~E(x51273,f328(f328(f81(x51272),x51274),x51271))+E(f328(f328(f286(x51272),x51273),x51271),x51274) % 167.77/167.51 [5128]~P60(x51282)+E(x51281,f2(x51282))+~E(x51283,f328(f328(f286(x51282),x51284),x51281))+E(f328(f328(f81(x51282),x51283),x51281),x51284) % 167.77/167.51 [5129]~P60(x51292)+E(x51291,f2(x51292))+~E(x51293,f328(f328(f81(x51292),x51294),x51291))+E(f328(f328(f286(x51292),x51293),x51291),x51294) % 167.77/167.51 [5161]~P60(x51612)+~E(x51611,f2(x51612))+~E(f328(f328(f81(x51612),x51611),x51614),x51613)+E(x51611,f328(f328(f286(x51612),x51613),x51614)) % 167.77/167.51 [5162]~P60(x51621)+~E(x51624,f2(x51621))+~E(x51622,f328(f328(f81(x51621),x51624),x51623))+E(f328(f328(f286(x51621),x51622),x51623),x51624) % 167.77/167.51 [5235]~E(x52353,x52354)+~E(x52352,x52353)+~P107(x52351)+E(f299(x52351,x52352,x52353),f328(f328(f306(x52351),x52354),f192(f879(x52351,a867)))) % 167.77/167.51 [5441]~E(f118(x54412,x54411),x54413)+~E(f141(x54412,x54411),x54414)+E(x54411,f117(x54412))+E(f328(f328(f125(x54412),x54413),f328(f328(f148(x54412),x54414),f117(x54412))),x54411) % 167.77/167.51 [6053]~P116(x60533)+E(x60531,x60532)+~E(f328(f328(f253(x60533),x60534),x60531),f328(f328(f253(x60533),x60534),x60532))+~P1(f328(f328(f243(x60533),f78(x60533)),x60534)) % 167.77/167.51 [6054]E(x60541,x60542)+~E(f328(f328(f306(x60543),x60544),x60541),f328(f328(f306(x60543),x60544),x60542))+P1(f328(f328(f330(x60543),x60544),x60542))+P1(f328(f328(f330(x60543),x60544),x60541)) % 167.77/167.51 [6092]E(f328(x60921,x60922),f78(a872))+~E(f328(f328(f9(x60923,a872),x60921),x60924),f78(a872))+~P1(f328(f38(x60923),x60924))+~P1(f328(f328(f330(x60923),x60922),x60924)) % 167.77/167.51 [6093]E(f328(x60931,x60932),f2(a872))+~E(f328(f328(f6(x60933,a872),x60931),x60934),f2(a872))+~P1(f328(f38(x60933),x60934))+~P1(f328(f328(f330(x60933),x60932),x60934)) % 167.77/167.51 [6316]~P107(x63161)+~P1(f328(f328(f243(x63161),x63164),x63163))+P1(f328(f328(f243(x63161),x63162),x63163))+~P1(f328(f328(f243(x63161),x63162),x63164)) % 167.77/167.51 [6317]~P107(x63171)+~P1(f328(f328(f242(x63171),x63174),x63173))+P1(f328(f328(f243(x63171),x63172),x63173))+~P1(f328(f328(f243(x63171),x63172),x63174)) % 167.77/167.51 [6318]~P107(x63181)+~P1(f328(f328(f242(x63181),x63182),x63184))+P1(f328(f328(f243(x63181),x63182),x63183))+~P1(f328(f328(f243(x63181),x63184),x63183)) % 167.77/167.51 [6319]~P106(x63191)+~P1(f328(f328(f243(x63191),x63192),x63194))+P1(f328(f328(f243(x63191),x63192),x63193))+~P1(f328(f328(f243(x63191),x63194),x63193)) % 167.77/167.51 [6320]~P106(x63201)+~P1(f328(f328(f242(x63201),x63202),x63204))+P1(f328(f328(f243(x63201),x63202),x63203))+~P1(f328(f328(f243(x63201),x63204),x63203)) % 167.77/167.51 [6321]~P106(x63211)+~P1(f328(f328(f242(x63211),x63214),x63213))+P1(f328(f328(f243(x63211),x63212),x63213))+~P1(f328(f328(f243(x63211),x63212),x63214)) % 167.77/167.51 [6322]~P107(x63221)+~P1(f328(f328(f242(x63221),x63224),x63223))+P1(f328(f328(f242(x63221),x63222),x63223))+~P1(f328(f328(f242(x63221),x63222),x63224)) % 167.77/167.51 [6323]~P106(x63231)+~P1(f328(f328(f242(x63231),x63232),x63234))+P1(f328(f328(f242(x63231),x63232),x63233))+~P1(f328(f328(f242(x63231),x63234),x63233)) % 167.77/167.51 [6403]~P36(x64034,x64033,x64032)+E(x64031,f805(x64032,x64033,x64034))+~P1(f328(x64033,x64031))+~P1(f328(f328(f330(x64034),x64031),f328(f170(x64034),x64032))) % 167.77/167.51 [6547]~P4(x65471)+~P1(f328(f328(f242(x65471),x65472),f42(x65471,x65474)))+P1(f328(f328(f242(x65471),x65472),x65473))+~P1(f328(f328(f330(x65471),x65473),x65474)) % 167.77/167.51 [6694]~P105(x66941)+~P15(x66941,f328(f328(f148(x66941),x66942),x66944))+~P1(f328(f328(f330(x66941),x66943),f328(f170(x66941),x66944)))+P1(f328(f328(f242(x66941),x66942),x66943)) % 167.77/167.51 [6784]~P4(x67841)+~P1(f328(f328(f242(x67841),f41(x67841,x67844)),x67843))+P1(f328(f328(f242(x67841),x67842),x67843))+~P1(f328(f328(f330(x67841),x67842),x67844)) % 167.77/167.51 [7190]~P105(x71901)+E(f328(f328(f114(f879(x71901,a867)),f328(f298(x71901,x71902),x71903)),f328(f298(x71901,x71903),x71904)),f328(f298(x71901,x71902),x71904))+~P1(f328(f328(f242(x71901),x71903),x71904))+~P1(f328(f328(f242(x71901),x71902),x71903)) % 167.77/167.51 [7227]P36(x72271,x72272,x72273)+~E(f809(x72273,x72272,x72271,x72274),x72274)+~P1(f328(x72272,x72274))+~P1(f328(f328(f330(x72271),x72274),f328(f170(x72271),x72273))) % 167.77/167.51 [7301]~P105(x73011)+E(f328(f328(f114(f879(x73011,a867)),f328(f298(x73011,x73012),x73013)),f299(x73011,x73013,x73014)),f299(x73011,x73012,x73014))+~P1(f328(f328(f242(x73011),x73013),x73014))+~P1(f328(f328(f242(x73011),x73012),x73013)) % 167.77/167.51 [7367]~P105(x73671)+E(f328(f328(f114(f879(x73671,a867)),f302(x73671,x73672,x73673)),f328(f298(x73671,x73673),x73674)),f302(x73671,x73672,x73674))+~P1(f328(f328(f243(x73671),x73672),x73673))+~P1(f328(f328(f242(x73671),x73673),x73674)) % 167.77/167.51 [7387]~P105(x73871)+E(f328(f328(f114(f879(x73871,a867)),f299(x73871,x73872,x73873)),f302(x73871,x73873,x73874)),f328(f298(x73871,x73872),x73874))+~P1(f328(f328(f243(x73871),x73873),x73874))+~P1(f328(f328(f242(x73871),x73872),x73873)) % 167.77/167.51 [7419]~P105(x74191)+E(f328(f328(f114(f879(x74191,a867)),f302(x74191,x74192,x74193)),f299(x74191,x74193,x74194)),f301(x74191,x74192,x74194))+~P1(f328(f328(f243(x74191),x74192),x74193))+~P1(f328(f328(f242(x74191),x74193),x74194)) % 167.77/167.51 [7420]~P105(x74201)+E(f328(f328(f114(f879(x74201,a867)),f301(x74201,x74202,x74203)),f302(x74201,x74203,x74204)),f302(x74201,x74202,x74204))+~P1(f328(f328(f243(x74201),x74203),x74204))+~P1(f328(f328(f242(x74201),x74202),x74203)) % 167.77/167.51 [7421]~P105(x74211)+E(f328(f328(f114(f879(x74211,a867)),f301(x74211,x74212,x74213)),f301(x74211,x74213,x74214)),f301(x74211,x74212,x74214))+~P1(f328(f328(f242(x74211),x74213),x74214))+~P1(f328(f328(f242(x74211),x74212),x74213)) % 167.77/167.51 [7422]~P105(x74221)+E(f328(f328(f114(f879(x74221,a867)),f299(x74221,x74222,x74223)),f301(x74221,x74223,x74224)),f299(x74221,x74222,x74224))+~P1(f328(f328(f242(x74221),x74223),x74224))+~P1(f328(f328(f242(x74221),x74222),x74223)) % 167.77/167.51 [8228]P26(x82281,x82282,f544(x82283,x82282,x82284,x82281),x82284)+~P1(f328(f38(x82282),x82283))+~P1(f328(f38(x82281),x82284))+~P1(f328(f328(f242(a872),f328(f39(x82281),x82284)),f328(f39(x82282),x82283))) % 167.77/167.51 [8249]P36(x82491,x82492,x82493)+~P1(f328(x82492,x82494))+P1(f328(x82492,f809(x82493,x82492,x82491,x82494)))+~P1(f328(f328(f330(x82491),x82494),f328(f170(x82491),x82493))) % 167.77/167.51 [8299]~P73(x82991)+~E(f328(x82993,f492(x82993,x82994,x82992,x82991)),f78(x82991))+E(f328(f328(f328(f66(x82991,x82992,f81(x82991)),x82993),f78(x82991)),x82994),f78(x82991))+~P1(f328(f38(x82992),x82994)) % 167.77/167.51 [8573]~P116(x85731)+~P1(f328(f328(f242(x85731),f2(x85731)),x85733))+P1(f328(f328(f242(x85731),x85732),x85733))+~P1(f328(f328(f242(x85731),f328(f328(f253(x85731),x85732),f328(a116,x85734))),f328(f328(f253(x85731),x85733),f328(a116,x85734)))) % 167.77/167.51 [8869]P36(x88691,x88692,x88693)+~P1(f328(x88692,x88694))+~P1(f328(f328(f330(x88691),x88694),f328(f170(x88691),x88693)))+P1(f328(f328(f330(x88691),f809(x88693,x88692,x88691,x88694)),f328(f170(x88691),x88693))) % 167.77/167.51 [8955]~P73(x89551)+E(f328(f328(f328(f66(x89551,x89552,f81(x89551)),x89553),f78(x89551)),x89554),f78(x89551))+~P1(f328(f38(x89552),x89554))+P1(f328(f328(f330(x89552),f492(x89553,x89554,x89552,x89551)),x89554)) % 167.77/167.51 [9442]~P1(f328(f328(f242(a1),x94424),f2(a1)))+P1(f328(f328(f242(a1),f328(f328(f80(a1),f328(f328(f81(a1),x94421),f46(a1,x94422,x94423))),x94424)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x94423))+~P1(f328(f328(f243(a1),x94421),x94424)) % 167.77/167.51 [9896]~P1(f328(f38(x98961),x98962))+~P1(f328(f328(f330(x98961),x98964),x98962))+~P1(f328(f328(f330(x98961),x98963),x98962))+P1(f328(f328(f243(a872),f328(f39(x98961),f328(f328(f22(f879(x98961,a867)),f328(f328(f22(f879(x98961,a867)),x98962),f328(f328(f306(x98961),x98963),f192(f879(x98961,a867))))),f328(f328(f306(x98961),x98964),f192(f879(x98961,a867)))))),f328(f39(x98961),x98962))) % 167.77/167.51 [6898]~P105(x68981)+~P1(f328(f328(f243(x68981),x68982),x68984))+~P1(f328(f328(f243(x68981),x68982),x68983))+P1(f328(f328(f243(x68981),x68982),f328(f328(f240(x68981),x68983),x68984))) % 167.77/167.51 [6901]~P100(x69011)+~P1(f328(f328(f242(x69011),x69012),x69014))+~P1(f328(f328(f242(x69011),x69012),x69013))+P1(f328(f328(f242(x69011),x69012),f328(f328(f105(x69011),x69013),x69014))) % 167.77/167.51 [6904]~P105(x69041)+~P1(f328(f328(f242(x69041),x69042),x69044))+~P1(f328(f328(f242(x69041),x69042),x69043))+P1(f328(f328(f242(x69041),x69042),f328(f328(f240(x69041),x69043),x69044))) % 167.77/167.51 [6923]~P61(x69232)+E(x69231,f2(x69232))+E(f328(f328(f286(x69232),f328(f328(f253(x69232),x69231),x69233)),f328(f328(f253(x69232),x69231),x69234)),f328(f328(f253(x69232),x69231),f328(f328(f22(a872),x69233),x69234)))+~P1(f328(f328(f242(a872),x69234),x69233)) % 167.77/167.51 [6968]~P105(x69681)+~P15(x69681,f328(f328(f148(x69681),x69683),x69684))+P15(x69681,f328(f328(f148(x69681),x69682),f328(f328(f148(x69681),x69683),x69684)))+~P1(f328(f328(f242(x69681),x69682),x69683)) % 167.77/167.51 [7007]~P116(x70071)+~P1(f328(f328(f243(x70071),f2(x70071)),x70073))+~P1(f328(f328(f243(x70071),x70072),x70074))+P1(f328(f328(f243(x70071),x70072),f328(f328(f80(x70071),x70073),x70074))) % 167.77/167.51 [7008]~P86(x70081)+~P1(f328(f328(f242(x70081),f2(x70081)),x70083))+~P1(f328(f328(f243(x70081),x70082),x70084))+P1(f328(f328(f243(x70081),x70082),f328(f328(f80(x70081),x70083),x70084))) % 167.77/167.51 [7009]~P86(x70091)+~P1(f328(f328(f242(x70091),x70092),x70094))+~P1(f328(f328(f243(x70091),f2(x70091)),x70093))+P1(f328(f328(f243(x70091),x70092),f328(f328(f80(x70091),x70093),x70094))) % 167.77/167.51 [7010]~P86(x70101)+~P1(f328(f328(f242(x70101),f2(x70101)),x70104))+~P1(f328(f328(f242(x70101),x70102),x70103))+P1(f328(f328(f242(x70101),x70102),f328(f328(f80(x70101),x70103),x70104))) % 167.77/167.51 [7011]~P86(x70111)+~P1(f328(f328(f242(x70111),f2(x70111)),x70113))+~P1(f328(f328(f242(x70111),x70112),x70114))+P1(f328(f328(f242(x70111),x70112),f328(f328(f80(x70111),x70113),x70114))) % 167.77/167.51 [7050]~P105(x70501)+P1(f328(f328(f243(x70501),x70502),x70503))+P1(f328(f328(f243(x70501),x70502),x70504))+~P1(f328(f328(f243(x70501),x70502),f328(f328(f241(x70501),x70504),x70503))) % 167.77/167.51 [7051]~P105(x70511)+P1(f328(f328(f242(x70511),x70512),x70513))+P1(f328(f328(f242(x70511),x70512),x70514))+~P1(f328(f328(f242(x70511),x70512),f328(f328(f241(x70511),x70514),x70513))) % 167.77/167.51 [7340]~P107(x73402)+~P59(x73401)+~P1(f328(f328(f243(f879(x73401,x73402)),x73403),x73404))+P1(f328(f328(f242(f879(x73401,x73402)),x73403),x73404)) % 167.77/167.51 [7710]~P63(x77101)+~P1(f328(f328(f243(x77101),x77104),f2(x77101)))+~P1(f328(f328(f243(x77101),x77103),f328(f328(f286(x77101),x77102),x77104)))+P1(f328(f328(f243(x77101),x77102),f328(f328(f81(x77101),x77103),x77104))) % 167.77/167.51 [7711]~P63(x77111)+~P1(f328(f328(f243(x77111),x77114),f2(x77111)))+~P1(f328(f328(f243(x77111),x77113),f328(f328(f81(x77111),x77112),x77114)))+P1(f328(f328(f243(x77111),x77112),f328(f328(f286(x77111),x77113),x77114))) % 167.77/167.51 [7712]~P63(x77121)+~P1(f328(f328(f243(x77121),x77124),f2(x77121)))+~P1(f328(f328(f242(x77121),x77123),f328(f328(f286(x77121),x77122),x77124)))+P1(f328(f328(f242(x77121),x77122),f328(f328(f81(x77121),x77123),x77124))) % 167.77/167.51 [7713]~P63(x77131)+~P1(f328(f328(f243(x77131),x77134),f2(x77131)))+~P1(f328(f328(f242(x77131),x77133),f328(f328(f81(x77131),x77132),x77134)))+P1(f328(f328(f242(x77131),x77132),f328(f328(f286(x77131),x77133),x77134))) % 167.77/167.51 [7826]~P123(x78261)+~P1(f328(f328(f243(x78261),x78263),f2(x78261)))+~P1(f328(f328(f243(x78261),x78264),x78262))+P1(f328(f328(f243(x78261),f328(f328(f81(x78261),x78262),x78263)),f328(f328(f81(x78261),x78264),x78263))) % 167.77/167.51 [7827]~P123(x78271)+~P1(f328(f328(f243(x78271),x78272),f2(x78271)))+~P1(f328(f328(f243(x78271),x78274),x78273))+P1(f328(f328(f243(x78271),f328(f328(f81(x78271),x78272),x78273)),f328(f328(f81(x78271),x78272),x78274))) % 167.77/167.51 [7828]~P63(x78281)+~P1(f328(f328(f243(x78281),x78283),f2(x78281)))+~P1(f328(f328(f243(x78281),x78284),x78282))+P1(f328(f328(f243(x78281),f328(f328(f286(x78281),x78282),x78283)),f328(f328(f286(x78281),x78284),x78283))) % 167.77/167.51 [7829]~P110(x78291)+~P1(f328(f328(f242(x78291),x78292),f2(x78291)))+~P1(f328(f328(f242(x78291),x78294),x78293))+P1(f328(f328(f242(x78291),f328(f328(f81(x78291),x78292),x78293)),f328(f328(f81(x78291),x78292),x78294))) % 167.77/167.51 [7830]~P123(x78301)+~P1(f328(f328(f243(x78301),x78302),f2(x78301)))+~P1(f328(f328(f242(x78301),x78304),x78303))+P1(f328(f328(f242(x78301),f328(f328(f81(x78301),x78302),x78303)),f328(f328(f81(x78301),x78302),x78304))) % 167.77/167.51 [7831]~P110(x78311)+~P1(f328(f328(f242(x78311),x78313),f2(x78311)))+~P1(f328(f328(f242(x78311),x78314),x78312))+P1(f328(f328(f242(x78311),f328(f328(f81(x78311),x78312),x78313)),f328(f328(f81(x78311),x78314),x78313))) % 167.77/167.51 [7832]~P62(x78321)+~P1(f328(f328(f242(x78321),x78323),f2(x78321)))+~P1(f328(f328(f242(x78321),x78324),x78322))+P1(f328(f328(f242(x78321),f328(f328(f286(x78321),x78322),x78323)),f328(f328(f286(x78321),x78324),x78323))) % 167.77/167.51 [7834]~P116(x78341)+~P1(f328(f328(f243(x78341),f78(x78341)),x78342))+~P1(f328(f328(f243(a872),x78343),x78344))+P1(f328(f328(f243(x78341),f328(f328(f253(x78341),x78342),x78343)),f328(f328(f253(x78341),x78342),x78344))) % 167.77/167.51 [7835]~P116(x78351)+~P1(f328(f328(f243(x78351),f78(x78351)),x78352))+~P1(f328(f328(f242(a872),x78353),x78354))+P1(f328(f328(f242(x78351),f328(f328(f253(x78351),x78352),x78353)),f328(f328(f253(x78351),x78352),x78354))) % 167.77/167.51 [7836]~P116(x78361)+~P1(f328(f328(f242(x78361),f78(x78361)),x78362))+~P1(f328(f328(f242(a872),x78363),x78364))+P1(f328(f328(f242(x78361),f328(f328(f253(x78361),x78362),x78363)),f328(f328(f253(x78361),x78362),x78364))) % 167.77/167.51 [7863]P1(f328(f328(f243(a872),f2(a872)),f328(x78631,x78632)))+~P1(f328(f38(x78633),x78634))+~P1(f328(f328(f330(x78633),x78632),x78634))+~P1(f328(f328(f243(a872),f2(a872)),f328(f328(f9(x78633,a872),x78631),x78634))) % 167.77/167.51 [7873]~P118(x78731)+~P1(f328(f328(f243(x78731),x78733),x78734))+~P1(f328(f328(f243(x78731),f2(x78731)),x78732))+P1(f328(f328(f243(x78731),f328(f328(f81(x78731),x78732),x78733)),f328(f328(f81(x78731),x78732),x78734))) % 167.77/167.51 [7874]~P127(x78741)+~P1(f328(f328(f243(x78741),x78743),x78744))+~P1(f328(f328(f243(x78741),f2(x78741)),x78742))+P1(f328(f328(f243(x78741),f328(f328(f81(x78741),x78742),x78743)),f328(f328(f81(x78741),x78742),x78744))) % 167.77/167.51 [7875]~P123(x78751)+~P1(f328(f328(f243(x78751),x78752),x78754))+~P1(f328(f328(f243(x78751),f2(x78751)),x78753))+P1(f328(f328(f243(x78751),f328(f328(f81(x78751),x78752),x78753)),f328(f328(f81(x78751),x78754),x78753))) % 167.77/167.51 [7876]~P127(x78761)+~P1(f328(f328(f243(x78761),x78762),x78764))+~P1(f328(f328(f243(x78761),f2(x78761)),x78763))+P1(f328(f328(f243(x78761),f328(f328(f81(x78761),x78762),x78763)),f328(f328(f81(x78761),x78764),x78763))) % 167.77/167.51 [7877]~P123(x78771)+~P1(f328(f328(f243(x78771),x78773),x78774))+~P1(f328(f328(f243(x78771),f2(x78771)),x78772))+P1(f328(f328(f243(x78771),f328(f328(f81(x78771),x78772),x78773)),f328(f328(f81(x78771),x78772),x78774))) % 167.77/167.51 [7878]~P63(x78781)+~P1(f328(f328(f243(x78781),x78782),x78784))+~P1(f328(f328(f243(x78781),f2(x78781)),x78783))+P1(f328(f328(f243(x78781),f328(f328(f286(x78781),x78782),x78783)),f328(f328(f286(x78781),x78784),x78783))) % 167.77/167.51 [7879]~P123(x78791)+~P1(f328(f328(f243(x78791),f2(x78791)),x78792))+~P1(f328(f328(f242(x78791),x78793),x78794))+P1(f328(f328(f242(x78791),f328(f328(f81(x78791),x78792),x78793)),f328(f328(f81(x78791),x78792),x78794))) % 167.77/167.51 [7880]~P133(x78801)+~P1(f328(f328(f242(x78801),x78803),x78804))+~P1(f328(f328(f242(x78801),f2(x78801)),x78802))+P1(f328(f328(f242(x78801),f328(f328(f81(x78801),x78802),x78803)),f328(f328(f81(x78801),x78802),x78804))) % 167.77/167.51 [7881]~P132(x78811)+~P1(f328(f328(f242(x78811),x78813),x78814))+~P1(f328(f328(f242(x78811),f2(x78811)),x78812))+P1(f328(f328(f242(x78811),f328(f328(f81(x78811),x78812),x78813)),f328(f328(f81(x78811),x78812),x78814))) % 167.77/167.51 [7882]~P133(x78821)+~P1(f328(f328(f242(x78821),x78822),x78824))+~P1(f328(f328(f242(x78821),f2(x78821)),x78823))+P1(f328(f328(f242(x78821),f328(f328(f81(x78821),x78822),x78823)),f328(f328(f81(x78821),x78824),x78823))) % 167.77/167.51 [7883]~P116(x78831)+~P1(f328(f328(f242(x78831),x78832),x78834))+~P1(f328(f328(f242(x78831),f2(x78831)),x78832))+P1(f328(f328(f242(x78831),f328(f328(f253(x78831),x78832),x78833)),f328(f328(f253(x78831),x78834),x78833))) % 167.77/167.51 [7884]~P62(x78841)+~P1(f328(f328(f242(x78841),x78842),x78844))+~P1(f328(f328(f242(x78841),f2(x78841)),x78843))+P1(f328(f328(f242(x78841),f328(f328(f286(x78841),x78842),x78843)),f328(f328(f286(x78841),x78844),x78843))) % 167.77/167.51 [7927]~P108(x79272)+P1(f328(f328(f242(f879(x79271,x79272)),x79274),x79273))+~P1(f328(f328(f242(f879(x79271,x79272)),x79273),x79274))+P1(f328(f328(f243(f879(x79271,x79272)),x79273),x79274)) % 167.77/167.51 [7966]P1(f328(f328(f330(x79661),x79662),x79663))+P1(f328(f328(f330(x79661),x79662),x79664))+~P1(f328(f328(f242(f879(x79661,a867)),x79664),x79663))+P1(f328(f328(f243(f879(x79661,a867)),x79664),f328(f328(f306(x79661),x79662),x79663))) % 167.77/167.51 [8123]P1(f328(f328(f330(x81231),x81232),x81233))+P1(f328(f328(f330(x81231),x81232),x81234))+~P1(f328(f328(f243(f879(x81231,a867)),x81234),f328(f328(f306(x81231),x81232),x81233)))+P1(f328(f328(f242(f879(x81231,a867)),x81234),x81233)) % 167.77/167.51 [8131]~P59(x81311)+P11(x81311,x81312,x81313)+~P1(f328(x81312,x81314))+~P1(f328(f328(f330(f873(x81311)),x81314),f328(f170(f873(x81311)),f56(x81311,x81313,f57(x81311))))) % 167.77/167.51 [8143]~P12(x81433,x81431,x81434)+~P59(x81433)+P1(f328(x81431,x81432))+~P1(f328(f328(f330(f873(x81433)),x81432),f328(f170(f873(x81433)),f56(x81433,x81434,f57(x81433))))) % 167.77/167.51 [8202]~P123(x82021)+P1(f328(f328(f243(x82021),x82023),x82022))+P1(f328(f328(f243(x82021),x82022),x82023))+~P1(f328(f328(f243(x82021),f328(f328(f81(x82021),x82024),x82022)),f328(f328(f81(x82021),x82024),x82023))) % 167.77/167.51 [8203]~P123(x82031)+P1(f328(f328(f243(x82031),x82033),x82032))+P1(f328(f328(f243(x82031),x82032),x82033))+~P1(f328(f328(f243(x82031),f328(f328(f81(x82031),x82032),x82034)),f328(f328(f81(x82031),x82033),x82034))) % 167.77/167.51 [8216]~P123(x82161)+P1(f328(f328(f243(x82161),x82164),f2(x82161)))+P1(f328(f328(f243(x82161),x82162),x82163))+~P1(f328(f328(f243(x82161),f328(f328(f81(x82161),x82162),x82164)),f328(f328(f81(x82161),x82163),x82164))) % 167.77/167.51 [8217]~P123(x82171)+P1(f328(f328(f243(x82171),x82174),f2(x82171)))+P1(f328(f328(f243(x82171),x82172),x82173))+~P1(f328(f328(f243(x82171),f328(f328(f81(x82171),x82174),x82172)),f328(f328(f81(x82171),x82174),x82173))) % 167.77/167.51 [8222]~P123(x82221)+P1(f328(f328(f243(x82221),x82222),x82223))+P1(f328(f328(f243(x82221),f2(x82221)),x82224))+~P1(f328(f328(f243(x82221),f328(f328(f81(x82221),x82224),x82223)),f328(f328(f81(x82221),x82224),x82222))) % 167.77/167.51 [8223]~P123(x82231)+P1(f328(f328(f243(x82231),x82232),x82233))+P1(f328(f328(f243(x82231),f2(x82231)),x82234))+~P1(f328(f328(f243(x82231),f328(f328(f81(x82231),x82233),x82234)),f328(f328(f81(x82231),x82232),x82234))) % 167.77/167.51 [8236]~P123(x82361)+P1(f328(f328(f243(x82361),x82362),f2(x82361)))+P1(f328(f328(f243(x82361),f2(x82361)),x82362))+~P1(f328(f328(f243(x82361),f328(f328(f81(x82361),x82363),x82362)),f328(f328(f81(x82361),x82364),x82362))) % 167.77/167.51 [8237]~P123(x82371)+P1(f328(f328(f243(x82371),x82372),f2(x82371)))+P1(f328(f328(f243(x82371),f2(x82371)),x82372))+~P1(f328(f328(f243(x82371),f328(f328(f81(x82371),x82372),x82373)),f328(f328(f81(x82371),x82372),x82374))) % 167.77/167.51 [8263]~P123(x82631)+~P1(f328(f328(f243(x82631),x82634),f2(x82631)))+P1(f328(f328(f243(x82631),x82632),x82633))+~P1(f328(f328(f243(x82631),f328(f328(f81(x82631),x82634),x82633)),f328(f328(f81(x82631),x82634),x82632))) % 167.77/167.51 [8264]~P123(x82641)+~P1(f328(f328(f243(x82641),x82644),f2(x82641)))+P1(f328(f328(f242(x82641),x82642),x82643))+~P1(f328(f328(f242(x82641),f328(f328(f81(x82641),x82644),x82643)),f328(f328(f81(x82641),x82644),x82642))) % 167.77/167.51 [8274]~P116(x82743)+~P1(f328(f328(f243(x82743),f78(x82743)),x82744))+P1(f328(f328(f243(a872),x82741),x82742))+~P1(f328(f328(f243(x82743),f328(f328(f253(x82743),x82744),x82741)),f328(f328(f253(x82743),x82744),x82742))) % 167.77/167.51 [8276]~P116(x82763)+~P1(f328(f328(f243(x82763),f78(x82763)),x82764))+P1(f328(f328(f242(a872),x82761),x82762))+~P1(f328(f328(f242(x82763),f328(f328(f253(x82763),x82764),x82761)),f328(f328(f253(x82763),x82764),x82762))) % 167.77/167.51 [8286]~P123(x82861)+P1(f328(f328(f243(x82861),x82862),x82863))+~P1(f328(f328(f243(x82861),f2(x82861)),x82864))+~P1(f328(f328(f243(x82861),f328(f328(f81(x82861),x82864),x82862)),f328(f328(f81(x82861),x82864),x82863))) % 167.77/167.51 [8287]~P127(x82871)+P1(f328(f328(f243(x82871),x82872),x82873))+~P1(f328(f328(f242(x82871),f2(x82871)),x82874))+~P1(f328(f328(f243(x82871),f328(f328(f81(x82871),x82874),x82872)),f328(f328(f81(x82871),x82874),x82873))) % 167.77/167.51 [8288]~P128(x82881)+P1(f328(f328(f243(x82881),x82882),x82883))+~P1(f328(f328(f242(x82881),f2(x82881)),x82884))+~P1(f328(f328(f243(x82881),f328(f328(f81(x82881),x82884),x82882)),f328(f328(f81(x82881),x82884),x82883))) % 167.77/167.51 [8289]~P116(x82891)+~P1(f328(f328(f242(x82891),f2(x82891)),x82893))+P1(f328(f328(f243(x82891),x82892),x82893))+~P1(f328(f328(f243(x82891),f328(f328(f253(x82891),x82892),x82894)),f328(f328(f253(x82891),x82893),x82894))) % 167.77/167.51 [8290]~P127(x82901)+P1(f328(f328(f243(x82901),x82902),x82903))+~P1(f328(f328(f242(x82901),f2(x82901)),x82904))+~P1(f328(f328(f243(x82901),f328(f328(f81(x82901),x82902),x82904)),f328(f328(f81(x82901),x82903),x82904))) % 167.77/167.51 [8291]~P128(x82911)+P1(f328(f328(f243(x82911),x82912),x82913))+~P1(f328(f328(f242(x82911),f2(x82911)),x82914))+~P1(f328(f328(f243(x82911),f328(f328(f81(x82911),x82912),x82914)),f328(f328(f81(x82911),x82913),x82914))) % 167.77/167.51 [8292]~P123(x82921)+P1(f328(f328(f242(x82921),x82922),x82923))+~P1(f328(f328(f243(x82921),f2(x82921)),x82924))+~P1(f328(f328(f242(x82921),f328(f328(f81(x82921),x82924),x82922)),f328(f328(f81(x82921),x82924),x82923))) % 167.77/167.51 [8293]~P127(x82931)+P1(f328(f328(f242(x82931),x82932),x82933))+~P1(f328(f328(f243(x82931),f2(x82931)),x82934))+~P1(f328(f328(f242(x82931),f328(f328(f81(x82931),x82934),x82932)),f328(f328(f81(x82931),x82934),x82933))) % 167.77/167.51 [8294]~P127(x82941)+P1(f328(f328(f242(x82941),x82942),x82943))+~P1(f328(f328(f243(x82941),f2(x82941)),x82944))+~P1(f328(f328(f242(x82941),f328(f328(f81(x82941),x82942),x82944)),f328(f328(f81(x82941),x82943),x82944))) % 167.77/167.51 [8338]P1(f328(f328(f330(x83381),x83382),x83383))+~P1(f328(f328(f242(f879(x83381,a867)),x83383),x83384))+~P1(f328(f328(f243(f879(x83381,a867)),x83383),x83384))+P1(f328(f328(f243(f879(x83381,a867)),x83383),f328(f328(f306(x83381),x83382),x83384))) % 167.77/167.51 [8596]~P59(x85961)+~P93(x85962)+~E(f328(x85963,f802(x85964,x85963,x85961,x85962)),f328(x85964,f802(x85964,x85963,x85961,x85962)))+P1(f328(f328(f91(f879(x85961,x85962)),x85963),x85964)) % 167.77/167.51 [8713]E(f328(f328(f22(a1),f418(x87131,x87132,x87133,x87134)),f419(x87131,x87132,x87133,x87134)),x87134)+~P1(f328(f328(f243(a1),f2(a1)),x87133))+~P1(f328(f328(f242(a1),x87131),x87134))+P1(f328(f328(f242(a1),x87131),f328(f328(f80(a1),x87134),x87133))) % 167.77/167.51 [8714]E(f328(f328(f22(a1),f428(x87141,x87142,x87143,x87144)),f429(x87141,x87142,x87143,x87144)),x87144)+~P1(f328(f328(f243(a1),f2(a1)),x87143))+~P1(f328(f328(f243(a1),x87141),x87144))+P1(f328(f328(f243(a1),x87141),f328(f328(f80(a1),x87144),x87143))) % 167.77/167.51 [8849]~E(f328(f328(f162(x88491),x88493),f691(x88494,x88493,x88491,x88492)),f328(f328(f162(x88491),x88494),f691(x88494,x88493,x88491,x88492)))+E(f328(f328(f173(x88491),x88492),x88493),f328(f328(f173(x88491),x88492),x88494))+~P1(f328(f328(f242(a872),x88492),f328(f193(f873(x88491)),x88493)))+~P1(f328(f328(f242(a872),x88492),f328(f193(f873(x88491)),x88494))) % 167.77/167.51 [8921]~P1(f328(f328(f243(a1),f2(a1)),x89213))+~P1(f328(f328(f242(a1),x89211),x89214))+P1(f328(f328(f330(a1),f418(x89211,x89212,x89213,x89214)),x89212))+P1(f328(f328(f242(a1),x89211),f328(f328(f80(a1),x89214),x89213))) % 167.77/167.51 [8922]~P1(f328(f328(f243(a1),f2(a1)),x89223))+~P1(f328(f328(f243(a1),x89221),x89224))+P1(f328(f328(f330(a1),f428(x89221,x89222,x89223,x89224)),x89222))+P1(f328(f328(f243(a1),x89221),f328(f328(f80(a1),x89224),x89223))) % 167.77/167.51 [8965]~P100(x89651)+~P1(f328(f38(x89651),x89653))+~P1(f328(f328(f330(x89651),x89654),x89653))+P1(f328(f328(f242(x89651),f328(f328(f65(x89651,x89651,f105(x89651)),x89652),x89653)),f328(f328(f105(x89651),x89654),x89652))) % 167.77/167.51 [8966]~P105(x89661)+~P1(f328(f38(x89661),x89663))+~P1(f328(f328(f330(x89661),x89664),x89663))+P1(f328(f328(f242(x89661),f328(f328(f65(x89661,x89661,f240(x89661)),x89662),x89663)),f328(f328(f240(x89661),x89664),x89662))) % 167.77/167.51 [9010]E(f328(f328(f173(x90101),x90102),x90103),f328(f328(f173(x90101),x90102),x90104))+P1(f328(f328(f243(a872),f691(x90103,x90104,x90101,x90102)),x90102))+~P1(f328(f328(f242(a872),x90102),f328(f193(f873(x90101)),x90103)))+~P1(f328(f328(f242(a872),x90102),f328(f193(f873(x90101)),x90104))) % 167.77/167.51 [9015]~P1(f328(f328(f243(a1),f2(a1)),x90153))+~P1(f328(f328(f243(a1),x90151),x90152))+P1(f328(f328(f330(a1),f429(x90151,x90154,x90153,x90152)),f299(a1,f78(a1),x90153)))+P1(f328(f328(f243(a1),x90151),f328(f328(f80(a1),x90152),x90153))) % 167.77/167.51 [9016]~P1(f328(f328(f243(a1),f2(a1)),x90163))+~P1(f328(f328(f242(a1),x90161),x90162))+P1(f328(f328(f330(a1),f419(x90161,x90164,x90163,x90162)),f299(a1,f78(a1),x90163)))+P1(f328(f328(f242(a1),x90161),f328(f328(f80(a1),x90162),x90163))) % 167.77/167.51 [9181]~E(f328(f176(x91811,x91812),x91813),f328(f176(x91811,x91812),x91814))+E(f328(f170(f878(x91811,x91812)),x91813),f328(f170(f878(x91811,x91812)),x91814))+~P1(f328(f134(x91811),f328(f328(f151(f878(x91811,x91812),x91811),f262(x91811,x91812)),x91814)))+~P1(f328(f134(x91811),f328(f328(f151(f878(x91811,x91812),x91811),f262(x91811,x91812)),x91813))) % 167.77/167.51 [9193]E(f328(f176(x91931,x91932),x91933),f328(f176(x91931,x91932),x91934))+~E(f328(f170(f878(x91931,x91932)),x91933),f328(f170(f878(x91931,x91932)),x91934))+~P1(f328(f134(x91931),f328(f328(f151(f878(x91931,x91932),x91931),f262(x91931,x91932)),x91934)))+~P1(f328(f134(x91931),f328(f328(f151(f878(x91931,x91932),x91931),f262(x91931,x91932)),x91933))) % 167.77/167.51 [9336]~P105(x93361)+~P1(f328(f38(x93361),x93364))+P1(f328(f328(f330(x93361),f495(x93362,x93363,x93364,x93361)),x93364))+P1(f328(f328(f242(x93361),f328(f328(f65(x93361,x93361,f241(x93361)),x93362),x93364)),f328(f328(f241(x93361),x93363),x93362))) % 167.77/167.51 [9337]~P99(x93371)+~P1(f328(f38(x93371),x93374))+P1(f328(f328(f330(x93371),f504(x93372,x93373,x93374,x93371)),x93374))+P1(f328(f328(f242(x93371),f328(f328(f65(x93371,x93371,f114(x93371)),x93372),x93374)),f328(f328(f114(x93371),x93373),x93372))) % 167.77/167.51 [9460]~P99(x94601)+~P1(f328(f38(x94601),x94603))+~P1(f328(f328(f242(x94601),f504(x94602,x94604,x94603,x94601)),x94604))+P1(f328(f328(f242(x94601),f328(f328(f65(x94601,x94601,f114(x94601)),x94602),x94603)),f328(f328(f114(x94601),x94604),x94602))) % 167.77/167.51 [9461]~P105(x94611)+~P1(f328(f38(x94611),x94613))+~P1(f328(f328(f242(x94611),f495(x94612,x94614,x94613,x94611)),x94614))+P1(f328(f328(f242(x94611),f328(f328(f65(x94611,x94611,f241(x94611)),x94612),x94613)),f328(f328(f241(x94611),x94614),x94612))) % 167.77/167.51 [9464]~P1(f328(f328(f243(a1),f2(a1)),x94643))+~P1(f328(f328(f242(a1),f2(a1)),x94644))+~P1(f328(f328(f243(a1),x94644),x94641))+P1(f328(f328(f243(a1),f328(f328(f80(a1),f328(f328(f81(a1),x94641),f46(a1,x94642,x94643))),x94644)),f328(f328(f81(a1),x94641),x94643))) % 167.77/167.51 [9865]E(x98651,x98652)+P1(f328(f328(f330(f878(f873(x98653),f873(x98653))),f328(f328(f263(f873(x98653),f873(x98653)),x98652),x98651)),f144(x98653,x98654)))+P1(f328(f328(f330(f878(f873(x98653),f873(x98653))),f328(f328(f263(f873(x98653),f873(x98653)),x98651),x98652)),f144(x98653,x98654)))+~P1(f328(f328(f330(f878(x98653,x98653)),f328(f328(f263(x98653,x98653),f671(x98651,x98652,x98654,x98653)),f672(x98651,x98652,x98654,x98653))),x98654)) % 167.77/167.51 [9866]E(x98661,x98662)+P1(f328(f328(f330(f878(f873(x98663),f873(x98663))),f328(f328(f263(f873(x98663),f873(x98663)),x98662),x98661)),f144(x98663,x98664)))+P1(f328(f328(f330(f878(f873(x98663),f873(x98663))),f328(f328(f263(f873(x98663),f873(x98663)),x98661),x98662)),f144(x98663,x98664)))+~P1(f328(f328(f330(f878(x98663,x98663)),f328(f328(f263(x98663,x98663),f672(x98661,x98662,x98664,x98663)),f671(x98661,x98662,x98664,x98663))),x98664)) % 167.77/167.51 [7407]~P105(x74071)+~P1(f328(f328(f243(x74071),x74073),x74074))+~P1(f328(f328(f243(x74071),x74072),x74074))+P1(f328(f328(f243(x74071),f328(f328(f241(x74071),x74072),x74073)),x74074)) % 167.77/167.51 [7410]~P99(x74101)+~P1(f328(f328(f242(x74101),x74103),x74104))+~P1(f328(f328(f242(x74101),x74102),x74104))+P1(f328(f328(f242(x74101),f328(f328(f114(x74101),x74102),x74103)),x74104)) % 167.77/167.51 [7413]~P105(x74131)+~P1(f328(f328(f242(x74131),x74133),x74134))+~P1(f328(f328(f242(x74131),x74132),x74134))+P1(f328(f328(f242(x74131),f328(f328(f241(x74131),x74132),x74133)),x74134)) % 167.77/167.51 [7735]~E(x77351,x77353)+E(f136(a872,f328(f298(a872,x77351),x77352)),f328(f328(f148(a872),x77353),x77354))+~E(f136(a872,f328(f298(a872,f328(f328(f80(a872),x77351),f78(a872))),x77352)),x77354)+~P1(f328(f328(f243(a872),x77351),x77352)) % 167.77/167.51 [7744]~P105(x77441)+P1(f328(f328(f243(x77441),x77442),x77443))+P1(f328(f328(f243(x77441),x77444),x77443))+~P1(f328(f328(f243(x77441),f328(f328(f240(x77441),x77444),x77442)),x77443)) % 167.77/167.51 [7745]~P105(x77451)+P1(f328(f328(f242(x77451),x77452),x77453))+P1(f328(f328(f242(x77451),x77454),x77453))+~P1(f328(f328(f242(x77451),f328(f328(f240(x77451),x77454),x77452)),x77453)) % 167.77/167.51 [8022]~P62(x80221)+~P1(f328(f328(f243(x80221),f2(x80221)),x80223))+~P1(f328(f328(f243(x80221),x80222),f328(f328(f286(x80221),x80224),x80223)))+P1(f328(f328(f243(x80221),f328(f328(f81(x80221),x80222),x80223)),x80224)) % 167.77/167.51 [8023]~P63(x80231)+~P1(f328(f328(f243(x80231),f2(x80231)),x80233))+~P1(f328(f328(f243(x80231),x80232),f328(f328(f286(x80231),x80234),x80233)))+P1(f328(f328(f243(x80231),f328(f328(f81(x80231),x80232),x80233)),x80234)) % 167.77/167.51 [8024]~P62(x80241)+~P1(f328(f328(f243(x80241),f2(x80241)),x80243))+~P1(f328(f328(f243(x80241),x80242),f328(f328(f81(x80241),x80244),x80243)))+P1(f328(f328(f243(x80241),f328(f328(f286(x80241),x80242),x80243)),x80244)) % 167.77/167.51 [8026]~P63(x80261)+~P1(f328(f328(f243(x80261),f2(x80261)),x80263))+~P1(f328(f328(f243(x80261),x80262),f328(f328(f81(x80261),x80264),x80263)))+P1(f328(f328(f243(x80261),f328(f328(f286(x80261),x80262),x80263)),x80264)) % 167.77/167.51 [8027]~P62(x80271)+~P1(f328(f328(f243(x80271),f2(x80271)),x80273))+~P1(f328(f328(f242(x80271),x80272),f328(f328(f286(x80271),x80274),x80273)))+P1(f328(f328(f242(x80271),f328(f328(f81(x80271),x80272),x80273)),x80274)) % 167.77/167.51 [8028]~P63(x80281)+~P1(f328(f328(f243(x80281),f2(x80281)),x80283))+~P1(f328(f328(f242(x80281),x80282),f328(f328(f286(x80281),x80284),x80283)))+P1(f328(f328(f242(x80281),f328(f328(f81(x80281),x80282),x80283)),x80284)) % 167.77/167.51 [8029]~P62(x80291)+~P1(f328(f328(f243(x80291),f2(x80291)),x80293))+~P1(f328(f328(f242(x80291),x80292),f328(f328(f81(x80291),x80294),x80293)))+P1(f328(f328(f242(x80291),f328(f328(f286(x80291),x80292),x80293)),x80294)) % 167.77/167.51 [8031]~P63(x80311)+~P1(f328(f328(f243(x80311),f2(x80311)),x80313))+~P1(f328(f328(f242(x80311),x80312),f328(f328(f81(x80311),x80314),x80313)))+P1(f328(f328(f242(x80311),f328(f328(f286(x80311),x80312),x80313)),x80314)) % 167.77/167.51 [8168]~P62(x81681)+~P1(f328(f328(f243(x81681),f2(x81681)),x81684))+P1(f328(f328(f243(x81681),x81682),f328(f328(f81(x81681),x81683),x81684)))+~P1(f328(f328(f243(x81681),f328(f328(f286(x81681),x81682),x81684)),x81683)) % 167.77/167.51 [8169]~P62(x81691)+~P1(f328(f328(f243(x81691),f2(x81691)),x81694))+P1(f328(f328(f243(x81691),x81692),f328(f328(f286(x81691),x81693),x81694)))+~P1(f328(f328(f243(x81691),f328(f328(f81(x81691),x81692),x81694)),x81693)) % 167.77/167.51 [8171]~P63(x81711)+~P1(f328(f328(f243(x81711),f2(x81711)),x81714))+P1(f328(f328(f243(x81711),x81712),f328(f328(f81(x81711),x81713),x81714)))+~P1(f328(f328(f243(x81711),f328(f328(f286(x81711),x81712),x81714)),x81713)) % 167.77/167.51 [8172]~P63(x81721)+~P1(f328(f328(f243(x81721),f2(x81721)),x81724))+P1(f328(f328(f243(x81721),x81722),f328(f328(f286(x81721),x81723),x81724)))+~P1(f328(f328(f243(x81721),f328(f328(f81(x81721),x81722),x81724)),x81723)) % 167.77/167.51 [8173]~P62(x81731)+~P1(f328(f328(f243(x81731),f2(x81731)),x81734))+P1(f328(f328(f242(x81731),x81732),f328(f328(f81(x81731),x81733),x81734)))+~P1(f328(f328(f242(x81731),f328(f328(f286(x81731),x81732),x81734)),x81733)) % 167.77/167.51 [8174]~P62(x81741)+~P1(f328(f328(f243(x81741),f2(x81741)),x81744))+P1(f328(f328(f242(x81741),x81742),f328(f328(f286(x81741),x81743),x81744)))+~P1(f328(f328(f242(x81741),f328(f328(f81(x81741),x81742),x81744)),x81743)) % 167.77/167.51 [8176]~P63(x81761)+~P1(f328(f328(f243(x81761),f2(x81761)),x81764))+P1(f328(f328(f242(x81761),x81762),f328(f328(f81(x81761),x81763),x81764)))+~P1(f328(f328(f242(x81761),f328(f328(f286(x81761),x81762),x81764)),x81763)) % 167.77/167.51 [8177]~P63(x81771)+~P1(f328(f328(f243(x81771),f2(x81771)),x81774))+P1(f328(f328(f242(x81771),x81772),f328(f328(f286(x81771),x81773),x81774)))+~P1(f328(f328(f242(x81771),f328(f328(f81(x81771),x81772),x81774)),x81773)) % 167.77/167.51 [8342]~P63(x83421)+~P1(f328(f328(f243(x83421),x83423),f2(x83421)))+~P1(f328(f328(f243(x83421),f328(f328(f286(x83421),x83424),x83423)),x83422))+P1(f328(f328(f243(x83421),f328(f328(f81(x83421),x83422),x83423)),x83424)) % 167.77/167.51 [8343]~P63(x83431)+~P1(f328(f328(f243(x83431),x83433),f2(x83431)))+~P1(f328(f328(f243(x83431),f328(f328(f81(x83431),x83434),x83433)),x83432))+P1(f328(f328(f243(x83431),f328(f328(f286(x83431),x83432),x83433)),x83434)) % 167.77/167.51 [8344]~P63(x83441)+~P1(f328(f328(f243(x83441),x83443),f2(x83441)))+~P1(f328(f328(f242(x83441),f328(f328(f286(x83441),x83444),x83443)),x83442))+P1(f328(f328(f242(x83441),f328(f328(f81(x83441),x83442),x83443)),x83444)) % 167.77/167.51 [8345]~P63(x83451)+~P1(f328(f328(f243(x83451),x83453),f2(x83451)))+~P1(f328(f328(f242(x83451),f328(f328(f81(x83451),x83454),x83453)),x83452))+P1(f328(f328(f242(x83451),f328(f328(f286(x83451),x83452),x83453)),x83454)) % 167.77/167.51 [8355]~P1(f328(x83551,x83554))+~P1(f328(f328(f243(a872),x83552),f328(f328(f81(a872),x83553),f328(a116,x83554))))+P1(f328(x83551,f328(f328(f40(a872),x83552),x83553)))+~P1(f328(f328(f242(a872),f328(f328(f81(a872),x83553),x83554)),x83552)) % 167.77/167.51 [8570]~P99(x85701)+~P1(f328(f38(x85701),x85704))+~P1(f328(f328(f330(x85701),x85702),x85704))+P1(f328(f328(f242(x85701),f328(f328(f114(x85701),x85702),x85703)),f328(f328(f65(x85701,x85701,f114(x85701)),x85703),x85704))) % 167.77/167.51 [8571]~P105(x85711)+~P1(f328(f38(x85711),x85714))+~P1(f328(f328(f330(x85711),x85712),x85714))+P1(f328(f328(f242(x85711),f328(f328(f241(x85711),x85712),x85713)),f328(f328(f65(x85711,x85711,f241(x85711)),x85713),x85714))) % 167.77/167.51 [8715]~P1(f328(f38(x87151),x87152))+E(f328(f39(x87151),f328(f328(f22(f879(x87151,a867)),x87152),f328(f328(f306(x87151),x87153),x87154))),f328(f328(f22(a872),f328(f39(x87151),f328(f328(f22(f879(x87151,a867)),x87152),x87154))),f78(a872)))+P1(f328(f328(f330(x87151),x87153),x87154))+~P1(f328(f328(f330(x87151),x87153),x87152)) % 167.77/167.51 [8785]E(f328(f328(f80(a1),f420(x87851,x87852,x87853,x87854)),f421(x87851,x87852,x87853,x87854)),x87854)+~P1(f328(f328(f243(a1),f2(a1)),x87853))+~P1(f328(f328(f242(a1),x87854),x87851))+P1(f328(f328(f242(a1),f328(f328(f22(a1),x87854),x87853)),x87851)) % 167.77/167.51 [8786]E(f328(f328(f80(a1),f430(x87861,x87862,x87863,x87864)),f431(x87861,x87862,x87863,x87864)),x87864)+~P1(f328(f328(f243(a1),f2(a1)),x87863))+~P1(f328(f328(f243(a1),x87864),x87861))+P1(f328(f328(f243(a1),f328(f328(f22(a1),x87864),x87863)),x87861)) % 167.77/167.51 [8995]~P1(f328(f328(f243(a1),f2(a1)),x89953))+~P1(f328(f328(f242(a1),x89954),x89951))+P1(f328(f328(f330(a1),f420(x89951,x89952,x89953,x89954)),x89952))+P1(f328(f328(f242(a1),f328(f328(f22(a1),x89954),x89953)),x89951)) % 167.77/167.51 [8996]~P1(f328(f328(f243(a1),f2(a1)),x89963))+~P1(f328(f328(f243(a1),x89964),x89961))+P1(f328(f328(f330(a1),f430(x89961,x89962,x89963,x89964)),x89962))+P1(f328(f328(f243(a1),f328(f328(f22(a1),x89964),x89963)),x89961)) % 167.77/167.51 [9083]~P1(f328(f328(f243(a1),f2(a1)),x90832))+~P1(f328(f328(f243(a1),x90831),x90833))+P1(f328(f328(f330(a1),f431(x90833,x90834,x90832,x90831)),f299(a1,f78(a1),x90832)))+P1(f328(f328(f243(a1),f328(f328(f22(a1),x90831),x90832)),x90833)) % 167.77/167.51 [9084]~P1(f328(f328(f243(a1),f2(a1)),x90842))+~P1(f328(f328(f242(a1),x90841),x90843))+P1(f328(f328(f330(a1),f421(x90843,x90844,x90842,x90841)),f299(a1,f78(a1),x90842)))+P1(f328(f328(f242(a1),f328(f328(f22(a1),x90841),x90842)),x90843)) % 167.77/167.51 [9100]~P1(f328(f328(f243(a1),f2(a1)),x91003))+~P1(f328(f328(f242(a1),f2(a1)),x91004))+~P1(f328(f328(f243(a1),x91004),x91001))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),f328(f328(f81(a1),x91001),f46(a1,x91002,x91003))),x91004))) % 167.77/167.51 [9164]~P100(x91641)+~P1(f328(f38(x91641),x91644))+~P1(f328(f328(f242(x91641),x91642),f503(x91643,x91642,x91644,x91641)))+P1(f328(f328(f242(x91641),f328(f328(f105(x91641),x91642),x91643)),f328(f328(f65(x91641,x91641,f105(x91641)),x91643),x91644))) % 167.77/167.51 [9165]~P105(x91651)+~P1(f328(f38(x91651),x91654))+~P1(f328(f328(f242(x91651),x91652),f494(x91653,x91652,x91654,x91651)))+P1(f328(f328(f242(x91651),f328(f328(f240(x91651),x91652),x91653)),f328(f328(f65(x91651,x91651,f240(x91651)),x91653),x91654))) % 167.77/167.51 [9180]~P1(f328(f328(f242(a1),x91804),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x91802))+~P1(f328(f328(f243(a1),x91801),x91804))+P1(f328(f328(f243(a1),f328(f328(f81(a1),x91801),x91802)),f328(f328(f80(a1),f328(f328(f81(a1),x91801),f46(a1,x91803,x91802))),x91804))) % 167.77/167.51 [9202]P1(f328(f38(x92021),x92022))+~P1(f328(f38(x92021),x92023))+~P1(f328(f328(f330(f879(x92021,a867)),x92022),f328(f328(f62(x92021),x92023),x92024)))+~P1(f328(f328(f242(f879(f878(x92021,x92021),a867)),x92024),f328(f328(f265(x92021,x92021),x92023),f328(f16(f879(x92021,a867),x92021),x92023)))) % 167.77/167.51 [9230]~P105(x92301)+~P1(f328(f38(x92301),x92304))+P1(f328(f328(f330(x92301),f494(x92302,x92303,x92304,x92301)),x92304))+P1(f328(f328(f242(x92301),f328(f328(f240(x92301),x92303),x92302)),f328(f328(f65(x92301,x92301,f240(x92301)),x92302),x92304))) % 167.77/167.51 [9231]~P100(x92311)+~P1(f328(f38(x92311),x92314))+P1(f328(f328(f330(x92311),f503(x92312,x92313,x92314,x92311)),x92314))+P1(f328(f328(f242(x92311),f328(f328(f105(x92311),x92313),x92312)),f328(f328(f65(x92311,x92311,f105(x92311)),x92312),x92314))) % 167.77/167.51 [9631]~P1(f328(f38(x96312),x96314))+~P1(f328(f38(x96311),x96313))+~P1(f328(f328(f242(a872),f328(f39(x96312),x96314)),f328(f39(x96311),x96313)))+P1(f328(f328(f242(f879(x96311,a867)),f328(f307(x96312,x96311,f544(x96313,x96311,x96314,x96312)),x96314)),x96313)) % 167.77/167.51 [9277]~P1(f328(f328(f330(x92771),x92772),x92774))+P1(f328(f328(f330(x92771),x92772),x92773))+~P1(f328(f328(f243(f879(x92771,a867)),x92774),f328(f328(f306(x92771),x92772),x92773)))+P1(f328(f328(f243(f879(x92771,a867)),f328(f328(f22(f879(x92771,a867)),x92774),f328(f328(f306(x92771),x92772),f192(f879(x92771,a867))))),x92773)) % 167.77/167.51 [9438]~P1(f328(f328(f330(x94381),x94382),x94384))+P1(f328(f328(f330(x94381),x94382),x94383))+P1(f328(f328(f243(f879(x94381,a867)),x94384),f328(f328(f306(x94381),x94382),x94383)))+~P1(f328(f328(f243(f879(x94381,a867)),f328(f328(f22(f879(x94381,a867)),x94384),f328(f328(f306(x94381),x94382),f192(f879(x94381,a867))))),x94383)) % 167.77/167.51 [9467]P1(f328(f328(f330(x94671),x94672),x94673))+~P1(f328(f328(f242(f879(x94671,a867)),x94674),x94673))+P1(f328(f328(f243(f879(x94671,a867)),x94674),f328(f328(f306(x94671),x94672),x94673)))+~P1(f328(f328(f243(f879(x94671,a867)),f328(f328(f22(f879(x94671,a867)),x94674),f328(f328(f306(x94671),x94672),f192(f879(x94671,a867))))),x94673)) % 167.77/167.51 [9472]~P1(f328(f328(f330(x94721),x94723),x94722))+~P1(f328(f328(f243(f879(x94721,a867)),x94722),x94724))+P1(f328(f328(f243(f879(x94721,a867)),x94722),f328(f328(f306(x94721),x94723),x94724)))+~P1(f328(f328(f243(f879(x94721,a867)),f328(f328(f22(f879(x94721,a867)),x94722),f328(f328(f306(x94721),x94723),f192(f879(x94721,a867))))),x94724)) % 167.77/167.51 [9485]~P1(f328(f328(f242(f879(x94851,a867)),x94852),x94854))+~P1(f328(f328(f243(f879(x94851,a867)),x94852),x94854))+P1(f328(f328(f243(f879(x94851,a867)),x94852),f328(f328(f306(x94851),x94853),x94854)))+~P1(f328(f328(f243(f879(x94851,a867)),f328(f328(f22(f879(x94851,a867)),x94852),f328(f328(f306(x94851),x94853),f192(f879(x94851,a867))))),x94854)) % 167.77/167.51 [9532]~P107(x95322)+~P59(x95321)+~P1(f328(f328(f242(f879(x95321,x95322)),x95323),x95324))+P1(f328(f60(x95321),f328(f328(f18(x95321,x95322,a867),f328(f328(f8(x95322,f879(x95322,a867),x95321),f242(x95322)),x95323)),x95324))) % 167.77/167.51 [9679]~P107(x96792)+~P59(x96791)+P1(f328(f328(f242(f879(x96791,x96792)),x96793),x96794))+~P1(f328(f60(x96791),f328(f328(f18(x96791,x96792,a867),f328(f328(f8(x96792,f879(x96792,a867),x96791),f242(x96792)),x96793)),x96794))) % 167.77/167.51 [9849]E(f328(f328(f162(x98491),f328(f328(f162(f873(x98491)),f178(x98491,x98492)),x98493)),x98494),f328(f328(f162(x98491),f328(f328(f162(f873(x98491)),x98492),x98494)),x98493))+~P1(f328(f328(f243(a872),x98493),f328(f193(f873(f873(x98491))),f178(x98491,x98492))))+~P15(a872,f328(f166(a872),f328(f328(f151(f873(x98491),a872),f193(f873(x98491))),x98492)))+~P1(f328(f328(f243(a872),x98494),f328(f193(f873(f873(x98491))),f328(f133(f873(x98491),f328(f328(f8(a872,a867,f873(x98491)),f328(f243(a872),x98493)),f193(f873(x98491)))),x98492)))) % 167.77/167.51 [9878]~P1(f328(f328(f330(f878(a872,a872)),x98784),x98781))+~P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),x98784),x98782)),a35))+~P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),x98781),x98783)),a36))+P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),x98781),f328(f328(f306(f878(a872,a872)),x98782),x98783))),a36)) % 167.77/167.51 [9879]~P1(f328(f328(f330(f878(a872,a872)),x98794),x98791))+~P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),x98794),x98792)),a70))+~P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),x98791),x98793)),a71))+P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),x98791),f328(f328(f306(f878(a872,a872)),x98792),x98793))),a71)) % 167.77/167.51 [9763]~P107(x97632)+~P59(x97631)+~P1(f328(f328(f243(f879(x97631,x97632)),x97633),x97634))+P1(f328(f59(x97631),f328(f328(f8(a867,a867,x97631),a323),f328(f328(f18(x97631,x97632,a867),f328(f328(f8(x97632,f879(x97632,a867),x97631),a325),x97633)),x97634)))) % 167.77/167.51 [9892]~P1(f328(f328(f330(f878(a872,a872)),x98924),x98923))+~P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),x98921),x98924)),a70))+~P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),x98922),x98923)),a69))+P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),f328(f328(f306(f878(a872,a872)),x98921),x98922)),x98923)),a69)) % 167.77/167.51 [9893]~P1(f328(f328(f330(f878(a872,a872)),x98934),x98933))+~P1(f328(f328(f330(f878(f878(a872,a872),f878(a872,a872))),f328(f328(f263(f878(a872,a872),f878(a872,a872)),x98931),x98934)),a35))+~P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),x98932),x98933)),a37))+P1(f328(f328(f330(f878(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867))),f328(f328(f263(f879(f878(a872,a872),a867),f879(f878(a872,a872),a867)),f328(f328(f306(f878(a872,a872)),x98931),x98932)),x98933)),a37)) % 167.77/167.51 [6002]~P6(x60024,x60021)+~P1(f328(f328(x60021,x60022),x60025))+P1(f328(f328(x60021,x60022),x60023))+~P1(f328(f328(x60021,x60025),x60023)) % 167.77/167.51 [5267]~P66(x52675)+E(x52671,x52672)+~E(x52673,x52674)+~E(f328(f328(f22(x52675),x52673),x52674),f328(f328(f22(x52675),x52671),x52672)) % 167.77/167.51 [6110]~P18(x61105,x61101,x61103)+E(f328(f328(x61101,x61102),f328(x61103,x61104)),f328(x61103,x61104))+~P1(f328(f38(x61105),x61104))+~P1(f328(f328(f330(x61105),x61102),x61104)) % 167.77/167.51 [6307]~P77(x63071)+~E(f328(f328(f22(x63071),x63074),x63075),f328(f328(f22(x63071),x63072),x63073))+~P1(f328(f328(f243(x63071),x63074),x63075))+P1(f328(f328(f243(x63071),x63072),x63073)) % 167.77/167.51 [6309]~P77(x63091)+~E(f328(f328(f22(x63091),x63094),x63095),f328(f328(f22(x63091),x63092),x63093))+~P1(f328(f328(f242(x63091),x63094),x63095))+P1(f328(f328(f242(x63091),x63092),x63093)) % 167.77/167.51 [7268]~E(x72682,f328(f328(f148(x72681),x72684),x72685))+P1(f328(f328(f330(f873(x72681)),x72682),f158(x72681,x72683)))+~P1(f328(f328(f330(f873(x72681)),x72685),f158(x72681,x72683)))+~P1(f328(f328(f330(x72681),x72684),x72683)) % 167.77/167.51 [7686]~E(f328(f193(f873(x76861)),x76863),f328(f193(f873(x76862)),x76864))+~E(f328(f328(f151(f878(x76861,x76862),x76862),f266(x76861,x76862)),x76865),x76864)+~E(f328(f328(f151(f878(x76861,x76862),x76861),f262(x76861,x76862)),x76865),x76863)+E(f328(f328(f180(x76861,x76862),x76863),x76864),x76865) % 167.77/167.51 [8019]~P107(x80191)+P1(f328(f328(f243(f879(x80191,a867)),f299(x80191,x80192,x80193)),f299(x80191,x80194,x80195)))+~P1(f328(f328(f242(x80191),x80194),x80195))+P1(f328(f328(f242(x80191),x80192),x80193)) % 167.77/167.51 [8116]~P107(x81161)+P1(f328(f328(f242(f879(x81161,a867)),f299(x81161,x81162,x81163)),f299(x81161,x81164,x81165)))+~P1(f328(f328(f242(x81161),x81163),x81165))+~P1(f328(f328(f242(x81161),x81164),x81162)) % 167.77/167.51 [8251]~P105(x82511)+P1(f328(f328(f242(x82511),x82512),x82513))+P1(f328(f328(f242(x82511),x82514),x82513))+~P1(f328(f328(f242(f879(x82511,a867)),f328(f298(x82511,x82513),x82512)),f328(f298(x82511,x82514),x82515))) % 167.77/167.51 [8252]~P105(x82521)+P1(f328(f328(f242(x82521),x82522),x82523))+P1(f328(f328(f242(x82521),x82522),x82524))+~P1(f328(f328(f242(f879(x82521,a867)),f328(f298(x82521,x82523),x82522)),f328(f298(x82521,x82525),x82524))) % 167.77/167.51 [8482]~P107(x84821)+~P1(f328(f328(f243(f879(x84821,a867)),f299(x84821,x84824,x84822)),f299(x84821,x84825,x84823)))+P1(f328(f328(f242(x84821),x84822),x84823))+~P1(f328(f328(f242(x84821),x84824),x84822)) % 167.77/167.51 [8483]~P107(x84831)+~P1(f328(f328(f242(f879(x84831,a867)),f299(x84831,x84834,x84832)),f299(x84831,x84835,x84833)))+P1(f328(f328(f242(x84831),x84832),x84833))+~P1(f328(f328(f242(x84831),x84834),x84832)) % 167.77/167.51 [8484]~P107(x84841)+~P1(f328(f328(f243(f879(x84841,a867)),f299(x84841,x84843,x84844)),f299(x84841,x84842,x84845)))+P1(f328(f328(f242(x84841),x84842),x84843))+~P1(f328(f328(f242(x84841),x84843),x84844)) % 167.77/167.51 [8485]~P107(x84851)+~P1(f328(f328(f242(f879(x84851,a867)),f299(x84851,x84853,x84854)),f299(x84851,x84852,x84855)))+P1(f328(f328(f242(x84851),x84852),x84853))+~P1(f328(f328(f242(x84851),x84853),x84854)) % 167.77/167.51 [6001]~P18(x60012,x60015,x60013)+E(x60011,f192(f879(x60012,a867)))+~P1(f328(f38(x60012),x60011))+E(f328(x60013,f328(f328(f306(x60012),x60014),x60011)),f328(f328(x60015,x60014),f328(x60013,x60011))) % 167.77/167.51 [6771]~E(x67711,x67712)+~E(f328(f328(f105(f879(x67713,a867)),x67714),x67715),f192(f879(x67713,a867)))+~P1(f328(f328(f330(x67713),x67712),x67715))+~P1(f328(f328(f330(x67713),x67711),x67714)) % 167.77/167.51 [6853]~P19(x68532,x68535,x68531)+~P1(f328(f38(x68532),x68534))+E(f328(x68531,f328(f328(f306(x68532),x68533),x68534)),f328(f328(f65(x68532,x68532,x68535),x68533),x68534))+P1(f328(f328(f330(x68532),x68533),x68534)) % 167.77/167.51 [6919]~P67(x69192)+~P1(f328(f38(x69191),x69195))+E(f328(f328(f6(x69191,x69192),x69193),f328(f328(f306(x69191),x69194),x69195)),f328(f328(f80(x69192),f328(x69193,x69194)),f328(f328(f6(x69191,x69192),x69193),x69195)))+P1(f328(f328(f330(x69191),x69194),x69195)) % 167.77/167.51 [6921]~P73(x69212)+~P1(f328(f38(x69211),x69215))+E(f328(f328(f9(x69211,x69212),x69213),f328(f328(f306(x69211),x69214),x69215)),f328(f328(f81(x69212),f328(x69213,x69214)),f328(f328(f9(x69211,x69212),x69213),x69215)))+P1(f328(f328(f330(x69211),x69214),x69215)) % 167.77/167.51 [7424]~P19(x74242,x74245,x74241)+~P1(f328(f38(x74242),x74244))+E(f328(x74241,f328(f328(f306(x74242),x74243),x74244)),x74243)+~E(f328(f328(f22(f879(x74242,a867)),x74244),f328(f328(f306(x74242),x74243),f192(f879(x74242,a867)))),f192(f879(x74242,a867))) % 167.77/167.51 [7792]~P81(x77921)+~P1(f328(f328(f243(x77921),x77923),x77925))+~P1(f328(f328(f243(x77921),x77922),x77924))+P1(f328(f328(f243(x77921),f328(f328(f80(x77921),x77922),x77923)),f328(f328(f80(x77921),x77924),x77925))) % 167.77/167.51 [7793]~P81(x77931)+~P1(f328(f328(f242(x77931),x77932),x77934))+~P1(f328(f328(f243(x77931),x77933),x77935))+P1(f328(f328(f243(x77931),f328(f328(f80(x77931),x77932),x77933)),f328(f328(f80(x77931),x77934),x77935))) % 167.77/167.51 [7794]~P81(x77941)+~P1(f328(f328(f242(x77941),x77943),x77945))+~P1(f328(f328(f243(x77941),x77942),x77944))+P1(f328(f328(f243(x77941),f328(f328(f80(x77941),x77942),x77943)),f328(f328(f80(x77941),x77944),x77945))) % 167.77/167.51 [7795]~P99(x77951)+~P1(f328(f328(f242(x77951),x77953),x77955))+~P1(f328(f328(f242(x77951),x77952),x77954))+P1(f328(f328(f242(x77951),f328(f328(f114(x77951),x77952),x77953)),f328(f328(f114(x77951),x77954),x77955))) % 167.77/167.51 [7796]~P100(x77961)+~P1(f328(f328(f242(x77961),x77963),x77965))+~P1(f328(f328(f242(x77961),x77962),x77964))+P1(f328(f328(f242(x77961),f328(f328(f105(x77961),x77962),x77963)),f328(f328(f105(x77961),x77964),x77965))) % 167.77/167.51 [7797]~P83(x77971)+~P1(f328(f328(f242(x77971),x77973),x77975))+~P1(f328(f328(f242(x77971),x77972),x77974))+P1(f328(f328(f242(x77971),f328(f328(f80(x77971),x77972),x77973)),f328(f328(f80(x77971),x77974),x77975))) % 167.77/167.51 [7798]~P105(x77981)+~P1(f328(f328(f242(x77981),x77983),x77985))+~P1(f328(f328(f242(x77981),x77982),x77984))+P1(f328(f328(f242(x77981),f328(f328(f240(x77981),x77982),x77983)),f328(f328(f240(x77981),x77984),x77985))) % 167.77/167.51 [7799]~P105(x77991)+~P1(f328(f328(f242(x77991),x77993),x77995))+~P1(f328(f328(f242(x77991),x77992),x77994))+P1(f328(f328(f242(x77991),f328(f328(f241(x77991),x77992),x77993)),f328(f328(f241(x77991),x77994),x77995))) % 167.77/167.51 [7937]~P140(x79375)+E(x79371,x79372)+E(x79373,x79374)+~E(f328(f328(f80(x79375),f328(f328(f81(x79375),x79373),x79371)),f328(f328(f81(x79375),x79374),x79372)),f328(f328(f80(x79375),f328(f328(f81(x79375),x79373),x79372)),f328(f328(f81(x79375),x79374),x79371))) % 167.77/167.51 [8070]P28(x80701,x80702,x80703)+~P29(x80701,x80704,x80705)+~P28(x80701,x80702,f597(x80705,x80704,x80701,x80702))+~P1(f328(f328(f330(f871(x80701)),x80703),x80705)) % 167.77/167.51 [8133]~P1(f328(x81331,x81333))+~P1(f328(f328(f328(a198,x81332),x81333),x81335))+~P1(f328(f328(f328(a198,f32(x81331,x81332)),x81335),x81334))+P1(f328(f328(f328(a198,f32(x81331,x81332)),x81333),x81334)) % 167.77/167.51 [8140]~P105(x81404)+~P1(f328(f134(x81401),x81403))+P1(f328(f328(f330(x81401),x81402),f328(f170(x81401),x81403)))+P1(f328(f134(x81401),f328(f328(f145(x81401,x81404,x81405),x81402),x81403))) % 167.77/167.51 [8295]~P66(x82951)+E(f328(f328(f22(x82951),f328(f328(f6(a872,x82951),x82952),f328(f298(a872,x82953),x82954))),f328(f328(f6(a872,x82951),x82952),f328(f298(a872,x82953),x82955))),f328(f328(f6(a872,x82951),x82952),f328(f298(a872,x82955),x82954)))+~P1(f328(f328(f242(a872),x82955),x82954))+~P1(f328(f328(f242(a872),x82953),x82955)) % 167.77/167.51 [8296]~P67(x82961)+E(f328(f328(f80(x82961),f328(f328(f6(a872,x82961),x82962),f328(f298(a872,x82963),x82964))),f328(f328(f6(a872,x82961),x82962),f328(f298(a872,x82964),x82965))),f328(f328(f6(a872,x82961),x82962),f328(f298(a872,x82963),x82965)))+~P1(f328(f328(f242(a872),x82964),x82965))+~P1(f328(f328(f242(a872),x82963),x82964)) % 167.77/167.51 [8627]~P61(x86272)+E(x86271,f2(x86272))+E(x86273,f2(x86272))+E(f328(f328(f286(x86272),f328(f328(f22(x86272),f328(f328(f81(x86272),x86274),x86271)),f328(f328(f81(x86272),x86275),x86273))),f328(f328(f81(x86272),x86273),x86271)),f328(f328(f22(x86272),f328(f328(f286(x86272),x86274),x86273)),f328(f328(f286(x86272),x86275),x86271))) % 167.77/167.51 [8628]~P61(x86282)+E(x86281,f2(x86282))+E(x86283,f2(x86282))+E(f328(f328(f286(x86282),f328(f328(f80(x86282),f328(f328(f81(x86282),x86284),x86281)),f328(f328(f81(x86282),x86285),x86283))),f328(f328(f81(x86282),x86283),x86281)),f328(f328(f80(x86282),f328(f328(f286(x86282),x86284),x86283)),f328(f328(f286(x86282),x86285),x86281))) % 167.77/167.51 [8640]~E(x86402,f328(x86403,x86401))+E(x86401,f540(x86402,x86403,x86404,x86405))+~P26(x86405,x86404,x86403,f251(f879(x86405,a867)))+~P1(f328(f328(f330(x86404),x86402),f328(f307(x86405,x86404,x86403),f251(f879(x86405,a867))))) % 167.77/167.51 [8834]~P117(x88341)+~P1(f328(f328(f243(x88341),f328(f75(x88341),x88342)),x88344))+P1(f328(f328(f243(x88341),f328(f328(f81(x88341),f328(f75(x88341),x88342)),f328(f75(x88341),x88343))),f328(f328(f81(x88341),x88344),x88345)))+~P1(f328(f328(f243(x88341),f328(f75(x88341),x88343)),x88345)) % 167.77/167.51 [8851]~P29(x88511,x88515,x88514)+P28(x88511,x88512,x88513)+P1(f328(f328(f330(f871(x88511)),f597(x88514,x88515,x88511,x88512)),x88515))+~P1(f328(f328(f330(f871(x88511)),x88513),x88514)) % 167.77/167.51 [8956]~P26(x89561,x89563,x89565,x89562)+~P1(f328(f38(x89563),x89564))+P1(f328(f328(f242(a872),f328(f39(x89561),x89562)),f328(f39(x89563),x89564)))+~P1(f328(f328(f242(f879(x89563,a867)),f328(f307(x89561,x89563,x89565),x89562)),x89564)) % 167.77/167.51 [9024]~P67(x90242)+~P26(x90241,x90241,x90244,x90245)+~P1(f328(f38(x90241),x90245))+E(f328(f328(f6(x90241,x90242),f328(f73(x90241,x90242,x90241,x90243),x90244)),x90245),f328(f328(f6(x90241,x90242),x90243),f328(f307(x90241,x90241,x90244),x90245))) % 167.77/167.51 [9025]~P73(x90252)+~P26(x90251,x90251,x90254,x90255)+~P1(f328(f38(x90251),x90255))+E(f328(f328(f9(x90251,x90252),f328(f73(x90251,x90252,x90251,x90253),x90254)),x90255),f328(f328(f9(x90251,x90252),x90253),f328(f307(x90251,x90251,x90254),x90255))) % 167.77/167.51 [9141]~P38(x91411,x91412)+~P1(f328(f328(f330(x91411),x91413),x91414))+~P1(f328(f328(f330(x91411),x91415),x91414))+~P1(f328(f328(f330(f878(x91411,x91411)),f328(f328(f263(x91411,x91411),x91415),f628(x91412,x91411,x91414))),x91412)) % 167.77/167.51 [9179]~P26(x91792,x91793,x91795,x91791)+E(x91791,f192(f879(x91792,a867)))+E(f328(f307(x91793,x91792,f542(x91794,x91793,x91792,x91791)),x91794),x91791)+~P1(f328(f328(f242(f879(x91793,a867)),f328(f307(x91792,x91793,x91795),x91791)),x91794)) % 167.77/167.51 [9660]~P4(x96605)+~P105(x96605)+P1(f328(f328(f330(x96601),f826(x96602,x96603,x96601,x96604,x96605)),x96603))+~P1(f328(f328(f243(x96605),x96604),f328(f328(f44(x96601,x96605),x96603),x96602))) % 167.77/167.51 [9665]~P4(x96651)+~P105(x96651)+P1(f328(f328(f243(x96651),x96652),f328(x96653,f826(x96653,x96654,x96655,x96652,x96651))))+~P1(f328(f328(f243(x96651),x96652),f328(f328(f44(x96655,x96651),x96654),x96653))) % 167.77/167.51 [9743]~P69(x97431)+~P1(f328(f67(x97431,x97431,f81(x97431),x97432,x97433),x97435))+P1(f328(f328(f330(x97431),x97432),x97433))+P1(f328(f67(x97431,x97431,f81(x97431),x97434,f328(f328(f306(x97431),x97432),x97433)),f328(f328(f81(x97431),x97434),x97435))) % 167.77/167.51 [9960]~P67(x99602)+~P1(f328(f38(x99601),x99605))+E(f328(f328(f6(x99601,x99602),f328(f328(f7(x99601,x99602,x99602),f328(f328(f18(x99601,x99602,f879(x99602,x99602)),f328(f328(f8(a867,f879(x99602,f879(x99602,x99602)),x99601),f100(x99602)),f328(a325,x99603))),x99604)),f2(x99602))),x99605),f2(x99602))+P1(f328(f328(f330(x99601),x99603),x99605)) % 167.77/167.51 [9961]~P73(x99612)+~P1(f328(f38(x99611),x99615))+E(f328(f328(f9(x99611,x99612),f328(f328(f7(x99611,x99612,x99612),f328(f328(f18(x99611,x99612,f879(x99612,x99612)),f328(f328(f8(a867,f879(x99612,f879(x99612,x99612)),x99611),f100(x99612)),f328(a325,x99613))),x99614)),f78(x99612))),x99615),f78(x99612))+P1(f328(f328(f330(x99611),x99613),x99615)) % 167.77/167.51 [9962]~P67(x99622)+~P1(f328(f38(x99621),x99625))+E(f328(f328(f6(x99621,x99622),f328(f328(f7(x99621,x99622,x99622),f328(f328(f18(x99621,x99622,f879(x99622,x99622)),f328(f328(f8(a867,f879(x99622,f879(x99622,x99622)),x99621),f100(x99622)),f328(a325,x99623))),x99624)),f2(x99622))),x99625),f328(x99624,x99623))+~P1(f328(f328(f330(x99621),x99623),x99625)) % 167.77/167.51 [9963]~P73(x99632)+~P1(f328(f38(x99631),x99635))+E(f328(f328(f9(x99631,x99632),f328(f328(f7(x99631,x99632,x99632),f328(f328(f18(x99631,x99632,f879(x99632,x99632)),f328(f328(f8(a867,f879(x99632,f879(x99632,x99632)),x99631),f100(x99632)),f328(a325,x99633))),x99634)),f78(x99632))),x99635),f328(x99634,x99633))+~P1(f328(f328(f330(x99631),x99633),x99635)) % 167.77/167.51 [10018]~P67(x100182)+~P1(f328(f38(x100181),x100185))+E(f328(f328(f6(x100181,x100182),f328(f328(f7(x100181,x100182,x100182),f328(f328(f18(x100181,x100182,f879(x100182,x100182)),f328(f328(f8(a867,f879(x100182,f879(x100182,x100182)),x100181),f100(x100182)),f328(f328(f7(x100181,x100181,a867),a325),x100183))),x100184)),f2(x100182))),x100185),f2(x100182))+P1(f328(f328(f330(x100181),x100183),x100185)) % 167.77/167.51 [10019]~P73(x100192)+~P1(f328(f38(x100191),x100195))+E(f328(f328(f9(x100191,x100192),f328(f328(f7(x100191,x100192,x100192),f328(f328(f18(x100191,x100192,f879(x100192,x100192)),f328(f328(f8(a867,f879(x100192,f879(x100192,x100192)),x100191),f100(x100192)),f328(f328(f7(x100191,x100191,a867),a325),x100193))),x100194)),f78(x100192))),x100195),f78(x100192))+P1(f328(f328(f330(x100191),x100193),x100195)) % 167.77/167.51 [10021]~P67(x100212)+~P1(f328(f38(x100211),x100215))+E(f328(f328(f6(x100211,x100212),f328(f328(f7(x100211,x100212,x100212),f328(f328(f18(x100211,x100212,f879(x100212,x100212)),f328(f328(f8(a867,f879(x100212,f879(x100212,x100212)),x100211),f100(x100212)),f328(f328(f7(x100211,x100211,a867),a325),x100213))),x100214)),f2(x100212))),x100215),f328(x100214,x100213))+~P1(f328(f328(f330(x100211),x100213),x100215)) % 167.77/167.51 [10022]~P73(x100222)+~P1(f328(f38(x100221),x100225))+E(f328(f328(f9(x100221,x100222),f328(f328(f7(x100221,x100222,x100222),f328(f328(f18(x100221,x100222,f879(x100222,x100222)),f328(f328(f8(a867,f879(x100222,f879(x100222,x100222)),x100221),f100(x100222)),f328(f328(f7(x100221,x100221,a867),a325),x100223))),x100224)),f78(x100222))),x100225),f328(x100224,x100223))+~P1(f328(f328(f330(x100221),x100223),x100225)) % 167.77/167.51 [7791]~P66(x77912)+~P1(f328(f38(x77911),x77914))+E(f328(f328(f6(x77911,x77912),x77913),f328(f328(f22(f879(x77911,a867)),x77914),f328(f328(f306(x77911),x77915),f192(f879(x77911,a867))))),f328(f328(f6(x77911,x77912),x77913),x77914))+P1(f328(f328(f330(x77911),x77915),x77914)) % 167.77/167.51 [8302]~P109(x83022)+~P1(f328(f38(x83021),x83024))+E(f328(f328(f6(x83021,x83022),x83023),f328(f328(f22(f879(x83021,a867)),x83024),f328(f328(f306(x83021),x83025),f192(f879(x83021,a867))))),f328(f328(f22(x83022),f328(f328(f6(x83021,x83022),x83023),x83024)),f328(x83023,x83025)))+~P1(f328(f328(f330(x83021),x83025),x83024)) % 167.77/167.51 [8303]~P66(x83032)+~P1(f328(f38(x83031),x83034))+E(f328(f328(f6(x83031,x83032),x83033),f328(f328(f22(f879(x83031,a867)),x83034),f328(f328(f306(x83031),x83035),f192(f879(x83031,a867))))),f328(f328(f22(x83032),f328(f328(f6(x83031,x83032),x83033),x83034)),f328(x83033,x83035)))+~P1(f328(f328(f330(x83031),x83035),x83034)) % 167.77/167.51 [8334]~P66(x83341)+~P1(f328(f38(x83342),x83344))+E(f328(f328(f22(x83341),f328(f328(f6(x83342,x83341),x83343),x83344)),f328(f328(f6(x83342,x83341),x83343),x83345)),f328(f328(f6(x83342,x83341),x83343),f328(f328(f22(f879(x83342,a867)),x83344),x83345)))+~P1(f328(f328(f242(f879(x83342,a867)),x83345),x83344)) % 167.77/167.51 [8354]P1(f328(f38(x83541),f328(x83542,x83543)))+~P1(f328(f38(x83544),x83545))+~P1(f328(f328(f330(x83544),x83543),x83545))+~P1(f328(f38(x83541),f328(f328(f44(x83544,f879(x83541,a867)),x83545),x83542))) % 167.77/167.51 [8797]~P7(x87971,x87975,x87974)+~E(f328(f282(x87971,x87971,x87974),f328(f328(f306(x87971),x87972),f192(f879(x87971,a867)))),f328(f282(x87971,x87971,x87974),f328(f328(f306(x87971),x87973),f192(f879(x87971,a867)))))+~P1(f328(f328(f330(x87971),x87973),x87975))+P1(f328(f328(f330(f878(x87971,x87971)),f328(f328(f263(x87971,x87971),x87972),x87973)),x87974)) % 167.77/167.51 [9098]~P1(f328(x90981,x90985))+P1(f328(x90981,f838(x90981,x90982,x90983,x90984)))+P1(f328(x90981,f825(x90981,x90982,x90983,x90984)))+~P1(f328(f328(f330(x90984),x90985),f328(f328(f114(f879(x90984,a867)),x90983),x90982))) % 167.77/167.51 [9282]~P1(f328(x92821,x92825))+P1(f328(x92821,f825(x92821,x92822,x92823,x92824)))+P1(f328(f328(f330(x92824),f838(x92821,x92822,x92823,x92824)),x92822))+~P1(f328(f328(f330(x92824),x92825),f328(f328(f114(f879(x92824,a867)),x92823),x92822))) % 167.77/167.51 [9283]~P1(f328(x92831,x92835))+P1(f328(x92831,f838(x92831,x92832,x92833,x92834)))+P1(f328(f328(f330(x92834),f825(x92831,x92832,x92833,x92834)),x92833))+~P1(f328(f328(f330(x92834),x92835),f328(f328(f114(f879(x92834,a867)),x92833),x92832))) % 167.77/167.51 [9289]P1(f328(x92891,x92892))+~P1(f328(x92891,f779(x92891,x92893,x92894,x92895)))+~P1(f328(x92891,f667(x92891,x92893,x92894,x92895)))+~P1(f328(f328(f330(x92895),x92892),f328(f328(f114(f879(x92895,a867)),x92894),x92893))) % 167.77/167.51 [9331]E(x93311,x93312)+~P1(f328(f328(f330(f878(x93313,x93313)),f328(f328(f263(x93313,x93313),x93311),x93312)),f304(x93313,x93315)))+P1(f328(f328(f330(x93313),x93311),x93314))+~P1(f328(f328(f242(f879(f878(x93313,x93313),a867)),x93315),f328(f328(f265(x93313,x93313),x93314),f328(f16(f879(x93313,a867),x93313),x93314)))) % 167.77/167.51 [9350]P1(f328(x93501,x93502))+~P1(f328(x93501,f667(x93501,x93504,x93505,x93503)))+P1(f328(f328(f330(x93503),f779(x93501,x93504,x93505,x93503)),x93504))+~P1(f328(f328(f330(x93503),x93502),f328(f328(f114(f879(x93503,a867)),x93505),x93504))) % 167.77/167.51 [9351]P1(f328(x93511,x93512))+~P1(f328(x93511,f779(x93511,x93514,x93515,x93513)))+P1(f328(f328(f330(x93513),f667(x93511,x93514,x93515,x93513)),x93515))+~P1(f328(f328(f330(x93513),x93512),f328(f328(f114(f879(x93513,a867)),x93515),x93514))) % 167.77/167.51 [9412]P1(f328(x94121,x94122))+P1(f328(f328(f330(x94123),f779(x94121,x94124,x94125,x94123)),x94124))+P1(f328(f328(f330(x94123),f667(x94121,x94124,x94125,x94123)),x94125))+~P1(f328(f328(f330(x94123),x94122),f328(f328(f114(f879(x94123,a867)),x94125),x94124))) % 167.77/167.51 [9414]~P1(f328(x94142,x94145))+P1(f328(f328(f330(x94141),f838(x94142,x94143,x94144,x94141)),x94143))+P1(f328(f328(f330(x94141),f825(x94142,x94143,x94144,x94141)),x94144))+~P1(f328(f328(f330(x94141),x94145),f328(f328(f114(f879(x94141,a867)),x94144),x94143))) % 167.77/167.51 [9565]~P7(x95651,x95655,x95654)+~P1(f328(f328(f330(x95651),x95653),x95655))+P1(f328(f328(f330(f878(x95651,x95651)),f328(f328(f263(x95651,x95651),x95652),x95653)),x95654))+~P1(f328(f328(f242(f879(x95651,a867)),f328(f282(x95651,x95651,x95654),f328(f328(f306(x95651),x95653),f192(f879(x95651,a867))))),f328(f282(x95651,x95651,x95654),f328(f328(f306(x95651),x95652),f192(f879(x95651,a867)))))) % 167.77/167.51 [9691]~P4(x96915)+~P105(x96915)+P1(f328(f328(f330(x96911),f827(x96912,x96913,x96914,x96911,x96915)),x96914))+~P1(f328(f328(f243(x96915),f328(f328(f43(x96911,x96915),x96914),x96913)),x96912)) % 167.77/167.51 [9723]~P79(x97235)+~P83(x97235)+P1(f328(f328(f330(x97231),f712(x97232,x97233,x97234,x97231,x97235)),f328(f170(x97231),x97234)))+P1(f328(f328(f242(x97235),f328(f163(x97235),f328(f328(f151(x97231,x97235),x97233),x97234))),f328(f163(x97235),f328(f328(f151(x97231,x97235),x97232),x97234)))) % 167.77/167.51 [9838]~P4(x98381)+~P105(x98381)+P1(f328(f328(f243(x98381),f328(x98382,f827(x98383,x98382,x98384,x98385,x98381))),x98383))+~P1(f328(f328(f243(x98381),f328(f328(f43(x98385,x98381),x98384),x98382)),x98383)) % 167.77/167.51 [9978]~P79(x99781)+~P83(x99781)+~P1(f328(f328(f242(x99781),f328(x99783,f712(x99785,x99783,x99784,x99782,x99781))),f328(x99785,f712(x99785,x99783,x99784,x99782,x99781))))+P1(f328(f328(f242(x99781),f328(f163(x99781),f328(f328(f151(x99782,x99781),x99783),x99784))),f328(f163(x99781),f328(f328(f151(x99782,x99781),x99785),x99784)))) % 167.77/167.51 [8648]~P67(x86481)+~P1(f328(f38(x86484),x86485))+~P1(f328(f328(f330(x86484),x86483),x86485))+E(f328(f328(f80(x86481),f328(x86482,x86483)),f328(f328(f6(x86484,x86481),x86482),f328(f328(f22(f879(x86484,a867)),x86485),f328(f328(f306(x86484),x86483),f192(f879(x86484,a867)))))),f328(f328(f6(x86484,x86481),x86482),x86485)) % 167.77/167.51 [8649]~P73(x86491)+~P1(f328(f38(x86494),x86495))+~P1(f328(f328(f330(x86494),x86493),x86495))+E(f328(f328(f81(x86491),f328(x86492,x86493)),f328(f328(f9(x86494,x86491),x86492),f328(f328(f22(f879(x86494,a867)),x86495),f328(f328(f306(x86494),x86493),f192(f879(x86494,a867)))))),f328(f328(f9(x86494,x86491),x86492),x86495)) % 167.77/167.51 [8704]~P19(x87041,x87044,x87045)+~P1(f328(f38(x87041),x87042))+E(f328(f328(f22(f879(x87041,a867)),x87042),f328(f328(f306(x87041),x87043),f192(f879(x87041,a867)))),f192(f879(x87041,a867)))+E(f328(f328(x87044,x87043),f328(x87045,f328(f328(f22(f879(x87041,a867)),x87042),f328(f328(f306(x87041),x87043),f192(f879(x87041,a867)))))),f328(x87045,f328(f328(f306(x87041),x87043),x87042))) % 167.77/167.51 [9078]~P67(x90781)+~P1(f328(f38(x90782),x90785))+~P1(f328(f38(x90782),x90784))+E(f328(f328(f80(x90781),f328(f328(f6(x90782,x90781),x90783),f328(f328(f114(f879(x90782,a867)),x90784),x90785))),f328(f328(f6(x90782,x90781),x90783),f328(f328(f105(f879(x90782,a867)),x90784),x90785))),f328(f328(f80(x90781),f328(f328(f6(x90782,x90781),x90783),x90784)),f328(f328(f6(x90782,x90781),x90783),x90785))) % 167.77/167.51 [9080]~P73(x90801)+~P1(f328(f38(x90802),x90805))+~P1(f328(f38(x90802),x90804))+E(f328(f328(f81(x90801),f328(f328(f9(x90802,x90801),x90803),f328(f328(f114(f879(x90802,a867)),x90804),x90805))),f328(f328(f9(x90802,x90801),x90803),f328(f328(f105(f879(x90802,a867)),x90804),x90805))),f328(f328(f81(x90801),f328(f328(f9(x90802,x90801),x90803),x90804)),f328(f328(f9(x90802,x90801),x90803),x90805))) % 167.77/167.51 [9221]~P66(x92211)+~P1(f328(f38(x92212),x92215))+~P1(f328(f38(x92212),x92214))+E(f328(f328(f22(x92211),f328(f328(f80(x92211),f328(f328(f6(x92212,x92211),x92213),x92214)),f328(f328(f6(x92212,x92211),x92213),x92215))),f328(f328(f6(x92212,x92211),x92213),f328(f328(f105(f879(x92212,a867)),x92214),x92215))),f328(f328(f6(x92212,x92211),x92213),f328(f328(f114(f879(x92212,a867)),x92214),x92215))) % 167.77/167.51 [9423]~P26(x94231,x94232,x94233,x94235)+~P26(x94231,x94232,x94233,x94234)+P26(x94231,x94232,x94233,f328(f328(f114(f879(x94231,a867)),x94234),x94235))+~E(f328(f328(f105(f879(x94232,a867)),f328(f307(x94231,x94232,x94233),f328(f328(f22(f879(x94231,a867)),x94234),x94235))),f328(f307(x94231,x94232,x94233),f328(f328(f22(f879(x94231,a867)),x94235),x94234))),f192(f879(x94232,a867))) % 167.77/167.51 [9540]E(x95401,f2(a1))+~P1(f328(f328(f243(a1),f2(a1)),x95403))+~P1(f328(f50(x95402,x95401),f328(f328(f263(a1,a1),x95404),x95405)))+P1(f328(f50(x95402,f328(f328(f81(a1),x95401),x95403)),f328(f328(f263(a1,a1),f328(f328(f40(a1),x95404),x95403)),f328(f328(f80(a1),f328(f328(f81(a1),x95401),f46(a1,x95404,x95403))),x95405)))) % 167.77/167.51 [9548]~P1(f328(f328(f243(a872),f2(a872)),x95483))+~P1(f328(f328(f243(a872),f2(a872)),x95482))+~P1(f328(f49(x95481,x95482),f328(f328(f263(a872,a872),x95484),x95485)))+P1(f328(f49(x95481,f328(f328(f81(a872),x95482),x95483)),f328(f328(f263(a872,a872),f328(f328(f40(a872),x95484),x95483)),f328(f328(f80(a872),f328(f328(f81(a872),x95482),f46(a872,x95484,x95483))),x95485)))) % 167.77/167.51 [9597]~P73(x95971)+~P1(f328(f38(x95972),x95975))+~P1(f328(f38(x95972),x95974))+E(f328(f328(f81(x95971),f328(f328(f328(f66(x95971,x95972,f81(x95971)),x95973),f78(x95971)),f328(f328(f114(f879(x95972,a867)),x95974),x95975))),f328(f328(f328(f66(x95971,x95972,f81(x95971)),x95973),f78(x95971)),f328(f328(f105(f879(x95972,a867)),x95974),x95975))),f328(f328(f81(x95971),f328(f328(f328(f66(x95971,x95972,f81(x95971)),x95973),f78(x95971)),x95974)),f328(f328(f328(f66(x95971,x95972,f81(x95971)),x95973),f78(x95971)),x95975))) % 167.77/167.51 [9599]~E(f328(f328(f173(x95991),x95995),x95992),f328(f328(f173(x95991),x95995),x95993))+P1(f328(f328(f330(f878(f873(x95991),f873(x95991))),f328(f328(f263(f873(x95991),f873(x95991)),x95992),x95993)),f144(x95991,x95994)))+~P1(f328(f328(f243(a872),x95995),f328(f328(f240(a872),f328(f193(f873(x95991)),x95992)),f328(f193(f873(x95991)),x95993))))+~P1(f328(f328(f330(f878(x95991,x95991)),f328(f328(f263(x95991,x95991),f328(f328(f162(x95991),x95992),x95995)),f328(f328(f162(x95991),x95993),x95995))),x95994)) % 167.77/167.51 [9711]~P83(x97115)+~P142(x97115)+P1(f328(f328(f330(x97111),f365(x97112,x97113,x97114,x97111,x97115)),x97114))+P1(f328(f328(f242(x97115),f328(f328(f6(x97111,x97115),x97113),x97114)),f328(f328(f81(x97115),f328(f104(x97115),f328(f39(x97111),x97114))),x97112))) % 167.77/167.51 [9906]~P83(x99061)+~P142(x99061)+~P1(f328(f328(f242(x99061),f328(x99063,f365(x99065,x99063,x99064,x99062,x99061))),x99065))+P1(f328(f328(f242(x99061),f328(f328(f6(x99062,x99061),x99063),x99064)),f328(f328(f81(x99061),f328(f104(x99061),f328(f39(x99062),x99064))),x99065))) % 167.77/167.51 [8676]E(f328(f328(f125(x86761),x86762),x86763),f328(f328(f125(x86761),x86764),x86765))+~E(f328(f328(f173(x86761),f328(f193(f873(x86761)),x86762)),x86764),x86762)+~E(f328(f328(f125(x86761),f328(f328(f135(x86761),f328(f193(f873(x86761)),x86762)),x86764)),x86765),x86763)+P1(f328(f328(f242(a872),f328(f193(f873(x86761)),x86764)),f328(f193(f873(x86761)),x86762))) % 167.77/167.51 [8796]E(f328(f328(f125(x87961),x87962),x87963),f328(f328(f125(x87961),x87964),x87965))+~E(f328(f328(f173(x87961),f328(f193(f873(x87961)),x87962)),x87964),x87962)+~E(x87963,f328(f328(f125(x87961),f328(f328(f135(x87961),f328(f193(f873(x87961)),x87962)),x87964)),x87965))+~P1(f328(f328(f242(a872),f328(f193(f873(x87961)),x87962)),f328(f193(f873(x87961)),x87964))) % 167.77/167.51 [10040]~P1(f328(x100405,x100404))+~P1(f328(f38(x100402),f328(f248(x100402),x100405)))+P1(f328(f38(x100401),f328(f248(x100401),f328(f328(f7(x100401,x100402,a867),x100403),x100404))))+~P1(f328(f38(x100401),f328(f248(x100401),f328(f328(f8(f879(x100402,a867),a867,x100401),f87(x100402)),f328(f328(f8(f879(x100402,a867),f879(x100402,a867),x100401),f328(f18(x100402,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100402),a326),x100405))),x100403))))) % 167.77/167.51 [8462]~P20(x84625,x84621,x84626,x84622)+E(f328(f73(x84621,x84621,x84621,f328(x84622,x84623)),f328(x84622,x84624)),f328(f73(x84621,x84621,x84621,f328(x84622,x84624)),f328(x84622,x84623)))+~P1(f328(f38(x84625),x84624))+~P1(f328(f38(x84625),x84623)) % 167.77/167.51 [7848]~P26(x78481,x78482,x78484,x78483)+~E(f328(x78484,x78486),x78485)+E(f328(f77(x78481,x78482,x78483,x78484),x78485),x78486)+~P1(f328(f328(f330(x78481),x78486),x78483)) % 167.77/167.51 [8039]~P21(x80396,x80391,x80394,x80392)+E(f328(f73(x80391,x80391,x80391,f328(x80392,x80393)),f328(x80394,x80395)),f328(x80392,x80393))+~P1(f328(f38(x80396),x80393))+~P1(f328(f328(f330(x80396),x80395),x80393)) % 167.77/167.51 [9268]~P20(x92683,x92681,x92686,x92682)+E(f328(f73(x92681,x92681,x92681,f328(x92682,f328(f328(f22(f879(x92683,a867)),x92684),f328(f328(f306(x92683),x92685),f192(f879(x92683,a867)))))),f328(x92686,x92685)),f328(x92682,x92684))+~P1(f328(f38(x92683),x92684))+~P1(f328(f328(f330(x92683),x92685),x92684)) % 167.77/167.51 [6924]~P58(x69241)+~E(f46(x69241,x69243,x69244),f46(x69241,x69246,x69244))+~E(f46(x69241,x69242,x69244),f46(x69241,x69245,x69244))+E(f46(x69241,f328(f328(f22(x69241),x69242),x69243),x69244),f46(x69241,f328(f328(f22(x69241),x69245),x69246),x69244)) % 167.77/167.51 [6925]~P57(x69251)+~E(f46(x69251,x69253,x69254),f46(x69251,x69256,x69254))+~E(f46(x69251,x69252,x69254),f46(x69251,x69255,x69254))+E(f46(x69251,f328(f328(f80(x69251),x69252),x69253),x69254),f46(x69251,f328(f328(f80(x69251),x69255),x69256),x69254)) % 167.77/167.51 [6926]~P57(x69261)+~E(f46(x69261,x69263,x69264),f46(x69261,x69266,x69264))+~E(f46(x69261,x69262,x69264),f46(x69261,x69265,x69264))+E(f46(x69261,f328(f328(f81(x69261),x69262),x69263),x69264),f46(x69261,f328(f328(f81(x69261),x69265),x69266),x69264)) % 167.77/167.51 [7739]~P17(x77391,x77392,x77393)+~P1(f328(f38(x77391),x77396))+E(f328(f328(f65(x77391,x77392,x77393),x77394),f328(f328(f306(x77391),x77395),x77396)),f328(f328(f65(x77391,x77392,x77393),f328(f328(x77393,x77395),x77394)),x77396))+P1(f328(f328(f330(x77391),x77395),x77396)) % 167.77/167.51 [7806]~P4(x78061)+P1(f328(f328(f242(x78061),x78062),f328(x78063,x78064)))+~P1(f328(f328(f330(x78065),x78064),x78066))+~P1(f328(f328(f242(x78061),x78062),f328(f328(f43(x78065,x78061),x78066),x78063))) % 167.77/167.51 [7963]~P17(x79631,x79632,x79633)+~P1(f328(f38(x79631),x79636))+E(f328(f328(f65(x79631,x79632,x79633),x79634),f328(f328(f306(x79631),x79635),x79636)),f328(f328(x79633,x79635),f328(f328(f65(x79631,x79632,x79633),x79634),x79636)))+P1(f328(f328(f330(x79631),x79635),x79636)) % 167.77/167.51 [8055]~P105(x80553)+~P1(f328(x80552,x80555))+~P15(x80553,f328(f328(f151(x80551,x80553),x80554),x80556))+E(f328(f133(x80551,x80552),f328(f328(f145(x80551,x80553,x80554),x80555),x80556)),f328(f328(f145(x80551,x80553,x80554),x80555),f328(f133(x80551,x80552),x80556))) % 167.77/167.51 [8078]E(x80781,x80782)+E(x80783,f2(a1))+~P1(f328(f50(x80784,x80783),f328(f328(f263(a1,a1),x80785),x80782)))+~P1(f328(f50(x80784,x80783),f328(f328(f263(a1,a1),x80786),x80781))) % 167.77/167.51 [8079]E(x80791,x80792)+E(x80793,f2(a1))+~P1(f328(f50(x80794,x80793),f328(f328(f263(a1,a1),x80792),x80795)))+~P1(f328(f50(x80794,x80793),f328(f328(f263(a1,a1),x80791),x80796))) % 167.77/167.51 [8100]~P20(x81002,x81005,x81006,x81001)+~P1(f328(f38(x81002),x81004))+E(f328(x81001,f328(f328(f306(x81002),x81003),x81004)),f328(f73(x81005,x81005,x81005,f328(x81001,x81004)),f328(x81006,x81003)))+P1(f328(f328(f330(x81002),x81003),x81004)) % 167.77/167.51 [8337]~P21(x83375,x83371,x83376,x83372)+E(f328(f73(x83371,x83371,x83371,f328(x83372,x83373)),f328(x83372,x83374)),f328(x83372,x83373))+~P1(f328(f38(x83375),x83373))+~P1(f328(f328(f242(f879(x83375,a867)),x83374),x83373)) % 167.77/167.51 [9469]~P26(x94691,x94692,x94694,x94693)+~P1(f328(f328(f330(x94692),x94695),f328(f307(x94691,x94692,x94694),x94693)))+P1(f328(f328(f330(x94691),f328(f77(x94691,x94692,x94693,x94694),x94695)),x94696))+~P1(f328(f328(f242(f879(x94691,a867)),x94693),x94696)) % 167.77/167.51 [9851]~P67(x98512)+~E(f600(x98511,x98513,x98515,x98516,x98514,x98512),f601(x98511,x98513,x98515,x98516,x98514,x98512))+~P1(f328(f38(x98514),x98516))+E(f328(f328(f6(x98511,x98512),x98513),f328(f307(x98514,x98511,x98515),x98516)),f328(f328(f6(x98514,x98512),f328(f73(x98511,x98512,x98514,x98513),x98515)),x98516)) % 167.77/167.51 [9888]~P67(x98886)+E(f328(x98881,f600(x98882,x98883,x98881,x98884,x98885,x98886)),f328(x98881,f601(x98882,x98883,x98881,x98884,x98885,x98886)))+E(f328(f328(f6(x98882,x98886),x98883),f328(f307(x98885,x98882,x98881),x98884)),f328(f328(f6(x98885,x98886),f328(f73(x98882,x98886,x98885,x98883),x98881)),x98884))+~P1(f328(f38(x98885),x98884)) % 167.77/167.51 [9928]~P67(x99282)+~E(f328(x99283,f328(x99285,f601(x99281,x99283,x99285,x99286,x99284,x99282))),f2(x99282))+~P1(f328(f38(x99284),x99286))+E(f328(f328(f6(x99281,x99282),x99283),f328(f307(x99284,x99281,x99285),x99286)),f328(f328(f6(x99284,x99282),f328(f73(x99281,x99282,x99284,x99283),x99285)),x99286)) % 167.77/167.51 [9986]~P67(x99862)+~P1(f328(f38(x99864),x99866))+E(f328(f328(f6(x99861,x99862),x99863),f328(f307(x99864,x99861,x99865),x99866)),f328(f328(f6(x99864,x99862),f328(f73(x99861,x99862,x99864,x99863),x99865)),x99866))+P1(f328(f328(f330(x99864),f601(x99861,x99863,x99865,x99866,x99864,x99862)),x99866)) % 167.77/167.51 [9987]~P67(x99872)+~P1(f328(f38(x99874),x99876))+E(f328(f328(f6(x99871,x99872),x99873),f328(f307(x99874,x99871,x99875),x99876)),f328(f328(f6(x99874,x99872),f328(f73(x99871,x99872,x99874,x99873),x99875)),x99876))+P1(f328(f328(f330(x99874),f600(x99871,x99873,x99875,x99876,x99874,x99872)),x99876)) % 167.77/167.51 [10099]~P73(x100991)+~P1(f328(f38(x100992),x100996))+E(f328(f328(f328(f66(x100991,x100992,f81(x100991)),f328(f328(f18(x100992,f879(x100993,a867),x100991),f328(f328(f7(x100992,x100991,f879(f879(x100993,a867),x100991)),f328(f328(f8(f879(x100993,x100991),f879(x100991,f879(f879(x100993,a867),x100991)),x100992),f66(x100991,x100993,f81(x100991))),x100994)),f78(x100991))),x100995)),f78(x100991)),x100996),f328(f328(f328(f66(x100991,f878(x100992,x100993),f81(x100991)),f328(f267(x100992,x100993,x100991),x100994)),f78(x100991)),f328(f328(f265(x100992,x100993),x100996),x100995)))+P1(f328(f328(f330(x100992),f566(x100994,x100995,x100993,x100996,x100992,x100991)),x100996)) % 167.77/167.51 [10117]~P73(x101171)+~P1(f328(f38(x101172),x101176))+E(f328(f328(f328(f66(x101171,x101172,f81(x101171)),f328(f328(f18(x101172,f879(x101173,a867),x101171),f328(f328(f7(x101172,x101171,f879(f879(x101173,a867),x101171)),f328(f328(f8(f879(x101173,x101171),f879(x101171,f879(f879(x101173,a867),x101171)),x101172),f66(x101171,x101173,f81(x101171))),x101174)),f78(x101171))),x101175)),f78(x101171)),x101176),f328(f328(f328(f66(x101171,f878(x101172,x101173),f81(x101171)),f328(f267(x101172,x101173,x101171),x101174)),f78(x101171)),f328(f328(f265(x101172,x101173),x101176),x101175)))+~P1(f328(f38(x101173),f328(x101175,f566(x101174,x101175,x101173,x101176,x101172,x101171)))) % 167.77/167.51 [8250]~P21(x82502,x82505,x82506,x82501)+~P1(f328(f38(x82502),x82504))+~P1(f328(f38(x82502),x82503))+E(f328(x82501,f328(f328(f114(f879(x82502,a867)),x82503),x82504)),f328(f73(x82505,x82505,x82505,f328(x82501,x82503)),f328(x82501,x82504))) % 167.77/167.51 [8463]~P4(x84631)+P1(f328(f328(f242(x84631),f328(x84632,x84633)),x84634))+~P1(f328(f328(f330(x84635),x84633),x84636))+~P1(f328(f328(f242(x84631),f328(f328(f44(x84635,x84631),x84636),x84632)),x84634)) % 167.77/167.51 [8875]~P26(x88752,x88751,x88753,x88756)+E(f328(f328(f22(f879(x88751,a867)),f328(f307(x88752,x88751,x88753),x88754)),f328(f307(x88752,x88751,x88753),x88755)),f328(f307(x88752,x88751,x88753),f328(f328(f22(f879(x88752,a867)),x88754),x88755)))+~P1(f328(f328(f242(f879(x88752,a867)),x88755),x88756))+~P1(f328(f328(f242(f879(x88752,a867)),x88754),x88756)) % 167.77/167.51 [8876]~P26(x88762,x88761,x88763,x88766)+E(f328(f328(f105(f879(x88761,a867)),f328(f307(x88762,x88761,x88763),x88764)),f328(f307(x88762,x88761,x88763),x88765)),f328(f307(x88762,x88761,x88763),f328(f328(f105(f879(x88762,a867)),x88764),x88765)))+~P1(f328(f328(f242(f879(x88762,a867)),x88765),x88766))+~P1(f328(f328(f242(f879(x88762,a867)),x88764),x88766)) % 167.77/167.51 [8914]~P1(f328(x89141,x89143))+~P1(f328(f328(f328(f328(a200,x89142),x89143),x89144),x89146))+~P1(f328(f328(f328(f328(a200,f32(x89141,x89142)),x89146),x89144),x89145))+P1(f328(f328(f328(f328(a200,f32(x89141,x89142)),x89143),x89144),x89145)) % 167.77/167.51 [9143]E(x91431,x91432)+~P51(x91433,x91434,x91435)+~P1(f328(f328(f330(f878(x91433,x91434)),f328(f328(f263(x91433,x91434),x91436),x91432)),x91435))+~P1(f328(f328(f330(f878(x91433,x91434)),f328(f328(f263(x91433,x91434),x91436),x91431)),x91435)) % 167.77/167.51 [9923]~P69(x99231)+~E(f328(x99233,f499(x99234,x99236,x99233,x99235,x99232,x99231)),f328(x99236,f499(x99234,x99236,x99233,x99235,x99232,x99231)))+~P1(f328(f38(x99232),x99235))+E(f328(f328(f328(f66(x99231,x99232,f81(x99231)),x99233),x99234),x99235),f328(f328(f328(f66(x99231,x99232,f81(x99231)),x99236),x99234),x99235)) % 167.77/167.51 [9984]~P69(x99841)+~P1(f328(f38(x99842),x99845))+E(f328(f328(f328(f66(x99841,x99842,f81(x99841)),x99843),x99844),x99845),f328(f328(f328(f66(x99841,x99842,f81(x99841)),x99846),x99844),x99845))+P1(f328(f328(f330(x99842),f499(x99844,x99843,x99846,x99845,x99842,x99841)),x99845)) % 167.77/167.51 [8689]~P69(x86891)+~P1(f328(f38(x86892),x86896))+P1(f328(f328(f330(x86892),x86895),x86896))+E(f328(f328(f328(f66(x86891,x86892,f81(x86891)),x86893),x86894),f328(f328(f306(x86892),x86895),x86896)),f328(f328(f81(x86891),f328(x86893,x86895)),f328(f328(f328(f66(x86891,x86892,f81(x86891)),x86893),x86894),x86896))) % 167.77/167.51 [8735]~P7(x87351,x87356,x87353)+~P13(x87351,f879(x87352,a867),x87353,x87355)+~P1(f328(f328(f330(x87351),x87354),x87356))+E(f328(f328(f44(x87351,f879(x87352,a867)),f328(f282(x87351,x87351,x87353),f328(f328(f306(x87351),x87354),f192(f879(x87351,a867))))),x87355),f328(x87355,x87354)) % 167.77/167.51 [8852]~P17(x88523,x88524,x88521)+~P1(f328(f38(x88523),x88526))+~P1(f328(f328(f330(x88523),x88522),x88526))+E(f328(f328(x88521,x88522),f328(f328(f65(x88523,x88524,x88521),x88525),f328(f328(f22(f879(x88523,a867)),x88526),f328(f328(f306(x88523),x88522),f192(f879(x88523,a867)))))),f328(f328(f65(x88523,x88524,x88521),x88525),x88526)) % 167.77/167.51 [9156]~P20(x91563,x91561,x91566,x91562)+~P1(f328(f38(x91563),x91565))+~P1(f328(f38(x91563),x91564))+E(f328(f73(x91561,x91561,x91561,f328(x91562,f328(f328(f114(f879(x91563,a867)),x91564),x91565))),f328(x91562,f328(f328(f105(f879(x91563,a867)),x91564),x91565))),f328(f73(x91561,x91561,x91561,f328(x91562,x91564)),f328(x91562,x91565))) % 167.77/167.51 [9491]~E(x94913,f328(f328(f156(x94911,x94912),x94915),x94916))+P1(f328(f328(f330(f878(f873(x94911),f873(x94911))),f328(f328(f263(f873(x94911),f873(x94911)),x94912),x94913)),f154(x94911,x94914)))+~P1(f328(f328(f243(a872),x94915),f328(f193(f873(x94911)),x94912)))+~P1(f328(f328(f330(f878(x94911,x94911)),f328(f328(f263(x94911,x94911),f328(f328(f162(x94911),x94912),x94915)),x94916)),x94914)) % 167.77/167.51 [9997]~P67(x99972)+~P1(f328(f38(x99971),x99976))+P1(f328(f328(f330(x99971),f564(x99974,x99975,x99973,x99976,x99971,x99972)),x99976))+E(f328(f328(f6(x99971,x99972),f328(f328(f18(x99971,f879(x99973,a867),x99972),f328(f328(f8(f879(x99973,x99972),f879(f879(x99973,a867),x99972),x99971),f6(x99973,x99972)),x99974)),x99975)),x99976),f328(f328(f6(f878(x99971,x99973),x99972),f328(f267(x99971,x99973,x99972),x99974)),f328(f328(f265(x99971,x99973),x99976),x99975))) % 167.77/167.51 [9998]~P73(x99982)+~P1(f328(f38(x99981),x99986))+P1(f328(f328(f330(x99981),f565(x99984,x99985,x99983,x99986,x99981,x99982)),x99986))+E(f328(f328(f9(x99981,x99982),f328(f328(f18(x99981,f879(x99983,a867),x99982),f328(f328(f8(f879(x99983,x99982),f879(f879(x99983,a867),x99982),x99981),f9(x99983,x99982)),x99984)),x99985)),x99986),f328(f328(f9(f878(x99981,x99983),x99982),f328(f267(x99981,x99983,x99982),x99984)),f328(f328(f265(x99981,x99983),x99986),x99985))) % 167.77/167.51 [10037]~P67(x100372)+~P1(f328(f38(x100371),x100376))+~P1(f328(f38(x100373),f328(x100375,f564(x100374,x100375,x100373,x100376,x100371,x100372))))+E(f328(f328(f6(x100371,x100372),f328(f328(f18(x100371,f879(x100373,a867),x100372),f328(f328(f8(f879(x100373,x100372),f879(f879(x100373,a867),x100372),x100371),f6(x100373,x100372)),x100374)),x100375)),x100376),f328(f328(f6(f878(x100371,x100373),x100372),f328(f267(x100371,x100373,x100372),x100374)),f328(f328(f265(x100371,x100373),x100376),x100375))) % 167.77/167.51 [10038]~P73(x100382)+~P1(f328(f38(x100381),x100386))+~P1(f328(f38(x100383),f328(x100385,f565(x100384,x100385,x100383,x100386,x100381,x100382))))+E(f328(f328(f9(x100381,x100382),f328(f328(f18(x100381,f879(x100383,a867),x100382),f328(f328(f8(f879(x100383,x100382),f879(f879(x100383,a867),x100382),x100381),f9(x100383,x100382)),x100384)),x100385)),x100386),f328(f328(f9(f878(x100381,x100383),x100382),f328(f267(x100381,x100383,x100382),x100384)),f328(f328(f265(x100381,x100383),x100386),x100385))) % 167.77/167.51 [10020]~P73(x100202)+~P1(f328(f38(x100201),x100206))+P1(f328(f328(f330(x100201),x100203),x100206))+E(f328(f328(f9(x100201,x100202),f328(f328(f7(x100201,x100202,x100202),f328(f328(f18(x100201,x100202,f879(x100202,x100202)),f328(f328(f8(a867,f879(x100202,f879(x100202,x100202)),x100201),f100(x100202)),f328(f328(f7(x100201,x100201,a867),a325),x100203))),x100204)),x100205)),x100206),f328(f328(f253(x100202),x100205),f328(f39(x100201),x100206))) % 167.77/167.51 [10025]~P73(x100252)+~P1(f328(f38(x100251),x100256))+~P1(f328(f328(f330(x100251),x100253),x100256))+E(f328(f328(f9(x100251,x100252),f328(f328(f7(x100251,x100252,x100252),f328(f328(f18(x100251,x100252,f879(x100252,x100252)),f328(f328(f8(a867,f879(x100252,f879(x100252,x100252)),x100251),f100(x100252)),f328(f328(f7(x100251,x100251,a867),a325),x100253))),x100254)),x100255)),x100256),f328(f328(f81(x100252),f328(x100254,x100253)),f328(f328(f253(x100252),x100255),f328(f328(f22(a872),f328(f39(x100251),x100256)),f78(a872))))) % 167.77/167.51 [10092]~P1(f328(f38(x100921),x100925))+~P1(f328(f38(x100922),x100923))+P1(f328(f328(f330(x100922),f462(x100926,x100924,x100923,x100922,x100925,x100921)),x100923))+E(f328(f328(f6(x100921,a872),f328(f328(f8(f879(x100922,a867),a872,x100921),f39(x100922)),f328(f328(f8(f879(x100922,a867),f879(x100922,a867),x100921),f248(x100922)),f328(f328(f8(f879(x100922,a867),f879(x100922,a867),x100921),f328(f18(x100922,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100922),a326),f328(f328(f7(x100922,f879(x100922,a867),a867),f330(x100922)),x100923)))),x100924)))),x100925),f328(f328(f81(a872),x100926),f328(f39(x100922),x100923))) % 167.77/167.51 [10093]~P1(f328(f38(x100931),x100935))+~P1(f328(f38(x100932),x100933))+P1(f328(f328(f330(x100932),f463(x100936,x100934,x100933,x100932,x100935,x100931)),x100933))+E(f328(f328(f6(x100931,a872),f328(f328(f8(f879(x100932,a867),a872,x100931),f39(x100932)),f328(f328(f8(f879(x100932,a867),f879(x100932,a867),x100931),f248(x100932)),f328(f328(f8(f879(x100932,a867),f879(x100932,a867),x100931),f328(f18(x100932,a867,a867),f328(f328(f8(a867,f879(a867,a867),x100932),a326),f328(f328(f7(x100932,f879(x100932,a867),a867),f330(x100932)),x100933)))),x100934)))),x100935),f328(f328(f6(x100932,a872),x100936),x100933)) % 167.77/167.51 [10123]~P1(f328(f38(x101232),x101233))+~P1(f328(f38(x101231),x101235))+~E(f328(f39(x101231),f328(f248(x101231),f328(f328(f18(x101231,a867,a867),f328(f328(f8(a867,f879(a867,a867),x101231),a326),f328(f328(f7(x101231,f879(x101231,a867),a867),f330(x101231)),x101235))),f328(f328(f7(x101231,x101232,a867),x101234),f462(x101236,x101234,x101233,x101232,x101235,x101231))))),x101236)+E(f328(f328(f6(x101231,a872),f328(f328(f8(f879(x101232,a867),a872,x101231),f39(x101232)),f328(f328(f8(f879(x101232,a867),f879(x101232,a867),x101231),f248(x101232)),f328(f328(f8(f879(x101232,a867),f879(x101232,a867),x101231),f328(f18(x101232,a867,a867),f328(f328(f8(a867,f879(a867,a867),x101232),a326),f328(f328(f7(x101232,f879(x101232,a867),a867),f330(x101232)),x101233)))),x101234)))),x101235),f328(f328(f81(a872),x101236),f328(f39(x101232),x101233))) % 167.77/167.51 [10125]~P1(f328(f38(x101252),x101253))+~P1(f328(f38(x101251),x101255))+~E(f328(f39(x101251),f328(f248(x101251),f328(f328(f18(x101251,a867,a867),f328(f328(f8(a867,f879(a867,a867),x101251),a326),f328(f328(f7(x101251,f879(x101251,a867),a867),f330(x101251)),x101255))),f328(f328(f7(x101251,x101252,a867),x101254),f463(x101256,x101254,x101253,x101252,x101255,x101251))))),f328(x101256,f463(x101256,x101254,x101253,x101252,x101255,x101251)))+E(f328(f328(f6(x101251,a872),f328(f328(f8(f879(x101252,a867),a872,x101251),f39(x101252)),f328(f328(f8(f879(x101252,a867),f879(x101252,a867),x101251),f248(x101252)),f328(f328(f8(f879(x101252,a867),f879(x101252,a867),x101251),f328(f18(x101252,a867,a867),f328(f328(f8(a867,f879(a867,a867),x101252),a326),f328(f328(f7(x101252,f879(x101252,a867),a867),f330(x101252)),x101253)))),x101254)))),x101255),f328(f328(f6(x101252,a872),x101256),x101253)) % 167.77/167.51 [9778]E(x97781,x97782)+~P17(x97783,x97784,x97785)+~P1(f328(f67(x97783,x97784,x97785,x97786,x97787),x97782))+~P1(f328(f67(x97783,x97784,x97785,x97786,x97787),x97781)) % 167.77/167.51 [9568]P1(f328(x95681,x95682))+~P1(f328(f328(f330(x95687),x95682),f328(x95686,x95684)))+~P1(f328(x95681,f733(x95681,x95686,x95685,x95683,x95687)))+~P1(f328(f328(f330(x95683),x95684),x95685)) % 167.77/167.51 [10012]~P17(x100127,x100126,x100121)+E(f328(f328(x100121,x100122),f841(x100122,x100123,x100124,x100125,x100121,x100126,x100127)),x100123)+~P1(f328(f67(x100127,x100126,x100121,x100125,x100124),x100123))+~P1(f328(f328(f330(x100127),x100122),x100124)) % 167.77/167.51 [10077]~P17(x100771,x100772,x100773)+~P1(f328(f67(x100771,x100772,x100773,x100774,x100775),x100777))+P1(f328(f67(x100771,x100772,x100773,x100774,f328(f328(f22(f879(x100771,a867)),x100775),f328(f328(f306(x100771),x100776),f192(f879(x100771,a867))))),f841(x100776,x100777,x100775,x100774,x100773,x100772,x100771)))+~P1(f328(f328(f330(x100771),x100776),x100775)) % 167.77/167.51 [9465]~P69(x94651)+~P26(x94655,x94652,x94656,x94657)+~P1(f328(f38(x94655),x94657))+E(f328(f328(f328(f66(x94651,x94652,f81(x94651)),x94653),x94654),f328(f307(x94655,x94652,x94656),x94657)),f328(f328(f328(f66(x94651,x94655,f81(x94651)),f328(f73(x94652,x94651,x94655,x94653),x94656)),x94654),x94657)) % 167.77/167.51 [9592]~E(f328(f328(f306(x95921),x95925),x95926),f328(f328(f306(x95921),x95922),x95923))+~P1(f328(f67(x95921,x95921,x95924,x95922,x95923),x95927))+P1(f328(f328(f330(x95921),x95922),x95923))+P1(f328(f63(x95921,x95924,f328(f328(f306(x95921),x95925),x95926)),x95927)) % 167.77/167.51 [9678]P1(f328(x96781,x96782))+~P1(f328(f328(f330(x96783),x96782),f328(x96784,x96787)))+~P1(f328(f328(f330(x96786),x96787),x96785))+P1(f328(f328(f330(x96783),f733(x96781,x96784,x96785,x96786,x96783)),f328(f328(f44(x96786,f879(x96783,a867)),x96785),x96784))) % 167.77/167.51 [9692]~P26(x96922,x96921,x96925,x96924)+~P26(x96921,x96923,x96926,f328(f307(x96922,x96921,x96925),x96924))+E(f328(f328(f73(x96921,x96922,x96923,f77(x96922,x96921,x96924,x96925)),f77(x96921,x96923,f328(f307(x96922,x96921,x96925),x96924),x96926)),x96927),f328(f77(x96922,x96923,x96924,f328(f73(x96921,x96923,x96922,x96926),x96925)),x96927))+~P1(f328(f328(f330(x96923),x96927),f328(f307(x96921,x96923,x96926),f328(f307(x96922,x96921,x96925),x96924)))) % 167.77/167.51 [10013]~P17(x100137,x100136,x100131)+E(f328(f328(x100131,x100132),f844(x100133,x100134,x100132,x100135,x100131,x100136,x100137)),x100133)+P1(f328(f328(f330(x100137),x100132),x100134))+~P1(f328(f67(x100137,x100136,x100131,x100135,f328(f328(f306(x100137),x100132),x100134)),x100133)) % 167.77/167.51 [10076]~P17(x100761,x100764,x100765)+P1(f328(f67(x100761,x100764,x100765,x100766,x100763),f844(x100767,x100763,x100762,x100766,x100765,x100764,x100761)))+P1(f328(f328(f330(x100761),x100762),x100763))+~P1(f328(f67(x100761,x100764,x100765,x100766,f328(f328(f306(x100761),x100762),x100763)),x100767)) % 167.77/167.51 [9760]E(x97601,f2(a1))+~P1(f328(f50(x97603,x97601),f328(f328(f263(a1,a1),x97605),x97607)))+~P1(f328(f50(x97602,x97601),f328(f328(f263(a1,a1),x97604),x97606)))+P1(f328(f50(f328(f328(f80(a1),x97602),x97603),x97601),f328(f328(f263(a1,a1),f328(f328(f80(a1),f328(f328(f80(a1),x97604),x97605)),f328(f328(f40(a1),f328(f328(f80(a1),x97606),x97607)),x97601))),f46(a1,f328(f328(f80(a1),x97606),x97607),x97601)))) % 167.77/167.51 [9762]~P1(f328(f328(f243(a872),f2(a872)),x97623))+~P1(f328(f49(x97622,x97623),f328(f328(f263(a872,a872),x97625),x97627)))+~P1(f328(f49(x97621,x97623),f328(f328(f263(a872,a872),x97624),x97626)))+P1(f328(f49(f328(f328(f80(a872),x97621),x97622),x97623),f328(f328(f263(a872,a872),f328(f328(f80(a872),f328(f328(f80(a872),x97624),x97625)),f328(f328(f40(a872),f328(f328(f80(a872),x97626),x97627)),x97623))),f46(a872,f328(f328(f80(a872),x97626),x97627),x97623)))) % 167.77/167.51 [10122]~P67(x101222)+~P1(f328(f38(x101223),x101225))+~P1(f328(f38(x101221),x101227))+E(f328(f328(f6(x101221,x101222),f328(f328(f18(x101221,f879(x101223,a867),x101222),f328(f328(f8(f879(x101223,x101222),f879(f879(x101223,a867),x101222),x101221),f6(x101223,x101222)),x101224)),f328(f328(f8(f879(x101223,a867),f879(x101223,a867),x101221),f248(x101223)),f328(f328(f8(f879(x101223,a867),f879(x101223,a867),x101221),f328(f18(x101223,a867,a867),f328(f328(f8(a867,f879(a867,a867),x101223),a326),f328(f328(f7(x101223,f879(x101223,a867),a867),f330(x101223)),x101225)))),x101226)))),x101227),f328(f328(f6(x101223,x101222),f328(f328(f18(x101223,f879(x101221,a867),x101222),f328(f328(f8(f879(x101221,x101222),f879(f879(x101221,a867),x101222),x101223),f6(x101221,x101222)),f328(f7(x101221,x101223,x101222),x101224))),f328(f328(f8(f879(x101221,a867),f879(x101221,a867),x101223),f248(x101221)),f328(f328(f8(f879(x101221,a867),f879(x101221,a867),x101223),f328(f18(x101221,a867,a867),f328(f328(f8(a867,f879(a867,a867),x101221),a326),f328(f328(f7(x101221,f879(x101221,a867),a867),f330(x101221)),x101227)))),f328(f7(x101221,x101223,a867),x101226))))),x101225)) % 167.77/167.51 [9630]~P23(x96307,x96306,x96301,x96308,x96302,x96304)+E(f328(f328(x96301,f328(x96302,x96303)),f328(x96304,x96305)),f328(x96304,x96305))+~P1(f328(f38(x96306),x96305))+~P1(f328(f328(f330(x96306),x96303),x96305)) % 167.77/167.51 [9634]~P14(x96346,x96341,x96342,x96348,x96343,x96344)+~P7(x96346,x96347,x96348)+P13(x96341,x96342,x96343,f328(x96344,x96345))+~P1(f328(f328(f330(x96346),x96345),x96347)) % 167.77/167.51 [8056]~P28(x80568,x80567,f328(f328(f328(f92(x80568),x80564),x80566),x80561))+P1(f328(f328(x80561,x80562),x80563))+~P1(f328(f328(x80564,x80562),x80565))+~P1(f328(f328(f328(f328(a200,x80566),x80565),x80567),x80563)) % 167.77/167.51 [9250]~P20(x92507,x92501,x92508,x92503)+~P1(f328(f38(x92507),x92505))+~P1(f328(f38(x92507),x92504))+E(f328(f73(x92501,x92501,x92502,f328(x92503,x92504)),f328(f73(x92501,x92501,x92502,f328(x92503,x92505)),x92506)),f328(f73(x92501,x92501,x92502,f328(x92503,x92505)),f328(f73(x92501,x92501,x92502,f328(x92503,x92504)),x92506))) % 167.77/167.51 [9258]~P35(x92581,x92582,x92583,x92584,x92587)+P35(x92581,x92582,x92583,f328(f328(f156(x92581,x92584),x92585),x92586),f328(f328(f156(x92582,x92587),x92585),x92588))+~P1(f328(f328(x92583,x92586),x92588))+~P1(f328(f328(f243(a872),x92585),f328(f193(f873(x92581)),x92584))) % 167.77/167.51 [9259]~P35(x92591,x92592,x92593,x92594,x92597)+P35(x92591,x92592,x92593,f328(f328(f156(x92591,x92594),x92595),x92596),f328(f328(f156(x92592,x92597),x92595),x92598))+~P1(f328(f328(x92593,x92596),x92598))+~P1(f328(f328(f243(a872),x92595),f328(f193(f873(x92592)),x92597))) % 167.77/167.51 [9338]~P26(x93382,x93382,x93385,x93386)+~P22(x93383,x93382,x93387,x93388,x93381)+~P1(f328(f38(x93382),x93386))+E(f328(f328(x93381,f328(f73(x93382,x93383,x93382,x93384),x93385)),x93386),f328(f328(x93381,x93384),f328(f307(x93382,x93382,x93385),x93386))) % 167.77/167.51 [9632]~P24(x96327,x96322,x96325,x96328,x96326,x96321)+~P1(f328(f38(x96322),x96324))+E(f328(x96321,f328(f328(f306(x96322),x96323),x96324)),f328(f328(x96325,f328(x96326,x96323)),f328(x96321,x96324)))+P1(f328(f328(f330(x96322),x96323),x96324)) % 167.77/167.51 [9643]~P23(x96436,x96435,x96431,x96437,x96438,x96432)+E(f328(f328(x96431,f328(x96432,x96433)),f328(x96432,x96434)),f328(x96432,x96434))+~P1(f328(f38(x96435),x96434))+~P1(f328(f328(f242(f879(x96435,a867)),x96433),x96434)) % 167.77/167.51 [9236]P1(f328(f328(f330(f878(f873(x92361),f873(x92361))),f328(f328(f263(f873(x92361),f873(x92361)),x92362),x92363)),f154(x92361,x92364)))+~E(x92363,f328(f328(f125(x92361),x92365),f328(f328(f148(x92361),x92366),x92367)))+~E(x92362,f328(f328(f125(x92361),x92365),f328(f328(f148(x92361),x92368),x92367)))+~P1(f328(f328(f330(f878(x92361,x92361)),f328(f328(f263(x92361,x92361),x92368),x92366)),x92364)) % 167.77/167.51 [9637]~P23(x96376,x96372,x96375,x96377,x96378,x96371)+~P1(f328(f38(x96372),x96374))+~P1(f328(f38(x96372),x96373))+E(f328(x96371,f328(f328(f114(f879(x96372,a867)),x96373),x96374)),f328(f328(x96375,f328(x96371,x96373)),f328(x96371,x96374))) % 167.77/167.51 [10160]~P26(x101604,x101602,x101605,x101608)+E(f328(f328(f43(x101601,f879(x101602,a867)),x101603),f328(f328(f8(f879(x101604,a867),f879(x101602,a867),x101601),f307(x101604,x101602,x101605)),x101606)),f328(f307(x101604,x101602,x101605),f328(f328(f43(x101601,f879(x101604,a867)),x101603),x101606)))+~P1(f328(f328(f330(x101601),x101607),x101603))+P1(f328(f328(f330(x101601),f546(x101607,x101606,x101603,x101601,x101608,x101605,x101602,x101604)),x101603)) % 167.77/167.51 [10184]~P26(x101844,x101842,x101845,x101847)+E(f328(f328(f43(x101841,f879(x101842,a867)),x101843),f328(f328(f8(f879(x101844,a867),f879(x101842,a867),x101841),f307(x101844,x101842,x101845)),x101846)),f328(f307(x101844,x101842,x101845),f328(f328(f43(x101841,f879(x101844,a867)),x101843),x101846)))+~P1(f328(f328(f330(x101841),x101848),x101843))+~P1(f328(f328(f242(f879(x101844,a867)),f328(x101846,f546(x101848,x101846,x101843,x101841,x101847,x101845,x101842,x101844))),x101847)) % 167.77/167.51 [9701]~P24(x97017,x97015,x97011,x97018,x97012,x97014)+~P1(f328(f38(x97015),x97016))+~P1(f328(f328(f330(x97015),x97013),x97016))+E(f328(f328(x97011,f328(x97012,x97013)),f328(x97014,f328(f328(f22(f879(x97015,a867)),x97016),f328(f328(f306(x97015),x97013),f192(f879(x97015,a867)))))),f328(x97014,x97016)) % 167.77/167.51 [9709]~P24(x97096,x97093,x97091,x97097,x97098,x97092)+~P1(f328(f38(x97093),x97095))+~P1(f328(f38(x97093),x97094))+E(f328(f328(x97091,f328(x97092,f328(f328(f114(f879(x97093,a867)),x97094),x97095))),f328(x97092,f328(f328(f105(f879(x97093,a867)),x97094),x97095))),f328(f328(x97091,f328(x97092,x97094)),f328(x97092,x97095))) % 167.77/167.51 [9801]P43(x98011,x98012,x98013,x98014,x98015,f328(f328(x98013,x98016),x98017))+~P43(x98011,x98012,x98013,x98014,f328(f328(f22(f879(x98011,a867)),x98015),f328(f328(f306(x98011),x98018),f192(f879(x98011,a867)))),x98019)+~E(f328(f328(x98013,x98016),x98017),f328(f328(x98013,x98018),x98019))+~P1(f328(f328(f330(x98011),x98018),x98015)) % 167.77/167.51 [10199]P25(x101991,x101992,f328(f328(f306(f871(x101991)),f328(f328(f328(f92(x101991),f328(x101993,f364(x101994,x101995,x101996,x101997,x101993,x101992,x101991,x101998,x101999))),f328(x101997,f364(x101994,x101995,x101996,x101997,x101993,x101992,x101991,x101998,x101999))),f328(x101996,f364(x101994,x101995,x101996,x101997,x101993,x101992,x101991,x101998,x101999)))),f192(f879(f871(x101991),a867))))+~P1(f328(f38(x101999),x101998))+~P25(x101991,x101992,f328(f307(x101999,f871(x101991),f328(f328(f18(x101999,f879(x101991,f879(a868,a867)),f871(x101991)),f328(f328(f18(x101999,a869,f879(f879(x101991,f879(a868,a867)),f871(x101991))),f328(f328(f8(f879(x101991,f879(a868,a867)),f879(a869,f879(f879(x101991,f879(a868,a867)),f871(x101991))),x101999),f92(x101991)),x101993)),x101997)),x101996)),x101998))+P25(x101991,x101992,f328(f307(x101999,f871(x101991),f328(f328(f18(x101999,f879(x101991,f879(a868,a867)),f871(x101991)),f328(f328(f18(x101999,a869,f879(f879(x101991,f879(a868,a867)),f871(x101991))),f328(f328(f8(f879(x101991,f879(a868,a867)),f879(a869,f879(f879(x101991,f879(a868,a867)),f871(x101991))),x101999),f92(x101991)),x101995)),x101997)),x101994)),x101998)) % 167.77/167.51 [10200]~P25(x102001,x102002,f328(f328(f306(f871(x102001)),f328(f328(f328(f92(x102001),f328(x102004,f364(x102006,x102004,x102008,x102005,x102009,x102002,x102001,x102007,x102003))),f328(x102005,f364(x102006,x102004,x102008,x102005,x102009,x102002,x102001,x102007,x102003))),f328(x102006,f364(x102006,x102004,x102008,x102005,x102009,x102002,x102001,x102007,x102003)))),f192(f879(f871(x102001),a867))))+~P1(f328(f38(x102003),x102007))+~P25(x102001,x102002,f328(f307(x102003,f871(x102001),f328(f328(f18(x102003,f879(x102001,f879(a868,a867)),f871(x102001)),f328(f328(f18(x102003,a869,f879(f879(x102001,f879(a868,a867)),f871(x102001))),f328(f328(f8(f879(x102001,f879(a868,a867)),f879(a869,f879(f879(x102001,f879(a868,a867)),f871(x102001))),x102003),f92(x102001)),x102009)),x102005)),x102008)),x102007))+P25(x102001,x102002,f328(f307(x102003,f871(x102001),f328(f328(f18(x102003,f879(x102001,f879(a868,a867)),f871(x102001)),f328(f328(f18(x102003,a869,f879(f879(x102001,f879(a868,a867)),f871(x102001))),f328(f328(f8(f879(x102001,f879(a868,a867)),f879(a869,f879(f879(x102001,f879(a868,a867)),f871(x102001))),x102003),f92(x102001)),x102004)),x102005)),x102006)),x102007)) % 167.77/167.51 [9735]~P14(x97356,x97357,x97358,x97359,x973510,x97351)+E(f328(f328(x97351,x97352),x97353),f328(f328(x97351,x97354),x97355))+~P1(f328(f328(f330(f878(x97357,x97357)),f328(f328(f263(x97357,x97357),x97353),x97355)),x973510))+~P1(f328(f328(f330(f878(x97356,x97356)),f328(f328(f263(x97356,x97356),x97352),x97354)),x97359)) % 167.77/167.51 [9340]~P2(x93402)+E(x93401,f192(f879(x93402,a867)))+~P1(f328(f38(x93402),x93401))+P1(f328(f328(f330(x93402),f13(x93402,x93401)),x93401))+~P1(f328(f328(f330(x93402),f328(f328(f114(x93402),f532(x93401,x93402)),f545(x93401,x93402))),f328(f328(f306(x93402),f532(x93401,x93402)),f328(f328(f306(x93402),f545(x93401,x93402)),f192(f879(x93402,a867)))))) % 167.77/167.51 [9341]~P2(x93412)+E(x93411,f192(f879(x93412,a867)))+~P1(f328(f38(x93412),x93411))+P1(f328(f328(f330(x93412),f10(x93412,x93411)),x93411))+~P1(f328(f328(f330(x93412),f328(f328(f105(x93412),f828(x93411,x93412)),f829(x93411,x93412))),f328(f328(f306(x93412),f828(x93411,x93412)),f328(f328(f306(x93412),f829(x93411,x93412)),f192(f879(x93412,a867)))))) % 167.77/167.51 [9372]~P69(x93722)+E(x93721,f192(f879(x93722,a867)))+~P1(f328(f38(x93722),x93721))+P1(f328(f328(f330(x93722),f328(f64(x93722,f81(x93722)),x93721)),x93721))+~P1(f328(f328(f330(x93722),f328(f328(f81(x93722),f840(x93721,x93722)),f842(x93721,x93722))),f328(f328(f306(x93722),f840(x93721,x93722)),f328(f328(f306(x93722),f842(x93721,x93722)),f192(f879(x93722,a867)))))) % 167.77/167.51 [9378]~P105(x93782)+E(x93781,f192(f879(x93782,a867)))+~P1(f328(f38(x93782),x93781))+P1(f328(f328(f330(x93782),f11(x93782,f240(x93782),x93781)),x93781))+~P1(f328(f328(f330(x93782),f328(f328(f240(x93782),f477(x93781,x93782)),f478(x93781,x93782))),f328(f328(f306(x93782),f477(x93781,x93782)),f328(f328(f306(x93782),f478(x93781,x93782)),f192(f879(x93782,a867)))))) % 167.77/167.51 [9379]~P105(x93792)+E(x93791,f192(f879(x93792,a867)))+~P1(f328(f38(x93792),x93791))+P1(f328(f328(f330(x93792),f12(x93792,f241(x93792),x93791)),x93791))+~P1(f328(f328(f330(x93792),f328(f328(f241(x93792),f485(x93791,x93792)),f486(x93791,x93792))),f328(f328(f306(x93792),f485(x93791,x93792)),f328(f328(f306(x93792),f486(x93791,x93792)),f192(f879(x93792,a867)))))) % 167.77/167.51 [6493]~P86(x64932)+E(x64931,f2(x64932))+~E(f328(f328(f80(x64932),x64933),x64931),f2(x64932))+~P1(f328(f328(f242(x64932),f2(x64932)),x64933))+~P1(f328(f328(f242(x64932),f2(x64932)),x64931)) % 167.77/167.51 [6494]~P86(x64942)+E(x64941,f2(x64942))+~E(f328(f328(f80(x64942),x64941),x64943),f2(x64942))+~P1(f328(f328(f242(x64942),f2(x64942)),x64943))+~P1(f328(f328(f242(x64942),f2(x64942)),x64941)) % 167.77/167.51 [7024]~P105(x70242)+~P15(x70242,x70241)+E(x70241,f117(x70242))+~P1(f328(f328(f330(x70242),x70243),f328(f170(x70242),f740(x70241,x70242))))+P1(f328(f328(f242(x70242),f759(x70241,x70242)),x70243)) % 167.77/167.51 [7192]~P105(x71921)+E(f14(x71921,x71922),x71923)+~P1(f328(f38(x71921),x71922))+~P1(f328(f328(f242(x71921),x71923),f498(x71923,x71922,x71921)))+~P1(f328(f328(f330(x71921),x71923),x71922)) % 167.77/167.51 [7223]~P105(x72231)+~P15(x72231,x72232)+~P15(x72231,x72233)+P15(x72231,f328(f328(f125(x72231),x72232),x72233))+P1(f328(f328(f330(x72231),f747(x72233,x72232,x72231)),f328(f170(x72231),x72232))) % 167.77/167.51 [7224]~P105(x72241)+~P15(x72241,x72242)+~P15(x72241,x72243)+P15(x72241,f328(f328(f125(x72241),x72242),x72243))+P1(f328(f328(f330(x72241),f748(x72243,x72242,x72241)),f328(f170(x72241),x72243))) % 167.77/167.51 [7280]~P105(x72801)+E(f14(x72801,x72802),x72803)+~P1(f328(f38(x72801),x72802))+P1(f328(f328(f330(x72801),f498(x72803,x72802,x72801)),x72802))+~P1(f328(f328(f330(x72801),x72803),x72802)) % 167.77/167.51 [7281]~P105(x72811)+E(f15(x72811,x72812),x72813)+~P1(f328(f38(x72811),x72812))+P1(f328(f328(f330(x72811),f501(x72813,x72812,x72811)),x72812))+~P1(f328(f328(f330(x72811),x72813),x72812)) % 167.77/167.51 [7866]~P105(x78661)+E(f15(x78661,x78662),x78663)+~P1(f328(f38(x78661),x78662))+~P1(f328(f328(f330(x78661),x78663),x78662))+~P1(f328(f328(f242(x78661),f501(x78663,x78662,x78661)),x78663)) % 167.77/167.51 [8192]~P105(x81921)+~P15(x81921,x81922)+~P15(x81921,x81923)+P15(x81921,f328(f328(f125(x81921),x81922),x81923))+~P1(f328(f328(f242(x81921),f747(x81923,x81922,x81921)),f748(x81923,x81922,x81921))) % 167.77/167.51 [8980]~P2(x89802)+E(x89801,f192(f879(x89802,a867)))+~E(f328(f328(f114(x89802),f328(x89803,f552(x89801,x89803,x89802))),f328(x89803,f562(x89801,x89803,x89802))),f328(x89803,f328(f328(f114(x89802),f552(x89801,x89803,x89802)),f562(x89801,x89803,x89802))))+E(f13(x89802,f328(f307(x89802,x89802,x89803),x89801)),f328(x89803,f13(x89802,x89801)))+~P1(f328(f38(x89802),x89801)) % 167.77/167.51 [8981]~P2(x89812)+E(x89811,f192(f879(x89812,a867)))+~E(f328(f328(f105(x89812),f328(x89813,f824(x89811,x89813,x89812))),f328(x89813,f830(x89811,x89813,x89812))),f328(x89813,f328(f328(f105(x89812),f824(x89811,x89813,x89812)),f830(x89811,x89813,x89812))))+E(f10(x89812,f328(f307(x89812,x89812,x89813),x89811)),f328(x89813,f10(x89812,x89811)))+~P1(f328(f38(x89812),x89811)) % 167.77/167.51 [8982]~P105(x89822)+E(x89821,f192(f879(x89822,a867)))+~E(f328(f328(f240(x89822),f328(x89823,f480(x89821,x89823,x89822))),f328(x89823,f489(x89821,x89823,x89822))),f328(x89823,f328(f328(f240(x89822),f480(x89821,x89823,x89822)),f489(x89821,x89823,x89822))))+E(f14(x89822,f328(f307(x89822,x89822,x89823),x89821)),f328(x89823,f14(x89822,x89821)))+~P1(f328(f38(x89822),x89821)) % 167.77/167.51 [8983]~P105(x89832)+E(x89831,f192(f879(x89832,a867)))+~E(f328(f328(f241(x89832),f328(x89833,f481(x89831,x89833,x89832))),f328(x89833,f488(x89831,x89833,x89832))),f328(x89833,f328(f328(f241(x89832),f481(x89831,x89833,x89832)),f488(x89831,x89833,x89832))))+E(f15(x89832,f328(f307(x89832,x89832,x89833),x89831)),f328(x89833,f15(x89832,x89831)))+~P1(f328(f38(x89832),x89831)) % 167.77/167.51 [9052]~P105(x90522)+E(x90521,f192(f879(x90522,a867)))+~E(f328(f328(f240(x90522),f328(x90523,f474(x90521,x90523,x90522))),f328(x90523,f479(x90521,x90523,x90522))),f328(x90523,f328(f328(f240(x90522),f474(x90521,x90523,x90522)),f479(x90521,x90523,x90522))))+E(f11(x90522,f240(x90522),f328(f307(x90522,x90522,x90523),x90521)),f328(x90523,f11(x90522,f240(x90522),x90521)))+~P1(f328(f38(x90522),x90521)) % 167.77/167.51 [9053]~P105(x90532)+E(x90531,f192(f879(x90532,a867)))+~E(f328(f328(f241(x90532),f328(x90533,f482(x90531,x90533,x90532))),f328(x90533,f487(x90531,x90533,x90532))),f328(x90533,f328(f328(f241(x90532),f482(x90531,x90533,x90532)),f487(x90531,x90533,x90532))))+E(f12(x90532,f241(x90532),f328(f307(x90532,x90532,x90533),x90531)),f328(x90533,f12(x90532,f241(x90532),x90531)))+~P1(f328(f38(x90532),x90531)) % 167.77/167.51 [6509]~P69(x65092)+E(x65091,f192(f879(x65092,a867)))+~P1(f328(f38(x65092),x65091))+E(f328(f64(x65092,f81(x65092)),f328(f328(f306(x65092),x65093),x65091)),f328(f328(f81(x65092),x65093),f328(f64(x65092,f81(x65092)),x65091)))+P1(f328(f328(f330(x65092),x65093),x65091)) % 167.77/167.51 [7030]~P2(x70302)+E(f328(f328(f114(x70302),f13(x70302,x70301)),f13(x70302,x70303)),f13(x70302,x70303))+E(x70301,f192(f879(x70302,a867)))+~P1(f328(f38(x70302),x70303))+~P1(f328(f328(f242(f879(x70302,a867)),x70301),x70303)) % 167.77/167.51 [7031]~P2(x70312)+E(f328(f328(f105(x70312),f10(x70312,x70311)),f10(x70312,x70313)),f10(x70312,x70313))+E(x70311,f192(f879(x70312,a867)))+~P1(f328(f38(x70312),x70313))+~P1(f328(f328(f242(f879(x70312,a867)),x70311),x70313)) % 167.77/167.51 [7032]~P105(x70322)+E(f328(f328(f240(x70322),f14(x70322,x70321)),f14(x70322,x70323)),f14(x70322,x70323))+E(x70321,f192(f879(x70322,a867)))+~P1(f328(f38(x70322),x70323))+~P1(f328(f328(f242(f879(x70322,a867)),x70321),x70323)) % 167.77/167.51 [7033]~P105(x70332)+E(f328(f328(f241(x70332),f15(x70332,x70331)),f15(x70332,x70333)),f15(x70332,x70333))+E(x70331,f192(f879(x70332,a867)))+~P1(f328(f38(x70332),x70333))+~P1(f328(f328(f242(f879(x70332,a867)),x70331),x70333)) % 167.77/167.51 [7332]~P105(x73322)+E(x73321,f192(f879(x73322,a867)))+~P1(f328(f38(x73322),x73323))+P1(f328(f328(f242(x73322),f14(x73322,x73323)),f14(x73322,x73321)))+~P1(f328(f328(f242(f879(x73322,a867)),x73321),x73323)) % 167.77/167.51 [7333]~P105(x73332)+E(x73331,f192(f879(x73332,a867)))+~P1(f328(f38(x73332),x73333))+P1(f328(f328(f242(x73332),f15(x73332,x73331)),f15(x73332,x73333)))+~P1(f328(f328(f242(f879(x73332,a867)),x73331),x73333)) % 167.77/167.51 [7391]~P2(x73911)+E(f13(x73911,x73912),x73913)+~P1(f328(f38(x73911),x73912))+~E(f328(f328(f22(f879(x73911,a867)),x73912),f328(f328(f306(x73911),x73913),f192(f879(x73911,a867)))),f192(f879(x73911,a867)))+~P1(f328(f328(f330(x73911),x73913),x73912)) % 167.77/167.51 [7392]~P2(x73921)+E(f10(x73921,x73922),x73923)+~P1(f328(f38(x73921),x73922))+~E(f328(f328(f22(f879(x73921,a867)),x73922),f328(f328(f306(x73921),x73923),f192(f879(x73921,a867)))),f192(f879(x73921,a867)))+~P1(f328(f328(f330(x73921),x73923),x73922)) % 167.77/167.51 [7393]~P105(x73931)+E(f14(x73931,x73932),x73933)+~P1(f328(f38(x73931),x73932))+~E(f328(f328(f22(f879(x73931,a867)),x73932),f328(f328(f306(x73931),x73933),f192(f879(x73931,a867)))),f192(f879(x73931,a867)))+~P1(f328(f328(f330(x73931),x73933),x73932)) % 167.77/167.51 [7394]~P105(x73941)+E(f15(x73941,x73942),x73943)+~P1(f328(f38(x73941),x73942))+~E(f328(f328(f22(f879(x73941,a867)),x73942),f328(f328(f306(x73941),x73943),f192(f879(x73941,a867)))),f192(f879(x73941,a867)))+~P1(f328(f328(f330(x73941),x73943),x73942)) % 167.77/167.51 [7492]~P105(x74921)+E(f11(x74921,f240(x74921),x74922),x74923)+~P1(f328(f38(x74921),x74922))+~E(f328(f328(f22(f879(x74921,a867)),x74922),f328(f328(f306(x74921),x74923),f192(f879(x74921,a867)))),f192(f879(x74921,a867)))+~P1(f328(f328(f330(x74921),x74923),x74922)) % 167.77/167.51 [7493]~P105(x74931)+E(f12(x74931,f241(x74931),x74932),x74933)+~P1(f328(f38(x74931),x74932))+~E(f328(f328(f22(f879(x74931,a867)),x74932),f328(f328(f306(x74931),x74933),f192(f879(x74931,a867)))),f192(f879(x74931,a867)))+~P1(f328(f328(f330(x74931),x74933),x74932)) % 167.77/167.51 [7529]~P105(x75292)+E(x75291,f192(f879(x75292,a867)))+~P1(f328(f38(x75292),x75291))+~P1(f328(f328(f243(x75292),x75293),f466(x75293,x75291,x75292)))+P1(f328(f328(f243(x75292),x75293),f328(f64(x75292,f240(x75292)),x75291))) % 167.77/167.51 [7530]~P100(x75302)+E(x75301,f192(f879(x75302,a867)))+~P1(f328(f38(x75302),x75301))+~P1(f328(f328(f242(x75302),x75303),f359(x75303,x75301,x75302)))+P1(f328(f328(f242(x75302),x75303),f328(f64(x75302,f105(x75302)),x75301))) % 167.77/167.51 [7531]~P105(x75312)+E(x75311,f192(f879(x75312,a867)))+~P1(f328(f38(x75312),x75311))+~P1(f328(f328(f242(x75312),x75313),f467(x75313,x75311,x75312)))+P1(f328(f328(f242(x75312),x75313),f328(f64(x75312,f240(x75312)),x75311))) % 167.77/167.51 [7618]~P100(x76182)+E(x76181,f192(f879(x76182,a867)))+~P1(f328(f38(x76182),x76181))+P1(f328(f328(f330(x76182),f359(x76183,x76181,x76182)),x76181))+P1(f328(f328(f242(x76182),x76183),f328(f64(x76182,f105(x76182)),x76181))) % 167.77/167.51 [7619]~P105(x76192)+E(x76191,f192(f879(x76192,a867)))+~P1(f328(f38(x76192),x76191))+P1(f328(f328(f330(x76192),f467(x76193,x76191,x76192)),x76191))+P1(f328(f328(f242(x76192),x76193),f328(f64(x76192,f240(x76192)),x76191))) % 167.77/167.51 [7620]~P105(x76202)+E(x76201,f192(f879(x76202,a867)))+~P1(f328(f38(x76202),x76201))+P1(f328(f328(f330(x76202),f466(x76203,x76201,x76202)),x76201))+P1(f328(f328(f243(x76202),x76203),f328(f64(x76202,f240(x76202)),x76201))) % 167.77/167.51 [7741]~P105(x77412)+E(x77411,f192(f879(x77412,a867)))+E(f328(f328(f240(x77412),f11(x77412,f240(x77412),x77411)),f11(x77412,f240(x77412),x77413)),f11(x77412,f240(x77412),x77413))+~P1(f328(f38(x77412),x77413))+~P1(f328(f328(f242(f879(x77412,a867)),x77411),x77413)) % 167.77/167.51 [7742]~P105(x77422)+E(x77421,f192(f879(x77422,a867)))+E(f328(f328(f241(x77422),f12(x77422,f241(x77422),x77421)),f12(x77422,f241(x77422),x77423)),f12(x77422,f241(x77422),x77423))+~P1(f328(f38(x77422),x77423))+~P1(f328(f328(f242(f879(x77422,a867)),x77421),x77423)) % 167.77/167.51 [7945]~E(f440(x79451,x79453,x79452),f441(x79451,x79453,x79452))+~E(f328(f39(x79452),f442(x79451,x79453,x79452)),x79451)+E(f328(f328(f81(a872),x79451),f328(f39(f879(x79452,a867)),x79453)),f328(f39(x79452),f41(f879(x79452,a867),x79453)))+~P1(f328(f38(x79452),f41(f879(x79452,a867),x79453)))+~P1(f328(f38(f879(x79452,a867)),x79453)) % 167.77/167.51 [8121]~P105(x81212)+E(x81211,f192(f879(x81212,a867)))+~P1(f328(f38(x81212),x81213))+P1(f328(f328(f242(x81212),f328(f64(x81212,f240(x81212)),x81213)),f328(f64(x81212,f240(x81212)),x81211)))+~P1(f328(f328(f242(f879(x81212,a867)),x81211),x81213)) % 167.77/167.51 [8435]~E(f440(x84351,x84353,x84352),f441(x84351,x84353,x84352))+E(f328(f328(f81(a872),x84351),f328(f39(f879(x84352,a867)),x84353)),f328(f39(x84352),f41(f879(x84352,a867),x84353)))+P1(f328(f328(f330(f879(x84352,a867)),f442(x84351,x84353,x84352)),x84353))+~P1(f328(f38(x84352),f41(f879(x84352,a867),x84353)))+~P1(f328(f38(f879(x84352,a867)),x84353)) % 167.77/167.51 [8459]~E(f328(f39(x84592),f442(x84591,x84593,x84592)),x84591)+E(f328(f328(f81(a872),x84591),f328(f39(f879(x84592,a867)),x84593)),f328(f39(x84592),f41(f879(x84592,a867),x84593)))+P1(f328(f328(f330(f879(x84592,a867)),f441(x84591,x84593,x84592)),x84593))+~P1(f328(f38(x84592),f41(f879(x84592,a867),x84593)))+~P1(f328(f38(f879(x84592,a867)),x84593)) % 167.77/167.51 [8460]~E(f328(f39(x84602),f442(x84601,x84603,x84602)),x84601)+E(f328(f328(f81(a872),x84601),f328(f39(f879(x84602,a867)),x84603)),f328(f39(x84602),f41(f879(x84602,a867),x84603)))+P1(f328(f328(f330(f879(x84602,a867)),f440(x84601,x84603,x84602)),x84603))+~P1(f328(f38(x84602),f41(f879(x84602,a867),x84603)))+~P1(f328(f38(f879(x84602,a867)),x84603)) % 167.77/167.51 [8486]~E(f328(f39(x84862),f442(x84861,x84863,x84862)),x84861)+~E(f328(f328(f105(f879(x84862,a867)),f441(x84861,x84863,x84862)),f440(x84861,x84863,x84862)),f192(f879(x84862,a867)))+E(f328(f328(f81(a872),x84861),f328(f39(f879(x84862,a867)),x84863)),f328(f39(x84862),f41(f879(x84862,a867),x84863)))+~P1(f328(f38(f879(x84862,a867)),x84863))+~P1(f328(f38(x84862),f41(f879(x84862,a867),x84863))) % 167.77/167.51 [8740]E(f328(f328(f81(a872),x87401),f328(f39(f879(x87402,a867)),x87403)),f328(f39(x87402),f41(f879(x87402,a867),x87403)))+P1(f328(f328(f330(f879(x87402,a867)),f442(x87401,x87403,x87402)),x87403))+P1(f328(f328(f330(f879(x87402,a867)),f441(x87401,x87403,x87402)),x87403))+~P1(f328(f38(f879(x87402,a867)),x87403))+~P1(f328(f38(x87402),f41(f879(x87402,a867),x87403))) % 167.77/167.51 [8741]E(f328(f328(f81(a872),x87411),f328(f39(f879(x87412,a867)),x87413)),f328(f39(x87412),f41(f879(x87412,a867),x87413)))+P1(f328(f328(f330(f879(x87412,a867)),f442(x87411,x87413,x87412)),x87413))+P1(f328(f328(f330(f879(x87412,a867)),f440(x87411,x87413,x87412)),x87413))+~P1(f328(f38(f879(x87412,a867)),x87413))+~P1(f328(f38(x87412),f41(f879(x87412,a867),x87413))) % 167.77/167.51 [8766]~E(f328(f328(f105(f879(x87662,a867)),f441(x87661,x87663,x87662)),f440(x87661,x87663,x87662)),f192(f879(x87662,a867)))+E(f328(f328(f81(a872),x87661),f328(f39(f879(x87662,a867)),x87663)),f328(f39(x87662),f41(f879(x87662,a867),x87663)))+~P1(f328(f38(f879(x87662,a867)),x87663))+P1(f328(f328(f330(f879(x87662,a867)),f442(x87661,x87663,x87662)),x87663))+~P1(f328(f38(x87662),f41(f879(x87662,a867),x87663))) % 167.77/167.51 [9026]~P95(x90262)+E(x90261,f192(f879(x90262,a867)))+~E(f328(f328(f81(x90262),f328(x90263,f839(x90261,x90263,x90262))),f328(x90263,f843(x90261,x90263,x90262))),f328(x90263,f328(f328(f81(x90262),f839(x90261,x90263,x90262)),f843(x90261,x90263,x90262))))+~P1(f328(f38(x90262),x90261))+E(f328(f64(x90262,f81(x90262)),f328(f307(x90262,x90262,x90263),x90261)),f328(x90263,f328(f64(x90262,f81(x90262)),x90261))) % 167.77/167.51 [9958]P1(f328(f328(x99581,x99582),x99583))+P1(f328(f328(f243(a1),f510(x99581,x99583,x99582)),f511(x99581,x99583,x99582)))+P1(f328(f328(f242(a1),f511(x99581,x99583,x99582)),f2(a1)))+P1(f328(f328(x99581,f510(x99581,x99583,x99582)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f511(x99581,x99583,x99582))))+~P1(f328(f316(f878(a1,a1),a58),f328(f328(f263(a1,a1),x99582),x99583))) % 167.77/167.51 [9964]P1(f328(f328(x99641,x99642),x99643))+P1(f328(f328(f242(a1),f509(x99641,x99643,x99642)),f2(a1)))+P1(f328(f328(x99641,f505(x99641,x99643,x99642)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f509(x99641,x99643,x99642))))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),f505(x99641,x99643,x99642)),f509(x99641,x99643,x99642))))+~P1(f328(f316(f878(a1,a1),a53),f328(f328(f263(a1,a1),x99642),x99643))) % 167.77/167.51 [7916]~P117(x79161)+~P1(f328(f328(f242(x79161),x79162),f78(x79161)))+~P1(f328(f328(f242(x79161),f2(x79161)),x79162))+~P1(f328(f328(f242(x79161),f2(x79161)),x79163))+P1(f328(f328(f242(x79161),f328(f328(f81(x79161),x79162),x79163)),x79163)) % 167.77/167.51 [7917]~P117(x79171)+~P1(f328(f328(f242(x79171),x79173),f78(x79171)))+~P1(f328(f328(f242(x79171),f2(x79171)),x79173))+~P1(f328(f328(f242(x79171),f2(x79171)),x79172))+P1(f328(f328(f242(x79171),f328(f328(f81(x79171),x79172),x79173)),x79172)) % 167.77/167.51 [8280]~P105(x82802)+E(x82801,f192(f879(x82802,a867)))+~P1(f328(f38(x82802),x82801))+P1(f328(f328(f330(x82802),f471(x82803,x82801,x82802)),x82801))+~P1(f328(f328(f242(x82802),f328(f64(x82802,f240(x82802)),x82801)),x82803)) % 167.77/167.51 [8281]~P105(x82812)+E(x82811,f192(f879(x82812,a867)))+~P1(f328(f38(x82812),x82811))+P1(f328(f328(f330(x82812),f472(x82813,x82811,x82812)),x82811))+~P1(f328(f328(f243(x82812),f328(f64(x82812,f240(x82812)),x82811)),x82813)) % 167.77/167.51 [8282]~P105(x82822)+E(x82821,f192(f879(x82822,a867)))+~P1(f328(f38(x82822),x82821))+P1(f328(f328(f243(x82822),f472(x82823,x82821,x82822)),x82823))+~P1(f328(f328(f243(x82822),f328(f64(x82822,f240(x82822)),x82821)),x82823)) % 167.77/167.51 [8283]~P105(x82832)+E(x82831,f192(f879(x82832,a867)))+~P1(f328(f38(x82832),x82831))+P1(f328(f328(f242(x82832),f471(x82833,x82831,x82832)),x82833))+~P1(f328(f328(f242(x82832),f328(f64(x82832,f240(x82832)),x82831)),x82833)) % 167.77/167.51 [8368]~P1(f328(x83681,x83683))+P1(f328(x83681,f424(x83681,x83682)))+P1(f328(x83681,f417(x83681,x83682)))+~P1(f328(f328(f243(a1),f2(a1)),x83682))+P1(f328(x83681,f328(f328(f22(a1),f417(x83681,x83682)),f328(f328(f81(a1),f425(x83681,x83682)),x83682)))) % 167.77/167.51 [8590]~P1(f328(x85901,x85903))+P1(f328(x85901,f417(x85901,x85902)))+~P1(f328(f328(f243(a1),f2(a1)),x85902))+P1(f328(f328(f330(a1),f424(x85901,x85902)),f299(a1,f78(a1),x85902)))+P1(f328(x85901,f328(f328(f22(a1),f417(x85901,x85902)),f328(f328(f81(a1),f425(x85901,x85902)),x85902)))) % 167.77/167.51 [8788]~P1(f328(x87881,x87883))+~P1(f328(x87881,f417(x87881,x87882)))+P1(f328(x87881,f424(x87881,x87882)))+~P1(f328(f328(f243(a1),f2(a1)),x87882))+~P1(f328(x87881,f328(f328(f22(a1),f417(x87881,x87882)),f328(f328(f81(a1),f425(x87881,x87882)),x87882)))) % 167.77/167.51 [8912]~P1(f328(x89121,x89123))+~P1(f328(x89121,f417(x89121,x89122)))+~P1(f328(f328(f243(a1),f2(a1)),x89122))+P1(f328(f328(f330(a1),f424(x89121,x89122)),f299(a1,f78(a1),x89122)))+~P1(f328(x89121,f328(f328(f22(a1),f417(x89121,x89122)),f328(f328(f81(a1),f425(x89121,x89122)),x89122)))) % 167.77/167.51 [8700]~P2(x87001)+~P1(f328(f38(x87001),x87002))+E(f328(f328(f22(f879(x87001,a867)),x87002),f328(f328(f306(x87001),x87003),f192(f879(x87001,a867)))),f192(f879(x87001,a867)))+~P1(f328(f328(f330(x87001),x87003),x87002))+E(f328(f328(f114(x87001),x87003),f13(x87001,f328(f328(f22(f879(x87001,a867)),x87002),f328(f328(f306(x87001),x87003),f192(f879(x87001,a867)))))),f13(x87001,x87002)) % 167.77/167.51 [8701]~P2(x87011)+~P1(f328(f38(x87011),x87012))+E(f328(f328(f22(f879(x87011,a867)),x87012),f328(f328(f306(x87011),x87013),f192(f879(x87011,a867)))),f192(f879(x87011,a867)))+~P1(f328(f328(f330(x87011),x87013),x87012))+E(f328(f328(f105(x87011),x87013),f10(x87011,f328(f328(f22(f879(x87011,a867)),x87012),f328(f328(f306(x87011),x87013),f192(f879(x87011,a867)))))),f10(x87011,x87012)) % 167.77/167.51 [8702]~P105(x87021)+~P1(f328(f38(x87021),x87022))+E(f328(f328(f22(f879(x87021,a867)),x87022),f328(f328(f306(x87021),x87023),f192(f879(x87021,a867)))),f192(f879(x87021,a867)))+~P1(f328(f328(f330(x87021),x87023),x87022))+E(f328(f328(f240(x87021),x87023),f14(x87021,f328(f328(f22(f879(x87021,a867)),x87022),f328(f328(f306(x87021),x87023),f192(f879(x87021,a867)))))),f14(x87021,x87022)) % 167.77/167.51 [8703]~P105(x87031)+~P1(f328(f38(x87031),x87032))+E(f328(f328(f22(f879(x87031,a867)),x87032),f328(f328(f306(x87031),x87033),f192(f879(x87031,a867)))),f192(f879(x87031,a867)))+~P1(f328(f328(f330(x87031),x87033),x87032))+E(f328(f328(f241(x87031),x87033),f15(x87031,f328(f328(f22(f879(x87031,a867)),x87032),f328(f328(f306(x87031),x87033),f192(f879(x87031,a867)))))),f15(x87031,x87032)) % 167.77/167.51 [8760]~P105(x87601)+~P1(f328(f38(x87601),x87602))+E(f328(f328(f22(f879(x87601,a867)),x87602),f328(f328(f306(x87601),x87603),f192(f879(x87601,a867)))),f192(f879(x87601,a867)))+~P1(f328(f328(f330(x87601),x87603),x87602))+E(f328(f328(f240(x87601),x87603),f11(x87601,f240(x87601),f328(f328(f22(f879(x87601,a867)),x87602),f328(f328(f306(x87601),x87603),f192(f879(x87601,a867)))))),f11(x87601,f240(x87601),x87602)) % 167.77/167.51 [8761]~P105(x87611)+~P1(f328(f38(x87611),x87612))+E(f328(f328(f22(f879(x87611,a867)),x87612),f328(f328(f306(x87611),x87613),f192(f879(x87611,a867)))),f192(f879(x87611,a867)))+~P1(f328(f328(f330(x87611),x87613),x87612))+E(f328(f328(f241(x87611),x87613),f12(x87611,f241(x87611),f328(f328(f22(f879(x87611,a867)),x87612),f328(f328(f306(x87611),x87613),f192(f879(x87611,a867)))))),f12(x87611,f241(x87611),x87612)) % 167.77/167.51 [8775]~P2(x87751)+~P1(f328(f38(x87751),x87753))+~P1(f328(f38(x87751),x87752))+E(f328(f328(f105(f879(x87751,a867)),x87752),x87753),f192(f879(x87751,a867)))+E(f328(f328(f114(x87751),f13(x87751,f328(f328(f114(f879(x87751,a867)),x87752),x87753))),f13(x87751,f328(f328(f105(f879(x87751,a867)),x87752),x87753))),f328(f328(f114(x87751),f13(x87751,x87752)),f13(x87751,x87753))) % 167.77/167.51 [8776]~P2(x87761)+~P1(f328(f38(x87761),x87763))+~P1(f328(f38(x87761),x87762))+E(f328(f328(f105(f879(x87761,a867)),x87762),x87763),f192(f879(x87761,a867)))+E(f328(f328(f105(x87761),f10(x87761,f328(f328(f114(f879(x87761,a867)),x87762),x87763))),f10(x87761,f328(f328(f105(f879(x87761,a867)),x87762),x87763))),f328(f328(f105(x87761),f10(x87761,x87762)),f10(x87761,x87763))) % 167.77/167.51 [8777]~P105(x87771)+~P1(f328(f38(x87771),x87773))+~P1(f328(f38(x87771),x87772))+E(f328(f328(f105(f879(x87771,a867)),x87772),x87773),f192(f879(x87771,a867)))+E(f328(f328(f240(x87771),f14(x87771,f328(f328(f114(f879(x87771,a867)),x87772),x87773))),f14(x87771,f328(f328(f105(f879(x87771,a867)),x87772),x87773))),f328(f328(f240(x87771),f14(x87771,x87772)),f14(x87771,x87773))) % 167.77/167.51 [8778]~P105(x87781)+~P1(f328(f38(x87781),x87783))+~P1(f328(f38(x87781),x87782))+E(f328(f328(f105(f879(x87781,a867)),x87782),x87783),f192(f879(x87781,a867)))+E(f328(f328(f241(x87781),f15(x87781,f328(f328(f114(f879(x87781,a867)),x87782),x87783))),f15(x87781,f328(f328(f105(f879(x87781,a867)),x87782),x87783))),f328(f328(f241(x87781),f15(x87781,x87782)),f15(x87781,x87783))) % 167.77/167.51 [8998]~P105(x89981)+~P1(f328(f38(x89981),x89983))+~P1(f328(f38(x89981),x89982))+E(f328(f328(f105(f879(x89981,a867)),x89982),x89983),f192(f879(x89981,a867)))+E(f328(f328(f240(x89981),f11(x89981,f240(x89981),f328(f328(f114(f879(x89981,a867)),x89982),x89983))),f11(x89981,f240(x89981),f328(f328(f105(f879(x89981,a867)),x89982),x89983))),f328(f328(f240(x89981),f11(x89981,f240(x89981),x89982)),f11(x89981,f240(x89981),x89983))) % 167.77/167.51 [8999]~P105(x89991)+~P1(f328(f38(x89991),x89993))+~P1(f328(f38(x89991),x89992))+E(f328(f328(f105(f879(x89991,a867)),x89992),x89993),f192(f879(x89991,a867)))+E(f328(f328(f241(x89991),f12(x89991,f241(x89991),f328(f328(f114(f879(x89991,a867)),x89992),x89993))),f12(x89991,f241(x89991),f328(f328(f105(f879(x89991,a867)),x89992),x89993))),f328(f328(f241(x89991),f12(x89991,f241(x89991),x89992)),f12(x89991,f241(x89991),x89993))) % 167.77/167.51 [9798]~P116(x97983)+E(x97981,x97982)+~P1(f328(f328(f242(x97983),f2(x97983)),x97982))+~P1(f328(f328(f242(x97983),f2(x97983)),x97981))+~E(f328(f328(f253(x97983),x97981),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f253(x97983),x97982),f328(f107(a872),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 167.77/167.51 [6311]E(f849(x63111,x63112,x63113),x63114)+E(f328(x63111,x63114),f2(a872))+~E(f328(f328(f6(x63113,a872),x63111),x63112),f78(a872))+~P1(f328(f38(x63113),x63112))+~P1(f328(f328(f330(x63113),x63114),x63112)) % 167.77/167.51 [6372]E(f851(x63721,x63722,x63723),x63724)+E(f328(x63721,x63724),f2(a872))+~E(f328(f328(f6(x63723,a872),x63721),x63722),f328(a116,f2(a872)))+~P1(f328(f38(x63723),x63722))+~P1(f328(f328(f330(x63723),x63724),x63722)) % 167.77/167.51 [6478]~P4(x64781)+~P105(x64781)+P1(f328(f328(f243(x64781),x64782),f41(x64781,x64783)))+~P1(f328(f328(f243(x64781),x64782),x64784))+~P1(f328(f328(f330(x64781),x64784),x64783)) % 167.77/167.51 [6651]~P4(x66511)+~P105(x66511)+~P1(f328(f328(f243(x66511),x66514),x66513))+P1(f328(f328(f243(x66511),f42(x66511,x66512)),x66513))+~P1(f328(f328(f330(x66511),x66514),x66512)) % 167.77/167.51 [6910]~P116(x69103)+E(x69101,x69102)+~E(f328(f328(f253(x69103),x69101),f328(a116,x69104)),f328(f328(f253(x69103),x69102),f328(a116,x69104)))+~P1(f328(f328(f242(x69103),f2(x69103)),x69102))+~P1(f328(f328(f242(x69103),f2(x69103)),x69101)) % 167.77/167.51 [7119]~E(f855(x71192,x71193,x71191,x71194),x71194)+~E(f328(x71192,x71194),f78(a872))+E(f328(f328(f6(x71191,a872),x71192),x71193),f78(a872))+~P1(f328(f38(x71191),x71193))+~P1(f328(f328(f330(x71191),x71194),x71193)) % 167.77/167.51 [7126]~P111(x71264)+~P125(x71264)+E(f328(x71261,f350(x71261,x71262,x71263,x71264)),f2(x71264))+~E(f328(f328(f9(x71263,x71264),x71261),x71262),f2(x71264))+~P1(f328(f38(x71263),x71262)) % 167.77/167.51 [7214]~E(f854(x72142,x72143,x72141,x72144),x72144)+~E(f328(x72142,x72144),f328(a116,f2(a872)))+E(f328(f328(f6(x72141,a872),x72142),x72143),f328(a116,f2(a872)))+~P1(f328(f38(x72141),x72143))+~P1(f328(f328(f330(x72141),x72144),x72143)) % 167.77/167.51 [7956]~E(f328(x79562,x79564),f78(a872))+~E(f328(x79562,f855(x79562,x79563,x79561,x79564)),f2(a872))+E(f328(f328(f6(x79561,a872),x79562),x79563),f78(a872))+~P1(f328(f38(x79561),x79563))+~P1(f328(f328(f330(x79561),x79564),x79563)) % 167.77/167.51 [7994]~E(f328(x79942,x79944),f328(a116,f2(a872)))+~E(f328(x79942,f854(x79942,x79943,x79941,x79944)),f2(a872))+E(f328(f328(f6(x79941,a872),x79942),x79943),f328(a116,f2(a872)))+~P1(f328(f38(x79941),x79943))+~P1(f328(f328(f330(x79941),x79944),x79943)) % 167.77/167.51 [8560]~P105(x85601)+~P15(x85601,x85604)+P15(x85601,x85602)+~E(x85602,f328(f328(f148(x85601),x85603),x85604))+~P1(f328(f328(f242(x85601),x85603),f761(x85602,x85601,x85604,x85603))) % 167.77/167.51 [8594]E(x85941,x85942)+E(f328(f328(f22(a1),f402(x85943,x85942,x85944,x85941)),f403(x85943,x85942,x85944,x85941)),x85941)+~E(f328(f328(f80(a1),x85941),x85944),x85942)+~P1(f328(f328(f243(a1),f2(a1)),x85944))+~P1(f328(f328(f330(a1),x85942),x85943)) % 167.77/167.51 [8595]E(x85951,x85952)+E(f328(f328(f80(a1),f410(x85953,x85952,x85954,x85951)),f411(x85953,x85952,x85954,x85951)),x85951)+~E(f328(f328(f22(a1),x85951),x85954),x85952)+~P1(f328(f328(f243(a1),f2(a1)),x85954))+~P1(f328(f328(f330(a1),x85952),x85953)) % 167.77/167.51 [8773]E(f328(x87731,f613(x87732,x87731,x87733,x87734)),x87732)+P1(f328(f328(f242(a872),x87734),f614(x87732,x87731,x87733,x87734)))+~P1(f328(f328(f242(a1),x87732),f328(x87731,x87733)))+~P1(f328(f328(f243(a872),x87734),x87733))+~P1(f328(f328(f242(a1),f328(x87731,x87734)),x87732)) % 167.77/167.51 [8774]~P105(x87741)+~P15(x87741,x87743)+P15(x87741,x87742)+~E(x87742,f328(f328(f148(x87741),x87744),x87743))+P1(f328(f328(f330(x87741),f761(x87742,x87741,x87743,x87744)),f328(f170(x87741),x87743))) % 167.77/167.51 [8792]~P111(x87924)+~P125(x87924)+~E(f328(f328(f9(x87921,x87924),x87922),x87923),f2(x87924))+~P1(f328(f38(x87921),x87923))+P1(f328(f328(f330(x87921),f350(x87922,x87923,x87921,x87924)),x87923)) % 167.77/167.51 [8826]~E(f328(x88262,x88264),f78(a872))+E(f328(f328(f6(x88261,a872),x88262),x88263),f78(a872))+~P1(f328(f38(x88261),x88263))+~P1(f328(f328(f330(x88261),x88264),x88263))+P1(f328(f328(f330(x88261),f855(x88262,x88263,x88261,x88264)),x88263)) % 167.77/167.51 [8835]E(x88351,x88352)+~E(f328(f328(f80(a1),x88352),x88354),x88351)+~P1(f328(f328(f243(a1),f2(a1)),x88354))+~P1(f328(f328(f330(a1),x88351),x88353))+P1(f328(f328(f330(a1),f402(x88353,x88351,x88354,x88352)),x88353)) % 167.77/167.51 [8836]E(x88361,x88362)+~E(f328(f328(f22(a1),x88362),x88364),x88361)+~P1(f328(f328(f243(a1),f2(a1)),x88364))+~P1(f328(f328(f330(a1),x88361),x88363))+P1(f328(f328(f330(a1),f410(x88363,x88361,x88364,x88362)),x88363)) % 167.77/167.51 [8838]~E(f328(x88382,x88384),f328(a116,f2(a872)))+E(f328(f328(f6(x88381,a872),x88382),x88383),f328(a116,f2(a872)))+~P1(f328(f38(x88381),x88383))+~P1(f328(f328(f330(x88381),x88384),x88383))+P1(f328(f328(f330(x88381),f854(x88382,x88383,x88381,x88384)),x88383)) % 167.77/167.51 [8843]P55(x88432,x88433,x88434,x88431)+E(x88431,f192(f879(x88432,a867)))+~P1(f328(f38(x88432),x88434))+~P1(f328(f38(x88432),x88431))+P1(f328(f328(f330(x88432),f547(x88431,x88434,x88433,x88432)),x88434)) % 167.77/167.51 [8926]E(x89261,x89262)+~E(f328(f328(f80(a1),x89262),x89264),x89261)+~P1(f328(f328(f243(a1),f2(a1)),x89264))+~P1(f328(f328(f330(a1),x89261),x89263))+P1(f328(f328(f330(a1),f403(x89263,x89261,x89264,x89262)),f299(a1,f78(a1),x89264))) % 167.77/167.51 [8927]E(x89271,x89272)+~E(f328(f328(f22(a1),x89272),x89274),x89271)+~P1(f328(f328(f243(a1),f2(a1)),x89274))+~P1(f328(f328(f330(a1),x89271),x89273))+P1(f328(f328(f330(a1),f411(x89273,x89271,x89274,x89272)),f299(a1,f78(a1),x89274))) % 167.77/167.51 [9004]P1(f328(f328(f242(a872),x90041),f613(x90042,x90043,x90044,x90041)))+~P1(f328(f328(f242(a1),x90042),f328(x90043,x90044)))+P1(f328(f328(f242(a872),x90041),f614(x90042,x90043,x90044,x90041)))+~P1(f328(f328(f243(a872),x90041),x90044))+~P1(f328(f328(f242(a1),f328(x90043,x90041)),x90042)) % 167.77/167.51 [9116]E(f328(x91161,f613(x91162,x91161,x91163,x91164)),x91162)+~P1(f328(f328(f242(a1),x91162),f328(x91161,x91163)))+P1(f328(f328(f243(a872),f614(x91162,x91161,x91163,x91164)),x91163))+~P1(f328(f328(f243(a872),x91164),x91163))+~P1(f328(f328(f242(a1),f328(x91161,x91164)),x91162)) % 167.77/167.51 [9247]~P1(f328(f328(f242(a1),x92472),f328(x92473,x92474)))+P1(f328(f328(f242(a872),x92471),f614(x92472,x92473,x92474,x92471)))+P1(f328(f328(f242(a872),f613(x92472,x92473,x92474,x92471)),x92474))+~P1(f328(f328(f243(a872),x92471),x92474))+~P1(f328(f328(f242(a1),f328(x92473,x92471)),x92472)) % 167.77/167.51 [9248]~P1(f328(f328(f242(a1),x92482),f328(x92483,x92484)))+P1(f328(f328(f242(a872),x92481),f613(x92482,x92483,x92484,x92481)))+P1(f328(f328(f243(a872),f614(x92482,x92483,x92484,x92481)),x92484))+~P1(f328(f328(f243(a872),x92481),x92484))+~P1(f328(f328(f242(a1),f328(x92483,x92481)),x92482)) % 167.77/167.51 [9355]~P1(f328(f328(f242(a1),x93551),f328(x93552,x93553)))+P1(f328(f328(f242(a872),f613(x93551,x93552,x93553,x93554)),x93553))+~P1(f328(f328(f243(a872),x93554),x93553))+~P1(f328(f328(f242(a1),f328(x93552,x93554)),x93551))+P1(f328(f328(f243(a872),f614(x93551,x93552,x93553,x93554)),x93553)) % 167.77/167.51 [9433]E(x94331,f192(f879(x94332,a867)))+~P1(f328(f38(x94332),x94334))+~P1(f328(f38(x94332),x94331))+P1(f328(f328(f330(f878(f879(x94332,a867),f879(x94332,a867))),f328(f328(f263(f879(x94332,a867),f879(x94332,a867)),x94334),x94331)),f320(x94332,x94333)))+P1(f328(f328(f330(x94332),f555(x94333,x94331,x94334,x94332)),x94334)) % 167.77/167.51 [9434]E(x94341,f192(f879(x94342,a867)))+~P1(f328(f38(x94342),x94344))+~P1(f328(f38(x94342),x94341))+P1(f328(f328(f330(f878(f879(x94342,a867),f879(x94342,a867))),f328(f328(f263(f879(x94342,a867),f879(x94342,a867)),x94344),x94341)),f320(x94342,x94343)))+P1(f328(f328(f330(x94342),f615(x94343,x94341,x94344,x94342)),x94344)) % 167.77/167.51 [10100]E(f328(x101001,f613(x101002,x101001,x101003,x101004)),x101002)+~P1(f328(f328(f242(a1),x101002),f328(x101001,x101003)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x101001,f328(f328(f80(a872),f614(x101002,x101001,x101003,x101004)),f78(a872)))),f328(x101001,f614(x101002,x101001,x101003,x101004))))),f78(a1)))+~P1(f328(f328(f243(a872),x101004),x101003))+~P1(f328(f328(f242(a1),f328(x101001,x101004)),x101002)) % 167.77/167.51 [10101]~P1(f328(f328(f242(a1),x101012),f328(x101013,x101014)))+P1(f328(f328(f242(a872),x101011),f613(x101012,x101013,x101014,x101011)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x101013,f328(f328(f80(a872),f614(x101012,x101013,x101014,x101011)),f78(a872)))),f328(x101013,f614(x101012,x101013,x101014,x101011))))),f78(a1)))+~P1(f328(f328(f243(a872),x101011),x101014))+~P1(f328(f328(f242(a1),f328(x101013,x101011)),x101012)) % 167.77/167.51 [10102]~P1(f328(f328(f242(a1),x101021),f328(x101022,x101023)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x101022,f328(f328(f80(a872),f614(x101021,x101022,x101023,x101024)),f78(a872)))),f328(x101022,f614(x101021,x101022,x101023,x101024))))),f78(a1)))+~P1(f328(f328(f243(a872),x101024),x101023))+~P1(f328(f328(f242(a1),f328(x101022,x101024)),x101021))+P1(f328(f328(f242(a872),f613(x101021,x101022,x101023,x101024)),x101023)) % 167.77/167.51 [7181]~P62(x71811)+P1(f328(f328(f243(x71811),x71812),f2(x71811)))+~P1(f328(f328(f243(x71811),x71813),f2(x71811)))+P1(f328(f328(f243(x71811),f2(x71811)),x71812))+P1(f328(f328(f243(x71811),x71813),f328(f328(f286(x71811),x71814),x71812))) % 167.77/167.51 [7182]~P62(x71821)+P1(f328(f328(f243(x71821),x71822),f2(x71821)))+~P1(f328(f328(f242(x71821),x71823),f2(x71821)))+P1(f328(f328(f243(x71821),f2(x71821)),x71822))+P1(f328(f328(f242(x71821),x71823),f328(f328(f286(x71821),x71824),x71822))) % 167.77/167.51 [7430]~P62(x74301)+P1(f328(f328(f243(x74301),x74302),f2(x74301)))+P1(f328(f328(f243(x74301),x74303),f2(x74301)))+P1(f328(f328(f243(x74301),f2(x74301)),x74303))+~P1(f328(f328(f243(x74301),x74302),f328(f328(f286(x74301),x74304),x74303))) % 167.77/167.51 [7431]~P62(x74311)+P1(f328(f328(f243(x74311),x74312),f2(x74311)))+P1(f328(f328(f242(x74311),x74313),f2(x74311)))+P1(f328(f328(f243(x74311),f2(x74311)),x74312))+~P1(f328(f328(f242(x74311),x74313),f328(f328(f286(x74311),x74314),x74312))) % 167.77/167.51 [7549]E(x75491,x75492)+~E(f328(f328(f162(x75493),x75494),x75491),f328(f328(f162(x75493),x75494),x75492))+~P1(f328(f134(x75493),x75494))+~P1(f328(f328(f243(a872),x75492),f328(f193(f873(x75493)),x75494)))+~P1(f328(f328(f243(a872),x75491),f328(f193(f873(x75493)),x75494))) % 167.77/167.51 [7918]~P62(x79181)+~P1(f328(f328(f243(x79181),x79183),f2(x79181)))+P1(f328(f328(f243(x79181),f2(x79181)),x79182))+~P1(f328(f328(f243(x79181),x79184),f328(f328(f81(x79181),x79183),x79182)))+P1(f328(f328(f243(x79181),x79183),f328(f328(f286(x79181),x79184),x79182))) % 167.77/167.51 [7919]~P62(x79191)+~P1(f328(f328(f242(x79191),x79193),f2(x79191)))+P1(f328(f328(f243(x79191),f2(x79191)),x79192))+~P1(f328(f328(f242(x79191),x79194),f328(f328(f81(x79191),x79193),x79192)))+P1(f328(f328(f242(x79191),x79193),f328(f328(f286(x79191),x79194),x79192))) % 167.77/167.51 [7920]~P62(x79201)+~P1(f328(f328(f243(x79201),x79202),f2(x79201)))+P1(f328(f328(f243(x79201),f2(x79201)),x79202))+~P1(f328(f328(f243(x79201),x79204),f328(f328(f81(x79201),x79203),x79202)))+P1(f328(f328(f243(x79201),x79203),f328(f328(f286(x79201),x79204),x79202))) % 167.77/167.51 [7921]~P62(x79211)+~P1(f328(f328(f243(x79211),x79212),f2(x79211)))+P1(f328(f328(f243(x79211),f2(x79211)),x79212))+~P1(f328(f328(f243(x79211),x79214),f328(f328(f286(x79211),x79213),x79212)))+P1(f328(f328(f243(x79211),x79213),f328(f328(f81(x79211),x79214),x79212))) % 167.77/167.51 [7922]~P62(x79221)+~P1(f328(f328(f243(x79221),x79222),f2(x79221)))+P1(f328(f328(f243(x79221),f2(x79221)),x79222))+~P1(f328(f328(f242(x79221),x79224),f328(f328(f81(x79221),x79223),x79222)))+P1(f328(f328(f242(x79221),x79223),f328(f328(f286(x79221),x79224),x79222))) % 167.77/167.51 [7923]~P62(x79231)+~P1(f328(f328(f243(x79231),x79232),f2(x79231)))+P1(f328(f328(f243(x79231),f2(x79231)),x79232))+~P1(f328(f328(f242(x79231),x79234),f328(f328(f286(x79231),x79233),x79232)))+P1(f328(f328(f242(x79231),x79233),f328(f328(f81(x79231),x79234),x79232))) % 167.77/167.51 [8060]~P105(x80601)+~P15(x80601,x80602)+~P1(f328(f328(f242(a872),x80603),x80604))+P1(f328(f328(f242(x80601),f328(f328(f162(x80601),x80602),x80603)),f328(f328(f162(x80601),x80602),x80604)))+~P1(f328(f328(f243(a872),x80604),f328(f193(f873(x80601)),x80602))) % 167.77/167.51 [8112]~P116(x81121)+~P1(f328(f328(f243(x81121),x81122),f78(x81121)))+~P1(f328(f328(f243(x81121),f2(x81121)),x81122))+~P1(f328(f328(f243(a872),x81124),x81123))+P1(f328(f328(f243(x81121),f328(f328(f253(x81121),x81122),x81123)),f328(f328(f253(x81121),x81122),x81124))) % 167.77/167.51 [8113]~P116(x81131)+~P1(f328(f328(f242(x81131),x81132),f78(x81131)))+~P1(f328(f328(f242(x81131),f2(x81131)),x81132))+~P1(f328(f328(f242(a872),x81134),x81133))+P1(f328(f328(f242(x81131),f328(f328(f253(x81131),x81132),x81133)),f328(f328(f253(x81131),x81132),x81134))) % 167.77/167.51 [8114]~P116(x81141)+~P1(f328(f328(f242(x81141),f2(x81141)),x81142))+~P1(f328(f328(f243(a872),f2(a872)),x81143))+~P1(f328(f328(f243(x81141),x81142),x81144))+P1(f328(f328(f243(x81141),f328(f328(f253(x81141),x81142),x81143)),f328(f328(f253(x81141),x81144),x81143))) % 167.77/167.51 [8135]~P105(x81351)+~P15(x81351,f328(f166(x81351),x81352))+~P1(f328(f328(f242(a872),x81354),x81353))+P1(f328(f328(f242(x81351),f328(f328(f162(x81351),x81352),x81353)),f328(f328(f162(x81351),x81352),x81354)))+~P1(f328(f328(f243(a872),x81353),f328(f193(f873(x81351)),x81352))) % 167.77/167.51 [8390]~P63(x83901)+~P1(f328(f328(f243(x83901),x83902),f2(x83901)))+~P1(f328(f328(f243(x83901),x83903),x83904))+~P1(f328(f328(f243(x83901),f2(x83901)),f328(f328(f81(x83901),x83903),x83904)))+P1(f328(f328(f243(x83901),f328(f328(f286(x83901),x83902),x83903)),f328(f328(f286(x83901),x83902),x83904))) % 167.77/167.51 [8391]~P62(x83911)+~P1(f328(f328(f242(x83911),x83912),f2(x83911)))+~P1(f328(f328(f242(x83911),x83913),x83914))+~P1(f328(f328(f243(x83911),f2(x83911)),f328(f328(f81(x83911),x83913),x83914)))+P1(f328(f328(f242(x83911),f328(f328(f286(x83911),x83912),x83913)),f328(f328(f286(x83911),x83912),x83914))) % 167.77/167.51 [8401]~P63(x84011)+~P1(f328(f328(f243(x84011),x84014),x84013))+~P1(f328(f328(f243(x84011),f2(x84011)),x84012))+~P1(f328(f328(f243(x84011),f2(x84011)),f328(f328(f81(x84011),x84013),x84014)))+P1(f328(f328(f243(x84011),f328(f328(f286(x84011),x84012),x84013)),f328(f328(f286(x84011),x84012),x84014))) % 167.77/167.51 [8402]~P63(x84021)+~P1(f328(f328(f242(x84021),x84024),x84023))+~P1(f328(f328(f242(x84021),f2(x84021)),x84022))+~P1(f328(f328(f243(x84021),f2(x84021)),f328(f328(f81(x84021),x84023),x84024)))+P1(f328(f328(f242(x84021),f328(f328(f286(x84021),x84022),x84023)),f328(f328(f286(x84021),x84022),x84024))) % 167.77/167.51 [8503]P1(f328(x85031,x85032))+~P1(f328(f38(x85034),x85032))+P1(f328(x85031,f434(x85031,x85033,x85032,x85034)))+~P1(f328(x85031,f192(f879(x85034,a867))))+~P1(f328(f328(f242(f879(x85034,a867)),x85032),x85033)) % 167.77/167.51 [8511]P1(f328(x85111,x85112))+P1(f328(f38(x85113),f434(x85111,x85114,x85112,x85113)))+~P1(f328(f38(x85113),x85112))+~P1(f328(x85111,f192(f879(x85113,a867))))+~P1(f328(f328(f242(f879(x85113,a867)),x85112),x85114)) % 167.77/167.51 [8768]E(f328(f328(f80(a1),f412(x87681,x87682,x87683,x87684)),f413(x87681,x87682,x87683,x87684)),x87684)+~P1(f328(f328(f243(a1),f2(a1)),x87683))+~P1(f328(f328(f243(a1),x87682),x87684))+~P1(f328(f328(f330(a1),x87682),x87681))+P1(f328(f328(f243(a1),x87682),f328(f328(f22(a1),x87684),x87683))) % 167.77/167.51 [8986]~P1(f328(f328(f243(a1),f2(a1)),x89863))+~P1(f328(f328(f243(a1),x89862),x89864))+~P1(f328(f328(f330(a1),x89862),x89861))+P1(f328(f328(f330(a1),f412(x89861,x89862,x89863,x89864)),x89861))+P1(f328(f328(f243(a1),x89862),f328(f328(f22(a1),x89864),x89863))) % 167.77/167.51 [8997]P1(f328(x89971,x89972))+~P1(f328(f38(x89973),x89972))+P1(f328(f328(f330(x89973),f435(x89971,x89974,x89972,x89973)),x89974))+~P1(f328(x89971,f192(f879(x89973,a867))))+~P1(f328(f328(f242(f879(x89973,a867)),x89972),x89974)) % 167.77/167.51 [9014]E(f328(f328(f80(a1),f404(x90141,x90142,x90143,x90144)),f405(x90141,x90142,x90143,x90144)),x90144)+~P1(f328(f328(f243(a1),f2(a1)),x90143))+~P1(f328(f328(f242(a1),x90142),x90144))+P1(f328(f328(f242(a1),x90142),f328(f328(f22(a1),x90144),x90143)))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x90142),f78(a1))),x90141)) % 167.77/167.51 [9068]~P1(f328(f328(f243(a1),f2(a1)),x90683))+~P1(f328(f328(f243(a1),x90681),x90682))+~P1(f328(f328(f330(a1),x90681),x90684))+P1(f328(f328(f330(a1),f413(x90684,x90681,x90683,x90682)),f299(a1,f78(a1),x90683)))+P1(f328(f328(f243(a1),x90681),f328(f328(f22(a1),x90682),x90683))) % 167.77/167.51 [9163]~P1(f328(f328(f243(a1),f2(a1)),x91633))+~P1(f328(f328(f242(a1),x91632),x91634))+P1(f328(f328(f330(a1),f404(x91631,x91632,x91633,x91634)),x91631))+P1(f328(f328(f242(a1),x91632),f328(f328(f22(a1),x91634),x91633)))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x91632),f78(a1))),x91631)) % 167.77/167.51 [9203]~P1(f328(f328(f243(a1),f2(a1)),x92033))+~P1(f328(f328(f242(a1),x92031),x92032))+P1(f328(f328(f330(a1),f405(x92034,x92031,x92033,x92032)),f299(a1,f78(a1),x92033)))+P1(f328(f328(f242(a1),x92031),f328(f328(f22(a1),x92032),x92033)))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x92031),f78(a1))),x92034)) % 167.77/167.51 [9436]P1(f328(x94361,x94362))+~P1(f328(f328(f330(x94363),f435(x94361,x94364,x94362,x94363)),f434(x94361,x94364,x94362,x94363)))+~P1(f328(f38(x94363),x94362))+~P1(f328(x94361,f192(f879(x94363,a867))))+~P1(f328(f328(f242(f879(x94363,a867)),x94362),x94364)) % 167.77/167.51 [9657]P1(f328(x96571,x96572))+~P1(f328(f38(x96573),x96572))+~P1(f328(x96571,f328(f328(f306(x96573),f435(x96571,x96574,x96572,x96573)),f434(x96571,x96574,x96572,x96573))))+~P1(f328(x96571,f192(f879(x96573,a867))))+~P1(f328(f328(f242(f879(x96573,a867)),x96572),x96574)) % 167.77/167.51 [7687]~P62(x76871)+P1(f328(f328(f243(x76871),x76872),f2(x76871)))+P1(f328(f328(f243(x76871),f2(x76871)),x76872))+~P1(f328(f328(f243(x76871),f2(x76871)),x76874))+P1(f328(f328(f243(x76871),f328(f328(f286(x76871),x76873),x76872)),x76874)) % 167.77/167.51 [7688]~P62(x76881)+P1(f328(f328(f243(x76881),x76882),f2(x76881)))+~P1(f328(f328(f242(x76881),f2(x76881)),x76884))+P1(f328(f328(f243(x76881),f2(x76881)),x76882))+P1(f328(f328(f242(x76881),f328(f328(f286(x76881),x76883),x76882)),x76884)) % 167.77/167.51 [7969]~P1(f328(f328(f242(a1),x79694),f2(a1)))+~E(x79692,f328(f328(f80(a1),f328(f328(f81(a1),x79691),x79693)),x79694))+P1(f328(f328(f243(a1),f2(a1)),x79691))+~P1(f328(f328(f243(a1),x79691),x79694))+P1(f328(f50(x79692,x79691),f328(f328(f263(a1,a1),x79693),x79694))) % 167.77/167.51 [8003]~P1(f328(x80031,x80034))+P1(f328(x80031,f398(x80032,x80031,x80033)))+~P1(f328(f328(f243(a1),f2(a1)),x80033))+~P1(f328(f328(f242(a1),f2(a1)),x80032))+P1(f328(x80031,f328(f328(f22(a1),x80034),f328(f328(f81(a1),x80032),x80033)))) % 167.77/167.51 [8004]~P1(f328(x80041,x80044))+P1(f328(x80041,f399(x80042,x80041,x80043)))+~P1(f328(f328(f243(a1),f2(a1)),x80043))+~P1(f328(f328(f242(a1),f2(a1)),x80042))+P1(f328(x80041,f328(f328(f80(a1),x80044),f328(f328(f81(a1),x80042),x80043)))) % 167.77/167.51 [8005]~P62(x80051)+P1(f328(f328(f243(x80051),x80052),f2(x80051)))+P1(f328(f328(f243(x80051),f2(x80051)),x80052))+P1(f328(f328(f243(x80051),f2(x80051)),x80053))+~P1(f328(f328(f243(x80051),f328(f328(f286(x80051),x80054),x80052)),x80053)) % 167.77/167.51 [8006]~P62(x80061)+P1(f328(f328(f243(x80061),x80062),f2(x80061)))+P1(f328(f328(f243(x80061),f2(x80061)),x80062))+P1(f328(f328(f242(x80061),f2(x80061)),x80063))+~P1(f328(f328(f242(x80061),f328(f328(f286(x80061),x80064),x80062)),x80063)) % 167.77/167.51 [8054]~E(x80541,f328(f328(f80(a1),f328(f328(f81(a1),x80542),x80543)),x80544))+~P1(f328(f328(f243(a1),f2(a1)),x80542))+~P1(f328(f328(f242(a1),f2(a1)),x80544))+~P1(f328(f328(f243(a1),x80544),x80542))+P1(f328(f50(x80541,x80542),f328(f328(f263(a1,a1),x80543),x80544))) % 167.77/167.51 [8182]~P62(x81821)+P1(f328(f328(f243(x81821),x81822),f2(x81821)))+~P1(f328(f328(f243(x81821),f2(x81821)),x81824))+~P1(f328(f328(f243(x81821),x81823),f328(f328(f81(x81821),x81824),x81822)))+P1(f328(f328(f243(x81821),f328(f328(f286(x81821),x81823),x81822)),x81824)) % 167.77/167.51 [8183]~P62(x81831)+P1(f328(f328(f243(x81831),x81832),f2(x81831)))+~P1(f328(f328(f242(x81831),f2(x81831)),x81834))+~P1(f328(f328(f242(x81831),x81833),f328(f328(f81(x81831),x81834),x81832)))+P1(f328(f328(f242(x81831),f328(f328(f286(x81831),x81833),x81832)),x81834)) % 167.77/167.51 [8270]~P62(x82701)+P1(f328(f328(f243(x82701),x82702),f2(x82701)))+~P1(f328(f328(f243(x82701),x82703),f2(x82701)))+P1(f328(f328(f243(x82701),x82703),f328(f328(f286(x82701),x82704),x82702)))+~P1(f328(f328(f243(x82701),f328(f328(f81(x82701),x82703),x82702)),x82704)) % 167.77/167.51 [8271]~P62(x82711)+P1(f328(f328(f243(x82711),x82712),f2(x82711)))+~P1(f328(f328(f242(x82711),x82713),f2(x82711)))+P1(f328(f328(f242(x82711),x82713),f328(f328(f286(x82711),x82714),x82712)))+~P1(f328(f328(f242(x82711),f328(f328(f81(x82711),x82713),x82712)),x82714)) % 167.77/167.51 [8424]~P62(x84241)+~P1(f328(f328(f243(x84241),x84242),f2(x84241)))+P1(f328(f328(f243(x84241),f2(x84241)),x84242))+~P1(f328(f328(f243(x84241),f328(f328(f286(x84241),x84244),x84242)),x84243))+P1(f328(f328(f243(x84241),f328(f328(f81(x84241),x84243),x84242)),x84244)) % 167.77/167.51 [8425]~P62(x84251)+~P1(f328(f328(f243(x84251),x84252),f2(x84251)))+P1(f328(f328(f243(x84251),f2(x84251)),x84252))+~P1(f328(f328(f243(x84251),f328(f328(f81(x84251),x84254),x84252)),x84253))+P1(f328(f328(f243(x84251),f328(f328(f286(x84251),x84253),x84252)),x84254)) % 167.77/167.51 [8426]~P62(x84261)+~P1(f328(f328(f243(x84261),x84262),f2(x84261)))+P1(f328(f328(f243(x84261),f2(x84261)),x84262))+~P1(f328(f328(f242(x84261),f328(f328(f286(x84261),x84264),x84262)),x84263))+P1(f328(f328(f242(x84261),f328(f328(f81(x84261),x84263),x84262)),x84264)) % 167.77/167.51 [8427]~P62(x84271)+~P1(f328(f328(f243(x84271),x84272),f2(x84271)))+P1(f328(f328(f243(x84271),f2(x84271)),x84272))+~P1(f328(f328(f242(x84271),f328(f328(f81(x84271),x84274),x84272)),x84273))+P1(f328(f328(f242(x84271),f328(f328(f286(x84271),x84273),x84272)),x84274)) % 167.77/167.51 [8446]~P62(x84461)+~P1(f328(f328(f243(x84461),f2(x84461)),x84464))+P1(f328(f328(f243(x84461),f2(x84461)),x84462))+~P1(f328(f328(f243(x84461),f328(f328(f81(x84461),x84464),x84462)),x84463))+P1(f328(f328(f243(x84461),f328(f328(f286(x84461),x84463),x84462)),x84464)) % 167.77/167.51 [8447]~P62(x84471)+~P1(f328(f328(f242(x84471),f2(x84471)),x84474))+P1(f328(f328(f243(x84471),f2(x84471)),x84472))+~P1(f328(f328(f242(x84471),f328(f328(f81(x84471),x84474),x84472)),x84473))+P1(f328(f328(f242(x84471),f328(f328(f286(x84471),x84473),x84472)),x84474)) % 167.77/167.51 [8519]~P62(x85191)+~P1(f328(f328(f243(x85191),x85194),f2(x85191)))+~P1(f328(f328(f243(x85191),x85193),f328(f328(f81(x85191),x85192),x85194)))+P1(f328(f328(f243(x85191),x85192),f328(f328(f286(x85191),x85193),x85194)))+~P1(f328(f328(f243(x85191),f328(f328(f81(x85191),x85192),x85194)),x85193)) % 167.77/167.51 [8520]~P62(x85201)+~P1(f328(f328(f243(x85201),x85202),f2(x85201)))+~P1(f328(f328(f243(x85201),x85203),f328(f328(f81(x85201),x85202),x85204)))+P1(f328(f328(f243(x85201),x85202),f328(f328(f286(x85201),x85203),x85204)))+~P1(f328(f328(f243(x85201),f328(f328(f81(x85201),x85202),x85204)),x85203)) % 167.77/167.51 [8521]~P62(x85211)+~P1(f328(f328(f243(x85211),x85214),f2(x85211)))+~P1(f328(f328(f242(x85211),x85213),f328(f328(f81(x85211),x85212),x85214)))+P1(f328(f328(f242(x85211),x85212),f328(f328(f286(x85211),x85213),x85214)))+~P1(f328(f328(f242(x85211),f328(f328(f81(x85211),x85212),x85214)),x85213)) % 167.77/167.51 [8522]~P62(x85221)+~P1(f328(f328(f242(x85221),x85222),f2(x85221)))+~P1(f328(f328(f242(x85221),x85223),f328(f328(f81(x85221),x85222),x85224)))+P1(f328(f328(f242(x85221),x85222),f328(f328(f286(x85221),x85223),x85224)))+~P1(f328(f328(f242(x85221),f328(f328(f81(x85221),x85222),x85224)),x85223)) % 167.77/167.51 [8645]~P62(x86451)+~P1(f328(f328(f243(x86451),x86453),f2(x86451)))+~P1(f328(f328(f243(x86451),x86452),f328(f328(f81(x86451),x86454),x86453)))+~P1(f328(f328(f243(x86451),f328(f328(f81(x86451),x86454),x86453)),x86452))+P1(f328(f328(f243(x86451),f328(f328(f286(x86451),x86452),x86453)),x86454)) % 167.77/167.51 [8646]~P62(x86461)+~P1(f328(f328(f243(x86461),x86463),f2(x86461)))+~P1(f328(f328(f242(x86461),x86462),f328(f328(f81(x86461),x86464),x86463)))+~P1(f328(f328(f242(x86461),f328(f328(f81(x86461),x86464),x86463)),x86462))+P1(f328(f328(f242(x86461),f328(f328(f286(x86461),x86462),x86463)),x86464)) % 167.77/167.51 [8661]~P62(x86611)+~P1(f328(f328(f243(x86611),f2(x86611)),x86614))+~P1(f328(f328(f243(x86611),x86612),f328(f328(f81(x86611),x86614),x86613)))+~P1(f328(f328(f243(x86611),f328(f328(f81(x86611),x86614),x86613)),x86612))+P1(f328(f328(f243(x86611),f328(f328(f286(x86611),x86612),x86613)),x86614)) % 167.77/167.51 [8662]~P62(x86621)+~P1(f328(f328(f242(x86621),f2(x86621)),x86624))+~P1(f328(f328(f242(x86621),x86622),f328(f328(f81(x86621),x86624),x86623)))+~P1(f328(f328(f242(x86621),f328(f328(f81(x86621),x86624),x86623)),x86622))+P1(f328(f328(f242(x86621),f328(f328(f286(x86621),x86622),x86623)),x86624)) % 167.77/167.51 [8828]E(f328(f328(f22(a1),f422(x88281,x88282,x88283,x88284)),f423(x88281,x88282,x88283,x88284)),x88284)+~P1(f328(f328(f243(a1),f2(a1)),x88283))+~P1(f328(f328(f330(a1),x88282),x88281))+~P1(f328(f328(f243(a1),x88284),x88282))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x88284),x88283)),x88282)) % 167.77/167.51 [8907]~P1(f328(x89071,x89072))+~P1(f328(f328(f243(a1),f2(a1)),x89074))+~P1(f328(f328(f242(a1),f2(a1)),x89073))+~P1(f328(x89071,f328(f328(f22(a1),f398(x89073,x89071,x89074)),x89074)))+P1(f328(x89071,f328(f328(f22(a1),x89072),f328(f328(f81(a1),x89073),x89074)))) % 167.77/167.51 [8908]~P1(f328(x89081,x89082))+~P1(f328(f328(f243(a1),f2(a1)),x89084))+~P1(f328(f328(f242(a1),f2(a1)),x89083))+~P1(f328(x89081,f328(f328(f80(a1),f399(x89083,x89081,x89084)),x89084)))+P1(f328(x89081,f328(f328(f80(a1),x89082),f328(f328(f81(a1),x89083),x89084)))) % 167.77/167.51 [9061]~P1(f328(f328(f243(a1),f2(a1)),x90613))+~P1(f328(f328(f330(a1),x90612),x90611))+~P1(f328(f328(f243(a1),x90614),x90612))+P1(f328(f328(f330(a1),f422(x90611,x90612,x90613,x90614)),x90611))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x90614),x90613)),x90612)) % 167.77/167.51 [9082]E(f328(f328(f22(a1),f406(x90821,x90822,x90823,x90824)),f407(x90821,x90822,x90823,x90824)),x90824)+~P1(f328(f328(f243(a1),f2(a1)),x90823))+~P1(f328(f328(f242(a1),x90824),x90822))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x90822),f78(a1))),x90821))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x90824),x90823)),x90822)) % 167.77/167.51 [9108]~P1(f328(f328(f243(a1),f2(a1)),x91082))+~P1(f328(f328(f330(a1),x91083),x91084))+~P1(f328(f328(f243(a1),x91081),x91083))+P1(f328(f328(f330(a1),f423(x91084,x91083,x91082,x91081)),f299(a1,f78(a1),x91082)))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x91081),x91082)),x91083)) % 167.77/167.51 [9198]~P1(f328(f328(f243(a1),f2(a1)),x91983))+~P1(f328(f328(f242(a1),x91984),x91982))+P1(f328(f328(f330(a1),f406(x91981,x91982,x91983,x91984)),x91981))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x91982),f78(a1))),x91981))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x91984),x91983)),x91982)) % 167.77/167.51 [9243]~P1(f328(f328(f243(a1),f2(a1)),x92432))+~P1(f328(f328(f242(a1),x92431),x92433))+P1(f328(f328(f330(a1),f407(x92434,x92433,x92432,x92431)),f299(a1,f78(a1),x92432)))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x92433),f78(a1))),x92434))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x92431),x92432)),x92433)) % 167.77/167.51 [9531]~P38(x95311,x95313)+~P27(x95311,x95314)+P38(x95311,f328(f328(f114(f879(f878(x95311,x95311),a867)),x95312),x95313))+~P1(f328(f328(f242(f879(f878(x95311,x95311),a867)),x95312),f328(f262(f879(f878(x95311,x95311),a867),f879(f878(x95311,x95311),a867)),x95314)))+~P1(f328(f328(f242(f879(f878(x95311,x95311),a867)),x95313),f328(f266(f879(f878(x95311,x95311),a867),f879(f878(x95311,x95311),a867)),x95314))) % 167.77/167.51 [9826]~E(f328(f723(x98261,x98264,x98263,x98262),f725(x98261,x98264,x98263,x98262)),f205(f873(a324)))+P1(f328(f328(f243(a1),f724(x98261,x98264,x98263,x98262)),f725(x98261,x98264,x98263,x98262)))+P1(f328(f328(f328(x98261,x98262),x98263),x98264))+P1(f328(f328(f328(x98261,f723(x98261,x98264,x98263,x98262)),f724(x98261,x98264,x98263,x98262)),f328(f328(f80(a1),f725(x98261,x98264,x98263,x98262)),f78(a1))))+~P1(f328(f316(f878(f879(a1,f876(f873(a324))),f878(a1,a1)),a314),f328(f328(f263(f879(a1,f876(f873(a324))),f878(a1,a1)),x98262),f328(f328(f263(a1,a1),x98263),x98264)))) % 167.77/167.51 [9927]~P19(x99272,x99274,x99273)+E(x99271,f192(f879(x99272,a867)))+~P1(f328(f38(x99272),x99271))+P1(f328(f328(f330(x99272),f328(x99273,x99271)),x99271))+~P1(f328(f328(f330(x99272),f328(f328(x99274,f393(x99271,x99273,x99274,x99272)),f409(x99271,x99273,x99274,x99272))),f328(f328(f306(x99272),f393(x99271,x99273,x99274,x99272)),f328(f328(f306(x99272),f409(x99271,x99273,x99274,x99272)),f192(f879(x99272,a867)))))) % 167.77/167.51 [9858]~P107(x98582)+~P59(x98581)+~P1(f328(f328(f242(f879(x98581,x98582)),x98583),x98584))+P1(f328(f328(f243(f879(x98581,x98582)),x98583),x98584))+~P1(f328(f59(x98581),f328(f328(f8(a867,a867,x98581),a323),f328(f328(f18(x98581,x98582,a867),f328(f328(f8(x98582,f879(x98582,a867),x98581),a325),x98583)),x98584)))) % 167.77/167.51 [9444]~P51(x94441,x94441,x94444)+P1(f328(f328(f330(f878(x94441,x94441)),f328(f328(f263(x94441,x94441),x94442),x94443)),f304(x94441,x94444)))+P1(f328(f328(f330(f878(x94441,x94441)),f328(f328(f263(x94441,x94441),x94443),x94442)),f304(x94441,x94444)))+~P1(f328(f328(f330(f878(x94441,x94441)),f328(f328(f263(x94441,x94441),x94445),x94442)),f304(x94441,x94444)))+~P1(f328(f328(f330(f878(x94441,x94441)),f328(f328(f263(x94441,x94441),x94445),x94443)),f304(x94441,x94444))) % 167.77/167.51 [5595]E(x55951,f2(a872))+~E(f328(f39(x55952),x55955),x55951)+E(f328(f39(x55952),x55953),f328(a116,x55951))+~E(x55953,f328(f328(f306(x55952),x55954),x55955))+P1(f328(f328(f330(x55952),x55954),x55955)) % 167.77/167.51 [5721]~P61(x57212)+E(x57211,f2(x57212))+E(x57213,f2(x57212))+~E(f328(f328(f286(x57212),x57214),x57213),f328(f328(f286(x57212),x57215),x57211))+E(f328(f328(f81(x57212),x57214),x57211),f328(f328(f81(x57212),x57215),x57213)) % 167.77/167.51 [5722]~P61(x57222)+E(x57221,f2(x57222))+E(x57223,f2(x57222))+~E(f328(f328(f81(x57222),x57224),x57223),f328(f328(f81(x57222),x57225),x57221))+E(f328(f328(f286(x57222),x57224),x57221),f328(f328(f286(x57222),x57225),x57223)) % 167.77/167.51 [5788]~E(f328(f39(x57881),x57885),x57883)+~E(x57885,f192(f879(x57881,a867)))+E(f328(f39(x57881),x57882),f328(a116,x57883))+~E(x57882,f328(f328(f306(x57881),x57884),x57885))+P1(f328(f328(f330(x57881),x57884),x57885)) % 167.77/167.51 [6011]~P111(x60112)+~E(f328(x60113,x60115),f2(x60112))+E(f328(f328(f9(x60111,x60112),x60113),x60114),f2(x60112))+~P1(f328(f38(x60111),x60114))+~P1(f328(f328(f330(x60111),x60115),x60114)) % 167.77/167.51 [6385]~P105(x63853)+E(x63851,x63852)+~E(f328(f298(x63853,x63854),x63851),f328(f298(x63853,x63855),x63852))+~P1(f328(f328(f243(x63853),x63855),x63852))+~P1(f328(f328(f243(x63853),x63854),x63851)) % 167.77/167.51 [6386]~P105(x63863)+E(x63861,x63862)+~E(f328(f298(x63863,x63861),x63864),f328(f298(x63863,x63862),x63865))+~P1(f328(f328(f243(x63863),x63862),x63865))+~P1(f328(f328(f243(x63863),x63861),x63864)) % 167.77/167.51 [7447]~P105(x74471)+~P15(x74471,f328(f328(f125(x74471),x74474),x74475))+~P1(f328(f328(f330(x74471),x74473),f328(f170(x74471),x74475)))+~P1(f328(f328(f330(x74471),x74472),f328(f170(x74471),x74474)))+P1(f328(f328(f242(x74471),x74472),x74473)) % 167.77/167.51 [8562]~P107(x85621)+~P1(f328(f328(f243(f879(x85621,a867)),f299(x85621,x85625,x85622)),f299(x85621,x85624,x85623)))+~P1(f328(f328(f242(x85621),x85625),x85622))+P1(f328(f328(f243(x85621),x85622),x85623))+P1(f328(f328(f243(x85621),x85624),x85625)) % 167.77/167.51 [9970]~P18(x99702,x99705,x99703)+E(x99701,f192(f879(x99702,a867)))+~E(f328(f328(x99705,f328(x99704,f459(x99701,x99704,x99703,x99705,x99702))),f328(x99704,f470(x99701,x99704,x99703,x99705,x99702))),f328(x99704,f328(f328(x99705,f459(x99701,x99704,x99703,x99705,x99702)),f470(x99701,x99704,x99703,x99705,x99702))))+E(f328(x99703,f328(f307(x99702,x99702,x99704),x99701)),f328(x99704,f328(x99703,x99701)))+~P1(f328(f38(x99702),x99701)) % 167.77/167.51 [6382]~P19(x63822,x63825,x63823)+E(x63821,f192(f879(x63822,a867)))+~P1(f328(f38(x63822),x63821))+E(f328(x63823,f328(f328(f306(x63822),x63824),x63821)),f328(f328(x63825,x63824),f328(x63823,x63821)))+P1(f328(f328(f330(x63822),x63824),x63821)) % 167.77/167.51 [7205]~P18(x72052,x72053,x72054)+E(f328(f328(x72053,f328(x72054,x72051)),f328(x72054,x72055)),f328(x72054,x72055))+E(x72051,f192(f879(x72052,a867)))+~P1(f328(f38(x72052),x72055))+~P1(f328(f328(f242(f879(x72052,a867)),x72051),x72055)) % 167.77/167.51 [7423]~P59(x74234)+~P93(x74235)+E(f328(x74231,x74232),f328(x74233,x74232))+~P1(f328(f328(f330(x74234),x74232),f328(f170(x74234),f57(x74234))))+~P1(f328(f328(f91(f879(x74234,x74235)),x74231),x74233)) % 167.77/167.51 [7584]~P19(x75844,x75845,x75841)+E(f328(x75841,x75842),x75843)+~P1(f328(f38(x75844),x75842))+~E(f328(f328(f22(f879(x75844,a867)),x75842),f328(f328(f306(x75844),x75843),f192(f879(x75844,a867)))),f192(f879(x75844,a867)))+~P1(f328(f328(f330(x75844),x75843),x75842)) % 167.77/167.51 [7670]E(x76701,x76702)+~E(f328(f193(f873(x76703)),x76702),f328(f193(f873(x76704)),x76705))+~E(f328(f193(f873(x76703)),x76701),f328(f193(f873(x76704)),x76705))+~E(f328(f176(x76704,x76703),f328(f328(f180(x76704,x76703),x76705),x76701)),f328(f176(x76704,x76703),f328(f328(f180(x76704,x76703),x76705),x76702)))+~P1(f328(f134(x76704),x76705)) % 167.77/167.51 [8527]E(x85271,x85272)+~P7(x85273,x85274,x85275)+E(f328(f328(f105(f879(x85273,a867)),x85271),x85272),f192(f879(x85273,a867)))+~P1(f328(f328(f330(f879(x85273,a867)),x85272),f328(f328(f62(x85273),x85274),x85275)))+~P1(f328(f328(f330(f879(x85273,a867)),x85271),f328(f328(f62(x85273),x85274),x85275))) % 167.77/167.51 [9325]~P67(x93252)+~E(f328(x93253,f436(x93253,x93254,x93255,x93251,x93252)),f2(x93252))+E(f328(f328(f6(x93251,x93252),x93253),x93254),f328(f328(f6(x93251,x93252),x93253),x93255))+~P1(f328(f38(x93251),x93255))+~P1(f328(f328(f242(f879(x93251,a867)),x93254),x93255)) % 167.77/167.51 [9326]~P67(x93262)+~E(f328(x93263,f437(x93263,x93264,x93265,x93261,x93262)),f2(x93262))+E(f328(f328(f6(x93261,x93262),x93263),x93264),f328(f328(f6(x93261,x93262),x93263),x93265))+~P1(f328(f38(x93261),x93265))+~P1(f328(f328(f242(f879(x93261,a867)),x93264),x93265)) % 167.77/167.51 [9327]~P73(x93272)+~E(f328(x93273,f408(x93273,x93274,x93275,x93271,x93272)),f78(x93272))+E(f328(f328(f9(x93271,x93272),x93273),x93274),f328(f328(f9(x93271,x93272),x93273),x93275))+~P1(f328(f38(x93271),x93275))+~P1(f328(f328(f242(f879(x93271,a867)),x93274),x93275)) % 167.77/167.51 [9328]~P73(x93282)+~E(f328(x93283,f432(x93283,x93284,x93285,x93281,x93282)),f78(x93282))+E(f328(f328(f9(x93281,x93282),x93283),x93284),f328(f328(f9(x93281,x93282),x93283),x93285))+~P1(f328(f38(x93281),x93285))+~P1(f328(f328(f242(f879(x93281,a867)),x93284),x93285)) % 167.77/167.51 [9806]~P86(x98061)+~P1(f328(f38(x98062),x98065))+~P1(f328(f328(f242(x98061),f2(x98061)),f328(x98063,f361(x98063,x98064,x98065,x98062,x98061))))+P1(f328(f328(f242(x98061),f328(f328(f6(x98062,x98061),x98063),x98064)),f328(f328(f6(x98062,x98061),x98063),x98065)))+~P1(f328(f328(f242(f879(x98062,a867)),x98064),x98065)) % 167.77/167.51 [7444]E(x74441,f2(a872))+P1(f328(x74442,x74443))+~E(x74444,f328(f328(f80(a872),f328(f328(f81(a872),x74441),x74443)),x74445))+~P1(f328(f328(f243(a872),x74445),x74441))+~P1(f328(x74442,f328(f328(f40(a872),x74444),x74441))) % 167.77/167.51 [7523]E(x75231,f2(a872))+P1(f328(x75232,x75233))+~P1(f328(x75232,f46(a872,x75234,x75231)))+~E(x75234,f328(f328(f80(a872),f328(f328(f81(a872),x75231),x75235)),x75233))+~P1(f328(f328(f243(a872),x75233),x75231)) % 167.77/167.51 [7819]~P61(x78193)+E(f328(x78191,x78192),f2(x78193))+~P1(f328(f38(x78194),x78195))+E(f328(f328(f9(x78194,x78193),x78191),f328(f328(f22(f879(x78194,a867)),x78195),f328(f328(f306(x78194),x78192),f192(f879(x78194,a867))))),f328(f328(f9(x78194,x78193),x78191),x78195))+P1(f328(f328(f330(x78194),x78192),x78195)) % 167.77/167.51 [8229]~P67(x82291)+~P1(f328(f38(x82292),x82295))+~P1(f328(f38(x82292),x82294))+~E(f328(f328(f105(f879(x82292,a867)),x82294),x82295),f192(f879(x82292,a867)))+E(f328(f328(f80(x82291),f328(f328(f6(x82292,x82291),x82293),x82294)),f328(f328(f6(x82292,x82291),x82293),x82295)),f328(f328(f6(x82292,x82291),x82293),f328(f328(f114(f879(x82292,a867)),x82294),x82295))) % 167.77/167.51 [8231]~P73(x82311)+~P1(f328(f38(x82312),x82315))+~P1(f328(f38(x82312),x82314))+~E(f328(f328(f105(f879(x82312,a867)),x82314),x82315),f192(f879(x82312,a867)))+E(f328(f328(f81(x82311),f328(f328(f9(x82312,x82311),x82313),x82314)),f328(f328(f9(x82312,x82311),x82313),x82315)),f328(f328(f9(x82312,x82311),x82313),f328(f328(f114(f879(x82312,a867)),x82314),x82315))) % 167.77/167.51 [8323]~P61(x83233)+E(f328(x83231,x83232),f2(x83233))+~P1(f328(f38(x83234),x83235))+E(f328(f328(f9(x83234,x83233),x83231),f328(f328(f22(f879(x83234,a867)),x83235),f328(f328(f306(x83234),x83232),f192(f879(x83234,a867))))),f328(f328(f286(x83233),f328(f328(f9(x83234,x83233),x83231),x83235)),f328(x83231,x83232)))+~P1(f328(f328(f330(x83234),x83232),x83235)) % 167.77/167.51 [9039]~P7(x90391,x90395,x90394)+~E(f328(f328(f62(x90391),f328(f328(f306(x90391),x90392),f192(f879(x90391,a867)))),x90394),f328(f328(f62(x90391),f328(f328(f306(x90391),x90393),f192(f879(x90391,a867)))),x90394))+~P1(f328(f328(f330(x90391),x90393),x90395))+~P1(f328(f328(f330(x90391),x90392),x90395))+P1(f328(f328(f330(f878(x90391,x90391)),f328(f328(f263(x90391,x90391),x90392),x90393)),x90394)) % 167.77/167.51 [9060]~P7(x90601,x90605,x90603)+E(f328(f328(f62(x90601),f328(f328(f306(x90601),x90602),f192(f879(x90601,a867)))),x90603),f328(f328(f62(x90601),f328(f328(f306(x90601),x90604),f192(f879(x90601,a867)))),x90603))+~P1(f328(f328(f330(x90601),x90604),x90605))+~P1(f328(f328(f330(x90601),x90602),x90605))+~P1(f328(f328(f330(f878(x90601,x90601)),f328(f328(f263(x90601,x90601),x90602),x90604)),x90603)) % 167.77/167.51 [9354]~P73(x93541)+~P1(f328(f38(x93542),x93545))+~P1(f328(f38(x93542),x93544))+~E(f328(f328(f105(f879(x93542,a867)),x93544),x93545),f192(f879(x93542,a867)))+E(f328(f328(f81(x93541),f328(f328(f328(f66(x93541,x93542,f81(x93541)),x93543),f78(x93541)),x93544)),f328(f328(f328(f66(x93541,x93542,f81(x93541)),x93543),f78(x93541)),x93545)),f328(f328(f328(f66(x93541,x93542,f81(x93541)),x93543),f78(x93541)),f328(f328(f114(f879(x93542,a867)),x93544),x93545))) % 167.77/167.51 [9363]~P67(x93631)+~E(f328(x93633,f858(x93633,x93635,x93634,x93632,x93631)),f2(x93631))+~P1(f328(f38(x93632),x93634))+~P1(f328(f38(x93632),x93635))+E(f328(f328(f80(x93631),f328(f328(f6(x93632,x93631),x93633),x93634)),f328(f328(f6(x93632,x93631),x93633),x93635)),f328(f328(f6(x93632,x93631),x93633),f328(f328(f114(f879(x93632,a867)),x93634),x93635))) % 167.77/167.51 [9364]~P67(x93641)+~E(f328(x93643,f859(x93643,x93645,x93644,x93642,x93641)),f2(x93641))+~P1(f328(f38(x93642),x93644))+~P1(f328(f38(x93642),x93645))+E(f328(f328(f80(x93641),f328(f328(f6(x93642,x93641),x93643),x93644)),f328(f328(f6(x93642,x93641),x93643),x93645)),f328(f328(f6(x93642,x93641),x93643),f328(f328(f114(f879(x93642,a867)),x93644),x93645))) % 167.77/167.51 [9365]~P73(x93651)+~E(f328(x93653,f360(x93653,x93655,x93654,x93652,x93651)),f78(x93651))+~P1(f328(f38(x93652),x93654))+~P1(f328(f38(x93652),x93655))+E(f328(f328(f81(x93651),f328(f328(f9(x93652,x93651),x93653),x93654)),f328(f328(f9(x93652,x93651),x93653),x93655)),f328(f328(f9(x93652,x93651),x93653),f328(f328(f114(f879(x93652,a867)),x93654),x93655))) % 167.77/167.51 [9366]~P73(x93661)+~E(f328(x93663,f362(x93663,x93665,x93664,x93662,x93661)),f78(x93661))+~P1(f328(f38(x93662),x93664))+~P1(f328(f38(x93662),x93665))+E(f328(f328(f81(x93661),f328(f328(f9(x93662,x93661),x93663),x93664)),f328(f328(f9(x93662,x93661),x93663),x93665)),f328(f328(f9(x93662,x93661),x93663),f328(f328(f114(f879(x93662,a867)),x93664),x93665))) % 167.77/167.51 [9575]~P73(x95751)+~E(f328(x95753,f833(x95753,x95755,x95754,x95752,x95751)),f78(x95751))+~P1(f328(f38(x95752),x95754))+~P1(f328(f38(x95752),x95755))+E(f328(f328(f81(x95751),f328(f328(f328(f66(x95751,x95752,f81(x95751)),x95753),f78(x95751)),x95754)),f328(f328(f328(f66(x95751,x95752,f81(x95751)),x95753),f78(x95751)),x95755)),f328(f328(f328(f66(x95751,x95752,f81(x95751)),x95753),f78(x95751)),f328(f328(f114(f879(x95752,a867)),x95754),x95755))) % 167.77/167.51 [9685]~P67(x96852)+E(f328(f328(f6(x96851,x96852),x96853),x96854),f328(f328(f6(x96851,x96852),x96853),x96855))+~P1(f328(f38(x96851),x96855))+~P1(f328(f328(f242(f879(x96851,a867)),x96854),x96855))+P1(f328(f328(f330(x96851),f436(x96853,x96854,x96855,x96851,x96852)),f328(f328(f22(f879(x96851,a867)),x96855),x96854))) % 167.77/167.51 [9686]~P67(x96862)+E(f328(f328(f6(x96861,x96862),x96863),x96864),f328(f328(f6(x96861,x96862),x96863),x96865))+~P1(f328(f38(x96861),x96865))+~P1(f328(f328(f242(f879(x96861,a867)),x96864),x96865))+P1(f328(f328(f330(x96861),f437(x96863,x96864,x96865,x96861,x96862)),f328(f328(f22(f879(x96861,a867)),x96865),x96864))) % 167.77/167.51 [9687]~P73(x96872)+E(f328(f328(f9(x96871,x96872),x96873),x96874),f328(f328(f9(x96871,x96872),x96873),x96875))+~P1(f328(f38(x96871),x96875))+~P1(f328(f328(f242(f879(x96871,a867)),x96874),x96875))+P1(f328(f328(f330(x96871),f408(x96873,x96874,x96875,x96871,x96872)),f328(f328(f22(f879(x96871,a867)),x96875),x96874))) % 167.77/167.51 [9688]~P73(x96882)+E(f328(f328(f9(x96881,x96882),x96883),x96884),f328(f328(f9(x96881,x96882),x96883),x96885))+~P1(f328(f38(x96881),x96885))+~P1(f328(f328(f242(f879(x96881,a867)),x96884),x96885))+P1(f328(f328(f330(x96881),f432(x96883,x96884,x96885,x96881,x96882)),f328(f328(f22(f879(x96881,a867)),x96885),x96884))) % 167.77/167.51 [9705]~P67(x97051)+~P1(f328(f38(x97052),x97054))+~P1(f328(f38(x97052),x97055))+E(f328(f328(f80(x97051),f328(f328(f6(x97052,x97051),x97053),x97054)),f328(f328(f6(x97052,x97051),x97053),x97055)),f328(f328(f6(x97052,x97051),x97053),f328(f328(f114(f879(x97052,a867)),x97054),x97055)))+P1(f328(f328(f330(x97052),f858(x97053,x97055,x97054,x97052,x97051)),f328(f328(f105(f879(x97052,a867)),x97054),x97055))) % 167.77/167.51 [9706]~P67(x97061)+~P1(f328(f38(x97062),x97064))+~P1(f328(f38(x97062),x97065))+E(f328(f328(f80(x97061),f328(f328(f6(x97062,x97061),x97063),x97064)),f328(f328(f6(x97062,x97061),x97063),x97065)),f328(f328(f6(x97062,x97061),x97063),f328(f328(f114(f879(x97062,a867)),x97064),x97065)))+P1(f328(f328(f330(x97062),f859(x97063,x97065,x97064,x97062,x97061)),f328(f328(f105(f879(x97062,a867)),x97064),x97065))) % 167.77/167.51 [9707]~P73(x97071)+~P1(f328(f38(x97072),x97074))+~P1(f328(f38(x97072),x97075))+E(f328(f328(f81(x97071),f328(f328(f9(x97072,x97071),x97073),x97074)),f328(f328(f9(x97072,x97071),x97073),x97075)),f328(f328(f9(x97072,x97071),x97073),f328(f328(f114(f879(x97072,a867)),x97074),x97075)))+P1(f328(f328(f330(x97072),f360(x97073,x97075,x97074,x97072,x97071)),f328(f328(f105(f879(x97072,a867)),x97074),x97075))) % 167.77/167.51 [9708]~P73(x97081)+~P1(f328(f38(x97082),x97084))+~P1(f328(f38(x97082),x97085))+E(f328(f328(f81(x97081),f328(f328(f9(x97082,x97081),x97083),x97084)),f328(f328(f9(x97082,x97081),x97083),x97085)),f328(f328(f9(x97082,x97081),x97083),f328(f328(f114(f879(x97082,a867)),x97084),x97085)))+P1(f328(f328(f330(x97082),f362(x97083,x97085,x97084,x97082,x97081)),f328(f328(f105(f879(x97082,a867)),x97084),x97085))) % 167.77/167.51 [9715]~P86(x97155)+~P1(f328(f38(x97151),x97154))+P1(f328(f328(f242(x97155),f328(f328(f6(x97151,x97155),x97152),x97153)),f328(f328(f6(x97151,x97155),x97152),x97154)))+~P1(f328(f328(f242(f879(x97151,a867)),x97153),x97154))+P1(f328(f328(f330(x97151),f361(x97152,x97153,x97154,x97151,x97155)),f328(f328(f22(f879(x97151,a867)),x97154),x97153))) % 167.77/167.51 [9769]~P73(x97691)+~P1(f328(f38(x97692),x97694))+~P1(f328(f38(x97692),x97695))+E(f328(f328(f81(x97691),f328(f328(f328(f66(x97691,x97692,f81(x97691)),x97693),f78(x97691)),x97694)),f328(f328(f328(f66(x97691,x97692,f81(x97691)),x97693),f78(x97691)),x97695)),f328(f328(f328(f66(x97691,x97692,f81(x97691)),x97693),f78(x97691)),f328(f328(f114(f879(x97692,a867)),x97694),x97695)))+P1(f328(f328(f330(x97692),f833(x97693,x97695,x97694,x97692,x97691)),f328(f328(f105(f879(x97692,a867)),x97694),x97695))) % 167.77/167.51 [8729]~P19(x87291,x87294,x87295)+~P1(f328(f38(x87291),x87292))+E(f328(f328(f22(f879(x87291,a867)),x87292),f328(f328(f306(x87291),x87293),f192(f879(x87291,a867)))),f192(f879(x87291,a867)))+~P1(f328(f328(f330(x87291),x87293),x87292))+E(f328(f328(x87294,x87293),f328(x87295,f328(f328(f22(f879(x87291,a867)),x87292),f328(f328(f306(x87291),x87293),f192(f879(x87291,a867)))))),f328(x87295,x87292)) % 167.77/167.51 [8802]~P19(x88021,x88024,x88025)+~P1(f328(f38(x88021),x88023))+~P1(f328(f38(x88021),x88022))+E(f328(f328(f105(f879(x88021,a867)),x88022),x88023),f192(f879(x88021,a867)))+E(f328(f328(x88024,f328(x88025,f328(f328(f114(f879(x88021,a867)),x88022),x88023))),f328(x88025,f328(f328(f105(f879(x88021,a867)),x88022),x88023))),f328(f328(x88024,f328(x88025,x88022)),f328(x88025,x88023))) % 167.77/167.51 [9368]~P1(f328(f328(f242(a1),x93684),f2(a1)))+~P1(f328(f328(f243(a1),x93683),x93685))+P1(f328(f328(f242(a1),x93681),x93682))+~P1(f328(f328(f243(a1),x93683),x93684))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),f328(f328(f81(a1),x93683),x93682)),x93685)),f328(f328(f80(a1),f328(f328(f81(a1),x93683),x93681)),x93684))) % 167.77/167.51 [9370]~P1(f328(f328(f242(a1),f2(a1)),x93705))+P1(f328(f328(f242(a1),x93701),x93702))+~P1(f328(f328(f243(a1),x93703),x93704))+~P1(f328(f328(f243(a1),x93705),x93704))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),f328(f328(f81(a1),x93704),x93701)),x93705)),f328(f328(f80(a1),f328(f328(f81(a1),x93704),x93702)),x93703))) % 167.77/167.51 [9481]~P61(x94815)+E(f328(x94811,f385(x94811,x94812,x94813,x94814,x94815)),f2(x94815))+~P1(f328(f38(x94814),x94813))+~P1(f328(f38(x94814),x94812))+E(f328(f328(f286(x94815),f328(f328(f81(x94815),f328(f328(f9(x94814,x94815),x94811),x94813)),f328(f328(f9(x94814,x94815),x94811),x94812))),f328(f328(f9(x94814,x94815),x94811),f328(f328(f105(f879(x94814,a867)),x94813),x94812))),f328(f328(f9(x94814,x94815),x94811),f328(f328(f114(f879(x94814,a867)),x94813),x94812))) % 167.77/167.51 [9761]~P61(x97611)+~P1(f328(f38(x97612),x97614))+~P1(f328(f38(x97612),x97615))+E(f328(f328(f286(x97611),f328(f328(f81(x97611),f328(f328(f9(x97612,x97611),x97613),x97614)),f328(f328(f9(x97612,x97611),x97613),x97615))),f328(f328(f9(x97612,x97611),x97613),f328(f328(f105(f879(x97612,a867)),x97614),x97615))),f328(f328(f9(x97612,x97611),x97613),f328(f328(f114(f879(x97612,a867)),x97614),x97615)))+P1(f328(f328(f330(x97612),f385(x97613,x97615,x97614,x97612,x97611)),f328(f328(f105(f879(x97612,a867)),x97614),x97615))) % 167.77/167.51 [9081]E(f328(f328(f125(x90811),x90812),x90813),f328(f328(f125(x90811),x90814),x90815))+~E(f328(f328(f173(x90811),f328(f193(f873(x90811)),x90814)),x90812),x90814)+~E(f328(f328(f173(x90811),f328(f193(f873(x90811)),x90812)),x90814),x90812)+~E(x90815,f328(f328(f125(x90811),f328(f328(f135(x90811),f328(f193(f873(x90811)),x90814)),x90812)),x90813))+~E(f328(f328(f125(x90811),f328(f328(f135(x90811),f328(f193(f873(x90811)),x90812)),x90814)),x90815),x90813) % 167.77/167.51 [9479]~P105(x94792)+E(f328(f328(f145(x94791,x94792,x94793),x94794),f167(x94791,x94794,x94795)),x94795)+~P15(x94792,f328(f328(f151(x94791,x94792),x94793),x94795))+~P1(f328(f328(f330(x94791),x94794),f328(f170(x94791),x94795)))+~E(f328(f138(x94791),f328(f133(x94791,f328(f328(f8(x94792,a867,x94791),f328(a325,f328(x94793,x94794))),x94793)),x94795)),x94794) % 167.77/167.51 [9823]~P69(x98231)+~P1(f328(f67(x98231,x98231,f81(x98231),x98232,x98233),x98235))+~P1(f328(f328(f330(x98231),x98234),x98233))+P1(f328(f328(f330(x98231),x98232),x98233))+P1(f328(f67(x98231,x98231,f81(x98231),x98234,f328(f328(f306(x98231),x98232),f328(f328(f22(f879(x98231,a867)),x98233),f328(f328(f306(x98231),x98234),f192(f879(x98231,a867)))))),x98235)) % 167.77/167.51 [7213]E(x72131,x72132)+~P26(x72134,x72135,x72133,x72136)+~E(f328(x72133,x72131),f328(x72133,x72132))+~P1(f328(f328(f330(x72134),x72132),x72136))+~P1(f328(f328(f330(x72134),x72131),x72136)) % 167.77/167.51 [6473]~P140(x64734)+E(x64731,x64732)+~E(x64735,x64736)+E(x64733,f2(x64734))+~E(f328(f328(f80(x64734),x64735),f328(f328(f81(x64734),x64733),x64731)),f328(f328(f80(x64734),x64736),f328(f328(f81(x64734),x64733),x64732))) % 167.77/167.51 [7504]~P4(x75041)+~P105(x75041)+~P1(f328(f328(f243(x75041),x75042),f328(x75045,x75046)))+~P1(f328(f328(f330(x75043),x75046),x75044))+P1(f328(f328(f243(x75041),x75042),f328(f328(f44(x75043,x75041),x75044),x75045))) % 167.77/167.51 [8193]~P4(x81931)+~P105(x81931)+~P1(f328(f328(f243(x81931),f328(x81934,x81936)),x81935))+~P1(f328(f328(f330(x81932),x81936),x81933))+P1(f328(f328(f243(x81931),f328(f328(f43(x81932,x81931),x81933),x81934)),x81935)) % 167.77/167.51 [8453]~P20(x84532,x84535,x84536,x84531)+~P1(f328(f38(x84532),x84534))+~P1(f328(f38(x84532),x84533))+~E(f328(f328(f105(f879(x84532,a867)),x84533),x84534),f192(f879(x84532,a867)))+E(f328(x84531,f328(f328(f114(f879(x84532,a867)),x84533),x84534)),f328(f73(x84535,x84535,x84535,f328(x84531,x84533)),f328(x84531,x84534))) % 167.77/167.51 [8772]E(x87721,x87722)+~P53(x87724,x87725,x87726,x87723,x87727)+~E(f328(x87723,x87721),f328(x87723,x87722))+~P1(f328(f328(f330(x87725),x87722),x87727))+~P1(f328(f328(f330(x87725),x87721),x87727)) % 167.77/167.51 [10068]~P1(f328(x100682,x100684))+~E(x100685,f328(f133(x100681,x100682),x100687))+E(f328(f133(x100681,x100682),x100683),f328(f328(f148(x100681),x100684),x100685))+~E(x100683,f328(f328(f125(x100681),x100686),f328(f328(f148(x100681),x100684),x100687)))+P1(f328(x100682,f787(x100685,x100684,x100683,x100682,x100681,x100686,x100687))) % 167.77/167.51 [10069]~P1(f328(x100694,x100692))+~E(x100693,f328(f133(x100691,x100694),x100697))+E(f328(f328(f148(x100691),x100692),x100693),f328(f133(x100691,x100694),x100695))+~E(x100695,f328(f328(f125(x100691),x100696),f328(f328(f148(x100691),x100692),x100697)))+P1(f328(x100694,f788(x100695,x100694,x100693,x100692,x100691,x100696,x100697))) % 167.77/167.51 [10103]~P1(f328(x101032,x101034))+~E(x101035,f328(f133(x101031,x101032),x101037))+E(f328(f133(x101031,x101032),x101033),f328(f328(f148(x101031),x101034),x101035))+~E(x101033,f328(f328(f125(x101031),x101036),f328(f328(f148(x101031),x101034),x101037)))+P1(f328(f328(f330(x101031),f787(x101035,x101034,x101033,x101032,x101031,x101036,x101037)),f328(f170(x101031),x101036))) % 167.77/167.51 [10104]~P1(f328(x101044,x101042))+~E(x101043,f328(f133(x101041,x101044),x101047))+E(f328(f328(f148(x101041),x101042),x101043),f328(f133(x101041,x101044),x101045))+~E(x101045,f328(f328(f125(x101041),x101046),f328(f328(f148(x101041),x101042),x101047)))+P1(f328(f328(f330(x101041),f788(x101045,x101044,x101043,x101042,x101041,x101046,x101047)),f328(f170(x101041),x101046))) % 167.77/167.51 [10107]~P7(x101071,x101077,x101076)+~P13(x101071,f879(x101075,a867),x101076,x101074)+P1(f328(f328(f330(x101071),f536(x101072,x101073,x101074,x101075,x101076,x101077,x101071)),x101077))+~P1(f328(f328(f330(f879(x101071,a867)),x101073),f328(f328(f62(x101071),x101077),x101076)))+P1(f328(f328(f330(f879(x101075,a867)),f328(f328(f44(x101071,f879(x101075,a867)),x101073),x101074)),x101072)) % 167.77/167.51 [10152]~P7(x101522,x101526,x101527)+~P13(x101522,f879(x101521,a867),x101527,x101524)+~P1(f328(f328(f330(f879(x101522,a867)),x101523),f328(f328(f62(x101522),x101526),x101527)))+~P1(f328(f328(f330(f879(x101521,a867)),f328(x101524,f536(x101525,x101523,x101524,x101521,x101527,x101526,x101522))),x101525))+P1(f328(f328(f330(f879(x101521,a867)),f328(f328(f44(x101522,f879(x101521,a867)),x101523),x101524)),x101525)) % 167.77/167.51 [8367]~P73(x83672)+~P26(x83671,x83675,x83678,x83674)+~E(x83673,f328(f73(x83675,x83672,x83671,x83676),x83678))+~E(x83677,f328(f307(x83671,x83675,x83678),x83674))+E(f328(f328(f9(x83671,x83672),x83673),x83674),f328(f328(f9(x83675,x83672),x83676),x83677)) % 167.77/167.51 [10156]~P73(x101562)+~P26(x101565,x101561,x101568,x101567)+~E(f328(x101566,f606(x101563,x101566,x101564,x101567,x101568,x101561,x101565,x101562)),f328(f328(f73(x101561,x101562,x101565,x101563),x101568),f606(x101563,x101566,x101564,x101567,x101568,x101561,x101565,x101562)))+~E(x101564,f328(f307(x101565,x101561,x101568),x101567))+E(f328(f328(f9(x101561,x101562),x101563),x101564),f328(f328(f9(x101565,x101562),x101566),x101567)) % 167.77/167.51 [10158]~P67(x101582)+~P26(x101581,x101585,x101588,x101584)+~E(x101587,f328(f307(x101581,x101585,x101588),x101584))+E(f328(f328(f6(x101581,x101582),x101583),x101584),f328(f328(f6(x101585,x101582),x101586),x101587))+P1(f328(f328(f330(x101581),f619(x101586,x101583,x101587,x101584,x101588,x101585,x101581,x101582)),x101584)) % 167.77/167.51 [10159]~P73(x101592)+~P26(x101591,x101595,x101598,x101594)+~E(x101597,f328(f307(x101591,x101595,x101598),x101594))+E(f328(f328(f9(x101591,x101592),x101593),x101594),f328(f328(f9(x101595,x101592),x101596),x101597))+P1(f328(f328(f330(x101591),f606(x101596,x101593,x101597,x101594,x101598,x101595,x101591,x101592)),x101594)) % 167.77/167.51 [10165]~P67(x101652)+~P26(x101655,x101651,x101658,x101657)+~E(x101654,f328(f307(x101655,x101651,x101658),x101657))+~E(f328(x101656,f619(x101653,x101656,x101654,x101657,x101658,x101651,x101655,x101652)),f328(x101653,f328(x101658,f619(x101653,x101656,x101654,x101657,x101658,x101651,x101655,x101652))))+E(f328(f328(f6(x101651,x101652),x101653),x101654),f328(f328(f6(x101655,x101652),x101656),x101657)) % 167.77/167.51 [9537]~E(f328(f193(f873(x95372)),x95375),f328(f193(f873(x95371)),x95373))+~E(f328(f193(f873(x95372)),x95374),f328(f193(f873(x95371)),x95373))+~E(f328(f328(f328(f72(x95371,f876(x95372)),f328(f176(x95371,x95372),f328(f328(f180(x95371,x95372),x95373),x95374))),x95376),f328(f235(x95372),x95377)),f328(f328(f328(f72(x95371,f876(x95372)),f328(f176(x95371,x95372),f328(f328(f180(x95371,x95372),x95373),x95375))),x95376),f328(f235(x95372),x95378)))+E(f328(f176(x95371,x95372),f328(f328(f180(x95371,x95372),x95373),x95374)),f328(f176(x95371,x95372),f328(f328(f180(x95371,x95372),x95373),x95375)))+P1(f328(f328(f330(x95371),x95376),f328(f170(x95371),x95373))) % 167.77/167.51 [9652]~P24(x96526,x96522,x96525,x96527,x96528,x96521)+~P1(f328(f38(x96522),x96524))+~P1(f328(f38(x96522),x96523))+~E(f328(f328(f105(f879(x96522,a867)),x96523),x96524),f192(f879(x96522,a867)))+E(f328(x96521,f328(f328(f114(f879(x96522,a867)),x96523),x96524)),f328(f328(x96525,f328(x96521,x96523)),f328(x96521,x96524))) % 167.77/167.51 [10055]~P24(x100558,x100552,x100555,x100557,x100556,x100551)+~E(f328(x100556,f834(x100554,x100553,x100551,x100556,x100557,x100555,x100552)),x100557)+~P1(f328(f38(x100552),x100553))+~P1(f328(f38(x100552),x100554))+E(f328(x100551,f328(f328(f114(f879(x100552,a867)),x100553),x100554)),f328(f328(x100555,f328(x100551,x100553)),f328(x100551,x100554))) % 167.77/167.51 [10112]~P24(x101128,x101122,x101125,x101127,x101126,x101121)+~P1(f328(f38(x101122),x101123))+~P1(f328(f38(x101122),x101124))+E(f328(x101121,f328(f328(f114(f879(x101122,a867)),x101123),x101124)),f328(f328(x101125,f328(x101121,x101123)),f328(x101121,x101124)))+P1(f328(f328(f330(x101122),f834(x101124,x101123,x101121,x101126,x101127,x101125,x101122)),f328(f328(f105(f879(x101122,a867)),x101123),x101124))) % 167.77/167.51 [9811]~P7(x98114,x98118,x98115)+~P7(x98111,x98119,x98113)+~P14(x98111,x98114,f879(x98112,a867),x98113,x98115,x98117)+P13(x98111,f879(x98112,a867),x98113,f328(f328(f8(f879(x98114,f879(x98112,a867)),f879(x98112,a867),x98111),f328(f44(x98114,f879(x98112,a867)),f328(f282(x98114,x98114,x98115),f328(f328(f306(x98114),x98116),f192(f879(x98114,a867)))))),x98117))+~P1(f328(f328(f330(x98114),x98116),x98118)) % 167.77/167.51 [5401]~P105(x54013)+~P15(x54013,x54011)+E(x54011,f758(x54012,x54013))+~E(f328(f170(x54013),x54011),x54012)+~P1(f328(f38(x54013),x54012))+~P1(f328(f134(x54013),x54011)) % 167.77/167.51 [5022]~P125(x50222)+~P126(x50222)+~P141(x50222)+~P113(x50222)+E(x50221,f2(x50222))+~E(f328(f328(f253(x50222),x50221),x50223),f2(x50222)) % 167.77/167.51 [5023]~P125(x50232)+~P126(x50232)+~P141(x50232)+~P113(x50232)+~E(x50231,f2(a872))+~E(f328(f328(f253(x50232),x50233),x50231),f2(x50232)) % 167.77/167.51 [6455]~P86(x64551)+~E(x64553,f2(x64551))+~E(x64552,f2(x64551))+E(f328(f328(f80(x64551),x64552),x64553),f2(x64551))+~P1(f328(f328(f242(x64551),f2(x64551)),x64553))+~P1(f328(f328(f242(x64551),f2(x64551)),x64552)) % 167.77/167.51 [8833]~E(f328(f262(a872,a872),x88333),f2(a872))+~E(x88331,f328(f328(f80(a872),f328(f328(f81(a872),f328(f262(a872,a872),x88333)),x88332)),f328(f266(a872,a872),x88333)))+P1(f328(f49(x88331,x88332),x88333))+~P1(f328(f328(f242(a872),f328(f266(a872,a872),x88333)),f2(a872)))+P1(f328(f328(f243(a872),f2(a872)),x88332))+~P1(f328(f328(f243(a872),x88332),f328(f266(a872,a872),x88333))) % 167.77/167.51 [8841]E(x88411,f2(a872))+~E(x88412,f328(f328(f80(a872),f328(f328(f81(a872),f328(f262(a872,a872),x88413)),x88411)),f328(f266(a872,a872),x88413)))+P1(f328(f49(x88412,x88411),x88413))+~P1(f328(f328(f243(a872),f2(a872)),x88411))+~P1(f328(f328(f242(a872),f2(a872)),f328(f266(a872,a872),x88413)))+~P1(f328(f328(f243(a872),f328(f266(a872,a872),x88413)),x88411)) % 167.77/167.51 [8859]~E(f328(f262(a872,a872),x88593),f2(a872))+~E(x88591,f328(f328(f80(a872),f328(f328(f81(a872),f328(f262(a872,a872),x88593)),x88592)),f328(f266(a872,a872),x88593)))+P1(f328(f49(x88591,x88592),x88593))+~P1(f328(f328(f243(a872),f2(a872)),x88592))+~P1(f328(f328(f242(a872),f2(a872)),f328(f266(a872,a872),x88593)))+~P1(f328(f328(f243(a872),f328(f266(a872,a872),x88593)),x88592)) % 167.77/167.51 [6837]~P2(x68372)+E(x68371,f192(f879(x68372,a867)))+E(x68373,f192(f879(x68372,a867)))+~P1(f328(f38(x68372),x68371))+~P1(f328(f38(x68372),x68373))+E(f13(x68372,f328(f328(f114(f879(x68372,a867)),x68373),x68371)),f328(f328(f114(x68372),f13(x68372,x68373)),f13(x68372,x68371))) % 167.77/167.51 [6838]~P2(x68382)+E(x68381,f192(f879(x68382,a867)))+E(x68383,f192(f879(x68382,a867)))+~P1(f328(f38(x68382),x68381))+~P1(f328(f38(x68382),x68383))+E(f10(x68382,f328(f328(f114(f879(x68382,a867)),x68383),x68381)),f328(f328(f105(x68382),f10(x68382,x68383)),f10(x68382,x68381))) % 167.77/167.51 [6839]~P105(x68392)+E(x68391,f192(f879(x68392,a867)))+E(x68393,f192(f879(x68392,a867)))+~P1(f328(f38(x68392),x68391))+~P1(f328(f38(x68392),x68393))+E(f14(x68392,f328(f328(f114(f879(x68392,a867)),x68393),x68391)),f328(f328(f240(x68392),f14(x68392,x68393)),f14(x68392,x68391))) % 167.77/167.51 [6840]~P105(x68402)+E(x68401,f192(f879(x68402,a867)))+E(x68403,f192(f879(x68402,a867)))+~P1(f328(f38(x68402),x68401))+~P1(f328(f38(x68402),x68403))+E(f15(x68402,f328(f328(f114(f879(x68402,a867)),x68403),x68401)),f328(f328(f241(x68402),f15(x68402,x68403)),f15(x68402,x68401))) % 167.77/167.51 [7479]~P95(x74792)+E(x74791,f192(f879(x74792,a867)))+E(x74793,f192(f879(x74792,a867)))+~P1(f328(f38(x74792),x74791))+~P1(f328(f38(x74792),x74793))+E(f328(f328(f81(x74792),f328(f64(x74792,f81(x74792)),x74793)),f328(f64(x74792,f81(x74792)),x74791)),f328(f64(x74792,f81(x74792)),f328(f328(f114(f879(x74792,a867)),x74793),x74791))) % 167.77/167.51 [7638]~P105(x76382)+E(x76381,f192(f879(x76382,a867)))+E(x76383,f192(f879(x76382,a867)))+~P1(f328(f38(x76382),x76381))+~P1(f328(f38(x76382),x76383))+E(f328(f328(f240(x76382),f11(x76382,f240(x76382),x76383)),f11(x76382,f240(x76382),x76381)),f11(x76382,f240(x76382),f328(f328(f114(f879(x76382,a867)),x76383),x76381))) % 167.77/167.51 [7639]~P105(x76392)+E(x76391,f192(f879(x76392,a867)))+E(x76393,f192(f879(x76392,a867)))+~P1(f328(f38(x76392),x76391))+~P1(f328(f38(x76392),x76393))+E(f328(f328(f241(x76392),f12(x76392,f241(x76392),x76393)),f12(x76392,f241(x76392),x76391)),f12(x76392,f241(x76392),f328(f328(f114(f879(x76392,a867)),x76393),x76391))) % 167.77/167.51 [8682]~P1(f328(x86821,x86823))+P1(f328(x86821,f427(x86821,x86822)))+P1(f328(x86821,f417(x86821,x86822)))+~P1(f328(f328(f243(a1),f2(a1)),x86822))+~P1(f328(f328(f330(a1),x86823),f299(a1,f78(a1),x86822)))+P1(f328(x86821,f328(f328(f22(a1),f417(x86821,x86822)),f328(f328(f81(a1),f425(x86821,x86822)),x86822)))) % 167.77/167.51 [8979]~P1(f328(x89791,x89793))+~P1(f328(x89791,f417(x89791,x89792)))+P1(f328(x89791,f427(x89791,x89792)))+~P1(f328(f328(f243(a1),f2(a1)),x89792))+~P1(f328(f328(f330(a1),x89793),f299(a1,f78(a1),x89792)))+~P1(f328(x89791,f328(f328(f22(a1),f417(x89791,x89792)),f328(f328(f81(a1),f425(x89791,x89792)),x89792)))) % 167.77/167.51 [10190]~P98(x101902)+E(x101901,f192(f879(x101902,a867)))+E(x101903,f192(f879(x101902,a867)))+~P1(f328(f38(x101902),x101901))+~P1(f328(f38(x101902),x101903))+E(f10(x101902,f328(f248(x101902),f328(f328(f8(f879(x101902,a867),a867,x101902),f87(x101902)),f328(f328(f8(f879(x101902,f879(x101902,a867)),f879(x101902,a867),x101902),f328(f8(f879(x101902,a867),a867,x101902),f87(x101902))),f328(f328(f7(x101902,f879(x101902,f879(x101902,a867)),f879(x101902,f879(x101902,a867))),f328(f328(f8(f879(x101902,f879(f879(x101902,a867),f879(x101902,a867))),f879(f879(x101902,f879(x101902,a867)),f879(x101902,f879(x101902,a867))),x101902),f18(x101902,f879(x101902,a867),f879(x101902,a867))),f328(f328(f8(f879(x101902,f879(x101902,f879(a867,a867))),f879(x101902,f879(f879(x101902,a867),f879(x101902,a867))),x101902),f328(f8(f879(x101902,f879(a867,a867)),f879(f879(x101902,a867),f879(x101902,a867)),x101902),f18(x101902,a867,a867))),f328(f328(f8(f879(x101902,f879(x101902,a867)),f879(x101902,f879(x101902,f879(a867,a867))),x101902),f328(f8(f879(x101902,a867),f879(x101902,f879(a867,a867)),x101902),f328(f8(a867,f879(a867,a867),x101902),a326))),f328(f328(f7(x101902,f879(x101902,f879(x101902,x101902)),f879(x101902,f879(x101902,a867))),f328(f328(f8(f879(f879(x101902,x101902),f879(x101902,a867)),f879(f879(x101902,f879(x101902,x101902)),f879(x101902,f879(x101902,a867))),x101902),f8(f879(x101902,x101902),f879(x101902,a867),x101902)),f328(f328(f8(f879(x101902,a867),f879(f879(x101902,x101902),f879(x101902,a867)),x101902),f8(x101902,a867,x101902)),a325))),f114(x101902)))))),f328(f328(f7(x101902,f879(x101902,a867),f879(x101902,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x101902,a867),f879(x101902,a867)),x101902),f8(a867,a867,x101902)),f328(f328(f8(a867,f879(a867,a867),x101902),a326),f328(f328(f7(x101902,f879(x101902,a867),a867),f330(x101902)),x101903)))),f328(f328(f7(x101902,f879(x101902,a867),a867),f330(x101902)),x101901))))))),f328(f328(f114(x101902),f10(x101902,x101903)),f10(x101902,x101901))) % 167.77/167.51 [10191]~P98(x101912)+E(x101911,f192(f879(x101912,a867)))+E(x101913,f192(f879(x101912,a867)))+~P1(f328(f38(x101912),x101911))+~P1(f328(f38(x101912),x101913))+E(f13(x101912,f328(f248(x101912),f328(f328(f8(f879(x101912,a867),a867,x101912),f87(x101912)),f328(f328(f8(f879(x101912,f879(x101912,a867)),f879(x101912,a867),x101912),f328(f8(f879(x101912,a867),a867,x101912),f87(x101912))),f328(f328(f7(x101912,f879(x101912,f879(x101912,a867)),f879(x101912,f879(x101912,a867))),f328(f328(f8(f879(x101912,f879(f879(x101912,a867),f879(x101912,a867))),f879(f879(x101912,f879(x101912,a867)),f879(x101912,f879(x101912,a867))),x101912),f18(x101912,f879(x101912,a867),f879(x101912,a867))),f328(f328(f8(f879(x101912,f879(x101912,f879(a867,a867))),f879(x101912,f879(f879(x101912,a867),f879(x101912,a867))),x101912),f328(f8(f879(x101912,f879(a867,a867)),f879(f879(x101912,a867),f879(x101912,a867)),x101912),f18(x101912,a867,a867))),f328(f328(f8(f879(x101912,f879(x101912,a867)),f879(x101912,f879(x101912,f879(a867,a867))),x101912),f328(f8(f879(x101912,a867),f879(x101912,f879(a867,a867)),x101912),f328(f8(a867,f879(a867,a867),x101912),a326))),f328(f328(f7(x101912,f879(x101912,f879(x101912,x101912)),f879(x101912,f879(x101912,a867))),f328(f328(f8(f879(f879(x101912,x101912),f879(x101912,a867)),f879(f879(x101912,f879(x101912,x101912)),f879(x101912,f879(x101912,a867))),x101912),f8(f879(x101912,x101912),f879(x101912,a867),x101912)),f328(f328(f8(f879(x101912,a867),f879(f879(x101912,x101912),f879(x101912,a867)),x101912),f8(x101912,a867,x101912)),a325))),f105(x101912)))))),f328(f328(f7(x101912,f879(x101912,a867),f879(x101912,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x101912,a867),f879(x101912,a867)),x101912),f8(a867,a867,x101912)),f328(f328(f8(a867,f879(a867,a867),x101912),a326),f328(f328(f7(x101912,f879(x101912,a867),a867),f330(x101912)),x101913)))),f328(f328(f7(x101912,f879(x101912,a867),a867),f330(x101912)),x101911))))))),f328(f328(f105(x101912),f13(x101912,x101913)),f13(x101912,x101911))) % 167.77/167.51 [10192]~P105(x101922)+E(x101921,f192(f879(x101922,a867)))+E(x101923,f192(f879(x101922,a867)))+~P1(f328(f38(x101922),x101921))+~P1(f328(f38(x101922),x101923))+E(f12(x101922,f241(x101922),f328(f248(x101922),f328(f328(f8(f879(x101922,a867),a867,x101922),f87(x101922)),f328(f328(f8(f879(x101922,f879(x101922,a867)),f879(x101922,a867),x101922),f328(f8(f879(x101922,a867),a867,x101922),f87(x101922))),f328(f328(f7(x101922,f879(x101922,f879(x101922,a867)),f879(x101922,f879(x101922,a867))),f328(f328(f8(f879(x101922,f879(f879(x101922,a867),f879(x101922,a867))),f879(f879(x101922,f879(x101922,a867)),f879(x101922,f879(x101922,a867))),x101922),f18(x101922,f879(x101922,a867),f879(x101922,a867))),f328(f328(f8(f879(x101922,f879(x101922,f879(a867,a867))),f879(x101922,f879(f879(x101922,a867),f879(x101922,a867))),x101922),f328(f8(f879(x101922,f879(a867,a867)),f879(f879(x101922,a867),f879(x101922,a867)),x101922),f18(x101922,a867,a867))),f328(f328(f8(f879(x101922,f879(x101922,a867)),f879(x101922,f879(x101922,f879(a867,a867))),x101922),f328(f8(f879(x101922,a867),f879(x101922,f879(a867,a867)),x101922),f328(f8(a867,f879(a867,a867),x101922),a326))),f328(f328(f7(x101922,f879(x101922,f879(x101922,x101922)),f879(x101922,f879(x101922,a867))),f328(f328(f8(f879(f879(x101922,x101922),f879(x101922,a867)),f879(f879(x101922,f879(x101922,x101922)),f879(x101922,f879(x101922,a867))),x101922),f8(f879(x101922,x101922),f879(x101922,a867),x101922)),f328(f328(f8(f879(x101922,a867),f879(f879(x101922,x101922),f879(x101922,a867)),x101922),f8(x101922,a867,x101922)),a325))),f240(x101922)))))),f328(f328(f7(x101922,f879(x101922,a867),f879(x101922,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x101922,a867),f879(x101922,a867)),x101922),f8(a867,a867,x101922)),f328(f328(f8(a867,f879(a867,a867),x101922),a326),f328(f328(f7(x101922,f879(x101922,a867),a867),f330(x101922)),x101923)))),f328(f328(f7(x101922,f879(x101922,a867),a867),f330(x101922)),x101921))))))),f328(f328(f240(x101922),f12(x101922,f241(x101922),x101923)),f12(x101922,f241(x101922),x101921))) % 167.77/167.51 [10193]~P105(x101932)+E(x101931,f192(f879(x101932,a867)))+E(x101933,f192(f879(x101932,a867)))+~P1(f328(f38(x101932),x101931))+~P1(f328(f38(x101932),x101933))+E(f11(x101932,f240(x101932),f328(f248(x101932),f328(f328(f8(f879(x101932,a867),a867,x101932),f87(x101932)),f328(f328(f8(f879(x101932,f879(x101932,a867)),f879(x101932,a867),x101932),f328(f8(f879(x101932,a867),a867,x101932),f87(x101932))),f328(f328(f7(x101932,f879(x101932,f879(x101932,a867)),f879(x101932,f879(x101932,a867))),f328(f328(f8(f879(x101932,f879(f879(x101932,a867),f879(x101932,a867))),f879(f879(x101932,f879(x101932,a867)),f879(x101932,f879(x101932,a867))),x101932),f18(x101932,f879(x101932,a867),f879(x101932,a867))),f328(f328(f8(f879(x101932,f879(x101932,f879(a867,a867))),f879(x101932,f879(f879(x101932,a867),f879(x101932,a867))),x101932),f328(f8(f879(x101932,f879(a867,a867)),f879(f879(x101932,a867),f879(x101932,a867)),x101932),f18(x101932,a867,a867))),f328(f328(f8(f879(x101932,f879(x101932,a867)),f879(x101932,f879(x101932,f879(a867,a867))),x101932),f328(f8(f879(x101932,a867),f879(x101932,f879(a867,a867)),x101932),f328(f8(a867,f879(a867,a867),x101932),a326))),f328(f328(f7(x101932,f879(x101932,f879(x101932,x101932)),f879(x101932,f879(x101932,a867))),f328(f328(f8(f879(f879(x101932,x101932),f879(x101932,a867)),f879(f879(x101932,f879(x101932,x101932)),f879(x101932,f879(x101932,a867))),x101932),f8(f879(x101932,x101932),f879(x101932,a867),x101932)),f328(f328(f8(f879(x101932,a867),f879(f879(x101932,x101932),f879(x101932,a867)),x101932),f8(x101932,a867,x101932)),a325))),f241(x101932)))))),f328(f328(f7(x101932,f879(x101932,a867),f879(x101932,a867)),f328(f328(f8(f879(a867,a867),f879(f879(x101932,a867),f879(x101932,a867)),x101932),f8(a867,a867,x101932)),f328(f328(f8(a867,f879(a867,a867),x101932),a326),f328(f328(f7(x101932,f879(x101932,a867),a867),f330(x101932)),x101933)))),f328(f328(f7(x101932,f879(x101932,a867),a867),f330(x101932)),x101931))))))),f328(f328(f241(x101932),f11(x101932,f240(x101932),x101933)),f11(x101932,f240(x101932),x101931))) % 167.77/167.51 [7162]~P116(x71623)+E(x71621,x71622)+~E(f328(f328(f253(x71623),x71621),x71624),f328(f328(f253(x71623),x71622),x71624))+~P1(f328(f328(f242(x71623),f2(x71623)),x71622))+~P1(f328(f328(f242(x71623),f2(x71623)),x71621))+~P1(f328(f328(f243(a872),f2(a872)),x71624)) % 167.77/167.51 [7436]~P105(x74362)+E(x74361,f192(f879(x74362,a867)))+~P1(f328(f38(x74362),x74361))+~P1(f328(f328(f330(x74362),x74364),x74361))+P1(f328(f328(f243(x74362),x74363),x74364))+~P1(f328(f328(f243(x74362),x74363),f328(f64(x74362,f240(x74362)),x74361))) % 167.77/167.51 [7437]~P100(x74372)+E(x74371,f192(f879(x74372,a867)))+~P1(f328(f38(x74372),x74371))+~P1(f328(f328(f330(x74372),x74374),x74371))+P1(f328(f328(f242(x74372),x74373),x74374))+~P1(f328(f328(f242(x74372),x74373),f328(f64(x74372,f105(x74372)),x74371))) % 167.77/167.51 [7438]~P105(x74382)+E(x74381,f192(f879(x74382,a867)))+~P1(f328(f38(x74382),x74381))+~P1(f328(f328(f330(x74382),x74384),x74381))+P1(f328(f328(f242(x74382),x74383),x74384))+~P1(f328(f328(f242(x74382),x74383),f328(f64(x74382,f240(x74382)),x74381))) % 167.77/167.51 [7338]E(x73381,f2(a1))+E(f328(f328(f40(a1),x73382),x73381),x73383)+~P1(f328(f328(f242(a1),x73384),f2(a1)))+~E(x73382,f328(f328(f80(a1),f328(f328(f81(a1),x73381),x73383)),x73384))+P1(f328(f328(f243(a1),f2(a1)),x73381))+~P1(f328(f328(f243(a1),x73381),x73384)) % 167.77/167.51 [7353]E(f46(a1,x73532,x73531),x73533)+E(x73531,f2(a1))+~P1(f328(f328(f242(a1),x73533),f2(a1)))+~E(x73532,f328(f328(f80(a1),f328(f328(f81(a1),x73531),x73534)),x73533))+P1(f328(f328(f243(a1),f2(a1)),x73531))+~P1(f328(f328(f243(a1),x73531),x73533)) % 167.77/167.51 [7478]E(x74781,f2(a1))+E(f328(f328(f40(a1),x74782),x74781),x74783)+~E(x74782,f328(f328(f80(a1),f328(f328(f81(a1),x74781),x74783)),x74784))+~P1(f328(f328(f243(a1),f2(a1)),x74781))+~P1(f328(f328(f242(a1),f2(a1)),x74784))+~P1(f328(f328(f243(a1),x74784),x74781)) % 167.77/167.51 [7500]E(f46(a1,x75002,x75001),x75003)+E(x75001,f2(a1))+~E(x75002,f328(f328(f80(a1),f328(f328(f81(a1),x75001),x75004)),x75003))+~P1(f328(f328(f243(a1),f2(a1)),x75001))+~P1(f328(f328(f242(a1),f2(a1)),x75003))+~P1(f328(f328(f243(a1),x75003),x75001)) % 167.77/167.51 [7642]~P105(x76422)+E(x76421,f192(f879(x76422,a867)))+~P1(f328(f38(x76422),x76421))+~P1(f328(f328(f243(x76422),x76424),x76423))+~P1(f328(f328(f330(x76422),x76424),x76421))+P1(f328(f328(f243(x76422),f328(f64(x76422,f240(x76422)),x76421)),x76423)) % 167.77/167.51 [7643]~P105(x76432)+E(x76431,f192(f879(x76432,a867)))+~P1(f328(f38(x76432),x76431))+~P1(f328(f328(f242(x76432),x76434),x76433))+~P1(f328(f328(f330(x76432),x76434),x76431))+P1(f328(f328(f242(x76432),f328(f64(x76432,f240(x76432)),x76431)),x76433)) % 167.77/167.51 [8224]~P1(f328(f328(f242(a1),x82244),f2(a1)))+~E(x82241,f328(f328(f80(a1),f328(f328(f81(a1),x82242),x82243)),x82244))+~P1(f328(f328(f242(a1),f2(a1)),x82244))+~P1(f328(f328(f243(a1),x82244),x82242))+~P1(f328(f328(f243(a1),x82242),x82244))+P1(f328(f50(x82241,x82242),f328(f328(f263(a1,a1),x82243),x82244))) % 167.77/167.51 [9173]~P59(x91733)+~P59(x91734)+E(x91731,x91732)+~E(f328(f193(f873(x91733)),x91732),f328(f193(f873(x91734)),f57(x91734)))+~E(f328(f193(f873(x91733)),x91731),f328(f193(f873(x91734)),f57(x91734)))+~E(f328(f73(f876(x91733),x91733,x91734,f239(x91733)),f328(f176(x91734,x91733),f328(f328(f180(x91734,x91733),f57(x91734)),x91731))),f328(f73(f876(x91733),x91733,x91734,f239(x91733)),f328(f176(x91734,x91733),f328(f328(f180(x91734,x91733),f57(x91734)),x91732)))) % 167.77/167.51 [8387]~P107(x83871)+P1(f328(f328(f243(f879(x83871,a867)),f299(x83871,x83872,x83873)),f299(x83871,x83874,x83875)))+~P1(f328(f328(f243(x83871),x83873),x83875))+~P1(f328(f328(f242(x83871),x83874),x83872))+~P1(f328(f328(f242(x83871),x83874),x83875))+~P1(f328(f328(f242(x83871),x83873),x83875)) % 167.77/167.51 [8388]~P107(x83881)+P1(f328(f328(f243(f879(x83881,a867)),f299(x83881,x83882,x83883)),f299(x83881,x83884,x83885)))+~P1(f328(f328(f243(x83881),x83884),x83882))+~P1(f328(f328(f242(x83881),x83883),x83885))+~P1(f328(f328(f242(x83881),x83884),x83885))+~P1(f328(f328(f242(x83881),x83884),x83882)) % 167.77/167.51 [9238]P55(x92382,x92383,x92384,x92381)+E(x92381,f192(f879(x92382,a867)))+~P1(f328(f38(x92382),x92384))+~P1(f328(f38(x92382),x92381))+~P1(f328(f328(x92383,f547(x92381,x92384,x92383,x92382)),x92385))+~P1(f328(f328(f330(x92382),x92385),x92381)) % 167.77/167.51 [9386]~E(x93863,x93865)+~P67(x93861)+~P73(x93861)+~P39(x93863)+E(f328(f328(f6(a1,x93861),x93862),x93863),f328(f328(f6(a1,x93861),x93864),x93865))+P1(f328(f328(f242(a1),f2(a1)),f454(x93862,x93864,x93863,x93865,x93861))) % 167.77/167.51 [9387]~E(x93873,x93875)+~P67(x93871)+~P73(x93871)+~P39(x93873)+E(f328(f328(f9(a1,x93871),x93872),x93873),f328(f328(f9(a1,x93871),x93874),x93875))+P1(f328(f328(f242(a1),f2(a1)),f444(x93872,x93874,x93873,x93875,x93871))) % 167.77/167.51 [9558]~E(x95585,x95583)+~P67(x95581)+~P73(x95581)+~P39(x95585)+~E(f328(x95582,f454(x95584,x95582,x95585,x95583,x95581)),f328(x95584,f454(x95584,x95582,x95585,x95583,x95581)))+E(f328(f328(f6(a1,x95581),x95582),x95583),f328(f328(f6(a1,x95581),x95584),x95585)) % 167.77/167.51 [9559]~E(x95595,x95593)+~P67(x95591)+~P73(x95591)+~P39(x95595)+~E(f328(x95592,f444(x95594,x95592,x95595,x95593,x95591)),f328(x95594,f444(x95594,x95592,x95595,x95593,x95591)))+E(f328(f328(f9(a1,x95591),x95592),x95593),f328(f328(f9(a1,x95591),x95594),x95595)) % 167.77/167.51 [9649]~P77(x96493)+E(f328(x96491,x96492),f2(x96493))+~E(f328(f328(f6(x96494,x96493),x96491),x96495),f2(x96493))+~P1(f328(f38(x96494),x96495))+P1(f328(f328(f330(x96494),f373(x96492,x96491,x96495,x96494,x96493)),x96495))+~P1(f328(f328(f330(x96494),x96492),x96495)) % 167.77/167.51 [9785]~P77(x97853)+E(f328(x97851,x97852),f2(x97853))+~E(f328(f328(f6(x97854,x97853),x97851),x97855),f2(x97853))+~P1(f328(f38(x97854),x97855))+~P1(f328(f328(f330(x97854),x97852),x97855))+~P1(f328(f328(f242(x97853),f2(x97853)),f328(x97851,f373(x97852,x97851,x97855,x97854,x97853)))) % 167.77/167.51 [8304]~P127(x83041)+~P1(f328(f328(f242(x83041),f2(x83041)),x83043))+~P1(f328(f328(f243(x83041),x83043),x83045))+~P1(f328(f328(f243(x83041),x83042),x83044))+~P1(f328(f328(f243(x83041),f2(x83041)),x83044))+P1(f328(f328(f243(x83041),f328(f328(f81(x83041),x83042),x83043)),f328(f328(f81(x83041),x83044),x83045))) % 167.77/167.51 [8305]~P127(x83051)+~P1(f328(f328(f242(x83051),f2(x83051)),x83053))+~P1(f328(f328(f242(x83051),f2(x83051)),x83052))+~P1(f328(f328(f243(x83051),x83053),x83055))+~P1(f328(f328(f243(x83051),x83052),x83054))+P1(f328(f328(f243(x83051),f328(f328(f81(x83051),x83052),x83053)),f328(f328(f81(x83051),x83054),x83055))) % 167.77/167.51 [8306]~P127(x83061)+~P1(f328(f328(f242(x83061),x83062),x83064))+~P1(f328(f328(f242(x83061),f2(x83061)),x83063))+~P1(f328(f328(f243(x83061),x83063),x83065))+~P1(f328(f328(f243(x83061),f2(x83061)),x83062))+P1(f328(f328(f243(x83061),f328(f328(f81(x83061),x83062),x83063)),f328(f328(f81(x83061),x83064),x83065))) % 167.77/167.51 [8307]~P127(x83071)+~P1(f328(f328(f242(x83071),x83073),x83075))+~P1(f328(f328(f242(x83071),f2(x83071)),x83072))+~P1(f328(f328(f243(x83071),x83072),x83074))+~P1(f328(f328(f243(x83071),f2(x83071)),x83073))+P1(f328(f328(f243(x83071),f328(f328(f81(x83071),x83072),x83073)),f328(f328(f81(x83071),x83074),x83075))) % 167.77/167.51 [8308]~P63(x83081)+~P1(f328(f328(f242(x83081),x83082),x83084))+~P1(f328(f328(f243(x83081),x83085),x83083))+~P1(f328(f328(f243(x83081),f2(x83081)),x83085))+~P1(f328(f328(f243(x83081),f2(x83081)),x83082))+P1(f328(f328(f243(x83081),f328(f328(f286(x83081),x83082),x83083)),f328(f328(f286(x83081),x83084),x83085))) % 167.77/167.51 [8309]~P63(x83091)+~P1(f328(f328(f242(x83091),x83095),x83093))+~P1(f328(f328(f242(x83091),f2(x83091)),x83092))+~P1(f328(f328(f243(x83091),x83092),x83094))+~P1(f328(f328(f243(x83091),f2(x83091)),x83095))+P1(f328(f328(f243(x83091),f328(f328(f286(x83091),x83092),x83093)),f328(f328(f286(x83091),x83094),x83095))) % 167.77/167.51 [8310]~P133(x83101)+~P1(f328(f328(f242(x83101),x83103),x83105))+~P1(f328(f328(f242(x83101),x83102),x83104))+~P1(f328(f328(f242(x83101),f2(x83101)),x83103))+~P1(f328(f328(f242(x83101),f2(x83101)),x83104))+P1(f328(f328(f242(x83101),f328(f328(f81(x83101),x83102),x83103)),f328(f328(f81(x83101),x83104),x83105))) % 167.77/167.51 [8311]~P133(x83111)+~P1(f328(f328(f242(x83111),x83113),x83115))+~P1(f328(f328(f242(x83111),x83112),x83114))+~P1(f328(f328(f242(x83111),f2(x83111)),x83113))+~P1(f328(f328(f242(x83111),f2(x83111)),x83112))+P1(f328(f328(f242(x83111),f328(f328(f81(x83111),x83112),x83113)),f328(f328(f81(x83111),x83114),x83115))) % 167.77/167.51 [8312]~P63(x83121)+~P1(f328(f328(f243(x83121),f2(x83121)),x83125))+~P1(f328(f328(f242(x83121),x83125),x83123))+~P1(f328(f328(f242(x83121),x83122),x83124))+~P1(f328(f328(f242(x83121),f2(x83121)),x83122))+P1(f328(f328(f242(x83121),f328(f328(f286(x83121),x83122),x83123)),f328(f328(f286(x83121),x83124),x83125))) % 167.77/167.51 [9689]~P67(x96895)+~P81(x96895)+E(x96891,f192(f879(x96892,a867)))+~P1(f328(f38(x96892),x96891))+P1(f328(f328(f330(x96892),f831(x96893,x96894,x96891,x96892,x96895)),x96891))+P1(f328(f328(f243(x96895),f328(f328(f6(x96892,x96895),x96894),x96891)),f328(f328(f6(x96892,x96895),x96893),x96891))) % 167.77/167.51 [9807]~P67(x98071)+~P83(x98071)+~P1(f328(f38(x98072),x98075))+~P1(f328(f328(f242(x98071),f2(x98071)),f328(x98073,f363(x98073,x98074,x98075,x98072,x98071))))+P1(f328(f328(f242(x98071),f328(f328(f6(x98072,x98071),x98073),x98074)),f328(f328(f6(x98072,x98071),x98073),x98075)))+~P1(f328(f328(f242(f879(x98072,a867)),x98074),x98075)) % 167.77/167.51 [9975]~P67(x99753)+~P81(x99753)+E(x99751,f192(f879(x99752,a867)))+~P1(f328(f38(x99752),x99751))+~P1(f328(f328(f243(x99753),f328(x99754,f831(x99755,x99754,x99751,x99752,x99753))),f328(x99755,f831(x99755,x99754,x99751,x99752,x99753))))+P1(f328(f328(f243(x99753),f328(f328(f6(x99752,x99753),x99754),x99751)),f328(f328(f6(x99752,x99753),x99755),x99751))) % 167.77/167.51 [7021]~P18(x70212,x70215,x70214)+E(x70211,f192(f879(x70212,a867)))+E(x70213,f192(f879(x70212,a867)))+~P1(f328(f38(x70212),x70211))+~P1(f328(f38(x70212),x70213))+E(f328(x70214,f328(f328(f114(f879(x70212,a867)),x70213),x70211)),f328(f328(x70215,f328(x70214,x70213)),f328(x70214,x70211))) % 167.77/167.51 [7608]~P145(x76081,x76083,x76084)+P1(f328(x76081,x76082))+~P1(f328(f328(f243(a1),x76084),f2(a1)))+~P1(f328(f328(f242(a1),x76085),f2(a1)))+~E(x76083,f328(f328(f80(a1),f328(f328(f81(a1),x76084),x76082)),x76085))+~P1(f328(f328(f243(a1),x76084),x76085)) % 167.77/167.51 [7609]~P144(x76091,x76093,x76094)+P1(f328(x76091,x76092))+~P1(f328(f328(f243(a1),x76094),f2(a1)))+~P1(f328(f328(f242(a1),x76092),f2(a1)))+~E(x76093,f328(f328(f80(a1),f328(f328(f81(a1),x76094),x76095)),x76092))+~P1(f328(f328(f243(a1),x76094),x76092)) % 167.77/167.51 [7651]~P145(x76511,x76513,x76514)+P1(f328(x76511,x76512))+~E(x76513,f328(f328(f80(a1),f328(f328(f81(a1),x76514),x76512)),x76515))+~P1(f328(f328(f243(a1),f2(a1)),x76514))+~P1(f328(f328(f242(a1),f2(a1)),x76515))+~P1(f328(f328(f243(a1),x76515),x76514)) % 167.77/167.51 [7652]~P144(x76521,x76523,x76524)+P1(f328(x76521,x76522))+~E(x76523,f328(f328(f80(a1),f328(f328(f81(a1),x76524),x76525)),x76522))+~P1(f328(f328(f243(a1),f2(a1)),x76524))+~P1(f328(f328(f242(a1),f2(a1)),x76522))+~P1(f328(f328(f243(a1),x76522),x76524)) % 167.77/167.51 [8601]P1(f328(f328(x86011,x86012),x86013))+~P1(f328(f328(x86011,f328(f328(f40(a1),x86014),x86015)),f46(a1,x86014,x86015)))+~P1(f328(f328(f243(a1),x86015),f2(a1)))+~P1(f328(f328(f242(a1),x86013),f2(a1)))+~E(x86014,f328(f328(f80(a1),f328(f328(f81(a1),x86015),x86012)),x86013))+~P1(f328(f328(f243(a1),x86015),x86013)) % 167.77/167.51 [8610]P1(f328(f328(x86101,x86102),x86103))+~P1(f328(f328(x86101,f328(f328(f40(a1),x86104),x86105)),f46(a1,x86104,x86105)))+~E(x86104,f328(f328(f80(a1),f328(f328(f81(a1),x86105),x86102)),x86103))+~P1(f328(f328(f243(a1),f2(a1)),x86105))+~P1(f328(f328(f242(a1),f2(a1)),x86103))+~P1(f328(f328(f243(a1),x86103),x86105)) % 167.77/167.51 [8847]E(x88471,x88472)+~P52(x88473,x88475,x88474)+~P1(f328(f328(f330(x88473),x88472),x88475))+~P1(f328(f328(f330(x88473),x88471),x88475))+P1(f328(f328(f330(f878(x88473,x88473)),f328(f328(f263(x88473,x88473),x88471),x88472)),x88474))+P1(f328(f328(f330(f878(x88473,x88473)),f328(f328(f263(x88473,x88473),x88472),x88471)),x88474)) % 167.77/167.51 [9716]~P67(x97165)+~P83(x97165)+~P1(f328(f38(x97161),x97164))+P1(f328(f328(f242(x97165),f328(f328(f6(x97161,x97165),x97162),x97163)),f328(f328(f6(x97161,x97165),x97162),x97164)))+~P1(f328(f328(f242(f879(x97161,a867)),x97163),x97164))+P1(f328(f328(f330(x97161),f363(x97162,x97163,x97164,x97161,x97165)),f328(f328(f22(f879(x97161,a867)),x97164),x97163))) % 167.77/167.51 [9815]E(x98151,f192(f879(x98152,a867)))+~P1(f328(f38(x98152),x98153))+~P1(f328(f38(x98152),x98151))+P1(f328(f328(f330(f878(f879(x98152,a867),f879(x98152,a867))),f328(f328(f263(f879(x98152,a867),f879(x98152,a867)),x98153),x98151)),f320(x98152,x98154)))+~P1(f328(f328(f330(x98152),x98155),x98151))+~P1(f328(f328(f330(f878(x98152,x98152)),f328(f328(f263(x98152,x98152),f555(x98154,x98151,x98153,x98152)),x98155)),x98154)) % 167.77/167.51 [9816]E(x98161,f192(f879(x98162,a867)))+~P1(f328(f38(x98162),x98163))+~P1(f328(f38(x98162),x98161))+P1(f328(f328(f330(f878(f879(x98162,a867),f879(x98162,a867))),f328(f328(f263(f879(x98162,a867),f879(x98162,a867)),x98163),x98161)),f320(x98162,x98164)))+~P1(f328(f328(f330(x98162),x98165),x98161))+~P1(f328(f328(f330(f878(x98162,x98162)),f328(f328(f263(x98162,x98162),f615(x98164,x98161,x98163,x98162)),x98165)),x98164)) % 167.77/167.51 [9979]~P77(x99791)+~E(f328(f328(f6(x99795,x99791),x99792),x99796),x99794)+~P1(f328(f38(x99795),x99796))+P1(f328(f328(f330(x99795),f392(x99793,x99794,x99792,x99796,x99795,x99791)),x99796))+P1(f328(f328(f242(x99791),f328(x99792,x99793)),x99794))+~P1(f328(f328(f330(x99795),x99793),x99796)) % 167.77/167.51 [10026]~P77(x100261)+~E(f328(f328(f6(x100265,x100261),x100262),x100266),x100264)+~P1(f328(f38(x100265),x100266))+~P1(f328(f328(f330(x100265),x100263),x100266))+~P1(f328(f328(f242(x100261),f2(x100261)),f328(x100262,f392(x100263,x100264,x100262,x100266,x100265,x100261))))+P1(f328(f328(f242(x100261),f328(x100262,x100263)),x100264)) % 167.77/167.51 [10138]~E(x101385,x101388)+~E(x101384,x101387)+~P67(x101382)+~P108(x101381)+E(f328(f328(f6(x101381,x101382),x101383),f328(f298(x101381,x101384),x101385)),f328(f328(f6(x101381,x101382),x101386),f328(f298(x101381,x101387),x101388)))+P1(f328(f328(f242(x101381),x101384),f618(x101383,x101386,x101385,x101388,x101384,x101387,x101381,x101382))) % 167.77/167.51 [10155]~E(x101557,x101554)+~E(x101558,x101555)+~P67(x101552)+~P108(x101551)+~E(f328(x101553,f618(x101556,x101553,x101558,x101555,x101557,x101554,x101551,x101552)),f328(x101556,f618(x101556,x101553,x101558,x101555,x101557,x101554,x101551,x101552)))+E(f328(f328(f6(x101551,x101552),x101553),f328(f298(x101551,x101554),x101555)),f328(f328(f6(x101551,x101552),x101556),f328(f298(x101551,x101557),x101558))) % 167.77/167.51 [10157]~E(x101574,x101577)+~E(x101575,x101578)+~P67(x101572)+~P108(x101571)+E(f328(f328(f6(x101571,x101572),x101573),f328(f298(x101571,x101574),x101575)),f328(f328(f6(x101571,x101572),x101576),f328(f298(x101571,x101577),x101578)))+P1(f328(f328(f243(x101571),f618(x101573,x101576,x101575,x101578,x101574,x101577,x101571,x101572)),x101575)) % 167.77/167.51 [9821]~P7(x98215,x98219,x98216)+~P7(x98211,x982110,x98213)+~P14(x98211,x98215,f879(x98212,a867),x98213,x98216,x98218)+~P1(f328(f328(f330(x98215),x98217),x98219))+~P1(f328(f328(f330(x98211),x98214),x982110))+E(f328(f328(f44(x98211,f879(x98212,a867)),f328(f282(x98211,x98211,x98213),f328(f328(f306(x98211),x98214),f192(f879(x98211,a867))))),f328(f328(f8(f879(x98215,f879(x98212,a867)),f879(x98212,a867),x98211),f328(f44(x98215,f879(x98212,a867)),f328(f282(x98215,x98215,x98216),f328(f328(f306(x98215),x98217),f192(f879(x98215,a867)))))),x98218)),f328(f328(x98218,x98214),x98217)) % 167.77/167.51 [5567]~P105(x55673)+~P15(x55673,x55672)+~P15(x55673,x55671)+E(x55671,x55672)+~E(f328(f170(x55673),x55671),f328(f170(x55673),x55672))+~P1(f328(f134(x55673),x55672))+~P1(f328(f134(x55673),x55671)) % 167.77/167.51 [4904]~P125(x49042)+~P126(x49042)+~P141(x49042)+~P113(x49042)+~E(x49043,f2(x49042))+E(x49041,f2(a872))+E(f328(f328(f253(x49042),x49043),x49041),f2(x49042)) % 167.77/167.51 [9114]E(x91141,f2(a872))+~E(x91142,f328(f328(f80(a872),f328(f328(f81(a872),f328(f262(a872,a872),x91143)),x91141)),f328(f266(a872,a872),x91143)))+P1(f328(f49(x91142,x91141),x91143))+~P1(f328(f328(f242(a872),f328(f266(a872,a872),x91143)),f2(a872)))+~P1(f328(f328(f242(a872),f2(a872)),f328(f266(a872,a872),x91143)))+~P1(f328(f328(f243(a872),x91141),f328(f266(a872,a872),x91143)))+~P1(f328(f328(f243(a872),f328(f266(a872,a872),x91143)),x91141)) % 167.77/167.51 [9123]~E(f328(f262(a872,a872),x91233),f2(a872))+~E(x91231,f328(f328(f80(a872),f328(f328(f81(a872),f328(f262(a872,a872),x91233)),x91232)),f328(f266(a872,a872),x91233)))+P1(f328(f49(x91231,x91232),x91233))+~P1(f328(f328(f242(a872),f328(f266(a872,a872),x91233)),f2(a872)))+~P1(f328(f328(f242(a872),f2(a872)),f328(f266(a872,a872),x91233)))+~P1(f328(f328(f243(a872),x91232),f328(f266(a872,a872),x91233)))+~P1(f328(f328(f243(a872),f328(f266(a872,a872),x91233)),x91232)) % 167.77/167.51 [7965]~P69(x79652)+E(x79651,f192(f879(x79652,a867)))+E(x79653,f192(f879(x79652,a867)))+~P1(f328(f38(x79652),x79651))+~P1(f328(f38(x79652),x79653))+~E(f328(f328(f105(f879(x79652,a867)),x79653),x79651),f192(f879(x79652,a867)))+E(f328(f328(f81(x79652),f328(f64(x79652,f81(x79652)),x79653)),f328(f64(x79652,f81(x79652)),x79651)),f328(f64(x79652,f81(x79652)),f328(f328(f114(f879(x79652,a867)),x79653),x79651))) % 167.77/167.51 [7747]E(x77471,f2(a1))+E(f328(f328(f40(a1),x77472),x77471),x77473)+~P1(f328(f328(f242(a1),x77474),f2(a1)))+~E(x77472,f328(f328(f80(a1),f328(f328(f81(a1),x77471),x77473)),x77474))+~P1(f328(f328(f242(a1),f2(a1)),x77474))+~P1(f328(f328(f243(a1),x77474),x77471))+~P1(f328(f328(f243(a1),x77471),x77474)) % 167.77/167.51 [7757]E(f46(a1,x77572,x77571),x77573)+E(x77571,f2(a1))+~P1(f328(f328(f242(a1),x77573),f2(a1)))+~E(x77572,f328(f328(f80(a1),f328(f328(f81(a1),x77571),x77574)),x77573))+~P1(f328(f328(f242(a1),f2(a1)),x77573))+~P1(f328(f328(f243(a1),x77573),x77571))+~P1(f328(f328(f243(a1),x77571),x77573)) % 167.77/167.51 [7660]~P19(x76602,x76605,x76604)+E(x76601,f192(f879(x76602,a867)))+E(x76603,f192(f879(x76602,a867)))+~P1(f328(f38(x76602),x76601))+~P1(f328(f38(x76602),x76603))+~E(f328(f328(f105(f879(x76602,a867)),x76603),x76601),f192(f879(x76602,a867)))+E(f328(x76604,f328(f328(f114(f879(x76602,a867)),x76603),x76601)),f328(f328(x76605,f328(x76604,x76603)),f328(x76604,x76601))) % 167.77/167.51 [9359]~P26(x93593,x93591,x93595,x93594)+~P26(x93591,x93593,x93596,x93592)+E(f328(f39(x93591),x93592),f328(f39(x93593),x93594))+~P1(f328(f38(x93593),x93594))+~P1(f328(f38(x93591),x93592))+~P1(f328(f328(f242(f879(x93593,a867)),f328(f307(x93591,x93593,x93596),x93592)),x93594))+~P1(f328(f328(f242(f879(x93591,a867)),f328(f307(x93593,x93591,x93595),x93594)),x93592)) % 167.77/167.51 [9303]~P1(f328(f328(f243(a1),f328(f328(f80(a1),f328(f328(f81(a1),x93035),x93031)),x93036)),f2(a1)))+~E(f328(f328(f80(a1),f328(f328(f81(a1),x93033),x93032)),x93034),f328(f328(f80(a1),f328(f328(f81(a1),x93035),x93031)),x93036))+~P1(f328(f328(f243(a1),f2(a1)),x93035))+~P1(f328(f328(f242(a1),f2(a1)),x93036))+~P1(f328(f328(f243(a1),x93034),x93033))+~P1(f328(f328(f242(a1),x93035),x93033))+P1(f328(f328(f242(a1),x93031),x93032)) % 167.77/167.51 [9067]~E(f328(f328(f80(a1),f328(f328(f81(a1),x90673),x90671)),x90674),f328(f328(f80(a1),f328(f328(f81(a1),x90675),x90672)),x90676))+~P1(f328(f328(f243(a1),f2(a1)),x90675))+~P1(f328(f328(f242(a1),f2(a1)),x90674))+~P1(f328(f328(f243(a1),x90676),x90675))+~P1(f328(f328(f242(a1),x90675),x90673))+P1(f328(f328(f242(a1),x90671),x90672))+~P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),f328(f328(f81(a1),x90675),x90672)),x90676))) % 167.77/167.51 [9244]~P130(x92441)+~E(f328(f328(f80(x92441),x92442),x92444),f78(x92441))+~P1(f328(f328(f242(x92441),f2(x92441)),x92444))+~P1(f328(f328(f242(x92441),f2(x92441)),x92442))+~P1(f328(f328(f243(x92441),x92445),x92446))+~P1(f328(f328(f243(x92441),x92443),x92446))+P1(f328(f328(f243(x92441),f328(f328(f80(x92441),f328(f328(f81(x92441),x92442),x92443)),f328(f328(f81(x92441),x92444),x92445))),x92446)) % 167.77/167.51 [9245]~P129(x92451)+~E(f328(f328(f80(x92451),x92452),x92454),f78(x92451))+~P1(f328(f328(f242(x92451),x92455),x92456))+~P1(f328(f328(f242(x92451),x92453),x92456))+~P1(f328(f328(f242(x92451),f2(x92451)),x92454))+~P1(f328(f328(f242(x92451),f2(x92451)),x92452))+P1(f328(f328(f242(x92451),f328(f328(f80(x92451),f328(f328(f81(x92451),x92452),x92453)),f328(f328(f81(x92451),x92454),x92455))),x92456)) % 167.77/167.51 [10071]~P7(x100717,x100716,x100715)+E(x100711,x100712)+~P13(x100717,f879(x100714,a867),x100715,x100713)+E(f328(x100713,f533(x100711,x100712,x100713,x100714,x100715,x100716,x100717)),f328(x100713,f534(x100711,x100712,x100713,x100714,x100715,x100716,x100717)))+~E(f328(f328(f44(x100717,f879(x100714,a867)),x100711),x100713),f328(f328(f44(x100717,f879(x100714,a867)),x100712),x100713))+~P1(f328(f328(f330(f879(x100717,a867)),x100712),f328(f328(f62(x100717),x100716),x100715)))+~P1(f328(f328(f330(f879(x100717,a867)),x100711),f328(f328(f62(x100717),x100716),x100715))) % 167.77/167.51 [10105]~P7(x101053,x101057,x101056)+E(x101051,x101052)+~P13(x101053,f879(x101055,a867),x101056,x101054)+~E(f328(f328(f44(x101053,f879(x101055,a867)),x101051),x101054),f328(f328(f44(x101053,f879(x101055,a867)),x101052),x101054))+P1(f328(f328(f330(x101053),f534(x101051,x101052,x101054,x101055,x101056,x101057,x101053)),x101057))+~P1(f328(f328(f330(f879(x101053,a867)),x101052),f328(f328(f62(x101053),x101057),x101056)))+~P1(f328(f328(f330(f879(x101053,a867)),x101051),f328(f328(f62(x101053),x101057),x101056))) % 167.77/167.51 [10106]~P7(x101063,x101067,x101066)+E(x101061,x101062)+~P13(x101063,f879(x101065,a867),x101066,x101064)+~E(f328(f328(f44(x101063,f879(x101065,a867)),x101061),x101064),f328(f328(f44(x101063,f879(x101065,a867)),x101062),x101064))+P1(f328(f328(f330(x101063),f533(x101061,x101062,x101064,x101065,x101066,x101067,x101063)),x101067))+~P1(f328(f328(f330(f879(x101063,a867)),x101062),f328(f328(f62(x101063),x101067),x101066)))+~P1(f328(f328(f330(f879(x101063,a867)),x101061),f328(f328(f62(x101063),x101067),x101066))) % 167.77/167.51 [10174]E(x101741,x101742)+~P7(x101743,x101746,x101747)+~P13(x101743,f879(x101744,a867),x101747,x101745)+~E(f328(f328(f44(x101743,f879(x101744,a867)),x101741),x101745),f328(f328(f44(x101743,f879(x101744,a867)),x101742),x101745))+~P1(f328(f328(f330(f878(x101743,x101743)),f328(f328(f263(x101743,x101743),f534(x101741,x101742,x101745,x101744,x101747,x101746,x101743)),f533(x101741,x101742,x101745,x101744,x101747,x101746,x101743))),x101747))+~P1(f328(f328(f330(f879(x101743,a867)),x101742),f328(f328(f62(x101743),x101746),x101747)))+~P1(f328(f328(f330(f879(x101743,a867)),x101741),f328(f328(f62(x101743),x101746),x101747))) % 167.77/167.51 [9066]~P7(x90661,x90667,x90664)+~E(x90665,x90666)+~P1(f328(f328(f330(x90661),x90663),x90666))+~P1(f328(f328(f330(x90661),x90662),x90665))+~P1(f328(f328(f330(f879(x90661,a867)),x90666),f328(f328(f62(x90661),x90667),x90664)))+~P1(f328(f328(f330(f879(x90661,a867)),x90665),f328(f328(f62(x90661),x90667),x90664)))+P1(f328(f328(f330(f878(x90661,x90661)),f328(f328(f263(x90661,x90661),x90662),x90663)),x90664)) % 167.77/167.51 [9201]E(x92011,x92012)+~P7(x92013,x92014,x92015)+~P1(f328(f328(f330(x92013),x92016),x92012))+~P1(f328(f328(f330(x92013),x92017),x92011))+~P1(f328(f328(f330(f879(x92013,a867)),x92012),f328(f328(f62(x92013),x92014),x92015)))+~P1(f328(f328(f330(f879(x92013,a867)),x92011),f328(f328(f62(x92013),x92014),x92015)))+~P1(f328(f328(f330(f878(x92013,x92013)),f328(f328(f263(x92013,x92013),x92017),x92016)),x92015)) % 167.77/167.51 [10197]~P7(x101979,x101978,x101977)+~P7(x101971,x1019711,x1019710)+~P14(x101971,x101979,f879(x101976,a867),x1019710,x101977,x101975)+P1(f328(f328(f330(x101971),f535(x101972,x101973,x101974,x101975,x101976,x101977,x101978,x101979,x1019710,x1019711,x101971)),x1019711))+~P1(f328(f328(f330(f879(x101979,a867)),x101973),f328(f328(f62(x101979),x101978),x101977)))+~P1(f328(f328(f330(f879(x101971,a867)),x101974),f328(f328(f62(x101971),x1019711),x1019710)))+P1(f328(f328(f330(f879(x101976,a867)),f328(f328(f44(x101971,f879(x101976,a867)),x101974),f328(f328(f8(f879(x101979,f879(x101976,a867)),f879(x101976,a867),x101971),f328(f44(x101979,f879(x101976,a867)),x101973)),x101975))),x101972)) % 167.77/167.51 [10198]~P7(x1019811,x1019810,x101989)+~P7(x101981,x101988,x101987)+~P14(x1019811,x101981,f879(x101986,a867),x101989,x101987,x101985)+P1(f328(f328(f330(x101981),f537(x101982,x101983,x101984,x101985,x101986,x101987,x101988,x101981,x101989,x1019810,x1019811)),x101988))+~P1(f328(f328(f330(f879(x1019811,a867)),x101984),f328(f328(f62(x1019811),x1019810),x101989)))+~P1(f328(f328(f330(f879(x101981,a867)),x101983),f328(f328(f62(x101981),x101988),x101987)))+P1(f328(f328(f330(f879(x101986,a867)),f328(f328(f44(x1019811,f879(x101986,a867)),x101984),f328(f328(f8(f879(x101981,f879(x101986,a867)),f879(x101986,a867),x1019811),f328(f44(x101981,f879(x101986,a867)),x101983)),x101985))),x101982)) % 167.77/167.51 [10201]~P7(x102012,x102018,x102019)+~P7(x102014,x1020110,x1020111)+~P14(x102012,x102014,f879(x102011,a867),x102019,x1020111,x102016)+~P1(f328(f328(f330(f879(x102012,a867)),x102013),f328(f328(f62(x102012),x102018),x102019)))+~P1(f328(f328(f330(f879(x102014,a867)),x102015),f328(f328(f62(x102014),x1020110),x1020111)))+~P1(f328(f328(f330(f879(x102011,a867)),f328(f328(x102016,f535(x102017,x102015,x102013,x102016,x102011,x1020111,x1020110,x102014,x102019,x102018,x102012)),f537(x102017,x102015,x102013,x102016,x102011,x1020111,x1020110,x102014,x102019,x102018,x102012))),x102017))+P1(f328(f328(f330(f879(x102011,a867)),f328(f328(f44(x102012,f879(x102011,a867)),x102013),f328(f328(f8(f879(x102014,f879(x102011,a867)),f879(x102011,a867),x102012),f328(f44(x102014,f879(x102011,a867)),x102015)),x102016))),x102017)) % 167.77/167.51 [9101]E(x91011,x91012)+~P105(x91014)+~P26(x91013,x91014,x91015,f328(f328(f114(f879(x91013,a867)),f328(f170(x91013),x91011)),f328(f170(x91013),x91012)))+~E(f328(f170(x91013),x91011),f328(f170(x91013),x91012))+~P15(x91014,f328(f328(f151(x91013,x91014),x91015),x91012))+~P15(x91014,f328(f328(f151(x91013,x91014),x91015),x91011))+~P1(f328(f134(x91014),f328(f328(f151(x91013,x91014),x91015),x91012)))+~P1(f328(f134(x91014),f328(f328(f151(x91013,x91014),x91015),x91011))) % 167.77/167.51 %EqnAxiom % 167.77/167.51 [1]E(x11,x11) % 167.77/167.51 [2]E(x22,x21)+~E(x21,x22) % 167.77/167.51 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 167.77/167.51 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 167.77/167.51 [5]~E(x51,x52)+E(f104(x51),f104(x52)) % 167.77/167.51 [6]~E(x61,x62)+E(f22(x61),f22(x62)) % 167.77/167.51 [7]~E(x71,x72)+E(f192(x71),f192(x72)) % 167.77/167.51 [8]~E(x81,x82)+E(f328(x81,x83),f328(x82,x83)) % 167.77/167.51 [9]~E(x91,x92)+E(f328(x93,x91),f328(x93,x92)) % 167.77/167.51 [10]~E(x101,x102)+E(f31(x101),f31(x102)) % 167.77/167.51 [11]~E(x111,x112)+E(f153(x111,x113,x114,x115),f153(x112,x113,x114,x115)) % 167.77/167.51 [12]~E(x121,x122)+E(f153(x123,x121,x124,x125),f153(x123,x122,x124,x125)) % 167.77/167.51 [13]~E(x131,x132)+E(f153(x133,x134,x131,x135),f153(x133,x134,x132,x135)) % 167.77/167.51 [14]~E(x141,x142)+E(f153(x143,x144,x145,x141),f153(x143,x144,x145,x142)) % 167.77/167.51 [15]~E(x151,x152)+E(f105(x151),f105(x152)) % 167.77/167.51 [16]~E(x161,x162)+E(f240(x161),f240(x162)) % 167.77/167.51 [17]~E(x171,x172)+E(f114(x171),f114(x172)) % 167.77/167.51 [18]~E(x181,x182)+E(f241(x181),f241(x182)) % 167.77/167.51 [19]~E(x191,x192)+E(f106(x191),f106(x192)) % 167.77/167.51 [20]~E(x201,x202)+E(f34(x201),f34(x202)) % 167.77/167.51 [21]~E(x211,x212)+E(f84(x211),f84(x212)) % 167.77/167.51 [22]~E(x221,x222)+E(f117(x221),f117(x222)) % 167.77/167.51 [23]~E(x231,x232)+E(f878(x231,x233),f878(x232,x233)) % 167.77/167.51 [24]~E(x241,x242)+E(f878(x243,x241),f878(x243,x242)) % 167.77/167.51 [25]~E(x251,x252)+E(f537(x251,x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512),f537(x252,x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512)) % 167.77/167.51 [26]~E(x261,x262)+E(f537(x263,x261,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612),f537(x263,x262,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612)) % 167.77/167.51 [27]~E(x271,x272)+E(f537(x273,x274,x271,x275,x276,x277,x278,x279,x2710,x2711,x2712),f537(x273,x274,x272,x275,x276,x277,x278,x279,x2710,x2711,x2712)) % 167.77/167.51 [28]~E(x281,x282)+E(f537(x283,x284,x285,x281,x286,x287,x288,x289,x2810,x2811,x2812),f537(x283,x284,x285,x282,x286,x287,x288,x289,x2810,x2811,x2812)) % 167.77/167.51 [29]~E(x291,x292)+E(f537(x293,x294,x295,x296,x291,x297,x298,x299,x2910,x2911,x2912),f537(x293,x294,x295,x296,x292,x297,x298,x299,x2910,x2911,x2912)) % 167.77/167.51 [30]~E(x301,x302)+E(f537(x303,x304,x305,x306,x307,x301,x308,x309,x3010,x3011,x3012),f537(x303,x304,x305,x306,x307,x302,x308,x309,x3010,x3011,x3012)) % 167.77/167.51 [31]~E(x311,x312)+E(f537(x313,x314,x315,x316,x317,x318,x311,x319,x3110,x3111,x3112),f537(x313,x314,x315,x316,x317,x318,x312,x319,x3110,x3111,x3112)) % 167.77/167.51 [32]~E(x321,x322)+E(f537(x323,x324,x325,x326,x327,x328,x329,x321,x3210,x3211,x3212),f537(x323,x324,x325,x326,x327,x328,x329,x322,x3210,x3211,x3212)) % 167.77/167.51 [33]~E(x331,x332)+E(f537(x333,x334,x335,x336,x337,x338,x339,x3310,x331,x3311,x3312),f537(x333,x334,x335,x336,x337,x338,x339,x3310,x332,x3311,x3312)) % 167.77/167.51 [34]~E(x341,x342)+E(f537(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x341,x3412),f537(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x342,x3412)) % 167.77/167.51 [35]~E(x351,x352)+E(f537(x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512,x351),f537(x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512,x352)) % 167.77/167.51 [36]~E(x361,x362)+E(f78(x361),f78(x362)) % 167.77/167.51 [37]~E(x371,x372)+E(f873(x371),f873(x372)) % 167.77/167.51 [38]~E(x381,x382)+E(f535(x381,x383,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f535(x382,x383,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812)) % 167.77/167.51 [39]~E(x391,x392)+E(f535(x393,x391,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912),f535(x393,x392,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912)) % 167.77/167.51 [40]~E(x401,x402)+E(f535(x403,x404,x401,x405,x406,x407,x408,x409,x4010,x4011,x4012),f535(x403,x404,x402,x405,x406,x407,x408,x409,x4010,x4011,x4012)) % 167.77/167.51 [41]~E(x411,x412)+E(f535(x413,x414,x415,x411,x416,x417,x418,x419,x4110,x4111,x4112),f535(x413,x414,x415,x412,x416,x417,x418,x419,x4110,x4111,x4112)) % 167.77/167.51 [42]~E(x421,x422)+E(f535(x423,x424,x425,x426,x421,x427,x428,x429,x4210,x4211,x4212),f535(x423,x424,x425,x426,x422,x427,x428,x429,x4210,x4211,x4212)) % 167.77/167.51 [43]~E(x431,x432)+E(f535(x433,x434,x435,x436,x437,x431,x438,x439,x4310,x4311,x4312),f535(x433,x434,x435,x436,x437,x432,x438,x439,x4310,x4311,x4312)) % 167.77/167.51 [44]~E(x441,x442)+E(f535(x443,x444,x445,x446,x447,x448,x441,x449,x4410,x4411,x4412),f535(x443,x444,x445,x446,x447,x448,x442,x449,x4410,x4411,x4412)) % 167.77/167.51 [45]~E(x451,x452)+E(f535(x453,x454,x455,x456,x457,x458,x459,x451,x4510,x4511,x4512),f535(x453,x454,x455,x456,x457,x458,x459,x452,x4510,x4511,x4512)) % 167.77/167.51 [46]~E(x461,x462)+E(f535(x463,x464,x465,x466,x467,x468,x469,x4610,x461,x4611,x4612),f535(x463,x464,x465,x466,x467,x468,x469,x4610,x462,x4611,x4612)) % 167.77/167.51 [47]~E(x471,x472)+E(f535(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x471,x4712),f535(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x472,x4712)) % 167.77/167.51 [48]~E(x481,x482)+E(f535(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x4812,x481),f535(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x4812,x482)) % 167.77/167.51 [49]~E(x491,x492)+E(f4(x491),f4(x492)) % 167.77/167.51 [50]~E(x501,x502)+E(f330(x501),f330(x502)) % 167.77/167.51 [51]~E(x511,x512)+E(f879(x511,x513),f879(x512,x513)) % 167.77/167.51 [52]~E(x521,x522)+E(f879(x523,x521),f879(x523,x522)) % 167.77/167.51 [53]~E(x531,x532)+E(f115(x531),f115(x532)) % 167.77/167.51 [54]~E(x541,x542)+E(f148(x541),f148(x542)) % 167.77/167.51 [55]~E(x551,x552)+E(f871(x551),f871(x552)) % 167.77/167.51 [56]~E(x561,x562)+E(f876(x561),f876(x562)) % 167.77/167.51 [57]~E(x571,x572)+E(f263(x571,x573),f263(x572,x573)) % 167.77/167.51 [58]~E(x581,x582)+E(f263(x583,x581),f263(x583,x582)) % 167.77/167.51 [59]~E(x591,x592)+E(f874(x591),f874(x592)) % 167.77/167.51 [60]~E(x601,x602)+E(f139(x601,x603,x604,x605),f139(x602,x603,x604,x605)) % 167.77/167.51 [61]~E(x611,x612)+E(f139(x613,x611,x614,x615),f139(x613,x612,x614,x615)) % 167.77/167.51 [62]~E(x621,x622)+E(f139(x623,x624,x621,x625),f139(x623,x624,x622,x625)) % 167.77/167.51 [63]~E(x631,x632)+E(f139(x633,x634,x635,x631),f139(x633,x634,x635,x632)) % 167.77/167.51 [64]~E(x641,x642)+E(f543(x641,x643,x644),f543(x642,x643,x644)) % 167.77/167.51 [65]~E(x651,x652)+E(f543(x653,x651,x654),f543(x653,x652,x654)) % 167.77/167.51 [66]~E(x661,x662)+E(f543(x663,x664,x661),f543(x663,x664,x662)) % 167.77/167.51 [67]~E(x671,x672)+E(f80(x671),f80(x672)) % 167.77/167.51 [68]~E(x681,x682)+E(f242(x681),f242(x682)) % 167.77/167.51 [69]~E(x691,x692)+E(f79(x691),f79(x692)) % 167.77/167.51 [70]~E(x701,x702)+E(f81(x701),f81(x702)) % 167.77/167.51 [71]~E(x711,x712)+E(f193(x711),f193(x712)) % 167.77/167.51 [72]~E(x721,x722)+E(f7(x721,x723,x724),f7(x722,x723,x724)) % 167.77/167.51 [73]~E(x731,x732)+E(f7(x733,x731,x734),f7(x733,x732,x734)) % 167.77/167.51 [74]~E(x741,x742)+E(f7(x743,x744,x741),f7(x743,x744,x742)) % 167.77/167.51 [75]~E(x751,x752)+E(f107(x751),f107(x752)) % 167.77/167.51 [76]~E(x761,x762)+E(f46(x761,x763,x764),f46(x762,x763,x764)) % 167.77/167.51 [77]~E(x771,x772)+E(f46(x773,x771,x774),f46(x773,x772,x774)) % 167.77/167.51 [78]~E(x781,x782)+E(f46(x783,x784,x781),f46(x783,x784,x782)) % 167.77/167.51 [79]~E(x791,x792)+E(f8(x791,x793,x794),f8(x792,x793,x794)) % 167.77/167.51 [80]~E(x801,x802)+E(f8(x803,x801,x804),f8(x803,x802,x804)) % 167.77/167.51 [81]~E(x811,x812)+E(f8(x813,x814,x811),f8(x813,x814,x812)) % 167.77/167.51 [82]~E(x821,x822)+E(f73(x821,x823,x824,x825),f73(x822,x823,x824,x825)) % 167.77/167.51 [83]~E(x831,x832)+E(f73(x833,x831,x834,x835),f73(x833,x832,x834,x835)) % 167.77/167.51 [84]~E(x841,x842)+E(f73(x843,x844,x841,x845),f73(x843,x844,x842,x845)) % 167.77/167.51 [85]~E(x851,x852)+E(f73(x853,x854,x855,x851),f73(x853,x854,x855,x852)) % 167.77/167.51 [86]~E(x861,x862)+E(f249(x861),f249(x862)) % 167.77/167.51 [87]~E(x871,x872)+E(f38(x871),f38(x872)) % 167.77/167.51 [88]~E(x881,x882)+E(f243(x881),f243(x882)) % 167.77/167.51 [89]~E(x891,x892)+E(f442(x891,x893,x894),f442(x892,x893,x894)) % 167.77/167.51 [90]~E(x901,x902)+E(f442(x903,x901,x904),f442(x903,x902,x904)) % 167.77/167.51 [91]~E(x911,x912)+E(f442(x913,x914,x911),f442(x913,x914,x912)) % 167.77/167.51 [92]~E(x921,x922)+E(f13(x921,x923),f13(x922,x923)) % 167.77/167.51 [93]~E(x931,x932)+E(f13(x933,x931),f13(x933,x932)) % 167.77/167.51 [94]~E(x941,x942)+E(f141(x941,x943),f141(x942,x943)) % 167.77/167.51 [95]~E(x951,x952)+E(f141(x953,x951),f141(x953,x952)) % 167.77/167.51 [96]~E(x961,x962)+E(f113(x961),f113(x962)) % 167.77/167.51 [97]~E(x971,x972)+E(f16(x971,x973),f16(x972,x973)) % 167.77/167.51 [98]~E(x981,x982)+E(f16(x983,x981),f16(x983,x982)) % 167.77/167.51 [99]~E(x991,x992)+E(f170(x991),f170(x992)) % 167.77/167.51 [100]~E(x1001,x1002)+E(f62(x1001),f62(x1002)) % 167.77/167.51 [101]~E(x1011,x1012)+E(f18(x1011,x1013,x1014),f18(x1012,x1013,x1014)) % 167.77/167.51 [102]~E(x1021,x1022)+E(f18(x1023,x1021,x1024),f18(x1023,x1022,x1024)) % 167.77/167.51 [103]~E(x1031,x1032)+E(f18(x1033,x1034,x1031),f18(x1033,x1034,x1032)) % 167.77/167.51 [104]~E(x1041,x1042)+E(f88(x1041),f88(x1042)) % 167.77/167.51 [105]~E(x1051,x1052)+E(f370(x1051,x1053),f370(x1052,x1053)) % 167.77/167.51 [106]~E(x1061,x1062)+E(f370(x1063,x1061),f370(x1063,x1062)) % 167.77/167.51 [107]~E(x1071,x1072)+E(f298(x1071,x1073),f298(x1072,x1073)) % 167.77/167.51 [108]~E(x1081,x1082)+E(f298(x1083,x1081),f298(x1083,x1082)) % 167.77/167.51 [109]~E(x1091,x1092)+E(f118(x1091,x1093),f118(x1092,x1093)) % 167.77/167.51 [110]~E(x1101,x1102)+E(f118(x1103,x1101),f118(x1103,x1102)) % 167.77/167.51 [111]~E(x1111,x1112)+E(f282(x1111,x1113,x1114),f282(x1112,x1113,x1114)) % 167.77/167.51 [112]~E(x1121,x1122)+E(f282(x1123,x1121,x1124),f282(x1123,x1122,x1124)) % 167.77/167.51 [113]~E(x1131,x1132)+E(f282(x1133,x1134,x1131),f282(x1133,x1134,x1132)) % 167.77/167.51 [114]~E(x1141,x1142)+E(f205(x1141),f205(x1142)) % 167.77/167.51 [115]~E(x1151,x1152)+E(f266(x1151,x1153),f266(x1152,x1153)) % 167.77/167.51 [116]~E(x1161,x1162)+E(f266(x1163,x1161),f266(x1163,x1162)) % 167.77/167.51 [117]~E(x1171,x1172)+E(f9(x1171,x1173),f9(x1172,x1173)) % 167.77/167.51 [118]~E(x1181,x1182)+E(f9(x1183,x1181),f9(x1183,x1182)) % 167.77/167.51 [119]~E(x1191,x1192)+E(f237(x1191,x1193,x1194,x1195),f237(x1192,x1193,x1194,x1195)) % 167.77/167.51 [120]~E(x1201,x1202)+E(f237(x1203,x1201,x1204,x1205),f237(x1203,x1202,x1204,x1205)) % 167.77/167.51 [121]~E(x1211,x1212)+E(f237(x1213,x1214,x1211,x1215),f237(x1213,x1214,x1212,x1215)) % 167.77/167.51 [122]~E(x1221,x1222)+E(f237(x1223,x1224,x1225,x1221),f237(x1223,x1224,x1225,x1222)) % 167.77/167.51 [123]~E(x1231,x1232)+E(f248(x1231),f248(x1232)) % 167.77/167.51 [124]~E(x1241,x1242)+E(f174(x1241,x1243,x1244),f174(x1242,x1243,x1244)) % 167.77/167.51 [125]~E(x1251,x1252)+E(f174(x1253,x1251,x1254),f174(x1253,x1252,x1254)) % 167.77/167.51 [126]~E(x1261,x1262)+E(f174(x1263,x1264,x1261),f174(x1263,x1264,x1262)) % 167.77/167.51 [127]~E(x1271,x1272)+E(f151(x1271,x1273),f151(x1272,x1273)) % 167.77/167.51 [128]~E(x1281,x1282)+E(f151(x1283,x1281),f151(x1283,x1282)) % 167.77/167.51 [129]~E(x1291,x1292)+E(f401(x1291,x1293,x1294),f401(x1292,x1293,x1294)) % 167.77/167.51 [130]~E(x1301,x1302)+E(f401(x1303,x1301,x1304),f401(x1303,x1302,x1304)) % 167.77/167.51 [131]~E(x1311,x1312)+E(f401(x1313,x1314,x1311),f401(x1313,x1314,x1312)) % 167.77/167.51 [132]~E(x1321,x1322)+E(f40(x1321),f40(x1322)) % 167.77/167.51 [133]~E(x1331,x1332)+E(f820(x1331,x1333,x1334,x1335),f820(x1332,x1333,x1334,x1335)) % 167.77/167.51 [134]~E(x1341,x1342)+E(f820(x1343,x1341,x1344,x1345),f820(x1343,x1342,x1344,x1345)) % 167.77/167.51 [135]~E(x1351,x1352)+E(f820(x1353,x1354,x1351,x1355),f820(x1353,x1354,x1352,x1355)) % 167.77/167.51 [136]~E(x1361,x1362)+E(f820(x1363,x1364,x1365,x1361),f820(x1363,x1364,x1365,x1362)) % 167.77/167.51 [137]~E(x1371,x1372)+E(f253(x1371),f253(x1372)) % 167.77/167.51 [138]~E(x1381,x1382)+E(f42(x1381,x1383),f42(x1382,x1383)) % 167.77/167.51 [139]~E(x1391,x1392)+E(f42(x1393,x1391),f42(x1393,x1392)) % 167.77/167.51 [140]~E(x1401,x1402)+E(f386(x1401,x1403),f386(x1402,x1403)) % 167.77/167.51 [141]~E(x1411,x1412)+E(f386(x1413,x1411),f386(x1413,x1412)) % 167.77/167.51 [142]~E(x1421,x1422)+E(f39(x1421),f39(x1422)) % 167.77/167.51 [143]~E(x1431,x1432)+E(f235(x1431),f235(x1432)) % 167.77/167.51 [144]~E(x1441,x1442)+E(f308(x1441,x1443,x1444),f308(x1442,x1443,x1444)) % 167.77/167.51 [145]~E(x1451,x1452)+E(f308(x1453,x1451,x1454),f308(x1453,x1452,x1454)) % 167.77/167.51 [146]~E(x1461,x1462)+E(f308(x1463,x1464,x1461),f308(x1463,x1464,x1462)) % 167.77/167.51 [147]~E(x1471,x1472)+E(f466(x1471,x1473,x1474),f466(x1472,x1473,x1474)) % 167.77/167.51 [148]~E(x1481,x1482)+E(f466(x1483,x1481,x1484),f466(x1483,x1482,x1484)) % 167.77/167.51 [149]~E(x1491,x1492)+E(f466(x1493,x1494,x1491),f466(x1493,x1494,x1492)) % 167.77/167.51 [150]~E(x1501,x1502)+E(f166(x1501),f166(x1502)) % 167.77/167.51 [151]~E(x1511,x1512)+E(f125(x1511),f125(x1512)) % 167.77/167.51 [152]~E(x1521,x1522)+E(f286(x1521),f286(x1522)) % 167.77/167.51 [153]~E(x1531,x1532)+E(f557(x1531,x1533,x1534,x1535),f557(x1532,x1533,x1534,x1535)) % 167.77/167.51 [154]~E(x1541,x1542)+E(f557(x1543,x1541,x1544,x1545),f557(x1543,x1542,x1544,x1545)) % 167.77/167.51 [155]~E(x1551,x1552)+E(f557(x1553,x1554,x1551,x1555),f557(x1553,x1554,x1552,x1555)) % 167.77/167.51 [156]~E(x1561,x1562)+E(f557(x1563,x1564,x1565,x1561),f557(x1563,x1564,x1565,x1562)) % 167.77/167.51 [157]~E(x1571,x1572)+E(f109(x1571),f109(x1572)) % 167.77/167.51 [158]~E(x1581,x1582)+E(f111(x1581),f111(x1582)) % 167.77/167.51 [159]~E(x1591,x1592)+E(f329(x1591),f329(x1592)) % 167.77/167.51 [160]~E(x1601,x1602)+E(f57(x1601),f57(x1602)) % 167.77/167.51 [161]~E(x1611,x1612)+E(f485(x1611,x1613),f485(x1612,x1613)) % 167.77/167.51 [162]~E(x1621,x1622)+E(f485(x1623,x1621),f485(x1623,x1622)) % 167.77/167.51 [163]~E(x1631,x1632)+E(f176(x1631,x1633),f176(x1632,x1633)) % 167.77/167.51 [164]~E(x1641,x1642)+E(f176(x1643,x1641),f176(x1643,x1642)) % 167.77/167.51 [165]~E(x1651,x1652)+E(f306(x1651),f306(x1652)) % 167.77/167.51 [166]~E(x1661,x1662)+E(f5(x1661),f5(x1662)) % 167.77/167.51 [167]~E(x1671,x1672)+E(f304(x1671,x1673),f304(x1672,x1673)) % 167.77/167.51 [168]~E(x1681,x1682)+E(f304(x1683,x1681),f304(x1683,x1682)) % 167.77/167.51 [169]~E(x1691,x1692)+E(f66(x1691,x1693,x1694),f66(x1692,x1693,x1694)) % 167.77/167.51 [170]~E(x1701,x1702)+E(f66(x1703,x1701,x1704),f66(x1703,x1702,x1704)) % 167.77/167.51 [171]~E(x1711,x1712)+E(f66(x1713,x1714,x1711),f66(x1713,x1714,x1712)) % 167.77/167.51 [172]~E(x1721,x1722)+E(f206(x1721,x1723),f206(x1722,x1723)) % 167.77/167.51 [173]~E(x1731,x1732)+E(f206(x1733,x1731),f206(x1733,x1732)) % 167.77/167.51 [174]~E(x1741,x1742)+E(f310(x1741,x1743,x1744),f310(x1742,x1743,x1744)) % 167.77/167.51 [175]~E(x1751,x1752)+E(f310(x1753,x1751,x1754),f310(x1753,x1752,x1754)) % 167.77/167.51 [176]~E(x1761,x1762)+E(f310(x1763,x1764,x1761),f310(x1763,x1764,x1762)) % 167.77/167.51 [177]~E(x1771,x1772)+E(f251(x1771),f251(x1772)) % 167.77/167.51 [178]~E(x1781,x1782)+E(f135(x1781),f135(x1782)) % 167.77/167.51 [179]~E(x1791,x1792)+E(f667(x1791,x1793,x1794,x1795),f667(x1792,x1793,x1794,x1795)) % 167.77/167.51 [180]~E(x1801,x1802)+E(f667(x1803,x1801,x1804,x1805),f667(x1803,x1802,x1804,x1805)) % 167.77/167.51 [181]~E(x1811,x1812)+E(f667(x1813,x1814,x1811,x1815),f667(x1813,x1814,x1812,x1815)) % 167.77/167.51 [182]~E(x1821,x1822)+E(f667(x1823,x1824,x1825,x1821),f667(x1823,x1824,x1825,x1822)) % 167.77/167.51 [183]~E(x1831,x1832)+E(f183(x1831,x1833,x1834,x1835),f183(x1832,x1833,x1834,x1835)) % 167.77/167.51 [184]~E(x1841,x1842)+E(f183(x1843,x1841,x1844,x1845),f183(x1843,x1842,x1844,x1845)) % 167.77/167.51 [185]~E(x1851,x1852)+E(f183(x1853,x1854,x1851,x1855),f183(x1853,x1854,x1852,x1855)) % 167.77/167.51 [186]~E(x1861,x1862)+E(f183(x1863,x1864,x1865,x1861),f183(x1863,x1864,x1865,x1862)) % 167.77/167.51 [187]~E(x1871,x1872)+E(f807(x1871,x1873,x1874),f807(x1872,x1873,x1874)) % 167.77/167.51 [188]~E(x1881,x1882)+E(f807(x1883,x1881,x1884),f807(x1883,x1882,x1884)) % 167.77/167.51 [189]~E(x1891,x1892)+E(f807(x1893,x1894,x1891),f807(x1893,x1894,x1892)) % 167.77/167.51 [190]~E(x1901,x1902)+E(f64(x1901,x1903),f64(x1902,x1903)) % 167.77/167.51 [191]~E(x1911,x1912)+E(f64(x1913,x1911),f64(x1913,x1912)) % 167.77/167.51 [192]~E(x1921,x1922)+E(f550(x1921,x1923,x1924,x1925),f550(x1922,x1923,x1924,x1925)) % 167.77/167.51 [193]~E(x1931,x1932)+E(f550(x1933,x1931,x1934,x1935),f550(x1933,x1932,x1934,x1935)) % 167.77/167.51 [194]~E(x1941,x1942)+E(f550(x1943,x1944,x1941,x1945),f550(x1943,x1944,x1942,x1945)) % 167.77/167.51 [195]~E(x1951,x1952)+E(f550(x1953,x1954,x1955,x1951),f550(x1953,x1954,x1955,x1952)) % 167.77/167.51 [196]~E(x1961,x1962)+E(f688(x1961),f688(x1962)) % 167.77/167.51 [197]~E(x1971,x1972)+E(f72(x1971,x1973),f72(x1972,x1973)) % 167.77/167.51 [198]~E(x1981,x1982)+E(f72(x1983,x1981),f72(x1983,x1982)) % 167.77/167.51 [199]~E(x1991,x1992)+E(f44(x1991,x1993),f44(x1992,x1993)) % 167.77/167.51 [200]~E(x2001,x2002)+E(f44(x2003,x2001),f44(x2003,x2002)) % 167.77/167.51 [201]~E(x2011,x2012)+E(f6(x2011,x2013),f6(x2012,x2013)) % 167.77/167.51 [202]~E(x2021,x2022)+E(f6(x2023,x2021),f6(x2023,x2022)) % 167.77/167.51 [203]~E(x2031,x2032)+E(f283(x2031,x2033),f283(x2032,x2033)) % 167.77/167.51 [204]~E(x2041,x2042)+E(f283(x2043,x2041),f283(x2043,x2042)) % 167.77/167.51 [205]~E(x2051,x2052)+E(f41(x2051,x2053),f41(x2052,x2053)) % 167.77/167.51 [206]~E(x2061,x2062)+E(f41(x2063,x2061),f41(x2063,x2062)) % 167.77/167.51 [207]~E(x2071,x2072)+E(f77(x2071,x2073,x2074,x2075),f77(x2072,x2073,x2074,x2075)) % 167.77/167.51 [208]~E(x2081,x2082)+E(f77(x2083,x2081,x2084,x2085),f77(x2083,x2082,x2084,x2085)) % 167.77/167.51 [209]~E(x2091,x2092)+E(f77(x2093,x2094,x2091,x2095),f77(x2093,x2094,x2092,x2095)) % 167.77/167.51 [210]~E(x2101,x2102)+E(f77(x2103,x2104,x2105,x2101),f77(x2103,x2104,x2105,x2102)) % 167.77/167.51 [211]~E(x2111,x2112)+E(f185(x2111,x2113,x2114,x2115,x2116),f185(x2112,x2113,x2114,x2115,x2116)) % 167.77/167.51 [212]~E(x2121,x2122)+E(f185(x2123,x2121,x2124,x2125,x2126),f185(x2123,x2122,x2124,x2125,x2126)) % 167.77/167.51 [213]~E(x2131,x2132)+E(f185(x2133,x2134,x2131,x2135,x2136),f185(x2133,x2134,x2132,x2135,x2136)) % 167.77/167.51 [214]~E(x2141,x2142)+E(f185(x2143,x2144,x2145,x2141,x2146),f185(x2143,x2144,x2145,x2142,x2146)) % 167.77/167.51 [215]~E(x2151,x2152)+E(f185(x2153,x2154,x2155,x2156,x2151),f185(x2153,x2154,x2155,x2156,x2152)) % 167.77/167.51 [216]~E(x2161,x2162)+E(f239(x2161),f239(x2162)) % 167.77/167.51 [217]~E(x2171,x2172)+E(f144(x2171,x2173),f144(x2172,x2173)) % 167.77/167.51 [218]~E(x2181,x2182)+E(f144(x2183,x2181),f144(x2183,x2182)) % 167.77/167.51 [219]~E(x2191,x2192)+E(f49(x2191,x2193),f49(x2192,x2193)) % 167.77/167.51 [220]~E(x2201,x2202)+E(f49(x2203,x2201),f49(x2203,x2202)) % 167.77/167.51 [221]~E(x2211,x2212)+E(f285(x2211,x2213,x2214),f285(x2212,x2213,x2214)) % 167.77/167.51 [222]~E(x2221,x2222)+E(f285(x2223,x2221,x2224),f285(x2223,x2222,x2224)) % 167.77/167.51 [223]~E(x2231,x2232)+E(f285(x2233,x2234,x2231),f285(x2233,x2234,x2232)) % 167.77/167.51 [224]~E(x2241,x2242)+E(f75(x2241),f75(x2242)) % 167.77/167.51 [225]~E(x2251,x2252)+E(f338(x2251),f338(x2252)) % 167.77/167.51 [226]~E(x2261,x2262)+E(f555(x2261,x2263,x2264,x2265),f555(x2262,x2263,x2264,x2265)) % 167.77/167.51 [227]~E(x2271,x2272)+E(f555(x2273,x2271,x2274,x2275),f555(x2273,x2272,x2274,x2275)) % 167.77/167.51 [228]~E(x2281,x2282)+E(f555(x2283,x2284,x2281,x2285),f555(x2283,x2284,x2282,x2285)) % 167.77/167.51 [229]~E(x2291,x2292)+E(f555(x2293,x2294,x2295,x2291),f555(x2293,x2294,x2295,x2292)) % 167.77/167.51 [230]~E(x2301,x2302)+E(f60(x2301),f60(x2302)) % 167.77/167.51 [231]~E(x2311,x2312)+E(f262(x2311,x2313),f262(x2312,x2313)) % 167.77/167.51 [232]~E(x2321,x2322)+E(f262(x2323,x2321),f262(x2323,x2322)) % 167.77/167.51 [233]~E(x2331,x2332)+E(f134(x2331),f134(x2332)) % 167.77/167.51 [234]~E(x2341,x2342)+E(f267(x2341,x2343,x2344),f267(x2342,x2343,x2344)) % 167.77/167.51 [235]~E(x2351,x2352)+E(f267(x2353,x2351,x2354),f267(x2353,x2352,x2354)) % 167.77/167.51 [236]~E(x2361,x2362)+E(f267(x2363,x2364,x2361),f267(x2363,x2364,x2362)) % 167.77/167.51 [237]~E(x2371,x2372)+E(f85(x2371,x2373),f85(x2372,x2373)) % 167.77/167.51 [238]~E(x2381,x2382)+E(f85(x2383,x2381),f85(x2383,x2382)) % 167.77/167.51 [239]~E(x2391,x2392)+E(f258(x2391,x2393,x2394),f258(x2392,x2393,x2394)) % 167.77/167.51 [240]~E(x2401,x2402)+E(f258(x2403,x2401,x2404),f258(x2403,x2402,x2404)) % 167.77/167.51 [241]~E(x2411,x2412)+E(f258(x2413,x2414,x2411),f258(x2413,x2414,x2412)) % 167.77/167.51 [242]~E(x2421,x2422)+E(f421(x2421,x2423,x2424,x2425),f421(x2422,x2423,x2424,x2425)) % 167.77/167.51 [243]~E(x2431,x2432)+E(f421(x2433,x2431,x2434,x2435),f421(x2433,x2432,x2434,x2435)) % 167.77/167.51 [244]~E(x2441,x2442)+E(f421(x2443,x2444,x2441,x2445),f421(x2443,x2444,x2442,x2445)) % 167.77/167.51 [245]~E(x2451,x2452)+E(f421(x2453,x2454,x2455,x2451),f421(x2453,x2454,x2455,x2452)) % 167.77/167.51 [246]~E(x2461,x2462)+E(f15(x2461,x2463),f15(x2462,x2463)) % 167.77/167.51 [247]~E(x2471,x2472)+E(f15(x2473,x2471),f15(x2473,x2472)) % 167.77/167.51 [248]~E(x2481,x2482)+E(f92(x2481),f92(x2482)) % 167.77/167.51 [249]~E(x2491,x2492)+E(f14(x2491,x2493),f14(x2492,x2493)) % 167.77/167.51 [250]~E(x2501,x2502)+E(f14(x2503,x2501),f14(x2503,x2502)) % 167.77/167.51 [251]~E(x2511,x2512)+E(f86(x2511,x2513),f86(x2512,x2513)) % 167.77/167.51 [252]~E(x2521,x2522)+E(f86(x2523,x2521),f86(x2523,x2522)) % 167.77/167.51 [253]~E(x2531,x2532)+E(f184(x2531,x2533,x2534),f184(x2532,x2533,x2534)) % 167.77/167.51 [254]~E(x2541,x2542)+E(f184(x2543,x2541,x2544),f184(x2543,x2542,x2544)) % 167.77/167.51 [255]~E(x2551,x2552)+E(f184(x2553,x2554,x2551),f184(x2553,x2554,x2552)) % 167.77/167.51 [256]~E(x2561,x2562)+E(f305(x2561),f305(x2562)) % 167.77/167.51 [257]~E(x2571,x2572)+E(f149(x2571,x2573),f149(x2572,x2573)) % 167.77/167.51 [258]~E(x2581,x2582)+E(f149(x2583,x2581),f149(x2583,x2582)) % 167.77/167.51 [259]~E(x2591,x2592)+E(f810(x2591,x2593,x2594,x2595),f810(x2592,x2593,x2594,x2595)) % 167.77/167.51 [260]~E(x2601,x2602)+E(f810(x2603,x2601,x2604,x2605),f810(x2603,x2602,x2604,x2605)) % 167.77/167.51 [261]~E(x2611,x2612)+E(f810(x2613,x2614,x2611,x2615),f810(x2613,x2614,x2612,x2615)) % 167.77/167.51 [262]~E(x2621,x2622)+E(f810(x2623,x2624,x2625,x2621),f810(x2623,x2624,x2625,x2622)) % 167.77/167.51 [263]~E(x2631,x2632)+E(f195(x2631),f195(x2632)) % 167.77/167.51 [264]~E(x2641,x2642)+E(f165(x2641),f165(x2642)) % 167.77/167.51 [265]~E(x2651,x2652)+E(f119(x2651),f119(x2652)) % 167.77/167.51 [266]~E(x2661,x2662)+E(f299(x2661,x2663,x2664),f299(x2662,x2663,x2664)) % 167.77/167.51 [267]~E(x2671,x2672)+E(f299(x2673,x2671,x2674),f299(x2673,x2672,x2674)) % 167.77/167.51 [268]~E(x2681,x2682)+E(f299(x2683,x2684,x2681),f299(x2683,x2684,x2682)) % 167.77/167.51 [269]~E(x2691,x2692)+E(f150(x2691,x2693),f150(x2692,x2693)) % 167.77/167.51 [270]~E(x2701,x2702)+E(f150(x2703,x2701),f150(x2703,x2702)) % 167.77/167.51 [271]~E(x2711,x2712)+E(f414(x2711,x2713,x2714),f414(x2712,x2713,x2714)) % 167.77/167.51 [272]~E(x2721,x2722)+E(f414(x2723,x2721,x2724),f414(x2723,x2722,x2724)) % 167.77/167.51 [273]~E(x2731,x2732)+E(f414(x2733,x2734,x2731),f414(x2733,x2734,x2732)) % 167.77/167.51 [274]~E(x2741,x2742)+E(f163(x2741),f163(x2742)) % 167.77/167.51 [275]~E(x2751,x2752)+E(f717(x2751,x2753),f717(x2752,x2753)) % 167.77/167.51 [276]~E(x2761,x2762)+E(f717(x2763,x2761),f717(x2763,x2762)) % 167.77/167.51 [277]~E(x2771,x2772)+E(f877(x2771,x2773),f877(x2772,x2773)) % 167.77/167.51 [278]~E(x2781,x2782)+E(f877(x2783,x2781),f877(x2783,x2782)) % 167.77/167.51 [279]~E(x2791,x2792)+E(f156(x2791,x2793),f156(x2792,x2793)) % 167.77/167.51 [280]~E(x2801,x2802)+E(f156(x2803,x2801),f156(x2803,x2802)) % 167.77/167.51 [281]~E(x2811,x2812)+E(f307(x2811,x2813,x2814),f307(x2812,x2813,x2814)) % 167.77/167.51 [282]~E(x2821,x2822)+E(f307(x2823,x2821,x2824),f307(x2823,x2822,x2824)) % 167.77/167.51 [283]~E(x2831,x2832)+E(f307(x2833,x2834,x2831),f307(x2833,x2834,x2832)) % 167.77/167.51 [284]~E(x2841,x2842)+E(f173(x2841),f173(x2842)) % 167.77/167.51 [285]~E(x2851,x2852)+E(f268(x2851,x2853,x2854,x2855,x2856,x2857),f268(x2852,x2853,x2854,x2855,x2856,x2857)) % 167.77/167.51 [286]~E(x2861,x2862)+E(f268(x2863,x2861,x2864,x2865,x2866,x2867),f268(x2863,x2862,x2864,x2865,x2866,x2867)) % 167.77/167.51 [287]~E(x2871,x2872)+E(f268(x2873,x2874,x2871,x2875,x2876,x2877),f268(x2873,x2874,x2872,x2875,x2876,x2877)) % 167.77/167.51 [288]~E(x2881,x2882)+E(f268(x2883,x2884,x2885,x2881,x2886,x2887),f268(x2883,x2884,x2885,x2882,x2886,x2887)) % 167.77/167.51 [289]~E(x2891,x2892)+E(f268(x2893,x2894,x2895,x2896,x2891,x2897),f268(x2893,x2894,x2895,x2896,x2892,x2897)) % 167.77/167.51 [290]~E(x2901,x2902)+E(f268(x2903,x2904,x2905,x2906,x2907,x2901),f268(x2903,x2904,x2905,x2906,x2907,x2902)) % 167.77/167.51 [291]~E(x2911,x2912)+E(f30(x2911,x2913,x2914),f30(x2912,x2913,x2914)) % 167.77/167.51 [292]~E(x2921,x2922)+E(f30(x2923,x2921,x2924),f30(x2923,x2922,x2924)) % 167.77/167.51 [293]~E(x2931,x2932)+E(f30(x2933,x2934,x2931),f30(x2933,x2934,x2932)) % 167.77/167.51 [294]~E(x2941,x2942)+E(f162(x2941),f162(x2942)) % 167.77/167.51 [295]~E(x2951,x2952)+E(f158(x2951,x2953),f158(x2952,x2953)) % 167.77/167.51 [296]~E(x2961,x2962)+E(f158(x2963,x2961),f158(x2963,x2962)) % 167.77/167.51 [297]~E(x2971,x2972)+E(f169(x2971),f169(x2972)) % 167.77/167.51 [298]~E(x2981,x2982)+E(f11(x2981,x2983,x2984),f11(x2982,x2983,x2984)) % 167.77/167.51 [299]~E(x2991,x2992)+E(f11(x2993,x2991,x2994),f11(x2993,x2992,x2994)) % 167.77/167.51 [300]~E(x3001,x3002)+E(f11(x3003,x3004,x3001),f11(x3003,x3004,x3002)) % 167.77/167.51 [301]~E(x3011,x3012)+E(f301(x3011,x3013,x3014),f301(x3012,x3013,x3014)) % 167.77/167.51 [302]~E(x3021,x3022)+E(f301(x3023,x3021,x3024),f301(x3023,x3022,x3024)) % 167.77/167.51 [303]~E(x3031,x3032)+E(f301(x3033,x3034,x3031),f301(x3033,x3034,x3032)) % 167.77/167.51 [304]~E(x3041,x3042)+E(f222(x3041,x3043),f222(x3042,x3043)) % 167.77/167.51 [305]~E(x3051,x3052)+E(f222(x3053,x3051),f222(x3053,x3052)) % 167.77/167.51 [306]~E(x3061,x3062)+E(f32(x3061,x3063),f32(x3062,x3063)) % 167.77/167.51 [307]~E(x3071,x3072)+E(f32(x3073,x3071),f32(x3073,x3072)) % 167.77/167.51 [308]~E(x3081,x3082)+E(f394(x3081,x3083),f394(x3082,x3083)) % 167.77/167.51 [309]~E(x3091,x3092)+E(f394(x3093,x3091),f394(x3093,x3092)) % 167.77/167.51 [310]~E(x3101,x3102)+E(f265(x3101,x3103),f265(x3102,x3103)) % 167.77/167.51 [311]~E(x3111,x3112)+E(f265(x3113,x3111),f265(x3113,x3112)) % 167.77/167.51 [312]~E(x3121,x3122)+E(f690(x3121,x3123,x3124),f690(x3122,x3123,x3124)) % 167.77/167.51 [313]~E(x3131,x3132)+E(f690(x3133,x3131,x3134),f690(x3133,x3132,x3134)) % 167.77/167.51 [314]~E(x3141,x3142)+E(f690(x3143,x3144,x3141),f690(x3143,x3144,x3142)) % 167.77/167.51 [315]~E(x3151,x3152)+E(f227(x3151,x3153),f227(x3152,x3153)) % 167.77/167.51 [316]~E(x3161,x3162)+E(f227(x3163,x3161),f227(x3163,x3162)) % 167.77/167.51 [317]~E(x3171,x3172)+E(f87(x3171),f87(x3172)) % 167.77/167.51 [318]~E(x3181,x3182)+E(f686(x3181,x3183),f686(x3182,x3183)) % 167.77/167.51 [319]~E(x3191,x3192)+E(f686(x3193,x3191),f686(x3193,x3192)) % 167.77/167.51 [320]~E(x3201,x3202)+E(f146(x3201,x3203,x3204,x3205,x3206),f146(x3202,x3203,x3204,x3205,x3206)) % 167.77/167.51 [321]~E(x3211,x3212)+E(f146(x3213,x3211,x3214,x3215,x3216),f146(x3213,x3212,x3214,x3215,x3216)) % 167.77/167.51 [322]~E(x3221,x3222)+E(f146(x3223,x3224,x3221,x3225,x3226),f146(x3223,x3224,x3222,x3225,x3226)) % 167.77/167.51 [323]~E(x3231,x3232)+E(f146(x3233,x3234,x3235,x3231,x3236),f146(x3233,x3234,x3235,x3232,x3236)) % 167.77/167.51 [324]~E(x3241,x3242)+E(f146(x3243,x3244,x3245,x3246,x3241),f146(x3243,x3244,x3245,x3246,x3242)) % 167.77/167.51 [325]~E(x3251,x3252)+E(f43(x3251,x3253),f43(x3252,x3253)) % 167.77/167.51 [326]~E(x3261,x3262)+E(f43(x3263,x3261),f43(x3263,x3262)) % 167.77/167.51 [327]~E(x3271,x3272)+E(f65(x3271,x3273,x3274),f65(x3272,x3273,x3274)) % 167.77/167.51 [328]~E(x3281,x3282)+E(f65(x3283,x3281,x3284),f65(x3283,x3282,x3284)) % 167.77/167.51 [329]~E(x3291,x3292)+E(f65(x3293,x3294,x3291),f65(x3293,x3294,x3292)) % 167.77/167.51 [330]~E(x3301,x3302)+E(f168(x3301,x3303,x3304),f168(x3302,x3303,x3304)) % 167.77/167.51 [331]~E(x3311,x3312)+E(f168(x3313,x3311,x3314),f168(x3313,x3312,x3314)) % 167.77/167.51 [332]~E(x3321,x3322)+E(f168(x3323,x3324,x3321),f168(x3323,x3324,x3322)) % 167.77/167.51 [333]~E(x3331,x3332)+E(f319(x3331,x3333),f319(x3332,x3333)) % 167.77/167.51 [334]~E(x3341,x3342)+E(f319(x3343,x3341),f319(x3343,x3342)) % 167.77/167.51 [335]~E(x3351,x3352)+E(f725(x3351,x3353,x3354,x3355),f725(x3352,x3353,x3354,x3355)) % 167.77/167.51 [336]~E(x3361,x3362)+E(f725(x3363,x3361,x3364,x3365),f725(x3363,x3362,x3364,x3365)) % 167.77/167.51 [337]~E(x3371,x3372)+E(f725(x3373,x3374,x3371,x3375),f725(x3373,x3374,x3372,x3375)) % 167.77/167.51 [338]~E(x3381,x3382)+E(f725(x3383,x3384,x3385,x3381),f725(x3383,x3384,x3385,x3382)) % 167.77/167.51 [339]~E(x3391,x3392)+E(f320(x3391,x3393),f320(x3392,x3393)) % 167.77/167.51 [340]~E(x3401,x3402)+E(f320(x3403,x3401),f320(x3403,x3402)) % 167.77/167.51 [341]~E(x3411,x3412)+E(f425(x3411,x3413),f425(x3412,x3413)) % 167.77/167.51 [342]~E(x3421,x3422)+E(f425(x3423,x3421),f425(x3423,x3422)) % 167.77/167.51 [343]~E(x3431,x3432)+E(f697(x3431,x3433,x3434,x3435),f697(x3432,x3433,x3434,x3435)) % 167.77/167.51 [344]~E(x3441,x3442)+E(f697(x3443,x3441,x3444,x3445),f697(x3443,x3442,x3444,x3445)) % 167.77/167.51 [345]~E(x3451,x3452)+E(f697(x3453,x3454,x3451,x3455),f697(x3453,x3454,x3452,x3455)) % 167.77/167.51 [346]~E(x3461,x3462)+E(f697(x3463,x3464,x3465,x3461),f697(x3463,x3464,x3465,x3462)) % 167.77/167.51 [347]~E(x3471,x3472)+E(f316(x3471,x3473),f316(x3472,x3473)) % 167.77/167.51 [348]~E(x3481,x3482)+E(f316(x3483,x3481),f316(x3483,x3482)) % 167.77/167.51 [349]~E(x3491,x3492)+E(f189(x3491,x3493,x3494,x3495),f189(x3492,x3493,x3494,x3495)) % 167.77/167.51 [350]~E(x3501,x3502)+E(f189(x3503,x3501,x3504,x3505),f189(x3503,x3502,x3504,x3505)) % 167.77/167.51 [351]~E(x3511,x3512)+E(f189(x3513,x3514,x3511,x3515),f189(x3513,x3514,x3512,x3515)) % 167.77/167.51 [352]~E(x3521,x3522)+E(f189(x3523,x3524,x3525,x3521),f189(x3523,x3524,x3525,x3522)) % 167.77/167.51 [353]~E(x3531,x3532)+E(f824(x3531,x3533,x3534),f824(x3532,x3533,x3534)) % 167.77/167.51 [354]~E(x3541,x3542)+E(f824(x3543,x3541,x3544),f824(x3543,x3542,x3544)) % 167.77/167.51 [355]~E(x3551,x3552)+E(f824(x3553,x3554,x3551),f824(x3553,x3554,x3552)) % 167.77/167.51 [356]~E(x3561,x3562)+E(f644(x3561,x3563,x3564,x3565,x3566),f644(x3562,x3563,x3564,x3565,x3566)) % 167.77/167.51 [357]~E(x3571,x3572)+E(f644(x3573,x3571,x3574,x3575,x3576),f644(x3573,x3572,x3574,x3575,x3576)) % 167.77/167.51 [358]~E(x3581,x3582)+E(f644(x3583,x3584,x3581,x3585,x3586),f644(x3583,x3584,x3582,x3585,x3586)) % 167.77/167.51 [359]~E(x3591,x3592)+E(f644(x3593,x3594,x3595,x3591,x3596),f644(x3593,x3594,x3595,x3592,x3596)) % 167.77/167.51 [360]~E(x3601,x3602)+E(f644(x3603,x3604,x3605,x3606,x3601),f644(x3603,x3604,x3605,x3606,x3602)) % 167.77/167.51 [361]~E(x3611,x3612)+E(f627(x3611,x3613),f627(x3612,x3613)) % 167.77/167.51 [362]~E(x3621,x3622)+E(f627(x3623,x3621),f627(x3623,x3622)) % 167.77/167.51 [363]~E(x3631,x3632)+E(f468(x3631,x3633),f468(x3632,x3633)) % 167.77/167.51 [364]~E(x3641,x3642)+E(f468(x3643,x3641),f468(x3643,x3642)) % 167.77/167.51 [365]~E(x3651,x3652)+E(f142(x3651,x3653),f142(x3652,x3653)) % 167.77/167.51 [366]~E(x3661,x3662)+E(f142(x3663,x3661),f142(x3663,x3662)) % 167.77/167.51 [367]~E(x3671,x3672)+E(f463(x3671,x3673,x3674,x3675,x3676,x3677),f463(x3672,x3673,x3674,x3675,x3676,x3677)) % 167.77/167.51 [368]~E(x3681,x3682)+E(f463(x3683,x3681,x3684,x3685,x3686,x3687),f463(x3683,x3682,x3684,x3685,x3686,x3687)) % 167.77/167.51 [369]~E(x3691,x3692)+E(f463(x3693,x3694,x3691,x3695,x3696,x3697),f463(x3693,x3694,x3692,x3695,x3696,x3697)) % 167.77/167.51 [370]~E(x3701,x3702)+E(f463(x3703,x3704,x3705,x3701,x3706,x3707),f463(x3703,x3704,x3705,x3702,x3706,x3707)) % 167.77/167.51 [371]~E(x3711,x3712)+E(f463(x3713,x3714,x3715,x3716,x3711,x3717),f463(x3713,x3714,x3715,x3716,x3712,x3717)) % 167.77/167.51 [372]~E(x3721,x3722)+E(f463(x3723,x3724,x3725,x3726,x3727,x3721),f463(x3723,x3724,x3725,x3726,x3727,x3722)) % 167.77/167.51 [373]~E(x3731,x3732)+E(f133(x3731,x3733),f133(x3732,x3733)) % 167.77/167.51 [374]~E(x3741,x3742)+E(f133(x3743,x3741),f133(x3743,x3742)) % 167.77/167.51 [375]~E(x3751,x3752)+E(f180(x3751,x3753),f180(x3752,x3753)) % 167.77/167.51 [376]~E(x3761,x3762)+E(f180(x3763,x3761),f180(x3763,x3762)) % 167.77/167.51 [377]~E(x3771,x3772)+E(f100(x3771),f100(x3772)) % 167.77/167.51 [378]~E(x3781,x3782)+E(f624(x3781,x3783,x3784),f624(x3782,x3783,x3784)) % 167.77/167.51 [379]~E(x3791,x3792)+E(f624(x3793,x3791,x3794),f624(x3793,x3792,x3794)) % 167.77/167.51 [380]~E(x3801,x3802)+E(f624(x3803,x3804,x3801),f624(x3803,x3804,x3802)) % 167.77/167.51 [381]~E(x3811,x3812)+E(f154(x3811,x3813),f154(x3812,x3813)) % 167.77/167.51 [382]~E(x3821,x3822)+E(f154(x3823,x3821),f154(x3823,x3822)) % 167.77/167.51 [383]~E(x3831,x3832)+E(f585(x3831,x3833,x3834),f585(x3832,x3833,x3834)) % 167.77/167.51 [384]~E(x3841,x3842)+E(f585(x3843,x3841,x3844),f585(x3843,x3842,x3844)) % 167.77/167.51 [385]~E(x3851,x3852)+E(f585(x3853,x3854,x3851),f585(x3853,x3854,x3852)) % 167.77/167.51 [386]~E(x3861,x3862)+E(f289(x3861,x3863,x3864),f289(x3862,x3863,x3864)) % 167.77/167.51 [387]~E(x3871,x3872)+E(f289(x3873,x3871,x3874),f289(x3873,x3872,x3874)) % 167.77/167.51 [388]~E(x3881,x3882)+E(f289(x3883,x3884,x3881),f289(x3883,x3884,x3882)) % 167.77/167.51 [389]~E(x3891,x3892)+E(f443(x3891,x3893,x3894),f443(x3892,x3893,x3894)) % 167.77/167.51 [390]~E(x3901,x3902)+E(f443(x3903,x3901,x3904),f443(x3903,x3902,x3904)) % 167.77/167.51 [391]~E(x3911,x3912)+E(f443(x3913,x3914,x3911),f443(x3913,x3914,x3912)) % 167.77/167.51 [392]~E(x3921,x3922)+E(f703(x3921,x3923,x3924),f703(x3922,x3923,x3924)) % 167.77/167.51 [393]~E(x3931,x3932)+E(f703(x3933,x3931,x3934),f703(x3933,x3932,x3934)) % 167.77/167.51 [394]~E(x3941,x3942)+E(f703(x3943,x3944,x3941),f703(x3943,x3944,x3942)) % 167.77/167.51 [395]~E(x3951,x3952)+E(f281(x3951),f281(x3952)) % 167.77/167.51 [396]~E(x3961,x3962)+E(f90(x3961,x3963),f90(x3962,x3963)) % 167.77/167.51 [397]~E(x3971,x3972)+E(f90(x3973,x3971),f90(x3973,x3972)) % 167.77/167.51 [398]~E(x3981,x3982)+E(f177(x3981,x3983),f177(x3982,x3983)) % 167.77/167.51 [399]~E(x3991,x3992)+E(f177(x3993,x3991),f177(x3993,x3992)) % 167.77/167.51 [400]~E(x4001,x4002)+E(f292(x4001,x4003,x4004,x4005),f292(x4002,x4003,x4004,x4005)) % 167.77/167.51 [401]~E(x4011,x4012)+E(f292(x4013,x4011,x4014,x4015),f292(x4013,x4012,x4014,x4015)) % 167.77/167.51 [402]~E(x4021,x4022)+E(f292(x4023,x4024,x4021,x4025),f292(x4023,x4024,x4022,x4025)) % 167.77/167.51 [403]~E(x4031,x4032)+E(f292(x4033,x4034,x4035,x4031),f292(x4033,x4034,x4035,x4032)) % 167.77/167.51 [404]~E(x4041,x4042)+E(f51(x4041,x4043),f51(x4042,x4043)) % 167.77/167.51 [405]~E(x4051,x4052)+E(f51(x4053,x4051),f51(x4053,x4052)) % 167.77/167.51 [406]~E(x4061,x4062)+E(f29(x4061,x4063,x4064),f29(x4062,x4063,x4064)) % 167.77/167.51 [407]~E(x4071,x4072)+E(f29(x4073,x4071,x4074),f29(x4073,x4072,x4074)) % 167.77/167.51 [408]~E(x4081,x4082)+E(f29(x4083,x4084,x4081),f29(x4083,x4084,x4082)) % 167.77/167.51 [409]~E(x4091,x4092)+E(f157(x4091,x4093),f157(x4092,x4093)) % 167.77/167.51 [410]~E(x4101,x4102)+E(f157(x4103,x4101),f157(x4103,x4102)) % 167.77/167.51 [411]~E(x4111,x4112)+E(f186(x4111,x4113,x4114,x4115),f186(x4112,x4113,x4114,x4115)) % 167.77/167.51 [412]~E(x4121,x4122)+E(f186(x4123,x4121,x4124,x4125),f186(x4123,x4122,x4124,x4125)) % 167.77/167.51 [413]~E(x4131,x4132)+E(f186(x4133,x4134,x4131,x4135),f186(x4133,x4134,x4132,x4135)) % 167.77/167.51 [414]~E(x4141,x4142)+E(f186(x4143,x4144,x4145,x4141),f186(x4143,x4144,x4145,x4142)) % 167.77/167.51 [415]~E(x4151,x4152)+E(f155(x4151,x4153),f155(x4152,x4153)) % 167.77/167.51 [416]~E(x4161,x4162)+E(f155(x4163,x4161),f155(x4163,x4162)) % 167.77/167.51 [417]~E(x4171,x4172)+E(f259(x4171,x4173),f259(x4172,x4173)) % 167.77/167.51 [418]~E(x4181,x4182)+E(f259(x4183,x4181),f259(x4183,x4182)) % 167.77/167.51 [419]~E(x4191,x4192)+E(f145(x4191,x4193,x4194),f145(x4192,x4193,x4194)) % 167.77/167.51 [420]~E(x4201,x4202)+E(f145(x4203,x4201,x4204),f145(x4203,x4202,x4204)) % 167.77/167.51 [421]~E(x4211,x4212)+E(f145(x4213,x4214,x4211),f145(x4213,x4214,x4212)) % 167.77/167.51 [422]~E(x4221,x4222)+E(f621(x4221,x4223,x4224),f621(x4222,x4223,x4224)) % 167.77/167.51 [423]~E(x4231,x4232)+E(f621(x4233,x4231,x4234),f621(x4233,x4232,x4234)) % 167.77/167.51 [424]~E(x4241,x4242)+E(f621(x4243,x4244,x4241),f621(x4243,x4244,x4242)) % 167.77/167.51 [425]~E(x4251,x4252)+E(f10(x4251,x4253),f10(x4252,x4253)) % 167.77/167.51 [426]~E(x4261,x4262)+E(f10(x4263,x4261),f10(x4263,x4262)) % 167.77/167.51 [427]~E(x4271,x4272)+E(f47(x4271,x4273),f47(x4272,x4273)) % 167.77/167.51 [428]~E(x4281,x4282)+E(f47(x4283,x4281),f47(x4283,x4282)) % 167.77/167.51 [429]~E(x4291,x4292)+E(f806(x4291,x4293,x4294),f806(x4292,x4293,x4294)) % 167.77/167.51 [430]~E(x4301,x4302)+E(f806(x4303,x4301,x4304),f806(x4303,x4302,x4304)) % 167.77/167.51 [431]~E(x4311,x4312)+E(f806(x4313,x4314,x4311),f806(x4313,x4314,x4312)) % 167.77/167.51 [432]~E(x4321,x4322)+E(f182(x4321,x4323,x4324),f182(x4322,x4323,x4324)) % 167.77/167.51 [433]~E(x4331,x4332)+E(f182(x4333,x4331,x4334),f182(x4333,x4332,x4334)) % 167.77/167.51 [434]~E(x4341,x4342)+E(f182(x4343,x4344,x4341),f182(x4343,x4344,x4342)) % 167.77/167.51 [435]~E(x4351,x4352)+E(f360(x4351,x4353,x4354,x4355,x4356),f360(x4352,x4353,x4354,x4355,x4356)) % 167.77/167.51 [436]~E(x4361,x4362)+E(f360(x4363,x4361,x4364,x4365,x4366),f360(x4363,x4362,x4364,x4365,x4366)) % 167.77/167.51 [437]~E(x4371,x4372)+E(f360(x4373,x4374,x4371,x4375,x4376),f360(x4373,x4374,x4372,x4375,x4376)) % 167.77/167.51 [438]~E(x4381,x4382)+E(f360(x4383,x4384,x4385,x4381,x4386),f360(x4383,x4384,x4385,x4382,x4386)) % 167.77/167.51 [439]~E(x4391,x4392)+E(f360(x4393,x4394,x4395,x4396,x4391),f360(x4393,x4394,x4395,x4396,x4392)) % 167.77/167.51 [440]~E(x4401,x4402)+E(f794(x4401,x4403,x4404),f794(x4402,x4403,x4404)) % 167.77/167.51 [441]~E(x4411,x4412)+E(f794(x4413,x4411,x4414),f794(x4413,x4412,x4414)) % 167.77/167.51 [442]~E(x4421,x4422)+E(f794(x4423,x4424,x4421),f794(x4423,x4424,x4422)) % 167.77/167.51 [443]~E(x4431,x4432)+E(f439(x4431,x4433,x4434),f439(x4432,x4433,x4434)) % 167.77/167.51 [444]~E(x4441,x4442)+E(f439(x4443,x4441,x4444),f439(x4443,x4442,x4444)) % 167.77/167.51 [445]~E(x4451,x4452)+E(f439(x4453,x4454,x4451),f439(x4453,x4454,x4452)) % 167.77/167.51 [446]~E(x4461,x4462)+E(f45(x4461),f45(x4462)) % 167.77/167.51 [447]~E(x4471,x4472)+E(f626(x4471,x4473),f626(x4472,x4473)) % 167.77/167.51 [448]~E(x4481,x4482)+E(f626(x4483,x4481),f626(x4483,x4482)) % 167.77/167.51 [449]~E(x4491,x4492)+E(f274(x4491,x4493),f274(x4492,x4493)) % 167.77/167.51 [450]~E(x4501,x4502)+E(f274(x4503,x4501),f274(x4503,x4502)) % 167.77/167.51 [451]~E(x4511,x4512)+E(f167(x4511,x4513,x4514),f167(x4512,x4513,x4514)) % 167.77/167.51 [452]~E(x4521,x4522)+E(f167(x4523,x4521,x4524),f167(x4523,x4522,x4524)) % 167.77/167.51 [453]~E(x4531,x4532)+E(f167(x4533,x4534,x4531),f167(x4533,x4534,x4532)) % 167.77/167.51 [454]~E(x4541,x4542)+E(f280(x4541,x4543,x4544,x4545),f280(x4542,x4543,x4544,x4545)) % 167.77/167.51 [455]~E(x4551,x4552)+E(f280(x4553,x4551,x4554,x4555),f280(x4553,x4552,x4554,x4555)) % 167.77/167.51 [456]~E(x4561,x4562)+E(f280(x4563,x4564,x4561,x4565),f280(x4563,x4564,x4562,x4565)) % 167.77/167.51 [457]~E(x4571,x4572)+E(f280(x4573,x4574,x4575,x4571),f280(x4573,x4574,x4575,x4572)) % 167.77/167.51 [458]~E(x4581,x4582)+E(f412(x4581,x4583,x4584,x4585),f412(x4582,x4583,x4584,x4585)) % 167.77/167.51 [459]~E(x4591,x4592)+E(f412(x4593,x4591,x4594,x4595),f412(x4593,x4592,x4594,x4595)) % 167.77/167.51 [460]~E(x4601,x4602)+E(f412(x4603,x4604,x4601,x4605),f412(x4603,x4604,x4602,x4605)) % 167.77/167.51 [461]~E(x4611,x4612)+E(f412(x4613,x4614,x4615,x4611),f412(x4613,x4614,x4615,x4612)) % 167.77/167.51 [462]~E(x4621,x4622)+E(f178(x4621,x4623),f178(x4622,x4623)) % 167.77/167.51 [463]~E(x4631,x4632)+E(f178(x4633,x4631),f178(x4633,x4632)) % 167.77/167.51 [464]~E(x4641,x4642)+E(f415(x4641,x4643,x4644),f415(x4642,x4643,x4644)) % 167.77/167.51 [465]~E(x4651,x4652)+E(f415(x4653,x4651,x4654),f415(x4653,x4652,x4654)) % 167.77/167.51 [466]~E(x4661,x4662)+E(f415(x4663,x4664,x4661),f415(x4663,x4664,x4662)) % 167.77/167.51 [467]~E(x4671,x4672)+E(f614(x4671,x4673,x4674,x4675),f614(x4672,x4673,x4674,x4675)) % 167.77/167.51 [468]~E(x4681,x4682)+E(f614(x4683,x4681,x4684,x4685),f614(x4683,x4682,x4684,x4685)) % 167.77/167.51 [469]~E(x4691,x4692)+E(f614(x4693,x4694,x4691,x4695),f614(x4693,x4694,x4692,x4695)) % 167.77/167.51 [470]~E(x4701,x4702)+E(f614(x4703,x4704,x4705,x4701),f614(x4703,x4704,x4705,x4702)) % 167.77/167.51 [471]~E(x4711,x4712)+E(f12(x4711,x4713,x4714),f12(x4712,x4713,x4714)) % 167.77/167.51 [472]~E(x4721,x4722)+E(f12(x4723,x4721,x4724),f12(x4723,x4722,x4724)) % 167.77/167.51 [473]~E(x4731,x4732)+E(f12(x4733,x4734,x4731),f12(x4733,x4734,x4732)) % 167.77/167.51 [474]~E(x4741,x4742)+E(f179(x4741),f179(x4742)) % 167.77/167.51 [475]~E(x4751,x4752)+E(f441(x4751,x4753,x4754),f441(x4752,x4753,x4754)) % 167.77/167.51 [476]~E(x4761,x4762)+E(f441(x4763,x4761,x4764),f441(x4763,x4762,x4764)) % 167.77/167.51 [477]~E(x4771,x4772)+E(f441(x4773,x4774,x4771),f441(x4773,x4774,x4772)) % 167.77/167.51 [478]~E(x4781,x4782)+E(f456(x4781,x4783,x4784),f456(x4782,x4783,x4784)) % 167.77/167.51 [479]~E(x4791,x4792)+E(f456(x4793,x4791,x4794),f456(x4793,x4792,x4794)) % 167.77/167.51 [480]~E(x4801,x4802)+E(f456(x4803,x4804,x4801),f456(x4803,x4804,x4802)) % 167.77/167.51 [481]~E(x4811,x4812)+E(f675(x4811,x4813,x4814,x4815),f675(x4812,x4813,x4814,x4815)) % 167.77/167.51 [482]~E(x4821,x4822)+E(f675(x4823,x4821,x4824,x4825),f675(x4823,x4822,x4824,x4825)) % 167.77/167.51 [483]~E(x4831,x4832)+E(f675(x4833,x4834,x4831,x4835),f675(x4833,x4834,x4832,x4835)) % 167.77/167.51 [484]~E(x4841,x4842)+E(f675(x4843,x4844,x4845,x4841),f675(x4843,x4844,x4845,x4842)) % 167.77/167.51 [485]~E(x4851,x4852)+E(f303(x4851),f303(x4852)) % 167.77/167.51 [486]~E(x4861,x4862)+E(f815(x4861,x4863,x4864),f815(x4862,x4863,x4864)) % 167.77/167.51 [487]~E(x4871,x4872)+E(f815(x4873,x4871,x4874),f815(x4873,x4872,x4874)) % 167.77/167.51 [488]~E(x4881,x4882)+E(f815(x4883,x4884,x4881),f815(x4883,x4884,x4882)) % 167.77/167.51 [489]~E(x4891,x4892)+E(f175(x4891,x4893,x4894),f175(x4892,x4893,x4894)) % 167.77/167.51 [490]~E(x4901,x4902)+E(f175(x4903,x4901,x4904),f175(x4903,x4902,x4904)) % 167.77/167.51 [491]~E(x4911,x4912)+E(f175(x4913,x4914,x4911),f175(x4913,x4914,x4912)) % 167.77/167.51 [492]~E(x4921,x4922)+E(f187(x4921,x4923),f187(x4922,x4923)) % 167.77/167.51 [493]~E(x4931,x4932)+E(f187(x4933,x4931),f187(x4933,x4932)) % 167.77/167.51 [494]~E(x4941,x4942)+E(f147(x4941,x4943,x4944,x4945),f147(x4942,x4943,x4944,x4945)) % 167.77/167.51 [495]~E(x4951,x4952)+E(f147(x4953,x4951,x4954,x4955),f147(x4953,x4952,x4954,x4955)) % 167.77/167.51 [496]~E(x4961,x4962)+E(f147(x4963,x4964,x4961,x4965),f147(x4963,x4964,x4962,x4965)) % 167.77/167.51 [497]~E(x4971,x4972)+E(f147(x4973,x4974,x4975,x4971),f147(x4973,x4974,x4975,x4972)) % 167.77/167.51 [498]~E(x4981,x4982)+E(f799(x4981,x4983,x4984),f799(x4982,x4983,x4984)) % 167.77/167.51 [499]~E(x4991,x4992)+E(f799(x4993,x4991,x4994),f799(x4993,x4992,x4994)) % 167.77/167.51 [500]~E(x5001,x5002)+E(f799(x5003,x5004,x5001),f799(x5003,x5004,x5002)) % 167.77/167.51 [501]~E(x5011,x5012)+E(f532(x5011,x5013),f532(x5012,x5013)) % 167.77/167.51 [502]~E(x5021,x5022)+E(f532(x5023,x5021),f532(x5023,x5022)) % 167.77/167.51 [503]~E(x5031,x5032)+E(f672(x5031,x5033,x5034,x5035),f672(x5032,x5033,x5034,x5035)) % 167.77/167.51 [504]~E(x5041,x5042)+E(f672(x5043,x5041,x5044,x5045),f672(x5043,x5042,x5044,x5045)) % 167.77/167.51 [505]~E(x5051,x5052)+E(f672(x5053,x5054,x5051,x5055),f672(x5053,x5054,x5052,x5055)) % 167.77/167.51 [506]~E(x5061,x5062)+E(f672(x5063,x5064,x5065,x5061),f672(x5063,x5064,x5065,x5062)) % 167.77/167.51 [507]~E(x5071,x5072)+E(f698(x5071,x5073,x5074,x5075),f698(x5072,x5073,x5074,x5075)) % 167.77/167.51 [508]~E(x5081,x5082)+E(f698(x5083,x5081,x5084,x5085),f698(x5083,x5082,x5084,x5085)) % 167.77/167.51 [509]~E(x5091,x5092)+E(f698(x5093,x5094,x5091,x5095),f698(x5093,x5094,x5092,x5095)) % 167.77/167.51 [510]~E(x5101,x5102)+E(f698(x5103,x5104,x5105,x5101),f698(x5103,x5104,x5105,x5102)) % 167.77/167.51 [511]~E(x5111,x5112)+E(f802(x5111,x5113,x5114,x5115),f802(x5112,x5113,x5114,x5115)) % 167.77/167.51 [512]~E(x5121,x5122)+E(f802(x5123,x5121,x5124,x5125),f802(x5123,x5122,x5124,x5125)) % 167.77/167.51 [513]~E(x5131,x5132)+E(f802(x5133,x5134,x5131,x5135),f802(x5133,x5134,x5132,x5135)) % 167.77/167.51 [514]~E(x5141,x5142)+E(f802(x5143,x5144,x5145,x5141),f802(x5143,x5144,x5145,x5142)) % 167.77/167.51 [515]~E(x5151,x5152)+E(f216(x5151,x5153,x5154,x5155),f216(x5152,x5153,x5154,x5155)) % 167.77/167.51 [516]~E(x5161,x5162)+E(f216(x5163,x5161,x5164,x5165),f216(x5163,x5162,x5164,x5165)) % 167.77/167.51 [517]~E(x5171,x5172)+E(f216(x5173,x5174,x5171,x5175),f216(x5173,x5174,x5172,x5175)) % 167.77/167.51 [518]~E(x5181,x5182)+E(f216(x5183,x5184,x5185,x5181),f216(x5183,x5184,x5185,x5182)) % 167.77/167.51 [519]~E(x5191,x5192)+E(f812(x5191,x5193,x5194,x5195,x5196),f812(x5192,x5193,x5194,x5195,x5196)) % 167.77/167.51 [520]~E(x5201,x5202)+E(f812(x5203,x5201,x5204,x5205,x5206),f812(x5203,x5202,x5204,x5205,x5206)) % 167.77/167.51 [521]~E(x5211,x5212)+E(f812(x5213,x5214,x5211,x5215,x5216),f812(x5213,x5214,x5212,x5215,x5216)) % 167.77/167.51 [522]~E(x5221,x5222)+E(f812(x5223,x5224,x5225,x5221,x5226),f812(x5223,x5224,x5225,x5222,x5226)) % 167.77/167.51 [523]~E(x5231,x5232)+E(f812(x5233,x5234,x5235,x5236,x5231),f812(x5233,x5234,x5235,x5236,x5232)) % 167.77/167.51 [524]~E(x5241,x5242)+E(f250(x5241),f250(x5242)) % 167.77/167.51 [525]~E(x5251,x5252)+E(f671(x5251,x5253,x5254,x5255),f671(x5252,x5253,x5254,x5255)) % 167.77/167.51 [526]~E(x5261,x5262)+E(f671(x5263,x5261,x5264,x5265),f671(x5263,x5262,x5264,x5265)) % 167.77/167.51 [527]~E(x5271,x5272)+E(f671(x5273,x5274,x5271,x5275),f671(x5273,x5274,x5272,x5275)) % 167.77/167.51 [528]~E(x5281,x5282)+E(f671(x5283,x5284,x5285,x5281),f671(x5283,x5284,x5285,x5282)) % 167.77/167.51 [529]~E(x5291,x5292)+E(f138(x5291),f138(x5292)) % 167.77/167.51 [530]~E(x5301,x5302)+E(f740(x5301,x5303),f740(x5302,x5303)) % 167.77/167.51 [531]~E(x5311,x5312)+E(f740(x5313,x5311),f740(x5313,x5312)) % 167.77/167.51 [532]~E(x5321,x5322)+E(f48(x5321,x5323),f48(x5322,x5323)) % 167.77/167.51 [533]~E(x5331,x5332)+E(f48(x5333,x5331),f48(x5333,x5332)) % 167.77/167.51 [534]~E(x5341,x5342)+E(f705(x5341,x5343,x5344),f705(x5342,x5343,x5344)) % 167.77/167.51 [535]~E(x5351,x5352)+E(f705(x5353,x5351,x5354),f705(x5353,x5352,x5354)) % 167.77/167.51 [536]~E(x5361,x5362)+E(f705(x5363,x5364,x5361),f705(x5363,x5364,x5362)) % 167.77/167.51 [537]~E(x5371,x5372)+E(f293(x5371,x5373,x5374,x5375,x5376),f293(x5372,x5373,x5374,x5375,x5376)) % 167.77/167.51 [538]~E(x5381,x5382)+E(f293(x5383,x5381,x5384,x5385,x5386),f293(x5383,x5382,x5384,x5385,x5386)) % 167.77/167.51 [539]~E(x5391,x5392)+E(f293(x5393,x5394,x5391,x5395,x5396),f293(x5393,x5394,x5392,x5395,x5396)) % 167.77/167.51 [540]~E(x5401,x5402)+E(f293(x5403,x5404,x5405,x5401,x5406),f293(x5403,x5404,x5405,x5402,x5406)) % 167.77/167.51 [541]~E(x5411,x5412)+E(f293(x5413,x5414,x5415,x5416,x5411),f293(x5413,x5414,x5415,x5416,x5412)) % 167.77/167.51 [542]~E(x5421,x5422)+E(f814(x5421,x5423,x5424),f814(x5422,x5423,x5424)) % 167.77/167.51 [543]~E(x5431,x5432)+E(f814(x5433,x5431,x5434),f814(x5433,x5432,x5434)) % 167.77/167.51 [544]~E(x5441,x5442)+E(f814(x5443,x5444,x5441),f814(x5443,x5444,x5442)) % 167.77/167.51 [545]~E(x5451,x5452)+E(f372(x5451,x5453),f372(x5452,x5453)) % 167.77/167.51 [546]~E(x5461,x5462)+E(f372(x5463,x5461),f372(x5463,x5462)) % 167.77/167.51 [547]~E(x5471,x5472)+E(f653(x5471,x5473,x5474,x5475,x5476),f653(x5472,x5473,x5474,x5475,x5476)) % 167.77/167.51 [548]~E(x5481,x5482)+E(f653(x5483,x5481,x5484,x5485,x5486),f653(x5483,x5482,x5484,x5485,x5486)) % 167.77/167.51 [549]~E(x5491,x5492)+E(f653(x5493,x5494,x5491,x5495,x5496),f653(x5493,x5494,x5492,x5495,x5496)) % 167.77/167.51 [550]~E(x5501,x5502)+E(f653(x5503,x5504,x5505,x5501,x5506),f653(x5503,x5504,x5505,x5502,x5506)) % 167.77/167.51 [551]~E(x5511,x5512)+E(f653(x5513,x5514,x5515,x5516,x5511),f653(x5513,x5514,x5515,x5516,x5512)) % 167.77/167.51 [552]~E(x5521,x5522)+E(f452(x5521,x5523,x5524),f452(x5522,x5523,x5524)) % 167.77/167.51 [553]~E(x5531,x5532)+E(f452(x5533,x5531,x5534),f452(x5533,x5532,x5534)) % 167.77/167.51 [554]~E(x5541,x5542)+E(f452(x5543,x5544,x5541),f452(x5543,x5544,x5542)) % 167.77/167.51 [555]~E(x5551,x5552)+E(f658(x5551,x5553,x5554,x5555),f658(x5552,x5553,x5554,x5555)) % 167.77/167.51 [556]~E(x5561,x5562)+E(f658(x5563,x5561,x5564,x5565),f658(x5563,x5562,x5564,x5565)) % 167.77/167.51 [557]~E(x5571,x5572)+E(f658(x5573,x5574,x5571,x5575),f658(x5573,x5574,x5572,x5575)) % 167.77/167.51 [558]~E(x5581,x5582)+E(f658(x5583,x5584,x5585,x5581),f658(x5583,x5584,x5585,x5582)) % 167.77/167.51 [559]~E(x5591,x5592)+E(f417(x5591,x5593),f417(x5592,x5593)) % 167.77/167.51 [560]~E(x5601,x5602)+E(f417(x5603,x5601),f417(x5603,x5602)) % 167.77/167.51 [561]~E(x5611,x5612)+E(f56(x5611,x5613,x5614),f56(x5612,x5613,x5614)) % 167.77/167.51 [562]~E(x5621,x5622)+E(f56(x5623,x5621,x5624),f56(x5623,x5622,x5624)) % 167.77/167.51 [563]~E(x5631,x5632)+E(f56(x5633,x5634,x5631),f56(x5633,x5634,x5632)) % 167.77/167.51 [564]~E(x5641,x5642)+E(f509(x5641,x5643,x5644),f509(x5642,x5643,x5644)) % 167.77/167.51 [565]~E(x5651,x5652)+E(f509(x5653,x5651,x5654),f509(x5653,x5652,x5654)) % 167.77/167.51 [566]~E(x5661,x5662)+E(f509(x5663,x5664,x5661),f509(x5663,x5664,x5662)) % 167.77/167.51 [567]~E(x5671,x5672)+E(f234(x5671,x5673),f234(x5672,x5673)) % 167.77/167.51 [568]~E(x5681,x5682)+E(f234(x5683,x5681),f234(x5683,x5682)) % 167.77/167.51 [569]~E(x5691,x5692)+E(f132(x5691),f132(x5692)) % 167.77/167.51 [570]~E(x5701,x5702)+E(f628(x5701,x5703,x5704),f628(x5702,x5703,x5704)) % 167.77/167.51 [571]~E(x5711,x5712)+E(f628(x5713,x5711,x5714),f628(x5713,x5712,x5714)) % 167.77/167.51 [572]~E(x5721,x5722)+E(f628(x5723,x5724,x5721),f628(x5723,x5724,x5722)) % 167.77/167.51 [573]~E(x5731,x5732)+E(f196(x5731,x5733),f196(x5732,x5733)) % 167.77/167.51 [574]~E(x5741,x5742)+E(f196(x5743,x5741),f196(x5743,x5742)) % 167.77/167.51 [575]~E(x5751,x5752)+E(f321(x5751,x5753,x5754,x5755),f321(x5752,x5753,x5754,x5755)) % 167.77/167.51 [576]~E(x5761,x5762)+E(f321(x5763,x5761,x5764,x5765),f321(x5763,x5762,x5764,x5765)) % 167.77/167.51 [577]~E(x5771,x5772)+E(f321(x5773,x5774,x5771,x5775),f321(x5773,x5774,x5772,x5775)) % 167.77/167.51 [578]~E(x5781,x5782)+E(f321(x5783,x5784,x5785,x5781),f321(x5783,x5784,x5785,x5782)) % 167.77/167.51 [579]~E(x5791,x5792)+E(f454(x5791,x5793,x5794,x5795,x5796),f454(x5792,x5793,x5794,x5795,x5796)) % 167.77/167.51 [580]~E(x5801,x5802)+E(f454(x5803,x5801,x5804,x5805,x5806),f454(x5803,x5802,x5804,x5805,x5806)) % 167.77/167.51 [581]~E(x5811,x5812)+E(f454(x5813,x5814,x5811,x5815,x5816),f454(x5813,x5814,x5812,x5815,x5816)) % 167.77/167.51 [582]~E(x5821,x5822)+E(f454(x5823,x5824,x5825,x5821,x5826),f454(x5823,x5824,x5825,x5822,x5826)) % 167.77/167.51 [583]~E(x5831,x5832)+E(f454(x5833,x5834,x5835,x5836,x5831),f454(x5833,x5834,x5835,x5836,x5832)) % 167.77/167.51 [584]~E(x5841,x5842)+E(f634(x5841,x5843,x5844,x5845,x5846),f634(x5842,x5843,x5844,x5845,x5846)) % 167.77/167.51 [585]~E(x5851,x5852)+E(f634(x5853,x5851,x5854,x5855,x5856),f634(x5853,x5852,x5854,x5855,x5856)) % 167.77/167.51 [586]~E(x5861,x5862)+E(f634(x5863,x5864,x5861,x5865,x5866),f634(x5863,x5864,x5862,x5865,x5866)) % 167.77/167.51 [587]~E(x5871,x5872)+E(f634(x5873,x5874,x5875,x5871,x5876),f634(x5873,x5874,x5875,x5872,x5876)) % 167.77/167.51 [588]~E(x5881,x5882)+E(f634(x5883,x5884,x5885,x5886,x5881),f634(x5883,x5884,x5885,x5886,x5882)) % 167.77/167.51 [589]~E(x5891,x5892)+E(f50(x5891,x5893),f50(x5892,x5893)) % 167.77/167.51 [590]~E(x5901,x5902)+E(f50(x5903,x5901),f50(x5903,x5902)) % 167.77/167.51 [591]~E(x5911,x5912)+E(f33(x5911,x5913),f33(x5912,x5913)) % 167.77/167.51 [592]~E(x5921,x5922)+E(f33(x5923,x5921),f33(x5923,x5922)) % 167.77/167.51 [593]~E(x5931,x5932)+E(f76(x5931,x5933,x5934,x5935,x5936),f76(x5932,x5933,x5934,x5935,x5936)) % 167.77/167.51 [594]~E(x5941,x5942)+E(f76(x5943,x5941,x5944,x5945,x5946),f76(x5943,x5942,x5944,x5945,x5946)) % 167.77/167.51 [595]~E(x5951,x5952)+E(f76(x5953,x5954,x5951,x5955,x5956),f76(x5953,x5954,x5952,x5955,x5956)) % 167.77/167.51 [596]~E(x5961,x5962)+E(f76(x5963,x5964,x5965,x5961,x5966),f76(x5963,x5964,x5965,x5962,x5966)) % 167.77/167.51 [597]~E(x5971,x5972)+E(f76(x5973,x5974,x5975,x5976,x5971),f76(x5973,x5974,x5975,x5976,x5972)) % 167.77/167.51 [598]~E(x5981,x5982)+E(f315(x5981,x5983,x5984,x5985),f315(x5982,x5983,x5984,x5985)) % 167.77/167.51 [599]~E(x5991,x5992)+E(f315(x5993,x5991,x5994,x5995),f315(x5993,x5992,x5994,x5995)) % 167.77/167.51 [600]~E(x6001,x6002)+E(f315(x6003,x6004,x6001,x6005),f315(x6003,x6004,x6002,x6005)) % 167.77/167.51 [601]~E(x6011,x6012)+E(f315(x6013,x6014,x6015,x6011),f315(x6013,x6014,x6015,x6012)) % 167.77/167.51 [602]~E(x6021,x6022)+E(f683(x6021,x6023,x6024,x6025),f683(x6022,x6023,x6024,x6025)) % 167.77/167.51 [603]~E(x6031,x6032)+E(f683(x6033,x6031,x6034,x6035),f683(x6033,x6032,x6034,x6035)) % 167.77/167.51 [604]~E(x6041,x6042)+E(f683(x6043,x6044,x6041,x6045),f683(x6043,x6044,x6042,x6045)) % 167.77/167.51 [605]~E(x6051,x6052)+E(f683(x6053,x6054,x6055,x6051),f683(x6053,x6054,x6055,x6052)) % 167.77/167.51 [606]~E(x6061,x6062)+E(f777(x6061,x6063,x6064),f777(x6062,x6063,x6064)) % 167.77/167.51 [607]~E(x6071,x6072)+E(f777(x6073,x6071,x6074),f777(x6073,x6072,x6074)) % 167.77/167.51 [608]~E(x6081,x6082)+E(f777(x6083,x6084,x6081),f777(x6083,x6084,x6082)) % 167.77/167.51 [609]~E(x6091,x6092)+E(f245(x6091,x6093),f245(x6092,x6093)) % 167.77/167.51 [610]~E(x6101,x6102)+E(f245(x6103,x6101),f245(x6103,x6102)) % 167.77/167.51 [611]~E(x6111,x6112)+E(f379(x6111),f379(x6112)) % 167.77/167.51 [612]~E(x6121,x6122)+E(f424(x6121,x6123),f424(x6122,x6123)) % 167.77/167.51 [613]~E(x6131,x6132)+E(f424(x6133,x6131),f424(x6133,x6132)) % 167.77/167.51 [614]~E(x6141,x6142)+E(f204(x6141,x6143,x6144,x6145),f204(x6142,x6143,x6144,x6145)) % 167.77/167.51 [615]~E(x6151,x6152)+E(f204(x6153,x6151,x6154,x6155),f204(x6153,x6152,x6154,x6155)) % 167.77/167.51 [616]~E(x6161,x6162)+E(f204(x6163,x6164,x6161,x6165),f204(x6163,x6164,x6162,x6165)) % 167.77/167.51 [617]~E(x6171,x6172)+E(f204(x6173,x6174,x6175,x6171),f204(x6173,x6174,x6175,x6172)) % 167.77/167.51 [618]~E(x6181,x6182)+E(f63(x6181,x6183,x6184),f63(x6182,x6183,x6184)) % 167.77/167.51 [619]~E(x6191,x6192)+E(f63(x6193,x6191,x6194),f63(x6193,x6192,x6194)) % 167.77/167.51 [620]~E(x6201,x6202)+E(f63(x6203,x6204,x6201),f63(x6203,x6204,x6202)) % 167.77/167.51 [621]~E(x6211,x6212)+E(f527(x6211),f527(x6212)) % 167.77/167.51 [622]~E(x6221,x6222)+E(f59(x6221),f59(x6222)) % 167.77/167.51 [623]~E(x6231,x6232)+E(f302(x6231,x6233,x6234),f302(x6232,x6233,x6234)) % 167.77/167.51 [624]~E(x6241,x6242)+E(f302(x6243,x6241,x6244),f302(x6243,x6242,x6244)) % 167.77/167.51 [625]~E(x6251,x6252)+E(f302(x6253,x6254,x6251),f302(x6253,x6254,x6252)) % 167.77/167.51 [626]~E(x6261,x6262)+E(f362(x6261,x6263,x6264,x6265,x6266),f362(x6262,x6263,x6264,x6265,x6266)) % 167.77/167.51 [627]~E(x6271,x6272)+E(f362(x6273,x6271,x6274,x6275,x6276),f362(x6273,x6272,x6274,x6275,x6276)) % 167.77/167.51 [628]~E(x6281,x6282)+E(f362(x6283,x6284,x6281,x6285,x6286),f362(x6283,x6284,x6282,x6285,x6286)) % 167.77/167.51 [629]~E(x6291,x6292)+E(f362(x6293,x6294,x6295,x6291,x6296),f362(x6293,x6294,x6295,x6292,x6296)) % 167.77/167.51 [630]~E(x6301,x6302)+E(f362(x6303,x6304,x6305,x6306,x6301),f362(x6303,x6304,x6305,x6306,x6302)) % 167.77/167.51 [631]~E(x6311,x6312)+E(f445(x6311,x6313,x6314),f445(x6312,x6313,x6314)) % 167.77/167.51 [632]~E(x6321,x6322)+E(f445(x6323,x6321,x6324),f445(x6323,x6322,x6324)) % 167.77/167.51 [633]~E(x6331,x6332)+E(f445(x6333,x6334,x6331),f445(x6333,x6334,x6332)) % 167.77/167.51 [634]~E(x6341,x6342)+E(f486(x6341,x6343),f486(x6342,x6343)) % 167.77/167.51 [635]~E(x6351,x6352)+E(f486(x6353,x6351),f486(x6353,x6352)) % 167.77/167.51 [636]~E(x6361,x6362)+E(f785(x6361,x6363,x6364,x6365,x6366),f785(x6362,x6363,x6364,x6365,x6366)) % 167.77/167.51 [637]~E(x6371,x6372)+E(f785(x6373,x6371,x6374,x6375,x6376),f785(x6373,x6372,x6374,x6375,x6376)) % 167.77/167.51 [638]~E(x6381,x6382)+E(f785(x6383,x6384,x6381,x6385,x6386),f785(x6383,x6384,x6382,x6385,x6386)) % 167.77/167.51 [639]~E(x6391,x6392)+E(f785(x6393,x6394,x6395,x6391,x6396),f785(x6393,x6394,x6395,x6392,x6396)) % 167.77/167.51 [640]~E(x6401,x6402)+E(f785(x6403,x6404,x6405,x6406,x6401),f785(x6403,x6404,x6405,x6406,x6402)) % 167.77/167.51 [641]~E(x6411,x6412)+E(f462(x6411,x6413,x6414,x6415,x6416,x6417),f462(x6412,x6413,x6414,x6415,x6416,x6417)) % 167.77/167.51 [642]~E(x6421,x6422)+E(f462(x6423,x6421,x6424,x6425,x6426,x6427),f462(x6423,x6422,x6424,x6425,x6426,x6427)) % 167.77/167.51 [643]~E(x6431,x6432)+E(f462(x6433,x6434,x6431,x6435,x6436,x6437),f462(x6433,x6434,x6432,x6435,x6436,x6437)) % 167.77/167.51 [644]~E(x6441,x6442)+E(f462(x6443,x6444,x6445,x6441,x6446,x6447),f462(x6443,x6444,x6445,x6442,x6446,x6447)) % 167.77/167.51 [645]~E(x6451,x6452)+E(f462(x6453,x6454,x6455,x6456,x6451,x6457),f462(x6453,x6454,x6455,x6456,x6452,x6457)) % 167.77/167.51 [646]~E(x6461,x6462)+E(f462(x6463,x6464,x6465,x6466,x6467,x6461),f462(x6463,x6464,x6465,x6466,x6467,x6462)) % 167.77/167.51 [647]~E(x6471,x6472)+E(f82(x6471,x6473),f82(x6472,x6473)) % 167.77/167.51 [648]~E(x6481,x6482)+E(f82(x6483,x6481),f82(x6483,x6482)) % 167.77/167.51 [649]~E(x6491,x6492)+E(f763(x6491,x6493),f763(x6492,x6493)) % 167.77/167.51 [650]~E(x6501,x6502)+E(f763(x6503,x6501),f763(x6503,x6502)) % 167.77/167.51 [651]~E(x6511,x6512)+E(f96(x6511,x6513,x6514,x6515),f96(x6512,x6513,x6514,x6515)) % 167.77/167.51 [652]~E(x6521,x6522)+E(f96(x6523,x6521,x6524,x6525),f96(x6523,x6522,x6524,x6525)) % 167.77/167.51 [653]~E(x6531,x6532)+E(f96(x6533,x6534,x6531,x6535),f96(x6533,x6534,x6532,x6535)) % 167.77/167.51 [654]~E(x6541,x6542)+E(f96(x6543,x6544,x6545,x6541),f96(x6543,x6544,x6545,x6542)) % 167.77/167.51 [655]~E(x6551,x6552)+E(f481(x6551,x6553,x6554),f481(x6552,x6553,x6554)) % 167.77/167.51 [656]~E(x6561,x6562)+E(f481(x6563,x6561,x6564),f481(x6563,x6562,x6564)) % 167.77/167.51 [657]~E(x6571,x6572)+E(f481(x6573,x6574,x6571),f481(x6573,x6574,x6572)) % 167.77/167.51 [658]~E(x6581,x6582)+E(f778(x6581,x6583,x6584,x6585),f778(x6582,x6583,x6584,x6585)) % 167.77/167.51 [659]~E(x6591,x6592)+E(f778(x6593,x6591,x6594,x6595),f778(x6593,x6592,x6594,x6595)) % 167.77/167.51 [660]~E(x6601,x6602)+E(f778(x6603,x6604,x6601,x6605),f778(x6603,x6604,x6602,x6605)) % 167.77/167.51 [661]~E(x6611,x6612)+E(f778(x6613,x6614,x6615,x6611),f778(x6613,x6614,x6615,x6612)) % 167.77/167.51 [662]~E(x6621,x6622)+E(f300(x6621),f300(x6622)) % 167.77/167.51 [663]~E(x6631,x6632)+E(f261(x6631,x6633),f261(x6632,x6633)) % 167.77/167.51 [664]~E(x6641,x6642)+E(f261(x6643,x6641),f261(x6643,x6642)) % 167.77/167.51 [665]~E(x6651,x6652)+E(f382(x6651,x6653,x6654),f382(x6652,x6653,x6654)) % 167.77/167.51 [666]~E(x6661,x6662)+E(f382(x6663,x6661,x6664),f382(x6663,x6662,x6664)) % 167.77/167.51 [667]~E(x6671,x6672)+E(f382(x6673,x6674,x6671),f382(x6673,x6674,x6672)) % 167.77/167.51 [668]~E(x6681,x6682)+E(f852(x6681,x6683,x6684),f852(x6682,x6683,x6684)) % 167.77/167.51 [669]~E(x6691,x6692)+E(f852(x6693,x6691,x6694),f852(x6693,x6692,x6694)) % 167.77/167.51 [670]~E(x6701,x6702)+E(f852(x6703,x6704,x6701),f852(x6703,x6704,x6702)) % 167.77/167.51 [671]~E(x6711,x6712)+E(f420(x6711,x6713,x6714,x6715),f420(x6712,x6713,x6714,x6715)) % 167.77/167.51 [672]~E(x6721,x6722)+E(f420(x6723,x6721,x6724,x6725),f420(x6723,x6722,x6724,x6725)) % 167.77/167.51 [673]~E(x6731,x6732)+E(f420(x6733,x6734,x6731,x6735),f420(x6733,x6734,x6732,x6735)) % 167.77/167.51 [674]~E(x6741,x6742)+E(f420(x6743,x6744,x6745,x6741),f420(x6743,x6744,x6745,x6742)) % 167.77/167.51 [675]~E(x6751,x6752)+E(f391(x6751,x6753,x6754),f391(x6752,x6753,x6754)) % 167.77/167.51 [676]~E(x6761,x6762)+E(f391(x6763,x6761,x6764),f391(x6763,x6762,x6764)) % 167.77/167.51 [677]~E(x6771,x6772)+E(f391(x6773,x6774,x6771),f391(x6773,x6774,x6772)) % 167.77/167.51 [678]~E(x6781,x6782)+E(f773(x6781,x6783,x6784),f773(x6782,x6783,x6784)) % 167.77/167.51 [679]~E(x6791,x6792)+E(f773(x6793,x6791,x6794),f773(x6793,x6792,x6794)) % 167.77/167.51 [680]~E(x6801,x6802)+E(f773(x6803,x6804,x6801),f773(x6803,x6804,x6802)) % 167.77/167.51 [681]~E(x6811,x6812)+E(f317(x6811,x6813),f317(x6812,x6813)) % 167.77/167.51 [682]~E(x6821,x6822)+E(f317(x6823,x6821),f317(x6823,x6822)) % 167.77/167.51 [683]~E(x6831,x6832)+E(f525(x6831,x6833,x6834,x6835),f525(x6832,x6833,x6834,x6835)) % 167.77/167.51 [684]~E(x6841,x6842)+E(f525(x6843,x6841,x6844,x6845),f525(x6843,x6842,x6844,x6845)) % 167.77/167.51 [685]~E(x6851,x6852)+E(f525(x6853,x6854,x6851,x6855),f525(x6853,x6854,x6852,x6855)) % 167.77/167.51 [686]~E(x6861,x6862)+E(f525(x6863,x6864,x6865,x6861),f525(x6863,x6864,x6865,x6862)) % 167.77/167.51 [687]~E(x6871,x6872)+E(f768(x6871,x6873,x6874,x6875),f768(x6872,x6873,x6874,x6875)) % 167.77/167.51 [688]~E(x6881,x6882)+E(f768(x6883,x6881,x6884,x6885),f768(x6883,x6882,x6884,x6885)) % 167.77/167.51 [689]~E(x6891,x6892)+E(f768(x6893,x6894,x6891,x6895),f768(x6893,x6894,x6892,x6895)) % 167.77/167.51 [690]~E(x6901,x6902)+E(f768(x6903,x6904,x6905,x6901),f768(x6903,x6904,x6905,x6902)) % 167.77/167.51 [691]~E(x6911,x6912)+E(f857(x6911,x6913,x6914),f857(x6912,x6913,x6914)) % 167.77/167.51 [692]~E(x6921,x6922)+E(f857(x6923,x6921,x6924),f857(x6923,x6922,x6924)) % 167.77/167.51 [693]~E(x6931,x6932)+E(f857(x6933,x6934,x6931),f857(x6933,x6934,x6932)) % 167.77/167.51 [694]~E(x6941,x6942)+E(f297(x6941),f297(x6942)) % 167.77/167.51 [695]~E(x6951,x6952)+E(f284(x6951,x6953),f284(x6952,x6953)) % 167.77/167.51 [696]~E(x6961,x6962)+E(f284(x6963,x6961),f284(x6963,x6962)) % 167.77/167.51 [697]~E(x6971,x6972)+E(f98(x6971,x6973,x6974,x6975),f98(x6972,x6973,x6974,x6975)) % 167.77/167.51 [698]~E(x6981,x6982)+E(f98(x6983,x6981,x6984,x6985),f98(x6983,x6982,x6984,x6985)) % 167.77/167.51 [699]~E(x6991,x6992)+E(f98(x6993,x6994,x6991,x6995),f98(x6993,x6994,x6992,x6995)) % 167.77/167.51 [700]~E(x7001,x7002)+E(f98(x7003,x7004,x7005,x7001),f98(x7003,x7004,x7005,x7002)) % 167.77/167.51 [701]~E(x7011,x7012)+E(f409(x7011,x7013,x7014,x7015),f409(x7012,x7013,x7014,x7015)) % 167.77/167.51 [702]~E(x7021,x7022)+E(f409(x7023,x7021,x7024,x7025),f409(x7023,x7022,x7024,x7025)) % 167.77/167.51 [703]~E(x7031,x7032)+E(f409(x7033,x7034,x7031,x7035),f409(x7033,x7034,x7032,x7035)) % 167.77/167.51 [704]~E(x7041,x7042)+E(f409(x7043,x7044,x7045,x7041),f409(x7043,x7044,x7045,x7042)) % 167.77/167.51 [705]~E(x7051,x7052)+E(f408(x7051,x7053,x7054,x7055,x7056),f408(x7052,x7053,x7054,x7055,x7056)) % 167.77/167.51 [706]~E(x7061,x7062)+E(f408(x7063,x7061,x7064,x7065,x7066),f408(x7063,x7062,x7064,x7065,x7066)) % 167.77/167.51 [707]~E(x7071,x7072)+E(f408(x7073,x7074,x7071,x7075,x7076),f408(x7073,x7074,x7072,x7075,x7076)) % 167.77/167.51 [708]~E(x7081,x7082)+E(f408(x7083,x7084,x7085,x7081,x7086),f408(x7083,x7084,x7085,x7082,x7086)) % 167.77/167.51 [709]~E(x7091,x7092)+E(f408(x7093,x7094,x7095,x7096,x7091),f408(x7093,x7094,x7095,x7096,x7092)) % 167.77/167.51 [710]~E(x7101,x7102)+E(f433(x7101,x7103,x7104),f433(x7102,x7103,x7104)) % 167.77/167.51 [711]~E(x7111,x7112)+E(f433(x7113,x7111,x7114),f433(x7113,x7112,x7114)) % 167.77/167.51 [712]~E(x7121,x7122)+E(f433(x7123,x7124,x7121),f433(x7123,x7124,x7122)) % 167.77/167.51 [713]~E(x7131,x7132)+E(f863(x7131,x7133,x7134,x7135,x7136),f863(x7132,x7133,x7134,x7135,x7136)) % 167.77/167.51 [714]~E(x7141,x7142)+E(f863(x7143,x7141,x7144,x7145,x7146),f863(x7143,x7142,x7144,x7145,x7146)) % 167.77/167.51 [715]~E(x7151,x7152)+E(f863(x7153,x7154,x7151,x7155,x7156),f863(x7153,x7154,x7152,x7155,x7156)) % 167.77/167.51 [716]~E(x7161,x7162)+E(f863(x7163,x7164,x7165,x7161,x7166),f863(x7163,x7164,x7165,x7162,x7166)) % 167.77/167.51 [717]~E(x7171,x7172)+E(f863(x7173,x7174,x7175,x7176,x7171),f863(x7173,x7174,x7175,x7176,x7172)) % 167.77/167.51 [718]~E(x7181,x7182)+E(f533(x7181,x7183,x7184,x7185,x7186,x7187,x7188),f533(x7182,x7183,x7184,x7185,x7186,x7187,x7188)) % 167.77/167.51 [719]~E(x7191,x7192)+E(f533(x7193,x7191,x7194,x7195,x7196,x7197,x7198),f533(x7193,x7192,x7194,x7195,x7196,x7197,x7198)) % 167.77/167.51 [720]~E(x7201,x7202)+E(f533(x7203,x7204,x7201,x7205,x7206,x7207,x7208),f533(x7203,x7204,x7202,x7205,x7206,x7207,x7208)) % 167.77/167.51 [721]~E(x7211,x7212)+E(f533(x7213,x7214,x7215,x7211,x7216,x7217,x7218),f533(x7213,x7214,x7215,x7212,x7216,x7217,x7218)) % 167.77/167.51 [722]~E(x7221,x7222)+E(f533(x7223,x7224,x7225,x7226,x7221,x7227,x7228),f533(x7223,x7224,x7225,x7226,x7222,x7227,x7228)) % 167.77/167.51 [723]~E(x7231,x7232)+E(f533(x7233,x7234,x7235,x7236,x7237,x7231,x7238),f533(x7233,x7234,x7235,x7236,x7237,x7232,x7238)) % 167.77/167.51 [724]~E(x7241,x7242)+E(f533(x7243,x7244,x7245,x7246,x7247,x7248,x7241),f533(x7243,x7244,x7245,x7246,x7247,x7248,x7242)) % 167.77/167.51 [725]~E(x7251,x7252)+E(f127(x7251,x7253,x7254),f127(x7252,x7253,x7254)) % 167.77/167.51 [726]~E(x7261,x7262)+E(f127(x7263,x7261,x7264),f127(x7263,x7262,x7264)) % 167.77/167.51 [727]~E(x7271,x7272)+E(f127(x7273,x7274,x7271),f127(x7273,x7274,x7272)) % 167.77/167.51 [728]~E(x7281,x7282)+E(f67(x7281,x7283,x7284,x7285,x7286),f67(x7282,x7283,x7284,x7285,x7286)) % 167.77/167.51 [729]~E(x7291,x7292)+E(f67(x7293,x7291,x7294,x7295,x7296),f67(x7293,x7292,x7294,x7295,x7296)) % 167.77/167.51 [730]~E(x7301,x7302)+E(f67(x7303,x7304,x7301,x7305,x7306),f67(x7303,x7304,x7302,x7305,x7306)) % 167.77/167.51 [731]~E(x7311,x7312)+E(f67(x7313,x7314,x7315,x7311,x7316),f67(x7313,x7314,x7315,x7312,x7316)) % 167.77/167.51 [732]~E(x7321,x7322)+E(f67(x7323,x7324,x7325,x7326,x7321),f67(x7323,x7324,x7325,x7326,x7322)) % 167.77/167.51 [733]~E(x7331,x7332)+E(f95(x7331,x7333,x7334),f95(x7332,x7333,x7334)) % 167.77/167.51 [734]~E(x7341,x7342)+E(f95(x7343,x7341,x7344),f95(x7343,x7342,x7344)) % 167.77/167.51 [735]~E(x7351,x7352)+E(f95(x7353,x7354,x7351),f95(x7353,x7354,x7352)) % 167.77/167.51 [736]~E(x7361,x7362)+E(f656(x7361,x7363,x7364,x7365),f656(x7362,x7363,x7364,x7365)) % 167.77/167.51 [737]~E(x7371,x7372)+E(f656(x7373,x7371,x7374,x7375),f656(x7373,x7372,x7374,x7375)) % 167.77/167.51 [738]~E(x7381,x7382)+E(f656(x7383,x7384,x7381,x7385),f656(x7383,x7384,x7382,x7385)) % 167.77/167.51 [739]~E(x7391,x7392)+E(f656(x7393,x7394,x7395,x7391),f656(x7393,x7394,x7395,x7392)) % 167.77/167.51 [740]~E(x7401,x7402)+E(f309(x7401,x7403),f309(x7402,x7403)) % 167.77/167.51 [741]~E(x7411,x7412)+E(f309(x7413,x7411),f309(x7413,x7412)) % 167.77/167.51 [742]~E(x7421,x7422)+E(f230(x7421,x7423,x7424),f230(x7422,x7423,x7424)) % 167.77/167.51 [743]~E(x7431,x7432)+E(f230(x7433,x7431,x7434),f230(x7433,x7432,x7434)) % 167.77/167.51 [744]~E(x7441,x7442)+E(f230(x7443,x7444,x7441),f230(x7443,x7444,x7442)) % 167.77/167.51 [745]~E(x7451,x7452)+E(f741(x7451,x7453),f741(x7452,x7453)) % 167.77/167.51 [746]~E(x7461,x7462)+E(f741(x7463,x7461),f741(x7463,x7462)) % 167.77/167.51 [747]~E(x7471,x7472)+E(f779(x7471,x7473,x7474,x7475),f779(x7472,x7473,x7474,x7475)) % 167.77/167.51 [748]~E(x7481,x7482)+E(f779(x7483,x7481,x7484,x7485),f779(x7483,x7482,x7484,x7485)) % 167.77/167.51 [749]~E(x7491,x7492)+E(f779(x7493,x7494,x7491,x7495),f779(x7493,x7494,x7492,x7495)) % 167.77/167.51 [750]~E(x7501,x7502)+E(f779(x7503,x7504,x7505,x7501),f779(x7503,x7504,x7505,x7502)) % 167.77/167.51 [751]~E(x7511,x7512)+E(f850(x7511,x7513,x7514),f850(x7512,x7513,x7514)) % 167.77/167.51 [752]~E(x7521,x7522)+E(f850(x7523,x7521,x7524),f850(x7523,x7522,x7524)) % 167.77/167.51 [753]~E(x7531,x7532)+E(f850(x7533,x7534,x7531),f850(x7533,x7534,x7532)) % 167.77/167.51 [754]~E(x7541,x7542)+E(f91(x7541),f91(x7542)) % 167.77/167.51 [755]~E(x7551,x7552)+E(f518(x7551,x7553,x7554),f518(x7552,x7553,x7554)) % 167.77/167.51 [756]~E(x7561,x7562)+E(f518(x7563,x7561,x7564),f518(x7563,x7562,x7564)) % 167.77/167.51 [757]~E(x7571,x7572)+E(f518(x7573,x7574,x7571),f518(x7573,x7574,x7572)) % 167.77/167.51 [758]~E(x7581,x7582)+E(f137(x7581,x7583,x7584),f137(x7582,x7583,x7584)) % 167.77/167.51 [759]~E(x7591,x7592)+E(f137(x7593,x7591,x7594),f137(x7593,x7592,x7594)) % 167.77/167.51 [760]~E(x7601,x7602)+E(f137(x7603,x7604,x7601),f137(x7603,x7604,x7602)) % 167.77/167.51 [761]~E(x7611,x7612)+E(f583(x7611,x7613),f583(x7612,x7613)) % 167.77/167.51 [762]~E(x7621,x7622)+E(f583(x7623,x7621),f583(x7623,x7622)) % 167.77/167.51 [763]~E(x7631,x7632)+E(f339(x7631),f339(x7632)) % 167.77/167.51 [764]~E(x7641,x7642)+E(f853(x7641,x7643,x7644),f853(x7642,x7643,x7644)) % 167.77/167.51 [765]~E(x7651,x7652)+E(f853(x7653,x7651,x7654),f853(x7653,x7652,x7654)) % 167.77/167.51 [766]~E(x7661,x7662)+E(f853(x7663,x7664,x7661),f853(x7663,x7664,x7662)) % 167.77/167.51 [767]~E(x7671,x7672)+E(f252(x7671,x7673,x7674),f252(x7672,x7673,x7674)) % 167.77/167.51 [768]~E(x7681,x7682)+E(f252(x7683,x7681,x7684),f252(x7683,x7682,x7684)) % 167.77/167.51 [769]~E(x7691,x7692)+E(f252(x7693,x7694,x7691),f252(x7693,x7694,x7692)) % 167.77/167.51 [770]~E(x7701,x7702)+E(f413(x7701,x7703,x7704,x7705),f413(x7702,x7703,x7704,x7705)) % 167.77/167.51 [771]~E(x7711,x7712)+E(f413(x7713,x7711,x7714,x7715),f413(x7713,x7712,x7714,x7715)) % 167.77/167.51 [772]~E(x7721,x7722)+E(f413(x7723,x7724,x7721,x7725),f413(x7723,x7724,x7722,x7725)) % 167.77/167.51 [773]~E(x7731,x7732)+E(f413(x7733,x7734,x7735,x7731),f413(x7733,x7734,x7735,x7732)) % 167.77/167.51 [774]~E(x7741,x7742)+E(f843(x7741,x7743,x7744),f843(x7742,x7743,x7744)) % 167.77/167.51 [775]~E(x7751,x7752)+E(f843(x7753,x7751,x7754),f843(x7753,x7752,x7754)) % 167.77/167.51 [776]~E(x7761,x7762)+E(f843(x7763,x7764,x7761),f843(x7763,x7764,x7762)) % 167.77/167.51 [777]~E(x7771,x7772)+E(f744(x7771,x7773,x7774,x7775,x7776),f744(x7772,x7773,x7774,x7775,x7776)) % 167.77/167.51 [778]~E(x7781,x7782)+E(f744(x7783,x7781,x7784,x7785,x7786),f744(x7783,x7782,x7784,x7785,x7786)) % 167.77/167.51 [779]~E(x7791,x7792)+E(f744(x7793,x7794,x7791,x7795,x7796),f744(x7793,x7794,x7792,x7795,x7796)) % 167.77/167.51 [780]~E(x7801,x7802)+E(f744(x7803,x7804,x7805,x7801,x7806),f744(x7803,x7804,x7805,x7802,x7806)) % 167.77/167.51 [781]~E(x7811,x7812)+E(f744(x7813,x7814,x7815,x7816,x7811),f744(x7813,x7814,x7815,x7816,x7812)) % 167.77/167.51 [782]~E(x7821,x7822)+E(f395(x7821,x7823),f395(x7822,x7823)) % 167.77/167.51 [783]~E(x7831,x7832)+E(f395(x7833,x7831),f395(x7833,x7832)) % 167.77/167.51 [784]~E(x7841,x7842)+E(f597(x7841,x7843,x7844,x7845),f597(x7842,x7843,x7844,x7845)) % 167.77/167.51 [785]~E(x7851,x7852)+E(f597(x7853,x7851,x7854,x7855),f597(x7853,x7852,x7854,x7855)) % 167.77/167.51 [786]~E(x7861,x7862)+E(f597(x7863,x7864,x7861,x7865),f597(x7863,x7864,x7862,x7865)) % 167.77/167.51 [787]~E(x7871,x7872)+E(f597(x7873,x7874,x7875,x7871),f597(x7873,x7874,x7875,x7872)) % 167.77/167.51 [788]~E(x7881,x7882)+E(f387(x7881),f387(x7882)) % 167.77/167.51 [789]~E(x7891,x7892)+E(f511(x7891,x7893,x7894),f511(x7892,x7893,x7894)) % 167.77/167.51 [790]~E(x7901,x7902)+E(f511(x7903,x7901,x7904),f511(x7903,x7902,x7904)) % 167.77/167.51 [791]~E(x7911,x7912)+E(f511(x7913,x7914,x7911),f511(x7913,x7914,x7912)) % 167.77/167.51 [792]~E(x7921,x7922)+E(f801(x7921,x7923,x7924),f801(x7922,x7923,x7924)) % 167.77/167.51 [793]~E(x7931,x7932)+E(f801(x7933,x7931,x7934),f801(x7933,x7932,x7934)) % 167.77/167.51 [794]~E(x7941,x7942)+E(f801(x7943,x7944,x7941),f801(x7943,x7944,x7942)) % 167.77/167.51 [795]~E(x7951,x7952)+E(f472(x7951,x7953,x7954),f472(x7952,x7953,x7954)) % 167.77/167.51 [796]~E(x7961,x7962)+E(f472(x7963,x7961,x7964),f472(x7963,x7962,x7964)) % 167.77/167.51 [797]~E(x7971,x7972)+E(f472(x7973,x7974,x7971),f472(x7973,x7974,x7972)) % 167.77/167.51 [798]~E(x7981,x7982)+E(f136(x7981,x7983),f136(x7982,x7983)) % 167.77/167.51 [799]~E(x7991,x7992)+E(f136(x7993,x7991),f136(x7993,x7992)) % 167.77/167.51 [800]~E(x8001,x8002)+E(f219(x8001),f219(x8002)) % 167.77/167.51 [801]~E(x8011,x8012)+E(f578(x8011,x8013,x8014),f578(x8012,x8013,x8014)) % 167.77/167.51 [802]~E(x8021,x8022)+E(f578(x8023,x8021,x8024),f578(x8023,x8022,x8024)) % 167.77/167.51 [803]~E(x8031,x8032)+E(f578(x8033,x8034,x8031),f578(x8033,x8034,x8032)) % 167.77/167.51 [804]~E(x8041,x8042)+E(f756(x8041,x8043,x8044,x8045),f756(x8042,x8043,x8044,x8045)) % 167.77/167.51 [805]~E(x8051,x8052)+E(f756(x8053,x8051,x8054,x8055),f756(x8053,x8052,x8054,x8055)) % 167.77/167.51 [806]~E(x8061,x8062)+E(f756(x8063,x8064,x8061,x8065),f756(x8063,x8064,x8062,x8065)) % 167.77/167.51 [807]~E(x8071,x8072)+E(f756(x8073,x8074,x8075,x8071),f756(x8073,x8074,x8075,x8072)) % 167.77/167.51 [808]~E(x8081,x8082)+E(f290(x8081,x8083,x8084),f290(x8082,x8083,x8084)) % 167.77/167.51 [809]~E(x8091,x8092)+E(f290(x8093,x8091,x8094),f290(x8093,x8092,x8094)) % 167.77/167.51 [810]~E(x8101,x8102)+E(f290(x8103,x8104,x8101),f290(x8103,x8104,x8102)) % 167.77/167.51 [811]~E(x8111,x8112)+E(f864(x8111,x8113,x8114,x8115,x8116),f864(x8112,x8113,x8114,x8115,x8116)) % 167.77/167.51 [812]~E(x8121,x8122)+E(f864(x8123,x8121,x8124,x8125,x8126),f864(x8123,x8122,x8124,x8125,x8126)) % 167.77/167.51 [813]~E(x8131,x8132)+E(f864(x8133,x8134,x8131,x8135,x8136),f864(x8133,x8134,x8132,x8135,x8136)) % 167.77/167.51 [814]~E(x8141,x8142)+E(f864(x8143,x8144,x8145,x8141,x8146),f864(x8143,x8144,x8145,x8142,x8146)) % 167.77/167.51 [815]~E(x8151,x8152)+E(f864(x8153,x8154,x8155,x8156,x8151),f864(x8153,x8154,x8155,x8156,x8152)) % 167.77/167.51 [816]~E(x8161,x8162)+E(f813(x8161,x8163,x8164),f813(x8162,x8163,x8164)) % 167.77/167.51 [817]~E(x8171,x8172)+E(f813(x8173,x8171,x8174),f813(x8173,x8172,x8174)) % 167.77/167.51 [818]~E(x8181,x8182)+E(f813(x8183,x8184,x8181),f813(x8183,x8184,x8182)) % 167.77/167.51 [819]~E(x8191,x8192)+E(f405(x8191,x8193,x8194,x8195),f405(x8192,x8193,x8194,x8195)) % 167.77/167.51 [820]~E(x8201,x8202)+E(f405(x8203,x8201,x8204,x8205),f405(x8203,x8202,x8204,x8205)) % 167.77/167.51 [821]~E(x8211,x8212)+E(f405(x8213,x8214,x8211,x8215),f405(x8213,x8214,x8212,x8215)) % 167.77/167.51 [822]~E(x8221,x8222)+E(f405(x8223,x8224,x8225,x8221),f405(x8223,x8224,x8225,x8222)) % 167.77/167.51 [823]~E(x8231,x8232)+E(f758(x8231,x8233),f758(x8232,x8233)) % 167.77/167.51 [824]~E(x8241,x8242)+E(f758(x8243,x8241),f758(x8243,x8242)) % 167.77/167.51 [825]~E(x8251,x8252)+E(f255(x8251,x8253,x8254),f255(x8252,x8253,x8254)) % 167.77/167.51 [826]~E(x8261,x8262)+E(f255(x8263,x8261,x8264),f255(x8263,x8262,x8264)) % 167.77/167.51 [827]~E(x8271,x8272)+E(f255(x8273,x8274,x8271),f255(x8273,x8274,x8272)) % 167.77/167.51 [828]~E(x8281,x8282)+E(f576(x8281,x8283,x8284,x8285,x8286,x8287,x8288,x8289),f576(x8282,x8283,x8284,x8285,x8286,x8287,x8288,x8289)) % 167.77/167.51 [829]~E(x8291,x8292)+E(f576(x8293,x8291,x8294,x8295,x8296,x8297,x8298,x8299),f576(x8293,x8292,x8294,x8295,x8296,x8297,x8298,x8299)) % 167.77/167.51 [830]~E(x8301,x8302)+E(f576(x8303,x8304,x8301,x8305,x8306,x8307,x8308,x8309),f576(x8303,x8304,x8302,x8305,x8306,x8307,x8308,x8309)) % 167.77/167.51 [831]~E(x8311,x8312)+E(f576(x8313,x8314,x8315,x8311,x8316,x8317,x8318,x8319),f576(x8313,x8314,x8315,x8312,x8316,x8317,x8318,x8319)) % 167.77/167.51 [832]~E(x8321,x8322)+E(f576(x8323,x8324,x8325,x8326,x8321,x8327,x8328,x8329),f576(x8323,x8324,x8325,x8326,x8322,x8327,x8328,x8329)) % 167.77/167.51 [833]~E(x8331,x8332)+E(f576(x8333,x8334,x8335,x8336,x8337,x8331,x8338,x8339),f576(x8333,x8334,x8335,x8336,x8337,x8332,x8338,x8339)) % 167.77/167.51 [834]~E(x8341,x8342)+E(f576(x8343,x8344,x8345,x8346,x8347,x8348,x8341,x8349),f576(x8343,x8344,x8345,x8346,x8347,x8348,x8342,x8349)) % 167.77/167.51 [835]~E(x8351,x8352)+E(f576(x8353,x8354,x8355,x8356,x8357,x8358,x8359,x8351),f576(x8353,x8354,x8355,x8356,x8357,x8358,x8359,x8352)) % 167.77/167.51 [836]~E(x8361,x8362)+E(f202(x8361,x8363,x8364,x8365),f202(x8362,x8363,x8364,x8365)) % 167.77/167.51 [837]~E(x8371,x8372)+E(f202(x8373,x8371,x8374,x8375),f202(x8373,x8372,x8374,x8375)) % 167.77/167.51 [838]~E(x8381,x8382)+E(f202(x8383,x8384,x8381,x8385),f202(x8383,x8384,x8382,x8385)) % 167.77/167.51 [839]~E(x8391,x8392)+E(f202(x8393,x8394,x8395,x8391),f202(x8393,x8394,x8395,x8392)) % 167.77/167.51 [840]~E(x8401,x8402)+E(f172(x8401,x8403,x8404),f172(x8402,x8403,x8404)) % 167.77/167.51 [841]~E(x8411,x8412)+E(f172(x8413,x8411,x8414),f172(x8413,x8412,x8414)) % 167.77/167.51 [842]~E(x8421,x8422)+E(f172(x8423,x8424,x8421),f172(x8423,x8424,x8422)) % 167.77/167.51 [843]~E(x8431,x8432)+E(f367(x8431,x8433),f367(x8432,x8433)) % 167.77/167.51 [844]~E(x8441,x8442)+E(f367(x8443,x8441),f367(x8443,x8442)) % 167.77/167.51 [845]~E(x8451,x8452)+E(f510(x8451,x8453,x8454),f510(x8452,x8453,x8454)) % 167.77/167.51 [846]~E(x8461,x8462)+E(f510(x8463,x8461,x8464),f510(x8463,x8462,x8464)) % 167.77/167.51 [847]~E(x8471,x8472)+E(f510(x8473,x8474,x8471),f510(x8473,x8474,x8472)) % 167.77/167.51 [848]~E(x8481,x8482)+E(f613(x8481,x8483,x8484,x8485),f613(x8482,x8483,x8484,x8485)) % 167.77/167.51 [849]~E(x8491,x8492)+E(f613(x8493,x8491,x8494,x8495),f613(x8493,x8492,x8494,x8495)) % 167.77/167.51 [850]~E(x8501,x8502)+E(f613(x8503,x8504,x8501,x8505),f613(x8503,x8504,x8502,x8505)) % 167.77/167.51 [851]~E(x8511,x8512)+E(f613(x8513,x8514,x8515,x8511),f613(x8513,x8514,x8515,x8512)) % 167.77/167.52 [852]~E(x8521,x8522)+E(f159(x8521,x8523),f159(x8522,x8523)) % 167.77/167.52 [853]~E(x8531,x8532)+E(f159(x8533,x8531),f159(x8533,x8532)) % 167.77/167.52 [854]~E(x8541,x8542)+E(f726(x8541,x8543),f726(x8542,x8543)) % 167.77/167.52 [855]~E(x8551,x8552)+E(f726(x8553,x8551),f726(x8553,x8552)) % 167.77/167.52 [856]~E(x8561,x8562)+E(f559(x8561,x8563),f559(x8562,x8563)) % 167.77/167.52 [857]~E(x8571,x8572)+E(f559(x8573,x8571),f559(x8573,x8572)) % 167.77/167.52 [858]~E(x8581,x8582)+E(f573(x8581,x8583),f573(x8582,x8583)) % 167.77/167.52 [859]~E(x8591,x8592)+E(f573(x8593,x8591),f573(x8593,x8592)) % 167.77/167.52 [860]~E(x8601,x8602)+E(f668(x8601,x8603,x8604,x8605,x8606),f668(x8602,x8603,x8604,x8605,x8606)) % 167.77/167.52 [861]~E(x8611,x8612)+E(f668(x8613,x8611,x8614,x8615,x8616),f668(x8613,x8612,x8614,x8615,x8616)) % 167.77/167.52 [862]~E(x8621,x8622)+E(f668(x8623,x8624,x8621,x8625,x8626),f668(x8623,x8624,x8622,x8625,x8626)) % 167.77/167.52 [863]~E(x8631,x8632)+E(f668(x8633,x8634,x8635,x8631,x8636),f668(x8633,x8634,x8635,x8632,x8636)) % 167.77/167.52 [864]~E(x8641,x8642)+E(f668(x8643,x8644,x8645,x8646,x8641),f668(x8643,x8644,x8645,x8646,x8642)) % 167.77/167.52 [865]~E(x8651,x8652)+E(f272(x8651,x8653),f272(x8652,x8653)) % 167.77/167.52 [866]~E(x8661,x8662)+E(f272(x8663,x8661),f272(x8663,x8662)) % 167.77/167.52 [867]~E(x8671,x8672)+E(f636(x8671,x8673,x8674,x8675,x8676),f636(x8672,x8673,x8674,x8675,x8676)) % 167.77/167.52 [868]~E(x8681,x8682)+E(f636(x8683,x8681,x8684,x8685,x8686),f636(x8683,x8682,x8684,x8685,x8686)) % 167.77/167.52 [869]~E(x8691,x8692)+E(f636(x8693,x8694,x8691,x8695,x8696),f636(x8693,x8694,x8692,x8695,x8696)) % 167.77/167.52 [870]~E(x8701,x8702)+E(f636(x8703,x8704,x8705,x8701,x8706),f636(x8703,x8704,x8705,x8702,x8706)) % 167.77/167.52 [871]~E(x8711,x8712)+E(f636(x8713,x8714,x8715,x8716,x8711),f636(x8713,x8714,x8715,x8716,x8712)) % 167.77/167.52 [872]~E(x8721,x8722)+E(f595(x8721,x8723,x8724),f595(x8722,x8723,x8724)) % 167.77/167.52 [873]~E(x8731,x8732)+E(f595(x8733,x8731,x8734),f595(x8733,x8732,x8734)) % 167.77/167.52 [874]~E(x8741,x8742)+E(f595(x8743,x8744,x8741),f595(x8743,x8744,x8742)) % 167.77/167.52 [875]~E(x8751,x8752)+E(f122(x8751,x8753),f122(x8752,x8753)) % 167.77/167.52 [876]~E(x8761,x8762)+E(f122(x8763,x8761),f122(x8763,x8762)) % 167.77/167.52 [877]~E(x8771,x8772)+E(f765(x8771,x8773,x8774,x8775,x8776),f765(x8772,x8773,x8774,x8775,x8776)) % 167.77/167.52 [878]~E(x8781,x8782)+E(f765(x8783,x8781,x8784,x8785,x8786),f765(x8783,x8782,x8784,x8785,x8786)) % 167.77/167.52 [879]~E(x8791,x8792)+E(f765(x8793,x8794,x8791,x8795,x8796),f765(x8793,x8794,x8792,x8795,x8796)) % 167.77/167.52 [880]~E(x8801,x8802)+E(f765(x8803,x8804,x8805,x8801,x8806),f765(x8803,x8804,x8805,x8802,x8806)) % 167.77/167.52 [881]~E(x8811,x8812)+E(f765(x8813,x8814,x8815,x8816,x8811),f765(x8813,x8814,x8815,x8816,x8812)) % 167.77/167.52 [882]~E(x8821,x8822)+E(f120(x8821,x8823,x8824),f120(x8822,x8823,x8824)) % 167.77/167.52 [883]~E(x8831,x8832)+E(f120(x8833,x8831,x8834),f120(x8833,x8832,x8834)) % 167.77/167.52 [884]~E(x8841,x8842)+E(f120(x8843,x8844,x8841),f120(x8843,x8844,x8842)) % 167.77/167.52 [885]~E(x8851,x8852)+E(f356(x8851,x8853,x8854),f356(x8852,x8853,x8854)) % 167.77/167.52 [886]~E(x8861,x8862)+E(f356(x8863,x8861,x8864),f356(x8863,x8862,x8864)) % 167.77/167.52 [887]~E(x8871,x8872)+E(f356(x8873,x8874,x8871),f356(x8873,x8874,x8872)) % 167.77/167.52 [888]~E(x8881,x8882)+E(f416(x8881,x8883,x8884,x8885,x8886,x8887),f416(x8882,x8883,x8884,x8885,x8886,x8887)) % 167.77/167.52 [889]~E(x8891,x8892)+E(f416(x8893,x8891,x8894,x8895,x8896,x8897),f416(x8893,x8892,x8894,x8895,x8896,x8897)) % 167.77/167.52 [890]~E(x8901,x8902)+E(f416(x8903,x8904,x8901,x8905,x8906,x8907),f416(x8903,x8904,x8902,x8905,x8906,x8907)) % 167.77/167.52 [891]~E(x8911,x8912)+E(f416(x8913,x8914,x8915,x8911,x8916,x8917),f416(x8913,x8914,x8915,x8912,x8916,x8917)) % 167.77/167.52 [892]~E(x8921,x8922)+E(f416(x8923,x8924,x8925,x8926,x8921,x8927),f416(x8923,x8924,x8925,x8926,x8922,x8927)) % 167.77/167.52 [893]~E(x8931,x8932)+E(f416(x8933,x8934,x8935,x8936,x8937,x8931),f416(x8933,x8934,x8935,x8936,x8937,x8932)) % 167.77/167.52 [894]~E(x8941,x8942)+E(f574(x8941,x8943,x8944),f574(x8942,x8943,x8944)) % 167.77/167.52 [895]~E(x8951,x8952)+E(f574(x8953,x8951,x8954),f574(x8953,x8952,x8954)) % 167.77/167.52 [896]~E(x8961,x8962)+E(f574(x8963,x8964,x8961),f574(x8963,x8964,x8962)) % 167.77/167.52 [897]~E(x8971,x8972)+E(f823(x8971,x8973,x8974,x8975),f823(x8972,x8973,x8974,x8975)) % 167.77/167.52 [898]~E(x8981,x8982)+E(f823(x8983,x8981,x8984,x8985),f823(x8983,x8982,x8984,x8985)) % 167.77/167.52 [899]~E(x8991,x8992)+E(f823(x8993,x8994,x8991,x8995),f823(x8993,x8994,x8992,x8995)) % 167.77/167.52 [900]~E(x9001,x9002)+E(f823(x9003,x9004,x9005,x9001),f823(x9003,x9004,x9005,x9002)) % 167.77/167.52 [901]~E(x9011,x9012)+E(f808(x9011,x9013,x9014),f808(x9012,x9013,x9014)) % 167.77/167.52 [902]~E(x9021,x9022)+E(f808(x9023,x9021,x9024),f808(x9023,x9022,x9024)) % 167.77/167.52 [903]~E(x9031,x9032)+E(f808(x9033,x9034,x9031),f808(x9033,x9034,x9032)) % 167.77/167.52 [904]~E(x9041,x9042)+E(f349(x9041,x9043,x9044),f349(x9042,x9043,x9044)) % 167.77/167.52 [905]~E(x9051,x9052)+E(f349(x9053,x9051,x9054),f349(x9053,x9052,x9054)) % 167.77/167.52 [906]~E(x9061,x9062)+E(f349(x9063,x9064,x9061),f349(x9063,x9064,x9062)) % 167.77/167.52 [907]~E(x9071,x9072)+E(f854(x9071,x9073,x9074,x9075),f854(x9072,x9073,x9074,x9075)) % 167.77/167.52 [908]~E(x9081,x9082)+E(f854(x9083,x9081,x9084,x9085),f854(x9083,x9082,x9084,x9085)) % 167.77/167.52 [909]~E(x9091,x9092)+E(f854(x9093,x9094,x9091,x9095),f854(x9093,x9094,x9092,x9095)) % 167.77/167.52 [910]~E(x9101,x9102)+E(f854(x9103,x9104,x9105,x9101),f854(x9103,x9104,x9105,x9102)) % 167.77/167.52 [911]~E(x9111,x9112)+E(f766(x9111,x9113,x9114,x9115,x9116,x9117),f766(x9112,x9113,x9114,x9115,x9116,x9117)) % 167.77/167.52 [912]~E(x9121,x9122)+E(f766(x9123,x9121,x9124,x9125,x9126,x9127),f766(x9123,x9122,x9124,x9125,x9126,x9127)) % 167.77/167.52 [913]~E(x9131,x9132)+E(f766(x9133,x9134,x9131,x9135,x9136,x9137),f766(x9133,x9134,x9132,x9135,x9136,x9137)) % 167.77/167.52 [914]~E(x9141,x9142)+E(f766(x9143,x9144,x9145,x9141,x9146,x9147),f766(x9143,x9144,x9145,x9142,x9146,x9147)) % 167.77/167.52 [915]~E(x9151,x9152)+E(f766(x9153,x9154,x9155,x9156,x9151,x9157),f766(x9153,x9154,x9155,x9156,x9152,x9157)) % 167.77/167.52 [916]~E(x9161,x9162)+E(f766(x9163,x9164,x9165,x9166,x9167,x9161),f766(x9163,x9164,x9165,x9166,x9167,x9162)) % 167.77/167.52 [917]~E(x9171,x9172)+E(f160(x9171,x9173,x9174,x9175),f160(x9172,x9173,x9174,x9175)) % 167.77/167.52 [918]~E(x9181,x9182)+E(f160(x9183,x9181,x9184,x9185),f160(x9183,x9182,x9184,x9185)) % 167.77/167.52 [919]~E(x9191,x9192)+E(f160(x9193,x9194,x9191,x9195),f160(x9193,x9194,x9192,x9195)) % 167.77/167.52 [920]~E(x9201,x9202)+E(f160(x9203,x9204,x9205,x9201),f160(x9203,x9204,x9205,x9202)) % 167.77/167.52 [921]~E(x9211,x9212)+E(f269(x9211,x9213,x9214,x9215),f269(x9212,x9213,x9214,x9215)) % 167.77/167.52 [922]~E(x9221,x9222)+E(f269(x9223,x9221,x9224,x9225),f269(x9223,x9222,x9224,x9225)) % 167.77/167.52 [923]~E(x9231,x9232)+E(f269(x9233,x9234,x9231,x9235),f269(x9233,x9234,x9232,x9235)) % 167.77/167.52 [924]~E(x9241,x9242)+E(f269(x9243,x9244,x9245,x9241),f269(x9243,x9244,x9245,x9242)) % 167.77/167.52 [925]~E(x9251,x9252)+E(f271(x9251,x9253,x9254,x9255,x9256),f271(x9252,x9253,x9254,x9255,x9256)) % 167.77/167.52 [926]~E(x9261,x9262)+E(f271(x9263,x9261,x9264,x9265,x9266),f271(x9263,x9262,x9264,x9265,x9266)) % 167.77/167.52 [927]~E(x9271,x9272)+E(f271(x9273,x9274,x9271,x9275,x9276),f271(x9273,x9274,x9272,x9275,x9276)) % 167.77/167.52 [928]~E(x9281,x9282)+E(f271(x9283,x9284,x9285,x9281,x9286),f271(x9283,x9284,x9285,x9282,x9286)) % 167.77/167.52 [929]~E(x9291,x9292)+E(f271(x9293,x9294,x9295,x9296,x9291),f271(x9293,x9294,x9295,x9296,x9292)) % 167.77/167.52 [930]~E(x9301,x9302)+E(f606(x9301,x9303,x9304,x9305,x9306,x9307,x9308,x9309),f606(x9302,x9303,x9304,x9305,x9306,x9307,x9308,x9309)) % 167.77/167.52 [931]~E(x9311,x9312)+E(f606(x9313,x9311,x9314,x9315,x9316,x9317,x9318,x9319),f606(x9313,x9312,x9314,x9315,x9316,x9317,x9318,x9319)) % 167.77/167.52 [932]~E(x9321,x9322)+E(f606(x9323,x9324,x9321,x9325,x9326,x9327,x9328,x9329),f606(x9323,x9324,x9322,x9325,x9326,x9327,x9328,x9329)) % 167.77/167.52 [933]~E(x9331,x9332)+E(f606(x9333,x9334,x9335,x9331,x9336,x9337,x9338,x9339),f606(x9333,x9334,x9335,x9332,x9336,x9337,x9338,x9339)) % 167.77/167.52 [934]~E(x9341,x9342)+E(f606(x9343,x9344,x9345,x9346,x9341,x9347,x9348,x9349),f606(x9343,x9344,x9345,x9346,x9342,x9347,x9348,x9349)) % 167.77/167.52 [935]~E(x9351,x9352)+E(f606(x9353,x9354,x9355,x9356,x9357,x9351,x9358,x9359),f606(x9353,x9354,x9355,x9356,x9357,x9352,x9358,x9359)) % 167.77/167.52 [936]~E(x9361,x9362)+E(f606(x9363,x9364,x9365,x9366,x9367,x9368,x9361,x9369),f606(x9363,x9364,x9365,x9366,x9367,x9368,x9362,x9369)) % 167.77/167.52 [937]~E(x9371,x9372)+E(f606(x9373,x9374,x9375,x9376,x9377,x9378,x9379,x9371),f606(x9373,x9374,x9375,x9376,x9377,x9378,x9379,x9372)) % 167.77/167.52 [938]~E(x9381,x9382)+E(f605(x9381,x9383,x9384,x9385,x9386,x9387),f605(x9382,x9383,x9384,x9385,x9386,x9387)) % 167.77/167.52 [939]~E(x9391,x9392)+E(f605(x9393,x9391,x9394,x9395,x9396,x9397),f605(x9393,x9392,x9394,x9395,x9396,x9397)) % 167.77/167.52 [940]~E(x9401,x9402)+E(f605(x9403,x9404,x9401,x9405,x9406,x9407),f605(x9403,x9404,x9402,x9405,x9406,x9407)) % 167.77/167.52 [941]~E(x9411,x9412)+E(f605(x9413,x9414,x9415,x9411,x9416,x9417),f605(x9413,x9414,x9415,x9412,x9416,x9417)) % 167.77/167.52 [942]~E(x9421,x9422)+E(f605(x9423,x9424,x9425,x9426,x9421,x9427),f605(x9423,x9424,x9425,x9426,x9422,x9427)) % 167.77/167.52 [943]~E(x9431,x9432)+E(f605(x9433,x9434,x9435,x9436,x9437,x9431),f605(x9433,x9434,x9435,x9436,x9437,x9432)) % 167.77/167.52 [944]~E(x9441,x9442)+E(f757(x9441,x9443,x9444,x9445),f757(x9442,x9443,x9444,x9445)) % 167.77/167.52 [945]~E(x9451,x9452)+E(f757(x9453,x9451,x9454,x9455),f757(x9453,x9452,x9454,x9455)) % 167.77/167.52 [946]~E(x9461,x9462)+E(f757(x9463,x9464,x9461,x9465),f757(x9463,x9464,x9462,x9465)) % 167.77/167.52 [947]~E(x9471,x9472)+E(f757(x9473,x9474,x9475,x9471),f757(x9473,x9474,x9475,x9472)) % 167.77/167.52 [948]~E(x9481,x9482)+E(f74(x9481,x9483),f74(x9482,x9483)) % 167.77/167.52 [949]~E(x9491,x9492)+E(f74(x9493,x9491),f74(x9493,x9492)) % 167.77/167.52 [950]~E(x9501,x9502)+E(f291(x9501,x9503,x9504),f291(x9502,x9503,x9504)) % 167.77/167.52 [951]~E(x9511,x9512)+E(f291(x9513,x9511,x9514),f291(x9513,x9512,x9514)) % 167.77/167.52 [952]~E(x9521,x9522)+E(f291(x9523,x9524,x9521),f291(x9523,x9524,x9522)) % 167.77/167.52 [953]~E(x9531,x9532)+E(f865(x9531,x9533,x9534,x9535,x9536),f865(x9532,x9533,x9534,x9535,x9536)) % 167.77/167.52 [954]~E(x9541,x9542)+E(f865(x9543,x9541,x9544,x9545,x9546),f865(x9543,x9542,x9544,x9545,x9546)) % 167.77/167.52 [955]~E(x9551,x9552)+E(f865(x9553,x9554,x9551,x9555,x9556),f865(x9553,x9554,x9552,x9555,x9556)) % 167.77/167.52 [956]~E(x9561,x9562)+E(f865(x9563,x9564,x9565,x9561,x9566),f865(x9563,x9564,x9565,x9562,x9566)) % 167.77/167.52 [957]~E(x9571,x9572)+E(f865(x9573,x9574,x9575,x9576,x9571),f865(x9573,x9574,x9575,x9576,x9572)) % 167.77/167.52 [958]~E(x9581,x9582)+E(f866(x9581,x9583,x9584,x9585,x9586),f866(x9582,x9583,x9584,x9585,x9586)) % 167.77/167.52 [959]~E(x9591,x9592)+E(f866(x9593,x9591,x9594,x9595,x9596),f866(x9593,x9592,x9594,x9595,x9596)) % 167.77/167.52 [960]~E(x9601,x9602)+E(f866(x9603,x9604,x9601,x9605,x9606),f866(x9603,x9604,x9602,x9605,x9606)) % 167.77/167.52 [961]~E(x9611,x9612)+E(f866(x9613,x9614,x9615,x9611,x9616),f866(x9613,x9614,x9615,x9612,x9616)) % 167.77/167.52 [962]~E(x9621,x9622)+E(f866(x9623,x9624,x9625,x9626,x9621),f866(x9623,x9624,x9625,x9626,x9622)) % 167.77/167.52 [963]~E(x9631,x9632)+E(f669(x9631,x9633,x9634,x9635,x9636),f669(x9632,x9633,x9634,x9635,x9636)) % 167.77/167.52 [964]~E(x9641,x9642)+E(f669(x9643,x9641,x9644,x9645,x9646),f669(x9643,x9642,x9644,x9645,x9646)) % 167.77/167.52 [965]~E(x9651,x9652)+E(f669(x9653,x9654,x9651,x9655,x9656),f669(x9653,x9654,x9652,x9655,x9656)) % 167.77/167.52 [966]~E(x9661,x9662)+E(f669(x9663,x9664,x9665,x9661,x9666),f669(x9663,x9664,x9665,x9662,x9666)) % 167.77/167.52 [967]~E(x9671,x9672)+E(f669(x9673,x9674,x9675,x9676,x9671),f669(x9673,x9674,x9675,x9676,x9672)) % 167.77/167.52 [968]~E(x9681,x9682)+E(f750(x9681,x9683,x9684),f750(x9682,x9683,x9684)) % 167.77/167.52 [969]~E(x9691,x9692)+E(f750(x9693,x9691,x9694),f750(x9693,x9692,x9694)) % 167.77/167.52 [970]~E(x9701,x9702)+E(f750(x9703,x9704,x9701),f750(x9703,x9704,x9702)) % 167.77/167.52 [971]~E(x9711,x9712)+E(f68(x9711,x9713,x9714),f68(x9712,x9713,x9714)) % 167.77/167.52 [972]~E(x9721,x9722)+E(f68(x9723,x9721,x9724),f68(x9723,x9722,x9724)) % 167.77/167.52 [973]~E(x9731,x9732)+E(f68(x9733,x9734,x9731),f68(x9733,x9734,x9732)) % 167.77/167.52 [974]~E(x9741,x9742)+E(f657(x9741,x9743,x9744,x9745),f657(x9742,x9743,x9744,x9745)) % 167.77/167.52 [975]~E(x9751,x9752)+E(f657(x9753,x9751,x9754,x9755),f657(x9753,x9752,x9754,x9755)) % 167.77/167.52 [976]~E(x9761,x9762)+E(f657(x9763,x9764,x9761,x9765),f657(x9763,x9764,x9762,x9765)) % 167.77/167.52 [977]~E(x9771,x9772)+E(f657(x9773,x9774,x9775,x9771),f657(x9773,x9774,x9775,x9772)) % 167.77/167.52 [978]~E(x9781,x9782)+E(f687(x9781,x9783,x9784),f687(x9782,x9783,x9784)) % 167.77/167.52 [979]~E(x9791,x9792)+E(f687(x9793,x9791,x9794),f687(x9793,x9792,x9794)) % 167.77/167.52 [980]~E(x9801,x9802)+E(f687(x9803,x9804,x9801),f687(x9803,x9804,x9802)) % 167.77/167.52 [981]~E(x9811,x9812)+E(f851(x9811,x9813,x9814),f851(x9812,x9813,x9814)) % 167.77/167.52 [982]~E(x9821,x9822)+E(f851(x9823,x9821,x9824),f851(x9823,x9822,x9824)) % 167.77/167.52 [983]~E(x9831,x9832)+E(f851(x9833,x9834,x9831),f851(x9833,x9834,x9832)) % 167.77/167.52 [984]~E(x9841,x9842)+E(f696(x9841,x9843,x9844,x9845,x9846),f696(x9842,x9843,x9844,x9845,x9846)) % 167.77/167.52 [985]~E(x9851,x9852)+E(f696(x9853,x9851,x9854,x9855,x9856),f696(x9853,x9852,x9854,x9855,x9856)) % 167.77/167.52 [986]~E(x9861,x9862)+E(f696(x9863,x9864,x9861,x9865,x9866),f696(x9863,x9864,x9862,x9865,x9866)) % 167.77/167.52 [987]~E(x9871,x9872)+E(f696(x9873,x9874,x9875,x9871,x9876),f696(x9873,x9874,x9875,x9872,x9876)) % 167.77/167.52 [988]~E(x9881,x9882)+E(f696(x9883,x9884,x9885,x9886,x9881),f696(x9883,x9884,x9885,x9886,x9882)) % 167.77/167.52 [989]~E(x9891,x9892)+E(f654(x9891,x9893,x9894),f654(x9892,x9893,x9894)) % 167.77/167.52 [990]~E(x9901,x9902)+E(f654(x9903,x9901,x9904),f654(x9903,x9902,x9904)) % 167.77/167.52 [991]~E(x9911,x9912)+E(f654(x9913,x9914,x9911),f654(x9913,x9914,x9912)) % 167.77/167.52 [992]~E(x9921,x9922)+E(f837(x9921,x9923,x9924),f837(x9922,x9923,x9924)) % 167.77/167.52 [993]~E(x9931,x9932)+E(f837(x9933,x9931,x9934),f837(x9933,x9932,x9934)) % 167.77/167.52 [994]~E(x9941,x9942)+E(f837(x9943,x9944,x9941),f837(x9943,x9944,x9942)) % 167.77/167.52 [995]~E(x9951,x9952)+E(f737(x9951,x9953),f737(x9952,x9953)) % 167.77/167.52 [996]~E(x9961,x9962)+E(f737(x9963,x9961),f737(x9963,x9962)) % 167.77/167.52 [997]~E(x9971,x9972)+E(f459(x9971,x9973,x9974,x9975,x9976),f459(x9972,x9973,x9974,x9975,x9976)) % 167.77/167.52 [998]~E(x9981,x9982)+E(f459(x9983,x9981,x9984,x9985,x9986),f459(x9983,x9982,x9984,x9985,x9986)) % 167.77/167.52 [999]~E(x9991,x9992)+E(f459(x9993,x9994,x9991,x9995,x9996),f459(x9993,x9994,x9992,x9995,x9996)) % 167.77/167.52 [1000]~E(x10001,x10002)+E(f459(x10003,x10004,x10005,x10001,x10006),f459(x10003,x10004,x10005,x10002,x10006)) % 167.77/167.52 [1001]~E(x10011,x10012)+E(f459(x10013,x10014,x10015,x10016,x10011),f459(x10013,x10014,x10015,x10016,x10012)) % 167.77/167.52 [1002]~E(x10021,x10022)+E(f724(x10021,x10023,x10024,x10025),f724(x10022,x10023,x10024,x10025)) % 167.77/167.52 [1003]~E(x10031,x10032)+E(f724(x10033,x10031,x10034,x10035),f724(x10033,x10032,x10034,x10035)) % 167.77/167.52 [1004]~E(x10041,x10042)+E(f724(x10043,x10044,x10041,x10045),f724(x10043,x10044,x10042,x10045)) % 167.77/167.52 [1005]~E(x10051,x10052)+E(f724(x10053,x10054,x10055,x10051),f724(x10053,x10054,x10055,x10052)) % 167.77/167.52 [1006]~E(x10061,x10062)+E(f547(x10061,x10063,x10064,x10065),f547(x10062,x10063,x10064,x10065)) % 167.77/167.52 [1007]~E(x10071,x10072)+E(f547(x10073,x10071,x10074,x10075),f547(x10073,x10072,x10074,x10075)) % 167.77/167.52 [1008]~E(x10081,x10082)+E(f547(x10083,x10084,x10081,x10085),f547(x10083,x10084,x10082,x10085)) % 167.77/167.52 [1009]~E(x10091,x10092)+E(f547(x10093,x10094,x10095,x10091),f547(x10093,x10094,x10095,x10092)) % 167.77/167.52 [1010]~E(x10101,x10102)+E(f832(x10101,x10103,x10104),f832(x10102,x10103,x10104)) % 167.77/167.52 [1011]~E(x10111,x10112)+E(f832(x10113,x10111,x10114),f832(x10113,x10112,x10114)) % 167.77/167.52 [1012]~E(x10121,x10122)+E(f832(x10123,x10124,x10121),f832(x10123,x10124,x10122)) % 167.77/167.52 [1013]~E(x10131,x10132)+E(f693(x10131,x10133,x10134,x10135,x10136),f693(x10132,x10133,x10134,x10135,x10136)) % 167.77/167.52 [1014]~E(x10141,x10142)+E(f693(x10143,x10141,x10144,x10145,x10146),f693(x10143,x10142,x10144,x10145,x10146)) % 167.77/167.52 [1015]~E(x10151,x10152)+E(f693(x10153,x10154,x10151,x10155,x10156),f693(x10153,x10154,x10152,x10155,x10156)) % 167.77/167.52 [1016]~E(x10161,x10162)+E(f693(x10163,x10164,x10165,x10161,x10166),f693(x10163,x10164,x10165,x10162,x10166)) % 167.77/167.52 [1017]~E(x10171,x10172)+E(f693(x10173,x10174,x10175,x10176,x10171),f693(x10173,x10174,x10175,x10176,x10172)) % 167.77/167.52 [1018]~E(x10181,x10182)+E(f161(x10181,x10183,x10184,x10185),f161(x10182,x10183,x10184,x10185)) % 167.77/167.52 [1019]~E(x10191,x10192)+E(f161(x10193,x10191,x10194,x10195),f161(x10193,x10192,x10194,x10195)) % 167.77/167.52 [1020]~E(x10201,x10202)+E(f161(x10203,x10204,x10201,x10205),f161(x10203,x10204,x10202,x10205)) % 167.77/167.52 [1021]~E(x10211,x10212)+E(f161(x10213,x10214,x10215,x10211),f161(x10213,x10214,x10215,x10212)) % 167.77/167.52 [1022]~E(x10221,x10222)+E(f400(x10221,x10223,x10224),f400(x10222,x10223,x10224)) % 167.77/167.52 [1023]~E(x10231,x10232)+E(f400(x10233,x10231,x10234),f400(x10233,x10232,x10234)) % 167.77/167.52 [1024]~E(x10241,x10242)+E(f400(x10243,x10244,x10241),f400(x10243,x10244,x10242)) % 167.77/167.52 [1025]~E(x10251,x10252)+E(f769(x10251,x10253,x10254,x10255,x10256),f769(x10252,x10253,x10254,x10255,x10256)) % 167.77/167.52 [1026]~E(x10261,x10262)+E(f769(x10263,x10261,x10264,x10265,x10266),f769(x10263,x10262,x10264,x10265,x10266)) % 167.77/167.52 [1027]~E(x10271,x10272)+E(f769(x10273,x10274,x10271,x10275,x10276),f769(x10273,x10274,x10272,x10275,x10276)) % 167.77/167.52 [1028]~E(x10281,x10282)+E(f769(x10283,x10284,x10285,x10281,x10286),f769(x10283,x10284,x10285,x10282,x10286)) % 167.77/167.52 [1029]~E(x10291,x10292)+E(f769(x10293,x10294,x10295,x10296,x10291),f769(x10293,x10294,x10295,x10296,x10292)) % 167.77/167.52 [1030]~E(x10301,x10302)+E(f345(x10301,x10303),f345(x10302,x10303)) % 167.77/167.52 [1031]~E(x10311,x10312)+E(f345(x10313,x10311),f345(x10313,x10312)) % 167.77/167.52 [1032]~E(x10321,x10322)+E(f836(x10321,x10323,x10324),f836(x10322,x10323,x10324)) % 167.77/167.52 [1033]~E(x10331,x10332)+E(f836(x10333,x10331,x10334),f836(x10333,x10332,x10334)) % 167.77/167.52 [1034]~E(x10341,x10342)+E(f836(x10343,x10344,x10341),f836(x10343,x10344,x10342)) % 167.77/167.52 [1035]~E(x10351,x10352)+E(f437(x10351,x10353,x10354,x10355,x10356),f437(x10352,x10353,x10354,x10355,x10356)) % 167.77/167.52 [1036]~E(x10361,x10362)+E(f437(x10363,x10361,x10364,x10365,x10366),f437(x10363,x10362,x10364,x10365,x10366)) % 167.77/167.52 [1037]~E(x10371,x10372)+E(f437(x10373,x10374,x10371,x10375,x10376),f437(x10373,x10374,x10372,x10375,x10376)) % 167.77/167.52 [1038]~E(x10381,x10382)+E(f437(x10383,x10384,x10385,x10381,x10386),f437(x10383,x10384,x10385,x10382,x10386)) % 167.77/167.52 [1039]~E(x10391,x10392)+E(f437(x10393,x10394,x10395,x10396,x10391),f437(x10393,x10394,x10395,x10396,x10392)) % 167.77/167.52 [1040]~E(x10401,x10402)+E(f809(x10401,x10403,x10404,x10405),f809(x10402,x10403,x10404,x10405)) % 167.77/167.52 [1041]~E(x10411,x10412)+E(f809(x10413,x10411,x10414,x10415),f809(x10413,x10412,x10414,x10415)) % 167.77/167.52 [1042]~E(x10421,x10422)+E(f809(x10423,x10424,x10421,x10425),f809(x10423,x10424,x10422,x10425)) % 167.77/167.52 [1043]~E(x10431,x10432)+E(f809(x10433,x10434,x10435,x10431),f809(x10433,x10434,x10435,x10432)) % 167.77/167.52 [1044]~E(x10441,x10442)+E(f479(x10441,x10443,x10444),f479(x10442,x10443,x10444)) % 167.77/167.52 [1045]~E(x10451,x10452)+E(f479(x10453,x10451,x10454),f479(x10453,x10452,x10454)) % 167.77/167.52 [1046]~E(x10461,x10462)+E(f479(x10463,x10464,x10461),f479(x10463,x10464,x10462)) % 167.77/167.52 [1047]~E(x10471,x10472)+E(f428(x10471,x10473,x10474,x10475),f428(x10472,x10473,x10474,x10475)) % 167.77/167.52 [1048]~E(x10481,x10482)+E(f428(x10483,x10481,x10484,x10485),f428(x10483,x10482,x10484,x10485)) % 167.77/167.52 [1049]~E(x10491,x10492)+E(f428(x10493,x10494,x10491,x10495),f428(x10493,x10494,x10492,x10495)) % 167.77/167.52 [1050]~E(x10501,x10502)+E(f428(x10503,x10504,x10505,x10501),f428(x10503,x10504,x10505,x10502)) % 167.77/167.52 [1051]~E(x10511,x10512)+E(f747(x10511,x10513,x10514),f747(x10512,x10513,x10514)) % 167.77/167.52 [1052]~E(x10521,x10522)+E(f747(x10523,x10521,x10524),f747(x10523,x10522,x10524)) % 167.77/167.52 [1053]~E(x10531,x10532)+E(f747(x10533,x10534,x10531),f747(x10533,x10534,x10532)) % 167.77/167.52 [1054]~E(x10541,x10542)+E(f61(x10541,x10543,x10544,x10545),f61(x10542,x10543,x10544,x10545)) % 167.77/167.52 [1055]~E(x10551,x10552)+E(f61(x10553,x10551,x10554,x10555),f61(x10553,x10552,x10554,x10555)) % 167.77/167.52 [1056]~E(x10561,x10562)+E(f61(x10563,x10564,x10561,x10565),f61(x10563,x10564,x10562,x10565)) % 167.77/167.52 [1057]~E(x10571,x10572)+E(f61(x10573,x10574,x10575,x10571),f61(x10573,x10574,x10575,x10572)) % 167.77/167.52 [1058]~E(x10581,x10582)+E(f526(x10581,x10583,x10584,x10585,x10586),f526(x10582,x10583,x10584,x10585,x10586)) % 167.77/167.52 [1059]~E(x10591,x10592)+E(f526(x10593,x10591,x10594,x10595,x10596),f526(x10593,x10592,x10594,x10595,x10596)) % 167.77/167.52 [1060]~E(x10601,x10602)+E(f526(x10603,x10604,x10601,x10605,x10606),f526(x10603,x10604,x10602,x10605,x10606)) % 167.77/167.52 [1061]~E(x10611,x10612)+E(f526(x10613,x10614,x10615,x10611,x10616),f526(x10613,x10614,x10615,x10612,x10616)) % 167.77/167.52 [1062]~E(x10621,x10622)+E(f526(x10623,x10624,x10625,x10626,x10621),f526(x10623,x10624,x10625,x10626,x10622)) % 167.77/167.52 [1063]~E(x10631,x10632)+E(f131(x10631,x10633,x10634,x10635),f131(x10632,x10633,x10634,x10635)) % 167.77/167.52 [1064]~E(x10641,x10642)+E(f131(x10643,x10641,x10644,x10645),f131(x10643,x10642,x10644,x10645)) % 167.77/167.52 [1065]~E(x10651,x10652)+E(f131(x10653,x10654,x10651,x10655),f131(x10653,x10654,x10652,x10655)) % 167.77/167.52 [1066]~E(x10661,x10662)+E(f131(x10663,x10664,x10665,x10661),f131(x10663,x10664,x10665,x10662)) % 167.77/167.52 [1067]~E(x10671,x10672)+E(f625(x10671,x10673,x10674),f625(x10672,x10673,x10674)) % 167.77/167.52 [1068]~E(x10681,x10682)+E(f625(x10683,x10681,x10684),f625(x10683,x10682,x10684)) % 167.77/167.52 [1069]~E(x10691,x10692)+E(f625(x10693,x10694,x10691),f625(x10693,x10694,x10692)) % 167.77/167.52 [1070]~E(x10701,x10702)+E(f426(x10701,x10703,x10704,x10705,x10706,x10707),f426(x10702,x10703,x10704,x10705,x10706,x10707)) % 167.77/167.52 [1071]~E(x10711,x10712)+E(f426(x10713,x10711,x10714,x10715,x10716,x10717),f426(x10713,x10712,x10714,x10715,x10716,x10717)) % 167.77/167.52 [1072]~E(x10721,x10722)+E(f426(x10723,x10724,x10721,x10725,x10726,x10727),f426(x10723,x10724,x10722,x10725,x10726,x10727)) % 167.77/167.52 [1073]~E(x10731,x10732)+E(f426(x10733,x10734,x10735,x10731,x10736,x10737),f426(x10733,x10734,x10735,x10732,x10736,x10737)) % 167.77/167.52 [1074]~E(x10741,x10742)+E(f426(x10743,x10744,x10745,x10746,x10741,x10747),f426(x10743,x10744,x10745,x10746,x10742,x10747)) % 167.77/167.52 [1075]~E(x10751,x10752)+E(f426(x10753,x10754,x10755,x10756,x10757,x10751),f426(x10753,x10754,x10755,x10756,x10757,x10752)) % 167.77/167.52 [1076]~E(x10761,x10762)+E(f190(x10761),f190(x10762)) % 167.77/167.52 [1077]~E(x10771,x10772)+E(f457(x10771,x10773,x10774),f457(x10772,x10773,x10774)) % 167.77/167.52 [1078]~E(x10781,x10782)+E(f457(x10783,x10781,x10784),f457(x10783,x10782,x10784)) % 167.77/167.52 [1079]~E(x10791,x10792)+E(f457(x10793,x10794,x10791),f457(x10793,x10794,x10792)) % 167.77/167.52 [1080]~E(x10801,x10802)+E(f649(x10801,x10803,x10804),f649(x10802,x10803,x10804)) % 167.77/167.52 [1081]~E(x10811,x10812)+E(f649(x10813,x10811,x10814),f649(x10813,x10812,x10814)) % 167.77/167.52 [1082]~E(x10821,x10822)+E(f649(x10823,x10824,x10821),f649(x10823,x10824,x10822)) % 167.77/167.52 [1083]~E(x10831,x10832)+E(f130(x10831,x10833,x10834,x10835,x10836),f130(x10832,x10833,x10834,x10835,x10836)) % 167.77/167.52 [1084]~E(x10841,x10842)+E(f130(x10843,x10841,x10844,x10845,x10846),f130(x10843,x10842,x10844,x10845,x10846)) % 167.77/167.52 [1085]~E(x10851,x10852)+E(f130(x10853,x10854,x10851,x10855,x10856),f130(x10853,x10854,x10852,x10855,x10856)) % 167.77/167.52 [1086]~E(x10861,x10862)+E(f130(x10863,x10864,x10865,x10861,x10866),f130(x10863,x10864,x10865,x10862,x10866)) % 167.77/167.52 [1087]~E(x10871,x10872)+E(f130(x10873,x10874,x10875,x10876,x10871),f130(x10873,x10874,x10875,x10876,x10872)) % 167.77/167.52 [1088]~E(x10881,x10882)+E(f736(x10881,x10883,x10884,x10885,x10886),f736(x10882,x10883,x10884,x10885,x10886)) % 167.77/167.52 [1089]~E(x10891,x10892)+E(f736(x10893,x10891,x10894,x10895,x10896),f736(x10893,x10892,x10894,x10895,x10896)) % 167.77/167.52 [1090]~E(x10901,x10902)+E(f736(x10903,x10904,x10901,x10905,x10906),f736(x10903,x10904,x10902,x10905,x10906)) % 167.77/167.52 [1091]~E(x10911,x10912)+E(f736(x10913,x10914,x10915,x10911,x10916),f736(x10913,x10914,x10915,x10912,x10916)) % 167.77/167.52 [1092]~E(x10921,x10922)+E(f736(x10923,x10924,x10925,x10926,x10921),f736(x10923,x10924,x10925,x10926,x10922)) % 167.77/167.52 [1093]~E(x10931,x10932)+E(f264(x10931,x10933,x10934,x10935,x10936),f264(x10932,x10933,x10934,x10935,x10936)) % 167.77/167.52 [1094]~E(x10941,x10942)+E(f264(x10943,x10941,x10944,x10945,x10946),f264(x10943,x10942,x10944,x10945,x10946)) % 167.77/167.52 [1095]~E(x10951,x10952)+E(f264(x10953,x10954,x10951,x10955,x10956),f264(x10953,x10954,x10952,x10955,x10956)) % 167.77/167.52 [1096]~E(x10961,x10962)+E(f264(x10963,x10964,x10965,x10961,x10966),f264(x10963,x10964,x10965,x10962,x10966)) % 167.77/167.52 [1097]~E(x10971,x10972)+E(f264(x10973,x10974,x10975,x10976,x10971),f264(x10973,x10974,x10975,x10976,x10972)) % 167.77/167.52 [1098]~E(x10981,x10982)+E(f637(x10981,x10983,x10984,x10985,x10986),f637(x10982,x10983,x10984,x10985,x10986)) % 167.77/167.52 [1099]~E(x10991,x10992)+E(f637(x10993,x10991,x10994,x10995,x10996),f637(x10993,x10992,x10994,x10995,x10996)) % 167.77/167.52 [1100]~E(x11001,x11002)+E(f637(x11003,x11004,x11001,x11005,x11006),f637(x11003,x11004,x11002,x11005,x11006)) % 167.77/167.52 [1101]~E(x11011,x11012)+E(f637(x11013,x11014,x11015,x11011,x11016),f637(x11013,x11014,x11015,x11012,x11016)) % 167.77/167.52 [1102]~E(x11021,x11022)+E(f637(x11023,x11024,x11025,x11026,x11021),f637(x11023,x11024,x11025,x11026,x11022)) % 167.77/167.52 [1103]~E(x11031,x11032)+E(f811(x11031,x11033,x11034,x11035),f811(x11032,x11033,x11034,x11035)) % 167.77/167.52 [1104]~E(x11041,x11042)+E(f811(x11043,x11041,x11044,x11045),f811(x11043,x11042,x11044,x11045)) % 167.77/167.52 [1105]~E(x11051,x11052)+E(f811(x11053,x11054,x11051,x11055),f811(x11053,x11054,x11052,x11055)) % 167.77/167.52 [1106]~E(x11061,x11062)+E(f811(x11063,x11064,x11065,x11061),f811(x11063,x11064,x11065,x11062)) % 167.77/167.52 [1107]~E(x11071,x11072)+E(f568(x11071,x11073,x11074,x11075,x11076),f568(x11072,x11073,x11074,x11075,x11076)) % 167.77/167.52 [1108]~E(x11081,x11082)+E(f568(x11083,x11081,x11084,x11085,x11086),f568(x11083,x11082,x11084,x11085,x11086)) % 167.77/167.52 [1109]~E(x11091,x11092)+E(f568(x11093,x11094,x11091,x11095,x11096),f568(x11093,x11094,x11092,x11095,x11096)) % 167.77/167.52 [1110]~E(x11101,x11102)+E(f568(x11103,x11104,x11105,x11101,x11106),f568(x11103,x11104,x11105,x11102,x11106)) % 167.77/167.52 [1111]~E(x11111,x11112)+E(f568(x11113,x11114,x11115,x11116,x11111),f568(x11113,x11114,x11115,x11116,x11112)) % 167.77/167.52 [1112]~E(x11121,x11122)+E(f476(x11121,x11123),f476(x11122,x11123)) % 167.77/167.52 [1113]~E(x11131,x11132)+E(f476(x11133,x11131),f476(x11133,x11132)) % 167.77/167.52 [1114]~E(x11141,x11142)+E(f652(x11141,x11143),f652(x11142,x11143)) % 167.77/167.52 [1115]~E(x11151,x11152)+E(f652(x11153,x11151),f652(x11153,x11152)) % 167.77/167.52 [1116]~E(x11161,x11162)+E(f685(x11161,x11163,x11164,x11165),f685(x11162,x11163,x11164,x11165)) % 167.77/167.52 [1117]~E(x11171,x11172)+E(f685(x11173,x11171,x11174,x11175),f685(x11173,x11172,x11174,x11175)) % 167.77/167.52 [1118]~E(x11181,x11182)+E(f685(x11183,x11184,x11181,x11185),f685(x11183,x11184,x11182,x11185)) % 167.77/167.52 [1119]~E(x11191,x11192)+E(f685(x11193,x11194,x11195,x11191),f685(x11193,x11194,x11195,x11192)) % 167.77/167.52 [1120]~E(x11201,x11202)+E(f99(x11201,x11203,x11204,x11205),f99(x11202,x11203,x11204,x11205)) % 167.77/167.52 [1121]~E(x11211,x11212)+E(f99(x11213,x11211,x11214,x11215),f99(x11213,x11212,x11214,x11215)) % 167.77/167.52 [1122]~E(x11221,x11222)+E(f99(x11223,x11224,x11221,x11225),f99(x11223,x11224,x11222,x11225)) % 167.77/167.52 [1123]~E(x11231,x11232)+E(f99(x11233,x11234,x11235,x11231),f99(x11233,x11234,x11235,x11232)) % 167.77/167.52 [1124]~E(x11241,x11242)+E(f577(x11241,x11243,x11244,x11245,x11246),f577(x11242,x11243,x11244,x11245,x11246)) % 167.77/167.52 [1125]~E(x11251,x11252)+E(f577(x11253,x11251,x11254,x11255,x11256),f577(x11253,x11252,x11254,x11255,x11256)) % 167.77/167.52 [1126]~E(x11261,x11262)+E(f577(x11263,x11264,x11261,x11265,x11266),f577(x11263,x11264,x11262,x11265,x11266)) % 167.77/167.52 [1127]~E(x11271,x11272)+E(f577(x11273,x11274,x11275,x11271,x11276),f577(x11273,x11274,x11275,x11272,x11276)) % 167.77/167.52 [1128]~E(x11281,x11282)+E(f577(x11283,x11284,x11285,x11286,x11281),f577(x11283,x11284,x11285,x11286,x11282)) % 167.77/167.52 [1129]~E(x11291,x11292)+E(f376(x11291,x11293,x11294,x11295),f376(x11292,x11293,x11294,x11295)) % 167.77/167.52 [1130]~E(x11301,x11302)+E(f376(x11303,x11301,x11304,x11305),f376(x11303,x11302,x11304,x11305)) % 167.77/167.52 [1131]~E(x11311,x11312)+E(f376(x11313,x11314,x11311,x11315),f376(x11313,x11314,x11312,x11315)) % 167.77/167.52 [1132]~E(x11321,x11322)+E(f376(x11323,x11324,x11325,x11321),f376(x11323,x11324,x11325,x11322)) % 167.77/167.52 [1133]~E(x11331,x11332)+E(f236(x11331,x11333,x11334),f236(x11332,x11333,x11334)) % 167.77/167.52 [1134]~E(x11341,x11342)+E(f236(x11343,x11341,x11344),f236(x11343,x11342,x11344)) % 167.77/167.52 [1135]~E(x11351,x11352)+E(f236(x11353,x11354,x11351),f236(x11353,x11354,x11352)) % 167.77/167.52 [1136]~E(x11361,x11362)+E(f260(x11361,x11363),f260(x11362,x11363)) % 167.77/167.52 [1137]~E(x11371,x11372)+E(f260(x11373,x11371),f260(x11373,x11372)) % 167.77/167.52 [1138]~E(x11381,x11382)+E(f188(x11381,x11383,x11384),f188(x11382,x11383,x11384)) % 167.77/167.52 [1139]~E(x11391,x11392)+E(f188(x11393,x11391,x11394),f188(x11393,x11392,x11394)) % 167.77/167.52 [1140]~E(x11401,x11402)+E(f188(x11403,x11404,x11401),f188(x11403,x11404,x11402)) % 167.77/167.52 [1141]~E(x11411,x11412)+E(f423(x11411,x11413,x11414,x11415),f423(x11412,x11413,x11414,x11415)) % 167.77/167.52 [1142]~E(x11421,x11422)+E(f423(x11423,x11421,x11424,x11425),f423(x11423,x11422,x11424,x11425)) % 167.77/167.52 [1143]~E(x11431,x11432)+E(f423(x11433,x11434,x11431,x11435),f423(x11433,x11434,x11432,x11435)) % 167.77/167.52 [1144]~E(x11441,x11442)+E(f423(x11443,x11444,x11445,x11441),f423(x11443,x11444,x11445,x11442)) % 167.77/167.52 [1145]~E(x11451,x11452)+E(f572(x11451),f572(x11452)) % 167.77/167.52 [1146]~E(x11461,x11462)+E(f322(x11461,x11463,x11464),f322(x11462,x11463,x11464)) % 167.77/167.52 [1147]~E(x11471,x11472)+E(f322(x11473,x11471,x11474),f322(x11473,x11472,x11474)) % 167.77/167.52 [1148]~E(x11481,x11482)+E(f322(x11483,x11484,x11481),f322(x11483,x11484,x11482)) % 167.77/167.52 [1149]~E(x11491,x11492)+E(f493(x11491,x11493,x11494),f493(x11492,x11493,x11494)) % 167.77/167.52 [1150]~E(x11501,x11502)+E(f493(x11503,x11501,x11504),f493(x11503,x11502,x11504)) % 167.77/167.52 [1151]~E(x11511,x11512)+E(f493(x11513,x11514,x11511),f493(x11513,x11514,x11512)) % 167.77/167.52 [1152]~E(x11521,x11522)+E(f764(x11521,x11523),f764(x11522,x11523)) % 167.77/167.52 [1153]~E(x11531,x11532)+E(f764(x11533,x11531),f764(x11533,x11532)) % 167.77/167.52 [1154]~E(x11541,x11542)+E(f295(x11541,x11543,x11544,x11545),f295(x11542,x11543,x11544,x11545)) % 167.77/167.52 [1155]~E(x11551,x11552)+E(f295(x11553,x11551,x11554,x11555),f295(x11553,x11552,x11554,x11555)) % 167.77/167.52 [1156]~E(x11561,x11562)+E(f295(x11563,x11564,x11561,x11565),f295(x11563,x11564,x11562,x11565)) % 167.77/167.52 [1157]~E(x11571,x11572)+E(f295(x11573,x11574,x11575,x11571),f295(x11573,x11574,x11575,x11572)) % 167.77/167.52 [1158]~E(x11581,x11582)+E(f731(x11581,x11583,x11584,x11585),f731(x11582,x11583,x11584,x11585)) % 167.77/167.52 [1159]~E(x11591,x11592)+E(f731(x11593,x11591,x11594,x11595),f731(x11593,x11592,x11594,x11595)) % 167.77/167.52 [1160]~E(x11601,x11602)+E(f731(x11603,x11604,x11601,x11605),f731(x11603,x11604,x11602,x11605)) % 167.77/167.52 [1161]~E(x11611,x11612)+E(f731(x11613,x11614,x11615,x11611),f731(x11613,x11614,x11615,x11612)) % 167.77/167.52 [1162]~E(x11621,x11622)+E(f199(x11621,x11623),f199(x11622,x11623)) % 167.77/167.52 [1163]~E(x11631,x11632)+E(f199(x11633,x11631),f199(x11633,x11632)) % 167.77/167.52 [1164]~E(x11641,x11642)+E(f361(x11641,x11643,x11644,x11645,x11646),f361(x11642,x11643,x11644,x11645,x11646)) % 167.77/167.52 [1165]~E(x11651,x11652)+E(f361(x11653,x11651,x11654,x11655,x11656),f361(x11653,x11652,x11654,x11655,x11656)) % 167.77/167.52 [1166]~E(x11661,x11662)+E(f361(x11663,x11664,x11661,x11665,x11666),f361(x11663,x11664,x11662,x11665,x11666)) % 167.77/167.52 [1167]~E(x11671,x11672)+E(f361(x11673,x11674,x11675,x11671,x11676),f361(x11673,x11674,x11675,x11672,x11676)) % 167.77/167.52 [1168]~E(x11681,x11682)+E(f361(x11683,x11684,x11685,x11686,x11681),f361(x11683,x11684,x11685,x11686,x11682)) % 167.77/167.52 [1169]~E(x11691,x11692)+E(f536(x11691,x11693,x11694,x11695,x11696,x11697,x11698),f536(x11692,x11693,x11694,x11695,x11696,x11697,x11698)) % 167.77/167.52 [1170]~E(x11701,x11702)+E(f536(x11703,x11701,x11704,x11705,x11706,x11707,x11708),f536(x11703,x11702,x11704,x11705,x11706,x11707,x11708)) % 167.77/167.52 [1171]~E(x11711,x11712)+E(f536(x11713,x11714,x11711,x11715,x11716,x11717,x11718),f536(x11713,x11714,x11712,x11715,x11716,x11717,x11718)) % 167.77/167.52 [1172]~E(x11721,x11722)+E(f536(x11723,x11724,x11725,x11721,x11726,x11727,x11728),f536(x11723,x11724,x11725,x11722,x11726,x11727,x11728)) % 167.77/167.52 [1173]~E(x11731,x11732)+E(f536(x11733,x11734,x11735,x11736,x11731,x11737,x11738),f536(x11733,x11734,x11735,x11736,x11732,x11737,x11738)) % 167.77/167.52 [1174]~E(x11741,x11742)+E(f536(x11743,x11744,x11745,x11746,x11747,x11741,x11748),f536(x11743,x11744,x11745,x11746,x11747,x11742,x11748)) % 167.77/167.52 [1175]~E(x11751,x11752)+E(f536(x11753,x11754,x11755,x11756,x11757,x11758,x11751),f536(x11753,x11754,x11755,x11756,x11757,x11758,x11752)) % 167.77/167.52 [1176]~E(x11761,x11762)+E(f580(x11761,x11763,x11764),f580(x11762,x11763,x11764)) % 167.77/167.52 [1177]~E(x11771,x11772)+E(f580(x11773,x11771,x11774),f580(x11773,x11772,x11774)) % 167.77/167.52 [1178]~E(x11781,x11782)+E(f580(x11783,x11784,x11781),f580(x11783,x11784,x11782)) % 167.77/167.52 [1179]~E(x11791,x11792)+E(f336(x11791),f336(x11792)) % 167.77/167.52 [1180]~E(x11801,x11802)+E(f344(x11801,x11803,x11804,x11805),f344(x11802,x11803,x11804,x11805)) % 167.77/167.52 [1181]~E(x11811,x11812)+E(f344(x11813,x11811,x11814,x11815),f344(x11813,x11812,x11814,x11815)) % 167.77/167.52 [1182]~E(x11821,x11822)+E(f344(x11823,x11824,x11821,x11825),f344(x11823,x11824,x11822,x11825)) % 167.77/167.52 [1183]~E(x11831,x11832)+E(f344(x11833,x11834,x11835,x11831),f344(x11833,x11834,x11835,x11832)) % 167.77/167.52 [1184]~E(x11841,x11842)+E(f478(x11841,x11843),f478(x11842,x11843)) % 167.77/167.52 [1185]~E(x11851,x11852)+E(f478(x11853,x11851),f478(x11853,x11852)) % 167.77/167.52 [1186]~E(x11861,x11862)+E(f406(x11861,x11863,x11864,x11865),f406(x11862,x11863,x11864,x11865)) % 167.77/167.52 [1187]~E(x11871,x11872)+E(f406(x11873,x11871,x11874,x11875),f406(x11873,x11872,x11874,x11875)) % 167.77/167.52 [1188]~E(x11881,x11882)+E(f406(x11883,x11884,x11881,x11885),f406(x11883,x11884,x11882,x11885)) % 167.77/167.52 [1189]~E(x11891,x11892)+E(f406(x11893,x11894,x11895,x11891),f406(x11893,x11894,x11895,x11892)) % 167.77/167.52 [1190]~E(x11901,x11902)+E(f371(x11901,x11903,x11904,x11905,x11906),f371(x11902,x11903,x11904,x11905,x11906)) % 167.77/167.52 [1191]~E(x11911,x11912)+E(f371(x11913,x11911,x11914,x11915,x11916),f371(x11913,x11912,x11914,x11915,x11916)) % 167.77/167.52 [1192]~E(x11921,x11922)+E(f371(x11923,x11924,x11921,x11925,x11926),f371(x11923,x11924,x11922,x11925,x11926)) % 167.77/167.52 [1193]~E(x11931,x11932)+E(f371(x11933,x11934,x11935,x11931,x11936),f371(x11933,x11934,x11935,x11932,x11936)) % 167.77/167.52 [1194]~E(x11941,x11942)+E(f371(x11943,x11944,x11945,x11946,x11941),f371(x11943,x11944,x11945,x11946,x11942)) % 167.77/167.52 [1195]~E(x11951,x11952)+E(f635(x11951,x11953,x11954,x11955,x11956),f635(x11952,x11953,x11954,x11955,x11956)) % 167.77/167.52 [1196]~E(x11961,x11962)+E(f635(x11963,x11961,x11964,x11965,x11966),f635(x11963,x11962,x11964,x11965,x11966)) % 167.77/167.52 [1197]~E(x11971,x11972)+E(f635(x11973,x11974,x11971,x11975,x11976),f635(x11973,x11974,x11972,x11975,x11976)) % 167.77/167.52 [1198]~E(x11981,x11982)+E(f635(x11983,x11984,x11985,x11981,x11986),f635(x11983,x11984,x11985,x11982,x11986)) % 167.77/167.52 [1199]~E(x11991,x11992)+E(f635(x11993,x11994,x11995,x11996,x11991),f635(x11993,x11994,x11995,x11996,x11992)) % 167.77/167.52 [1200]~E(x12001,x12002)+E(f276(x12001,x12003),f276(x12002,x12003)) % 167.77/167.52 [1201]~E(x12011,x12012)+E(f276(x12013,x12011),f276(x12013,x12012)) % 167.77/167.52 [1202]~E(x12021,x12022)+E(f706(x12021,x12023,x12024),f706(x12022,x12023,x12024)) % 167.77/167.52 [1203]~E(x12031,x12032)+E(f706(x12033,x12031,x12034),f706(x12033,x12032,x12034)) % 167.77/167.52 [1204]~E(x12041,x12042)+E(f706(x12043,x12044,x12041),f706(x12043,x12044,x12042)) % 167.77/167.52 [1205]~E(x12051,x12052)+E(f207(x12051,x12053),f207(x12052,x12053)) % 167.77/167.52 [1206]~E(x12061,x12062)+E(f207(x12063,x12061),f207(x12063,x12062)) % 167.77/167.52 [1207]~E(x12071,x12072)+E(f129(x12071,x12073),f129(x12072,x12073)) % 167.77/167.52 [1208]~E(x12081,x12082)+E(f129(x12083,x12081),f129(x12083,x12082)) % 167.77/167.52 [1209]~E(x12091,x12092)+E(f126(x12091),f126(x12092)) % 167.77/167.52 [1210]~E(x12101,x12102)+E(f383(x12101,x12103,x12104),f383(x12102,x12103,x12104)) % 167.77/167.52 [1211]~E(x12111,x12112)+E(f383(x12113,x12111,x12114),f383(x12113,x12112,x12114)) % 167.77/167.52 [1212]~E(x12121,x12122)+E(f383(x12123,x12124,x12121),f383(x12123,x12124,x12122)) % 167.77/167.52 [1213]~E(x12131,x12132)+E(f845(x12131,x12133,x12134,x12135),f845(x12132,x12133,x12134,x12135)) % 167.77/167.52 [1214]~E(x12141,x12142)+E(f845(x12143,x12141,x12144,x12145),f845(x12143,x12142,x12144,x12145)) % 167.77/167.52 [1215]~E(x12151,x12152)+E(f845(x12153,x12154,x12151,x12155),f845(x12153,x12154,x12152,x12155)) % 167.77/167.52 [1216]~E(x12161,x12162)+E(f845(x12163,x12164,x12165,x12161),f845(x12163,x12164,x12165,x12162)) % 167.77/167.52 [1217]~E(x12171,x12172)+E(f499(x12171,x12173,x12174,x12175,x12176,x12177),f499(x12172,x12173,x12174,x12175,x12176,x12177)) % 167.77/167.52 [1218]~E(x12181,x12182)+E(f499(x12183,x12181,x12184,x12185,x12186,x12187),f499(x12183,x12182,x12184,x12185,x12186,x12187)) % 167.77/167.52 [1219]~E(x12191,x12192)+E(f499(x12193,x12194,x12191,x12195,x12196,x12197),f499(x12193,x12194,x12192,x12195,x12196,x12197)) % 167.77/167.52 [1220]~E(x12201,x12202)+E(f499(x12203,x12204,x12205,x12201,x12206,x12207),f499(x12203,x12204,x12205,x12202,x12206,x12207)) % 167.77/167.52 [1221]~E(x12211,x12212)+E(f499(x12213,x12214,x12215,x12216,x12211,x12217),f499(x12213,x12214,x12215,x12216,x12212,x12217)) % 167.77/167.52 [1222]~E(x12221,x12222)+E(f499(x12223,x12224,x12225,x12226,x12227,x12221),f499(x12223,x12224,x12225,x12226,x12227,x12222)) % 167.77/167.52 [1223]~E(x12231,x12232)+E(f54(x12231,x12233),f54(x12232,x12233)) % 167.77/167.52 [1224]~E(x12241,x12242)+E(f54(x12243,x12241),f54(x12243,x12242)) % 167.77/167.52 [1225]~E(x12251,x12252)+E(f519(x12251,x12253,x12254,x12255,x12256),f519(x12252,x12253,x12254,x12255,x12256)) % 167.77/167.52 [1226]~E(x12261,x12262)+E(f519(x12263,x12261,x12264,x12265,x12266),f519(x12263,x12262,x12264,x12265,x12266)) % 167.77/167.52 [1227]~E(x12271,x12272)+E(f519(x12273,x12274,x12271,x12275,x12276),f519(x12273,x12274,x12272,x12275,x12276)) % 167.77/167.52 [1228]~E(x12281,x12282)+E(f519(x12283,x12284,x12285,x12281,x12286),f519(x12283,x12284,x12285,x12282,x12286)) % 167.77/167.52 [1229]~E(x12291,x12292)+E(f519(x12293,x12294,x12295,x12296,x12291),f519(x12293,x12294,x12295,x12296,x12292)) % 167.77/167.52 [1230]~E(x12301,x12302)+E(f775(x12301,x12303,x12304),f775(x12302,x12303,x12304)) % 167.77/167.52 [1231]~E(x12311,x12312)+E(f775(x12313,x12311,x12314),f775(x12313,x12312,x12314)) % 167.77/167.52 [1232]~E(x12321,x12322)+E(f775(x12323,x12324,x12321),f775(x12323,x12324,x12322)) % 167.77/167.52 [1233]~E(x12331,x12332)+E(f214(x12331,x12333,x12334,x12335,x12336,x12337,x12338),f214(x12332,x12333,x12334,x12335,x12336,x12337,x12338)) % 167.77/167.52 [1234]~E(x12341,x12342)+E(f214(x12343,x12341,x12344,x12345,x12346,x12347,x12348),f214(x12343,x12342,x12344,x12345,x12346,x12347,x12348)) % 167.77/167.52 [1235]~E(x12351,x12352)+E(f214(x12353,x12354,x12351,x12355,x12356,x12357,x12358),f214(x12353,x12354,x12352,x12355,x12356,x12357,x12358)) % 167.77/167.52 [1236]~E(x12361,x12362)+E(f214(x12363,x12364,x12365,x12361,x12366,x12367,x12368),f214(x12363,x12364,x12365,x12362,x12366,x12367,x12368)) % 167.77/167.52 [1237]~E(x12371,x12372)+E(f214(x12373,x12374,x12375,x12376,x12371,x12377,x12378),f214(x12373,x12374,x12375,x12376,x12372,x12377,x12378)) % 167.77/167.52 [1238]~E(x12381,x12382)+E(f214(x12383,x12384,x12385,x12386,x12387,x12381,x12388),f214(x12383,x12384,x12385,x12386,x12387,x12382,x12388)) % 167.77/167.52 [1239]~E(x12391,x12392)+E(f214(x12393,x12394,x12395,x12396,x12397,x12398,x12391),f214(x12393,x12394,x12395,x12396,x12397,x12398,x12392)) % 167.77/167.52 [1240]~E(x12401,x12402)+E(f294(x12401,x12403,x12404),f294(x12402,x12403,x12404)) % 167.77/167.52 [1241]~E(x12411,x12412)+E(f294(x12413,x12411,x12414),f294(x12413,x12412,x12414)) % 167.77/167.52 [1242]~E(x12421,x12422)+E(f294(x12423,x12424,x12421),f294(x12423,x12424,x12422)) % 167.77/167.52 [1243]~E(x12431,x12432)+E(f520(x12431,x12433,x12434,x12435,x12436,x12437,x12438),f520(x12432,x12433,x12434,x12435,x12436,x12437,x12438)) % 167.77/167.52 [1244]~E(x12441,x12442)+E(f520(x12443,x12441,x12444,x12445,x12446,x12447,x12448),f520(x12443,x12442,x12444,x12445,x12446,x12447,x12448)) % 167.77/167.52 [1245]~E(x12451,x12452)+E(f520(x12453,x12454,x12451,x12455,x12456,x12457,x12458),f520(x12453,x12454,x12452,x12455,x12456,x12457,x12458)) % 167.77/167.52 [1246]~E(x12461,x12462)+E(f520(x12463,x12464,x12465,x12461,x12466,x12467,x12468),f520(x12463,x12464,x12465,x12462,x12466,x12467,x12468)) % 167.77/167.52 [1247]~E(x12471,x12472)+E(f520(x12473,x12474,x12475,x12476,x12471,x12477,x12478),f520(x12473,x12474,x12475,x12476,x12472,x12477,x12478)) % 167.77/167.52 [1248]~E(x12481,x12482)+E(f520(x12483,x12484,x12485,x12486,x12487,x12481,x12488),f520(x12483,x12484,x12485,x12486,x12487,x12482,x12488)) % 167.77/167.52 [1249]~E(x12491,x12492)+E(f520(x12493,x12494,x12495,x12496,x12497,x12498,x12491),f520(x12493,x12494,x12495,x12496,x12497,x12498,x12492)) % 167.77/167.52 [1250]~E(x12501,x12502)+E(f257(x12501,x12503,x12504),f257(x12502,x12503,x12504)) % 167.77/167.52 [1251]~E(x12511,x12512)+E(f257(x12513,x12511,x12514),f257(x12513,x12512,x12514)) % 167.77/167.52 [1252]~E(x12521,x12522)+E(f257(x12523,x12524,x12521),f257(x12523,x12524,x12522)) % 167.77/167.52 [1253]~E(x12531,x12532)+E(f623(x12531,x12533,x12534,x12535,x12536),f623(x12532,x12533,x12534,x12535,x12536)) % 167.77/167.52 [1254]~E(x12541,x12542)+E(f623(x12543,x12541,x12544,x12545,x12546),f623(x12543,x12542,x12544,x12545,x12546)) % 167.77/167.52 [1255]~E(x12551,x12552)+E(f623(x12553,x12554,x12551,x12555,x12556),f623(x12553,x12554,x12552,x12555,x12556)) % 167.77/167.52 [1256]~E(x12561,x12562)+E(f623(x12563,x12564,x12565,x12561,x12566),f623(x12563,x12564,x12565,x12562,x12566)) % 167.77/167.52 [1257]~E(x12571,x12572)+E(f623(x12573,x12574,x12575,x12576,x12571),f623(x12573,x12574,x12575,x12576,x12572)) % 167.77/167.52 [1258]~E(x12581,x12582)+E(f461(x12581,x12583,x12584,x12585),f461(x12582,x12583,x12584,x12585)) % 167.77/167.52 [1259]~E(x12591,x12592)+E(f461(x12593,x12591,x12594,x12595),f461(x12593,x12592,x12594,x12595)) % 167.77/167.52 [1260]~E(x12601,x12602)+E(f461(x12603,x12604,x12601,x12605),f461(x12603,x12604,x12602,x12605)) % 167.77/167.52 [1261]~E(x12611,x12612)+E(f461(x12613,x12614,x12615,x12611),f461(x12613,x12614,x12615,x12612)) % 167.77/167.52 [1262]~E(x12621,x12622)+E(f664(x12621,x12623),f664(x12622,x12623)) % 167.77/167.52 [1263]~E(x12631,x12632)+E(f664(x12633,x12631),f664(x12633,x12632)) % 167.77/167.52 [1264]~E(x12641,x12642)+E(f171(x12641,x12643,x12644),f171(x12642,x12643,x12644)) % 167.77/167.52 [1265]~E(x12651,x12652)+E(f171(x12653,x12651,x12654),f171(x12653,x12652,x12654)) % 167.77/167.52 [1266]~E(x12661,x12662)+E(f171(x12663,x12664,x12661),f171(x12663,x12664,x12662)) % 167.77/167.52 [1267]~E(x12671,x12672)+E(f618(x12671,x12673,x12674,x12675,x12676,x12677,x12678,x12679),f618(x12672,x12673,x12674,x12675,x12676,x12677,x12678,x12679)) % 167.77/167.52 [1268]~E(x12681,x12682)+E(f618(x12683,x12681,x12684,x12685,x12686,x12687,x12688,x12689),f618(x12683,x12682,x12684,x12685,x12686,x12687,x12688,x12689)) % 167.77/167.52 [1269]~E(x12691,x12692)+E(f618(x12693,x12694,x12691,x12695,x12696,x12697,x12698,x12699),f618(x12693,x12694,x12692,x12695,x12696,x12697,x12698,x12699)) % 167.77/167.52 [1270]~E(x12701,x12702)+E(f618(x12703,x12704,x12705,x12701,x12706,x12707,x12708,x12709),f618(x12703,x12704,x12705,x12702,x12706,x12707,x12708,x12709)) % 167.77/167.52 [1271]~E(x12711,x12712)+E(f618(x12713,x12714,x12715,x12716,x12711,x12717,x12718,x12719),f618(x12713,x12714,x12715,x12716,x12712,x12717,x12718,x12719)) % 167.77/167.52 [1272]~E(x12721,x12722)+E(f618(x12723,x12724,x12725,x12726,x12727,x12721,x12728,x12729),f618(x12723,x12724,x12725,x12726,x12727,x12722,x12728,x12729)) % 167.77/167.52 [1273]~E(x12731,x12732)+E(f618(x12733,x12734,x12735,x12736,x12737,x12738,x12731,x12739),f618(x12733,x12734,x12735,x12736,x12737,x12738,x12732,x12739)) % 167.77/167.52 [1274]~E(x12741,x12742)+E(f618(x12743,x12744,x12745,x12746,x12747,x12748,x12749,x12741),f618(x12743,x12744,x12745,x12746,x12747,x12748,x12749,x12742)) % 167.77/167.52 [1275]~E(x12751,x12752)+E(f484(x12751,x12753),f484(x12752,x12753)) % 167.77/167.52 [1276]~E(x12761,x12762)+E(f484(x12763,x12761),f484(x12763,x12762)) % 167.77/167.52 [1277]~E(x12771,x12772)+E(f357(x12771,x12773),f357(x12772,x12773)) % 167.77/167.52 [1278]~E(x12781,x12782)+E(f357(x12783,x12781),f357(x12783,x12782)) % 167.77/167.52 [1279]~E(x12791,x12792)+E(f599(x12791,x12793,x12794,x12795),f599(x12792,x12793,x12794,x12795)) % 167.77/167.52 [1280]~E(x12801,x12802)+E(f599(x12803,x12801,x12804,x12805),f599(x12803,x12802,x12804,x12805)) % 167.77/167.52 [1281]~E(x12811,x12812)+E(f599(x12813,x12814,x12811,x12815),f599(x12813,x12814,x12812,x12815)) % 167.77/167.52 [1282]~E(x12821,x12822)+E(f599(x12823,x12824,x12825,x12821),f599(x12823,x12824,x12825,x12822)) % 167.77/167.52 [1283]~E(x12831,x12832)+E(f825(x12831,x12833,x12834,x12835),f825(x12832,x12833,x12834,x12835)) % 167.77/167.52 [1284]~E(x12841,x12842)+E(f825(x12843,x12841,x12844,x12845),f825(x12843,x12842,x12844,x12845)) % 167.77/167.52 [1285]~E(x12851,x12852)+E(f825(x12853,x12854,x12851,x12855),f825(x12853,x12854,x12852,x12855)) % 167.77/167.52 [1286]~E(x12861,x12862)+E(f825(x12863,x12864,x12865,x12861),f825(x12863,x12864,x12865,x12862)) % 167.77/167.52 [1287]~E(x12871,x12872)+E(f770(x12871,x12873,x12874,x12875,x12876,x12877,x12878,x12879),f770(x12872,x12873,x12874,x12875,x12876,x12877,x12878,x12879)) % 167.77/167.52 [1288]~E(x12881,x12882)+E(f770(x12883,x12881,x12884,x12885,x12886,x12887,x12888,x12889),f770(x12883,x12882,x12884,x12885,x12886,x12887,x12888,x12889)) % 167.77/167.52 [1289]~E(x12891,x12892)+E(f770(x12893,x12894,x12891,x12895,x12896,x12897,x12898,x12899),f770(x12893,x12894,x12892,x12895,x12896,x12897,x12898,x12899)) % 167.77/167.52 [1290]~E(x12901,x12902)+E(f770(x12903,x12904,x12905,x12901,x12906,x12907,x12908,x12909),f770(x12903,x12904,x12905,x12902,x12906,x12907,x12908,x12909)) % 167.77/167.52 [1291]~E(x12911,x12912)+E(f770(x12913,x12914,x12915,x12916,x12911,x12917,x12918,x12919),f770(x12913,x12914,x12915,x12916,x12912,x12917,x12918,x12919)) % 167.77/167.52 [1292]~E(x12921,x12922)+E(f770(x12923,x12924,x12925,x12926,x12927,x12921,x12928,x12929),f770(x12923,x12924,x12925,x12926,x12927,x12922,x12928,x12929)) % 167.77/167.52 [1293]~E(x12931,x12932)+E(f770(x12933,x12934,x12935,x12936,x12937,x12938,x12931,x12939),f770(x12933,x12934,x12935,x12936,x12937,x12938,x12932,x12939)) % 167.77/167.52 [1294]~E(x12941,x12942)+E(f770(x12943,x12944,x12945,x12946,x12947,x12948,x12949,x12941),f770(x12943,x12944,x12945,x12946,x12947,x12948,x12949,x12942)) % 167.77/167.52 [1295]~E(x12951,x12952)+E(f829(x12951,x12953),f829(x12952,x12953)) % 167.77/167.52 [1296]~E(x12961,x12962)+E(f829(x12963,x12961),f829(x12963,x12962)) % 167.77/167.52 [1297]~E(x12971,x12972)+E(f164(x12971,x12973,x12974),f164(x12972,x12973,x12974)) % 167.77/167.52 [1298]~E(x12981,x12982)+E(f164(x12983,x12981,x12984),f164(x12983,x12982,x12984)) % 167.77/167.52 [1299]~E(x12991,x12992)+E(f164(x12993,x12994,x12991),f164(x12993,x12994,x12992)) % 167.77/167.52 [1300]~E(x13001,x13002)+E(f680(x13001,x13003,x13004,x13005),f680(x13002,x13003,x13004,x13005)) % 167.77/167.52 [1301]~E(x13011,x13012)+E(f680(x13013,x13011,x13014,x13015),f680(x13013,x13012,x13014,x13015)) % 167.77/167.52 [1302]~E(x13021,x13022)+E(f680(x13023,x13024,x13021,x13025),f680(x13023,x13024,x13022,x13025)) % 167.77/167.52 [1303]~E(x13031,x13032)+E(f680(x13033,x13034,x13035,x13031),f680(x13033,x13034,x13035,x13032)) % 167.77/167.52 [1304]~E(x13041,x13042)+E(f152(x13041,x13043,x13044),f152(x13042,x13043,x13044)) % 167.77/167.52 [1305]~E(x13051,x13052)+E(f152(x13053,x13051,x13054),f152(x13053,x13052,x13054)) % 167.77/167.52 [1306]~E(x13061,x13062)+E(f152(x13063,x13064,x13061),f152(x13063,x13064,x13062)) % 167.77/167.52 [1307]~E(x13071,x13072)+E(f631(x13071,x13073,x13074),f631(x13072,x13073,x13074)) % 167.77/167.52 [1308]~E(x13081,x13082)+E(f631(x13083,x13081,x13084),f631(x13083,x13082,x13084)) % 167.77/167.52 [1309]~E(x13091,x13092)+E(f631(x13093,x13094,x13091),f631(x13093,x13094,x13092)) % 167.77/167.52 [1310]~E(x13101,x13102)+E(f473(x13101,x13103,x13104),f473(x13102,x13103,x13104)) % 167.77/167.52 [1311]~E(x13111,x13112)+E(f473(x13113,x13111,x13114),f473(x13113,x13112,x13114)) % 167.77/167.52 [1312]~E(x13121,x13122)+E(f473(x13123,x13124,x13121),f473(x13123,x13124,x13122)) % 167.77/167.52 [1313]~E(x13131,x13132)+E(f530(x13131,x13133,x13134,x13135),f530(x13132,x13133,x13134,x13135)) % 167.77/167.52 [1314]~E(x13141,x13142)+E(f530(x13143,x13141,x13144,x13145),f530(x13143,x13142,x13144,x13145)) % 167.77/167.52 [1315]~E(x13151,x13152)+E(f530(x13153,x13154,x13151,x13155),f530(x13153,x13154,x13152,x13155)) % 167.77/167.52 [1316]~E(x13161,x13162)+E(f530(x13163,x13164,x13165,x13161),f530(x13163,x13164,x13165,x13162)) % 167.77/167.52 [1317]~E(x13171,x13172)+E(f447(x13171,x13173),f447(x13172,x13173)) % 167.77/167.52 [1318]~E(x13181,x13182)+E(f447(x13183,x13181),f447(x13183,x13182)) % 167.77/167.52 [1319]~E(x13191,x13192)+E(f279(x13191,x13193),f279(x13192,x13193)) % 167.77/167.52 [1320]~E(x13201,x13202)+E(f279(x13203,x13201),f279(x13203,x13202)) % 167.77/167.52 [1321]~E(x13211,x13212)+E(f704(x13211,x13213),f704(x13212,x13213)) % 167.77/167.52 [1322]~E(x13221,x13222)+E(f704(x13223,x13221),f704(x13223,x13222)) % 167.77/167.52 [1323]~E(x13231,x13232)+E(f622(x13231,x13233,x13234,x13235,x13236),f622(x13232,x13233,x13234,x13235,x13236)) % 167.77/167.52 [1324]~E(x13241,x13242)+E(f622(x13243,x13241,x13244,x13245,x13246),f622(x13243,x13242,x13244,x13245,x13246)) % 167.77/167.52 [1325]~E(x13251,x13252)+E(f622(x13253,x13254,x13251,x13255,x13256),f622(x13253,x13254,x13252,x13255,x13256)) % 167.77/167.52 [1326]~E(x13261,x13262)+E(f622(x13263,x13264,x13265,x13261,x13266),f622(x13263,x13264,x13265,x13262,x13266)) % 167.77/167.52 [1327]~E(x13271,x13272)+E(f622(x13273,x13274,x13275,x13276,x13271),f622(x13273,x13274,x13275,x13276,x13272)) % 167.77/167.52 [1328]~E(x13281,x13282)+E(f642(x13281,x13283,x13284,x13285,x13286),f642(x13282,x13283,x13284,x13285,x13286)) % 167.77/167.52 [1329]~E(x13291,x13292)+E(f642(x13293,x13291,x13294,x13295,x13296),f642(x13293,x13292,x13294,x13295,x13296)) % 167.77/167.52 [1330]~E(x13301,x13302)+E(f642(x13303,x13304,x13301,x13305,x13306),f642(x13303,x13304,x13302,x13305,x13306)) % 167.77/167.52 [1331]~E(x13311,x13312)+E(f642(x13313,x13314,x13315,x13311,x13316),f642(x13313,x13314,x13315,x13312,x13316)) % 167.77/167.52 [1332]~E(x13321,x13322)+E(f642(x13323,x13324,x13325,x13326,x13321),f642(x13323,x13324,x13325,x13326,x13322)) % 167.77/167.52 [1333]~E(x13331,x13332)+E(f332(x13331,x13333,x13334,x13335),f332(x13332,x13333,x13334,x13335)) % 167.77/167.52 [1334]~E(x13341,x13342)+E(f332(x13343,x13341,x13344,x13345),f332(x13343,x13342,x13344,x13345)) % 167.77/167.52 [1335]~E(x13351,x13352)+E(f332(x13353,x13354,x13351,x13355),f332(x13353,x13354,x13352,x13355)) % 167.77/167.52 [1336]~E(x13361,x13362)+E(f332(x13363,x13364,x13365,x13361),f332(x13363,x13364,x13365,x13362)) % 167.77/167.52 [1337]~E(x13371,x13372)+E(f488(x13371,x13373,x13374),f488(x13372,x13373,x13374)) % 167.77/167.52 [1338]~E(x13381,x13382)+E(f488(x13383,x13381,x13384),f488(x13383,x13382,x13384)) % 167.77/167.52 [1339]~E(x13391,x13392)+E(f488(x13393,x13394,x13391),f488(x13393,x13394,x13392)) % 167.77/167.52 [1340]~E(x13401,x13402)+E(f691(x13401,x13403,x13404,x13405),f691(x13402,x13403,x13404,x13405)) % 167.77/167.52 [1341]~E(x13411,x13412)+E(f691(x13413,x13411,x13414,x13415),f691(x13413,x13412,x13414,x13415)) % 167.77/167.52 [1342]~E(x13421,x13422)+E(f691(x13423,x13424,x13421,x13425),f691(x13423,x13424,x13422,x13425)) % 167.77/167.52 [1343]~E(x13431,x13432)+E(f691(x13433,x13434,x13435,x13431),f691(x13433,x13434,x13435,x13432)) % 167.77/167.52 [1344]~E(x13441,x13442)+E(f55(x13441,x13443),f55(x13442,x13443)) % 167.77/167.52 [1345]~E(x13451,x13452)+E(f55(x13453,x13451),f55(x13453,x13452)) % 167.77/167.52 [1346]~E(x13461,x13462)+E(f616(x13461,x13463,x13464,x13465,x13466),f616(x13462,x13463,x13464,x13465,x13466)) % 167.77/167.52 [1347]~E(x13471,x13472)+E(f616(x13473,x13471,x13474,x13475,x13476),f616(x13473,x13472,x13474,x13475,x13476)) % 167.77/167.52 [1348]~E(x13481,x13482)+E(f616(x13483,x13484,x13481,x13485,x13486),f616(x13483,x13484,x13482,x13485,x13486)) % 167.77/167.52 [1349]~E(x13491,x13492)+E(f616(x13493,x13494,x13495,x13491,x13496),f616(x13493,x13494,x13495,x13492,x13496)) % 167.77/167.52 [1350]~E(x13501,x13502)+E(f616(x13503,x13504,x13505,x13506,x13501),f616(x13503,x13504,x13505,x13506,x13502)) % 167.77/167.52 [1351]~E(x13511,x13512)+E(f540(x13511,x13513,x13514,x13515),f540(x13512,x13513,x13514,x13515)) % 167.77/167.52 [1352]~E(x13521,x13522)+E(f540(x13523,x13521,x13524,x13525),f540(x13523,x13522,x13524,x13525)) % 167.77/167.52 [1353]~E(x13531,x13532)+E(f540(x13533,x13534,x13531,x13535),f540(x13533,x13534,x13532,x13535)) % 167.77/167.52 [1354]~E(x13541,x13542)+E(f540(x13543,x13544,x13545,x13541),f540(x13543,x13544,x13545,x13542)) % 167.77/167.52 [1355]~E(x13551,x13552)+E(f660(x13551,x13553,x13554,x13555,x13556,x13557),f660(x13552,x13553,x13554,x13555,x13556,x13557)) % 167.77/167.52 [1356]~E(x13561,x13562)+E(f660(x13563,x13561,x13564,x13565,x13566,x13567),f660(x13563,x13562,x13564,x13565,x13566,x13567)) % 167.77/167.52 [1357]~E(x13571,x13572)+E(f660(x13573,x13574,x13571,x13575,x13576,x13577),f660(x13573,x13574,x13572,x13575,x13576,x13577)) % 167.77/167.52 [1358]~E(x13581,x13582)+E(f660(x13583,x13584,x13585,x13581,x13586,x13587),f660(x13583,x13584,x13585,x13582,x13586,x13587)) % 167.77/167.52 [1359]~E(x13591,x13592)+E(f660(x13593,x13594,x13595,x13596,x13591,x13597),f660(x13593,x13594,x13595,x13596,x13592,x13597)) % 167.77/167.52 [1360]~E(x13601,x13602)+E(f660(x13603,x13604,x13605,x13606,x13607,x13601),f660(x13603,x13604,x13605,x13606,x13607,x13602)) % 167.77/167.52 [1361]~E(x13611,x13612)+E(f661(x13611,x13613,x13614,x13615,x13616,x13617),f661(x13612,x13613,x13614,x13615,x13616,x13617)) % 167.77/167.52 [1362]~E(x13621,x13622)+E(f661(x13623,x13621,x13624,x13625,x13626,x13627),f661(x13623,x13622,x13624,x13625,x13626,x13627)) % 167.77/167.52 [1363]~E(x13631,x13632)+E(f661(x13633,x13634,x13631,x13635,x13636,x13637),f661(x13633,x13634,x13632,x13635,x13636,x13637)) % 167.77/167.52 [1364]~E(x13641,x13642)+E(f661(x13643,x13644,x13645,x13641,x13646,x13647),f661(x13643,x13644,x13645,x13642,x13646,x13647)) % 167.77/167.52 [1365]~E(x13651,x13652)+E(f661(x13653,x13654,x13655,x13656,x13651,x13657),f661(x13653,x13654,x13655,x13656,x13652,x13657)) % 167.77/167.52 [1366]~E(x13661,x13662)+E(f661(x13663,x13664,x13665,x13666,x13667,x13661),f661(x13663,x13664,x13665,x13666,x13667,x13662)) % 167.77/167.52 [1367]~E(x13671,x13672)+E(f393(x13671,x13673,x13674,x13675),f393(x13672,x13673,x13674,x13675)) % 167.77/167.52 [1368]~E(x13681,x13682)+E(f393(x13683,x13681,x13684,x13685),f393(x13683,x13682,x13684,x13685)) % 167.77/167.52 [1369]~E(x13691,x13692)+E(f393(x13693,x13694,x13691,x13695),f393(x13693,x13694,x13692,x13695)) % 167.77/167.52 [1370]~E(x13701,x13702)+E(f393(x13703,x13704,x13705,x13701),f393(x13703,x13704,x13705,x13702)) % 167.77/167.52 [1371]~E(x13711,x13712)+E(f435(x13711,x13713,x13714,x13715),f435(x13712,x13713,x13714,x13715)) % 167.77/167.52 [1372]~E(x13721,x13722)+E(f435(x13723,x13721,x13724,x13725),f435(x13723,x13722,x13724,x13725)) % 167.77/167.52 [1373]~E(x13731,x13732)+E(f435(x13733,x13734,x13731,x13735),f435(x13733,x13734,x13732,x13735)) % 167.77/167.52 [1374]~E(x13741,x13742)+E(f435(x13743,x13744,x13745,x13741),f435(x13743,x13744,x13745,x13742)) % 167.77/167.52 [1375]~E(x13751,x13752)+E(f313(x13751),f313(x13752)) % 167.77/167.52 [1376]~E(x13761,x13762)+E(f761(x13761,x13763,x13764,x13765),f761(x13762,x13763,x13764,x13765)) % 167.77/167.52 [1377]~E(x13771,x13772)+E(f761(x13773,x13771,x13774,x13775),f761(x13773,x13772,x13774,x13775)) % 167.77/167.52 [1378]~E(x13781,x13782)+E(f761(x13783,x13784,x13781,x13785),f761(x13783,x13784,x13782,x13785)) % 167.77/167.52 [1379]~E(x13791,x13792)+E(f761(x13793,x13794,x13795,x13791),f761(x13793,x13794,x13795,x13792)) % 167.77/167.52 [1380]~E(x13801,x13802)+E(f350(x13801,x13803,x13804,x13805),f350(x13802,x13803,x13804,x13805)) % 167.77/167.52 [1381]~E(x13811,x13812)+E(f350(x13813,x13811,x13814,x13815),f350(x13813,x13812,x13814,x13815)) % 167.77/167.52 [1382]~E(x13821,x13822)+E(f350(x13823,x13824,x13821,x13825),f350(x13823,x13824,x13822,x13825)) % 167.77/167.52 [1383]~E(x13831,x13832)+E(f350(x13833,x13834,x13835,x13831),f350(x13833,x13834,x13835,x13832)) % 167.77/167.52 [1384]~E(x13841,x13842)+E(f752(x13841,x13843,x13844,x13845,x13846),f752(x13842,x13843,x13844,x13845,x13846)) % 167.77/167.52 [1385]~E(x13851,x13852)+E(f752(x13853,x13851,x13854,x13855,x13856),f752(x13853,x13852,x13854,x13855,x13856)) % 167.77/167.52 [1386]~E(x13861,x13862)+E(f752(x13863,x13864,x13861,x13865,x13866),f752(x13863,x13864,x13862,x13865,x13866)) % 167.77/167.52 [1387]~E(x13871,x13872)+E(f752(x13873,x13874,x13875,x13871,x13876),f752(x13873,x13874,x13875,x13872,x13876)) % 167.77/167.52 [1388]~E(x13881,x13882)+E(f752(x13883,x13884,x13885,x13886,x13881),f752(x13883,x13884,x13885,x13886,x13882)) % 167.77/167.52 [1389]~E(x13891,x13892)+E(f723(x13891,x13893,x13894,x13895),f723(x13892,x13893,x13894,x13895)) % 167.77/167.52 [1390]~E(x13901,x13902)+E(f723(x13903,x13901,x13904,x13905),f723(x13903,x13902,x13904,x13905)) % 167.77/167.52 [1391]~E(x13911,x13912)+E(f723(x13913,x13914,x13911,x13915),f723(x13913,x13914,x13912,x13915)) % 167.77/167.52 [1392]~E(x13921,x13922)+E(f723(x13923,x13924,x13925,x13921),f723(x13923,x13924,x13925,x13922)) % 167.77/167.52 [1393]~E(x13931,x13932)+E(f862(x13931,x13933,x13934,x13935),f862(x13932,x13933,x13934,x13935)) % 167.77/167.52 [1394]~E(x13941,x13942)+E(f862(x13943,x13941,x13944,x13945),f862(x13943,x13942,x13944,x13945)) % 167.77/167.52 [1395]~E(x13951,x13952)+E(f862(x13953,x13954,x13951,x13955),f862(x13953,x13954,x13952,x13955)) % 167.77/167.52 [1396]~E(x13961,x13962)+E(f862(x13963,x13964,x13965,x13961),f862(x13963,x13964,x13965,x13962)) % 167.77/167.52 [1397]~E(x13971,x13972)+E(f449(x13971,x13973,x13974),f449(x13972,x13973,x13974)) % 167.77/167.52 [1398]~E(x13981,x13982)+E(f449(x13983,x13981,x13984),f449(x13983,x13982,x13984)) % 167.77/167.52 [1399]~E(x13991,x13992)+E(f449(x13993,x13994,x13991),f449(x13993,x13994,x13992)) % 167.77/167.52 [1400]~E(x14001,x14002)+E(f256(x14001,x14003),f256(x14002,x14003)) % 167.77/167.52 [1401]~E(x14011,x14012)+E(f256(x14013,x14011),f256(x14013,x14012)) % 167.77/167.52 [1402]~E(x14021,x14022)+E(f539(x14021,x14023,x14024,x14025),f539(x14022,x14023,x14024,x14025)) % 167.77/167.52 [1403]~E(x14031,x14032)+E(f539(x14033,x14031,x14034,x14035),f539(x14033,x14032,x14034,x14035)) % 167.77/167.52 [1404]~E(x14041,x14042)+E(f539(x14043,x14044,x14041,x14045),f539(x14043,x14044,x14042,x14045)) % 167.77/167.52 [1405]~E(x14051,x14052)+E(f539(x14053,x14054,x14055,x14051),f539(x14053,x14054,x14055,x14052)) % 167.77/167.52 [1406]~E(x14061,x14062)+E(f404(x14061,x14063,x14064,x14065),f404(x14062,x14063,x14064,x14065)) % 167.77/167.52 [1407]~E(x14071,x14072)+E(f404(x14073,x14071,x14074,x14075),f404(x14073,x14072,x14074,x14075)) % 167.77/167.52 [1408]~E(x14081,x14082)+E(f404(x14083,x14084,x14081,x14085),f404(x14083,x14084,x14082,x14085)) % 167.77/167.52 [1409]~E(x14091,x14092)+E(f404(x14093,x14094,x14095,x14091),f404(x14093,x14094,x14095,x14092)) % 167.77/167.52 [1410]~E(x14101,x14102)+E(f490(x14101,x14103,x14104,x14105),f490(x14102,x14103,x14104,x14105)) % 167.77/167.52 [1411]~E(x14111,x14112)+E(f490(x14113,x14111,x14114,x14115),f490(x14113,x14112,x14114,x14115)) % 167.77/167.52 [1412]~E(x14121,x14122)+E(f490(x14123,x14124,x14121,x14125),f490(x14123,x14124,x14122,x14125)) % 167.77/167.52 [1413]~E(x14131,x14132)+E(f490(x14133,x14134,x14135,x14131),f490(x14133,x14134,x14135,x14132)) % 167.77/167.52 [1414]~E(x14141,x14142)+E(f846(x14141,x14143,x14144,x14145),f846(x14142,x14143,x14144,x14145)) % 167.77/167.52 [1415]~E(x14151,x14152)+E(f846(x14153,x14151,x14154,x14155),f846(x14153,x14152,x14154,x14155)) % 167.77/167.52 [1416]~E(x14161,x14162)+E(f846(x14163,x14164,x14161,x14165),f846(x14163,x14164,x14162,x14165)) % 167.77/167.52 [1417]~E(x14171,x14172)+E(f846(x14173,x14174,x14175,x14171),f846(x14173,x14174,x14175,x14172)) % 167.77/167.52 [1418]~E(x14181,x14182)+E(f659(x14181,x14183,x14184,x14185,x14186,x14187),f659(x14182,x14183,x14184,x14185,x14186,x14187)) % 167.77/167.52 [1419]~E(x14191,x14192)+E(f659(x14193,x14191,x14194,x14195,x14196,x14197),f659(x14193,x14192,x14194,x14195,x14196,x14197)) % 167.77/167.52 [1420]~E(x14201,x14202)+E(f659(x14203,x14204,x14201,x14205,x14206,x14207),f659(x14203,x14204,x14202,x14205,x14206,x14207)) % 167.77/167.52 [1421]~E(x14211,x14212)+E(f659(x14213,x14214,x14215,x14211,x14216,x14217),f659(x14213,x14214,x14215,x14212,x14216,x14217)) % 167.77/167.52 [1422]~E(x14221,x14222)+E(f659(x14223,x14224,x14225,x14226,x14221,x14227),f659(x14223,x14224,x14225,x14226,x14222,x14227)) % 167.77/167.52 [1423]~E(x14231,x14232)+E(f659(x14233,x14234,x14235,x14236,x14237,x14231),f659(x14233,x14234,x14235,x14236,x14237,x14232)) % 167.77/167.52 [1424]~E(x14241,x14242)+E(f620(x14241,x14243),f620(x14242,x14243)) % 167.77/167.52 [1425]~E(x14251,x14252)+E(f620(x14253,x14251),f620(x14253,x14252)) % 167.77/167.52 [1426]~E(x14261,x14262)+E(f655(x14261,x14263),f655(x14262,x14263)) % 167.77/167.52 [1427]~E(x14271,x14272)+E(f655(x14273,x14271),f655(x14273,x14272)) % 167.77/167.52 [1428]~E(x14281,x14282)+E(f666(x14281,x14283,x14284,x14285),f666(x14282,x14283,x14284,x14285)) % 167.77/167.52 [1429]~E(x14291,x14292)+E(f666(x14293,x14291,x14294,x14295),f666(x14293,x14292,x14294,x14295)) % 167.77/167.52 [1430]~E(x14301,x14302)+E(f666(x14303,x14304,x14301,x14305),f666(x14303,x14304,x14302,x14305)) % 167.77/167.52 [1431]~E(x14311,x14312)+E(f666(x14313,x14314,x14315,x14311),f666(x14313,x14314,x14315,x14312)) % 167.77/167.52 [1432]~E(x14321,x14322)+E(f508(x14321,x14323,x14324),f508(x14322,x14323,x14324)) % 167.77/167.52 [1433]~E(x14331,x14332)+E(f508(x14333,x14331,x14334),f508(x14333,x14332,x14334)) % 167.77/167.52 [1434]~E(x14341,x14342)+E(f508(x14343,x14344,x14341),f508(x14343,x14344,x14342)) % 167.77/167.52 [1435]~E(x14351,x14352)+E(f551(x14351,x14353,x14354,x14355),f551(x14352,x14353,x14354,x14355)) % 167.77/167.52 [1436]~E(x14361,x14362)+E(f551(x14363,x14361,x14364,x14365),f551(x14363,x14362,x14364,x14365)) % 167.77/167.52 [1437]~E(x14371,x14372)+E(f551(x14373,x14374,x14371,x14375),f551(x14373,x14374,x14372,x14375)) % 167.77/167.52 [1438]~E(x14381,x14382)+E(f551(x14383,x14384,x14385,x14381),f551(x14383,x14384,x14385,x14382)) % 167.77/167.52 [1439]~E(x14391,x14392)+E(f734(x14391,x14393,x14394,x14395,x14396),f734(x14392,x14393,x14394,x14395,x14396)) % 167.77/167.52 [1440]~E(x14401,x14402)+E(f734(x14403,x14401,x14404,x14405,x14406),f734(x14403,x14402,x14404,x14405,x14406)) % 167.77/167.52 [1441]~E(x14411,x14412)+E(f734(x14413,x14414,x14411,x14415,x14416),f734(x14413,x14414,x14412,x14415,x14416)) % 167.77/167.52 [1442]~E(x14421,x14422)+E(f734(x14423,x14424,x14425,x14421,x14426),f734(x14423,x14424,x14425,x14422,x14426)) % 167.77/167.52 [1443]~E(x14431,x14432)+E(f734(x14433,x14434,x14435,x14436,x14431),f734(x14433,x14434,x14435,x14436,x14432)) % 167.77/167.52 [1444]~E(x14441,x14442)+E(f465(x14441,x14443,x14444),f465(x14442,x14443,x14444)) % 167.77/167.52 [1445]~E(x14451,x14452)+E(f465(x14453,x14451,x14454),f465(x14453,x14452,x14454)) % 167.77/167.52 [1446]~E(x14461,x14462)+E(f465(x14463,x14464,x14461),f465(x14463,x14464,x14462)) % 167.77/167.52 [1447]~E(x14471,x14472)+E(f434(x14471,x14473,x14474,x14475),f434(x14472,x14473,x14474,x14475)) % 167.77/167.52 [1448]~E(x14481,x14482)+E(f434(x14483,x14481,x14484,x14485),f434(x14483,x14482,x14484,x14485)) % 167.77/167.52 [1449]~E(x14491,x14492)+E(f434(x14493,x14494,x14491,x14495),f434(x14493,x14494,x14492,x14495)) % 167.77/167.52 [1450]~E(x14501,x14502)+E(f434(x14503,x14504,x14505,x14501),f434(x14503,x14504,x14505,x14502)) % 167.77/167.52 [1451]~E(x14511,x14512)+E(f364(x14511,x14513,x14514,x14515,x14516,x14517,x14518,x14519,x145110),f364(x14512,x14513,x14514,x14515,x14516,x14517,x14518,x14519,x145110)) % 167.77/167.52 [1452]~E(x14521,x14522)+E(f364(x14523,x14521,x14524,x14525,x14526,x14527,x14528,x14529,x145210),f364(x14523,x14522,x14524,x14525,x14526,x14527,x14528,x14529,x145210)) % 167.77/167.52 [1453]~E(x14531,x14532)+E(f364(x14533,x14534,x14531,x14535,x14536,x14537,x14538,x14539,x145310),f364(x14533,x14534,x14532,x14535,x14536,x14537,x14538,x14539,x145310)) % 167.77/167.52 [1454]~E(x14541,x14542)+E(f364(x14543,x14544,x14545,x14541,x14546,x14547,x14548,x14549,x145410),f364(x14543,x14544,x14545,x14542,x14546,x14547,x14548,x14549,x145410)) % 167.77/167.52 [1455]~E(x14551,x14552)+E(f364(x14553,x14554,x14555,x14556,x14551,x14557,x14558,x14559,x145510),f364(x14553,x14554,x14555,x14556,x14552,x14557,x14558,x14559,x145510)) % 167.77/167.52 [1456]~E(x14561,x14562)+E(f364(x14563,x14564,x14565,x14566,x14567,x14561,x14568,x14569,x145610),f364(x14563,x14564,x14565,x14566,x14567,x14562,x14568,x14569,x145610)) % 167.77/167.52 [1457]~E(x14571,x14572)+E(f364(x14573,x14574,x14575,x14576,x14577,x14578,x14571,x14579,x145710),f364(x14573,x14574,x14575,x14576,x14577,x14578,x14572,x14579,x145710)) % 167.77/167.52 [1458]~E(x14581,x14582)+E(f364(x14583,x14584,x14585,x14586,x14587,x14588,x14589,x14581,x145810),f364(x14583,x14584,x14585,x14586,x14587,x14588,x14589,x14582,x145810)) % 167.77/167.52 [1459]~E(x14591,x14592)+E(f364(x14593,x14594,x14595,x14596,x14597,x14598,x14599,x145910,x14591),f364(x14593,x14594,x14595,x14596,x14597,x14598,x14599,x145910,x14592)) % 167.77/167.52 [1460]~E(x14601,x14602)+E(f337(x14601),f337(x14602)) % 167.77/167.52 [1461]~E(x14611,x14612)+E(f505(x14611,x14613,x14614),f505(x14612,x14613,x14614)) % 167.77/167.52 [1462]~E(x14621,x14622)+E(f505(x14623,x14621,x14624),f505(x14623,x14622,x14624)) % 167.77/167.52 [1463]~E(x14631,x14632)+E(f505(x14633,x14634,x14631),f505(x14633,x14634,x14632)) % 167.77/167.52 [1464]~E(x14641,x14642)+E(f524(x14641),f524(x14642)) % 167.77/167.52 [1465]~E(x14651,x14652)+E(f514(x14651,x14653,x14654),f514(x14652,x14653,x14654)) % 167.77/167.52 [1466]~E(x14661,x14662)+E(f514(x14663,x14661,x14664),f514(x14663,x14662,x14664)) % 167.77/167.52 [1467]~E(x14671,x14672)+E(f514(x14673,x14674,x14671),f514(x14673,x14674,x14672)) % 167.77/167.52 [1468]~E(x14681,x14682)+E(f553(x14681,x14683),f553(x14682,x14683)) % 167.77/167.52 [1469]~E(x14691,x14692)+E(f553(x14693,x14691),f553(x14693,x14692)) % 167.77/167.52 [1470]~E(x14701,x14702)+E(f498(x14701,x14703,x14704),f498(x14702,x14703,x14704)) % 167.77/167.52 [1471]~E(x14711,x14712)+E(f498(x14713,x14711,x14714),f498(x14713,x14712,x14714)) % 167.77/167.52 [1472]~E(x14721,x14722)+E(f498(x14723,x14724,x14721),f498(x14723,x14724,x14722)) % 167.77/167.52 [1473]~E(x14731,x14732)+E(f491(x14731,x14733,x14734,x14735),f491(x14732,x14733,x14734,x14735)) % 167.77/167.52 [1474]~E(x14741,x14742)+E(f491(x14743,x14741,x14744,x14745),f491(x14743,x14742,x14744,x14745)) % 167.77/167.52 [1475]~E(x14751,x14752)+E(f491(x14753,x14754,x14751,x14755),f491(x14753,x14754,x14752,x14755)) % 167.77/167.52 [1476]~E(x14761,x14762)+E(f491(x14763,x14764,x14765,x14761),f491(x14763,x14764,x14765,x14762)) % 167.77/167.52 [1477]~E(x14771,x14772)+E(f534(x14771,x14773,x14774,x14775,x14776,x14777,x14778),f534(x14772,x14773,x14774,x14775,x14776,x14777,x14778)) % 167.77/167.52 [1478]~E(x14781,x14782)+E(f534(x14783,x14781,x14784,x14785,x14786,x14787,x14788),f534(x14783,x14782,x14784,x14785,x14786,x14787,x14788)) % 167.77/167.52 [1479]~E(x14791,x14792)+E(f534(x14793,x14794,x14791,x14795,x14796,x14797,x14798),f534(x14793,x14794,x14792,x14795,x14796,x14797,x14798)) % 167.77/167.52 [1480]~E(x14801,x14802)+E(f534(x14803,x14804,x14805,x14801,x14806,x14807,x14808),f534(x14803,x14804,x14805,x14802,x14806,x14807,x14808)) % 167.77/167.52 [1481]~E(x14811,x14812)+E(f534(x14813,x14814,x14815,x14816,x14811,x14817,x14818),f534(x14813,x14814,x14815,x14816,x14812,x14817,x14818)) % 167.77/167.52 [1482]~E(x14821,x14822)+E(f534(x14823,x14824,x14825,x14826,x14827,x14821,x14828),f534(x14823,x14824,x14825,x14826,x14827,x14822,x14828)) % 167.77/167.52 [1483]~E(x14831,x14832)+E(f534(x14833,x14834,x14835,x14836,x14837,x14838,x14831),f534(x14833,x14834,x14835,x14836,x14837,x14838,x14832)) % 167.77/167.52 [1484]~E(x14841,x14842)+E(f639(x14841,x14843,x14844,x14845,x14846),f639(x14842,x14843,x14844,x14845,x14846)) % 167.77/167.52 [1485]~E(x14851,x14852)+E(f639(x14853,x14851,x14854,x14855,x14856),f639(x14853,x14852,x14854,x14855,x14856)) % 167.77/167.52 [1486]~E(x14861,x14862)+E(f639(x14863,x14864,x14861,x14865,x14866),f639(x14863,x14864,x14862,x14865,x14866)) % 167.77/167.52 [1487]~E(x14871,x14872)+E(f639(x14873,x14874,x14875,x14871,x14876),f639(x14873,x14874,x14875,x14872,x14876)) % 167.77/167.52 [1488]~E(x14881,x14882)+E(f639(x14883,x14884,x14885,x14886,x14881),f639(x14883,x14884,x14885,x14886,x14882)) % 167.77/167.52 [1489]~E(x14891,x14892)+E(f646(x14891,x14893,x14894,x14895),f646(x14892,x14893,x14894,x14895)) % 167.77/167.52 [1490]~E(x14901,x14902)+E(f646(x14903,x14901,x14904,x14905),f646(x14903,x14902,x14904,x14905)) % 167.77/167.52 [1491]~E(x14911,x14912)+E(f646(x14913,x14914,x14911,x14915),f646(x14913,x14914,x14912,x14915)) % 167.77/167.52 [1492]~E(x14921,x14922)+E(f646(x14923,x14924,x14925,x14921),f646(x14923,x14924,x14925,x14922)) % 167.77/167.52 [1493]~E(x14931,x14932)+E(f709(x14931,x14933,x14934,x14935,x14936),f709(x14932,x14933,x14934,x14935,x14936)) % 167.77/167.52 [1494]~E(x14941,x14942)+E(f709(x14943,x14941,x14944,x14945,x14946),f709(x14943,x14942,x14944,x14945,x14946)) % 167.77/167.52 [1495]~E(x14951,x14952)+E(f709(x14953,x14954,x14951,x14955,x14956),f709(x14953,x14954,x14952,x14955,x14956)) % 167.77/167.52 [1496]~E(x14961,x14962)+E(f709(x14963,x14964,x14965,x14961,x14966),f709(x14963,x14964,x14965,x14962,x14966)) % 167.77/167.52 [1497]~E(x14971,x14972)+E(f709(x14973,x14974,x14975,x14976,x14971),f709(x14973,x14974,x14975,x14976,x14972)) % 167.77/167.52 [1498]~E(x14981,x14982)+E(f819(x14981,x14983,x14984,x14985),f819(x14982,x14983,x14984,x14985)) % 167.77/167.52 [1499]~E(x14991,x14992)+E(f819(x14993,x14991,x14994,x14995),f819(x14993,x14992,x14994,x14995)) % 167.77/167.52 [1500]~E(x15001,x15002)+E(f819(x15003,x15004,x15001,x15005),f819(x15003,x15004,x15002,x15005)) % 167.77/167.52 [1501]~E(x15011,x15012)+E(f819(x15013,x15014,x15015,x15011),f819(x15013,x15014,x15015,x15012)) % 167.77/167.52 [1502]~E(x15021,x15022)+E(f277(x15021,x15023,x15024,x15025),f277(x15022,x15023,x15024,x15025)) % 167.77/167.52 [1503]~E(x15031,x15032)+E(f277(x15033,x15031,x15034,x15035),f277(x15033,x15032,x15034,x15035)) % 167.77/167.52 [1504]~E(x15041,x15042)+E(f277(x15043,x15044,x15041,x15045),f277(x15043,x15044,x15042,x15045)) % 167.77/167.52 [1505]~E(x15051,x15052)+E(f277(x15053,x15054,x15055,x15051),f277(x15053,x15054,x15055,x15052)) % 167.77/167.52 [1506]~E(x15061,x15062)+E(f579(x15061,x15063,x15064),f579(x15062,x15063,x15064)) % 167.77/167.52 [1507]~E(x15071,x15072)+E(f579(x15073,x15071,x15074),f579(x15073,x15072,x15074)) % 167.77/167.52 [1508]~E(x15081,x15082)+E(f579(x15083,x15084,x15081),f579(x15083,x15084,x15082)) % 167.77/167.52 [1509]~E(x15091,x15092)+E(f451(x15091,x15093,x15094),f451(x15092,x15093,x15094)) % 167.77/167.52 [1510]~E(x15101,x15102)+E(f451(x15103,x15101,x15104),f451(x15103,x15102,x15104)) % 167.77/167.52 [1511]~E(x15111,x15112)+E(f451(x15113,x15114,x15111),f451(x15113,x15114,x15112)) % 167.77/167.52 [1512]~E(x15121,x15122)+E(f817(x15121,x15123,x15124),f817(x15122,x15123,x15124)) % 167.77/167.52 [1513]~E(x15131,x15132)+E(f817(x15133,x15131,x15134),f817(x15133,x15132,x15134)) % 167.77/167.52 [1514]~E(x15141,x15142)+E(f817(x15143,x15144,x15141),f817(x15143,x15144,x15142)) % 167.77/167.52 [1515]~E(x15151,x15152)+E(f562(x15151,x15153,x15154),f562(x15152,x15153,x15154)) % 167.77/167.52 [1516]~E(x15161,x15162)+E(f562(x15163,x15161,x15164),f562(x15163,x15162,x15164)) % 167.77/167.52 [1517]~E(x15171,x15172)+E(f562(x15173,x15174,x15171),f562(x15173,x15174,x15172)) % 167.77/167.52 [1518]~E(x15181,x15182)+E(f856(x15181,x15183,x15184),f856(x15182,x15183,x15184)) % 167.77/167.52 [1519]~E(x15191,x15192)+E(f856(x15193,x15191,x15194),f856(x15193,x15192,x15194)) % 167.77/167.52 [1520]~E(x15201,x15202)+E(f856(x15203,x15204,x15201),f856(x15203,x15204,x15202)) % 167.77/167.52 [1521]~E(x15211,x15212)+E(f733(x15211,x15213,x15214,x15215,x15216),f733(x15212,x15213,x15214,x15215,x15216)) % 167.77/167.52 [1522]~E(x15221,x15222)+E(f733(x15223,x15221,x15224,x15225,x15226),f733(x15223,x15222,x15224,x15225,x15226)) % 167.77/167.52 [1523]~E(x15231,x15232)+E(f733(x15233,x15234,x15231,x15235,x15236),f733(x15233,x15234,x15232,x15235,x15236)) % 167.77/167.52 [1524]~E(x15241,x15242)+E(f733(x15243,x15244,x15245,x15241,x15246),f733(x15243,x15244,x15245,x15242,x15246)) % 167.77/167.52 [1525]~E(x15251,x15252)+E(f733(x15253,x15254,x15255,x15256,x15251),f733(x15253,x15254,x15255,x15256,x15252)) % 167.77/167.52 [1526]~E(x15261,x15262)+E(f771(x15261,x15263,x15264,x15265),f771(x15262,x15263,x15264,x15265)) % 167.77/167.52 [1527]~E(x15271,x15272)+E(f771(x15273,x15271,x15274,x15275),f771(x15273,x15272,x15274,x15275)) % 167.77/167.52 [1528]~E(x15281,x15282)+E(f771(x15283,x15284,x15281,x15285),f771(x15283,x15284,x15282,x15285)) % 167.77/167.52 [1529]~E(x15291,x15292)+E(f771(x15293,x15294,x15295,x15291),f771(x15293,x15294,x15295,x15292)) % 167.77/167.52 [1530]~E(x15301,x15302)+E(f643(x15301,x15303,x15304,x15305,x15306),f643(x15302,x15303,x15304,x15305,x15306)) % 167.77/167.52 [1531]~E(x15311,x15312)+E(f643(x15313,x15311,x15314,x15315,x15316),f643(x15313,x15312,x15314,x15315,x15316)) % 167.77/167.52 [1532]~E(x15321,x15322)+E(f643(x15323,x15324,x15321,x15325,x15326),f643(x15323,x15324,x15322,x15325,x15326)) % 167.77/167.52 [1533]~E(x15331,x15332)+E(f643(x15333,x15334,x15335,x15331,x15336),f643(x15333,x15334,x15335,x15332,x15336)) % 167.77/167.52 [1534]~E(x15341,x15342)+E(f643(x15343,x15344,x15345,x15346,x15341),f643(x15343,x15344,x15345,x15346,x15342)) % 167.77/167.52 [1535]~E(x15351,x15352)+E(f793(x15351,x15353,x15354),f793(x15352,x15353,x15354)) % 167.77/167.52 [1536]~E(x15361,x15362)+E(f793(x15363,x15361,x15364),f793(x15363,x15362,x15364)) % 167.77/167.52 [1537]~E(x15371,x15372)+E(f793(x15373,x15374,x15371),f793(x15373,x15374,x15372)) % 167.77/167.52 [1538]~E(x15381,x15382)+E(f570(x15381,x15383,x15384,x15385,x15386),f570(x15382,x15383,x15384,x15385,x15386)) % 167.77/167.52 [1539]~E(x15391,x15392)+E(f570(x15393,x15391,x15394,x15395,x15396),f570(x15393,x15392,x15394,x15395,x15396)) % 167.77/167.52 [1540]~E(x15401,x15402)+E(f570(x15403,x15404,x15401,x15405,x15406),f570(x15403,x15404,x15402,x15405,x15406)) % 167.77/167.52 [1541]~E(x15411,x15412)+E(f570(x15413,x15414,x15415,x15411,x15416),f570(x15413,x15414,x15415,x15412,x15416)) % 167.77/167.52 [1542]~E(x15421,x15422)+E(f570(x15423,x15424,x15425,x15426,x15421),f570(x15423,x15424,x15425,x15426,x15422)) % 167.77/167.52 [1543]~E(x15431,x15432)+E(f380(x15431,x15433),f380(x15432,x15433)) % 167.77/167.52 [1544]~E(x15441,x15442)+E(f380(x15443,x15441),f380(x15443,x15442)) % 167.77/167.52 [1545]~E(x15451,x15452)+E(f600(x15451,x15453,x15454,x15455,x15456,x15457),f600(x15452,x15453,x15454,x15455,x15456,x15457)) % 167.77/167.52 [1546]~E(x15461,x15462)+E(f600(x15463,x15461,x15464,x15465,x15466,x15467),f600(x15463,x15462,x15464,x15465,x15466,x15467)) % 167.77/167.52 [1547]~E(x15471,x15472)+E(f600(x15473,x15474,x15471,x15475,x15476,x15477),f600(x15473,x15474,x15472,x15475,x15476,x15477)) % 167.77/167.52 [1548]~E(x15481,x15482)+E(f600(x15483,x15484,x15485,x15481,x15486,x15487),f600(x15483,x15484,x15485,x15482,x15486,x15487)) % 167.77/167.52 [1549]~E(x15491,x15492)+E(f600(x15493,x15494,x15495,x15496,x15491,x15497),f600(x15493,x15494,x15495,x15496,x15492,x15497)) % 167.77/167.52 [1550]~E(x15501,x15502)+E(f600(x15503,x15504,x15505,x15506,x15507,x15501),f600(x15503,x15504,x15505,x15506,x15507,x15502)) % 167.77/167.52 [1551]~E(x15511,x15512)+E(f581(x15511,x15513,x15514,x15515,x15516,x15517),f581(x15512,x15513,x15514,x15515,x15516,x15517)) % 167.77/167.52 [1552]~E(x15521,x15522)+E(f581(x15523,x15521,x15524,x15525,x15526,x15527),f581(x15523,x15522,x15524,x15525,x15526,x15527)) % 167.77/167.52 [1553]~E(x15531,x15532)+E(f581(x15533,x15534,x15531,x15535,x15536,x15537),f581(x15533,x15534,x15532,x15535,x15536,x15537)) % 167.77/167.52 [1554]~E(x15541,x15542)+E(f581(x15543,x15544,x15545,x15541,x15546,x15547),f581(x15543,x15544,x15545,x15542,x15546,x15547)) % 167.77/167.52 [1555]~E(x15551,x15552)+E(f581(x15553,x15554,x15555,x15556,x15551,x15557),f581(x15553,x15554,x15555,x15556,x15552,x15557)) % 167.77/167.52 [1556]~E(x15561,x15562)+E(f581(x15563,x15564,x15565,x15566,x15567,x15561),f581(x15563,x15564,x15565,x15566,x15567,x15562)) % 167.77/167.52 [1557]~E(x15571,x15572)+E(f590(x15571,x15573,x15574,x15575),f590(x15572,x15573,x15574,x15575)) % 167.77/167.52 [1558]~E(x15581,x15582)+E(f590(x15583,x15581,x15584,x15585),f590(x15583,x15582,x15584,x15585)) % 167.77/167.52 [1559]~E(x15591,x15592)+E(f590(x15593,x15594,x15591,x15595),f590(x15593,x15594,x15592,x15595)) % 167.77/167.52 [1560]~E(x15601,x15602)+E(f590(x15603,x15604,x15605,x15601),f590(x15603,x15604,x15605,x15602)) % 167.77/167.52 [1561]~E(x15611,x15612)+E(f745(x15611,x15613,x15614),f745(x15612,x15613,x15614)) % 167.77/167.52 [1562]~E(x15621,x15622)+E(f745(x15623,x15621,x15624),f745(x15623,x15622,x15624)) % 167.77/167.52 [1563]~E(x15631,x15632)+E(f745(x15633,x15634,x15631),f745(x15633,x15634,x15632)) % 167.77/167.52 [1564]~E(x15641,x15642)+E(f822(x15641,x15643,x15644,x15645),f822(x15642,x15643,x15644,x15645)) % 167.77/167.52 [1565]~E(x15651,x15652)+E(f822(x15653,x15651,x15654,x15655),f822(x15653,x15652,x15654,x15655)) % 167.77/167.52 [1566]~E(x15661,x15662)+E(f822(x15663,x15664,x15661,x15665),f822(x15663,x15664,x15662,x15665)) % 167.77/167.52 [1567]~E(x15671,x15672)+E(f822(x15673,x15674,x15675,x15671),f822(x15673,x15674,x15675,x15672)) % 167.77/167.52 [1568]~E(x15681,x15682)+E(f760(x15681,x15683,x15684),f760(x15682,x15683,x15684)) % 167.77/167.52 [1569]~E(x15691,x15692)+E(f760(x15693,x15691,x15694),f760(x15693,x15692,x15694)) % 167.77/167.52 [1570]~E(x15701,x15702)+E(f760(x15703,x15704,x15701),f760(x15703,x15704,x15702)) % 167.77/167.52 [1571]~E(x15711,x15712)+E(f440(x15711,x15713,x15714),f440(x15712,x15713,x15714)) % 167.77/167.52 [1572]~E(x15721,x15722)+E(f440(x15723,x15721,x15724),f440(x15723,x15722,x15724)) % 167.77/167.52 [1573]~E(x15731,x15732)+E(f440(x15733,x15734,x15731),f440(x15733,x15734,x15732)) % 167.77/167.52 [1574]~E(x15741,x15742)+E(f831(x15741,x15743,x15744,x15745,x15746),f831(x15742,x15743,x15744,x15745,x15746)) % 167.77/167.52 [1575]~E(x15751,x15752)+E(f831(x15753,x15751,x15754,x15755,x15756),f831(x15753,x15752,x15754,x15755,x15756)) % 167.77/167.52 [1576]~E(x15761,x15762)+E(f831(x15763,x15764,x15761,x15765,x15766),f831(x15763,x15764,x15762,x15765,x15766)) % 167.77/167.52 [1577]~E(x15771,x15772)+E(f831(x15773,x15774,x15775,x15771,x15776),f831(x15773,x15774,x15775,x15772,x15776)) % 167.77/167.52 [1578]~E(x15781,x15782)+E(f831(x15783,x15784,x15785,x15786,x15781),f831(x15783,x15784,x15785,x15786,x15782)) % 167.77/167.52 [1579]~E(x15791,x15792)+E(f556(x15791,x15793,x15794,x15795),f556(x15792,x15793,x15794,x15795)) % 167.77/167.52 [1580]~E(x15801,x15802)+E(f556(x15803,x15801,x15804,x15805),f556(x15803,x15802,x15804,x15805)) % 167.77/167.52 [1581]~E(x15811,x15812)+E(f556(x15813,x15814,x15811,x15815),f556(x15813,x15814,x15812,x15815)) % 167.77/167.52 [1582]~E(x15821,x15822)+E(f556(x15823,x15824,x15825,x15821),f556(x15823,x15824,x15825,x15822)) % 167.77/167.52 [1583]~E(x15831,x15832)+E(f375(x15831,x15833,x15834,x15835),f375(x15832,x15833,x15834,x15835)) % 167.77/167.52 [1584]~E(x15841,x15842)+E(f375(x15843,x15841,x15844,x15845),f375(x15843,x15842,x15844,x15845)) % 167.77/167.52 [1585]~E(x15851,x15852)+E(f375(x15853,x15854,x15851,x15855),f375(x15853,x15854,x15852,x15855)) % 167.77/167.52 [1586]~E(x15861,x15862)+E(f375(x15863,x15864,x15865,x15861),f375(x15863,x15864,x15865,x15862)) % 167.77/167.52 [1587]~E(x15871,x15872)+E(f223(x15871,x15873),f223(x15872,x15873)) % 167.77/167.52 [1588]~E(x15881,x15882)+E(f223(x15883,x15881),f223(x15883,x15882)) % 167.77/167.52 [1589]~E(x15891,x15892)+E(f369(x15891),f369(x15892)) % 167.77/167.52 [1590]~E(x15901,x15902)+E(f384(x15901,x15903,x15904),f384(x15902,x15903,x15904)) % 167.77/167.52 [1591]~E(x15911,x15912)+E(f384(x15913,x15911,x15914),f384(x15913,x15912,x15914)) % 167.77/167.52 [1592]~E(x15921,x15922)+E(f384(x15923,x15924,x15921),f384(x15923,x15924,x15922)) % 167.77/167.52 [1593]~E(x15931,x15932)+E(f589(x15931,x15933,x15934,x15935),f589(x15932,x15933,x15934,x15935)) % 167.77/167.52 [1594]~E(x15941,x15942)+E(f589(x15943,x15941,x15944,x15945),f589(x15943,x15942,x15944,x15945)) % 167.77/167.52 [1595]~E(x15951,x15952)+E(f589(x15953,x15954,x15951,x15955),f589(x15953,x15954,x15952,x15955)) % 167.77/167.52 [1596]~E(x15961,x15962)+E(f589(x15963,x15964,x15965,x15961),f589(x15963,x15964,x15965,x15962)) % 167.77/167.52 [1597]~E(x15971,x15972)+E(f366(x15971),f366(x15972)) % 167.77/167.52 [1598]~E(x15981,x15982)+E(f531(x15981,x15983,x15984),f531(x15982,x15983,x15984)) % 167.77/167.52 [1599]~E(x15991,x15992)+E(f531(x15993,x15991,x15994),f531(x15993,x15992,x15994)) % 167.77/167.52 [1600]~E(x16001,x16002)+E(f531(x16003,x16004,x16001),f531(x16003,x16004,x16002)) % 167.77/167.52 [1601]~E(x16011,x16012)+E(f565(x16011,x16013,x16014,x16015,x16016,x16017),f565(x16012,x16013,x16014,x16015,x16016,x16017)) % 167.77/167.52 [1602]~E(x16021,x16022)+E(f565(x16023,x16021,x16024,x16025,x16026,x16027),f565(x16023,x16022,x16024,x16025,x16026,x16027)) % 167.77/167.52 [1603]~E(x16031,x16032)+E(f565(x16033,x16034,x16031,x16035,x16036,x16037),f565(x16033,x16034,x16032,x16035,x16036,x16037)) % 167.77/167.52 [1604]~E(x16041,x16042)+E(f565(x16043,x16044,x16045,x16041,x16046,x16047),f565(x16043,x16044,x16045,x16042,x16046,x16047)) % 167.77/167.52 [1605]~E(x16051,x16052)+E(f565(x16053,x16054,x16055,x16056,x16051,x16057),f565(x16053,x16054,x16055,x16056,x16052,x16057)) % 167.77/167.52 [1606]~E(x16061,x16062)+E(f565(x16063,x16064,x16065,x16066,x16067,x16061),f565(x16063,x16064,x16065,x16066,x16067,x16062)) % 167.77/167.52 [1607]~E(x16071,x16072)+E(f221(x16071,x16073),f221(x16072,x16073)) % 167.77/167.52 [1608]~E(x16081,x16082)+E(f221(x16083,x16081),f221(x16083,x16082)) % 167.77/167.52 [1609]~E(x16091,x16092)+E(f513(x16091,x16093,x16094),f513(x16092,x16093,x16094)) % 167.77/167.52 [1610]~E(x16101,x16102)+E(f513(x16103,x16101,x16104),f513(x16103,x16102,x16104)) % 167.77/167.52 [1611]~E(x16111,x16112)+E(f513(x16113,x16114,x16111),f513(x16113,x16114,x16112)) % 167.77/167.52 [1612]~E(x16121,x16122)+E(f419(x16121,x16123,x16124,x16125),f419(x16122,x16123,x16124,x16125)) % 167.77/167.52 [1613]~E(x16131,x16132)+E(f419(x16133,x16131,x16134,x16135),f419(x16133,x16132,x16134,x16135)) % 167.77/167.52 [1614]~E(x16141,x16142)+E(f419(x16143,x16144,x16141,x16145),f419(x16143,x16144,x16142,x16145)) % 167.77/167.52 [1615]~E(x16151,x16152)+E(f419(x16153,x16154,x16155,x16151),f419(x16153,x16154,x16155,x16152)) % 167.77/167.52 [1616]~E(x16161,x16162)+E(f521(x16161,x16163,x16164,x16165,x16166,x16167,x16168),f521(x16162,x16163,x16164,x16165,x16166,x16167,x16168)) % 167.77/167.52 [1617]~E(x16171,x16172)+E(f521(x16173,x16171,x16174,x16175,x16176,x16177,x16178),f521(x16173,x16172,x16174,x16175,x16176,x16177,x16178)) % 167.77/167.52 [1618]~E(x16181,x16182)+E(f521(x16183,x16184,x16181,x16185,x16186,x16187,x16188),f521(x16183,x16184,x16182,x16185,x16186,x16187,x16188)) % 167.77/167.52 [1619]~E(x16191,x16192)+E(f521(x16193,x16194,x16195,x16191,x16196,x16197,x16198),f521(x16193,x16194,x16195,x16192,x16196,x16197,x16198)) % 167.77/167.52 [1620]~E(x16201,x16202)+E(f521(x16203,x16204,x16205,x16206,x16201,x16207,x16208),f521(x16203,x16204,x16205,x16206,x16202,x16207,x16208)) % 167.77/167.52 [1621]~E(x16211,x16212)+E(f521(x16213,x16214,x16215,x16216,x16217,x16211,x16218),f521(x16213,x16214,x16215,x16216,x16217,x16212,x16218)) % 167.77/167.52 [1622]~E(x16221,x16222)+E(f521(x16223,x16224,x16225,x16226,x16227,x16228,x16221),f521(x16223,x16224,x16225,x16226,x16227,x16228,x16222)) % 167.77/167.52 [1623]~E(x16231,x16232)+E(f584(x16231,x16233),f584(x16232,x16233)) % 167.77/167.52 [1624]~E(x16241,x16242)+E(f584(x16243,x16241),f584(x16243,x16242)) % 167.77/167.52 [1625]~E(x16251,x16252)+E(f841(x16251,x16253,x16254,x16255,x16256,x16257,x16258),f841(x16252,x16253,x16254,x16255,x16256,x16257,x16258)) % 167.77/167.52 [1626]~E(x16261,x16262)+E(f841(x16263,x16261,x16264,x16265,x16266,x16267,x16268),f841(x16263,x16262,x16264,x16265,x16266,x16267,x16268)) % 167.77/167.52 [1627]~E(x16271,x16272)+E(f841(x16273,x16274,x16271,x16275,x16276,x16277,x16278),f841(x16273,x16274,x16272,x16275,x16276,x16277,x16278)) % 167.77/167.52 [1628]~E(x16281,x16282)+E(f841(x16283,x16284,x16285,x16281,x16286,x16287,x16288),f841(x16283,x16284,x16285,x16282,x16286,x16287,x16288)) % 167.77/167.52 [1629]~E(x16291,x16292)+E(f841(x16293,x16294,x16295,x16296,x16291,x16297,x16298),f841(x16293,x16294,x16295,x16296,x16292,x16297,x16298)) % 167.77/167.52 [1630]~E(x16301,x16302)+E(f841(x16303,x16304,x16305,x16306,x16307,x16301,x16308),f841(x16303,x16304,x16305,x16306,x16307,x16302,x16308)) % 167.77/167.52 [1631]~E(x16311,x16312)+E(f841(x16313,x16314,x16315,x16316,x16317,x16318,x16311),f841(x16313,x16314,x16315,x16316,x16317,x16318,x16312)) % 167.77/167.52 [1632]~E(x16321,x16322)+E(f480(x16321,x16323,x16324),f480(x16322,x16323,x16324)) % 167.77/167.52 [1633]~E(x16331,x16332)+E(f480(x16333,x16331,x16334),f480(x16333,x16332,x16334)) % 167.77/167.52 [1634]~E(x16341,x16342)+E(f480(x16343,x16344,x16341),f480(x16343,x16344,x16342)) % 167.77/167.52 [1635]~E(x16351,x16352)+E(f641(x16351,x16353,x16354,x16355,x16356),f641(x16352,x16353,x16354,x16355,x16356)) % 167.77/167.52 [1636]~E(x16361,x16362)+E(f641(x16363,x16361,x16364,x16365,x16366),f641(x16363,x16362,x16364,x16365,x16366)) % 167.77/167.52 [1637]~E(x16371,x16372)+E(f641(x16373,x16374,x16371,x16375,x16376),f641(x16373,x16374,x16372,x16375,x16376)) % 167.77/167.52 [1638]~E(x16381,x16382)+E(f641(x16383,x16384,x16385,x16381,x16386),f641(x16383,x16384,x16385,x16382,x16386)) % 167.77/167.52 [1639]~E(x16391,x16392)+E(f641(x16393,x16394,x16395,x16396,x16391),f641(x16393,x16394,x16395,x16396,x16392)) % 167.77/167.52 [1640]~E(x16401,x16402)+E(f835(x16401,x16403,x16404),f835(x16402,x16403,x16404)) % 167.77/167.52 [1641]~E(x16411,x16412)+E(f835(x16413,x16411,x16414),f835(x16413,x16412,x16414)) % 167.77/167.52 [1642]~E(x16421,x16422)+E(f835(x16423,x16424,x16421),f835(x16423,x16424,x16422)) % 167.77/167.52 [1643]~E(x16431,x16432)+E(f694(x16431,x16433,x16434,x16435,x16436),f694(x16432,x16433,x16434,x16435,x16436)) % 167.77/167.52 [1644]~E(x16441,x16442)+E(f694(x16443,x16441,x16444,x16445,x16446),f694(x16443,x16442,x16444,x16445,x16446)) % 167.77/167.52 [1645]~E(x16451,x16452)+E(f694(x16453,x16454,x16451,x16455,x16456),f694(x16453,x16454,x16452,x16455,x16456)) % 167.77/167.52 [1646]~E(x16461,x16462)+E(f694(x16463,x16464,x16465,x16461,x16466),f694(x16463,x16464,x16465,x16462,x16466)) % 167.77/167.52 [1647]~E(x16471,x16472)+E(f694(x16473,x16474,x16475,x16476,x16471),f694(x16473,x16474,x16475,x16476,x16472)) % 167.77/167.52 [1648]~E(x16481,x16482)+E(f755(x16481,x16483,x16484),f755(x16482,x16483,x16484)) % 167.77/167.52 [1649]~E(x16491,x16492)+E(f755(x16493,x16491,x16494),f755(x16493,x16492,x16494)) % 167.77/167.52 [1650]~E(x16501,x16502)+E(f755(x16503,x16504,x16501),f755(x16503,x16504,x16502)) % 167.77/167.52 [1651]~E(x16511,x16512)+E(f762(x16511,x16513),f762(x16512,x16513)) % 167.77/167.52 [1652]~E(x16521,x16522)+E(f762(x16523,x16521),f762(x16523,x16522)) % 167.77/167.52 [1653]~E(x16531,x16532)+E(f378(x16531),f378(x16532)) % 167.77/167.52 [1654]~E(x16541,x16542)+E(f795(x16541,x16543,x16544),f795(x16542,x16543,x16544)) % 167.77/167.52 [1655]~E(x16551,x16552)+E(f795(x16553,x16551,x16554),f795(x16553,x16552,x16554)) % 167.77/167.52 [1656]~E(x16561,x16562)+E(f795(x16563,x16564,x16561),f795(x16563,x16564,x16562)) % 167.77/167.52 [1657]~E(x16571,x16572)+E(f232(x16571,x16573,x16574),f232(x16572,x16573,x16574)) % 167.77/167.52 [1658]~E(x16581,x16582)+E(f232(x16583,x16581,x16584),f232(x16583,x16582,x16584)) % 167.77/167.52 [1659]~E(x16591,x16592)+E(f232(x16593,x16594,x16591),f232(x16593,x16594,x16592)) % 167.77/167.52 [1660]~E(x16601,x16602)+E(f663(x16601,x16603,x16604),f663(x16602,x16603,x16604)) % 167.77/167.52 [1661]~E(x16611,x16612)+E(f663(x16613,x16611,x16614),f663(x16613,x16612,x16614)) % 167.77/167.52 [1662]~E(x16621,x16622)+E(f663(x16623,x16624,x16621),f663(x16623,x16624,x16622)) % 167.77/167.52 [1663]~E(x16631,x16632)+E(f566(x16631,x16633,x16634,x16635,x16636,x16637),f566(x16632,x16633,x16634,x16635,x16636,x16637)) % 167.77/167.52 [1664]~E(x16641,x16642)+E(f566(x16643,x16641,x16644,x16645,x16646,x16647),f566(x16643,x16642,x16644,x16645,x16646,x16647)) % 167.77/167.52 [1665]~E(x16651,x16652)+E(f566(x16653,x16654,x16651,x16655,x16656,x16657),f566(x16653,x16654,x16652,x16655,x16656,x16657)) % 167.77/167.52 [1666]~E(x16661,x16662)+E(f566(x16663,x16664,x16665,x16661,x16666,x16667),f566(x16663,x16664,x16665,x16662,x16666,x16667)) % 167.77/167.52 [1667]~E(x16671,x16672)+E(f566(x16673,x16674,x16675,x16676,x16671,x16677),f566(x16673,x16674,x16675,x16676,x16672,x16677)) % 167.77/167.52 [1668]~E(x16681,x16682)+E(f566(x16683,x16684,x16685,x16686,x16687,x16681),f566(x16683,x16684,x16685,x16686,x16687,x16682)) % 167.77/167.52 [1669]~E(x16691,x16692)+E(f471(x16691,x16693,x16694),f471(x16692,x16693,x16694)) % 167.77/167.52 [1670]~E(x16701,x16702)+E(f471(x16703,x16701,x16704),f471(x16703,x16702,x16704)) % 167.77/167.52 [1671]~E(x16711,x16712)+E(f471(x16713,x16714,x16711),f471(x16713,x16714,x16712)) % 167.77/167.52 [1672]~E(x16721,x16722)+E(f381(x16721,x16723,x16724,x16725,x16726),f381(x16722,x16723,x16724,x16725,x16726)) % 167.77/167.52 [1673]~E(x16731,x16732)+E(f381(x16733,x16731,x16734,x16735,x16736),f381(x16733,x16732,x16734,x16735,x16736)) % 167.77/167.52 [1674]~E(x16741,x16742)+E(f381(x16743,x16744,x16741,x16745,x16746),f381(x16743,x16744,x16742,x16745,x16746)) % 167.77/167.52 [1675]~E(x16751,x16752)+E(f381(x16753,x16754,x16755,x16751,x16756),f381(x16753,x16754,x16755,x16752,x16756)) % 167.77/167.52 [1676]~E(x16761,x16762)+E(f381(x16763,x16764,x16765,x16766,x16761),f381(x16763,x16764,x16765,x16766,x16762)) % 167.77/167.52 [1677]~E(x16771,x16772)+E(f670(x16771,x16773,x16774,x16775,x16776),f670(x16772,x16773,x16774,x16775,x16776)) % 167.77/167.52 [1678]~E(x16781,x16782)+E(f670(x16783,x16781,x16784,x16785,x16786),f670(x16783,x16782,x16784,x16785,x16786)) % 167.77/167.52 [1679]~E(x16791,x16792)+E(f670(x16793,x16794,x16791,x16795,x16796),f670(x16793,x16794,x16792,x16795,x16796)) % 167.77/167.52 [1680]~E(x16801,x16802)+E(f670(x16803,x16804,x16805,x16801,x16806),f670(x16803,x16804,x16805,x16802,x16806)) % 167.77/167.52 [1681]~E(x16811,x16812)+E(f670(x16813,x16814,x16815,x16816,x16811),f670(x16813,x16814,x16815,x16816,x16812)) % 167.77/167.52 [1682]~E(x16821,x16822)+E(f296(x16821,x16823,x16824,x16825,x16826),f296(x16822,x16823,x16824,x16825,x16826)) % 167.77/167.52 [1683]~E(x16831,x16832)+E(f296(x16833,x16831,x16834,x16835,x16836),f296(x16833,x16832,x16834,x16835,x16836)) % 167.77/167.52 [1684]~E(x16841,x16842)+E(f296(x16843,x16844,x16841,x16845,x16846),f296(x16843,x16844,x16842,x16845,x16846)) % 167.77/167.52 [1685]~E(x16851,x16852)+E(f296(x16853,x16854,x16855,x16851,x16856),f296(x16853,x16854,x16855,x16852,x16856)) % 167.77/167.52 [1686]~E(x16861,x16862)+E(f296(x16863,x16864,x16865,x16866,x16861),f296(x16863,x16864,x16865,x16866,x16862)) % 167.77/167.52 [1687]~E(x16871,x16872)+E(f213(x16871,x16873,x16874,x16875),f213(x16872,x16873,x16874,x16875)) % 167.77/167.52 [1688]~E(x16881,x16882)+E(f213(x16883,x16881,x16884,x16885),f213(x16883,x16882,x16884,x16885)) % 167.77/167.52 [1689]~E(x16891,x16892)+E(f213(x16893,x16894,x16891,x16895),f213(x16893,x16894,x16892,x16895)) % 167.77/167.52 [1690]~E(x16901,x16902)+E(f213(x16903,x16904,x16905,x16901),f213(x16903,x16904,x16905,x16902)) % 167.77/167.52 [1691]~E(x16911,x16912)+E(f591(x16911,x16913,x16914),f591(x16912,x16913,x16914)) % 167.77/167.52 [1692]~E(x16921,x16922)+E(f591(x16923,x16921,x16924),f591(x16923,x16922,x16924)) % 167.77/167.52 [1693]~E(x16931,x16932)+E(f591(x16933,x16934,x16931),f591(x16933,x16934,x16932)) % 167.77/167.52 [1694]~E(x16941,x16942)+E(f645(x16941,x16943),f645(x16942,x16943)) % 167.77/167.52 [1695]~E(x16951,x16952)+E(f645(x16953,x16951),f645(x16953,x16952)) % 167.77/167.52 [1696]~E(x16961,x16962)+E(f470(x16961,x16963,x16964,x16965,x16966),f470(x16962,x16963,x16964,x16965,x16966)) % 167.77/167.52 [1697]~E(x16971,x16972)+E(f470(x16973,x16971,x16974,x16975,x16976),f470(x16973,x16972,x16974,x16975,x16976)) % 167.77/167.52 [1698]~E(x16981,x16982)+E(f470(x16983,x16984,x16981,x16985,x16986),f470(x16983,x16984,x16982,x16985,x16986)) % 167.77/167.52 [1699]~E(x16991,x16992)+E(f470(x16993,x16994,x16995,x16991,x16996),f470(x16993,x16994,x16995,x16992,x16996)) % 167.77/167.52 [1700]~E(x17001,x17002)+E(f470(x17003,x17004,x17005,x17006,x17001),f470(x17003,x17004,x17005,x17006,x17002)) % 167.77/167.52 [1701]~E(x17011,x17012)+E(f821(x17011,x17013,x17014,x17015,x17016),f821(x17012,x17013,x17014,x17015,x17016)) % 167.77/167.52 [1702]~E(x17021,x17022)+E(f821(x17023,x17021,x17024,x17025,x17026),f821(x17023,x17022,x17024,x17025,x17026)) % 167.77/167.52 [1703]~E(x17031,x17032)+E(f821(x17033,x17034,x17031,x17035,x17036),f821(x17033,x17034,x17032,x17035,x17036)) % 167.77/167.52 [1704]~E(x17041,x17042)+E(f821(x17043,x17044,x17045,x17041,x17046),f821(x17043,x17044,x17045,x17042,x17046)) % 167.77/167.52 [1705]~E(x17051,x17052)+E(f821(x17053,x17054,x17055,x17056,x17051),f821(x17053,x17054,x17055,x17056,x17052)) % 167.77/167.52 [1706]~E(x17061,x17062)+E(f233(x17061,x17063,x17064,x17065),f233(x17062,x17063,x17064,x17065)) % 167.77/167.52 [1707]~E(x17071,x17072)+E(f233(x17073,x17071,x17074,x17075),f233(x17073,x17072,x17074,x17075)) % 167.77/167.52 [1708]~E(x17081,x17082)+E(f233(x17083,x17084,x17081,x17085),f233(x17083,x17084,x17082,x17085)) % 167.77/167.52 [1709]~E(x17091,x17092)+E(f233(x17093,x17094,x17095,x17091),f233(x17093,x17094,x17095,x17092)) % 167.77/167.52 [1710]~E(x17101,x17102)+E(f143(x17101,x17103),f143(x17102,x17103)) % 167.77/167.52 [1711]~E(x17111,x17112)+E(f143(x17113,x17111),f143(x17113,x17112)) % 167.77/167.52 [1712]~E(x17121,x17122)+E(f561(x17121,x17123,x17124,x17125),f561(x17122,x17123,x17124,x17125)) % 167.77/167.52 [1713]~E(x17131,x17132)+E(f561(x17133,x17131,x17134,x17135),f561(x17133,x17132,x17134,x17135)) % 167.77/167.52 [1714]~E(x17141,x17142)+E(f561(x17143,x17144,x17141,x17145),f561(x17143,x17144,x17142,x17145)) % 167.77/167.52 [1715]~E(x17151,x17152)+E(f561(x17153,x17154,x17155,x17151),f561(x17153,x17154,x17155,x17152)) % 167.77/167.52 [1716]~E(x17161,x17162)+E(f728(x17161,x17163,x17164),f728(x17162,x17163,x17164)) % 167.77/167.52 [1717]~E(x17171,x17172)+E(f728(x17173,x17171,x17174),f728(x17173,x17172,x17174)) % 167.77/167.52 [1718]~E(x17181,x17182)+E(f728(x17183,x17184,x17181),f728(x17183,x17184,x17182)) % 167.77/167.52 [1719]~E(x17191,x17192)+E(f859(x17191,x17193,x17194,x17195,x17196),f859(x17192,x17193,x17194,x17195,x17196)) % 167.77/167.52 [1720]~E(x17201,x17202)+E(f859(x17203,x17201,x17204,x17205,x17206),f859(x17203,x17202,x17204,x17205,x17206)) % 167.77/167.52 [1721]~E(x17211,x17212)+E(f859(x17213,x17214,x17211,x17215,x17216),f859(x17213,x17214,x17212,x17215,x17216)) % 167.77/167.52 [1722]~E(x17221,x17222)+E(f859(x17223,x17224,x17225,x17221,x17226),f859(x17223,x17224,x17225,x17222,x17226)) % 167.77/167.52 [1723]~E(x17231,x17232)+E(f859(x17233,x17234,x17235,x17236,x17231),f859(x17233,x17234,x17235,x17236,x17232)) % 167.77/167.52 [1724]~E(x17241,x17242)+E(f603(x17241,x17243,x17244,x17245,x17246,x17247),f603(x17242,x17243,x17244,x17245,x17246,x17247)) % 167.77/167.52 [1725]~E(x17251,x17252)+E(f603(x17253,x17251,x17254,x17255,x17256,x17257),f603(x17253,x17252,x17254,x17255,x17256,x17257)) % 167.77/167.52 [1726]~E(x17261,x17262)+E(f603(x17263,x17264,x17261,x17265,x17266,x17267),f603(x17263,x17264,x17262,x17265,x17266,x17267)) % 167.77/167.52 [1727]~E(x17271,x17272)+E(f603(x17273,x17274,x17275,x17271,x17276,x17277),f603(x17273,x17274,x17275,x17272,x17276,x17277)) % 167.77/167.52 [1728]~E(x17281,x17282)+E(f603(x17283,x17284,x17285,x17286,x17281,x17287),f603(x17283,x17284,x17285,x17286,x17282,x17287)) % 167.77/167.52 [1729]~E(x17291,x17292)+E(f603(x17293,x17294,x17295,x17296,x17297,x17291),f603(x17293,x17294,x17295,x17296,x17297,x17292)) % 167.77/167.52 [1730]~E(x17301,x17302)+E(f208(x17301),f208(x17302)) % 167.77/167.52 [1731]~E(x17311,x17312)+E(f746(x17311,x17313,x17314),f746(x17312,x17313,x17314)) % 167.77/167.52 [1732]~E(x17321,x17322)+E(f746(x17323,x17321,x17324),f746(x17323,x17322,x17324)) % 167.77/167.52 [1733]~E(x17331,x17332)+E(f746(x17333,x17334,x17331),f746(x17333,x17334,x17332)) % 167.77/167.52 [1734]~E(x17341,x17342)+E(f273(x17341),f273(x17342)) % 167.77/167.52 [1735]~E(x17351,x17352)+E(f201(x17351,x17353,x17354,x17355),f201(x17352,x17353,x17354,x17355)) % 167.77/167.52 [1736]~E(x17361,x17362)+E(f201(x17363,x17361,x17364,x17365),f201(x17363,x17362,x17364,x17365)) % 167.77/167.52 [1737]~E(x17371,x17372)+E(f201(x17373,x17374,x17371,x17375),f201(x17373,x17374,x17372,x17375)) % 167.77/167.52 [1738]~E(x17381,x17382)+E(f201(x17383,x17384,x17385,x17381),f201(x17383,x17384,x17385,x17382)) % 167.77/167.52 [1739]~E(x17391,x17392)+E(f287(x17391,x17393),f287(x17392,x17393)) % 167.77/167.52 [1740]~E(x17401,x17402)+E(f287(x17403,x17401),f287(x17403,x17402)) % 167.77/167.52 [1741]~E(x17411,x17412)+E(f347(x17411,x17413,x17414),f347(x17412,x17413,x17414)) % 167.77/167.52 [1742]~E(x17421,x17422)+E(f347(x17423,x17421,x17424),f347(x17423,x17422,x17424)) % 167.77/167.52 [1743]~E(x17431,x17432)+E(f347(x17433,x17434,x17431),f347(x17433,x17434,x17432)) % 167.77/167.52 [1744]~E(x17441,x17442)+E(f640(x17441,x17443,x17444,x17445,x17446),f640(x17442,x17443,x17444,x17445,x17446)) % 167.77/167.52 [1745]~E(x17451,x17452)+E(f640(x17453,x17451,x17454,x17455,x17456),f640(x17453,x17452,x17454,x17455,x17456)) % 167.77/167.52 [1746]~E(x17461,x17462)+E(f640(x17463,x17464,x17461,x17465,x17466),f640(x17463,x17464,x17462,x17465,x17466)) % 167.77/167.52 [1747]~E(x17471,x17472)+E(f640(x17473,x17474,x17475,x17471,x17476),f640(x17473,x17474,x17475,x17472,x17476)) % 167.77/167.52 [1748]~E(x17481,x17482)+E(f640(x17483,x17484,x17485,x17486,x17481),f640(x17483,x17484,x17485,x17486,x17482)) % 167.77/167.52 [1749]~E(x17491,x17492)+E(f353(x17491,x17493,x17494,x17495,x17496),f353(x17492,x17493,x17494,x17495,x17496)) % 167.77/167.52 [1750]~E(x17501,x17502)+E(f353(x17503,x17501,x17504,x17505,x17506),f353(x17503,x17502,x17504,x17505,x17506)) % 167.77/167.52 [1751]~E(x17511,x17512)+E(f353(x17513,x17514,x17511,x17515,x17516),f353(x17513,x17514,x17512,x17515,x17516)) % 167.77/167.52 [1752]~E(x17521,x17522)+E(f353(x17523,x17524,x17525,x17521,x17526),f353(x17523,x17524,x17525,x17522,x17526)) % 167.77/167.52 [1753]~E(x17531,x17532)+E(f353(x17533,x17534,x17535,x17536,x17531),f353(x17533,x17534,x17535,x17536,x17532)) % 167.77/167.52 [1754]~E(x17541,x17542)+E(f689(x17541,x17543,x17544),f689(x17542,x17543,x17544)) % 167.77/167.52 [1755]~E(x17551,x17552)+E(f689(x17553,x17551,x17554),f689(x17553,x17552,x17554)) % 167.77/167.52 [1756]~E(x17561,x17562)+E(f689(x17563,x17564,x17561),f689(x17563,x17564,x17562)) % 167.77/167.52 [1757]~E(x17571,x17572)+E(f860(x17571,x17573),f860(x17572,x17573)) % 167.77/167.52 [1758]~E(x17581,x17582)+E(f860(x17583,x17581),f860(x17583,x17582)) % 167.77/167.52 [1759]~E(x17591,x17592)+E(f838(x17591,x17593,x17594,x17595),f838(x17592,x17593,x17594,x17595)) % 167.77/167.52 [1760]~E(x17601,x17602)+E(f838(x17603,x17601,x17604,x17605),f838(x17603,x17602,x17604,x17605)) % 167.77/167.52 [1761]~E(x17611,x17612)+E(f838(x17613,x17614,x17611,x17615),f838(x17613,x17614,x17612,x17615)) % 167.77/167.52 [1762]~E(x17621,x17622)+E(f838(x17623,x17624,x17625,x17621),f838(x17623,x17624,x17625,x17622)) % 167.77/167.52 [1763]~E(x17631,x17632)+E(f503(x17631,x17633,x17634,x17635),f503(x17632,x17633,x17634,x17635)) % 167.77/167.52 [1764]~E(x17641,x17642)+E(f503(x17643,x17641,x17644,x17645),f503(x17643,x17642,x17644,x17645)) % 167.77/167.52 [1765]~E(x17651,x17652)+E(f503(x17653,x17654,x17651,x17655),f503(x17653,x17654,x17652,x17655)) % 167.77/167.52 [1766]~E(x17661,x17662)+E(f503(x17663,x17664,x17665,x17661),f503(x17663,x17664,x17665,x17662)) % 167.77/167.52 [1767]~E(x17671,x17672)+E(f792(x17671,x17673,x17674),f792(x17672,x17673,x17674)) % 167.77/167.52 [1768]~E(x17681,x17682)+E(f792(x17683,x17681,x17684),f792(x17683,x17682,x17684)) % 167.77/167.52 [1769]~E(x17691,x17692)+E(f792(x17693,x17694,x17691),f792(x17693,x17694,x17692)) % 167.77/167.52 [1770]~E(x17701,x17702)+E(f783(x17701,x17703,x17704,x17705,x17706),f783(x17702,x17703,x17704,x17705,x17706)) % 167.77/167.52 [1771]~E(x17711,x17712)+E(f783(x17713,x17711,x17714,x17715,x17716),f783(x17713,x17712,x17714,x17715,x17716)) % 167.77/167.52 [1772]~E(x17721,x17722)+E(f783(x17723,x17724,x17721,x17725,x17726),f783(x17723,x17724,x17722,x17725,x17726)) % 167.77/167.52 [1773]~E(x17731,x17732)+E(f783(x17733,x17734,x17735,x17731,x17736),f783(x17733,x17734,x17735,x17732,x17736)) % 167.77/167.52 [1774]~E(x17741,x17742)+E(f783(x17743,x17744,x17745,x17746,x17741),f783(x17743,x17744,x17745,x17746,x17742)) % 167.77/167.52 [1775]~E(x17751,x17752)+E(f238(x17751,x17753,x17754,x17755,x17756),f238(x17752,x17753,x17754,x17755,x17756)) % 167.77/167.52 [1776]~E(x17761,x17762)+E(f238(x17763,x17761,x17764,x17765,x17766),f238(x17763,x17762,x17764,x17765,x17766)) % 167.77/167.52 [1777]~E(x17771,x17772)+E(f238(x17773,x17774,x17771,x17775,x17776),f238(x17773,x17774,x17772,x17775,x17776)) % 167.77/167.52 [1778]~E(x17781,x17782)+E(f238(x17783,x17784,x17785,x17781,x17786),f238(x17783,x17784,x17785,x17782,x17786)) % 167.77/167.52 [1779]~E(x17791,x17792)+E(f238(x17793,x17794,x17795,x17796,x17791),f238(x17793,x17794,x17795,x17796,x17792)) % 167.77/167.52 [1780]~E(x17801,x17802)+E(f436(x17801,x17803,x17804,x17805,x17806),f436(x17802,x17803,x17804,x17805,x17806)) % 167.77/167.52 [1781]~E(x17811,x17812)+E(f436(x17813,x17811,x17814,x17815,x17816),f436(x17813,x17812,x17814,x17815,x17816)) % 167.77/167.52 [1782]~E(x17821,x17822)+E(f436(x17823,x17824,x17821,x17825,x17826),f436(x17823,x17824,x17822,x17825,x17826)) % 167.77/167.52 [1783]~E(x17831,x17832)+E(f436(x17833,x17834,x17835,x17831,x17836),f436(x17833,x17834,x17835,x17832,x17836)) % 167.77/167.52 [1784]~E(x17841,x17842)+E(f436(x17843,x17844,x17845,x17846,x17841),f436(x17843,x17844,x17845,x17846,x17842)) % 167.77/167.52 [1785]~E(x17851,x17852)+E(f701(x17851,x17853,x17854,x17855,x17856),f701(x17852,x17853,x17854,x17855,x17856)) % 167.77/167.52 [1786]~E(x17861,x17862)+E(f701(x17863,x17861,x17864,x17865,x17866),f701(x17863,x17862,x17864,x17865,x17866)) % 167.77/167.52 [1787]~E(x17871,x17872)+E(f701(x17873,x17874,x17871,x17875,x17876),f701(x17873,x17874,x17872,x17875,x17876)) % 167.77/167.52 [1788]~E(x17881,x17882)+E(f701(x17883,x17884,x17885,x17881,x17886),f701(x17883,x17884,x17885,x17882,x17886)) % 167.77/167.52 [1789]~E(x17891,x17892)+E(f701(x17893,x17894,x17895,x17896,x17891),f701(x17893,x17894,x17895,x17896,x17892)) % 167.77/167.52 [1790]~E(x17901,x17902)+E(f816(x17901,x17903,x17904),f816(x17902,x17903,x17904)) % 167.77/167.52 [1791]~E(x17911,x17912)+E(f816(x17913,x17911,x17914),f816(x17913,x17912,x17914)) % 167.77/167.52 [1792]~E(x17921,x17922)+E(f816(x17923,x17924,x17921),f816(x17923,x17924,x17922)) % 167.77/167.52 [1793]~E(x17931,x17932)+E(f121(x17931,x17933,x17934),f121(x17932,x17933,x17934)) % 167.77/167.52 [1794]~E(x17941,x17942)+E(f121(x17943,x17941,x17944),f121(x17943,x17942,x17944)) % 167.77/167.52 [1795]~E(x17951,x17952)+E(f121(x17953,x17954,x17951),f121(x17953,x17954,x17952)) % 167.77/167.52 [1796]~E(x17961,x17962)+E(f596(x17961,x17963,x17964),f596(x17962,x17963,x17964)) % 167.77/167.52 [1797]~E(x17971,x17972)+E(f596(x17973,x17971,x17974),f596(x17973,x17972,x17974)) % 167.77/167.52 [1798]~E(x17981,x17982)+E(f596(x17983,x17984,x17981),f596(x17983,x17984,x17982)) % 167.77/167.52 [1799]~E(x17991,x17992)+E(f798(x17991,x17993,x17994),f798(x17992,x17993,x17994)) % 167.77/167.52 [1800]~E(x18001,x18002)+E(f798(x18003,x18001,x18004),f798(x18003,x18002,x18004)) % 167.77/167.52 [1801]~E(x18011,x18012)+E(f798(x18013,x18014,x18011),f798(x18013,x18014,x18012)) % 167.77/167.52 [1802]~E(x18021,x18022)+E(f786(x18021,x18023,x18024,x18025,x18026),f786(x18022,x18023,x18024,x18025,x18026)) % 167.77/167.52 [1803]~E(x18031,x18032)+E(f786(x18033,x18031,x18034,x18035,x18036),f786(x18033,x18032,x18034,x18035,x18036)) % 167.77/167.52 [1804]~E(x18041,x18042)+E(f786(x18043,x18044,x18041,x18045,x18046),f786(x18043,x18044,x18042,x18045,x18046)) % 167.77/167.52 [1805]~E(x18051,x18052)+E(f786(x18053,x18054,x18055,x18051,x18056),f786(x18053,x18054,x18055,x18052,x18056)) % 167.77/167.52 [1806]~E(x18061,x18062)+E(f786(x18063,x18064,x18065,x18066,x18061),f786(x18063,x18064,x18065,x18066,x18062)) % 167.77/167.52 [1807]~E(x18071,x18072)+E(f587(x18071,x18073),f587(x18072,x18073)) % 167.77/167.52 [1808]~E(x18081,x18082)+E(f587(x18083,x18081),f587(x18083,x18082)) % 167.77/167.52 [1809]~E(x18091,x18092)+E(f784(x18091,x18093,x18094,x18095,x18096),f784(x18092,x18093,x18094,x18095,x18096)) % 167.77/167.52 [1810]~E(x18101,x18102)+E(f784(x18103,x18101,x18104,x18105,x18106),f784(x18103,x18102,x18104,x18105,x18106)) % 167.77/167.52 [1811]~E(x18111,x18112)+E(f784(x18113,x18114,x18111,x18115,x18116),f784(x18113,x18114,x18112,x18115,x18116)) % 167.77/167.52 [1812]~E(x18121,x18122)+E(f784(x18123,x18124,x18125,x18121,x18126),f784(x18123,x18124,x18125,x18122,x18126)) % 167.77/167.52 [1813]~E(x18131,x18132)+E(f784(x18133,x18134,x18135,x18136,x18131),f784(x18133,x18134,x18135,x18136,x18132)) % 167.77/167.52 [1814]~E(x18141,x18142)+E(f665(x18141,x18143,x18144,x18145,x18146),f665(x18142,x18143,x18144,x18145,x18146)) % 167.77/167.52 [1815]~E(x18151,x18152)+E(f665(x18153,x18151,x18154,x18155,x18156),f665(x18153,x18152,x18154,x18155,x18156)) % 167.77/167.52 [1816]~E(x18161,x18162)+E(f665(x18163,x18164,x18161,x18165,x18166),f665(x18163,x18164,x18162,x18165,x18166)) % 167.77/167.52 [1817]~E(x18171,x18172)+E(f665(x18173,x18174,x18175,x18171,x18176),f665(x18173,x18174,x18175,x18172,x18176)) % 167.77/167.52 [1818]~E(x18181,x18182)+E(f665(x18183,x18184,x18185,x18186,x18181),f665(x18183,x18184,x18185,x18186,x18182)) % 167.77/167.52 [1819]~E(x18191,x18192)+E(f334(x18191),f334(x18192)) % 167.77/167.52 [1820]~E(x18201,x18202)+E(f797(x18201,x18203,x18204),f797(x18202,x18203,x18204)) % 167.77/167.52 [1821]~E(x18211,x18212)+E(f797(x18213,x18211,x18214),f797(x18213,x18212,x18214)) % 167.77/167.52 [1822]~E(x18221,x18222)+E(f797(x18223,x18224,x18221),f797(x18223,x18224,x18222)) % 167.77/167.52 [1823]~E(x18231,x18232)+E(f399(x18231,x18233,x18234),f399(x18232,x18233,x18234)) % 167.77/167.52 [1824]~E(x18241,x18242)+E(f399(x18243,x18241,x18244),f399(x18243,x18242,x18244)) % 167.77/167.52 [1825]~E(x18251,x18252)+E(f399(x18253,x18254,x18251),f399(x18253,x18254,x18252)) % 167.77/167.52 [1826]~E(x18261,x18262)+E(f772(x18261,x18263,x18264,x18265,x18266),f772(x18262,x18263,x18264,x18265,x18266)) % 167.77/167.52 [1827]~E(x18271,x18272)+E(f772(x18273,x18271,x18274,x18275,x18276),f772(x18273,x18272,x18274,x18275,x18276)) % 167.77/167.52 [1828]~E(x18281,x18282)+E(f772(x18283,x18284,x18281,x18285,x18286),f772(x18283,x18284,x18282,x18285,x18286)) % 167.77/167.52 [1829]~E(x18291,x18292)+E(f772(x18293,x18294,x18295,x18291,x18296),f772(x18293,x18294,x18295,x18292,x18296)) % 167.77/167.52 [1830]~E(x18301,x18302)+E(f772(x18303,x18304,x18305,x18306,x18301),f772(x18303,x18304,x18305,x18306,x18302)) % 167.77/167.52 [1831]~E(x18311,x18312)+E(f229(x18311,x18313,x18314,x18315),f229(x18312,x18313,x18314,x18315)) % 167.77/167.52 [1832]~E(x18321,x18322)+E(f229(x18323,x18321,x18324,x18325),f229(x18323,x18322,x18324,x18325)) % 167.77/167.52 [1833]~E(x18331,x18332)+E(f229(x18333,x18334,x18331,x18335),f229(x18333,x18334,x18332,x18335)) % 167.77/167.52 [1834]~E(x18341,x18342)+E(f229(x18343,x18344,x18345,x18341),f229(x18343,x18344,x18345,x18342)) % 167.77/167.52 [1835]~E(x18351,x18352)+E(f403(x18351,x18353,x18354,x18355),f403(x18352,x18353,x18354,x18355)) % 167.77/167.52 [1836]~E(x18361,x18362)+E(f403(x18363,x18361,x18364,x18365),f403(x18363,x18362,x18364,x18365)) % 167.77/167.52 [1837]~E(x18371,x18372)+E(f403(x18373,x18374,x18371,x18375),f403(x18373,x18374,x18372,x18375)) % 167.77/167.52 [1838]~E(x18381,x18382)+E(f403(x18383,x18384,x18385,x18381),f403(x18383,x18384,x18385,x18382)) % 167.77/167.52 [1839]~E(x18391,x18392)+E(f389(x18391,x18393,x18394),f389(x18392,x18393,x18394)) % 167.77/167.52 [1840]~E(x18401,x18402)+E(f389(x18403,x18401,x18404),f389(x18403,x18402,x18404)) % 167.77/167.52 [1841]~E(x18411,x18412)+E(f389(x18413,x18414,x18411),f389(x18413,x18414,x18412)) % 167.77/167.52 [1842]~E(x18421,x18422)+E(f827(x18421,x18423,x18424,x18425,x18426),f827(x18422,x18423,x18424,x18425,x18426)) % 167.77/167.52 [1843]~E(x18431,x18432)+E(f827(x18433,x18431,x18434,x18435,x18436),f827(x18433,x18432,x18434,x18435,x18436)) % 167.77/167.52 [1844]~E(x18441,x18442)+E(f827(x18443,x18444,x18441,x18445,x18446),f827(x18443,x18444,x18442,x18445,x18446)) % 167.77/167.52 [1845]~E(x18451,x18452)+E(f827(x18453,x18454,x18455,x18451,x18456),f827(x18453,x18454,x18455,x18452,x18456)) % 167.77/167.52 [1846]~E(x18461,x18462)+E(f827(x18463,x18464,x18465,x18466,x18461),f827(x18463,x18464,x18465,x18466,x18462)) % 167.77/167.52 [1847]~E(x18471,x18472)+E(f203(x18471,x18473,x18474,x18475),f203(x18472,x18473,x18474,x18475)) % 167.77/167.52 [1848]~E(x18481,x18482)+E(f203(x18483,x18481,x18484,x18485),f203(x18483,x18482,x18484,x18485)) % 167.77/167.52 [1849]~E(x18491,x18492)+E(f203(x18493,x18494,x18491,x18495),f203(x18493,x18494,x18492,x18495)) % 167.77/167.52 [1850]~E(x18501,x18502)+E(f203(x18503,x18504,x18505,x18501),f203(x18503,x18504,x18505,x18502)) % 167.77/167.52 [1851]~E(x18511,x18512)+E(f715(x18511,x18513),f715(x18512,x18513)) % 167.77/167.52 [1852]~E(x18521,x18522)+E(f715(x18523,x18521),f715(x18523,x18522)) % 167.77/167.52 [1853]~E(x18531,x18532)+E(f818(x18531,x18533,x18534),f818(x18532,x18533,x18534)) % 167.77/167.52 [1854]~E(x18541,x18542)+E(f818(x18543,x18541,x18544),f818(x18543,x18542,x18544)) % 167.77/167.52 [1855]~E(x18551,x18552)+E(f818(x18553,x18554,x18551),f818(x18553,x18554,x18552)) % 167.77/167.52 [1856]~E(x18561,x18562)+E(f215(x18561),f215(x18562)) % 167.77/167.52 [1857]~E(x18571,x18572)+E(f385(x18571,x18573,x18574,x18575,x18576),f385(x18572,x18573,x18574,x18575,x18576)) % 167.77/167.52 [1858]~E(x18581,x18582)+E(f385(x18583,x18581,x18584,x18585,x18586),f385(x18583,x18582,x18584,x18585,x18586)) % 167.77/167.52 [1859]~E(x18591,x18592)+E(f385(x18593,x18594,x18591,x18595,x18596),f385(x18593,x18594,x18592,x18595,x18596)) % 167.77/167.52 [1860]~E(x18601,x18602)+E(f385(x18603,x18604,x18605,x18601,x18606),f385(x18603,x18604,x18605,x18602,x18606)) % 167.77/167.52 [1861]~E(x18611,x18612)+E(f385(x18613,x18614,x18615,x18616,x18611),f385(x18613,x18614,x18615,x18616,x18612)) % 167.77/167.52 [1862]~E(x18621,x18622)+E(f352(x18621,x18623,x18624,x18625,x18626),f352(x18622,x18623,x18624,x18625,x18626)) % 167.77/167.52 [1863]~E(x18631,x18632)+E(f352(x18633,x18631,x18634,x18635,x18636),f352(x18633,x18632,x18634,x18635,x18636)) % 167.77/167.52 [1864]~E(x18641,x18642)+E(f352(x18643,x18644,x18641,x18645,x18646),f352(x18643,x18644,x18642,x18645,x18646)) % 167.77/167.52 [1865]~E(x18651,x18652)+E(f352(x18653,x18654,x18655,x18651,x18656),f352(x18653,x18654,x18655,x18652,x18656)) % 167.77/167.52 [1866]~E(x18661,x18662)+E(f352(x18663,x18664,x18665,x18666,x18661),f352(x18663,x18664,x18665,x18666,x18662)) % 167.77/167.52 [1867]~E(x18671,x18672)+E(f410(x18671,x18673,x18674,x18675),f410(x18672,x18673,x18674,x18675)) % 167.77/167.52 [1868]~E(x18681,x18682)+E(f410(x18683,x18681,x18684,x18685),f410(x18683,x18682,x18684,x18685)) % 167.77/167.52 [1869]~E(x18691,x18692)+E(f410(x18693,x18694,x18691,x18695),f410(x18693,x18694,x18692,x18695)) % 167.77/167.52 [1870]~E(x18701,x18702)+E(f410(x18703,x18704,x18705,x18701),f410(x18703,x18704,x18705,x18702)) % 167.77/167.52 [1871]~E(x18711,x18712)+E(f861(x18711,x18713),f861(x18712,x18713)) % 167.77/167.52 [1872]~E(x18721,x18722)+E(f861(x18723,x18721),f861(x18723,x18722)) % 167.77/167.52 [1873]~E(x18731,x18732)+E(f712(x18731,x18733,x18734,x18735,x18736),f712(x18732,x18733,x18734,x18735,x18736)) % 167.77/167.52 [1874]~E(x18741,x18742)+E(f712(x18743,x18741,x18744,x18745,x18746),f712(x18743,x18742,x18744,x18745,x18746)) % 167.77/167.52 [1875]~E(x18751,x18752)+E(f712(x18753,x18754,x18751,x18755,x18756),f712(x18753,x18754,x18752,x18755,x18756)) % 167.77/167.52 [1876]~E(x18761,x18762)+E(f712(x18763,x18764,x18765,x18761,x18766),f712(x18763,x18764,x18765,x18762,x18766)) % 167.77/167.52 [1877]~E(x18771,x18772)+E(f712(x18773,x18774,x18775,x18776,x18771),f712(x18773,x18774,x18775,x18776,x18772)) % 167.77/167.52 [1878]~E(x18781,x18782)+E(f699(x18781,x18783,x18784,x18785),f699(x18782,x18783,x18784,x18785)) % 167.77/167.52 [1879]~E(x18791,x18792)+E(f699(x18793,x18791,x18794,x18795),f699(x18793,x18792,x18794,x18795)) % 167.77/167.52 [1880]~E(x18801,x18802)+E(f699(x18803,x18804,x18801,x18805),f699(x18803,x18804,x18802,x18805)) % 167.77/167.52 [1881]~E(x18811,x18812)+E(f699(x18813,x18814,x18815,x18811),f699(x18813,x18814,x18815,x18812)) % 167.77/167.52 [1882]~E(x18821,x18822)+E(f211(x18821),f211(x18822)) % 167.77/167.52 [1883]~E(x18831,x18832)+E(f545(x18831,x18833),f545(x18832,x18833)) % 167.77/167.52 [1884]~E(x18841,x18842)+E(f545(x18843,x18841),f545(x18843,x18842)) % 167.77/167.52 [1885]~E(x18851,x18852)+E(f544(x18851,x18853,x18854,x18855),f544(x18852,x18853,x18854,x18855)) % 167.77/167.52 [1886]~E(x18861,x18862)+E(f544(x18863,x18861,x18864,x18865),f544(x18863,x18862,x18864,x18865)) % 167.77/167.52 [1887]~E(x18871,x18872)+E(f544(x18873,x18874,x18871,x18875),f544(x18873,x18874,x18872,x18875)) % 167.77/167.52 [1888]~E(x18881,x18882)+E(f544(x18883,x18884,x18885,x18881),f544(x18883,x18884,x18885,x18882)) % 167.77/167.52 [1889]~E(x18891,x18892)+E(f94(x18891),f94(x18892)) % 167.77/167.52 [1890]~E(x18901,x18902)+E(f749(x18901,x18903),f749(x18902,x18903)) % 167.77/167.52 [1891]~E(x18911,x18912)+E(f749(x18913,x18911),f749(x18913,x18912)) % 167.77/167.52 [1892]~E(x18921,x18922)+E(f805(x18921,x18923,x18924),f805(x18922,x18923,x18924)) % 167.77/167.52 [1893]~E(x18931,x18932)+E(f805(x18933,x18931,x18934),f805(x18933,x18932,x18934)) % 167.77/167.52 [1894]~E(x18941,x18942)+E(f805(x18943,x18944,x18941),f805(x18943,x18944,x18942)) % 167.77/167.52 [1895]~E(x18951,x18952)+E(f730(x18951,x18953),f730(x18952,x18953)) % 167.77/167.52 [1896]~E(x18961,x18962)+E(f730(x18963,x18961),f730(x18963,x18962)) % 167.77/167.52 [1897]~E(x18971,x18972)+E(f494(x18971,x18973,x18974,x18975),f494(x18972,x18973,x18974,x18975)) % 167.77/167.52 [1898]~E(x18981,x18982)+E(f494(x18983,x18981,x18984,x18985),f494(x18983,x18982,x18984,x18985)) % 167.77/167.52 [1899]~E(x18991,x18992)+E(f494(x18993,x18994,x18991,x18995),f494(x18993,x18994,x18992,x18995)) % 167.77/167.52 [1900]~E(x19001,x19002)+E(f494(x19003,x19004,x19005,x19001),f494(x19003,x19004,x19005,x19002)) % 167.77/167.52 [1901]~E(x19011,x19012)+E(f359(x19011,x19013,x19014),f359(x19012,x19013,x19014)) % 167.77/167.52 [1902]~E(x19021,x19022)+E(f359(x19023,x19021,x19024),f359(x19023,x19022,x19024)) % 167.77/167.52 [1903]~E(x19031,x19032)+E(f359(x19033,x19034,x19031),f359(x19033,x19034,x19032)) % 167.77/167.52 [1904]~E(x19041,x19042)+E(f564(x19041,x19043,x19044,x19045,x19046,x19047),f564(x19042,x19043,x19044,x19045,x19046,x19047)) % 167.77/167.52 [1905]~E(x19051,x19052)+E(f564(x19053,x19051,x19054,x19055,x19056,x19057),f564(x19053,x19052,x19054,x19055,x19056,x19057)) % 167.77/167.52 [1906]~E(x19061,x19062)+E(f564(x19063,x19064,x19061,x19065,x19066,x19067),f564(x19063,x19064,x19062,x19065,x19066,x19067)) % 167.77/167.52 [1907]~E(x19071,x19072)+E(f564(x19073,x19074,x19075,x19071,x19076,x19077),f564(x19073,x19074,x19075,x19072,x19076,x19077)) % 167.77/167.52 [1908]~E(x19081,x19082)+E(f564(x19083,x19084,x19085,x19086,x19081,x19087),f564(x19083,x19084,x19085,x19086,x19082,x19087)) % 167.77/167.52 [1909]~E(x19091,x19092)+E(f564(x19093,x19094,x19095,x19096,x19097,x19091),f564(x19093,x19094,x19095,x19096,x19097,x19092)) % 167.77/167.52 [1910]~E(x19101,x19102)+E(f682(x19101,x19103),f682(x19102,x19103)) % 167.77/167.52 [1911]~E(x19111,x19112)+E(f682(x19113,x19111),f682(x19113,x19112)) % 167.77/167.52 [1912]~E(x19121,x19122)+E(f432(x19121,x19123,x19124,x19125,x19126),f432(x19122,x19123,x19124,x19125,x19126)) % 167.77/167.52 [1913]~E(x19131,x19132)+E(f432(x19133,x19131,x19134,x19135,x19136),f432(x19133,x19132,x19134,x19135,x19136)) % 167.77/167.52 [1914]~E(x19141,x19142)+E(f432(x19143,x19144,x19141,x19145,x19146),f432(x19143,x19144,x19142,x19145,x19146)) % 167.77/167.52 [1915]~E(x19151,x19152)+E(f432(x19153,x19154,x19155,x19151,x19156),f432(x19153,x19154,x19155,x19152,x19156)) % 167.77/167.52 [1916]~E(x19161,x19162)+E(f432(x19163,x19164,x19165,x19166,x19161),f432(x19163,x19164,x19165,x19166,x19162)) % 167.77/167.52 [1917]~E(x19171,x19172)+E(f849(x19171,x19173,x19174),f849(x19172,x19173,x19174)) % 167.77/167.52 [1918]~E(x19181,x19182)+E(f849(x19183,x19181,x19184),f849(x19183,x19182,x19184)) % 167.77/167.52 [1919]~E(x19191,x19192)+E(f849(x19193,x19194,x19191),f849(x19193,x19194,x19192)) % 167.77/167.52 [1920]~E(x19201,x19202)+E(f753(x19201,x19203,x19204,x19205,x19206),f753(x19202,x19203,x19204,x19205,x19206)) % 167.77/167.52 [1921]~E(x19211,x19212)+E(f753(x19213,x19211,x19214,x19215,x19216),f753(x19213,x19212,x19214,x19215,x19216)) % 167.77/167.52 [1922]~E(x19221,x19222)+E(f753(x19223,x19224,x19221,x19225,x19226),f753(x19223,x19224,x19222,x19225,x19226)) % 167.77/167.52 [1923]~E(x19231,x19232)+E(f753(x19233,x19234,x19235,x19231,x19236),f753(x19233,x19234,x19235,x19232,x19236)) % 167.77/167.52 [1924]~E(x19241,x19242)+E(f753(x19243,x19244,x19245,x19246,x19241),f753(x19243,x19244,x19245,x19246,x19242)) % 167.77/167.52 [1925]~E(x19251,x19252)+E(f482(x19251,x19253,x19254),f482(x19252,x19253,x19254)) % 167.77/167.52 [1926]~E(x19261,x19262)+E(f482(x19263,x19261,x19264),f482(x19263,x19262,x19264)) % 167.77/167.52 [1927]~E(x19271,x19272)+E(f482(x19273,x19274,x19271),f482(x19273,x19274,x19272)) % 167.77/167.52 [1928]~E(x19281,x19282)+E(f718(x19281,x19283,x19284),f718(x19282,x19283,x19284)) % 167.77/167.52 [1929]~E(x19291,x19292)+E(f718(x19293,x19291,x19294),f718(x19293,x19292,x19294)) % 167.77/167.52 [1930]~E(x19301,x19302)+E(f718(x19303,x19304,x19301),f718(x19303,x19304,x19302)) % 167.77/167.52 [1931]~E(x19311,x19312)+E(f487(x19311,x19313,x19314),f487(x19312,x19313,x19314)) % 167.77/167.52 [1932]~E(x19321,x19322)+E(f487(x19323,x19321,x19324),f487(x19323,x19322,x19324)) % 167.77/167.52 [1933]~E(x19331,x19332)+E(f487(x19333,x19334,x19331),f487(x19333,x19334,x19332)) % 167.77/167.52 [1934]~E(x19341,x19342)+E(f754(x19341,x19343),f754(x19342,x19343)) % 167.77/167.52 [1935]~E(x19351,x19352)+E(f754(x19353,x19351),f754(x19353,x19352)) % 167.77/167.52 [1936]~E(x19361,x19362)+E(f855(x19361,x19363,x19364,x19365),f855(x19362,x19363,x19364,x19365)) % 167.77/167.52 [1937]~E(x19371,x19372)+E(f855(x19373,x19371,x19374,x19375),f855(x19373,x19372,x19374,x19375)) % 167.77/167.52 [1938]~E(x19381,x19382)+E(f855(x19383,x19384,x19381,x19385),f855(x19383,x19384,x19382,x19385)) % 167.77/167.52 [1939]~E(x19391,x19392)+E(f855(x19393,x19394,x19395,x19391),f855(x19393,x19394,x19395,x19392)) % 167.77/167.52 [1940]~E(x19401,x19402)+E(f713(x19401,x19403,x19404,x19405,x19406),f713(x19402,x19403,x19404,x19405,x19406)) % 167.77/167.52 [1941]~E(x19411,x19412)+E(f713(x19413,x19411,x19414,x19415,x19416),f713(x19413,x19412,x19414,x19415,x19416)) % 167.77/167.52 [1942]~E(x19421,x19422)+E(f713(x19423,x19424,x19421,x19425,x19426),f713(x19423,x19424,x19422,x19425,x19426)) % 167.77/167.52 [1943]~E(x19431,x19432)+E(f713(x19433,x19434,x19435,x19431,x19436),f713(x19433,x19434,x19435,x19432,x19436)) % 167.77/167.52 [1944]~E(x19441,x19442)+E(f713(x19443,x19444,x19445,x19446,x19441),f713(x19443,x19444,x19445,x19446,x19442)) % 167.77/167.52 [1945]~E(x19451,x19452)+E(f502(x19451,x19453,x19454,x19455),f502(x19452,x19453,x19454,x19455)) % 167.77/167.52 [1946]~E(x19461,x19462)+E(f502(x19463,x19461,x19464,x19465),f502(x19463,x19462,x19464,x19465)) % 167.77/167.52 [1947]~E(x19471,x19472)+E(f502(x19473,x19474,x19471,x19475),f502(x19473,x19474,x19472,x19475)) % 167.77/167.52 [1948]~E(x19481,x19482)+E(f502(x19483,x19484,x19485,x19481),f502(x19483,x19484,x19485,x19482)) % 167.77/167.52 [1949]~E(x19491,x19492)+E(f97(x19491,x19493,x19494),f97(x19492,x19493,x19494)) % 167.77/167.52 [1950]~E(x19501,x19502)+E(f97(x19503,x19501,x19504),f97(x19503,x19502,x19504)) % 167.77/167.52 [1951]~E(x19511,x19512)+E(f97(x19513,x19514,x19511),f97(x19513,x19514,x19512)) % 167.77/167.52 [1952]~E(x19521,x19522)+E(f93(x19521,x19523,x19524),f93(x19522,x19523,x19524)) % 167.77/167.52 [1953]~E(x19531,x19532)+E(f93(x19533,x19531,x19534),f93(x19533,x19532,x19534)) % 167.77/167.52 [1954]~E(x19541,x19542)+E(f93(x19543,x19544,x19541),f93(x19543,x19544,x19542)) % 167.77/167.52 [1955]~E(x19551,x19552)+E(f516(x19551,x19553,x19554,x19555),f516(x19552,x19553,x19554,x19555)) % 167.77/167.52 [1956]~E(x19561,x19562)+E(f516(x19563,x19561,x19564,x19565),f516(x19563,x19562,x19564,x19565)) % 167.77/167.52 [1957]~E(x19571,x19572)+E(f516(x19573,x19574,x19571,x19575),f516(x19573,x19574,x19572,x19575)) % 167.77/167.52 [1958]~E(x19581,x19582)+E(f516(x19583,x19584,x19585,x19581),f516(x19583,x19584,x19585,x19582)) % 167.77/167.52 [1959]~E(x19591,x19592)+E(f630(x19591,x19593,x19594,x19595),f630(x19592,x19593,x19594,x19595)) % 167.77/167.52 [1960]~E(x19601,x19602)+E(f630(x19603,x19601,x19604,x19605),f630(x19603,x19602,x19604,x19605)) % 167.77/167.52 [1961]~E(x19611,x19612)+E(f630(x19613,x19614,x19611,x19615),f630(x19613,x19614,x19612,x19615)) % 167.77/167.52 [1962]~E(x19621,x19622)+E(f630(x19623,x19624,x19625,x19621),f630(x19623,x19624,x19625,x19622)) % 167.77/167.52 [1963]~E(x19631,x19632)+E(f651(x19631,x19633,x19634),f651(x19632,x19633,x19634)) % 167.77/167.52 [1964]~E(x19641,x19642)+E(f651(x19643,x19641,x19644),f651(x19643,x19642,x19644)) % 167.77/167.52 [1965]~E(x19651,x19652)+E(f651(x19653,x19654,x19651),f651(x19653,x19654,x19652)) % 167.77/167.52 [1966]~E(x19661,x19662)+E(f743(x19661,x19663,x19664),f743(x19662,x19663,x19664)) % 167.77/167.52 [1967]~E(x19671,x19672)+E(f743(x19673,x19671,x19674),f743(x19673,x19672,x19674)) % 167.77/167.52 [1968]~E(x19681,x19682)+E(f743(x19683,x19684,x19681),f743(x19683,x19684,x19682)) % 167.77/167.52 [1969]~E(x19691,x19692)+E(f674(x19691,x19693,x19694),f674(x19692,x19693,x19694)) % 167.77/167.52 [1970]~E(x19701,x19702)+E(f674(x19703,x19701,x19704),f674(x19703,x19702,x19704)) % 167.77/167.52 [1971]~E(x19711,x19712)+E(f674(x19713,x19714,x19711),f674(x19713,x19714,x19712)) % 167.77/167.52 [1972]~E(x19721,x19722)+E(f225(x19721,x19723),f225(x19722,x19723)) % 167.77/167.52 [1973]~E(x19731,x19732)+E(f225(x19733,x19731),f225(x19733,x19732)) % 167.77/167.52 [1974]~E(x19741,x19742)+E(f477(x19741,x19743),f477(x19742,x19743)) % 167.77/167.52 [1975]~E(x19751,x19752)+E(f477(x19753,x19751),f477(x19753,x19752)) % 167.77/167.52 [1976]~E(x19761,x19762)+E(f209(x19761),f209(x19762)) % 167.77/167.52 [1977]~E(x19771,x19772)+E(f840(x19771,x19773),f840(x19772,x19773)) % 167.77/167.52 [1978]~E(x19781,x19782)+E(f840(x19783,x19781),f840(x19783,x19782)) % 167.77/167.52 [1979]~E(x19791,x19792)+E(f673(x19791,x19793,x19794),f673(x19792,x19793,x19794)) % 167.77/167.52 [1980]~E(x19801,x19802)+E(f673(x19803,x19801,x19804),f673(x19803,x19802,x19804)) % 167.77/167.52 [1981]~E(x19811,x19812)+E(f673(x19813,x19814,x19811),f673(x19813,x19814,x19812)) % 167.77/167.52 [1982]~E(x19821,x19822)+E(f647(x19821,x19823,x19824,x19825),f647(x19822,x19823,x19824,x19825)) % 167.77/167.52 [1983]~E(x19831,x19832)+E(f647(x19833,x19831,x19834,x19835),f647(x19833,x19832,x19834,x19835)) % 167.77/167.52 [1984]~E(x19841,x19842)+E(f647(x19843,x19844,x19841,x19845),f647(x19843,x19844,x19842,x19845)) % 167.77/167.52 [1985]~E(x19851,x19852)+E(f647(x19853,x19854,x19855,x19851),f647(x19853,x19854,x19855,x19852)) % 167.77/167.52 [1986]~E(x19861,x19862)+E(f210(x19861,x19863),f210(x19862,x19863)) % 167.77/167.52 [1987]~E(x19871,x19872)+E(f210(x19873,x19871),f210(x19873,x19872)) % 167.77/167.52 [1988]~E(x19881,x19882)+E(f496(x19881,x19883,x19884),f496(x19882,x19883,x19884)) % 167.77/167.52 [1989]~E(x19891,x19892)+E(f496(x19893,x19891,x19894),f496(x19893,x19892,x19894)) % 167.77/167.52 [1990]~E(x19901,x19902)+E(f496(x19903,x19904,x19901),f496(x19903,x19904,x19902)) % 167.77/167.52 [1991]~E(x19911,x19912)+E(f548(x19911,x19913,x19914,x19915,x19916),f548(x19912,x19913,x19914,x19915,x19916)) % 167.77/167.52 [1992]~E(x19921,x19922)+E(f548(x19923,x19921,x19924,x19925,x19926),f548(x19923,x19922,x19924,x19925,x19926)) % 167.77/167.52 [1993]~E(x19931,x19932)+E(f548(x19933,x19934,x19931,x19935,x19936),f548(x19933,x19934,x19932,x19935,x19936)) % 167.77/167.52 [1994]~E(x19941,x19942)+E(f548(x19943,x19944,x19945,x19941,x19946),f548(x19943,x19944,x19945,x19942,x19946)) % 167.77/167.52 [1995]~E(x19951,x19952)+E(f548(x19953,x19954,x19955,x19956,x19951),f548(x19953,x19954,x19955,x19956,x19952)) % 167.77/167.52 [1996]~E(x19961,x19962)+E(f390(x19961,x19963,x19964),f390(x19962,x19963,x19964)) % 167.77/167.52 [1997]~E(x19971,x19972)+E(f390(x19973,x19971,x19974),f390(x19973,x19972,x19974)) % 167.77/167.52 [1998]~E(x19981,x19982)+E(f390(x19983,x19984,x19981),f390(x19983,x19984,x19982)) % 167.77/167.52 [1999]~E(x19991,x19992)+E(f411(x19991,x19993,x19994,x19995),f411(x19992,x19993,x19994,x19995)) % 167.77/167.52 [2000]~E(x20001,x20002)+E(f411(x20003,x20001,x20004,x20005),f411(x20003,x20002,x20004,x20005)) % 167.77/167.52 [2001]~E(x20011,x20012)+E(f411(x20013,x20014,x20011,x20015),f411(x20013,x20014,x20012,x20015)) % 167.77/167.52 [2002]~E(x20021,x20022)+E(f411(x20023,x20024,x20025,x20021),f411(x20023,x20024,x20025,x20022)) % 167.77/167.52 [2003]~E(x20031,x20032)+E(f343(x20031,x20033,x20034,x20035,x20036),f343(x20032,x20033,x20034,x20035,x20036)) % 167.77/167.52 [2004]~E(x20041,x20042)+E(f343(x20043,x20041,x20044,x20045,x20046),f343(x20043,x20042,x20044,x20045,x20046)) % 167.77/167.52 [2005]~E(x20051,x20052)+E(f343(x20053,x20054,x20051,x20055,x20056),f343(x20053,x20054,x20052,x20055,x20056)) % 167.77/167.52 [2006]~E(x20061,x20062)+E(f343(x20063,x20064,x20065,x20061,x20066),f343(x20063,x20064,x20065,x20062,x20066)) % 167.77/167.52 [2007]~E(x20071,x20072)+E(f343(x20073,x20074,x20075,x20076,x20071),f343(x20073,x20074,x20075,x20076,x20072)) % 167.77/167.52 [2008]~E(x20081,x20082)+E(f729(x20081,x20083,x20084),f729(x20082,x20083,x20084)) % 167.77/167.52 [2009]~E(x20091,x20092)+E(f729(x20093,x20091,x20094),f729(x20093,x20092,x20094)) % 167.77/167.52 [2010]~E(x20101,x20102)+E(f729(x20103,x20104,x20101),f729(x20103,x20104,x20102)) % 167.77/167.52 [2011]~E(x20111,x20112)+E(f629(x20111,x20113,x20114),f629(x20112,x20113,x20114)) % 167.77/167.52 [2012]~E(x20121,x20122)+E(f629(x20123,x20121,x20124),f629(x20123,x20122,x20124)) % 167.77/167.52 [2013]~E(x20131,x20132)+E(f629(x20133,x20134,x20131),f629(x20133,x20134,x20132)) % 167.77/167.52 [2014]~E(x20141,x20142)+E(f430(x20141,x20143,x20144,x20145),f430(x20142,x20143,x20144,x20145)) % 167.77/167.52 [2015]~E(x20151,x20152)+E(f430(x20153,x20151,x20154,x20155),f430(x20153,x20152,x20154,x20155)) % 167.77/167.52 [2016]~E(x20161,x20162)+E(f430(x20163,x20164,x20161,x20165),f430(x20163,x20164,x20162,x20165)) % 167.77/167.52 [2017]~E(x20171,x20172)+E(f430(x20173,x20174,x20175,x20171),f430(x20173,x20174,x20175,x20172)) % 167.77/167.52 [2018]~E(x20181,x20182)+E(f607(x20181,x20183,x20184),f607(x20182,x20183,x20184)) % 167.77/167.52 [2019]~E(x20191,x20192)+E(f607(x20193,x20191,x20194),f607(x20193,x20192,x20194)) % 167.77/167.52 [2020]~E(x20201,x20202)+E(f607(x20203,x20204,x20201),f607(x20203,x20204,x20202)) % 167.77/167.52 [2021]~E(x20211,x20212)+E(f467(x20211,x20213,x20214),f467(x20212,x20213,x20214)) % 167.77/167.52 [2022]~E(x20221,x20222)+E(f467(x20223,x20221,x20224),f467(x20223,x20222,x20224)) % 167.77/167.52 [2023]~E(x20231,x20232)+E(f467(x20233,x20234,x20231),f467(x20233,x20234,x20232)) % 167.77/167.52 [2024]~E(x20241,x20242)+E(f418(x20241,x20243,x20244,x20245),f418(x20242,x20243,x20244,x20245)) % 167.77/167.52 [2025]~E(x20251,x20252)+E(f418(x20253,x20251,x20254,x20255),f418(x20253,x20252,x20254,x20255)) % 167.77/167.52 [2026]~E(x20261,x20262)+E(f418(x20263,x20264,x20261,x20265),f418(x20263,x20264,x20262,x20265)) % 167.77/167.52 [2027]~E(x20271,x20272)+E(f418(x20273,x20274,x20275,x20271),f418(x20273,x20274,x20275,x20272)) % 167.77/167.52 [2028]~E(x20281,x20282)+E(f720(x20281,x20283,x20284),f720(x20282,x20283,x20284)) % 167.77/167.52 [2029]~E(x20291,x20292)+E(f720(x20293,x20291,x20294),f720(x20293,x20292,x20294)) % 167.77/167.52 [2030]~E(x20301,x20302)+E(f720(x20303,x20304,x20301),f720(x20303,x20304,x20302)) % 167.77/167.52 [2031]~E(x20311,x20312)+E(f517(x20311,x20313,x20314),f517(x20312,x20313,x20314)) % 167.77/167.52 [2032]~E(x20321,x20322)+E(f517(x20323,x20321,x20324),f517(x20323,x20322,x20324)) % 167.77/167.52 [2033]~E(x20331,x20332)+E(f517(x20333,x20334,x20331),f517(x20333,x20334,x20332)) % 167.77/167.52 [2034]~E(x20341,x20342)+E(f455(x20341,x20343,x20344),f455(x20342,x20343,x20344)) % 167.77/167.52 [2035]~E(x20351,x20352)+E(f455(x20353,x20351,x20354),f455(x20353,x20352,x20354)) % 167.77/167.52 [2036]~E(x20361,x20362)+E(f455(x20363,x20364,x20361),f455(x20363,x20364,x20362)) % 167.77/167.52 [2037]~E(x20371,x20372)+E(f648(x20371,x20373,x20374),f648(x20372,x20373,x20374)) % 167.77/167.52 [2038]~E(x20381,x20382)+E(f648(x20383,x20381,x20384),f648(x20383,x20382,x20384)) % 167.77/167.52 [2039]~E(x20391,x20392)+E(f648(x20393,x20394,x20391),f648(x20393,x20394,x20392)) % 167.77/167.52 [2040]~E(x20401,x20402)+E(f124(x20401),f124(x20402)) % 167.77/167.52 [2041]~E(x20411,x20412)+E(f552(x20411,x20413,x20414),f552(x20412,x20413,x20414)) % 167.77/167.52 [2042]~E(x20421,x20422)+E(f552(x20423,x20421,x20424),f552(x20423,x20422,x20424)) % 167.77/167.52 [2043]~E(x20431,x20432)+E(f552(x20433,x20434,x20431),f552(x20433,x20434,x20432)) % 167.77/167.52 [2044]~E(x20441,x20442)+E(f388(x20441,x20443),f388(x20442,x20443)) % 167.77/167.52 [2045]~E(x20451,x20452)+E(f388(x20453,x20451),f388(x20453,x20452)) % 167.77/167.52 [2046]~E(x20461,x20462)+E(f601(x20461,x20463,x20464,x20465,x20466,x20467),f601(x20462,x20463,x20464,x20465,x20466,x20467)) % 167.77/167.52 [2047]~E(x20471,x20472)+E(f601(x20473,x20471,x20474,x20475,x20476,x20477),f601(x20473,x20472,x20474,x20475,x20476,x20477)) % 167.77/167.52 [2048]~E(x20481,x20482)+E(f601(x20483,x20484,x20481,x20485,x20486,x20487),f601(x20483,x20484,x20482,x20485,x20486,x20487)) % 167.77/167.52 [2049]~E(x20491,x20492)+E(f601(x20493,x20494,x20495,x20491,x20496,x20497),f601(x20493,x20494,x20495,x20492,x20496,x20497)) % 167.77/167.52 [2050]~E(x20501,x20502)+E(f601(x20503,x20504,x20505,x20506,x20501,x20507),f601(x20503,x20504,x20505,x20506,x20502,x20507)) % 167.77/167.52 [2051]~E(x20511,x20512)+E(f601(x20513,x20514,x20515,x20516,x20517,x20511),f601(x20513,x20514,x20515,x20516,x20517,x20512)) % 167.77/167.52 [2052]~E(x20521,x20522)+E(f504(x20521,x20523,x20524,x20525),f504(x20522,x20523,x20524,x20525)) % 167.77/167.52 [2053]~E(x20531,x20532)+E(f504(x20533,x20531,x20534,x20535),f504(x20533,x20532,x20534,x20535)) % 167.77/167.52 [2054]~E(x20541,x20542)+E(f504(x20543,x20544,x20541,x20545),f504(x20543,x20544,x20542,x20545)) % 167.77/167.52 [2055]~E(x20551,x20552)+E(f504(x20553,x20554,x20555,x20551),f504(x20553,x20554,x20555,x20552)) % 167.77/167.52 [2056]~E(x20561,x20562)+E(f695(x20561,x20563,x20564,x20565,x20566),f695(x20562,x20563,x20564,x20565,x20566)) % 167.77/167.52 [2057]~E(x20571,x20572)+E(f695(x20573,x20571,x20574,x20575,x20576),f695(x20573,x20572,x20574,x20575,x20576)) % 167.77/167.52 [2058]~E(x20581,x20582)+E(f695(x20583,x20584,x20581,x20585,x20586),f695(x20583,x20584,x20582,x20585,x20586)) % 167.77/167.52 [2059]~E(x20591,x20592)+E(f695(x20593,x20594,x20595,x20591,x20596),f695(x20593,x20594,x20595,x20592,x20596)) % 167.77/167.52 [2060]~E(x20601,x20602)+E(f695(x20603,x20604,x20605,x20606,x20601),f695(x20603,x20604,x20605,x20606,x20602)) % 167.77/167.52 [2061]~E(x20611,x20612)+E(f542(x20611,x20613,x20614,x20615),f542(x20612,x20613,x20614,x20615)) % 167.77/167.52 [2062]~E(x20621,x20622)+E(f542(x20623,x20621,x20624,x20625),f542(x20623,x20622,x20624,x20625)) % 167.77/167.52 [2063]~E(x20631,x20632)+E(f542(x20633,x20634,x20631,x20635),f542(x20633,x20634,x20632,x20635)) % 167.77/167.52 [2064]~E(x20641,x20642)+E(f542(x20643,x20644,x20645,x20641),f542(x20643,x20644,x20645,x20642)) % 167.77/167.52 [2065]~E(x20651,x20652)+E(f858(x20651,x20653,x20654,x20655,x20656),f858(x20652,x20653,x20654,x20655,x20656)) % 167.77/167.52 [2066]~E(x20661,x20662)+E(f858(x20663,x20661,x20664,x20665,x20666),f858(x20663,x20662,x20664,x20665,x20666)) % 167.77/167.52 [2067]~E(x20671,x20672)+E(f858(x20673,x20674,x20671,x20675,x20676),f858(x20673,x20674,x20672,x20675,x20676)) % 167.77/167.52 [2068]~E(x20681,x20682)+E(f858(x20683,x20684,x20685,x20681,x20686),f858(x20683,x20684,x20685,x20682,x20686)) % 167.77/167.52 [2069]~E(x20691,x20692)+E(f858(x20693,x20694,x20695,x20696,x20691),f858(x20693,x20694,x20695,x20696,x20692)) % 167.77/167.52 [2070]~E(x20701,x20702)+E(f788(x20701,x20703,x20704,x20705,x20706,x20707,x20708),f788(x20702,x20703,x20704,x20705,x20706,x20707,x20708)) % 167.77/167.52 [2071]~E(x20711,x20712)+E(f788(x20713,x20711,x20714,x20715,x20716,x20717,x20718),f788(x20713,x20712,x20714,x20715,x20716,x20717,x20718)) % 167.77/167.52 [2072]~E(x20721,x20722)+E(f788(x20723,x20724,x20721,x20725,x20726,x20727,x20728),f788(x20723,x20724,x20722,x20725,x20726,x20727,x20728)) % 167.77/167.52 [2073]~E(x20731,x20732)+E(f788(x20733,x20734,x20735,x20731,x20736,x20737,x20738),f788(x20733,x20734,x20735,x20732,x20736,x20737,x20738)) % 167.77/167.52 [2074]~E(x20741,x20742)+E(f788(x20743,x20744,x20745,x20746,x20741,x20747,x20748),f788(x20743,x20744,x20745,x20746,x20742,x20747,x20748)) % 167.77/167.52 [2075]~E(x20751,x20752)+E(f788(x20753,x20754,x20755,x20756,x20757,x20751,x20758),f788(x20753,x20754,x20755,x20756,x20757,x20752,x20758)) % 167.77/167.52 [2076]~E(x20761,x20762)+E(f788(x20763,x20764,x20765,x20766,x20767,x20768,x20761),f788(x20763,x20764,x20765,x20766,x20767,x20768,x20762)) % 167.77/167.52 [2077]~E(x20771,x20772)+E(f538(x20771,x20773,x20774,x20775),f538(x20772,x20773,x20774,x20775)) % 167.77/167.52 [2078]~E(x20781,x20782)+E(f538(x20783,x20781,x20784,x20785),f538(x20783,x20782,x20784,x20785)) % 167.77/167.52 [2079]~E(x20791,x20792)+E(f538(x20793,x20794,x20791,x20795),f538(x20793,x20794,x20792,x20795)) % 167.77/167.52 [2080]~E(x20801,x20802)+E(f538(x20803,x20804,x20805,x20801),f538(x20803,x20804,x20805,x20802)) % 167.77/167.52 [2081]~E(x20811,x20812)+E(f719(x20811,x20813,x20814),f719(x20812,x20813,x20814)) % 167.77/167.52 [2082]~E(x20821,x20822)+E(f719(x20823,x20821,x20824),f719(x20823,x20822,x20824)) % 167.77/167.52 [2083]~E(x20831,x20832)+E(f719(x20833,x20834,x20831),f719(x20833,x20834,x20832)) % 167.77/167.52 [2084]~E(x20841,x20842)+E(f464(x20841,x20843),f464(x20842,x20843)) % 167.77/167.52 [2085]~E(x20851,x20852)+E(f464(x20853,x20851),f464(x20853,x20852)) % 167.77/167.52 [2086]~E(x20861,x20862)+E(f363(x20861,x20863,x20864,x20865,x20866),f363(x20862,x20863,x20864,x20865,x20866)) % 167.77/167.52 [2087]~E(x20871,x20872)+E(f363(x20873,x20871,x20874,x20875,x20876),f363(x20873,x20872,x20874,x20875,x20876)) % 167.77/167.52 [2088]~E(x20881,x20882)+E(f363(x20883,x20884,x20881,x20885,x20886),f363(x20883,x20884,x20882,x20885,x20886)) % 167.77/167.52 [2089]~E(x20891,x20892)+E(f363(x20893,x20894,x20895,x20891,x20896),f363(x20893,x20894,x20895,x20892,x20896)) % 167.77/167.52 [2090]~E(x20901,x20902)+E(f363(x20903,x20904,x20905,x20906,x20901),f363(x20903,x20904,x20905,x20906,x20902)) % 167.77/167.52 [2091]~E(x20911,x20912)+E(f848(x20911,x20913),f848(x20912,x20913)) % 167.77/167.52 [2092]~E(x20921,x20922)+E(f848(x20923,x20921),f848(x20923,x20922)) % 167.77/167.52 [2093]~E(x20931,x20932)+E(f722(x20931,x20933,x20934,x20935),f722(x20932,x20933,x20934,x20935)) % 167.77/167.52 [2094]~E(x20941,x20942)+E(f722(x20943,x20941,x20944,x20945),f722(x20943,x20942,x20944,x20945)) % 167.77/167.52 [2095]~E(x20951,x20952)+E(f722(x20953,x20954,x20951,x20955),f722(x20953,x20954,x20952,x20955)) % 167.77/167.52 [2096]~E(x20961,x20962)+E(f722(x20963,x20964,x20965,x20961),f722(x20963,x20964,x20965,x20962)) % 167.77/167.52 [2097]~E(x20971,x20972)+E(f676(x20971,x20973,x20974),f676(x20972,x20973,x20974)) % 167.77/167.52 [2098]~E(x20981,x20982)+E(f676(x20983,x20981,x20984),f676(x20983,x20982,x20984)) % 167.77/167.52 [2099]~E(x20991,x20992)+E(f676(x20993,x20994,x20991),f676(x20993,x20994,x20992)) % 167.77/167.52 [2100]~E(x21001,x21002)+E(f495(x21001,x21003,x21004,x21005),f495(x21002,x21003,x21004,x21005)) % 167.77/167.52 [2101]~E(x21011,x21012)+E(f495(x21013,x21011,x21014,x21015),f495(x21013,x21012,x21014,x21015)) % 167.77/167.52 [2102]~E(x21021,x21022)+E(f495(x21023,x21024,x21021,x21025),f495(x21023,x21024,x21022,x21025)) % 167.77/167.52 [2103]~E(x21031,x21032)+E(f495(x21033,x21034,x21035,x21031),f495(x21033,x21034,x21035,x21032)) % 167.77/167.52 [2104]~E(x21041,x21042)+E(f123(x21041,x21043,x21044,x21045),f123(x21042,x21043,x21044,x21045)) % 167.77/167.52 [2105]~E(x21051,x21052)+E(f123(x21053,x21051,x21054,x21055),f123(x21053,x21052,x21054,x21055)) % 167.77/167.52 [2106]~E(x21061,x21062)+E(f123(x21063,x21064,x21061,x21065),f123(x21063,x21064,x21062,x21065)) % 167.77/167.52 [2107]~E(x21071,x21072)+E(f123(x21073,x21074,x21075,x21071),f123(x21073,x21074,x21075,x21072)) % 167.77/167.52 [2108]~E(x21081,x21082)+E(f407(x21081,x21083,x21084,x21085),f407(x21082,x21083,x21084,x21085)) % 167.77/167.52 [2109]~E(x21091,x21092)+E(f407(x21093,x21091,x21094,x21095),f407(x21093,x21092,x21094,x21095)) % 167.77/167.52 [2110]~E(x21101,x21102)+E(f407(x21103,x21104,x21101,x21105),f407(x21103,x21104,x21102,x21105)) % 167.77/167.52 [2111]~E(x21111,x21112)+E(f407(x21113,x21114,x21115,x21111),f407(x21113,x21114,x21115,x21112)) % 167.77/167.52 [2112]~E(x21121,x21122)+E(f522(x21121,x21123),f522(x21122,x21123)) % 167.77/167.52 [2113]~E(x21131,x21132)+E(f522(x21133,x21131),f522(x21133,x21132)) % 167.77/167.52 [2114]~E(x21141,x21142)+E(f529(x21141,x21143),f529(x21142,x21143)) % 167.77/167.52 [2115]~E(x21151,x21152)+E(f529(x21153,x21151),f529(x21153,x21152)) % 167.77/167.52 [2116]~E(x21161,x21162)+E(f254(x21161,x21163,x21164),f254(x21162,x21163,x21164)) % 167.77/167.52 [2117]~E(x21171,x21172)+E(f254(x21173,x21171,x21174),f254(x21173,x21172,x21174)) % 167.77/167.52 [2118]~E(x21181,x21182)+E(f254(x21183,x21184,x21181),f254(x21183,x21184,x21182)) % 167.77/167.52 [2119]~E(x21191,x21192)+E(f738(x21191,x21193,x21194),f738(x21192,x21193,x21194)) % 167.77/167.52 [2120]~E(x21201,x21202)+E(f738(x21203,x21201,x21204),f738(x21203,x21202,x21204)) % 167.77/167.52 [2121]~E(x21211,x21212)+E(f738(x21213,x21214,x21211),f738(x21213,x21214,x21212)) % 167.77/167.52 [2122]~E(x21221,x21222)+E(f619(x21221,x21223,x21224,x21225,x21226,x21227,x21228,x21229),f619(x21222,x21223,x21224,x21225,x21226,x21227,x21228,x21229)) % 167.77/167.52 [2123]~E(x21231,x21232)+E(f619(x21233,x21231,x21234,x21235,x21236,x21237,x21238,x21239),f619(x21233,x21232,x21234,x21235,x21236,x21237,x21238,x21239)) % 167.77/167.52 [2124]~E(x21241,x21242)+E(f619(x21243,x21244,x21241,x21245,x21246,x21247,x21248,x21249),f619(x21243,x21244,x21242,x21245,x21246,x21247,x21248,x21249)) % 167.77/167.52 [2125]~E(x21251,x21252)+E(f619(x21253,x21254,x21255,x21251,x21256,x21257,x21258,x21259),f619(x21253,x21254,x21255,x21252,x21256,x21257,x21258,x21259)) % 167.77/167.52 [2126]~E(x21261,x21262)+E(f619(x21263,x21264,x21265,x21266,x21261,x21267,x21268,x21269),f619(x21263,x21264,x21265,x21266,x21262,x21267,x21268,x21269)) % 167.77/167.52 [2127]~E(x21271,x21272)+E(f619(x21273,x21274,x21275,x21276,x21277,x21271,x21278,x21279),f619(x21273,x21274,x21275,x21276,x21277,x21272,x21278,x21279)) % 167.77/167.52 [2128]~E(x21281,x21282)+E(f619(x21283,x21284,x21285,x21286,x21287,x21288,x21281,x21289),f619(x21283,x21284,x21285,x21286,x21287,x21288,x21282,x21289)) % 167.77/167.52 [2129]~E(x21291,x21292)+E(f619(x21293,x21294,x21295,x21296,x21297,x21298,x21299,x21291),f619(x21293,x21294,x21295,x21296,x21297,x21298,x21299,x21292)) % 167.77/167.52 [2130]~E(x21301,x21302)+E(f458(x21301,x21303,x21304),f458(x21302,x21303,x21304)) % 167.77/167.52 [2131]~E(x21311,x21312)+E(f458(x21313,x21311,x21314),f458(x21313,x21312,x21314)) % 167.77/167.52 [2132]~E(x21321,x21322)+E(f458(x21323,x21324,x21321),f458(x21323,x21324,x21322)) % 167.77/167.52 [2133]~E(x21331,x21332)+E(f446(x21331,x21333,x21334,x21335,x21336,x21337),f446(x21332,x21333,x21334,x21335,x21336,x21337)) % 167.77/167.52 [2134]~E(x21341,x21342)+E(f446(x21343,x21341,x21344,x21345,x21346,x21347),f446(x21343,x21342,x21344,x21345,x21346,x21347)) % 167.77/167.52 [2135]~E(x21351,x21352)+E(f446(x21353,x21354,x21351,x21355,x21356,x21357),f446(x21353,x21354,x21352,x21355,x21356,x21357)) % 167.77/167.52 [2136]~E(x21361,x21362)+E(f446(x21363,x21364,x21365,x21361,x21366,x21367),f446(x21363,x21364,x21365,x21362,x21366,x21367)) % 167.77/167.52 [2137]~E(x21371,x21372)+E(f446(x21373,x21374,x21375,x21376,x21371,x21377),f446(x21373,x21374,x21375,x21376,x21372,x21377)) % 167.77/167.52 [2138]~E(x21381,x21382)+E(f446(x21383,x21384,x21385,x21386,x21387,x21381),f446(x21383,x21384,x21385,x21386,x21387,x21382)) % 167.77/167.52 [2139]~E(x21391,x21392)+E(f759(x21391,x21393),f759(x21392,x21393)) % 167.77/167.52 [2140]~E(x21401,x21402)+E(f759(x21403,x21401),f759(x21403,x21402)) % 167.77/167.52 [2141]~E(x21411,x21412)+E(f377(x21411),f377(x21412)) % 167.77/167.52 [2142]~E(x21421,x21422)+E(f17(x21421,x21423,x21424,x21425),f17(x21422,x21423,x21424,x21425)) % 167.77/167.52 [2143]~E(x21431,x21432)+E(f17(x21433,x21431,x21434,x21435),f17(x21433,x21432,x21434,x21435)) % 167.77/167.52 [2144]~E(x21441,x21442)+E(f17(x21443,x21444,x21441,x21445),f17(x21443,x21444,x21442,x21445)) % 167.77/167.52 [2145]~E(x21451,x21452)+E(f17(x21453,x21454,x21455,x21451),f17(x21453,x21454,x21455,x21452)) % 167.77/167.52 [2146]~E(x21461,x21462)+E(f604(x21461,x21463,x21464,x21465,x21466,x21467),f604(x21462,x21463,x21464,x21465,x21466,x21467)) % 167.77/167.52 [2147]~E(x21471,x21472)+E(f604(x21473,x21471,x21474,x21475,x21476,x21477),f604(x21473,x21472,x21474,x21475,x21476,x21477)) % 167.77/167.52 [2148]~E(x21481,x21482)+E(f604(x21483,x21484,x21481,x21485,x21486,x21487),f604(x21483,x21484,x21482,x21485,x21486,x21487)) % 167.77/167.52 [2149]~E(x21491,x21492)+E(f604(x21493,x21494,x21495,x21491,x21496,x21497),f604(x21493,x21494,x21495,x21492,x21496,x21497)) % 167.77/167.52 [2150]~E(x21501,x21502)+E(f604(x21503,x21504,x21505,x21506,x21501,x21507),f604(x21503,x21504,x21505,x21506,x21502,x21507)) % 167.77/167.52 [2151]~E(x21511,x21512)+E(f604(x21513,x21514,x21515,x21516,x21517,x21511),f604(x21513,x21514,x21515,x21516,x21517,x21512)) % 167.77/167.52 [2152]~E(x21521,x21522)+E(f346(x21521),f346(x21522)) % 167.77/167.52 [2153]~E(x21531,x21532)+E(f593(x21531,x21533),f593(x21532,x21533)) % 167.77/167.52 [2154]~E(x21541,x21542)+E(f593(x21543,x21541),f593(x21543,x21542)) % 167.77/167.52 [2155]~E(x21551,x21552)+E(f567(x21551,x21553,x21554,x21555),f567(x21552,x21553,x21554,x21555)) % 167.77/167.52 [2156]~E(x21561,x21562)+E(f567(x21563,x21561,x21564,x21565),f567(x21563,x21562,x21564,x21565)) % 167.77/167.52 [2157]~E(x21571,x21572)+E(f567(x21573,x21574,x21571,x21575),f567(x21573,x21574,x21572,x21575)) % 167.77/167.52 [2158]~E(x21581,x21582)+E(f567(x21583,x21584,x21585,x21581),f567(x21583,x21584,x21585,x21582)) % 167.77/167.52 [2159]~E(x21591,x21592)+E(f275(x21591,x21593),f275(x21592,x21593)) % 167.77/167.52 [2160]~E(x21601,x21602)+E(f275(x21603,x21601),f275(x21603,x21602)) % 167.77/167.52 [2161]~E(x21611,x21612)+E(f711(x21611,x21613,x21614,x21615,x21616),f711(x21612,x21613,x21614,x21615,x21616)) % 167.77/167.52 [2162]~E(x21621,x21622)+E(f711(x21623,x21621,x21624,x21625,x21626),f711(x21623,x21622,x21624,x21625,x21626)) % 167.77/167.52 [2163]~E(x21631,x21632)+E(f711(x21633,x21634,x21631,x21635,x21636),f711(x21633,x21634,x21632,x21635,x21636)) % 167.77/167.52 [2164]~E(x21641,x21642)+E(f711(x21643,x21644,x21645,x21641,x21646),f711(x21643,x21644,x21645,x21642,x21646)) % 167.77/167.52 [2165]~E(x21651,x21652)+E(f711(x21653,x21654,x21655,x21656,x21651),f711(x21653,x21654,x21655,x21656,x21652)) % 167.77/167.52 [2166]~E(x21661,x21662)+E(f492(x21661,x21663,x21664,x21665),f492(x21662,x21663,x21664,x21665)) % 167.77/167.52 [2167]~E(x21671,x21672)+E(f492(x21673,x21671,x21674,x21675),f492(x21673,x21672,x21674,x21675)) % 167.77/167.52 [2168]~E(x21681,x21682)+E(f492(x21683,x21684,x21681,x21685),f492(x21683,x21684,x21682,x21685)) % 167.77/167.52 [2169]~E(x21691,x21692)+E(f492(x21693,x21694,x21695,x21691),f492(x21693,x21694,x21695,x21692)) % 167.77/167.52 [2170]~E(x21701,x21702)+E(f774(x21701,x21703),f774(x21702,x21703)) % 167.77/167.52 [2171]~E(x21711,x21712)+E(f774(x21713,x21711),f774(x21713,x21712)) % 167.77/167.52 [2172]~E(x21721,x21722)+E(f475(x21721,x21723),f475(x21722,x21723)) % 167.77/167.52 [2173]~E(x21731,x21732)+E(f475(x21733,x21731),f475(x21733,x21732)) % 167.77/167.52 [2174]~E(x21741,x21742)+E(f348(x21741,x21743,x21744),f348(x21742,x21743,x21744)) % 167.77/167.52 [2175]~E(x21751,x21752)+E(f348(x21753,x21751,x21754),f348(x21753,x21752,x21754)) % 167.77/167.52 [2176]~E(x21761,x21762)+E(f348(x21763,x21764,x21761),f348(x21763,x21764,x21762)) % 167.77/167.52 [2177]~E(x21771,x21772)+E(f716(x21771,x21773),f716(x21772,x21773)) % 167.77/167.52 [2178]~E(x21781,x21782)+E(f716(x21783,x21781),f716(x21783,x21782)) % 167.77/167.52 [2179]~E(x21791,x21792)+E(f444(x21791,x21793,x21794,x21795,x21796),f444(x21792,x21793,x21794,x21795,x21796)) % 167.77/167.52 [2180]~E(x21801,x21802)+E(f444(x21803,x21801,x21804,x21805,x21806),f444(x21803,x21802,x21804,x21805,x21806)) % 167.77/167.52 [2181]~E(x21811,x21812)+E(f444(x21813,x21814,x21811,x21815,x21816),f444(x21813,x21814,x21812,x21815,x21816)) % 167.77/167.52 [2182]~E(x21821,x21822)+E(f444(x21823,x21824,x21825,x21821,x21826),f444(x21823,x21824,x21825,x21822,x21826)) % 167.77/167.52 [2183]~E(x21831,x21832)+E(f444(x21833,x21834,x21835,x21836,x21831),f444(x21833,x21834,x21835,x21836,x21832)) % 167.77/167.52 [2184]~E(x21841,x21842)+E(f742(x21841,x21843),f742(x21842,x21843)) % 167.77/167.52 [2185]~E(x21851,x21852)+E(f742(x21853,x21851),f742(x21853,x21852)) % 167.77/167.52 [2186]~E(x21861,x21862)+E(f739(x21861,x21863,x21864),f739(x21862,x21863,x21864)) % 167.77/167.52 [2187]~E(x21871,x21872)+E(f739(x21873,x21871,x21874),f739(x21873,x21872,x21874)) % 167.77/167.52 [2188]~E(x21881,x21882)+E(f739(x21883,x21884,x21881),f739(x21883,x21884,x21882)) % 167.77/167.52 [2189]~E(x21891,x21892)+E(f727(x21891,x21893),f727(x21892,x21893)) % 167.77/167.52 [2190]~E(x21901,x21902)+E(f727(x21903,x21901),f727(x21903,x21902)) % 167.77/167.52 [2191]~E(x21911,x21912)+E(f781(x21911,x21913,x21914,x21915),f781(x21912,x21913,x21914,x21915)) % 167.77/167.52 [2192]~E(x21921,x21922)+E(f781(x21923,x21921,x21924,x21925),f781(x21923,x21922,x21924,x21925)) % 167.77/167.52 [2193]~E(x21931,x21932)+E(f781(x21933,x21934,x21931,x21935),f781(x21933,x21934,x21932,x21935)) % 167.77/167.52 [2194]~E(x21941,x21942)+E(f781(x21943,x21944,x21945,x21941),f781(x21943,x21944,x21945,x21942)) % 167.77/167.52 [2195]~E(x21951,x21952)+E(f633(x21951,x21953,x21954),f633(x21952,x21953,x21954)) % 167.77/167.52 [2196]~E(x21961,x21962)+E(f633(x21963,x21961,x21964),f633(x21963,x21962,x21964)) % 167.77/167.52 [2197]~E(x21971,x21972)+E(f633(x21973,x21974,x21971),f633(x21973,x21974,x21972)) % 167.77/167.52 [2198]~E(x21981,x21982)+E(f501(x21981,x21983,x21984),f501(x21982,x21983,x21984)) % 167.77/167.52 [2199]~E(x21991,x21992)+E(f501(x21993,x21991,x21994),f501(x21993,x21992,x21994)) % 167.77/167.52 [2200]~E(x22001,x22002)+E(f501(x22003,x22004,x22001),f501(x22003,x22004,x22002)) % 167.77/167.52 [2201]~E(x22011,x22012)+E(f751(x22011,x22013,x22014),f751(x22012,x22013,x22014)) % 167.77/167.52 [2202]~E(x22021,x22022)+E(f751(x22023,x22021,x22024),f751(x22023,x22022,x22024)) % 167.77/167.52 [2203]~E(x22031,x22032)+E(f751(x22033,x22034,x22031),f751(x22033,x22034,x22032)) % 167.77/167.52 [2204]~E(x22041,x22042)+E(f365(x22041,x22043,x22044,x22045,x22046),f365(x22042,x22043,x22044,x22045,x22046)) % 167.77/167.52 [2205]~E(x22051,x22052)+E(f365(x22053,x22051,x22054,x22055,x22056),f365(x22053,x22052,x22054,x22055,x22056)) % 167.77/167.52 [2206]~E(x22061,x22062)+E(f365(x22063,x22064,x22061,x22065,x22066),f365(x22063,x22064,x22062,x22065,x22066)) % 167.77/167.52 [2207]~E(x22071,x22072)+E(f365(x22073,x22074,x22075,x22071,x22076),f365(x22073,x22074,x22075,x22072,x22076)) % 167.77/167.52 [2208]~E(x22081,x22082)+E(f365(x22083,x22084,x22085,x22086,x22081),f365(x22083,x22084,x22085,x22086,x22082)) % 167.77/167.52 [2209]~E(x22091,x22092)+E(f392(x22091,x22093,x22094,x22095,x22096,x22097),f392(x22092,x22093,x22094,x22095,x22096,x22097)) % 167.77/167.52 [2210]~E(x22101,x22102)+E(f392(x22103,x22101,x22104,x22105,x22106,x22107),f392(x22103,x22102,x22104,x22105,x22106,x22107)) % 167.77/167.52 [2211]~E(x22111,x22112)+E(f392(x22113,x22114,x22111,x22115,x22116,x22117),f392(x22113,x22114,x22112,x22115,x22116,x22117)) % 167.77/167.52 [2212]~E(x22121,x22122)+E(f392(x22123,x22124,x22125,x22121,x22126,x22127),f392(x22123,x22124,x22125,x22122,x22126,x22127)) % 167.77/167.52 [2213]~E(x22131,x22132)+E(f392(x22133,x22134,x22135,x22136,x22131,x22137),f392(x22133,x22134,x22135,x22136,x22132,x22137)) % 167.77/167.52 [2214]~E(x22141,x22142)+E(f392(x22143,x22144,x22145,x22146,x22147,x22141),f392(x22143,x22144,x22145,x22146,x22147,x22142)) % 167.77/167.52 [2215]~E(x22151,x22152)+E(f374(x22151,x22153,x22154),f374(x22152,x22153,x22154)) % 167.77/167.52 [2216]~E(x22161,x22162)+E(f374(x22163,x22161,x22164),f374(x22163,x22162,x22164)) % 167.77/167.52 [2217]~E(x22171,x22172)+E(f374(x22173,x22174,x22171),f374(x22173,x22174,x22172)) % 167.77/167.52 [2218]~E(x22181,x22182)+E(f483(x22181,x22183),f483(x22182,x22183)) % 167.77/167.52 [2219]~E(x22191,x22192)+E(f483(x22193,x22191),f483(x22193,x22192)) % 167.77/167.52 [2220]~E(x22201,x22202)+E(f402(x22201,x22203,x22204,x22205),f402(x22202,x22203,x22204,x22205)) % 167.77/167.52 [2221]~E(x22211,x22212)+E(f402(x22213,x22211,x22214,x22215),f402(x22213,x22212,x22214,x22215)) % 167.77/167.52 [2222]~E(x22221,x22222)+E(f402(x22223,x22224,x22221,x22225),f402(x22223,x22224,x22222,x22225)) % 167.77/167.52 [2223]~E(x22231,x22232)+E(f402(x22233,x22234,x22235,x22231),f402(x22233,x22234,x22235,x22232)) % 167.77/167.52 [2224]~E(x22241,x22242)+E(f610(x22241,x22243,x22244,x22245,x22246,x22247),f610(x22242,x22243,x22244,x22245,x22246,x22247)) % 167.77/167.52 [2225]~E(x22251,x22252)+E(f610(x22253,x22251,x22254,x22255,x22256,x22257),f610(x22253,x22252,x22254,x22255,x22256,x22257)) % 167.77/167.52 [2226]~E(x22261,x22262)+E(f610(x22263,x22264,x22261,x22265,x22266,x22267),f610(x22263,x22264,x22262,x22265,x22266,x22267)) % 167.77/167.52 [2227]~E(x22271,x22272)+E(f610(x22273,x22274,x22275,x22271,x22276,x22277),f610(x22273,x22274,x22275,x22272,x22276,x22277)) % 167.77/167.52 [2228]~E(x22281,x22282)+E(f610(x22283,x22284,x22285,x22286,x22281,x22287),f610(x22283,x22284,x22285,x22286,x22282,x22287)) % 167.77/167.52 [2229]~E(x22291,x22292)+E(f610(x22293,x22294,x22295,x22296,x22297,x22291),f610(x22293,x22294,x22295,x22296,x22297,x22292)) % 167.77/167.52 [2230]~E(x22301,x22302)+E(f355(x22301,x22303,x22304,x22305,x22306),f355(x22302,x22303,x22304,x22305,x22306)) % 167.77/167.52 [2231]~E(x22311,x22312)+E(f355(x22313,x22311,x22314,x22315,x22316),f355(x22313,x22312,x22314,x22315,x22316)) % 167.77/167.52 [2232]~E(x22321,x22322)+E(f355(x22323,x22324,x22321,x22325,x22326),f355(x22323,x22324,x22322,x22325,x22326)) % 167.77/167.52 [2233]~E(x22331,x22332)+E(f355(x22333,x22334,x22335,x22331,x22336),f355(x22333,x22334,x22335,x22332,x22336)) % 167.77/167.52 [2234]~E(x22341,x22342)+E(f355(x22343,x22344,x22345,x22346,x22341),f355(x22343,x22344,x22345,x22346,x22342)) % 167.77/167.52 [2235]~E(x22351,x22352)+E(f140(x22351,x22353),f140(x22352,x22353)) % 167.77/167.52 [2236]~E(x22361,x22362)+E(f140(x22363,x22361),f140(x22363,x22362)) % 167.77/167.52 [2237]~E(x22371,x22372)+E(f632(x22371,x22373),f632(x22372,x22373)) % 167.77/167.52 [2238]~E(x22381,x22382)+E(f632(x22383,x22381),f632(x22383,x22382)) % 167.77/167.52 [2239]~E(x22391,x22392)+E(f598(x22391,x22393,x22394),f598(x22392,x22393,x22394)) % 167.77/167.52 [2240]~E(x22401,x22402)+E(f598(x22403,x22401,x22404),f598(x22403,x22402,x22404)) % 167.77/167.52 [2241]~E(x22411,x22412)+E(f598(x22413,x22414,x22411),f598(x22413,x22414,x22412)) % 167.77/167.52 [2242]~E(x22421,x22422)+E(f194(x22421,x22423,x22424,x22425),f194(x22422,x22423,x22424,x22425)) % 167.77/167.52 [2243]~E(x22431,x22432)+E(f194(x22433,x22431,x22434,x22435),f194(x22433,x22432,x22434,x22435)) % 167.77/167.52 [2244]~E(x22441,x22442)+E(f194(x22443,x22444,x22441,x22445),f194(x22443,x22444,x22442,x22445)) % 167.77/167.52 [2245]~E(x22451,x22452)+E(f194(x22453,x22454,x22455,x22451),f194(x22453,x22454,x22455,x22452)) % 167.77/167.52 [2246]~E(x22461,x22462)+E(f677(x22461,x22463,x22464),f677(x22462,x22463,x22464)) % 167.77/167.52 [2247]~E(x22471,x22472)+E(f677(x22473,x22471,x22474),f677(x22473,x22472,x22474)) % 167.77/167.52 [2248]~E(x22481,x22482)+E(f677(x22483,x22484,x22481),f677(x22483,x22484,x22482)) % 167.77/167.52 [2249]~E(x22491,x22492)+E(f828(x22491,x22493),f828(x22492,x22493)) % 167.77/167.52 [2250]~E(x22501,x22502)+E(f828(x22503,x22501),f828(x22503,x22502)) % 167.77/167.52 [2251]~E(x22511,x22512)+E(f515(x22511,x22513,x22514),f515(x22512,x22513,x22514)) % 167.77/167.52 [2252]~E(x22521,x22522)+E(f515(x22523,x22521,x22524),f515(x22523,x22522,x22524)) % 167.77/167.52 [2253]~E(x22531,x22532)+E(f515(x22533,x22534,x22531),f515(x22533,x22534,x22532)) % 167.77/167.52 [2254]~E(x22541,x22542)+E(f212(x22541,x22543,x22544,x22545),f212(x22542,x22543,x22544,x22545)) % 167.77/167.52 [2255]~E(x22551,x22552)+E(f212(x22553,x22551,x22554,x22555),f212(x22553,x22552,x22554,x22555)) % 167.77/167.52 [2256]~E(x22561,x22562)+E(f212(x22563,x22564,x22561,x22565),f212(x22563,x22564,x22562,x22565)) % 167.77/167.52 [2257]~E(x22571,x22572)+E(f212(x22573,x22574,x22575,x22571),f212(x22573,x22574,x22575,x22572)) % 167.77/167.52 [2258]~E(x22581,x22582)+E(f708(x22581,x22583,x22584),f708(x22582,x22583,x22584)) % 167.77/167.52 [2259]~E(x22591,x22592)+E(f708(x22593,x22591,x22594),f708(x22593,x22592,x22594)) % 167.77/167.52 [2260]~E(x22601,x22602)+E(f708(x22603,x22604,x22601),f708(x22603,x22604,x22602)) % 167.77/167.52 [2261]~E(x22611,x22612)+E(f396(x22611,x22613),f396(x22612,x22613)) % 167.77/167.52 [2262]~E(x22621,x22622)+E(f396(x22623,x22621),f396(x22623,x22622)) % 167.77/167.52 [2263]~E(x22631,x22632)+E(f592(x22631,x22633,x22634),f592(x22632,x22633,x22634)) % 167.77/167.52 [2264]~E(x22641,x22642)+E(f592(x22643,x22641,x22644),f592(x22643,x22642,x22644)) % 167.77/167.52 [2265]~E(x22651,x22652)+E(f592(x22653,x22654,x22651),f592(x22653,x22654,x22652)) % 167.77/167.52 [2266]~E(x22661,x22662)+E(f398(x22661,x22663,x22664),f398(x22662,x22663,x22664)) % 167.77/167.52 [2267]~E(x22671,x22672)+E(f398(x22673,x22671,x22674),f398(x22673,x22672,x22674)) % 167.77/167.52 [2268]~E(x22681,x22682)+E(f398(x22683,x22684,x22681),f398(x22683,x22684,x22682)) % 167.77/167.52 [2269]~E(x22691,x22692)+E(f615(x22691,x22693,x22694,x22695),f615(x22692,x22693,x22694,x22695)) % 167.77/167.52 [2270]~E(x22701,x22702)+E(f615(x22703,x22701,x22704,x22705),f615(x22703,x22702,x22704,x22705)) % 167.77/167.52 [2271]~E(x22711,x22712)+E(f615(x22713,x22714,x22711,x22715),f615(x22713,x22714,x22712,x22715)) % 167.77/167.52 [2272]~E(x22721,x22722)+E(f615(x22723,x22724,x22725,x22721),f615(x22723,x22724,x22725,x22722)) % 167.77/167.52 [2273]~E(x22731,x22732)+E(f354(x22731,x22733,x22734,x22735,x22736),f354(x22732,x22733,x22734,x22735,x22736)) % 167.77/167.52 [2274]~E(x22741,x22742)+E(f354(x22743,x22741,x22744,x22745,x22746),f354(x22743,x22742,x22744,x22745,x22746)) % 167.77/167.52 [2275]~E(x22751,x22752)+E(f354(x22753,x22754,x22751,x22755,x22756),f354(x22753,x22754,x22752,x22755,x22756)) % 167.77/167.52 [2276]~E(x22761,x22762)+E(f354(x22763,x22764,x22765,x22761,x22766),f354(x22763,x22764,x22765,x22762,x22766)) % 167.77/167.52 [2277]~E(x22771,x22772)+E(f354(x22773,x22774,x22775,x22776,x22771),f354(x22773,x22774,x22775,x22776,x22772)) % 167.77/167.52 [2278]~E(x22781,x22782)+E(f803(x22781),f803(x22782)) % 167.77/167.52 [2279]~E(x22791,x22792)+E(f575(x22791,x22793,x22794,x22795,x22796,x22797,x22798,x22799),f575(x22792,x22793,x22794,x22795,x22796,x22797,x22798,x22799)) % 167.77/167.52 [2280]~E(x22801,x22802)+E(f575(x22803,x22801,x22804,x22805,x22806,x22807,x22808,x22809),f575(x22803,x22802,x22804,x22805,x22806,x22807,x22808,x22809)) % 167.77/167.52 [2281]~E(x22811,x22812)+E(f575(x22813,x22814,x22811,x22815,x22816,x22817,x22818,x22819),f575(x22813,x22814,x22812,x22815,x22816,x22817,x22818,x22819)) % 167.77/167.52 [2282]~E(x22821,x22822)+E(f575(x22823,x22824,x22825,x22821,x22826,x22827,x22828,x22829),f575(x22823,x22824,x22825,x22822,x22826,x22827,x22828,x22829)) % 167.77/167.52 [2283]~E(x22831,x22832)+E(f575(x22833,x22834,x22835,x22836,x22831,x22837,x22838,x22839),f575(x22833,x22834,x22835,x22836,x22832,x22837,x22838,x22839)) % 167.77/167.52 [2284]~E(x22841,x22842)+E(f575(x22843,x22844,x22845,x22846,x22847,x22841,x22848,x22849),f575(x22843,x22844,x22845,x22846,x22847,x22842,x22848,x22849)) % 167.77/167.52 [2285]~E(x22851,x22852)+E(f575(x22853,x22854,x22855,x22856,x22857,x22858,x22851,x22859),f575(x22853,x22854,x22855,x22856,x22857,x22858,x22852,x22859)) % 167.77/167.52 [2286]~E(x22861,x22862)+E(f575(x22863,x22864,x22865,x22866,x22867,x22868,x22869,x22861),f575(x22863,x22864,x22865,x22866,x22867,x22868,x22869,x22862)) % 167.77/167.52 [2287]~E(x22871,x22872)+E(f611(x22871,x22873,x22874),f611(x22872,x22873,x22874)) % 167.77/167.52 [2288]~E(x22881,x22882)+E(f611(x22883,x22881,x22884),f611(x22883,x22882,x22884)) % 167.77/167.52 [2289]~E(x22891,x22892)+E(f611(x22893,x22894,x22891),f611(x22893,x22894,x22892)) % 167.77/167.52 [2290]~E(x22901,x22902)+E(f617(x22901,x22903,x22904),f617(x22902,x22903,x22904)) % 167.77/167.52 [2291]~E(x22911,x22912)+E(f617(x22913,x22911,x22914),f617(x22913,x22912,x22914)) % 167.77/167.52 [2292]~E(x22921,x22922)+E(f617(x22923,x22924,x22921),f617(x22923,x22924,x22922)) % 167.77/167.52 [2293]~E(x22931,x22932)+E(f546(x22931,x22933,x22934,x22935,x22936,x22937,x22938,x22939),f546(x22932,x22933,x22934,x22935,x22936,x22937,x22938,x22939)) % 167.77/167.52 [2294]~E(x22941,x22942)+E(f546(x22943,x22941,x22944,x22945,x22946,x22947,x22948,x22949),f546(x22943,x22942,x22944,x22945,x22946,x22947,x22948,x22949)) % 167.77/167.52 [2295]~E(x22951,x22952)+E(f546(x22953,x22954,x22951,x22955,x22956,x22957,x22958,x22959),f546(x22953,x22954,x22952,x22955,x22956,x22957,x22958,x22959)) % 167.77/167.52 [2296]~E(x22961,x22962)+E(f546(x22963,x22964,x22965,x22961,x22966,x22967,x22968,x22969),f546(x22963,x22964,x22965,x22962,x22966,x22967,x22968,x22969)) % 167.77/167.52 [2297]~E(x22971,x22972)+E(f546(x22973,x22974,x22975,x22976,x22971,x22977,x22978,x22979),f546(x22973,x22974,x22975,x22976,x22972,x22977,x22978,x22979)) % 167.77/167.52 [2298]~E(x22981,x22982)+E(f546(x22983,x22984,x22985,x22986,x22987,x22981,x22988,x22989),f546(x22983,x22984,x22985,x22986,x22987,x22982,x22988,x22989)) % 167.77/167.52 [2299]~E(x22991,x22992)+E(f546(x22993,x22994,x22995,x22996,x22997,x22998,x22991,x22999),f546(x22993,x22994,x22995,x22996,x22997,x22998,x22992,x22999)) % 167.77/167.52 [2300]~E(x23001,x23002)+E(f546(x23003,x23004,x23005,x23006,x23007,x23008,x23009,x23001),f546(x23003,x23004,x23005,x23006,x23007,x23008,x23009,x23002)) % 167.77/167.52 [2301]~E(x23011,x23012)+E(f830(x23011,x23013,x23014),f830(x23012,x23013,x23014)) % 167.77/167.52 [2302]~E(x23021,x23022)+E(f830(x23023,x23021,x23024),f830(x23023,x23022,x23024)) % 167.77/167.52 [2303]~E(x23031,x23032)+E(f830(x23033,x23034,x23031),f830(x23033,x23034,x23032)) % 167.77/167.52 [2304]~E(x23041,x23042)+E(f767(x23041,x23043,x23044,x23045,x23046,x23047,x23048),f767(x23042,x23043,x23044,x23045,x23046,x23047,x23048)) % 167.77/167.52 [2305]~E(x23051,x23052)+E(f767(x23053,x23051,x23054,x23055,x23056,x23057,x23058),f767(x23053,x23052,x23054,x23055,x23056,x23057,x23058)) % 167.77/167.52 [2306]~E(x23061,x23062)+E(f767(x23063,x23064,x23061,x23065,x23066,x23067,x23068),f767(x23063,x23064,x23062,x23065,x23066,x23067,x23068)) % 167.77/167.52 [2307]~E(x23071,x23072)+E(f767(x23073,x23074,x23075,x23071,x23076,x23077,x23078),f767(x23073,x23074,x23075,x23072,x23076,x23077,x23078)) % 167.77/167.52 [2308]~E(x23081,x23082)+E(f767(x23083,x23084,x23085,x23086,x23081,x23087,x23088),f767(x23083,x23084,x23085,x23086,x23082,x23087,x23088)) % 167.77/167.52 [2309]~E(x23091,x23092)+E(f767(x23093,x23094,x23095,x23096,x23097,x23091,x23098),f767(x23093,x23094,x23095,x23096,x23097,x23092,x23098)) % 167.77/167.52 [2310]~E(x23101,x23102)+E(f767(x23103,x23104,x23105,x23106,x23107,x23108,x23101),f767(x23103,x23104,x23105,x23106,x23107,x23108,x23102)) % 167.77/167.52 [2311]~E(x23111,x23112)+E(f586(x23111,x23113),f586(x23112,x23113)) % 167.77/167.52 [2312]~E(x23121,x23122)+E(f586(x23123,x23121),f586(x23123,x23122)) % 167.77/167.52 [2313]~E(x23131,x23132)+E(f427(x23131,x23133),f427(x23132,x23133)) % 167.77/167.52 [2314]~E(x23141,x23142)+E(f427(x23143,x23141),f427(x23143,x23142)) % 167.77/167.52 [2315]~E(x23151,x23152)+E(f839(x23151,x23153,x23154),f839(x23152,x23153,x23154)) % 167.77/167.52 [2316]~E(x23161,x23162)+E(f839(x23163,x23161,x23164),f839(x23163,x23162,x23164)) % 167.77/167.52 [2317]~E(x23171,x23172)+E(f839(x23173,x23174,x23171),f839(x23173,x23174,x23172)) % 167.77/167.52 [2318]~E(x23181,x23182)+E(f453(x23181,x23183,x23184),f453(x23182,x23183,x23184)) % 167.77/167.52 [2319]~E(x23191,x23192)+E(f453(x23193,x23191,x23194),f453(x23193,x23192,x23194)) % 167.77/167.52 [2320]~E(x23201,x23202)+E(f453(x23203,x23204,x23201),f453(x23203,x23204,x23202)) % 167.77/167.52 [2321]~E(x23211,x23212)+E(f489(x23211,x23213,x23214),f489(x23212,x23213,x23214)) % 167.77/167.52 [2322]~E(x23221,x23222)+E(f489(x23223,x23221,x23224),f489(x23223,x23222,x23224)) % 167.77/167.52 [2323]~E(x23231,x23232)+E(f489(x23233,x23234,x23231),f489(x23233,x23234,x23232)) % 167.77/167.52 [2324]~E(x23241,x23242)+E(f594(x23241,x23243,x23244),f594(x23242,x23243,x23244)) % 167.77/167.52 [2325]~E(x23251,x23252)+E(f594(x23253,x23251,x23254),f594(x23253,x23252,x23254)) % 167.77/167.52 [2326]~E(x23261,x23262)+E(f594(x23263,x23264,x23261),f594(x23263,x23264,x23262)) % 167.77/167.52 [2327]~E(x23271,x23272)+E(f844(x23271,x23273,x23274,x23275,x23276,x23277,x23278),f844(x23272,x23273,x23274,x23275,x23276,x23277,x23278)) % 167.77/167.52 [2328]~E(x23281,x23282)+E(f844(x23283,x23281,x23284,x23285,x23286,x23287,x23288),f844(x23283,x23282,x23284,x23285,x23286,x23287,x23288)) % 167.77/167.52 [2329]~E(x23291,x23292)+E(f844(x23293,x23294,x23291,x23295,x23296,x23297,x23298),f844(x23293,x23294,x23292,x23295,x23296,x23297,x23298)) % 167.77/167.52 [2330]~E(x23301,x23302)+E(f844(x23303,x23304,x23305,x23301,x23306,x23307,x23308),f844(x23303,x23304,x23305,x23302,x23306,x23307,x23308)) % 167.77/167.52 [2331]~E(x23311,x23312)+E(f844(x23313,x23314,x23315,x23316,x23311,x23317,x23318),f844(x23313,x23314,x23315,x23316,x23312,x23317,x23318)) % 167.77/167.52 [2332]~E(x23321,x23322)+E(f844(x23323,x23324,x23325,x23326,x23327,x23321,x23328),f844(x23323,x23324,x23325,x23326,x23327,x23322,x23328)) % 167.77/167.52 [2333]~E(x23331,x23332)+E(f844(x23333,x23334,x23335,x23336,x23337,x23338,x23331),f844(x23333,x23334,x23335,x23336,x23337,x23338,x23332)) % 167.77/167.52 [2334]~E(x23341,x23342)+E(f278(x23341,x23343,x23344),f278(x23342,x23343,x23344)) % 167.77/167.52 [2335]~E(x23351,x23352)+E(f278(x23353,x23351,x23354),f278(x23353,x23352,x23354)) % 167.77/167.52 [2336]~E(x23361,x23362)+E(f278(x23363,x23364,x23361),f278(x23363,x23364,x23362)) % 167.77/167.52 [2337]~E(x23371,x23372)+E(f571(x23371,x23373,x23374,x23375),f571(x23372,x23373,x23374,x23375)) % 167.77/167.52 [2338]~E(x23381,x23382)+E(f571(x23383,x23381,x23384,x23385),f571(x23383,x23382,x23384,x23385)) % 167.77/167.52 [2339]~E(x23391,x23392)+E(f571(x23393,x23394,x23391,x23395),f571(x23393,x23394,x23392,x23395)) % 167.77/167.52 [2340]~E(x23401,x23402)+E(f571(x23403,x23404,x23405,x23401),f571(x23403,x23404,x23405,x23402)) % 167.77/167.52 [2341]~E(x23411,x23412)+E(f612(x23411,x23413,x23414),f612(x23412,x23413,x23414)) % 167.77/167.52 [2342]~E(x23421,x23422)+E(f612(x23423,x23421,x23424),f612(x23423,x23422,x23424)) % 167.77/167.52 [2343]~E(x23431,x23432)+E(f612(x23433,x23434,x23431),f612(x23433,x23434,x23432)) % 167.77/167.52 [2344]~E(x23441,x23442)+E(f780(x23441,x23443,x23444,x23445,x23446),f780(x23442,x23443,x23444,x23445,x23446)) % 167.77/167.52 [2345]~E(x23451,x23452)+E(f780(x23453,x23451,x23454,x23455,x23456),f780(x23453,x23452,x23454,x23455,x23456)) % 167.77/167.52 [2346]~E(x23461,x23462)+E(f780(x23463,x23464,x23461,x23465,x23466),f780(x23463,x23464,x23462,x23465,x23466)) % 167.77/167.52 [2347]~E(x23471,x23472)+E(f780(x23473,x23474,x23475,x23471,x23476),f780(x23473,x23474,x23475,x23472,x23476)) % 167.77/167.52 [2348]~E(x23481,x23482)+E(f780(x23483,x23484,x23485,x23486,x23481),f780(x23483,x23484,x23485,x23486,x23482)) % 167.77/167.52 [2349]~E(x23491,x23492)+E(f826(x23491,x23493,x23494,x23495,x23496),f826(x23492,x23493,x23494,x23495,x23496)) % 167.77/167.52 [2350]~E(x23501,x23502)+E(f826(x23503,x23501,x23504,x23505,x23506),f826(x23503,x23502,x23504,x23505,x23506)) % 167.77/167.52 [2351]~E(x23511,x23512)+E(f826(x23513,x23514,x23511,x23515,x23516),f826(x23513,x23514,x23512,x23515,x23516)) % 167.77/167.52 [2352]~E(x23521,x23522)+E(f826(x23523,x23524,x23525,x23521,x23526),f826(x23523,x23524,x23525,x23522,x23526)) % 167.77/167.52 [2353]~E(x23531,x23532)+E(f826(x23533,x23534,x23535,x23536,x23531),f826(x23533,x23534,x23535,x23536,x23532)) % 167.77/167.52 [2354]~E(x23541,x23542)+E(f834(x23541,x23543,x23544,x23545,x23546,x23547,x23548),f834(x23542,x23543,x23544,x23545,x23546,x23547,x23548)) % 167.77/167.52 [2355]~E(x23551,x23552)+E(f834(x23553,x23551,x23554,x23555,x23556,x23557,x23558),f834(x23553,x23552,x23554,x23555,x23556,x23557,x23558)) % 167.77/167.52 [2356]~E(x23561,x23562)+E(f834(x23563,x23564,x23561,x23565,x23566,x23567,x23568),f834(x23563,x23564,x23562,x23565,x23566,x23567,x23568)) % 167.77/167.52 [2357]~E(x23571,x23572)+E(f834(x23573,x23574,x23575,x23571,x23576,x23577,x23578),f834(x23573,x23574,x23575,x23572,x23576,x23577,x23578)) % 167.77/167.52 [2358]~E(x23581,x23582)+E(f834(x23583,x23584,x23585,x23586,x23581,x23587,x23588),f834(x23583,x23584,x23585,x23586,x23582,x23587,x23588)) % 167.77/167.52 [2359]~E(x23591,x23592)+E(f834(x23593,x23594,x23595,x23596,x23597,x23591,x23598),f834(x23593,x23594,x23595,x23596,x23597,x23592,x23598)) % 167.77/167.52 [2360]~E(x23601,x23602)+E(f834(x23603,x23604,x23605,x23606,x23607,x23608,x23601),f834(x23603,x23604,x23605,x23606,x23607,x23608,x23602)) % 167.77/167.52 [2361]~E(x23611,x23612)+E(f373(x23611,x23613,x23614,x23615,x23616),f373(x23612,x23613,x23614,x23615,x23616)) % 167.77/167.52 [2362]~E(x23621,x23622)+E(f373(x23623,x23621,x23624,x23625,x23626),f373(x23623,x23622,x23624,x23625,x23626)) % 167.77/167.52 [2363]~E(x23631,x23632)+E(f373(x23633,x23634,x23631,x23635,x23636),f373(x23633,x23634,x23632,x23635,x23636)) % 167.77/167.52 [2364]~E(x23641,x23642)+E(f373(x23643,x23644,x23645,x23641,x23646),f373(x23643,x23644,x23645,x23642,x23646)) % 167.77/167.52 [2365]~E(x23651,x23652)+E(f373(x23653,x23654,x23655,x23656,x23651),f373(x23653,x23654,x23655,x23656,x23652)) % 167.77/167.52 [2366]~E(x23661,x23662)+E(f474(x23661,x23663,x23664),f474(x23662,x23663,x23664)) % 167.77/167.52 [2367]~E(x23671,x23672)+E(f474(x23673,x23671,x23674),f474(x23673,x23672,x23674)) % 167.77/167.52 [2368]~E(x23681,x23682)+E(f474(x23683,x23684,x23681),f474(x23683,x23684,x23682)) % 167.77/167.52 [2369]~E(x23691,x23692)+E(f244(x23691,x23693),f244(x23692,x23693)) % 167.77/167.52 [2370]~E(x23701,x23702)+E(f244(x23703,x23701),f244(x23703,x23702)) % 167.77/167.52 [2371]~E(x23711,x23712)+E(f397(x23711,x23713),f397(x23712,x23713)) % 167.77/167.52 [2372]~E(x23721,x23722)+E(f397(x23723,x23721),f397(x23723,x23722)) % 167.77/167.52 [2373]~E(x23731,x23732)+E(f582(x23731),f582(x23732)) % 167.77/167.52 [2374]~E(x23741,x23742)+E(f732(x23741,x23743,x23744,x23745),f732(x23742,x23743,x23744,x23745)) % 167.77/167.52 [2375]~E(x23751,x23752)+E(f732(x23753,x23751,x23754,x23755),f732(x23753,x23752,x23754,x23755)) % 167.77/167.52 [2376]~E(x23761,x23762)+E(f732(x23763,x23764,x23761,x23765),f732(x23763,x23764,x23762,x23765)) % 167.77/167.52 [2377]~E(x23771,x23772)+E(f732(x23773,x23774,x23775,x23771),f732(x23773,x23774,x23775,x23772)) % 167.77/167.52 [2378]~E(x23781,x23782)+E(f429(x23781,x23783,x23784,x23785),f429(x23782,x23783,x23784,x23785)) % 167.77/167.52 [2379]~E(x23791,x23792)+E(f429(x23793,x23791,x23794,x23795),f429(x23793,x23792,x23794,x23795)) % 167.77/167.52 [2380]~E(x23801,x23802)+E(f429(x23803,x23804,x23801,x23805),f429(x23803,x23804,x23802,x23805)) % 167.77/167.52 [2381]~E(x23811,x23812)+E(f429(x23813,x23814,x23815,x23811),f429(x23813,x23814,x23815,x23812)) % 167.77/167.52 [2382]~E(x23821,x23822)+E(f692(x23821,x23823,x23824),f692(x23822,x23823,x23824)) % 167.77/167.52 [2383]~E(x23831,x23832)+E(f692(x23833,x23831,x23834),f692(x23833,x23832,x23834)) % 167.77/167.52 [2384]~E(x23841,x23842)+E(f692(x23843,x23844,x23841),f692(x23843,x23844,x23842)) % 167.77/167.52 [2385]~E(x23851,x23852)+E(f500(x23851,x23853,x23854),f500(x23852,x23853,x23854)) % 167.77/167.52 [2386]~E(x23861,x23862)+E(f500(x23863,x23861,x23864),f500(x23863,x23862,x23864)) % 167.77/167.52 [2387]~E(x23871,x23872)+E(f500(x23873,x23874,x23871),f500(x23873,x23874,x23872)) % 167.77/167.52 [2388]~E(x23881,x23882)+E(f679(x23881,x23883,x23884),f679(x23882,x23883,x23884)) % 167.77/167.52 [2389]~E(x23891,x23892)+E(f679(x23893,x23891,x23894),f679(x23893,x23892,x23894)) % 167.77/167.52 [2390]~E(x23901,x23902)+E(f679(x23903,x23904,x23901),f679(x23903,x23904,x23902)) % 167.77/167.52 [2391]~E(x23911,x23912)+E(f609(x23911,x23913,x23914),f609(x23912,x23913,x23914)) % 167.77/167.52 [2392]~E(x23921,x23922)+E(f609(x23923,x23921,x23924),f609(x23923,x23922,x23924)) % 167.77/167.52 [2393]~E(x23931,x23932)+E(f609(x23933,x23934,x23931),f609(x23933,x23934,x23932)) % 167.77/167.52 [2394]~E(x23941,x23942)+E(f311(x23941,x23943,x23944),f311(x23942,x23943,x23944)) % 167.77/167.52 [2395]~E(x23951,x23952)+E(f311(x23953,x23951,x23954),f311(x23953,x23952,x23954)) % 167.77/167.52 [2396]~E(x23961,x23962)+E(f311(x23963,x23964,x23961),f311(x23963,x23964,x23962)) % 167.77/167.52 [2397]~E(x23971,x23972)+E(f563(x23971,x23973,x23974,x23975),f563(x23972,x23973,x23974,x23975)) % 167.77/167.52 [2398]~E(x23981,x23982)+E(f563(x23983,x23981,x23984,x23985),f563(x23983,x23982,x23984,x23985)) % 167.77/167.52 [2399]~E(x23991,x23992)+E(f563(x23993,x23994,x23991,x23995),f563(x23993,x23994,x23992,x23995)) % 167.77/167.52 [2400]~E(x24001,x24002)+E(f563(x24003,x24004,x24005,x24001),f563(x24003,x24004,x24005,x24002)) % 167.77/167.52 [2401]~E(x24011,x24012)+E(f341(x24011,x24013),f341(x24012,x24013)) % 167.77/167.52 [2402]~E(x24021,x24022)+E(f341(x24023,x24021),f341(x24023,x24022)) % 167.77/167.52 [2403]~E(x24031,x24032)+E(f128(x24031),f128(x24032)) % 167.77/167.52 [2404]~E(x24041,x24042)+E(f650(x24041,x24043,x24044),f650(x24042,x24043,x24044)) % 167.77/167.52 [2405]~E(x24051,x24052)+E(f650(x24053,x24051,x24054),f650(x24053,x24052,x24054)) % 167.77/167.52 [2406]~E(x24061,x24062)+E(f650(x24063,x24064,x24061),f650(x24063,x24064,x24062)) % 167.77/167.52 [2407]~E(x24071,x24072)+E(f469(x24071,x24073),f469(x24072,x24073)) % 167.77/167.52 [2408]~E(x24081,x24082)+E(f469(x24083,x24081),f469(x24083,x24082)) % 167.77/167.52 [2409]~E(x24091,x24092)+E(f791(x24091,x24093,x24094),f791(x24092,x24093,x24094)) % 167.77/167.52 [2410]~E(x24101,x24102)+E(f791(x24103,x24101,x24104),f791(x24103,x24102,x24104)) % 167.77/167.52 [2411]~E(x24111,x24112)+E(f791(x24113,x24114,x24111),f791(x24113,x24114,x24112)) % 167.77/167.52 [2412]~E(x24121,x24122)+E(f335(x24121),f335(x24122)) % 167.77/167.52 [2413]~E(x24131,x24132)+E(f549(x24131,x24133,x24134,x24135),f549(x24132,x24133,x24134,x24135)) % 167.77/167.52 [2414]~E(x24141,x24142)+E(f549(x24143,x24141,x24144,x24145),f549(x24143,x24142,x24144,x24145)) % 167.77/167.52 [2415]~E(x24151,x24152)+E(f549(x24153,x24154,x24151,x24155),f549(x24153,x24154,x24152,x24155)) % 167.77/167.52 [2416]~E(x24161,x24162)+E(f549(x24163,x24164,x24165,x24161),f549(x24163,x24164,x24165,x24162)) % 167.77/167.52 [2417]~E(x24171,x24172)+E(f340(x24171,x24173),f340(x24172,x24173)) % 167.77/167.52 [2418]~E(x24181,x24182)+E(f340(x24183,x24181),f340(x24183,x24182)) % 167.77/167.52 [2419]~E(x24191,x24192)+E(f288(x24191,x24193),f288(x24192,x24193)) % 167.77/167.52 [2420]~E(x24201,x24202)+E(f288(x24203,x24201),f288(x24203,x24202)) % 167.77/167.52 [2421]~E(x24211,x24212)+E(f787(x24211,x24213,x24214,x24215,x24216,x24217,x24218),f787(x24212,x24213,x24214,x24215,x24216,x24217,x24218)) % 167.77/167.52 [2422]~E(x24221,x24222)+E(f787(x24223,x24221,x24224,x24225,x24226,x24227,x24228),f787(x24223,x24222,x24224,x24225,x24226,x24227,x24228)) % 167.77/167.52 [2423]~E(x24231,x24232)+E(f787(x24233,x24234,x24231,x24235,x24236,x24237,x24238),f787(x24233,x24234,x24232,x24235,x24236,x24237,x24238)) % 167.77/167.52 [2424]~E(x24241,x24242)+E(f787(x24243,x24244,x24245,x24241,x24246,x24247,x24248),f787(x24243,x24244,x24245,x24242,x24246,x24247,x24248)) % 167.77/167.52 [2425]~E(x24251,x24252)+E(f787(x24253,x24254,x24255,x24256,x24251,x24257,x24258),f787(x24253,x24254,x24255,x24256,x24252,x24257,x24258)) % 167.77/167.52 [2426]~E(x24261,x24262)+E(f787(x24263,x24264,x24265,x24266,x24267,x24261,x24268),f787(x24263,x24264,x24265,x24266,x24267,x24262,x24268)) % 167.77/167.52 [2427]~E(x24271,x24272)+E(f787(x24273,x24274,x24275,x24276,x24277,x24278,x24271),f787(x24273,x24274,x24275,x24276,x24277,x24278,x24272)) % 167.77/167.52 [2428]~E(x24281,x24282)+E(f721(x24281,x24283,x24284,x24285),f721(x24282,x24283,x24284,x24285)) % 167.77/167.52 [2429]~E(x24291,x24292)+E(f721(x24293,x24291,x24294,x24295),f721(x24293,x24292,x24294,x24295)) % 167.77/167.52 [2430]~E(x24301,x24302)+E(f721(x24303,x24304,x24301,x24305),f721(x24303,x24304,x24302,x24305)) % 167.77/167.52 [2431]~E(x24311,x24312)+E(f721(x24313,x24314,x24315,x24311),f721(x24313,x24314,x24315,x24312)) % 167.77/167.52 [2432]~E(x24321,x24322)+E(f804(x24321,x24323),f804(x24322,x24323)) % 167.77/167.52 [2433]~E(x24331,x24332)+E(f804(x24333,x24331),f804(x24333,x24332)) % 167.77/167.52 [2434]~E(x24341,x24342)+E(f541(x24341,x24343,x24344,x24345,x24346),f541(x24342,x24343,x24344,x24345,x24346)) % 167.77/167.52 [2435]~E(x24351,x24352)+E(f541(x24353,x24351,x24354,x24355,x24356),f541(x24353,x24352,x24354,x24355,x24356)) % 167.77/167.52 [2436]~E(x24361,x24362)+E(f541(x24363,x24364,x24361,x24365,x24366),f541(x24363,x24364,x24362,x24365,x24366)) % 167.77/167.52 [2437]~E(x24371,x24372)+E(f541(x24373,x24374,x24375,x24371,x24376),f541(x24373,x24374,x24375,x24372,x24376)) % 167.77/167.52 [2438]~E(x24381,x24382)+E(f541(x24383,x24384,x24385,x24386,x24381),f541(x24383,x24384,x24385,x24386,x24382)) % 167.77/167.52 [2439]~E(x24391,x24392)+E(f512(x24391,x24393,x24394,x24395),f512(x24392,x24393,x24394,x24395)) % 167.77/167.52 [2440]~E(x24401,x24402)+E(f512(x24403,x24401,x24404,x24405),f512(x24403,x24402,x24404,x24405)) % 167.77/167.52 [2441]~E(x24411,x24412)+E(f512(x24413,x24414,x24411,x24415),f512(x24413,x24414,x24412,x24415)) % 167.77/167.52 [2442]~E(x24421,x24422)+E(f512(x24423,x24424,x24425,x24421),f512(x24423,x24424,x24425,x24422)) % 167.77/167.52 [2443]~E(x24431,x24432)+E(f460(x24431),f460(x24432)) % 167.77/167.52 [2444]~E(x24441,x24442)+E(f833(x24441,x24443,x24444,x24445,x24446),f833(x24442,x24443,x24444,x24445,x24446)) % 167.77/167.52 [2445]~E(x24451,x24452)+E(f833(x24453,x24451,x24454,x24455,x24456),f833(x24453,x24452,x24454,x24455,x24456)) % 167.77/167.52 [2446]~E(x24461,x24462)+E(f833(x24463,x24464,x24461,x24465,x24466),f833(x24463,x24464,x24462,x24465,x24466)) % 167.77/167.52 [2447]~E(x24471,x24472)+E(f833(x24473,x24474,x24475,x24471,x24476),f833(x24473,x24474,x24475,x24472,x24476)) % 167.77/167.52 [2448]~E(x24481,x24482)+E(f833(x24483,x24484,x24485,x24486,x24481),f833(x24483,x24484,x24485,x24486,x24482)) % 167.77/167.52 [2449]~E(x24491,x24492)+E(f438(x24491,x24493,x24494,x24495,x24496,x24497),f438(x24492,x24493,x24494,x24495,x24496,x24497)) % 167.77/167.52 [2450]~E(x24501,x24502)+E(f438(x24503,x24501,x24504,x24505,x24506,x24507),f438(x24503,x24502,x24504,x24505,x24506,x24507)) % 167.77/167.52 [2451]~E(x24511,x24512)+E(f438(x24513,x24514,x24511,x24515,x24516,x24517),f438(x24513,x24514,x24512,x24515,x24516,x24517)) % 167.77/167.52 [2452]~E(x24521,x24522)+E(f438(x24523,x24524,x24525,x24521,x24526,x24527),f438(x24523,x24524,x24525,x24522,x24526,x24527)) % 167.77/167.52 [2453]~E(x24531,x24532)+E(f438(x24533,x24534,x24535,x24536,x24531,x24537),f438(x24533,x24534,x24535,x24536,x24532,x24537)) % 167.77/167.52 [2454]~E(x24541,x24542)+E(f438(x24543,x24544,x24545,x24546,x24547,x24541),f438(x24543,x24544,x24545,x24546,x24547,x24542)) % 167.77/167.52 [2455]~E(x24551,x24552)+E(f358(x24551,x24553),f358(x24552,x24553)) % 167.77/167.52 [2456]~E(x24561,x24562)+E(f358(x24563,x24561),f358(x24563,x24562)) % 167.77/167.52 [2457]~E(x24571,x24572)+E(f662(x24571,x24573,x24574,x24575),f662(x24572,x24573,x24574,x24575)) % 167.77/167.52 [2458]~E(x24581,x24582)+E(f662(x24583,x24581,x24584,x24585),f662(x24583,x24582,x24584,x24585)) % 167.77/167.52 [2459]~E(x24591,x24592)+E(f662(x24593,x24594,x24591,x24595),f662(x24593,x24594,x24592,x24595)) % 167.77/167.52 [2460]~E(x24601,x24602)+E(f662(x24603,x24604,x24605,x24601),f662(x24603,x24604,x24605,x24602)) % 167.77/167.52 [2461]~E(x24611,x24612)+E(f700(x24611,x24613,x24614,x24615),f700(x24612,x24613,x24614,x24615)) % 167.77/167.52 [2462]~E(x24621,x24622)+E(f700(x24623,x24621,x24624,x24625),f700(x24623,x24622,x24624,x24625)) % 167.77/167.52 [2463]~E(x24631,x24632)+E(f700(x24633,x24634,x24631,x24635),f700(x24633,x24634,x24632,x24635)) % 167.77/167.52 [2464]~E(x24641,x24642)+E(f700(x24643,x24644,x24645,x24641),f700(x24643,x24644,x24645,x24642)) % 167.77/167.52 [2465]~E(x24651,x24652)+E(f847(x24651,x24653),f847(x24652,x24653)) % 167.77/167.52 [2466]~E(x24661,x24662)+E(f847(x24663,x24661),f847(x24663,x24662)) % 167.77/167.52 [2467]~E(x24671,x24672)+E(f608(x24671,x24673,x24674),f608(x24672,x24673,x24674)) % 167.77/167.52 [2468]~E(x24681,x24682)+E(f608(x24683,x24681,x24684),f608(x24683,x24682,x24684)) % 167.77/167.52 [2469]~E(x24691,x24692)+E(f608(x24693,x24694,x24691),f608(x24693,x24694,x24692)) % 167.77/167.52 [2470]~E(x24701,x24702)+E(f431(x24701,x24703,x24704,x24705),f431(x24702,x24703,x24704,x24705)) % 167.77/167.52 [2471]~E(x24711,x24712)+E(f431(x24713,x24711,x24714,x24715),f431(x24713,x24712,x24714,x24715)) % 167.77/167.52 [2472]~E(x24721,x24722)+E(f431(x24723,x24724,x24721,x24725),f431(x24723,x24724,x24722,x24725)) % 167.77/167.52 [2473]~E(x24731,x24732)+E(f431(x24733,x24734,x24735,x24731),f431(x24733,x24734,x24735,x24732)) % 167.77/167.52 [2474]~E(x24741,x24742)+E(f506(x24741,x24743),f506(x24742,x24743)) % 167.77/167.52 [2475]~E(x24751,x24752)+E(f506(x24753,x24751),f506(x24753,x24752)) % 167.77/167.52 [2476]~E(x24761,x24762)+E(f558(x24761,x24763,x24764,x24765),f558(x24762,x24763,x24764,x24765)) % 167.77/167.52 [2477]~E(x24771,x24772)+E(f558(x24773,x24771,x24774,x24775),f558(x24773,x24772,x24774,x24775)) % 167.77/167.52 [2478]~E(x24781,x24782)+E(f558(x24783,x24784,x24781,x24785),f558(x24783,x24784,x24782,x24785)) % 167.77/167.52 [2479]~E(x24791,x24792)+E(f558(x24793,x24794,x24795,x24791),f558(x24793,x24794,x24795,x24792)) % 167.77/167.52 [2480]~E(x24801,x24802)+E(f684(x24801,x24803,x24804,x24805),f684(x24802,x24803,x24804,x24805)) % 167.77/167.52 [2481]~E(x24811,x24812)+E(f684(x24813,x24811,x24814,x24815),f684(x24813,x24812,x24814,x24815)) % 167.77/167.52 [2482]~E(x24821,x24822)+E(f684(x24823,x24824,x24821,x24825),f684(x24823,x24824,x24822,x24825)) % 167.77/167.52 [2483]~E(x24831,x24832)+E(f684(x24833,x24834,x24835,x24831),f684(x24833,x24834,x24835,x24832)) % 167.77/167.52 [2484]~E(x24841,x24842)+E(f776(x24841,x24843,x24844),f776(x24842,x24843,x24844)) % 167.77/167.52 [2485]~E(x24851,x24852)+E(f776(x24853,x24851,x24854),f776(x24853,x24852,x24854)) % 167.77/167.52 [2486]~E(x24861,x24862)+E(f776(x24863,x24864,x24861),f776(x24863,x24864,x24862)) % 167.77/167.52 [2487]~E(x24871,x24872)+E(f448(x24871,x24873),f448(x24872,x24873)) % 167.77/167.52 [2488]~E(x24881,x24882)+E(f448(x24883,x24881),f448(x24883,x24882)) % 167.77/167.52 [2489]~E(x24891,x24892)+E(f602(x24891,x24893,x24894,x24895,x24896,x24897),f602(x24892,x24893,x24894,x24895,x24896,x24897)) % 167.77/167.52 [2490]~E(x24901,x24902)+E(f602(x24903,x24901,x24904,x24905,x24906,x24907),f602(x24903,x24902,x24904,x24905,x24906,x24907)) % 167.77/167.52 [2491]~E(x24911,x24912)+E(f602(x24913,x24914,x24911,x24915,x24916,x24917),f602(x24913,x24914,x24912,x24915,x24916,x24917)) % 167.77/167.52 [2492]~E(x24921,x24922)+E(f602(x24923,x24924,x24925,x24921,x24926,x24927),f602(x24923,x24924,x24925,x24922,x24926,x24927)) % 167.77/167.52 [2493]~E(x24931,x24932)+E(f602(x24933,x24934,x24935,x24936,x24931,x24937),f602(x24933,x24934,x24935,x24936,x24932,x24937)) % 167.77/167.52 [2494]~E(x24941,x24942)+E(f602(x24943,x24944,x24945,x24946,x24947,x24941),f602(x24943,x24944,x24945,x24946,x24947,x24942)) % 167.77/167.52 [2495]~E(x24951,x24952)+E(f554(x24951,x24953,x24954),f554(x24952,x24953,x24954)) % 167.77/167.52 [2496]~E(x24961,x24962)+E(f554(x24963,x24961,x24964),f554(x24963,x24962,x24964)) % 167.77/167.52 [2497]~E(x24971,x24972)+E(f554(x24973,x24974,x24971),f554(x24973,x24974,x24972)) % 167.77/167.52 [2498]~E(x24981,x24982)+E(f422(x24981,x24983,x24984,x24985),f422(x24982,x24983,x24984,x24985)) % 167.77/167.52 [2499]~E(x24991,x24992)+E(f422(x24993,x24991,x24994,x24995),f422(x24993,x24992,x24994,x24995)) % 167.77/167.52 [2500]~E(x25001,x25002)+E(f422(x25003,x25004,x25001,x25005),f422(x25003,x25004,x25002,x25005)) % 167.77/167.52 [2501]~E(x25011,x25012)+E(f422(x25013,x25014,x25015,x25011),f422(x25013,x25014,x25015,x25012)) % 167.77/167.52 [2502]~E(x25021,x25022)+E(f312(x25021,x25023,x25024),f312(x25022,x25023,x25024)) % 167.77/167.52 [2503]~E(x25031,x25032)+E(f312(x25033,x25031,x25034),f312(x25033,x25032,x25034)) % 167.77/167.52 [2504]~E(x25041,x25042)+E(f312(x25043,x25044,x25041),f312(x25043,x25044,x25042)) % 167.77/167.52 [2505]~E(x25051,x25052)+E(f588(x25051),f588(x25052)) % 167.77/167.52 [2506]~E(x25061,x25062)+E(f217(x25061,x25063,x25064,x25065),f217(x25062,x25063,x25064,x25065)) % 167.77/167.52 [2507]~E(x25071,x25072)+E(f217(x25073,x25071,x25074,x25075),f217(x25073,x25072,x25074,x25075)) % 167.77/167.52 [2508]~E(x25081,x25082)+E(f217(x25083,x25084,x25081,x25085),f217(x25083,x25084,x25082,x25085)) % 167.77/167.52 [2509]~E(x25091,x25092)+E(f217(x25093,x25094,x25095,x25091),f217(x25093,x25094,x25095,x25092)) % 167.77/167.52 [2510]~E(x25101,x25102)+E(f333(x25101),f333(x25102)) % 167.77/167.52 [2511]~E(x25111,x25112)+E(f789(x25111,x25113,x25114),f789(x25112,x25113,x25114)) % 167.77/167.52 [2512]~E(x25121,x25122)+E(f789(x25123,x25121,x25124),f789(x25123,x25122,x25124)) % 167.77/167.52 [2513]~E(x25131,x25132)+E(f789(x25133,x25134,x25131),f789(x25133,x25134,x25132)) % 167.77/167.52 [2514]~E(x25141,x25142)+E(f702(x25141),f702(x25142)) % 167.77/167.52 [2515]~E(x25151,x25152)+E(f450(x25151,x25153,x25154),f450(x25152,x25153,x25154)) % 167.77/167.52 [2516]~E(x25161,x25162)+E(f450(x25163,x25161,x25164),f450(x25163,x25162,x25164)) % 167.77/167.52 [2517]~E(x25171,x25172)+E(f450(x25173,x25174,x25171),f450(x25173,x25174,x25172)) % 167.77/167.52 [2518]~E(x25181,x25182)+E(f707(x25181,x25183,x25184),f707(x25182,x25183,x25184)) % 167.77/167.52 [2519]~E(x25191,x25192)+E(f707(x25193,x25191,x25194),f707(x25193,x25192,x25194)) % 167.77/167.52 [2520]~E(x25201,x25202)+E(f707(x25203,x25204,x25201),f707(x25203,x25204,x25202)) % 167.77/167.52 [2521]~E(x25211,x25212)+E(f497(x25211,x25213,x25214),f497(x25212,x25213,x25214)) % 167.77/167.52 [2522]~E(x25221,x25222)+E(f497(x25223,x25221,x25224),f497(x25223,x25222,x25224)) % 167.77/167.52 [2523]~E(x25231,x25232)+E(f497(x25233,x25234,x25231),f497(x25233,x25234,x25232)) % 167.77/167.52 [2524]~E(x25241,x25242)+E(f842(x25241,x25243),f842(x25242,x25243)) % 167.77/167.52 [2525]~E(x25251,x25252)+E(f842(x25253,x25251),f842(x25253,x25252)) % 167.77/167.52 [2526]~E(x25261,x25262)+E(f368(x25261,x25263),f368(x25262,x25263)) % 167.77/167.52 [2527]~E(x25271,x25272)+E(f368(x25273,x25271),f368(x25273,x25272)) % 167.77/167.52 [2528]~E(x25281,x25282)+E(f638(x25281,x25283,x25284,x25285,x25286),f638(x25282,x25283,x25284,x25285,x25286)) % 167.77/167.52 [2529]~E(x25291,x25292)+E(f638(x25293,x25291,x25294,x25295,x25296),f638(x25293,x25292,x25294,x25295,x25296)) % 167.77/167.52 [2530]~E(x25301,x25302)+E(f638(x25303,x25304,x25301,x25305,x25306),f638(x25303,x25304,x25302,x25305,x25306)) % 167.77/167.52 [2531]~E(x25311,x25312)+E(f638(x25313,x25314,x25315,x25311,x25316),f638(x25313,x25314,x25315,x25312,x25316)) % 167.77/167.52 [2532]~E(x25321,x25322)+E(f638(x25323,x25324,x25325,x25326,x25321),f638(x25323,x25324,x25325,x25326,x25322)) % 167.77/167.52 [2533]~E(x25331,x25332)+E(f800(x25331,x25333,x25334,x25335,x25336,x25337,x25338),f800(x25332,x25333,x25334,x25335,x25336,x25337,x25338)) % 167.77/167.52 [2534]~E(x25341,x25342)+E(f800(x25343,x25341,x25344,x25345,x25346,x25347,x25348),f800(x25343,x25342,x25344,x25345,x25346,x25347,x25348)) % 167.77/167.52 [2535]~E(x25351,x25352)+E(f800(x25353,x25354,x25351,x25355,x25356,x25357,x25358),f800(x25353,x25354,x25352,x25355,x25356,x25357,x25358)) % 167.77/167.52 [2536]~E(x25361,x25362)+E(f800(x25363,x25364,x25365,x25361,x25366,x25367,x25368),f800(x25363,x25364,x25365,x25362,x25366,x25367,x25368)) % 167.77/167.52 [2537]~E(x25371,x25372)+E(f800(x25373,x25374,x25375,x25376,x25371,x25377,x25378),f800(x25373,x25374,x25375,x25376,x25372,x25377,x25378)) % 167.77/167.52 [2538]~E(x25381,x25382)+E(f800(x25383,x25384,x25385,x25386,x25387,x25381,x25388),f800(x25383,x25384,x25385,x25386,x25387,x25382,x25388)) % 167.77/167.52 [2539]~E(x25391,x25392)+E(f800(x25393,x25394,x25395,x25396,x25397,x25398,x25391),f800(x25393,x25394,x25395,x25396,x25397,x25398,x25392)) % 167.77/167.52 [2540]~E(x25401,x25402)+E(f351(x25401,x25403,x25404,x25405),f351(x25402,x25403,x25404,x25405)) % 167.77/167.52 [2541]~E(x25411,x25412)+E(f351(x25413,x25411,x25414,x25415),f351(x25413,x25412,x25414,x25415)) % 167.77/167.52 [2542]~E(x25421,x25422)+E(f351(x25423,x25424,x25421,x25425),f351(x25423,x25424,x25422,x25425)) % 167.77/167.52 [2543]~E(x25431,x25432)+E(f351(x25433,x25434,x25435,x25431),f351(x25433,x25434,x25435,x25432)) % 167.77/167.52 [2544]~E(x25441,x25442)+E(f681(x25441,x25443),f681(x25442,x25443)) % 167.77/167.52 [2545]~E(x25451,x25452)+E(f681(x25453,x25451),f681(x25453,x25452)) % 167.77/167.52 [2546]~E(x25461,x25462)+E(f228(x25461,x25463,x25464),f228(x25462,x25463,x25464)) % 167.77/167.52 [2547]~E(x25471,x25472)+E(f228(x25473,x25471,x25474),f228(x25473,x25472,x25474)) % 167.77/167.52 [2548]~E(x25481,x25482)+E(f228(x25483,x25484,x25481),f228(x25483,x25484,x25482)) % 167.77/167.52 [2549]~E(x25491,x25492)+E(f270(x25491,x25493,x25494,x25495,x25496),f270(x25492,x25493,x25494,x25495,x25496)) % 167.77/167.52 [2550]~E(x25501,x25502)+E(f270(x25503,x25501,x25504,x25505,x25506),f270(x25503,x25502,x25504,x25505,x25506)) % 167.77/167.52 [2551]~E(x25511,x25512)+E(f270(x25513,x25514,x25511,x25515,x25516),f270(x25513,x25514,x25512,x25515,x25516)) % 167.77/167.52 [2552]~E(x25521,x25522)+E(f270(x25523,x25524,x25525,x25521,x25526),f270(x25523,x25524,x25525,x25522,x25526)) % 167.77/167.52 [2553]~E(x25531,x25532)+E(f270(x25533,x25534,x25535,x25536,x25531),f270(x25533,x25534,x25535,x25536,x25532)) % 167.77/167.52 [2554]~E(x25541,x25542)+E(f735(x25541,x25543,x25544,x25545,x25546),f735(x25542,x25543,x25544,x25545,x25546)) % 167.77/167.52 [2555]~E(x25551,x25552)+E(f735(x25553,x25551,x25554,x25555,x25556),f735(x25553,x25552,x25554,x25555,x25556)) % 167.77/167.52 [2556]~E(x25561,x25562)+E(f735(x25563,x25564,x25561,x25565,x25566),f735(x25563,x25564,x25562,x25565,x25566)) % 167.77/167.52 [2557]~E(x25571,x25572)+E(f735(x25573,x25574,x25575,x25571,x25576),f735(x25573,x25574,x25575,x25572,x25576)) % 167.77/167.52 [2558]~E(x25581,x25582)+E(f735(x25583,x25584,x25585,x25586,x25581),f735(x25583,x25584,x25585,x25586,x25582)) % 167.77/167.52 [2559]~E(x25591,x25592)+E(f714(x25591,x25593),f714(x25592,x25593)) % 167.77/167.52 [2560]~E(x25601,x25602)+E(f714(x25603,x25601),f714(x25603,x25602)) % 167.77/167.52 [2561]~E(x25611,x25612)+E(f748(x25611,x25613,x25614),f748(x25612,x25613,x25614)) % 167.77/167.52 [2562]~E(x25621,x25622)+E(f748(x25623,x25621,x25624),f748(x25623,x25622,x25624)) % 167.77/167.52 [2563]~E(x25631,x25632)+E(f748(x25633,x25634,x25631),f748(x25633,x25634,x25632)) % 167.77/167.52 [2564]~E(x25641,x25642)+E(f528(x25641,x25643),f528(x25642,x25643)) % 167.77/167.52 [2565]~E(x25651,x25652)+E(f528(x25653,x25651),f528(x25653,x25652)) % 167.77/167.52 [2566]~E(x25661,x25662)+E(f790(x25661,x25663,x25664,x25665,x25666,x25667,x25668),f790(x25662,x25663,x25664,x25665,x25666,x25667,x25668)) % 167.77/167.52 [2567]~E(x25671,x25672)+E(f790(x25673,x25671,x25674,x25675,x25676,x25677,x25678),f790(x25673,x25672,x25674,x25675,x25676,x25677,x25678)) % 167.77/167.52 [2568]~E(x25681,x25682)+E(f790(x25683,x25684,x25681,x25685,x25686,x25687,x25688),f790(x25683,x25684,x25682,x25685,x25686,x25687,x25688)) % 167.77/167.52 [2569]~E(x25691,x25692)+E(f790(x25693,x25694,x25695,x25691,x25696,x25697,x25698),f790(x25693,x25694,x25695,x25692,x25696,x25697,x25698)) % 167.77/167.52 [2570]~E(x25701,x25702)+E(f790(x25703,x25704,x25705,x25706,x25701,x25707,x25708),f790(x25703,x25704,x25705,x25706,x25702,x25707,x25708)) % 167.77/167.52 [2571]~E(x25711,x25712)+E(f790(x25713,x25714,x25715,x25716,x25717,x25711,x25718),f790(x25713,x25714,x25715,x25716,x25717,x25712,x25718)) % 167.77/167.52 [2572]~E(x25721,x25722)+E(f790(x25723,x25724,x25725,x25726,x25727,x25728,x25721),f790(x25723,x25724,x25725,x25726,x25727,x25728,x25722)) % 167.77/167.52 [2573]~E(x25731,x25732)+E(f569(x25731,x25733,x25734,x25735),f569(x25732,x25733,x25734,x25735)) % 167.77/167.52 [2574]~E(x25741,x25742)+E(f569(x25743,x25741,x25744,x25745),f569(x25743,x25742,x25744,x25745)) % 167.77/167.52 [2575]~E(x25751,x25752)+E(f569(x25753,x25754,x25751,x25755),f569(x25753,x25754,x25752,x25755)) % 167.77/167.52 [2576]~E(x25761,x25762)+E(f569(x25763,x25764,x25765,x25761),f569(x25763,x25764,x25765,x25762)) % 167.77/167.52 [2577]~E(x25771,x25772)+E(f796(x25771,x25773,x25774),f796(x25772,x25773,x25774)) % 167.77/167.52 [2578]~E(x25781,x25782)+E(f796(x25783,x25781,x25784),f796(x25783,x25782,x25784)) % 167.77/167.52 [2579]~E(x25791,x25792)+E(f796(x25793,x25794,x25791),f796(x25793,x25794,x25792)) % 167.77/167.52 [2580]~E(x25801,x25802)+E(f218(x25801,x25803,x25804,x25805,x25806,x25807,x25808),f218(x25802,x25803,x25804,x25805,x25806,x25807,x25808)) % 167.77/167.52 [2581]~E(x25811,x25812)+E(f218(x25813,x25811,x25814,x25815,x25816,x25817,x25818),f218(x25813,x25812,x25814,x25815,x25816,x25817,x25818)) % 167.77/167.52 [2582]~E(x25821,x25822)+E(f218(x25823,x25824,x25821,x25825,x25826,x25827,x25828),f218(x25823,x25824,x25822,x25825,x25826,x25827,x25828)) % 167.77/167.52 [2583]~E(x25831,x25832)+E(f218(x25833,x25834,x25835,x25831,x25836,x25837,x25838),f218(x25833,x25834,x25835,x25832,x25836,x25837,x25838)) % 167.77/167.52 [2584]~E(x25841,x25842)+E(f218(x25843,x25844,x25845,x25846,x25841,x25847,x25848),f218(x25843,x25844,x25845,x25846,x25842,x25847,x25848)) % 167.77/167.52 [2585]~E(x25851,x25852)+E(f218(x25853,x25854,x25855,x25856,x25857,x25851,x25858),f218(x25853,x25854,x25855,x25856,x25857,x25852,x25858)) % 167.77/167.52 [2586]~E(x25861,x25862)+E(f218(x25863,x25864,x25865,x25866,x25867,x25868,x25861),f218(x25863,x25864,x25865,x25866,x25867,x25868,x25862)) % 167.77/167.52 [2587]~E(x25871,x25872)+E(f342(x25871),f342(x25872)) % 167.77/167.52 [2588]~E(x25881,x25882)+E(f21(x25881,x25883),f21(x25882,x25883)) % 167.77/167.52 [2589]~E(x25891,x25892)+E(f21(x25893,x25891),f21(x25893,x25892)) % 167.77/167.52 [2590]~E(x25901,x25902)+E(f507(x25901,x25903,x25904),f507(x25902,x25903,x25904)) % 167.77/167.52 [2591]~E(x25911,x25912)+E(f507(x25913,x25911,x25914),f507(x25913,x25912,x25914)) % 167.77/167.52 [2592]~E(x25921,x25922)+E(f507(x25923,x25924,x25921),f507(x25923,x25924,x25922)) % 167.77/167.52 [2593]~E(x25931,x25932)+E(f523(x25931),f523(x25932)) % 167.77/167.52 [2594]~E(x25941,x25942)+E(f782(x25941,x25943,x25944,x25945,x25946),f782(x25942,x25943,x25944,x25945,x25946)) % 167.77/167.52 [2595]~E(x25951,x25952)+E(f782(x25953,x25951,x25954,x25955,x25956),f782(x25953,x25952,x25954,x25955,x25956)) % 167.77/167.52 [2596]~E(x25961,x25962)+E(f782(x25963,x25964,x25961,x25965,x25966),f782(x25963,x25964,x25962,x25965,x25966)) % 167.77/167.52 [2597]~E(x25971,x25972)+E(f782(x25973,x25974,x25975,x25971,x25976),f782(x25973,x25974,x25975,x25972,x25976)) % 167.77/167.52 [2598]~E(x25981,x25982)+E(f782(x25983,x25984,x25985,x25986,x25981),f782(x25983,x25984,x25985,x25986,x25982)) % 167.77/167.52 [2599]~E(x25991,x25992)+E(f710(x25991,x25993,x25994,x25995,x25996),f710(x25992,x25993,x25994,x25995,x25996)) % 167.77/167.52 [2600]~E(x26001,x26002)+E(f710(x26003,x26001,x26004,x26005,x26006),f710(x26003,x26002,x26004,x26005,x26006)) % 167.77/167.52 [2601]~E(x26011,x26012)+E(f710(x26013,x26014,x26011,x26015,x26016),f710(x26013,x26014,x26012,x26015,x26016)) % 167.77/167.52 [2602]~E(x26021,x26022)+E(f710(x26023,x26024,x26025,x26021,x26026),f710(x26023,x26024,x26025,x26022,x26026)) % 167.77/167.52 [2603]~E(x26031,x26032)+E(f710(x26033,x26034,x26035,x26036,x26031),f710(x26033,x26034,x26035,x26036,x26032)) % 167.77/167.52 [2604]~E(x26041,x26042)+E(f560(x26041,x26043),f560(x26042,x26043)) % 167.77/167.52 [2605]~E(x26051,x26052)+E(f560(x26053,x26051),f560(x26053,x26052)) % 167.77/167.52 [2606]~P1(x26061)+P1(x26062)+~E(x26061,x26062) % 167.77/167.52 [2607]~P2(x26071)+P2(x26072)+~E(x26071,x26072) % 167.77/167.52 [2608]P15(x26082,x26083)+~E(x26081,x26082)+~P15(x26081,x26083) % 167.77/167.52 [2609]P15(x26093,x26092)+~E(x26091,x26092)+~P15(x26093,x26091) % 167.77/167.52 [2610]~P105(x26101)+P105(x26102)+~E(x26101,x26102) % 167.77/167.52 [2611]~P3(x26111)+P3(x26112)+~E(x26111,x26112) % 167.77/167.52 [2612]P144(x26122,x26123,x26124)+~E(x26121,x26122)+~P144(x26121,x26123,x26124) % 167.77/167.52 [2613]P144(x26133,x26132,x26134)+~E(x26131,x26132)+~P144(x26133,x26131,x26134) % 167.77/167.52 [2614]P144(x26143,x26144,x26142)+~E(x26141,x26142)+~P144(x26143,x26144,x26141) % 167.77/167.52 [2615]~P99(x26151)+P99(x26152)+~E(x26151,x26152) % 167.77/167.52 [2616]~P142(x26161)+P142(x26162)+~E(x26161,x26162) % 167.77/167.52 [2617]~P86(x26171)+P86(x26172)+~E(x26171,x26172) % 167.77/167.52 [2618]~P64(x26181)+P64(x26182)+~E(x26181,x26182) % 167.77/167.52 [2619]~P97(x26191)+P97(x26192)+~E(x26191,x26192) % 167.77/167.52 [2620]~P101(x26201)+P101(x26202)+~E(x26201,x26202) % 167.77/167.52 [2621]~P100(x26211)+P100(x26212)+~E(x26211,x26212) % 167.77/167.52 [2622]~P104(x26221)+P104(x26222)+~E(x26221,x26222) % 167.77/167.52 [2623]~P65(x26231)+P65(x26232)+~E(x26231,x26232) % 167.77/167.52 [2624]P21(x26242,x26243,x26244,x26245)+~E(x26241,x26242)+~P21(x26241,x26243,x26244,x26245) % 167.77/167.52 [2625]P21(x26253,x26252,x26254,x26255)+~E(x26251,x26252)+~P21(x26253,x26251,x26254,x26255) % 167.77/167.52 [2626]P21(x26263,x26264,x26262,x26265)+~E(x26261,x26262)+~P21(x26263,x26264,x26261,x26265) % 167.77/167.52 [2627]P21(x26273,x26274,x26275,x26272)+~E(x26271,x26272)+~P21(x26273,x26274,x26275,x26271) % 167.77/167.52 [2628]P38(x26282,x26283)+~E(x26281,x26282)+~P38(x26281,x26283) % 167.77/167.52 [2629]P38(x26293,x26292)+~E(x26291,x26292)+~P38(x26293,x26291) % 167.77/167.52 [2630]P56(x26302,x26303)+~E(x26301,x26302)+~P56(x26301,x26303) % 167.77/167.52 [2631]P56(x26313,x26312)+~E(x26311,x26312)+~P56(x26313,x26311) % 167.77/167.52 [2632]~P109(x26321)+P109(x26322)+~E(x26321,x26322) % 167.77/167.52 [2633]~P66(x26331)+P66(x26332)+~E(x26331,x26332) % 167.77/167.52 [2634]P26(x26342,x26343,x26344,x26345)+~E(x26341,x26342)+~P26(x26341,x26343,x26344,x26345) % 167.77/167.52 [2635]P26(x26353,x26352,x26354,x26355)+~E(x26351,x26352)+~P26(x26353,x26351,x26354,x26355) % 167.77/167.52 [2636]P26(x26363,x26364,x26362,x26365)+~E(x26361,x26362)+~P26(x26363,x26364,x26361,x26365) % 167.77/167.52 [2637]P26(x26373,x26374,x26375,x26372)+~E(x26371,x26372)+~P26(x26373,x26374,x26375,x26371) % 167.77/167.52 [2638]~P62(x26381)+P62(x26382)+~E(x26381,x26382) % 167.77/167.52 [2639]~P4(x26391)+P4(x26392)+~E(x26391,x26392) % 167.77/167.52 [2640]~P67(x26401)+P67(x26402)+~E(x26401,x26402) % 167.77/167.52 [2641]~P107(x26411)+P107(x26412)+~E(x26411,x26412) % 167.77/167.52 [2642]~P127(x26421)+P127(x26422)+~E(x26421,x26422) % 167.77/167.52 [2643]~P98(x26431)+P98(x26432)+~E(x26431,x26432) % 167.77/167.52 [2644]P7(x26442,x26443,x26444)+~E(x26441,x26442)+~P7(x26441,x26443,x26444) % 167.77/167.52 [2645]P7(x26453,x26452,x26454)+~E(x26451,x26452)+~P7(x26453,x26451,x26454) % 167.77/167.52 [2646]P7(x26463,x26464,x26462)+~E(x26461,x26462)+~P7(x26463,x26464,x26461) % 167.77/167.52 [2647]~P117(x26471)+P117(x26472)+~E(x26471,x26472) % 167.77/167.52 [2648]~P83(x26481)+P83(x26482)+~E(x26481,x26482) % 167.77/167.52 [2649]P16(x26492,x26493,x26494)+~E(x26491,x26492)+~P16(x26491,x26493,x26494) % 167.77/167.52 [2650]P16(x26503,x26502,x26504)+~E(x26501,x26502)+~P16(x26503,x26501,x26504) % 167.77/167.52 [2651]P16(x26513,x26514,x26512)+~E(x26511,x26512)+~P16(x26513,x26514,x26511) % 167.77/167.52 [2652]~P75(x26521)+P75(x26522)+~E(x26521,x26522) % 167.77/167.52 [2653]~P92(x26531)+P92(x26532)+~E(x26531,x26532) % 167.77/167.52 [2654]~P106(x26541)+P106(x26542)+~E(x26541,x26542) % 167.77/167.52 [2655]~P116(x26551)+P116(x26552)+~E(x26551,x26552) % 167.77/167.52 [2656]P18(x26562,x26563,x26564)+~E(x26561,x26562)+~P18(x26561,x26563,x26564) % 167.77/167.52 [2657]P18(x26573,x26572,x26574)+~E(x26571,x26572)+~P18(x26573,x26571,x26574) % 167.77/167.52 [2658]P18(x26583,x26584,x26582)+~E(x26581,x26582)+~P18(x26583,x26584,x26581) % 167.77/167.52 [2659]P145(x26592,x26593,x26594)+~E(x26591,x26592)+~P145(x26591,x26593,x26594) % 167.77/167.52 [2660]P145(x26603,x26602,x26604)+~E(x26601,x26602)+~P145(x26603,x26601,x26604) % 167.77/167.52 [2661]P145(x26613,x26614,x26612)+~E(x26611,x26612)+~P145(x26613,x26614,x26611) % 167.77/167.52 [2662]~P58(x26621)+P58(x26622)+~E(x26621,x26622) % 167.77/167.52 [2663]~P94(x26631)+P94(x26632)+~E(x26631,x26632) % 167.77/167.52 [2664]~P61(x26641)+P61(x26642)+~E(x26641,x26642) % 167.77/167.52 [2665]~P73(x26651)+P73(x26652)+~E(x26651,x26652) % 167.77/167.52 [2666]~P108(x26661)+P108(x26662)+~E(x26661,x26662) % 167.77/167.52 [2667]~P135(x26671)+P135(x26672)+~E(x26671,x26672) % 167.77/167.52 [2668]~P123(x26681)+P123(x26682)+~E(x26681,x26682) % 167.77/167.52 [2669]P33(x26692,x26693,x26694,x26695)+~E(x26691,x26692)+~P33(x26691,x26693,x26694,x26695) % 167.77/167.52 [2670]P33(x26703,x26702,x26704,x26705)+~E(x26701,x26702)+~P33(x26703,x26701,x26704,x26705) % 167.77/167.52 [2671]P33(x26713,x26714,x26712,x26715)+~E(x26711,x26712)+~P33(x26713,x26714,x26711,x26715) % 167.77/167.52 [2672]P33(x26723,x26724,x26725,x26722)+~E(x26721,x26722)+~P33(x26723,x26724,x26725,x26721) % 167.77/167.52 [2673]~P77(x26731)+P77(x26732)+~E(x26731,x26732) % 167.77/167.52 [2674]~P57(x26741)+P57(x26742)+~E(x26741,x26742) % 167.77/167.52 [2675]P40(x26752,x26753,x26754)+~E(x26751,x26752)+~P40(x26751,x26753,x26754) % 167.77/167.52 [2676]P40(x26763,x26762,x26764)+~E(x26761,x26762)+~P40(x26763,x26761,x26764) % 167.77/167.52 [2677]P40(x26773,x26774,x26772)+~E(x26771,x26772)+~P40(x26773,x26774,x26771) % 167.77/167.52 [2678]~P91(x26781)+P91(x26782)+~E(x26781,x26782) % 167.77/167.52 [2679]~P81(x26791)+P81(x26792)+~E(x26791,x26792) % 167.77/167.52 [2680]P25(x26802,x26803,x26804)+~E(x26801,x26802)+~P25(x26801,x26803,x26804) % 167.77/167.52 [2681]P25(x26813,x26812,x26814)+~E(x26811,x26812)+~P25(x26813,x26811,x26814) % 167.77/167.52 [2682]P25(x26823,x26824,x26822)+~E(x26821,x26822)+~P25(x26823,x26824,x26821) % 167.77/167.52 [2683]~P84(x26831)+P84(x26832)+~E(x26831,x26832) % 167.77/167.52 [2684]~P68(x26841)+P68(x26842)+~E(x26841,x26842) % 167.77/167.52 [2685]P24(x26852,x26853,x26854,x26855,x26856,x26857)+~E(x26851,x26852)+~P24(x26851,x26853,x26854,x26855,x26856,x26857) % 167.77/167.52 [2686]P24(x26863,x26862,x26864,x26865,x26866,x26867)+~E(x26861,x26862)+~P24(x26863,x26861,x26864,x26865,x26866,x26867) % 167.77/167.52 [2687]P24(x26873,x26874,x26872,x26875,x26876,x26877)+~E(x26871,x26872)+~P24(x26873,x26874,x26871,x26875,x26876,x26877) % 167.77/167.52 [2688]P24(x26883,x26884,x26885,x26882,x26886,x26887)+~E(x26881,x26882)+~P24(x26883,x26884,x26885,x26881,x26886,x26887) % 167.77/167.52 [2689]P24(x26893,x26894,x26895,x26896,x26892,x26897)+~E(x26891,x26892)+~P24(x26893,x26894,x26895,x26896,x26891,x26897) % 167.77/167.52 [2690]P24(x26903,x26904,x26905,x26906,x26907,x26902)+~E(x26901,x26902)+~P24(x26903,x26904,x26905,x26906,x26907,x26901) % 167.77/167.52 [2691]P6(x26912,x26913)+~E(x26911,x26912)+~P6(x26911,x26913) % 167.77/167.52 [2692]P6(x26923,x26922)+~E(x26921,x26922)+~P6(x26923,x26921) % 167.77/167.52 [2693]~P69(x26931)+P69(x26932)+~E(x26931,x26932) % 167.77/167.52 [2694]~P138(x26941)+P138(x26942)+~E(x26941,x26942) % 167.77/167.52 [2695]P14(x26952,x26953,x26954,x26955,x26956,x26957)+~E(x26951,x26952)+~P14(x26951,x26953,x26954,x26955,x26956,x26957) % 167.77/167.52 [2696]P14(x26963,x26962,x26964,x26965,x26966,x26967)+~E(x26961,x26962)+~P14(x26963,x26961,x26964,x26965,x26966,x26967) % 167.77/167.52 [2697]P14(x26973,x26974,x26972,x26975,x26976,x26977)+~E(x26971,x26972)+~P14(x26973,x26974,x26971,x26975,x26976,x26977) % 167.77/167.52 [2698]P14(x26983,x26984,x26985,x26982,x26986,x26987)+~E(x26981,x26982)+~P14(x26983,x26984,x26985,x26981,x26986,x26987) % 167.77/167.52 [2699]P14(x26993,x26994,x26995,x26996,x26992,x26997)+~E(x26991,x26992)+~P14(x26993,x26994,x26995,x26996,x26991,x26997) % 167.77/167.52 [2700]P14(x27003,x27004,x27005,x27006,x27007,x27002)+~E(x27001,x27002)+~P14(x27003,x27004,x27005,x27006,x27007,x27001) % 167.77/167.52 [2701]~P70(x27011)+P70(x27012)+~E(x27011,x27012) % 167.77/167.52 [2702]P54(x27022,x27023)+~E(x27021,x27022)+~P54(x27021,x27023) % 167.77/167.52 [2703]P54(x27033,x27032)+~E(x27031,x27032)+~P54(x27033,x27031) % 167.77/167.52 [2704]~P59(x27041)+P59(x27042)+~E(x27041,x27042) % 167.77/167.52 [2705]~P71(x27051)+P71(x27052)+~E(x27051,x27052) % 167.77/167.52 [2706]~P90(x27061)+P90(x27062)+~E(x27061,x27062) % 167.77/167.52 [2707]P32(x27072,x27073,x27074)+~E(x27071,x27072)+~P32(x27071,x27073,x27074) % 167.77/167.52 [2708]P32(x27083,x27082,x27084)+~E(x27081,x27082)+~P32(x27083,x27081,x27084) % 167.77/167.52 [2709]P32(x27093,x27094,x27092)+~E(x27091,x27092)+~P32(x27093,x27094,x27091) % 167.77/167.52 [2710]~P82(x27101)+P82(x27102)+~E(x27101,x27102) % 167.77/167.52 [2711]P35(x27112,x27113,x27114,x27115,x27116)+~E(x27111,x27112)+~P35(x27111,x27113,x27114,x27115,x27116) % 167.77/167.52 [2712]P35(x27123,x27122,x27124,x27125,x27126)+~E(x27121,x27122)+~P35(x27123,x27121,x27124,x27125,x27126) % 167.77/167.52 [2713]P35(x27133,x27134,x27132,x27135,x27136)+~E(x27131,x27132)+~P35(x27133,x27134,x27131,x27135,x27136) % 167.77/167.52 [2714]P35(x27143,x27144,x27145,x27142,x27146)+~E(x27141,x27142)+~P35(x27143,x27144,x27145,x27141,x27146) % 167.77/167.52 [2715]P35(x27153,x27154,x27155,x27156,x27152)+~E(x27151,x27152)+~P35(x27153,x27154,x27155,x27156,x27151) % 167.77/167.52 [2716]P17(x27162,x27163,x27164)+~E(x27161,x27162)+~P17(x27161,x27163,x27164) % 167.77/167.52 [2717]P17(x27173,x27172,x27174)+~E(x27171,x27172)+~P17(x27173,x27171,x27174) % 167.77/167.52 [2718]P17(x27183,x27184,x27182)+~E(x27181,x27182)+~P17(x27183,x27184,x27181) % 167.77/167.52 [2719]~P74(x27191)+P74(x27192)+~E(x27191,x27192) % 167.77/167.52 [2720]~P78(x27201)+P78(x27202)+~E(x27201,x27202) % 167.77/167.52 [2721]~P5(x27211)+P5(x27212)+~E(x27211,x27212) % 167.77/167.52 [2722]~P63(x27221)+P63(x27222)+~E(x27221,x27222) % 167.77/167.52 [2723]P51(x27232,x27233,x27234)+~E(x27231,x27232)+~P51(x27231,x27233,x27234) % 167.77/167.52 [2724]P51(x27243,x27242,x27244)+~E(x27241,x27242)+~P51(x27243,x27241,x27244) % 167.77/167.52 [2725]P51(x27253,x27254,x27252)+~E(x27251,x27252)+~P51(x27253,x27254,x27251) % 167.77/167.52 [2726]~P110(x27261)+P110(x27262)+~E(x27261,x27262) % 167.77/167.52 [2727]P11(x27272,x27273,x27274)+~E(x27271,x27272)+~P11(x27271,x27273,x27274) % 167.77/167.52 [2728]P11(x27283,x27282,x27284)+~E(x27281,x27282)+~P11(x27283,x27281,x27284) % 167.77/167.52 [2729]P11(x27293,x27294,x27292)+~E(x27291,x27292)+~P11(x27293,x27294,x27291) % 167.77/167.52 [2730]~P80(x27301)+P80(x27302)+~E(x27301,x27302) % 167.77/167.52 [2731]~P111(x27311)+P111(x27312)+~E(x27311,x27312) % 167.77/167.52 [2732]~P139(x27321)+P139(x27322)+~E(x27321,x27322) % 167.77/167.52 [2733]~P39(x27331)+P39(x27332)+~E(x27331,x27332) % 167.77/167.52 [2734]P31(x27342,x27343)+~E(x27341,x27342)+~P31(x27341,x27343) % 167.77/167.52 [2735]P31(x27353,x27352)+~E(x27351,x27352)+~P31(x27353,x27351) % 167.77/167.52 [2736]P52(x27362,x27363,x27364)+~E(x27361,x27362)+~P52(x27361,x27363,x27364) % 167.77/167.52 [2737]P52(x27373,x27372,x27374)+~E(x27371,x27372)+~P52(x27373,x27371,x27374) % 167.77/167.52 [2738]P52(x27383,x27384,x27382)+~E(x27381,x27382)+~P52(x27383,x27384,x27381) % 167.77/167.52 [2739]P12(x27392,x27393,x27394)+~E(x27391,x27392)+~P12(x27391,x27393,x27394) % 167.77/167.52 [2740]P12(x27403,x27402,x27404)+~E(x27401,x27402)+~P12(x27403,x27401,x27404) % 167.77/167.52 [2741]P12(x27413,x27414,x27412)+~E(x27411,x27412)+~P12(x27413,x27414,x27411) % 167.77/167.52 [2742]~P131(x27421)+P131(x27422)+~E(x27421,x27422) % 167.77/167.52 [2743]P46(x27432,x27433)+~E(x27431,x27432)+~P46(x27431,x27433) % 167.77/167.52 [2744]P46(x27443,x27442)+~E(x27441,x27442)+~P46(x27443,x27441) % 167.77/167.52 [2745]~P125(x27451)+P125(x27452)+~E(x27451,x27452) % 167.77/167.52 [2746]P43(x27462,x27463,x27464,x27465,x27466,x27467)+~E(x27461,x27462)+~P43(x27461,x27463,x27464,x27465,x27466,x27467) % 167.77/167.52 [2747]P43(x27473,x27472,x27474,x27475,x27476,x27477)+~E(x27471,x27472)+~P43(x27473,x27471,x27474,x27475,x27476,x27477) % 167.77/167.52 [2748]P43(x27483,x27484,x27482,x27485,x27486,x27487)+~E(x27481,x27482)+~P43(x27483,x27484,x27481,x27485,x27486,x27487) % 167.77/167.52 [2749]P43(x27493,x27494,x27495,x27492,x27496,x27497)+~E(x27491,x27492)+~P43(x27493,x27494,x27495,x27491,x27496,x27497) % 167.77/167.52 [2750]P43(x27503,x27504,x27505,x27506,x27502,x27507)+~E(x27501,x27502)+~P43(x27503,x27504,x27505,x27506,x27501,x27507) % 167.77/167.52 [2751]P43(x27513,x27514,x27515,x27516,x27517,x27512)+~E(x27511,x27512)+~P43(x27513,x27514,x27515,x27516,x27517,x27511) % 167.77/167.52 [2752]~P140(x27521)+P140(x27522)+~E(x27521,x27522) % 167.77/167.52 [2753]~P93(x27531)+P93(x27532)+~E(x27531,x27532) % 167.77/167.52 [2754]~P136(x27541)+P136(x27542)+~E(x27541,x27542) % 167.77/167.52 [2755]~P96(x27551)+P96(x27552)+~E(x27551,x27552) % 167.77/167.52 [2756]~P79(x27561)+P79(x27562)+~E(x27561,x27562) % 167.77/167.52 [2757]~P112(x27571)+P112(x27572)+~E(x27571,x27572) % 167.77/167.52 [2758]P19(x27582,x27583,x27584)+~E(x27581,x27582)+~P19(x27581,x27583,x27584) % 167.77/167.52 [2759]P19(x27593,x27592,x27594)+~E(x27591,x27592)+~P19(x27593,x27591,x27594) % 167.77/167.52 [2760]P19(x27603,x27604,x27602)+~E(x27601,x27602)+~P19(x27603,x27604,x27601) % 167.77/167.52 [2761]P34(x27612,x27613,x27614)+~E(x27611,x27612)+~P34(x27611,x27613,x27614) % 167.77/167.52 [2762]P34(x27623,x27622,x27624)+~E(x27621,x27622)+~P34(x27623,x27621,x27624) % 167.77/167.52 [2763]P34(x27633,x27634,x27632)+~E(x27631,x27632)+~P34(x27633,x27634,x27631) % 167.77/167.52 [2764]~P85(x27641)+P85(x27642)+~E(x27641,x27642) % 167.77/167.52 [2765]~P60(x27651)+P60(x27652)+~E(x27651,x27652) % 167.77/167.52 [2766]~P95(x27661)+P95(x27662)+~E(x27661,x27662) % 167.77/167.52 [2767]P44(x27672,x27673)+~E(x27671,x27672)+~P44(x27671,x27673) % 167.77/167.52 [2768]P44(x27683,x27682)+~E(x27681,x27682)+~P44(x27683,x27681) % 167.77/167.52 [2769]P50(x27692,x27693,x27694,x27695,x27696,x27697)+~E(x27691,x27692)+~P50(x27691,x27693,x27694,x27695,x27696,x27697) % 167.77/167.52 [2770]P50(x27703,x27702,x27704,x27705,x27706,x27707)+~E(x27701,x27702)+~P50(x27703,x27701,x27704,x27705,x27706,x27707) % 167.77/167.52 [2771]P50(x27713,x27714,x27712,x27715,x27716,x27717)+~E(x27711,x27712)+~P50(x27713,x27714,x27711,x27715,x27716,x27717) % 167.77/167.52 [2772]P50(x27723,x27724,x27725,x27722,x27726,x27727)+~E(x27721,x27722)+~P50(x27723,x27724,x27725,x27721,x27726,x27727) % 167.77/167.52 [2773]P50(x27733,x27734,x27735,x27736,x27732,x27737)+~E(x27731,x27732)+~P50(x27733,x27734,x27735,x27736,x27731,x27737) % 167.77/167.52 [2774]P50(x27743,x27744,x27745,x27746,x27747,x27742)+~E(x27741,x27742)+~P50(x27743,x27744,x27745,x27746,x27747,x27741) % 167.77/167.52 [2775]P28(x27752,x27753,x27754)+~E(x27751,x27752)+~P28(x27751,x27753,x27754) % 167.77/167.52 [2776]P28(x27763,x27762,x27764)+~E(x27761,x27762)+~P28(x27763,x27761,x27764) % 167.77/167.52 [2777]P28(x27773,x27774,x27772)+~E(x27771,x27772)+~P28(x27773,x27774,x27771) % 167.77/167.52 [2778]P53(x27782,x27783,x27784,x27785,x27786)+~E(x27781,x27782)+~P53(x27781,x27783,x27784,x27785,x27786) % 167.77/167.52 [2779]P53(x27793,x27792,x27794,x27795,x27796)+~E(x27791,x27792)+~P53(x27793,x27791,x27794,x27795,x27796) % 167.77/167.52 [2780]P53(x27803,x27804,x27802,x27805,x27806)+~E(x27801,x27802)+~P53(x27803,x27804,x27801,x27805,x27806) % 167.77/167.52 [2781]P53(x27813,x27814,x27815,x27812,x27816)+~E(x27811,x27812)+~P53(x27813,x27814,x27815,x27811,x27816) % 167.77/167.52 [2782]P53(x27823,x27824,x27825,x27826,x27822)+~E(x27821,x27822)+~P53(x27823,x27824,x27825,x27826,x27821) % 167.77/167.52 [2783]P55(x27832,x27833,x27834,x27835)+~E(x27831,x27832)+~P55(x27831,x27833,x27834,x27835) % 167.77/167.52 [2784]P55(x27843,x27842,x27844,x27845)+~E(x27841,x27842)+~P55(x27843,x27841,x27844,x27845) % 167.77/167.52 [2785]P55(x27853,x27854,x27852,x27855)+~E(x27851,x27852)+~P55(x27853,x27854,x27851,x27855) % 167.77/167.52 [2786]P55(x27863,x27864,x27865,x27862)+~E(x27861,x27862)+~P55(x27863,x27864,x27865,x27861) % 167.77/167.52 [2787]~P128(x27871)+P128(x27872)+~E(x27871,x27872) % 167.77/167.52 [2788]~P143(x27881)+P143(x27882)+~E(x27881,x27882) % 167.77/167.52 [2789]~P137(x27891)+P137(x27892)+~E(x27891,x27892) % 167.77/167.52 [2790]~P126(x27901)+P126(x27902)+~E(x27901,x27902) % 167.77/167.52 [2791]P13(x27912,x27913,x27914,x27915)+~E(x27911,x27912)+~P13(x27911,x27913,x27914,x27915) % 167.77/167.52 [2792]P13(x27923,x27922,x27924,x27925)+~E(x27921,x27922)+~P13(x27923,x27921,x27924,x27925) % 167.77/167.52 [2793]P13(x27933,x27934,x27932,x27935)+~E(x27931,x27932)+~P13(x27933,x27934,x27931,x27935) % 167.77/167.52 [2794]P13(x27943,x27944,x27945,x27942)+~E(x27941,x27942)+~P13(x27943,x27944,x27945,x27941) % 167.77/167.52 [2795]P36(x27952,x27953,x27954)+~E(x27951,x27952)+~P36(x27951,x27953,x27954) % 167.77/167.52 [2796]P36(x27963,x27962,x27964)+~E(x27961,x27962)+~P36(x27963,x27961,x27964) % 167.77/167.52 [2797]P36(x27973,x27974,x27972)+~E(x27971,x27972)+~P36(x27973,x27974,x27971) % 167.77/167.52 [2798]~P141(x27981)+P141(x27982)+~E(x27981,x27982) % 167.77/167.52 [2799]P41(x27992,x27993,x27994,x27995)+~E(x27991,x27992)+~P41(x27991,x27993,x27994,x27995) % 167.77/167.52 [2800]P41(x28003,x28002,x28004,x28005)+~E(x28001,x28002)+~P41(x28003,x28001,x28004,x28005) % 167.77/167.52 [2801]P41(x28013,x28014,x28012,x28015)+~E(x28011,x28012)+~P41(x28013,x28014,x28011,x28015) % 167.77/167.52 [2802]P41(x28023,x28024,x28025,x28022)+~E(x28021,x28022)+~P41(x28023,x28024,x28025,x28021) % 167.77/167.52 [2803]P27(x28032,x28033)+~E(x28031,x28032)+~P27(x28031,x28033) % 167.77/167.52 [2804]P27(x28043,x28042)+~E(x28041,x28042)+~P27(x28043,x28041) % 167.77/167.52 [2805]~P134(x28051)+P134(x28052)+~E(x28051,x28052) % 167.77/167.52 [2806]~P120(x28061)+P120(x28062)+~E(x28061,x28062) % 167.77/167.52 [2807]~P88(x28071)+P88(x28072)+~E(x28071,x28072) % 167.77/167.52 [2808]~P8(x28081)+P8(x28082)+~E(x28081,x28082) % 167.77/167.52 [2809]~P118(x28091)+P118(x28092)+~E(x28091,x28092) % 167.77/167.52 [2810]P22(x28102,x28103,x28104,x28105,x28106)+~E(x28101,x28102)+~P22(x28101,x28103,x28104,x28105,x28106) % 167.77/167.52 [2811]P22(x28113,x28112,x28114,x28115,x28116)+~E(x28111,x28112)+~P22(x28113,x28111,x28114,x28115,x28116) % 167.77/167.52 [2812]P22(x28123,x28124,x28122,x28125,x28126)+~E(x28121,x28122)+~P22(x28123,x28124,x28121,x28125,x28126) % 167.77/167.52 [2813]P22(x28133,x28134,x28135,x28132,x28136)+~E(x28131,x28132)+~P22(x28133,x28134,x28135,x28131,x28136) % 167.77/167.52 [2814]P22(x28143,x28144,x28145,x28146,x28142)+~E(x28141,x28142)+~P22(x28143,x28144,x28145,x28146,x28141) % 167.77/167.52 [2815]~P132(x28151)+P132(x28152)+~E(x28151,x28152) % 167.77/167.52 [2816]P20(x28162,x28163,x28164,x28165)+~E(x28161,x28162)+~P20(x28161,x28163,x28164,x28165) % 167.77/167.52 [2817]P20(x28173,x28172,x28174,x28175)+~E(x28171,x28172)+~P20(x28173,x28171,x28174,x28175) % 167.77/167.52 [2818]P20(x28183,x28184,x28182,x28185)+~E(x28181,x28182)+~P20(x28183,x28184,x28181,x28185) % 167.77/167.52 [2819]P20(x28193,x28194,x28195,x28192)+~E(x28191,x28192)+~P20(x28193,x28194,x28195,x28191) % 167.77/167.52 [2820]~P30(x28201)+P30(x28202)+~E(x28201,x28202) % 167.77/167.52 [2821]P29(x28212,x28213,x28214)+~E(x28211,x28212)+~P29(x28211,x28213,x28214) % 167.77/167.52 [2822]P29(x28223,x28222,x28224)+~E(x28221,x28222)+~P29(x28223,x28221,x28224) % 167.77/167.52 [2823]P29(x28233,x28234,x28232)+~E(x28231,x28232)+~P29(x28233,x28234,x28231) % 167.77/167.52 [2824]~P124(x28241)+P124(x28242)+~E(x28241,x28242) % 167.77/167.52 [2825]~P130(x28251)+P130(x28252)+~E(x28251,x28252) % 167.77/167.52 [2826]~P89(x28261)+P89(x28262)+~E(x28261,x28262) % 167.77/167.52 [2827]P9(x28272,x28273,x28274)+~E(x28271,x28272)+~P9(x28271,x28273,x28274) % 167.77/167.52 [2828]P9(x28283,x28282,x28284)+~E(x28281,x28282)+~P9(x28283,x28281,x28284) % 167.77/167.52 [2829]P9(x28293,x28294,x28292)+~E(x28291,x28292)+~P9(x28293,x28294,x28291) % 167.77/167.52 [2830]~P102(x28301)+P102(x28302)+~E(x28301,x28302) % 167.77/167.52 [2831]P42(x28312,x28313)+~E(x28311,x28312)+~P42(x28311,x28313) % 167.77/167.52 [2832]P42(x28323,x28322)+~E(x28321,x28322)+~P42(x28323,x28321) % 167.77/167.52 [2833]P10(x28332,x28333,x28334,x28335,x28336)+~E(x28331,x28332)+~P10(x28331,x28333,x28334,x28335,x28336) % 167.77/167.52 [2834]P10(x28343,x28342,x28344,x28345,x28346)+~E(x28341,x28342)+~P10(x28343,x28341,x28344,x28345,x28346) % 167.77/167.52 [2835]P10(x28353,x28354,x28352,x28355,x28356)+~E(x28351,x28352)+~P10(x28353,x28354,x28351,x28355,x28356) % 167.77/167.52 [2836]P10(x28363,x28364,x28365,x28362,x28366)+~E(x28361,x28362)+~P10(x28363,x28364,x28365,x28361,x28366) % 167.77/167.52 [2837]P10(x28373,x28374,x28375,x28376,x28372)+~E(x28371,x28372)+~P10(x28373,x28374,x28375,x28376,x28371) % 167.77/167.52 [2838]~P133(x28381)+P133(x28382)+~E(x28381,x28382) % 167.77/167.52 [2839]P49(x28392,x28393)+~E(x28391,x28392)+~P49(x28391,x28393) % 167.77/167.52 [2840]P49(x28403,x28402)+~E(x28401,x28402)+~P49(x28403,x28401) % 167.77/167.52 [2841]~P103(x28411)+P103(x28412)+~E(x28411,x28412) % 167.77/167.52 [2842]~P121(x28421)+P121(x28422)+~E(x28421,x28422) % 167.77/167.52 [2843]P48(x28432,x28433,x28434)+~E(x28431,x28432)+~P48(x28431,x28433,x28434) % 167.77/167.52 [2844]P48(x28443,x28442,x28444)+~E(x28441,x28442)+~P48(x28443,x28441,x28444) % 167.77/167.52 [2845]P48(x28453,x28454,x28452)+~E(x28451,x28452)+~P48(x28453,x28454,x28451) % 167.77/167.52 [2846]~P119(x28461)+P119(x28462)+~E(x28461,x28462) % 167.77/167.52 [2847]~P37(x28471)+P37(x28472)+~E(x28471,x28472) % 167.77/167.52 [2848]P23(x28482,x28483,x28484,x28485,x28486,x28487)+~E(x28481,x28482)+~P23(x28481,x28483,x28484,x28485,x28486,x28487) % 167.77/167.52 [2849]P23(x28493,x28492,x28494,x28495,x28496,x28497)+~E(x28491,x28492)+~P23(x28493,x28491,x28494,x28495,x28496,x28497) % 167.77/167.52 [2850]P23(x28503,x28504,x28502,x28505,x28506,x28507)+~E(x28501,x28502)+~P23(x28503,x28504,x28501,x28505,x28506,x28507) % 167.77/167.52 [2851]P23(x28513,x28514,x28515,x28512,x28516,x28517)+~E(x28511,x28512)+~P23(x28513,x28514,x28515,x28511,x28516,x28517) % 167.77/167.52 [2852]P23(x28523,x28524,x28525,x28526,x28522,x28527)+~E(x28521,x28522)+~P23(x28523,x28524,x28525,x28526,x28521,x28527) % 167.77/167.52 [2853]P23(x28533,x28534,x28535,x28536,x28537,x28532)+~E(x28531,x28532)+~P23(x28533,x28534,x28535,x28536,x28537,x28531) % 167.77/167.52 [2854]~P87(x28541)+P87(x28542)+~E(x28541,x28542) % 167.77/167.52 [2855]P47(x28552,x28553,x28554)+~E(x28551,x28552)+~P47(x28551,x28553,x28554) % 167.77/167.52 [2856]P47(x28563,x28562,x28564)+~E(x28561,x28562)+~P47(x28563,x28561,x28564) % 167.77/167.52 [2857]P47(x28573,x28574,x28572)+~E(x28571,x28572)+~P47(x28573,x28574,x28571) % 167.77/167.52 [2858]~P115(x28581)+P115(x28582)+~E(x28581,x28582) % 167.77/167.52 [2859]~P129(x28591)+P129(x28592)+~E(x28591,x28592) % 167.77/167.52 [2860]~P45(x28601)+P45(x28602)+~E(x28601,x28602) % 167.77/167.52 [2861]~P113(x28611)+P113(x28612)+~E(x28611,x28612) % 167.77/167.52 [2862]~P72(x28621)+P72(x28622)+~E(x28621,x28622) % 167.77/167.52 [2863]~P76(x28631)+P76(x28632)+~E(x28631,x28632) % 167.77/167.52 [2864]~P122(x28641)+P122(x28642)+~E(x28641,x28642) % 167.77/167.52 [2865]~P114(x28651)+P114(x28652)+~E(x28651,x28652) % 167.77/167.52 % 167.77/167.52 %------------------------------------------- % 167.77/167.57 cnf(10205,plain, % 167.77/167.57 (~E(f328(a116,x102051),x102051)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(10208,plain, % 167.77/167.57 (E(f328(f259(x102081,x102081),f260(x102081,x102082)),x102082)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(10215,plain, % 167.77/167.57 (~E(f328(a116,x102151),x102151)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(10226,plain, % 167.77/167.57 (~E(f328(a116,x102261),x102261)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(10231,plain, % 167.77/167.57 (~P1(f328(f63(x102311,x102312,f192(f879(x102311,a867))),x102313))), % 167.77/167.57 inference(rename_variables,[],[4541])). % 167.77/167.57 cnf(10234,plain, % 167.77/167.57 (~P1(f328(f63(x102341,x102342,f192(f879(x102341,a867))),x102343))), % 167.77/167.57 inference(rename_variables,[],[4541])). % 167.77/167.57 cnf(10237,plain, % 167.77/167.57 (~E(f328(a116,x102371),x102371)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(10240,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x102401),f2(a872)))), % 167.77/167.57 inference(rename_variables,[],[4521])). % 167.77/167.57 cnf(10243,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x102431),f2(a872)))), % 167.77/167.57 inference(rename_variables,[],[4521])). % 167.77/167.57 cnf(10260,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(a116,x102601)),x102601))), % 167.77/167.57 inference(rename_variables,[],[4526])). % 167.77/167.57 cnf(10263,plain, % 167.77/167.57 (~E(f328(f328(f148(x102631),x102632),x102633),x102633)), % 167.77/167.57 inference(rename_variables,[],[4481])). % 167.77/167.57 cnf(10269,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x102691),f2(a872)))), % 167.77/167.57 inference(rename_variables,[],[4521])). % 167.77/167.57 cnf(10271,plain, % 167.77/167.57 (E(f46(a872,f328(f259(x102711,x102711),f260(x102711,f328(f328(f81(a872),x102712),x102713))),x102712),f2(a872))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,3063,3232,10208,3106,3170,3135,3113,4481,3258,4521,10240,10243,4518,4476,4526,4524,3249,4511,4541,10231,4545,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042])). % 167.77/167.57 cnf(10272,plain, % 167.77/167.57 (E(f328(f259(x102721,x102721),f260(x102721,x102722)),x102722)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(10275,plain, % 167.77/167.57 (E(f328(f259(x102751,x102751),f260(x102751,x102752)),x102752)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(10282,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),f328(f328(f80(a872),x102821),x102822)),x102822))), % 167.77/167.57 inference(rename_variables,[],[4543])). % 167.77/167.57 cnf(10285,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),f328(f328(f80(a872),x102851),x102852)),x102852))), % 167.77/167.57 inference(rename_variables,[],[4543])). % 167.77/167.57 cnf(10306,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x103061),x103061))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(10309,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),f46(a872,x103091,x103092)),x103091))), % 167.77/167.57 inference(rename_variables,[],[3735])). % 167.77/167.57 cnf(10330,plain, % 167.77/167.57 (E(f328(f39(a872),f328(f249(a872),x103301)),x103301)), % 167.77/167.57 inference(rename_variables,[],[3165])). % 167.77/167.57 cnf(10338,plain, % 167.77/167.57 (~E(f328(a116,x103381),x103381)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(10341,plain, % 167.77/167.57 (~E(f328(a116,x103411),x103411)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(10344,plain, % 167.77/167.57 (~E(f328(a116,x103441),x103441)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(10346,plain, % 167.77/167.57 (P1(f328(a197,a101))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,3063,3232,10208,10272,3106,3170,3135,3113,3203,4481,3165,4550,3186,3342,3258,4521,10240,10243,3866,3277,4518,4476,4517,10306,3370,3797,3735,4526,10260,4107,4524,4507,3249,4511,4512,4541,10231,4545,4543,10282,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300])). % 167.77/167.57 cnf(10349,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x103491),f328(a116,x103491)))), % 167.77/167.57 inference(rename_variables,[],[3342])). % 167.77/167.57 cnf(10358,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x103581),x103581))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10365,plain, % 167.77/167.57 (E(f328(f259(x103651,x103651),f260(x103651,x103652)),x103652)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(10368,plain, % 167.77/167.57 (E(f328(f259(x103681,x103681),f260(x103681,x103682)),x103682)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(10387,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),x103871),x103871))), % 167.77/167.57 inference(rename_variables,[],[3275])). % 167.77/167.57 cnf(10396,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x103961),x103961))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(10401,plain, % 167.77/167.57 (~E(f328(f328(f328(f72(x104011,f876(x104012)),x104013),x104014),f328(f235(x104012),x104015)),f328(f16(f876(x104012),x104011),f205(x104012)))), % 167.77/167.57 inference(rename_variables,[],[4538])). % 167.77/167.57 cnf(10428,plain, % 167.77/167.57 (~E(f328(f328(f148(x104281),x104282),x104283),x104283)), % 167.77/167.57 inference(rename_variables,[],[4481])). % 167.77/167.57 cnf(10431,plain, % 167.77/167.57 (~E(f328(a26,x104311),f33(x104312,x104313))), % 167.77/167.57 inference(rename_variables,[],[4471])). % 167.77/167.57 cnf(10442,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),x104421),x104421))), % 167.77/167.57 inference(rename_variables,[],[3275])). % 167.77/167.57 cnf(10447,plain, % 167.77/167.57 (~E(f328(a116,x104471),x104471)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(10454,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x104541),x104541))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10467,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x104671),f328(a116,x104671)))), % 167.77/167.57 inference(rename_variables,[],[3342])). % 167.77/167.57 cnf(10472,plain, % 167.77/167.57 (E(f328(f328(f125(x104721),f117(x104721)),x104722),x104722)), % 167.77/167.57 inference(rename_variables,[],[3227])). % 167.77/167.57 cnf(10475,plain, % 167.77/167.57 (E(f328(f328(f125(x104751),f117(x104751)),x104752),x104752)), % 167.77/167.57 inference(rename_variables,[],[3227])). % 167.77/167.57 cnf(10490,plain, % 167.77/167.57 (~P1(f328(f63(x104901,x104902,f192(f879(x104901,a867))),x104903))), % 167.77/167.57 inference(rename_variables,[],[4541])). % 167.77/167.57 cnf(10509,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x105091),x105091))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(10521,plain, % 167.77/167.57 (E(f328(f328(f253(a872),f328(f107(a872),a101)),x105211),f328(f328(f253(a872),f2(a872)),x105211))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,4471,3063,3232,10208,10272,10275,10365,3106,3170,3135,3113,3203,3227,10472,4538,4481,10263,3165,4063,4550,3186,3641,3342,10349,10467,3258,4521,10240,10243,10269,4533,3717,3866,3302,3303,3277,4518,4476,4016,3274,10358,10454,3275,10387,3276,4517,10306,10396,3370,3797,3735,10309,4526,10260,4107,4524,4507,3249,3250,4508,4511,4512,4541,10231,10234,4545,3757,4543,10282,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806])). % 167.77/167.57 cnf(10524,plain, % 167.77/167.57 (~E(f328(a26,x105241),f33(x105242,x105243))), % 167.77/167.57 inference(rename_variables,[],[4471])). % 167.77/167.57 cnf(10533,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x105331),x105331))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(10538,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x105381),f328(a116,x105381)))), % 167.77/167.57 inference(rename_variables,[],[3342])). % 167.77/167.57 cnf(10541,plain, % 167.77/167.57 (~P1(f328(f63(x105411,x105412,f192(f879(x105411,a867))),x105413))), % 167.77/167.57 inference(rename_variables,[],[4541])). % 167.77/167.57 cnf(10544,plain, % 167.77/167.57 (~P1(f328(f63(x105441,x105442,f192(f879(x105441,a867))),x105443))), % 167.77/167.57 inference(rename_variables,[],[4541])). % 167.77/167.57 cnf(10549,plain, % 167.77/167.57 (~P1(f328(f63(x105491,x105492,f192(f879(x105491,a867))),x105493))), % 167.77/167.57 inference(rename_variables,[],[4541])). % 167.77/167.57 cnf(10559,plain, % 167.77/167.57 (~E(f328(f166(x105591),f328(a116,f328(f328(f125(x105591),f328(f166(x105591),x105592)),f328(f328(f148(x105591),x105593),f117(x105591))))),f328(f328(f148(x105591),x105593),x105592))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,10447,4471,10431,3063,3232,10208,10272,10275,10365,3106,3170,3135,3113,3203,3227,10472,4538,4481,10263,3165,4063,4550,3186,3641,3342,10349,10467,10538,3258,4521,10240,10243,10269,4533,3717,3866,3302,3303,3277,4518,4476,4016,3274,10358,10454,3275,10387,3276,4517,10306,10396,10509,3370,3797,3735,10309,4526,10260,4107,4524,4507,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,4545,3757,4543,10282,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978])). % 167.77/167.57 cnf(10560,plain, % 167.77/167.57 (~E(f328(a116,x105601),x105601)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(10574,plain, % 167.77/167.57 (P1(f328(f328(f243(a103),f328(a3,x105741)),f328(a3,f328(a116,x105741))))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,10447,4471,10431,3063,3232,10208,10272,10275,10365,3106,3170,3135,3113,3203,3227,10472,4538,4481,10263,3165,4063,4550,3186,3641,3342,10349,10467,10538,3730,3258,4521,10240,10243,10269,4533,3717,3866,3302,3303,3277,4518,4476,4016,3274,10358,10454,3275,10387,3276,4517,10306,10396,10509,3370,3797,3735,10309,4526,10260,4107,4524,4507,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,4545,3757,4543,10282,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058])). % 167.77/167.57 cnf(10585,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x105851),x105851))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10588,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x105881),f328(a116,f328(f328(f80(a872),x105882),x105881))))), % 167.77/167.57 inference(rename_variables,[],[3728])). % 167.77/167.57 cnf(10590,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x105901),f328(f328(f81(a872),f328(a116,x105901)),f328(a116,x105901))))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,10447,4471,10431,3063,3232,10208,10272,10275,10365,3106,3170,3135,3113,3203,3227,10472,4538,4481,10263,3165,4063,4550,3186,3641,3342,10349,10467,10538,3730,3258,4521,10240,10243,10269,4533,3717,3866,3302,3303,3277,4518,4476,4016,3274,10358,10454,3275,10387,3276,4517,10306,10396,10509,3370,3797,3735,10309,4526,10260,4107,4524,4507,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,3546,4545,3757,4543,10282,3728,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083])). % 167.77/167.57 cnf(10591,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x105911),f328(f328(f81(a872),x105911),x105911)))), % 167.77/167.57 inference(rename_variables,[],[3546])). % 167.77/167.57 cnf(10594,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x105941),f328(f328(f81(a872),x105941),x105941)))), % 167.77/167.57 inference(rename_variables,[],[3546])). % 167.77/167.57 cnf(10599,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x105991),f328(a116,x105991)))), % 167.77/167.57 inference(rename_variables,[],[3342])). % 167.77/167.57 cnf(10602,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x106021),f328(a116,x106021)))), % 167.77/167.57 inference(rename_variables,[],[3342])). % 167.77/167.57 cnf(10605,plain, % 167.77/167.57 (P1(f328(f328(f330(x106051),x106052),f251(f879(x106051,a867))))), % 167.77/167.57 inference(rename_variables,[],[3434])). % 167.77/167.57 cnf(10622,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),f328(f328(f80(a872),x106221),x106222)),x106222))), % 167.77/167.57 inference(rename_variables,[],[4543])). % 167.77/167.57 cnf(10625,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),f328(f328(f80(a872),x106251),x106252)),x106252))), % 167.77/167.57 inference(rename_variables,[],[4543])). % 167.77/167.57 cnf(10628,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(a116,x106281)),x106281))), % 167.77/167.57 inference(rename_variables,[],[4526])). % 167.77/167.57 cnf(10631,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(a116,x106311)),x106311))), % 167.77/167.57 inference(rename_variables,[],[4526])). % 167.77/167.57 cnf(10634,plain, % 167.77/167.57 (P1(f328(f251(f879(x106341,a867)),x106342))), % 167.77/167.57 inference(rename_variables,[],[3336])). % 167.77/167.57 cnf(10637,plain, % 167.77/167.57 (E(f328(f39(a872),f328(f249(a872),x106371)),x106371)), % 167.77/167.57 inference(rename_variables,[],[3165])). % 167.77/167.57 cnf(10640,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x106401),f328(a116,x106401)))), % 167.77/167.57 inference(rename_variables,[],[3342])). % 167.77/167.57 cnf(10647,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x106471),x106471))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10652,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),x106521),x106521))), % 167.77/167.57 inference(rename_variables,[],[3275])). % 167.77/167.57 cnf(10661,plain, % 167.77/167.57 (E(f328(f259(x106611,x106611),f260(x106611,x106612)),x106612)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(10664,plain, % 167.77/167.57 (P1(f328(f251(f879(x106641,a867)),x106642))), % 167.77/167.57 inference(rename_variables,[],[3336])). % 167.77/167.57 cnf(10667,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),f2(a872)),x106671))), % 167.77/167.57 inference(rename_variables,[],[3296])). % 167.77/167.57 cnf(10670,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x106701,a867)),f192(f879(x106701,a867))),x106702))), % 167.77/167.57 inference(rename_variables,[],[3726])). % 167.77/167.57 cnf(10673,plain, % 167.77/167.57 (P1(f328(f251(f879(x106731,a867)),x106732))), % 167.77/167.57 inference(rename_variables,[],[3336])). % 167.77/167.57 cnf(10675,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(f328(f81(a872),f328(a116,x106751)),f328(a116,x106751))),x106751))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,10447,4471,10431,3063,3232,10208,10272,10275,10365,10368,3106,3170,3135,3113,3203,3227,10472,4538,4481,10263,3165,10330,4063,4550,3186,3641,3580,3342,10349,10467,10538,10599,10602,3730,3258,4521,10240,10243,10269,4533,3717,3488,3866,3302,3303,3277,4518,4476,4016,3274,10358,10454,10585,3275,10387,10442,3276,4517,10306,10396,10509,3434,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,3296,4107,4524,4507,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,4548,3726,3546,10591,10594,4545,3757,4543,10282,10285,10622,3728,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298])). % 167.77/167.57 cnf(10676,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x106761),f328(f328(f81(a872),x106761),x106761)))), % 167.77/167.57 inference(rename_variables,[],[3546])). % 167.77/167.57 cnf(10693,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(a116,f328(a116,f328(f328(f80(a872),x106931),x106932)))),f328(a116,x106932)))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,10447,4471,10431,3063,3232,10208,10272,10275,10365,10368,3210,3106,3170,3135,3113,3203,3227,10472,4538,4481,10263,3165,10330,4063,4550,3186,3641,3580,3342,10349,10467,10538,10599,10602,10640,3730,3258,4521,10240,10243,10269,4533,3717,3488,3866,3302,3303,3277,4518,4476,4016,3274,10358,10454,10585,3275,10387,10442,3276,4517,10306,10396,10509,3434,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,3296,4107,4524,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,4548,3726,3546,10591,10594,4545,3757,4543,10282,10285,10622,3728,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345])). % 167.77/167.57 cnf(10716,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x107161),x107161))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10727,plain, % 167.77/167.57 (~P1(f328(f328(f192(f879(x107271,f879(x107272,a867))),x107273),x107274))), % 167.77/167.57 inference(rename_variables,[],[4546])). % 167.77/167.57 cnf(10734,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x107341),f328(a116,x107341)))), % 167.77/167.57 inference(rename_variables,[],[3342])). % 167.77/167.57 cnf(10736,plain, % 167.77/167.57 (P1(f328(f328(f243(a1),f328(f328(f22(a1),x107361),f78(a1))),x107361))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,10447,4471,10431,3063,3232,10208,10272,10275,10365,10368,3210,3106,3170,3135,3113,3203,3227,10472,4538,4481,10263,3165,10330,4063,3918,4550,3186,3641,3580,3342,10349,10467,10538,10599,10602,10640,3730,3258,4521,10240,10243,10269,4533,3717,3488,3866,3302,3303,3277,4518,4476,4016,3274,10358,10454,10585,10647,10716,3275,10387,10442,10652,3276,4517,10306,10396,10509,3434,4529,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,10631,3296,4107,4524,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,4548,3726,3546,10591,10594,4545,4546,3757,4543,10282,10285,10622,3728,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599])). % 167.77/167.57 cnf(10737,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),x107371),x107371))), % 167.77/167.57 inference(rename_variables,[],[3275])). % 167.77/167.57 cnf(10742,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x107421),f2(a872)))), % 167.77/167.57 inference(rename_variables,[],[4521])). % 167.77/167.57 cnf(10755,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x107551),f2(a872)))), % 167.77/167.57 inference(rename_variables,[],[4521])). % 167.77/167.57 cnf(10758,plain, % 167.77/167.57 (~P1(f328(f328(f243(f879(x107581,a867)),x107582),f192(f879(x107581,a867))))), % 167.77/167.57 inference(rename_variables,[],[4539])). % 167.77/167.57 cnf(10761,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x107611),x107611))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10764,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x107641),x107641))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10779,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x107791),x107791))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(10788,plain, % 167.77/167.57 (~P1(f328(f328(f330(x107881),x107882),f192(f879(x107881,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(10797,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x107971),x107971))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10800,plain, % 167.77/167.57 (~P1(f328(f328(f330(x108001),x108002),f192(f879(x108001,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(10803,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x108031,a867)),f328(f307(x108032,x108031,x108033),f328(f308(x108032,x108031,x108033),x108034))),x108034))), % 167.77/167.57 inference(rename_variables,[],[4167])). % 167.77/167.57 cnf(10810,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x108101,a867)),f328(f170(x108101),f328(f133(x108101,x108102),x108103))),f328(f170(x108101),x108103)))), % 167.77/167.57 inference(rename_variables,[],[3928])). % 167.77/167.57 cnf(10813,plain, % 167.77/167.57 (E(f328(f307(x108131,x108131,f5(x108131)),x108132),x108132)), % 167.77/167.57 inference(rename_variables,[],[3332])). % 167.77/167.57 cnf(10818,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),f2(a872)),x108181))), % 167.77/167.57 inference(rename_variables,[],[3296])). % 167.77/167.57 cnf(10821,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x108211),x108211))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10824,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x108241),x108241))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(10827,plain, % 167.77/167.57 (~P1(f328(f328(f192(f879(x108271,f879(x108272,a867))),x108273),x108274))), % 167.77/167.57 inference(rename_variables,[],[4546])). % 167.77/167.57 cnf(10834,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x108341),x108341))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(10845,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x108451),f328(a116,f328(f328(f80(a872),x108452),x108451))))), % 167.77/167.57 inference(rename_variables,[],[3728])). % 167.77/167.57 cnf(10848,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x108481),f328(f328(f81(a872),x108481),x108481)))), % 167.77/167.57 inference(rename_variables,[],[3546])). % 167.77/167.57 cnf(10858,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x108581),x108581))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10861,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),x108611),x108611))), % 167.77/167.57 inference(rename_variables,[],[3275])). % 167.77/167.57 cnf(10864,plain, % 167.77/167.57 (~E(f328(a116,x108641),x108641)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(10869,plain, % 167.77/167.57 (P1(f328(f328(f330(x108691),x108692),f251(f879(x108691,a867))))), % 167.77/167.57 inference(rename_variables,[],[3434])). % 167.77/167.57 cnf(10874,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x108741),f2(a872)))), % 167.77/167.57 inference(rename_variables,[],[4521])). % 167.77/167.57 cnf(10889,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),f2(a872)),x108891))), % 167.77/167.57 inference(rename_variables,[],[3296])). % 167.77/167.57 cnf(10896,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x108961),x108961))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10905,plain, % 167.77/167.57 (~P1(f328(f328(f330(x109051),x109052),f192(f879(x109051,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(10912,plain, % 167.77/167.57 (P1(f328(f328(f330(f873(x109121)),x109122),f158(x109121,f251(f879(x109121,a867)))))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,4471,10431,3063,3232,10208,10272,10275,10365,10368,3210,3106,3170,3135,3113,3332,3203,3227,10472,4538,4481,10263,3165,10330,4063,3918,4550,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,3730,3258,4521,10240,10243,10269,10742,10755,4533,3717,3488,3866,3302,3303,3277,4518,4476,4027,3928,10810,3642,4016,4539,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,3434,10605,10869,4529,10788,10800,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,10631,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,4548,3726,3546,10591,10594,10676,10848,4545,4546,10727,4167,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762])). % 167.77/167.57 cnf(10913,plain, % 167.77/167.57 (P1(f328(f328(f330(x109131),x109132),f251(f879(x109131,a867))))), % 167.77/167.57 inference(rename_variables,[],[3434])). % 167.77/167.57 cnf(10916,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x109161),f873(x109161))),f328(f328(f263(f873(x109161),f873(x109161)),x109162),f117(x109161))),f142(x109161,x109163)))), % 167.77/167.57 inference(rename_variables,[],[4550])). % 167.77/167.57 cnf(10922,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(x109221,x109221)),x109222),f260(x109221,f192(f879(x109221,a867)))))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,4471,10431,3063,3232,10208,10272,10275,10365,10368,3210,3106,3170,3135,3113,3332,3203,3227,10472,4538,4481,10263,3165,10330,4063,3918,4550,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,3730,3258,4521,10240,10243,10269,10742,10755,4533,3717,3488,3866,3302,3303,3277,4518,4476,4027,3928,10810,3642,4016,4539,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,3434,10605,10869,4529,10788,10800,10905,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,10631,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,4548,3726,3546,10591,10594,10676,10848,4545,4546,10727,4167,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895])). % 167.77/167.57 cnf(10923,plain, % 167.77/167.57 (~P1(f328(f328(f330(x109231),x109232),f192(f879(x109231,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(10925,plain, % 167.77/167.57 (~P1(f328(f328(f330(x109251),x109252),f328(f308(x109251,x109253,x109254),f192(f879(x109253,a867)))))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,4471,10431,3063,3232,10208,10272,10275,10365,10368,3210,3106,3170,3135,3113,3332,3203,3227,10472,4538,4481,10263,3165,10330,4063,3918,4550,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,3730,3258,4521,10240,10243,10269,10742,10755,4533,3717,3488,3866,3302,3303,3277,4518,4476,4027,3928,10810,3642,4016,4539,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,3434,10605,10869,4529,10788,10800,10905,10923,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,10631,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,4548,3726,3546,10591,10594,10676,10848,4545,4546,10727,4167,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929])). % 167.77/167.57 cnf(10926,plain, % 167.77/167.57 (~P1(f328(f328(f330(x109261),x109262),f192(f879(x109261,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(10929,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x109291,a867)),x109292),f328(f328(f306(x109291),x109293),x109292)))), % 167.77/167.57 inference(rename_variables,[],[3724])). % 167.77/167.57 cnf(10932,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x109321),x109321))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(10935,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x109351,a867)),x109352),f328(f328(f306(x109351),x109353),x109352)))), % 167.77/167.57 inference(rename_variables,[],[3724])). % 167.77/167.57 cnf(10937,plain, % 167.77/167.57 (P35(x109371,x109372,x109373,f118(x109371,f117(x109371)),f117(x109372))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,4471,10431,3063,3116,3232,10208,10272,10275,10365,10368,3210,3106,3170,3135,3113,3332,3203,3227,10472,4538,4481,10263,3165,10330,4063,3918,4550,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,3730,3258,4521,10240,10243,10269,10742,10755,4533,3717,3488,3866,3302,3303,3277,4518,4476,4027,3928,10810,3642,4016,4539,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,3434,10605,10869,4529,10788,10800,10905,10923,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,10631,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,4548,3724,10929,3726,3546,10591,10594,10676,10848,4545,4546,10727,4167,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032])). % 167.77/167.57 cnf(10950,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x109501,a867)),x109502),f328(f328(f306(x109501),x109503),x109502)))), % 167.77/167.57 inference(rename_variables,[],[3724])). % 167.77/167.57 cnf(10955,plain, % 167.77/167.57 (~P1(f328(f63(x109551,x109552,f192(f879(x109551,a867))),x109553))), % 167.77/167.57 inference(rename_variables,[],[4541])). % 167.77/167.57 cnf(10968,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x109681),f328(a116,x109681)))), % 167.77/167.57 inference(rename_variables,[],[3342])). % 167.77/167.57 cnf(10978,plain, % 167.77/167.57 (~E(f328(f307(x109781,f879(x109781,a867),x109782),x109783),f328(f305(x109781),x109783))), % 167.77/167.57 inference(rename_variables,[],[4527])). % 167.77/167.57 cnf(10981,plain, % 167.77/167.57 (~P1(f328(f328(f330(x109811),x109812),f192(f879(x109811,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(10984,plain, % 167.77/167.57 (P1(f328(f328(f330(f878(x109841,x109841)),f328(f328(f263(x109841,x109841),x109842),x109842)),f304(x109841,x109843)))), % 167.77/167.57 inference(rename_variables,[],[3918])). % 167.77/167.57 cnf(10987,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x109871,a867)),f328(f170(x109871),f174(x109871,x109872,x109873))),f328(f170(x109871),x109872)))), % 167.77/167.57 inference(rename_variables,[],[3979])). % 167.77/167.57 cnf(10990,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x109901,a867)),x109902),f251(f879(x109901,a867))))), % 167.77/167.57 inference(rename_variables,[],[3660])). % 167.77/167.57 cnf(11006,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x110061,a867)),f192(f879(x110061,a867))),x110062))), % 167.77/167.57 inference(rename_variables,[],[3726])). % 167.77/167.57 cnf(11017,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x110171),f873(x110171))),f328(f328(f263(f873(x110171),f873(x110171)),x110172),f117(x110171))),f144(x110171,x110173)))), % 167.77/167.57 inference(rename_variables,[],[4551])). % 167.77/167.57 cnf(11028,plain, % 167.77/167.57 (~E(f328(a116,x110281),x110281)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11031,plain, % 167.77/167.57 (~E(f328(a116,x110311),x110311)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11033,plain, % 167.77/167.57 (P1(f328(f328(f330(f878(f873(x110331),f873(x110331))),f328(f328(f263(f873(x110331),f873(x110331)),f117(x110331)),f117(x110331))),f328(f328(f285(f873(x110331),f873(x110331),f873(x110331)),f155(x110331,x110332)),f304(f873(x110331),f155(x110331,x110332)))))), % 167.77/167.57 inference(scs_inference,[],[4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,4471,10431,3063,3116,3232,10208,10272,10275,10365,10368,3210,3737,3106,3170,3135,3113,3332,3203,3227,10472,4538,3916,4481,10263,4527,3165,10330,4063,3918,10984,4550,10916,4551,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,3730,3258,4521,10240,10243,10269,10742,10755,10874,4533,3717,3488,3866,3302,3303,3277,4518,4476,4027,3928,10810,3979,3642,4016,3660,4539,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,3434,10605,10869,10913,4529,10788,10800,10905,10923,10926,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,10631,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,10549,4548,3883,3724,10929,10935,3726,10670,3546,10591,10594,10676,10848,4545,4546,10727,4167,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597])). % 167.77/167.57 cnf(11043,plain, % 167.77/167.57 (P26(x110431,x110431,f5(x110431),x110432)), % 167.77/167.57 inference(rename_variables,[],[3518])). % 167.77/167.57 cnf(11048,plain, % 167.77/167.57 (~E(f328(f307(x110481,f879(x110481,a867),x110482),x110483),f328(f305(x110481),x110483))), % 167.77/167.57 inference(rename_variables,[],[4527])). % 167.77/167.57 cnf(11053,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x110531,a867)),x110532),f251(f879(x110531,a867))))), % 167.77/167.57 inference(rename_variables,[],[3660])). % 167.77/167.57 cnf(11067,plain, % 167.77/167.57 (~P1(f328(f328(f330(x110671),x110672),f192(f879(x110671,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11070,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(a116,x110701)),x110701))), % 167.77/167.57 inference(rename_variables,[],[4526])). % 167.77/167.57 cnf(11075,plain, % 167.77/167.57 (~P1(f328(f328(f330(x110751),x110752),f192(f879(x110751,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11088,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(a116,x110881)),x110881))), % 167.77/167.57 inference(rename_variables,[],[4526])). % 167.77/167.57 cnf(11091,plain, % 167.77/167.57 (~P1(f328(f328(f330(x110911),x110912),f192(f879(x110911,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11101,plain, % 167.77/167.57 (E(f328(x111011,f709(f328(x111011,x111012),f328(f235(x111013),x111012),x111011,x111014,x111013)),f328(x111011,x111012))), % 167.77/167.57 inference(scs_inference,[],[3518,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,4471,10431,10524,3063,3116,3232,10208,10272,10275,10365,10368,3210,3737,3106,3170,3135,3113,3332,3203,3227,10472,3380,4538,3916,4481,10263,4527,10978,3381,3165,10330,4063,3918,10984,4550,10916,4551,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,3730,3258,4521,10240,10243,10269,10742,10755,10874,4533,3717,3488,3866,3302,3303,3277,4518,4476,4027,3928,10810,3979,3642,4016,3660,10990,4539,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,3434,10605,10869,10913,4529,10788,10800,10905,10923,10926,10981,11067,11075,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,10631,11070,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,10549,4548,3883,3724,10929,10935,3726,10670,3546,10591,10594,10676,10848,4545,4546,10727,4167,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891])). % 167.77/167.57 cnf(11110,plain, % 167.77/167.57 (P1(f328(f328(f330(f878(x111101,x111101)),f328(f328(f263(x111101,x111101),x111102),x111102)),f304(x111101,x111103)))), % 167.77/167.57 inference(rename_variables,[],[3918])). % 167.77/167.57 cnf(11115,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x111151),f873(x111151))),f328(f328(f263(f873(x111151),f873(x111151)),x111152),f117(x111151))),f142(x111151,x111153)))), % 167.77/167.57 inference(rename_variables,[],[4550])). % 167.77/167.57 cnf(11118,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x111181),f873(x111181))),f328(f328(f263(f873(x111181),f873(x111181)),x111182),f117(x111181))),f144(x111181,x111183)))), % 167.77/167.57 inference(rename_variables,[],[4551])). % 167.77/167.57 cnf(11121,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x111211),f873(x111211))),f328(f328(f263(f873(x111211),f873(x111211)),x111212),f117(x111211))),f154(x111211,x111213)))), % 167.77/167.57 inference(rename_variables,[],[4552])). % 167.77/167.57 cnf(11126,plain, % 167.77/167.57 (~P1(f328(f328(f243(f879(x111261,a867)),x111262),f192(f879(x111261,a867))))), % 167.77/167.57 inference(rename_variables,[],[4539])). % 167.77/167.57 cnf(11129,plain, % 167.77/167.57 (~P1(f328(f328(f330(x111291),x111292),f192(f879(x111291,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11134,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x111341,a867)),x111342),f251(f879(x111341,a867))))), % 167.77/167.57 inference(rename_variables,[],[3660])). % 167.77/167.57 cnf(11137,plain, % 167.77/167.57 (~P1(f328(f328(f192(f879(x111371,f879(x111372,a867))),x111373),x111374))), % 167.77/167.57 inference(rename_variables,[],[4546])). % 167.77/167.57 cnf(11146,plain, % 167.77/167.57 (~P1(f328(f328(f330(x111461),x111462),f192(f879(x111461,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11149,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(x111491,x111491)),f328(f328(f263(x111491,x111491),x111492),x111493)),f150(x111491,f117(f879(x111491,a872)))))), % 167.77/167.57 inference(rename_variables,[],[4548])). % 167.77/167.57 cnf(11152,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x111521,a867)),x111522),x111522))), % 167.77/167.57 inference(rename_variables,[],[3576])). % 167.77/167.57 cnf(11155,plain, % 167.77/167.57 (~P1(f328(f328(f330(x111551),x111552),f192(f879(x111551,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11157,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x111571,a867)),f328(f282(x111572,x111571,f192(f879(f878(x111572,x111571),a867))),x111573)),x111574))), % 167.77/167.57 inference(scs_inference,[],[3518,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,4471,10431,10524,3063,3116,3232,10208,10272,10275,10365,10368,3210,3737,3106,3170,3135,3113,3332,3203,3227,10472,3380,4538,3916,4481,10263,4527,10978,3381,3165,10330,4063,3918,10984,4550,10916,11115,4551,11017,4552,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,3730,3258,4521,10240,10243,10269,10742,10755,10874,4533,3717,3488,3866,3302,3303,3277,4518,4476,4027,3928,10810,3979,3642,4016,3660,10990,11053,4539,10758,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,3434,10605,10869,10913,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,10631,11070,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,10549,4548,3883,3724,10929,10935,3576,3726,10670,11006,3546,10591,10594,10676,10848,4545,4546,10727,10827,4167,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263])). % 167.77/167.57 cnf(11158,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x111581,a867)),f192(f879(x111581,a867))),x111582))), % 167.77/167.57 inference(rename_variables,[],[3726])). % 167.77/167.57 cnf(11161,plain, % 167.77/167.57 (P1(f328(f328(f330(f878(x111611,x111611)),f328(f328(f263(x111611,x111611),x111612),x111612)),f304(x111611,x111613)))), % 167.77/167.57 inference(rename_variables,[],[3918])). % 167.77/167.57 cnf(11163,plain, % 167.77/167.57 (~P35(x111631,x111632,x111633,f328(f328(f151(x111634,x111631),x111635),f328(a116,f117(x111634))),f117(x111632))), % 167.77/167.57 inference(scs_inference,[],[3518,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,4471,10431,10524,3063,3116,3232,10208,10272,10275,10365,10368,3210,3737,3106,3170,3135,3113,3332,3203,3227,10472,3380,4538,3916,4481,10263,4527,10978,3381,3165,10330,4063,3918,10984,11110,4550,10916,11115,4551,11017,4552,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,3730,3258,4521,10240,10243,10269,10742,10755,10874,4533,3717,3488,3866,3302,3303,3277,4518,4476,4027,3928,10810,3979,3642,4016,3660,10990,11053,4539,10758,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,3434,10605,10869,10913,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,10631,11070,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,10549,4548,3883,3724,10929,10935,3576,3726,10670,11006,3546,10591,10594,10676,10848,4545,4546,10727,10827,4167,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272])). % 167.77/167.57 cnf(11172,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x111721),f873(x111721))),f328(f328(f263(f873(x111721),f873(x111721)),x111722),f117(x111721))),f154(x111721,x111723)))), % 167.77/167.57 inference(rename_variables,[],[4552])). % 167.77/167.57 cnf(11175,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x111751),f873(x111751))),f328(f328(f263(f873(x111751),f873(x111751)),f117(x111751)),x111752)),f142(x111751,x111753)))), % 167.77/167.57 inference(rename_variables,[],[4553])). % 167.77/167.57 cnf(11180,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f879(x111801,a867),f879(x111801,a867))),f328(f328(f263(f879(x111801,a867),f879(x111801,a867)),x111802),f192(f879(x111801,a867)))),f303(x111801)))), % 167.77/167.57 inference(scs_inference,[],[3518,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,4471,10431,10524,3063,3116,3232,10208,10272,10275,10365,10368,3210,3737,3106,3170,3135,3113,3332,3203,3227,10472,3380,4538,3916,4481,10263,4527,10978,3381,3165,10330,4063,3918,10984,11110,4550,10916,11115,4551,11017,4552,11121,4553,4554,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,3730,3258,4521,10240,10243,10269,10742,10755,10874,4533,3717,3488,3866,3302,3303,3277,4518,4476,4027,3928,10810,3979,3642,4016,3660,10990,11053,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,3434,10605,10869,10913,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,10631,11070,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,10549,4548,3883,3724,10929,10935,3576,3726,10670,11006,3546,10591,10594,10676,10848,4545,4546,10727,10827,4167,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422])). % 167.77/167.57 cnf(11183,plain, % 167.77/167.57 (P1(f328(f328(f330(x111831),x111832),f251(f879(x111831,a867))))), % 167.77/167.57 inference(rename_variables,[],[3434])). % 167.77/167.57 cnf(11188,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x111881,a867)),f192(f879(x111881,a867))),x111882))), % 167.77/167.57 inference(rename_variables,[],[3726])). % 167.77/167.57 cnf(11191,plain, % 167.77/167.57 (~P1(f328(f328(f330(x111911),x111912),f192(f879(x111911,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11194,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),x111941),f328(a116,x111941)))), % 167.77/167.57 inference(rename_variables,[],[3342])). % 167.77/167.57 cnf(11197,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x111971,a867)),x111972),f251(f879(x111971,a867))))), % 167.77/167.57 inference(rename_variables,[],[3660])). % 167.77/167.57 cnf(11201,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x112011,a867)),f328(f282(x112012,x112011,x112013),f192(f879(x112012,a867)))),x112014))), % 167.77/167.57 inference(scs_inference,[],[3518,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,4471,10431,10524,3063,3116,3232,10208,10272,10275,10365,10368,3210,3737,3106,3170,3135,3113,3332,3203,3227,10472,3380,4538,3916,4481,10263,4527,10978,3381,3165,10330,4063,3918,10984,11110,4550,10916,11115,4551,11017,4552,11121,4553,4554,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,3730,3258,4521,10240,10243,10269,10742,10755,10874,4533,3717,3488,3866,3302,3303,3277,4518,4476,4027,3928,10810,3979,3642,4016,3660,10990,11053,11134,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,3434,10605,10869,10913,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,3336,10634,10664,3370,3797,3735,10309,4526,10260,10628,10631,11070,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,10549,4548,3883,3724,10929,10935,3576,3726,10670,11006,11158,11188,3546,10591,10594,10676,10848,4545,4546,10727,10827,4167,4068,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530])). % 167.77/167.57 cnf(11202,plain, % 167.77/167.57 (P1(f328(f328(f242(f879(x112021,a867)),f192(f879(x112021,a867))),x112022))), % 167.77/167.57 inference(rename_variables,[],[3726])). % 167.77/167.57 cnf(11215,plain, % 167.77/167.57 (P1(f328(f251(f879(x112151,a867)),x112152))), % 167.77/167.57 inference(rename_variables,[],[3336])). % 167.77/167.57 cnf(11223,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x112231),f873(x112231))),f328(f328(f263(f873(x112231),f873(x112231)),x112232),f117(x112231))),f142(x112231,x112233)))), % 167.77/167.57 inference(rename_variables,[],[4550])). % 167.77/167.57 cnf(11226,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x112261),f873(x112261))),f328(f328(f263(f873(x112261),f873(x112261)),x112262),f117(x112261))),f144(x112261,x112263)))), % 167.77/167.57 inference(rename_variables,[],[4551])). % 167.77/167.57 cnf(11229,plain, % 167.77/167.57 (~E(f328(f328(f148(x112291),x112292),x112293),x112293)), % 167.77/167.57 inference(rename_variables,[],[4481])). % 167.77/167.57 cnf(11232,plain, % 167.77/167.57 (~E(f328(a116,x112321),x112321)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11235,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x112351),x112351))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(11238,plain, % 167.77/167.57 (~P1(f328(f328(f330(x112381),x112382),f192(f879(x112381,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11243,plain, % 167.77/167.57 (P1(f328(f328(f330(f878(f873(x112431),f873(x112431))),f328(f328(f263(f873(x112431),f873(x112431)),x112432),x112432)),f155(x112431,f304(x112431,x112433))))), % 167.77/167.57 inference(rename_variables,[],[4057])). % 167.77/167.57 cnf(11248,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x112481),f873(x112481))),f328(f328(f263(f873(x112481),f873(x112481)),x112482),f117(x112481))),f142(x112481,x112483)))), % 167.77/167.57 inference(rename_variables,[],[4550])). % 167.77/167.57 cnf(11250,plain, % 167.77/167.57 (E(f328(f328(f148(x112501),f669(f304(x112501,x112502),f328(f328(f148(x112501),x112503),x112504),x112504,x112503,x112501)),f670(f304(x112501,x112502),f328(f328(f148(x112501),x112503),x112504),x112504,x112503,x112501)),f328(f328(f148(x112501),x112503),x112504))), % 167.77/167.57 inference(scs_inference,[],[3518,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,4471,10431,10524,3063,3116,3232,10208,10272,10275,10365,10368,3210,3737,3106,3170,3135,3113,3332,3203,3227,10472,3380,4538,3916,4481,10263,10428,4527,10978,3381,3165,10330,4063,3918,10984,11110,4550,10916,11115,11223,4551,11017,11118,4552,11121,4553,11175,4554,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,3730,3258,4521,10240,10243,10269,10742,10755,10874,4533,3717,3488,3866,3302,3303,3277,4518,4476,4057,11243,4027,3928,10810,3979,3642,4016,3660,10990,11053,11134,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,10834,3434,10605,10869,10913,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,3336,10634,10664,10673,3370,3797,3735,10309,4526,10260,10628,10631,11070,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,10549,4548,3883,3724,10929,10935,3576,3726,10670,11006,11158,11188,3546,10591,10594,10676,10848,4545,4546,10727,10827,4167,4068,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725])). % 167.77/167.57 cnf(11255,plain, % 167.77/167.57 (~P1(f328(f328(f330(x112551),x112552),f184(x112553,x112551,f186(x112553,x112551,x112554,f192(f879(x112553,a867))))))), % 167.77/167.57 inference(scs_inference,[],[3518,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,4471,10431,10524,3063,3116,3232,10208,10272,10275,10365,10368,3210,3737,3106,3170,3135,3113,3332,3203,3227,10472,3380,4538,3916,4481,10263,10428,4527,10978,3381,3165,10330,4063,3918,10984,11110,4550,10916,11115,11223,4551,11017,11118,4552,11121,4553,11175,4554,3186,3479,3641,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,3730,3258,4521,10240,10243,10269,10742,10755,10874,4533,3717,3488,3866,3302,3303,3277,4518,4476,4057,11243,4027,3928,10810,3979,3642,4016,3660,10990,11053,11134,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,3275,10387,10442,10652,10737,3276,4517,10306,10396,10509,10533,10779,10824,10834,3434,10605,10869,10913,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,3336,10634,10664,10673,3370,3797,3735,10309,4526,10260,10628,10631,11070,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4541,10231,10234,10490,10541,10544,10549,4548,3883,3724,10929,10935,3576,3726,10670,11006,11158,11188,3546,10591,10594,10676,10848,4545,4546,10727,10827,4167,4068,3757,4543,10282,10285,10622,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748])). % 167.77/167.57 cnf(11256,plain, % 167.77/167.57 (~P1(f328(f328(f330(x112561),x112562),f192(f879(x112561,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11259,plain, % 167.77/167.57 (~P1(f328(f328(f330(x112591),x112592),f192(f879(x112591,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11262,plain, % 167.77/167.57 (~P1(f328(f328(f330(x112621),x112622),f192(f879(x112621,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11265,plain, % 167.77/167.57 (P1(f328(f328(f330(x112651),x112652),f251(f879(x112651,a867))))), % 167.77/167.57 inference(rename_variables,[],[3434])). % 167.77/167.57 cnf(11268,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x112681),f2(a872)))), % 167.77/167.57 inference(rename_variables,[],[4521])). % 167.77/167.57 cnf(11273,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(x112731,x112731)),f328(f328(f263(x112731,x112731),x112732),x112733)),f150(x112731,f117(f879(x112731,a872)))))), % 167.77/167.57 inference(rename_variables,[],[4548])). % 167.77/167.57 cnf(11276,plain, % 167.77/167.57 (~E(f328(f307(x112761,f879(x112761,a867),x112762),x112763),f328(f305(x112761),x112763))), % 167.77/167.57 inference(rename_variables,[],[4527])). % 167.77/167.57 cnf(11279,plain, % 167.77/167.57 (~E(f328(f307(x112791,f879(x112791,a867),x112792),x112793),f328(f305(x112791),x112793))), % 167.77/167.57 inference(rename_variables,[],[4527])). % 167.77/167.57 cnf(11282,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x112821),f873(x112821))),f328(f328(f263(f873(x112821),f873(x112821)),x112822),f117(x112821))),f142(x112821,x112823)))), % 167.77/167.57 inference(rename_variables,[],[4550])). % 167.77/167.57 cnf(11288,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(f873(x112881),f873(x112881))),f328(f328(f263(f873(x112881),f873(x112881)),x112882),f117(x112881))),f142(x112881,x112883)))), % 167.77/167.57 inference(rename_variables,[],[4550])). % 167.77/167.57 cnf(11291,plain, % 167.77/167.57 (~P1(f328(f328(f330(x112911),x112912),f192(f879(x112911,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11298,plain, % 167.77/167.57 (~P1(f328(f328(f330(x112981),x112982),f192(f879(x112981,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11301,plain, % 167.77/167.57 (~P1(f328(f328(f330(x113011),x113012),f192(f879(x113011,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11304,plain, % 167.77/167.57 (P1(f328(f328(f330(x113041),f328(x113042,x113043)),f328(f307(x113044,x113041,x113042),f251(f879(x113044,a867)))))), % 167.77/167.57 inference(rename_variables,[],[3883])). % 167.77/167.57 cnf(11307,plain, % 167.77/167.57 (~P1(f328(f328(f330(f878(x113071,x113071)),f328(f328(f263(x113071,x113071),x113072),x113073)),f150(x113071,f117(f879(x113071,a872)))))), % 167.77/167.57 inference(rename_variables,[],[4548])). % 167.77/167.57 cnf(11315,plain, % 167.77/167.57 (E(f118(x113151,f117(x113151)),f117(x113151))), % 167.77/167.57 inference(rename_variables,[],[3116])). % 167.77/167.57 cnf(11318,plain, % 167.77/167.57 (~E(f328(a116,x113181),x113181)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11325,plain, % 167.77/167.57 (~E(f328(a116,x113251),x113251)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11330,plain, % 167.77/167.57 (E(f328(f259(x113301,x113301),f260(x113301,x113302)),x113302)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(11333,plain, % 167.77/167.57 (E(f328(f259(x113331,x113331),f260(x113331,x113332)),x113332)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(11339,plain, % 167.77/167.57 (~E(f328(a116,x113391),x113391)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11346,plain, % 167.77/167.57 (~E(f328(f328(f80(a1),x113461),x113461),a101)), % 167.77/167.57 inference(rename_variables,[],[4479])). % 167.77/167.57 cnf(11355,plain, % 167.77/167.57 (E(f328(f328(f22(a872),f2(a872)),x113551),f2(a872))), % 167.77/167.57 inference(rename_variables,[],[3187])). % 167.77/167.57 cnf(11358,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x113581),f2(a872)))), % 167.77/167.57 inference(rename_variables,[],[4521])). % 167.77/167.57 cnf(11365,plain, % 167.77/167.57 (E(f328(f328(f80(a1),f328(f328(f81(a1),x113651),f328(f328(f40(a1),x113652),x113651))),f46(a1,x113652,x113651)),x113652)), % 167.77/167.57 inference(rename_variables,[],[3829])). % 167.77/167.57 cnf(11391,plain, % 167.77/167.57 (~E(f328(a116,x113911),x113911)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11394,plain, % 167.77/167.57 (~E(f328(a116,x113941),x113941)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11420,plain, % 167.77/167.57 (~P1(f328(f63(x114201,x114202,f192(f879(x114201,a867))),x114203))), % 167.77/167.57 inference(rename_variables,[],[4541])). % 167.77/167.57 cnf(11423,plain, % 167.77/167.57 (~P1(f328(f328(f192(f879(x114231,f879(x114232,a867))),x114233),x114234))), % 167.77/167.57 inference(rename_variables,[],[4546])). % 167.77/167.57 cnf(11426,plain, % 167.77/167.57 (P1(f328(f328(f330(x114261),x114262),f251(f879(x114261,a867))))), % 167.77/167.57 inference(rename_variables,[],[3434])). % 167.77/167.57 cnf(11438,plain, % 167.77/167.57 (~E(f328(a116,x114381),x114381)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11441,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),x114411),x114411))), % 167.77/167.57 inference(rename_variables,[],[3275])). % 167.77/167.57 cnf(11448,plain, % 167.77/167.57 (P1(f328(f67(x114481,x114482,x114483,x114484,f192(f879(x114481,a867))),x114484))), % 167.77/167.57 inference(rename_variables,[],[4206])). % 167.77/167.57 cnf(11449,plain, % 167.77/167.57 (E(f328(f259(x114491,x114491),f260(x114491,x114492)),x114492)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(11454,plain, % 167.77/167.57 (~P1(f328(f328(f192(f879(x114541,f879(x114542,a867))),x114543),x114544))), % 167.77/167.57 inference(rename_variables,[],[4546])). % 167.77/167.57 cnf(11465,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),f328(f328(f80(a872),x114651),x114652)),x114652))), % 167.77/167.57 inference(rename_variables,[],[4543])). % 167.77/167.57 cnf(11468,plain, % 167.77/167.57 (~P1(f328(f328(f243(a1),f328(f104(a1),x114681)),f2(a1)))), % 167.77/167.57 inference(rename_variables,[],[4533])). % 167.77/167.57 cnf(11484,plain, % 167.77/167.57 (~E(f328(f328(f105(a872),f328(a116,x114841)),x114841),f328(a116,x114841))), % 167.77/167.57 inference(scs_inference,[],[3518,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,4471,10431,10524,3191,2871,2876,2888,2890,2892,2899,2904,2907,2908,2915,2927,2936,2953,2954,2955,2968,2990,3012,3013,3030,3045,3052,3063,4452,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,3210,3737,3106,3829,11365,3170,3135,3113,3332,3203,3227,10472,3380,4538,3916,4481,10263,10428,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3085,3187,11355,4063,3918,10984,11110,11161,4550,10916,11115,11223,11248,11282,11288,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,3641,4479,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,3730,3258,4521,10240,10243,10269,10742,10755,10874,11268,11358,4533,3717,3488,3866,3302,3303,3277,4518,4476,3471,4534,4057,11243,3601,4027,3928,10810,3979,3642,4016,3660,10990,11053,11134,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,3275,10387,10442,10652,10737,10861,3276,4517,10306,10396,10509,10533,10779,10824,10834,3434,10605,10869,10913,11183,11265,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,3336,10634,10664,10673,3370,3797,3735,10309,4526,10260,10628,10631,11070,11088,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4206,4541,10231,10234,10490,10541,10544,10549,10955,4548,11149,11273,3883,3724,10929,10935,3576,3726,10670,11006,11158,11188,3546,10591,10594,10676,10848,4545,4535,4546,10727,10827,11137,11423,4167,4068,3757,4543,10282,10285,10622,10625,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346])). % 167.77/167.57 cnf(11491,plain, % 167.77/167.57 (E(f328(f259(x114911,x114911),f260(x114911,x114912)),x114912)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(11496,plain, % 167.77/167.57 (E(f328(f259(x114961,x114961),f260(x114961,x114962)),x114962)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(11499,plain, % 167.77/167.57 (~P1(f328(f328(f243(a1),f328(f104(a1),x114991)),f2(a1)))), % 167.77/167.57 inference(rename_variables,[],[4533])). % 167.77/167.57 cnf(11504,plain, % 167.77/167.57 (~E(f328(a116,x115041),x115041)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11508,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),f2(a1)),a83))), % 167.77/167.57 inference(scs_inference,[],[3518,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,4471,10431,10524,3191,2871,2876,2888,2890,2892,2899,2900,2904,2907,2908,2915,2927,2936,2953,2954,2955,2968,2990,3012,3013,3030,3045,3052,3063,4452,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,3210,3737,3106,3829,11365,3170,3135,3129,3113,3114,3332,3203,3227,10472,3380,4538,3916,4481,10263,10428,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3085,3187,11355,4063,3918,10984,11110,11161,4550,10916,11115,11223,11248,11282,11288,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,3641,4479,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,3730,3258,4521,10240,10243,10269,10742,10755,10874,11268,11358,4533,11468,11499,3717,3488,3866,3302,3303,3277,4518,4476,3471,4534,4057,11243,3601,4027,3928,10810,3979,3642,4016,3660,10990,11053,11134,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,3275,10387,10442,10652,10737,10861,3276,4517,10306,10396,10509,10533,10779,10824,10834,3434,10605,10869,10913,11183,11265,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,3336,10634,10664,10673,3376,3370,3797,3735,10309,4526,10260,10628,10631,11070,11088,3296,10667,10818,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,4206,4541,10231,10234,10490,10541,10544,10549,10955,4548,11149,11273,3883,3724,10929,10935,3576,3726,10670,11006,11158,11188,3546,10591,10594,10676,10848,4545,4535,4546,10727,10827,11137,11423,4167,4068,3757,4543,10282,10285,10622,10625,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438])). % 167.77/167.57 cnf(11513,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x115131),x115131))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(11534,plain, % 167.77/167.57 (~P1(f328(f328(f243(a1),f328(f104(a1),x115341)),f2(a1)))), % 167.77/167.57 inference(rename_variables,[],[4533])). % 167.77/167.57 cnf(11547,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),x115471),x115471))), % 167.77/167.57 inference(rename_variables,[],[3275])). % 167.77/167.57 cnf(11550,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(a116,x115501)),x115501))), % 167.77/167.57 inference(rename_variables,[],[4526])). % 167.77/167.57 cnf(11551,plain, % 167.77/167.57 (~E(f328(a116,x115511),x115511)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11561,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),f328(f328(f80(a872),x115611),x115612)),x115611))), % 167.77/167.57 inference(rename_variables,[],[4544])). % 167.77/167.57 cnf(11564,plain, % 167.77/167.57 (~P1(f328(f328(f243(a1),f328(f104(a1),x115641)),f2(a1)))), % 167.77/167.57 inference(rename_variables,[],[4533])). % 167.77/167.57 cnf(11567,plain, % 167.77/167.57 (~E(f328(a116,x115671),x115671)), % 167.77/167.57 inference(rename_variables,[],[4456])). % 167.77/167.57 cnf(11580,plain, % 167.77/167.57 (P1(f328(f328(f330(x115801),x115802),f328(f328(f306(x115801),x115802),x115803)))), % 167.77/167.57 inference(rename_variables,[],[3591])). % 167.77/167.57 cnf(11581,plain, % 167.77/167.57 (~P1(f328(f328(f242(a1),f2(a1)),f328(f79(a1),f328(f104(a1),f328(a116,x115811)))))), % 167.77/167.57 inference(rename_variables,[],[4545])). % 167.77/167.57 cnf(11584,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),f328(f328(f22(a872),x115841),x115842)),f328(a116,x115841)))), % 167.77/167.57 inference(rename_variables,[],[3730])). % 167.77/167.57 cnf(11587,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),f46(a872,x115871,x115872)),x115871))), % 167.77/167.57 inference(rename_variables,[],[3735])). % 167.77/167.57 cnf(11593,plain, % 167.77/167.57 (E(f328(f259(x115931,x115931),f260(x115931,x115932)),x115932)), % 167.77/167.57 inference(rename_variables,[],[3232])). % 167.77/167.57 cnf(11598,plain, % 167.77/167.57 (E(f328(f328(f125(x115981),f168(x115981,x115982,x115983)),f168(x115981,x115984,x115983)),f328(f328(f125(x115981),f168(x115981,x115984,x115983)),f168(x115981,x115982,x115983)))), % 167.77/167.57 inference(rename_variables,[],[3844])). % 167.77/167.57 cnf(11603,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(a116,x116031)),x116031))), % 167.77/167.57 inference(rename_variables,[],[4526])). % 167.77/167.57 cnf(11612,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x116121),x116121))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(11615,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),f46(a872,x116151,x116152)),x116151))), % 167.77/167.57 inference(rename_variables,[],[3735])). % 167.77/167.57 cnf(11616,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),f2(a872)),x116161))), % 167.77/167.57 inference(rename_variables,[],[3296])). % 167.77/167.57 cnf(11633,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x116331),x116331))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(11636,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x116361),x116361))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(11639,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x116391),x116391))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(11642,plain, % 167.77/167.57 (P1(f328(f328(f330(x116421),f328(x116422,x116423)),f328(f307(x116424,x116421,x116422),f251(f879(x116424,a867)))))), % 167.77/167.57 inference(rename_variables,[],[3883])). % 167.77/167.57 cnf(11643,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),f328(f328(f80(a872),x116431),x116432)),x116432))), % 167.77/167.57 inference(rename_variables,[],[4543])). % 167.77/167.57 cnf(11646,plain, % 167.77/167.57 (P1(f328(f328(f330(x116461),f328(x116462,x116463)),f328(f307(x116464,x116461,x116462),f251(f879(x116464,a867)))))), % 167.77/167.57 inference(rename_variables,[],[3883])). % 167.77/167.57 cnf(11647,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(a116,x116471)),x116471))), % 167.77/167.57 inference(rename_variables,[],[4526])). % 167.77/167.57 cnf(11652,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),f328(f328(f80(a872),x116521),x116522)),x116521))), % 167.77/167.57 inference(rename_variables,[],[4544])). % 167.77/167.57 cnf(11655,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x116551),x116551))), % 167.77/167.57 inference(rename_variables,[],[4517])). % 167.77/167.57 cnf(11658,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x116581),x116581))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(11664,plain, % 167.77/167.57 (~P36(x116641,x116642,f117(x116641))), % 167.77/167.57 inference(rename_variables,[],[4490])). % 167.77/167.57 cnf(11667,plain, % 167.77/167.57 (P1(f328(f328(f330(x116671),x116672),f251(f879(x116671,a867))))), % 167.77/167.57 inference(rename_variables,[],[3434])). % 167.77/167.57 cnf(11668,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(a116,x116681)),x116681))), % 167.77/167.57 inference(rename_variables,[],[4526])). % 167.77/167.57 cnf(11671,plain, % 167.77/167.57 (~P1(f328(f63(x116711,x116712,f192(f879(x116711,a867))),x116713))), % 167.77/167.57 inference(rename_variables,[],[4541])). % 167.77/167.57 cnf(11684,plain, % 167.77/167.57 (~P1(f328(f328(f330(x116841),x116842),f192(f879(x116841,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11687,plain, % 167.77/167.57 (E(f328(f328(f16(x116871,x116872),x116873),x116874),x116873)), % 167.77/167.57 inference(rename_variables,[],[3265])). % 167.77/167.57 cnf(11690,plain, % 167.77/167.57 (E(f328(f328(f16(x116901,x116902),x116903),x116904),x116903)), % 167.77/167.57 inference(rename_variables,[],[3265])). % 167.77/167.57 cnf(11702,plain, % 167.77/167.57 (P1(f328(f328(f243(a872),f2(a872)),f328(a116,x117021)))), % 167.77/167.57 inference(rename_variables,[],[3354])). % 167.77/167.57 cnf(11705,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),x117051),x117051))), % 167.77/167.57 inference(rename_variables,[],[3274])). % 167.77/167.57 cnf(11708,plain, % 167.77/167.57 (P1(f328(f328(f330(x117081),f328(x117082,x117083)),f328(f307(x117084,x117081,x117082),f251(f879(x117084,a867)))))), % 167.77/167.57 inference(rename_variables,[],[3883])). % 167.77/167.57 cnf(11711,plain, % 167.77/167.57 (P1(f328(f38(x117111),f328(f170(x117111),x117112)))), % 167.77/167.57 inference(rename_variables,[],[3315])). % 167.77/167.57 cnf(11714,plain, % 167.77/167.57 (P1(f328(f38(x117141),f328(f170(x117141),x117142)))), % 167.77/167.57 inference(rename_variables,[],[3315])). % 167.77/167.57 cnf(11717,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),f328(f79(a1),f328(f104(a1),x117171))),f328(f104(a1),x117172)))), % 167.77/167.57 inference(rename_variables,[],[3758])). % 167.77/167.57 cnf(11720,plain, % 167.77/167.57 (~P1(f328(f328(f330(x117201),x117202),f192(f879(x117201,a867))))), % 167.77/167.57 inference(rename_variables,[],[4529])). % 167.77/167.57 cnf(11730,plain, % 167.77/167.57 (~P1(f328(f328(f330(a872),f2(a872)),f328(f300(a872),x117301)))), % 167.77/167.57 inference(scs_inference,[],[3518,4489,4490,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,4471,10431,10524,3191,2871,2876,2877,2888,2890,2891,2892,2898,2899,2900,2903,2904,2907,2908,2911,2915,2927,2936,2953,2954,2955,2968,2990,3012,3013,3022,3030,3045,3052,3063,4452,3844,11598,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,3210,3737,3106,3481,3829,11365,3170,3135,3129,3113,3114,3332,3203,3227,10472,3380,4538,3916,4481,10263,10428,3265,11687,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3439,3085,3187,11355,4063,3918,10984,11110,11161,4550,10916,11115,11223,11248,11282,11288,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,3641,4346,4347,4479,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,3730,11584,3258,3354,4521,10240,10243,10269,10742,10755,10874,11268,11358,4533,11468,11499,11534,3717,3488,3866,3302,3303,3277,4518,4476,3471,4534,4057,11243,3601,3315,11711,4027,3928,10810,3979,3642,4016,3660,10990,11053,11134,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,3275,10387,10442,10652,10737,10861,11441,3276,3350,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,3434,10605,10869,10913,11183,11265,11426,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,3336,10634,10664,10673,3376,3370,3797,3735,10309,11587,4526,10260,10628,10631,11070,11088,11550,11603,11647,3296,10667,10818,10889,3758,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,3591,4206,4541,10231,10234,10490,10541,10544,10549,10955,11420,4548,11149,11273,3993,3883,11304,11642,11646,3724,10929,10935,3576,3726,10670,11006,11158,11188,3546,10591,10594,10676,10848,4545,11581,4535,4546,10727,10827,11137,11423,4167,4068,3757,3704,4543,10282,10285,10622,10625,11465,4544,11561,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112])). % 167.77/167.57 cnf(11732,plain, % 167.77/167.57 (~P1(f328(f328(f330(a872),x117321),f328(f249(a872),f2(a872))))), % 167.77/167.57 inference(scs_inference,[],[3518,4489,4490,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,4471,10431,10524,3191,2871,2876,2877,2888,2890,2891,2892,2898,2899,2900,2903,2904,2907,2908,2911,2915,2927,2936,2953,2954,2955,2968,2990,3012,3013,3022,3030,3045,3052,3063,4452,3844,11598,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,3210,3737,3106,3481,3829,11365,3170,3135,3129,3113,3114,3332,3203,3227,10472,3380,4538,3916,4481,10263,10428,3265,11687,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3439,3085,3187,11355,4063,3918,10984,11110,11161,4550,10916,11115,11223,11248,11282,11288,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,3641,4346,4347,4479,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,3730,11584,3258,3354,4521,10240,10243,10269,10742,10755,10874,11268,11358,4533,11468,11499,11534,3717,3488,3866,3302,3303,3277,4518,4476,3471,4534,4057,11243,3601,3315,11711,4027,3928,10810,3979,3642,4016,3660,10990,11053,11134,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,3275,10387,10442,10652,10737,10861,11441,3276,3350,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,3434,10605,10869,10913,11183,11265,11426,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,3336,10634,10664,10673,3376,3370,3797,3735,10309,11587,4526,10260,10628,10631,11070,11088,11550,11603,11647,3296,10667,10818,10889,3758,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,3591,4206,4541,10231,10234,10490,10541,10544,10549,10955,11420,4548,11149,11273,3993,3883,11304,11642,11646,3724,10929,10935,3576,3726,10670,11006,11158,11188,3546,10591,10594,10676,10848,4545,11581,4535,4546,10727,10827,11137,11423,4167,4068,3757,3704,4543,10282,10285,10622,10625,11465,4544,11561,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113])). % 167.77/167.57 cnf(11739,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),x117391),x117391))), % 167.77/167.57 inference(rename_variables,[],[3275])). % 167.77/167.57 cnf(11742,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),x117421),x117421))), % 167.77/167.57 inference(rename_variables,[],[3275])). % 167.77/167.57 cnf(11751,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x117511),f2(a872)))), % 167.77/167.57 inference(rename_variables,[],[4521])). % 167.77/167.57 cnf(11754,plain, % 167.77/167.57 (P1(f328(f328(f242(a1),x117541),x117541))), % 167.77/167.57 inference(rename_variables,[],[3275])). % 167.77/167.57 cnf(11759,plain, % 167.77/167.57 (~P1(f328(f328(f243(a872),x117591),f2(a872)))), % 167.77/167.57 inference(rename_variables,[],[4521])). % 167.77/167.57 cnf(11766,plain, % 167.77/167.57 (P1(f328(f251(f879(x117661,a867)),x117662))), % 167.77/167.57 inference(rename_variables,[],[3336])). % 167.77/167.57 cnf(11771,plain, % 167.77/167.57 (P1(f328(f328(f242(a872),f2(a872)),x117711))), % 167.77/167.57 inference(rename_variables,[],[3296])). % 167.77/167.57 cnf(11772,plain, % 167.77/167.57 (~P1(f328(f328(f242(a872),f328(a116,x117721)),x117721))), % 167.77/167.57 inference(rename_variables,[],[4526])). % 167.77/167.57 cnf(11775,plain, % 167.77/167.57 (~P1(f328(f63(x117751,x117752,f192(f879(x117751,a867))),x117753))), % 167.77/167.57 inference(rename_variables,[],[4541])). % 167.77/167.57 cnf(11792,plain, % 167.77/167.58 (P1(f328(f328(f243(a1),f328(f79(a1),f78(a1))),f2(a1)))), % 167.77/167.58 inference(scs_inference,[],[3518,4489,4490,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,4471,10431,10524,3191,2871,2876,2877,2888,2890,2891,2892,2898,2899,2900,2903,2904,2907,2908,2911,2914,2915,2927,2936,2950,2953,2954,2955,2968,2990,3012,3013,3022,3030,3035,3045,3052,3063,4452,3844,11598,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,3210,3737,3106,3481,3829,11365,3170,3135,3129,3113,3114,3332,3203,3227,10472,3380,4538,3916,4481,10263,10428,3265,11687,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3439,3085,3187,11355,4063,3918,10984,11110,11161,4550,10916,11115,11223,11248,11282,11288,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,3641,4346,4347,4479,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,3730,11584,3258,3354,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,4533,11468,11499,11534,11564,3717,3488,3866,3302,3303,3277,4518,4476,3471,4534,4057,11243,3601,3315,11711,4027,3928,10810,3979,3642,4016,3660,10990,11053,11134,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,3276,3350,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,3434,10605,10869,10913,11183,11265,11426,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,3336,10634,10664,10673,11215,3376,3370,3797,3735,10309,11587,11615,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,3296,10667,10818,10889,11616,3758,4107,4524,3805,4507,4509,3249,3250,4508,4511,4512,3591,4206,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,3993,3883,11304,11642,11646,3724,10929,10935,3576,3726,10670,11006,11158,11188,3546,10591,10594,10676,10848,4545,11581,4535,4546,10727,10827,11137,11423,4167,4068,3757,3704,4543,10282,10285,10622,10625,11465,4544,11561,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423])). % 167.77/167.58 cnf(11797,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x117971),x117971))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(11800,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x118001),x118001))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(11803,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x118031),x118031))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(11806,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x118061),x118061))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(11809,plain, % 167.77/167.58 (~P1(f328(f328(f242(a872),f328(a116,x118091)),x118091))), % 167.77/167.58 inference(rename_variables,[],[4526])). % 167.77/167.58 cnf(11812,plain, % 167.77/167.58 (~P1(f328(f328(f242(a872),f328(a116,x118121)),x118121))), % 167.77/167.58 inference(rename_variables,[],[4526])). % 167.77/167.58 cnf(11815,plain, % 167.77/167.58 (~P1(f328(f328(f242(a872),f328(a116,x118151)),x118151))), % 167.77/167.58 inference(rename_variables,[],[4526])). % 167.77/167.58 cnf(11818,plain, % 167.77/167.58 (~P1(f328(f328(f242(a872),f328(a116,x118181)),x118181))), % 167.77/167.58 inference(rename_variables,[],[4526])). % 167.77/167.58 cnf(11835,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x118351),x118351))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(11841,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x118411),x118411))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(11852,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x118521),x118521))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(11855,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(f878(f873(x118551),f873(x118551)),a867)),f155(x118551,x118552)),f304(f873(x118551),f154(x118551,x118552))))), % 167.77/167.58 inference(rename_variables,[],[3984])). % 167.77/167.58 cnf(11862,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x118621),f328(a116,x118621)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(11865,plain, % 167.77/167.58 (P1(f328(f328(f330(f879(x118651,a867)),x118652),f328(f305(x118651),x118652)))), % 167.77/167.58 inference(rename_variables,[],[3642])). % 167.77/167.58 cnf(11866,plain, % 167.77/167.58 (~E(f328(a116,x118661),x118661)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(11873,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x118731),x118731))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(11878,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x118781),x118781))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(11887,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x118871,a867)),x118872),f328(f328(f306(x118871),x118873),x118872)))), % 167.77/167.58 inference(rename_variables,[],[3724])). % 167.77/167.58 cnf(11890,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x118901),x118901))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(11891,plain, % 167.77/167.58 (~E(f328(a116,x118911),x118911)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(11902,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x119021),x119021))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(11903,plain, % 167.77/167.58 (~E(f328(a116,x119031),x119031)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(11906,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x119061),x119061))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(11909,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x119091),x119091))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(11912,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x119121),x119121))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(11915,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x119151),x119151))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(11918,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x119181),x119181))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(11921,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x119211),x119211))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(11924,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x119241),x119241))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(11925,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x119251),f328(a116,x119251)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(11932,plain, % 167.77/167.58 (~E(f328(a116,x119321),x119321)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(11937,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x119371),x119371))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(11938,plain, % 167.77/167.58 (~E(f328(a116,x119381),x119381)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(11943,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x119431),x119431))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(11958,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x119581),x119581))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(11963,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),f2(a872)),x119631))), % 167.77/167.58 inference(rename_variables,[],[3296])). % 167.77/167.58 cnf(11980,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x119801),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(11983,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x119831),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(11986,plain, % 167.77/167.58 (~P1(f328(f328(f330(x119861),x119862),f192(f879(x119861,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(11989,plain, % 167.77/167.58 (~P1(f328(f328(f330(x119891),x119892),f192(f879(x119891,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(11991,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x119911),f328(f328(f105(a872),x119912),x119911)))), % 167.77/167.58 inference(scs_inference,[],[3518,4489,4490,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,4471,10431,10524,3487,3191,2871,2876,2877,2888,2890,2891,2892,2898,2899,2900,2903,2904,2907,2908,2911,2914,2915,2927,2936,2950,2953,2954,2955,2968,2990,3012,3013,3022,3030,3035,3045,3052,3063,4452,3844,11598,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,3210,3217,3737,3976,3106,3481,3829,11365,3170,3135,3129,3113,3114,3332,3203,3227,10472,3380,4538,3916,4481,10263,10428,3265,11687,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3439,3085,3187,11355,4063,3918,10984,11110,11161,4550,10916,11115,11223,11248,11282,11288,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,3641,4346,4347,4479,3580,3793,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,3730,11584,3258,3354,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,4533,11468,11499,11534,11564,3717,3488,3866,3302,3303,3277,4518,4476,3471,4534,4057,11243,3601,3315,11711,4027,3984,3928,10810,3979,3642,4016,3660,10990,11053,11134,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,3276,3350,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,3434,10605,10869,10913,11183,11265,11426,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,3336,10634,10664,10673,11215,3376,3370,3797,3735,10309,11587,11615,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,3296,10667,10818,10889,11616,11771,3758,4107,4524,3769,3805,4507,4509,3249,3250,4508,4511,4512,3776,3591,4206,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,3993,3883,11304,11642,11646,3724,10929,10935,10950,3576,3726,10670,11006,11158,11188,3546,10591,10594,10676,10848,4545,11581,4535,4546,10727,10827,11137,11423,4167,4068,3757,3704,4543,10282,10285,10622,10625,11465,4544,11561,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339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% 167.77/167.58 cnf(11992,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x119921),x119921))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(11995,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x119951),x119951))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(11998,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x119981),x119981))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(12001,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x120011),x120011))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(12004,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x120041),f328(a116,x120041)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12011,plain, % 167.77/167.58 (P1(f328(f328(f330(f879(x120111,a867)),x120112),f328(f305(x120111),x120112)))), % 167.77/167.58 inference(rename_variables,[],[3642])). % 167.77/167.58 cnf(12016,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x120161,a867)),x120162),f328(f328(f306(x120161),x120163),x120162)))), % 167.77/167.58 inference(rename_variables,[],[3724])). % 167.77/167.58 cnf(12023,plain, % 167.77/167.58 (~P1(f328(f328(f330(x120231),x120232),f192(f879(x120231,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12032,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x120321,a867)),x120322),f251(f879(x120321,a867))))), % 167.77/167.58 inference(rename_variables,[],[3660])). % 167.77/167.58 cnf(12033,plain, % 167.77/167.58 (~E(f328(a116,x120331),x120331)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(12036,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x120361,a867)),f328(f170(x120361),f328(f133(x120361,x120362),x120363))),f328(f170(x120361),x120363)))), % 167.77/167.58 inference(rename_variables,[],[3928])). % 167.77/167.58 cnf(12042,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x120421),f328(a116,x120421)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12051,plain, % 167.77/167.58 (E(f328(f259(x120511,x120511),f260(x120511,x120512)),x120512)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12062,plain, % 167.77/167.58 (P1(f328(f38(x120621),f192(f879(x120621,a867))))), % 167.77/167.58 inference(rename_variables,[],[3350])). % 167.77/167.58 cnf(12063,plain, % 167.77/167.58 (~P1(f328(f328(f330(x120631),x120632),f192(f879(x120631,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12068,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x120681),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12069,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x120691),x120691))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(12074,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x120741,a867)),f328(f170(x120741),f174(x120741,x120742,x120743))),f328(f170(x120741),x120742)))), % 167.77/167.58 inference(rename_variables,[],[3979])). % 167.77/167.58 cnf(12077,plain, % 167.77/167.58 (P26(x120771,x120771,f5(x120771),x120772)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12082,plain, % 167.77/167.58 (P1(f328(f328(f330(f879(x120821,a867)),x120822),f328(f305(x120821),x120822)))), % 167.77/167.58 inference(rename_variables,[],[3642])). % 167.77/167.58 cnf(12089,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x120891),x120891))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12092,plain, % 167.77/167.58 (~P1(f328(f328(f330(x120921),x120922),f192(f879(x120921,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12095,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x120951,a867)),x120952),f328(f328(f306(x120951),x120953),x120952)))), % 167.77/167.58 inference(rename_variables,[],[3724])). % 167.77/167.58 cnf(12096,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x120961,a867)),x120962),f251(f879(x120961,a867))))), % 167.77/167.58 inference(rename_variables,[],[3660])). % 167.77/167.58 cnf(12103,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x121031),f328(a116,x121031)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12106,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x121061),f328(a116,x121061)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12109,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x121091),x121091))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12112,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x121121),x121121))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12115,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x121151),x121151))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12118,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x121181),x121181))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12121,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x121211,a867)),x121212),x121212))), % 167.77/167.58 inference(rename_variables,[],[3576])). % 167.77/167.58 cnf(12125,plain, % 167.77/167.58 (~P1(f328(f328(f242(a1),f328(f328(f22(a1),a83),a101)),f2(a1)))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,4489,4490,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,4471,10431,10524,3487,3191,2871,2876,2877,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2927,2936,2950,2953,2954,2955,2968,2990,3012,3013,3022,3030,3035,3045,3052,3063,4452,3844,11598,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,3210,3217,3737,3976,3106,3481,3829,11365,3170,3135,3129,3113,3114,3332,3203,3227,10472,3380,4538,3916,4481,10263,10428,3265,11687,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3439,3085,3187,11355,4063,3918,10984,11110,11161,4550,10916,11115,11223,11248,11282,11288,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,3641,4346,4347,4479,3580,3793,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,3730,11584,3258,3354,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,4533,11468,11499,11534,11564,3717,3488,3866,3302,3303,3277,4518,4476,3471,4534,4057,11243,3601,3315,11711,11714,4027,3984,3928,10810,3979,10987,3642,11865,12011,4016,3660,10990,11053,11134,11197,12032,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,3276,3350,12062,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,3434,10605,10869,10913,11183,11265,11426,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,3336,10634,10664,10673,11215,3376,3370,3797,3735,10309,11587,11615,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,3296,10667,10818,10889,11616,11771,3758,4107,4524,3769,3805,4507,4509,3249,3250,4508,4511,4512,3776,3591,4206,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,3993,3883,11304,11642,11646,3724,10929,10935,10950,11887,12016,3576,11152,3726,10670,11006,11158,11188,3546,10591,10594,10676,10848,4545,11581,4535,4546,10727,10827,11137,11423,4167,4068,3757,3704,4543,10282,10285,10622,10625,11465,4544,11561,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6557,6562,6564,6569,6570,6578,6582,6595,6620,6621,6622,6623,6635,6640,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6792,6795,6831,6834,6835,6848,6849,6850,6851,6871,6872,6887,6913,6935,6946,6948,6949,6951,6953,6954,6987,6988,6993,6994,6995,6996,6998,7000,7025,7034,7035,7047,7057,7096,7106,7110,7117,7128,7134,7136,7142,7151,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7385,7399,7416,7448,7451,7477,7501,7518,7521,7522,7532,7550,7551,7553,7555,7557,7559,7587,7612,7613])). % 167.77/167.58 cnf(12128,plain, % 167.77/167.58 (P1(f328(f328(f330(f879(x121281,a867)),x121282),f328(f305(x121281),x121282)))), % 167.77/167.58 inference(rename_variables,[],[3642])). % 167.77/167.58 cnf(12137,plain, % 167.77/167.58 (~E(f328(a116,x121371),x121371)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(12138,plain, % 167.77/167.58 (E(f328(f307(x121381,x121381,f5(x121381)),x121382),x121382)), % 167.77/167.58 inference(rename_variables,[],[3332])). % 167.77/167.58 cnf(12141,plain, % 167.77/167.58 (P33(x121411,x121412,f117(x121411),f117(x121411))), % 167.77/167.58 inference(rename_variables,[],[3527])). % 167.77/167.58 cnf(12144,plain, % 167.77/167.58 (~E(f328(a116,x121441),x121441)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(12147,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x121471,a867)),f328(f170(x121471),f174(x121471,x121472,x121473))),f328(f170(x121471),x121472)))), % 167.77/167.58 inference(rename_variables,[],[3979])). % 167.77/167.58 cnf(12148,plain, % 167.77/167.58 (P1(f328(f38(x121481),f328(f170(x121481),x121482)))), % 167.77/167.58 inference(rename_variables,[],[3315])). % 167.77/167.58 cnf(12159,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x121591),x121591))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(12162,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x121621),x121621))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(12171,plain, % 167.77/167.58 (P15(a872,f328(f166(a872),f328(f328(f151(f873(x121711),a872),f193(f873(x121711))),f178(x121711,x121712))))), % 167.77/167.58 inference(rename_variables,[],[3839])). % 167.77/167.58 cnf(12174,plain, % 167.77/167.58 (P26(x121741,x121741,f5(x121741),x121742)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12177,plain, % 167.77/167.58 (P1(f328(f328(f330(f873(x121771)),f117(x121771)),f158(x121771,x121772)))), % 167.77/167.58 inference(rename_variables,[],[3479])). % 167.77/167.58 cnf(12180,plain, % 167.77/167.58 (~P1(f328(f328(f192(f879(x121801,f879(x121802,a867))),x121803),x121804))), % 167.77/167.58 inference(rename_variables,[],[4546])). % 167.77/167.58 cnf(12185,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x121851),x121851))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12186,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),f2(a872)),x121861))), % 167.77/167.58 inference(rename_variables,[],[3296])). % 167.77/167.58 cnf(12189,plain, % 167.77/167.58 (~P1(f328(f328(f192(f879(x121891,f879(x121892,a867))),x121893),x121894))), % 167.77/167.58 inference(rename_variables,[],[4546])). % 167.77/167.58 cnf(12192,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(f878(f873(x121921),f873(x121921)),a867)),f155(x121921,x121922)),f304(f873(x121921),f154(x121921,x121922))))), % 167.77/167.58 inference(rename_variables,[],[3984])). % 167.77/167.58 cnf(12198,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x121981,a867)),f192(f879(x121981,a867))),x121982))), % 167.77/167.58 inference(rename_variables,[],[3726])). % 167.77/167.58 cnf(12201,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x122011,a867)),f328(f307(x122012,x122011,x122013),f328(f308(x122012,x122011,x122013),x122014))),x122014))), % 167.77/167.58 inference(rename_variables,[],[4167])). % 167.77/167.58 cnf(12204,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x122041,a867)),f328(f170(x122041),f174(x122041,x122042,x122043))),f328(f170(x122041),x122042)))), % 167.77/167.58 inference(rename_variables,[],[3979])). % 167.77/167.58 cnf(12205,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x122051,a867)),f328(f170(x122051),f328(f133(x122051,x122052),x122053))),f328(f170(x122051),x122053)))), % 167.77/167.58 inference(rename_variables,[],[3928])). % 167.77/167.58 cnf(12208,plain, % 167.77/167.58 (P26(x122081,f876(x122081),f235(x122081),x122082)), % 167.77/167.58 inference(rename_variables,[],[3528])). % 167.77/167.58 cnf(12213,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x122131,a867)),f328(f307(x122132,x122131,x122133),f328(f308(x122132,x122131,x122133),x122134))),x122134))), % 167.77/167.58 inference(rename_variables,[],[4167])). % 167.77/167.58 cnf(12216,plain, % 167.77/167.58 (P1(f328(f38(f876(x122161)),f328(f307(x122162,f876(x122161),f328(f176(x122162,x122161),x122163)),f251(f879(x122162,a867)))))), % 167.77/167.58 inference(rename_variables,[],[3993])). % 167.77/167.58 cnf(12221,plain, % 167.77/167.58 (P1(f328(f328(f330(f873(x122211)),f117(x122211)),f158(x122211,x122212)))), % 167.77/167.58 inference(rename_variables,[],[3479])). % 167.77/167.58 cnf(12224,plain, % 167.77/167.58 (~P1(f328(f328(f330(f878(f873(x122241),f873(x122241))),f328(f328(f263(f873(x122241),f873(x122241)),x122242),f117(x122241))),f142(x122241,x122243)))), % 167.77/167.58 inference(rename_variables,[],[4550])). % 167.77/167.58 cnf(12227,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x122271),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12229,plain, % 167.77/167.58 (~P1(f328(f38(x122291),f251(f879(x122291,a867))))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,3527,3528,3243,4489,4490,3144,4474,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,4471,10431,10524,3487,3191,2871,2876,2877,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2927,2933,2936,2950,2953,2954,2955,2968,2990,3012,3013,3022,3030,3035,3045,3052,3063,4452,3844,11598,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,3210,3217,3737,3976,3106,3481,3829,11365,3170,3135,3129,3113,3114,3120,3150,3332,10813,3203,3227,10472,3380,4538,3916,4481,10263,10428,3265,11687,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3439,3085,3187,11355,4063,3918,10984,11110,11161,4550,10916,11115,11223,11248,11282,11288,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,12177,12221,3641,4346,4347,4479,3580,3793,3839,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,3730,11584,3258,3354,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,4533,11468,11499,11534,11564,3717,3488,3866,3302,3303,3277,4518,4476,3471,4534,4057,11243,3601,3315,11711,11714,4027,3984,11855,12192,3928,10810,12036,3979,10987,12074,12147,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,3276,3350,12062,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,3434,10605,10869,10913,11183,11265,11426,11667,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,3336,10634,10664,10673,11215,3376,3370,3797,3735,10309,11587,11615,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,3296,10667,10818,10889,11616,11771,11963,3758,4107,4524,3769,3805,4507,4509,3249,3250,4508,4511,4512,3776,3591,4206,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,3993,3883,11304,11642,11646,3724,10929,10935,10950,11887,12016,3576,11152,12121,3726,10670,11006,11158,11188,11202,3546,10591,10594,10676,10848,4545,11581,4535,4546,10727,10827,11137,11423,11454,12180,4167,10803,12201,4068,3757,3704,4543,10282,10285,10622,10625,11465,4544,11561,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9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% 167.77/167.58 cnf(12230,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x122301,a867)),x122302),x122302))), % 167.77/167.58 inference(rename_variables,[],[3576])). % 167.77/167.58 cnf(12233,plain, % 167.77/167.58 (~P1(f328(f328(f330(x122331),x122332),f192(f879(x122331,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12236,plain, % 167.77/167.58 (~P1(f328(f328(f192(f879(x122361,f879(x122362,a867))),x122363),x122364))), % 167.77/167.58 inference(rename_variables,[],[4546])). % 167.77/167.58 cnf(12239,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x122391,a867)),f328(f307(x122392,x122391,x122393),f328(f308(x122392,x122391,x122393),x122394))),x122394))), % 167.77/167.58 inference(rename_variables,[],[4167])). % 167.77/167.58 cnf(12240,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x122401,a867)),x122402),x122402))), % 167.77/167.58 inference(rename_variables,[],[3576])). % 167.77/167.58 cnf(12245,plain, % 167.77/167.58 (E(f328(f259(x122451,x122451),f260(x122451,x122452)),x122452)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12248,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x122481,a867)),f328(f170(x122481),f174(x122481,x122482,x122483))),f328(f170(x122481),x122482)))), % 167.77/167.58 inference(rename_variables,[],[3979])). % 167.77/167.58 cnf(12249,plain, % 167.77/167.58 (P1(f328(f38(x122491),f328(f170(x122491),x122492)))), % 167.77/167.58 inference(rename_variables,[],[3315])). % 167.77/167.58 cnf(12252,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x122521),x122521))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12255,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x122551),x122551))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(12258,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x122581),x122581))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(12269,plain, % 167.77/167.58 (P26(x122691,x122691,f5(x122691),x122692)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12274,plain, % 167.77/167.58 (~P1(f328(f328(f330(x122741),x122742),f192(f879(x122741,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12277,plain, % 167.77/167.58 (P1(f328(f328(f330(f878(x122771,x122771)),f328(f328(f263(x122771,x122771),x122772),x122772)),f304(x122771,x122773)))), % 167.77/167.58 inference(rename_variables,[],[3918])). % 167.77/167.58 cnf(12280,plain, % 167.77/167.58 (~P1(f328(f328(f330(x122801),x122802),f192(f879(x122801,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12283,plain, % 167.77/167.58 (P1(f328(f328(f330(f878(x122831,x122831)),f328(f328(f263(x122831,x122831),x122832),x122832)),f304(x122831,x122833)))), % 167.77/167.58 inference(rename_variables,[],[3918])). % 167.77/167.58 cnf(12293,plain, % 167.77/167.58 (~E(f328(f328(f148(x122931),x122932),x122933),x122933)), % 167.77/167.58 inference(rename_variables,[],[4481])). % 167.77/167.58 cnf(12296,plain, % 167.77/167.58 (P1(f328(f328(f330(x122961),x122962),f251(f879(x122961,a867))))), % 167.77/167.58 inference(rename_variables,[],[3434])). % 167.77/167.58 cnf(12297,plain, % 167.77/167.58 (~E(f328(a116,x122971),x122971)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(12300,plain, % 167.77/167.58 (P1(f328(f328(f330(f873(x123001)),f117(x123001)),f158(x123001,x123002)))), % 167.77/167.58 inference(rename_variables,[],[3479])). % 167.77/167.58 cnf(12301,plain, % 167.77/167.58 (~E(f328(f328(f148(x123011),x123012),x123013),f117(x123011))), % 167.77/167.58 inference(rename_variables,[],[4488])). % 167.77/167.58 cnf(12304,plain, % 167.77/167.58 (P1(f328(f328(f330(x123041),f328(x123042,x123043)),f328(f307(x123044,x123041,x123042),f251(f879(x123044,a867)))))), % 167.77/167.58 inference(rename_variables,[],[3883])). % 167.77/167.58 cnf(12305,plain, % 167.77/167.58 (P26(x123051,x123051,f5(x123051),x123052)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12308,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x123081,a867)),f192(f879(x123081,a867))),x123082))), % 167.77/167.58 inference(rename_variables,[],[3726])). % 167.77/167.58 cnf(12309,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x123091,a867)),x123092),x123092))), % 167.77/167.58 inference(rename_variables,[],[3576])). % 167.77/167.58 cnf(12312,plain, % 167.77/167.58 (P1(f328(f328(f330(x123121),f328(x123122,x123123)),f328(f307(x123124,x123121,x123122),f251(f879(x123124,a867)))))), % 167.77/167.58 inference(rename_variables,[],[3883])). % 167.77/167.58 cnf(12313,plain, % 167.77/167.58 (P26(x123131,x123131,f5(x123131),x123132)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12316,plain, % 167.77/167.58 (P1(f328(f328(f330(f878(f873(x123161),f873(x123161))),f328(f328(f263(f873(x123161),f873(x123161)),f117(x123161)),f117(x123161))),f155(x123161,x123162)))), % 167.77/167.58 inference(rename_variables,[],[4063])). % 167.77/167.58 cnf(12319,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x123191),x123191))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(12320,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x123201),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12326,plain, % 167.77/167.58 (P26(x123261,x123261,f5(x123261),x123262)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12329,plain, % 167.77/167.58 (E(f328(f328(f125(x123291),x123292),f117(x123291)),x123292)), % 167.77/167.58 inference(rename_variables,[],[3204])). % 167.77/167.58 cnf(12330,plain, % 167.77/167.58 (~E(f328(f328(f148(x123301),x123302),x123303),x123303)), % 167.77/167.58 inference(rename_variables,[],[4481])). % 167.77/167.58 cnf(12333,plain, % 167.77/167.58 (E(f328(f328(f125(x123331),x123332),f117(x123331)),x123332)), % 167.77/167.58 inference(rename_variables,[],[3204])). % 167.77/167.58 cnf(12334,plain, % 167.77/167.58 (~E(f328(f328(f148(x123341),x123342),x123343),x123343)), % 167.77/167.58 inference(rename_variables,[],[4481])). % 167.77/167.58 cnf(12337,plain, % 167.77/167.58 (E(f328(f328(f125(x123371),x123372),f117(x123371)),x123372)), % 167.77/167.58 inference(rename_variables,[],[3204])). % 167.77/167.58 cnf(12346,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x123461,a867)),x123462),f251(f879(x123461,a867))))), % 167.77/167.58 inference(rename_variables,[],[3660])). % 167.77/167.58 cnf(12350,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x123501),x123501))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(12351,plain, % 167.77/167.58 (~E(f328(a116,x123511),x123511)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(12354,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x123541,a867)),f192(f879(x123541,a867))),x123542))), % 167.77/167.58 inference(rename_variables,[],[3726])). % 167.77/167.58 cnf(12357,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x123571),x123571))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12360,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x123601,a867)),x123602),x123602))), % 167.77/167.58 inference(rename_variables,[],[3576])). % 167.77/167.58 cnf(12365,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x123651,a867)),x123652),f328(f328(f306(x123651),x123653),x123652)))), % 167.77/167.58 inference(rename_variables,[],[3724])). % 167.77/167.58 cnf(12368,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x123681,a867)),x123682),x123682))), % 167.77/167.58 inference(rename_variables,[],[3576])). % 167.77/167.58 cnf(12369,plain, % 167.77/167.58 (~P1(f328(f328(f330(x123691),x123692),f192(f879(x123691,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12372,plain, % 167.77/167.58 (~P1(f328(f328(f330(x123721),x123722),f192(f879(x123721,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12381,plain, % 167.77/167.58 (P26(x123811,x123811,f5(x123811),x123812)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12384,plain, % 167.77/167.58 (E(f328(f193(f873(x123841)),f328(f165(x123841),x123842)),f328(f193(f873(x123841)),x123842))), % 167.77/167.58 inference(rename_variables,[],[3287])). % 167.77/167.58 cnf(12387,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x123871),x123871))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(12388,plain, % 167.77/167.58 (P1(f328(f251(f879(x123881,a867)),x123882))), % 167.77/167.58 inference(rename_variables,[],[3336])). % 167.77/167.58 cnf(12391,plain, % 167.77/167.58 (~P1(f328(f328(f330(x123911),x123912),f192(f879(x123911,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12394,plain, % 167.77/167.58 (P1(f328(f328(f330(x123941),f328(x123942,x123943)),f328(f307(x123944,x123941,x123942),f251(f879(x123944,a867)))))), % 167.77/167.58 inference(rename_variables,[],[3883])). % 167.77/167.58 cnf(12395,plain, % 167.77/167.58 (P1(f328(f328(f330(f878(x123951,x123951)),f328(f328(f263(x123951,x123951),x123952),x123952)),f304(x123951,x123953)))), % 167.77/167.58 inference(rename_variables,[],[3918])). % 167.77/167.58 cnf(12398,plain, % 167.77/167.58 (P1(f328(f328(f330(f878(x123981,x123981)),f328(f328(f263(x123981,x123981),x123982),x123982)),f304(x123981,x123983)))), % 167.77/167.58 inference(rename_variables,[],[3918])). % 167.77/167.58 cnf(12401,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x124011),x124011))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12402,plain, % 167.77/167.58 (P1(f328(f251(f879(x124021,a867)),x124022))), % 167.77/167.58 inference(rename_variables,[],[3336])). % 167.77/167.58 cnf(12405,plain, % 167.77/167.58 (P1(f328(f38(x124051),f328(f170(x124051),x124052)))), % 167.77/167.58 inference(rename_variables,[],[3315])). % 167.77/167.58 cnf(12412,plain, % 167.77/167.58 (P1(f328(f328(f330(f878(x124121,x124121)),f328(f328(f263(x124121,x124121),x124122),x124122)),f328(f328(f285(x124121,x124121,x124121),f304(x124121,x124123)),f304(x124121,f304(x124121,x124123)))))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,3527,3528,3243,4489,4490,3144,4474,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,4471,10431,10524,3331,3487,3191,2871,2876,2877,2887,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2927,2933,2936,2950,2953,2954,2955,2968,2990,3012,3013,3022,3030,3035,3045,3052,3063,4452,3844,11598,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,3204,12329,12333,12337,3210,3217,3737,3976,3106,4468,3481,3829,11365,3170,3135,3129,3113,3114,3120,3150,3287,3332,10813,12138,3202,3203,3227,10472,3380,4538,3916,4481,10263,10428,11229,12293,12330,4488,12301,3265,11687,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3439,3085,3187,11355,4063,12316,3918,10984,11110,11161,12277,12283,12395,12398,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,4479,11346,3580,3793,3839,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,3730,11584,3258,3354,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,4533,11468,11499,11534,11564,3717,3488,3866,3302,3303,3277,4518,4476,3669,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,4027,3984,11855,12192,3928,10810,12036,3979,10987,12074,12147,12204,12248,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,3276,3350,12062,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,3434,10605,10869,10913,11183,11265,11426,11667,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,3336,10634,10664,10673,11215,11766,12388,3376,3370,3797,3735,10309,11587,11615,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,3296,10667,10818,10889,11616,11771,11963,3758,4107,4524,3769,3805,4507,4509,3249,3250,4508,4511,4512,3776,3591,4206,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,3883,11304,11642,11646,11708,12304,12312,3724,10929,10935,10950,11887,12016,12095,3576,11152,12121,12230,12240,12309,12360,3726,10670,11006,11158,11188,11202,12198,12308,3546,10591,10594,10676,10848,4545,11581,4535,4546,10727,10827,11137,11423,11454,12180,12189,4167,10803,12201,12213,4068,3757,3704,4543,10282,10285,10622,10625,11465,4544,11561,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8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% 167.77/167.58 cnf(12415,plain, % 167.77/167.58 (~P1(f328(f328(f192(f879(x124151,f879(x124152,a867))),x124153),x124154))), % 167.77/167.58 inference(rename_variables,[],[4546])). % 167.77/167.58 cnf(12418,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x124181,a867)),x124182),f251(f879(x124181,a867))))), % 167.77/167.58 inference(rename_variables,[],[3660])). % 167.77/167.58 cnf(12421,plain, % 167.77/167.58 (P1(f328(f328(f330(f878(x124211,x124211)),f328(f328(f263(x124211,x124211),x124212),x124212)),f304(x124211,x124213)))), % 167.77/167.58 inference(rename_variables,[],[3918])). % 167.77/167.58 cnf(12424,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),f328(f328(f80(a872),x124241),x124242)),x124242))), % 167.77/167.58 inference(rename_variables,[],[4543])). % 167.77/167.58 cnf(12425,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x124251),f328(a116,x124251)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12428,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x124281,a867)),f328(f170(x124281),f328(f133(x124281,x124282),x124283))),f328(f170(x124281),x124283)))), % 167.77/167.58 inference(rename_variables,[],[3928])). % 167.77/167.58 cnf(12431,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x124311,a867)),x124312),f251(f879(x124311,a867))))), % 167.77/167.58 inference(rename_variables,[],[3660])). % 167.77/167.58 cnf(12434,plain, % 167.77/167.58 (E(f328(f259(x124341,x124341),f260(x124341,x124342)),x124342)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12445,plain, % 167.77/167.58 (~P1(f328(f328(f330(x124451),x124452),f192(f879(x124451,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12446,plain, % 167.77/167.58 (P1(f328(f328(f330(f878(f873(x124461),f873(x124461))),f328(f328(f263(f873(x124461),f873(x124461)),f117(x124461)),f117(x124461))),f155(x124461,x124462)))), % 167.77/167.58 inference(rename_variables,[],[4063])). % 167.77/167.58 cnf(12448,plain, % 167.77/167.58 (P1(f328(f328(f330(f878(a872,a872)),f328(f328(f263(a872,a872),f328(a116,x124481)),f328(a116,f328(a116,x124481)))),f328(f328(f285(a872,a872,a872),f304(a872,a318)),f304(a872,f304(a872,a318)))))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,3527,3528,3243,4489,4490,3144,4474,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,4471,10431,10524,3331,3487,3191,2871,2876,2877,2887,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2927,2933,2936,2950,2953,2954,2955,2968,2990,3012,3013,3022,3030,3035,3045,3052,3063,4452,3616,3844,11598,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,3204,12329,12333,12337,3210,3217,3737,3976,3106,4468,3481,3829,11365,3170,3135,3129,3113,3114,3120,3150,3287,3332,10813,12138,3202,3203,3227,10472,3380,4538,3916,4481,10263,10428,11229,12293,12330,4488,12301,3265,11687,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3439,3085,3187,11355,4063,12316,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,4479,11346,3580,3793,3839,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,3730,11584,3258,3354,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,4533,11468,11499,11534,11564,3717,3488,3866,3302,3303,3277,4518,4476,3669,4200,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,4027,3984,11855,12192,3928,10810,12036,12205,3979,10987,12074,12147,12204,12248,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,3276,3350,12062,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,3434,10605,10869,10913,11183,11265,11426,11667,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,3336,10634,10664,10673,11215,11766,12388,3376,3370,3797,3735,10309,11587,11615,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,3296,10667,10818,10889,11616,11771,11963,3758,4107,4524,3769,3805,4507,4509,3249,3250,4508,4511,4512,3776,3591,4206,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,3883,11304,11642,11646,11708,12304,12312,3724,10929,10935,10950,11887,12016,12095,3576,11152,12121,12230,12240,12309,12360,4061,3726,10670,11006,11158,11188,11202,12198,12308,3546,10591,10594,10676,10848,4545,11581,4535,4546,10727,10827,11137,11423,11454,12180,12189,12236,4167,10803,12201,12213,4068,3757,3704,4543,10282,10285,10622,10625,11465,11643,4544,11561,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6557,6562,6564,6569,6570,6578,6582,6595,6620,6621,6622,6623,6635,6640,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6792,6795,6831,6834,6835,6848,6849,6850,6851,6871,6872,6887,6913,6935,6946,6948,6949,6951,6953,6954,6987,6988,6993,6994,6995,6996,6998,7000,7025,7034,7035,7047,7057,7096,7106,7110,7117,7128,7134,7136,7142,7151,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7385,7399,7416,7448,7451,7477,7501,7518,7521,7522,7532,7550,7551,7553,7555,7557,7559,7587,7612,7613,7645,7647,7648,7649,7654,7676,7685,7695,7700,7706,7708,7714,7726,7727,7729,7760,7783,7850,7851,7898,7906,7907,7931,7932,7949,7950,8008,8009,8010,8035,8068,8075,8077,8087,8099,8130,8138,8145,8158,8180,8186,8213,8257,8285,8298,8316,8319,8349,8372,8433,8434,8437,8439,8544,8545,8546,8547,8576,8605,8636,8680,8698,8753,8798,8801,8814,8821,8858,8877,8905,8906,8924,8925,9065,9069,9089,9099,9122,9124,9127,9131,9134,9135,9148,9149,9169,9175,9187,9235,9253,9307,9308,9315,9376,9381,9417,9424,9427,9430,9431,9446,9462,9471,9483,9495,9496,9499,9501,9528])). % 167.77/167.58 cnf(12451,plain, % 167.77/167.58 (~P1(f328(f328(f330(x124511),x124512),f192(f879(x124511,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12454,plain, % 167.77/167.58 (P32(x124541,x124542,f117(x124541))), % 167.77/167.58 inference(rename_variables,[],[3209])). % 167.77/167.58 cnf(12457,plain, % 167.77/167.58 (E(f328(f193(f873(x124571)),f328(f165(x124571),x124572)),f328(f193(f873(x124571)),x124572))), % 167.77/167.58 inference(rename_variables,[],[3287])). % 167.77/167.58 cnf(12460,plain, % 167.77/167.58 (~P1(f328(f328(f330(x124601),x124602),f192(f879(x124601,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12464,plain, % 167.77/167.58 (~P1(f328(f328(f330(f878(f873(x124641),f873(x124641))),f328(f328(f263(f873(x124641),f873(x124641)),x124642),x124642)),f144(x124641,f150(x124641,f117(f879(x124641,a872))))))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,3527,3528,3243,3209,4489,4490,3144,4474,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,4471,10431,10524,3331,3487,3191,2871,2876,2877,2887,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2927,2933,2936,2950,2953,2954,2955,2968,2990,3012,3013,3022,3030,3035,3045,3052,3063,4452,3616,3844,11598,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,3204,12329,12333,12337,3210,3217,3737,3976,3106,4468,3481,3829,11365,3170,3135,3129,3113,3114,3120,3150,3287,12384,3332,10813,12138,3202,3203,3227,10472,3380,4538,3916,4481,10263,10428,11229,12293,12330,4488,12301,3265,11687,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3439,3085,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,4479,11346,3580,3793,3839,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,3730,11584,3258,3354,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,4533,11468,11499,11534,11564,3717,3488,3866,3302,3303,3277,4518,4476,3669,4200,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,4027,3984,11855,12192,3928,10810,12036,12205,3979,10987,12074,12147,12204,12248,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,3276,3350,12062,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,3434,10605,10869,10913,11183,11265,11426,11667,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,3336,10634,10664,10673,11215,11766,12388,3376,3370,3797,3735,10309,11587,11615,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,3296,10667,10818,10889,11616,11771,11963,3758,4107,4524,3769,3805,4507,4509,3249,3250,4508,4511,4512,3776,3591,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,3883,11304,11642,11646,11708,12304,12312,3724,10929,10935,10950,11887,12016,12095,3576,11152,12121,12230,12240,12309,12360,4061,3726,10670,11006,11158,11188,11202,12198,12308,3546,10591,10594,10676,10848,4545,11581,4535,4546,10727,10827,11137,11423,11454,12180,12189,12236,4167,10803,12201,12213,4068,3757,3704,4543,10282,10285,10622,10625,11465,11643,4544,11561,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6557,6562,6564,6569,6570,6578,6582,6595,6620,6621,6622,6623,6635,6640,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6792,6795,6831,6834,6835,6848,6849,6850,6851,6871,6872,6887,6913,6935,6946,6948,6949,6951,6953,6954,6987,6988,6993,6994,6995,6996,6998,7000,7025,7034,7035,7047,7057,7096,7106,7110,7117,7128,7134,7136,7142,7151,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7385,7399,7416,7448,7451,7477,7501,7518,7521,7522,7532,7550,7551,7553,7555,7557,7559,7587,7612,7613,7645,7647,7648,7649,7654,7676,7685,7695,7700,7706,7708,7714,7726,7727,7729,7760,7783,7850,7851,7898,7906,7907,7931,7932,7949,7950,8008,8009,8010,8035,8068,8075,8077,8087,8099,8130,8138,8145,8158,8180,8186,8213,8257,8285,8298,8316,8319,8349,8372,8433,8434,8437,8439,8544,8545,8546,8547,8576,8605,8636,8680,8698,8753,8798,8801,8814,8821,8858,8877,8905,8906,8924,8925,9065,9069,9089,9099,9122,9124,9127,9131,9134,9135,9148,9149,9169,9175,9187,9235,9253,9307,9308,9315,9376,9381,9417,9424,9427,9430,9431,9446,9462,9471,9483,9495,9496,9499,9501,9528,9653,9698,9699,9741,9786,9902])). % 167.77/167.58 cnf(12466,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x124661),x124661))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(12468,plain, % 167.77/167.58 (P1(f328(f328(f330(f878(f873(x124681),f873(x124681))),f328(f328(f263(f873(x124681),f873(x124681)),f328(f165(x124681),x124682)),x124682)),f155(x124681,f251(f879(f878(x124681,x124681),a867)))))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,3527,3528,3243,3209,4489,4490,3144,4474,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,4471,10431,10524,3331,3487,3191,2871,2876,2877,2887,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2927,2933,2936,2950,2953,2954,2955,2968,2990,3012,3013,3022,3030,3035,3045,3052,3063,4452,3616,3844,11598,3116,11315,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,3204,12329,12333,12337,3210,3217,3737,3976,3106,4468,3481,3829,11365,3170,3135,3129,3113,3114,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,3380,4538,3916,4481,10263,10428,11229,12293,12330,4488,12301,3265,11687,4527,10978,11048,11276,11279,3381,3165,10330,10637,3166,3439,3085,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,4479,11346,3580,3793,3839,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,3730,11584,3258,3354,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,4533,11468,11499,11534,11564,3717,3488,3866,3302,3303,3277,4518,4476,3669,4200,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,4027,3984,11855,12192,3928,10810,12036,12205,3979,10987,12074,12147,12204,12248,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,3276,3350,12062,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,3434,10605,10869,10913,11183,11265,11426,11667,12296,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,3336,10634,10664,10673,11215,11766,12388,3376,3370,3797,3735,10309,11587,11615,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,3296,10667,10818,10889,11616,11771,11963,3758,4107,4524,3769,3805,4507,4509,3249,3250,4508,4511,4512,3776,3591,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,3883,11304,11642,11646,11708,12304,12312,3724,10929,10935,10950,11887,12016,12095,3576,11152,12121,12230,12240,12309,12360,4061,3726,10670,11006,11158,11188,11202,12198,12308,3546,10591,10594,10676,10848,4545,11581,4535,4546,10727,10827,11137,11423,11454,12180,12189,12236,4167,10803,12201,12213,4068,3757,3704,4543,10282,10285,10622,10625,11465,11643,4544,11561,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6557,6562,6564,6569,6570,6578,6582,6595,6620,6621,6622,6623,6635,6640,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6792,6795,6831,6834,6835,6848,6849,6850,6851,6871,6872,6887,6913,6935,6946,6948,6949,6951,6953,6954,6987,6988,6993,6994,6995,6996,6998,7000,7025,7034,7035,7047,7057,7096,7106,7110,7117,7128,7134,7136,7142,7151,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7385,7399,7416,7448,7451,7477,7501,7518,7521,7522,7532,7550,7551,7553,7555,7557,7559,7587,7612,7613,7645,7647,7648,7649,7654,7676,7685,7695,7700,7706,7708,7714,7726,7727,7729,7760,7783,7850,7851,7898,7906,7907,7931,7932,7949,7950,8008,8009,8010,8035,8068,8075,8077,8087,8099,8130,8138,8145,8158,8180,8186,8213,8257,8285,8298,8316,8319,8349,8372,8433,8434,8437,8439,8544,8545,8546,8547,8576,8605,8636,8680,8698,8753,8798,8801,8814,8821,8858,8877,8905,8906,8924,8925,9065,9069,9089,9099,9122,9124,9127,9131,9134,9135,9148,9149,9169,9175,9187,9235,9253,9307,9308,9315,9376,9381,9417,9424,9427,9430,9431,9446,9462,9471,9483,9495,9496,9499,9501,9528,9653,9698,9699,9741,9786,9902,9959])). % 167.77/167.58 cnf(12469,plain, % 167.77/167.58 (P1(f328(f328(f330(x124691),x124692),f251(f879(x124691,a867))))), % 167.77/167.58 inference(rename_variables,[],[3434])). % 167.77/167.58 cnf(12476,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x124761,a867)),x124762),x124762))), % 167.77/167.58 inference(rename_variables,[],[3576])). % 167.77/167.58 cnf(12479,plain, % 167.77/167.58 (~P1(f328(f328(f330(x124791),x124792),f192(f879(x124791,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12482,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),f2(a1)),f328(f328(f253(a1),f328(f75(a1),x124821)),x124822)))), % 167.77/167.58 inference(rename_variables,[],[3757])). % 167.77/167.58 cnf(12485,plain, % 167.77/167.58 (~E(f328(a116,x124851),x124851)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(12487,plain, % 167.77/167.58 (E(f328(f259(x124871,x124871),f260(x124871,x124872)),x124872)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12491,plain, % 167.77/167.58 (E(f328(f259(x124911,x124911),f260(x124911,x124912)),x124912)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12496,plain, % 167.77/167.58 (E(f328(f259(x124961,x124961),f260(x124961,x124962)),x124962)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12498,plain, % 167.77/167.58 (P38(x124981,f150(x124981,x124982))), % 167.77/167.58 inference(rename_variables,[],[3144])). % 167.77/167.58 cnf(12504,plain, % 167.77/167.58 (E(f328(f259(x125041,x125041),f260(x125041,x125042)),x125042)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12506,plain, % 167.77/167.58 (P26(x125061,x125061,f5(x125061),x125062)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12508,plain, % 167.77/167.58 (P26(x125081,x125081,f5(x125081),x125082)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12514,plain, % 167.77/167.58 (E(f328(f259(x125141,x125141),f260(x125141,x125142)),x125142)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12518,plain, % 167.77/167.58 (E(f192(f879(f878(x125181,x125181),a867)),f260(x125181,f192(f879(x125181,a867))))), % 167.77/167.58 inference(rename_variables,[],[3345])). % 167.77/167.58 cnf(12520,plain, % 167.77/167.58 (E(f328(f259(x125201,x125201),f260(x125201,x125202)),x125202)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12522,plain, % 167.77/167.58 (P16(x125221,f879(x125221,a867),f306(x125221))), % 167.77/167.58 inference(rename_variables,[],[3246])). % 167.77/167.58 cnf(12529,plain, % 167.77/167.58 (P33(x125291,x125292,f117(x125291),f117(x125291))), % 167.77/167.58 inference(rename_variables,[],[3527])). % 167.77/167.58 cnf(12531,plain, % 167.77/167.58 (P33(x125311,x125312,f117(x125311),f117(x125311))), % 167.77/167.58 inference(rename_variables,[],[3527])). % 167.77/167.58 cnf(12535,plain, % 167.77/167.58 (E(f328(f259(x125351,x125351),f260(x125351,x125352)),x125352)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12537,plain, % 167.77/167.58 (P40(x125371,x125372,f260(x125371,x125372))), % 167.77/167.58 inference(rename_variables,[],[3242])). % 167.77/167.58 cnf(12539,plain, % 167.77/167.58 (P40(x125391,x125392,f260(x125391,x125392))), % 167.77/167.58 inference(rename_variables,[],[3242])). % 167.77/167.58 cnf(12559,plain, % 167.77/167.58 (E(f328(f259(x125591,x125591),f260(x125591,x125592)),x125592)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12561,plain, % 167.77/167.58 (E(f328(f259(x125611,x125611),f260(x125611,x125612)),x125612)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12563,plain, % 167.77/167.58 (P51(x125631,x125631,f260(x125631,x125632))), % 167.77/167.58 inference(rename_variables,[],[3243])). % 167.77/167.58 cnf(12569,plain, % 167.77/167.58 (E(f328(f259(x125691,x125691),f260(x125691,x125692)),x125692)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12572,plain, % 167.77/167.58 (P52(x125721,f192(f879(x125721,a867)),x125722)), % 167.77/167.58 inference(rename_variables,[],[3294])). % 167.77/167.58 cnf(12577,plain, % 167.77/167.58 (P43(x125771,x125772,x125773,x125774,f192(f879(x125771,a867)),x125774)), % 167.77/167.58 inference(rename_variables,[],[4230])). % 167.77/167.58 cnf(12580,plain, % 167.77/167.58 (P43(x125801,x125802,x125803,x125804,f192(f879(x125801,a867)),x125804)), % 167.77/167.58 inference(rename_variables,[],[4230])). % 167.77/167.58 cnf(12584,plain, % 167.77/167.58 (P28(x125841,f2(a872),f328(f328(f328(f92(x125841),x125842),f328(a26,x125843)),x125844))), % 167.77/167.58 inference(rename_variables,[],[3653])). % 167.77/167.58 cnf(12602,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),f2(a872)),f328(a116,x126021)))), % 167.77/167.58 inference(rename_variables,[],[3354])). % 167.77/167.58 cnf(12603,plain, % 167.77/167.58 (~E(f328(a116,x126031),x126031)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(12609,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x126091),f328(a116,x126091)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12614,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x126141),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12617,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x126171),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12624,plain, % 167.77/167.58 (~P1(f328(f328(f243(a1),f328(f104(a1),x126241)),f328(f79(a1),f328(f104(a1),x126242))))), % 167.77/167.58 inference(rename_variables,[],[4540])). % 167.77/167.58 cnf(12634,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x126341),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12637,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x126371),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12640,plain, % 167.77/167.58 (P1(f328(f38(a872),f301(a872,x126401,x126402)))), % 167.77/167.58 inference(rename_variables,[],[3489])). % 167.77/167.58 cnf(12643,plain, % 167.77/167.58 (P1(f328(f38(a872),f301(a872,x126431,x126432)))), % 167.77/167.58 inference(rename_variables,[],[3489])). % 167.77/167.58 cnf(12646,plain, % 167.77/167.58 (P1(f328(f38(a872),f301(a872,x126461,x126462)))), % 167.77/167.58 inference(rename_variables,[],[3489])). % 167.77/167.58 cnf(12649,plain, % 167.77/167.58 (P1(f328(f38(a872),f301(a872,x126491,x126492)))), % 167.77/167.58 inference(rename_variables,[],[3489])). % 167.77/167.58 cnf(12656,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),f328(f79(a1),f328(f104(a1),x126561))),f328(f104(a1),x126562)))), % 167.77/167.58 inference(rename_variables,[],[3758])). % 167.77/167.58 cnf(12659,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x126591),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12660,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x126601),x126601))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12667,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x126671),f328(a116,x126671)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12670,plain, % 167.77/167.58 (P1(f328(f328(f330(x126701),f328(x126702,x126703)),f328(f307(x126704,x126701,x126702),f251(f879(x126704,a867)))))), % 167.77/167.58 inference(rename_variables,[],[3883])). % 167.77/167.58 cnf(12671,plain, % 167.77/167.58 (~E(f328(a116,x126711),f2(a872))), % 167.77/167.58 inference(rename_variables,[],[4466])). % 167.77/167.58 cnf(12673,plain, % 167.77/167.58 (~P1(f328(f328(f243(a1),f2(a1)),f328(f107(a1),f2(a1))))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,12381,12506,3527,12141,12529,12531,3528,12208,3242,12537,12539,3243,12563,3209,12454,4489,4490,11664,4230,12577,12580,3246,12522,3084,3144,12498,4474,3578,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,12351,12485,4471,10431,10524,3331,3294,12572,3487,3191,4466,2871,2876,2877,2887,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2927,2933,2936,2950,2953,2954,2955,2968,2990,3012,3013,3022,3030,3034,3035,3045,3052,4451,3063,3143,4452,3616,3844,11598,3116,11315,3256,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,12434,12487,12491,12496,12504,12514,12520,12535,12559,12561,3204,12329,12333,12337,3210,3217,3737,3976,3106,4468,3481,3829,11365,3330,3170,3135,3653,12584,3129,3950,3658,4435,3113,3114,3094,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,3380,4538,10401,3916,4481,10263,10428,11229,12293,12330,4488,12301,3265,11687,4527,10978,11048,11276,11279,3678,3381,3602,3345,12518,3165,10330,10637,3166,3439,3158,3085,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,3570,4479,11346,3580,3619,3793,3839,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,12425,12609,3730,11584,3258,3354,11702,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,12320,12614,12617,12634,12637,4533,11468,11499,11534,11564,3717,3488,3489,12640,12643,12646,3866,3302,3303,3277,4518,3164,4476,3669,4200,3985,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,4027,3984,11855,12192,3928,10810,12036,12205,3979,10987,12074,12147,12204,12248,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,12431,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,12401,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,3276,3350,12062,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,3434,10605,10869,10913,11183,11265,11426,11667,12296,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,12460,3336,10634,10664,10673,11215,11766,12388,3376,3370,3797,3735,10309,11587,11615,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,3296,10667,10818,10889,11616,11771,11963,3758,11717,4107,3494,4524,3769,3805,4507,4509,4510,3249,3250,4508,4511,4512,4416,4237,3776,3591,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,12216,3883,11304,11642,11646,11708,12304,12312,12394,3724,10929,10935,10950,11887,12016,12095,3576,11152,12121,12230,12240,12309,12360,12368,4061,3726,10670,11006,11158,11188,11202,12198,12308,3546,10591,10594,10676,10848,3545,4545,11581,4535,4540,12624,4546,10727,10827,11137,11423,11454,12180,12189,12236,12415,4167,10803,12201,12213,4068,3757,3704,3705,4543,10282,10285,10622,10625,11465,11643,4544,11561,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859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% 167.77/167.58 cnf(12676,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x126761),x126761))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(12679,plain, % 167.77/167.58 (P1(f328(f38(a872),f301(a872,x126791,x126792)))), % 167.77/167.58 inference(rename_variables,[],[3489])). % 167.77/167.58 cnf(12682,plain, % 167.77/167.58 (P1(f328(f38(a872),f301(a872,x126821,x126822)))), % 167.77/167.58 inference(rename_variables,[],[3489])). % 167.77/167.58 cnf(12685,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x126851),x126851))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12698,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x126981),f328(a116,x126981)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12703,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),f46(a872,x127031,x127032)),x127031))), % 167.77/167.58 inference(rename_variables,[],[3735])). % 167.77/167.58 cnf(12710,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x127101),f328(a116,x127101)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12711,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x127111),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12720,plain, % 167.77/167.58 (~P1(f328(f328(f243(a1),f328(f104(a1),x127201)),f2(a1)))), % 167.77/167.58 inference(rename_variables,[],[4533])). % 167.77/167.58 cnf(12721,plain, % 167.77/167.58 (P1(f328(f251(f879(x127211,a867)),x127212))), % 167.77/167.58 inference(rename_variables,[],[3336])). % 167.77/167.58 cnf(12724,plain, % 167.77/167.58 (~P1(f328(f328(f243(a1),f328(f104(a1),x127241)),f2(a1)))), % 167.77/167.58 inference(rename_variables,[],[4533])). % 167.77/167.58 cnf(12725,plain, % 167.77/167.58 (P1(f328(f251(f879(x127251,a867)),x127252))), % 167.77/167.58 inference(rename_variables,[],[3336])). % 167.77/167.58 cnf(12728,plain, % 167.77/167.58 (P1(f328(f251(f879(x127281,a867)),x127282))), % 167.77/167.58 inference(rename_variables,[],[3336])). % 167.77/167.58 cnf(12739,plain, % 167.77/167.58 (~P1(f328(f328(f330(x127391),x127392),f192(f879(x127391,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12740,plain, % 167.77/167.58 (P1(f328(f38(x127401),f192(f879(x127401,a867))))), % 167.77/167.58 inference(rename_variables,[],[3350])). % 167.77/167.58 cnf(12749,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),f2(a872)),x127491))), % 167.77/167.58 inference(rename_variables,[],[3296])). % 167.77/167.58 cnf(12752,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x127521),f328(a116,x127521)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12753,plain, % 167.77/167.58 (~E(f328(a116,x127531),x127531)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(12756,plain, % 167.77/167.58 (~P1(f328(f328(f330(x127561),x127562),f192(f879(x127561,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12759,plain, % 167.77/167.58 (~P1(f328(f328(f330(x127591),x127592),f192(f879(x127591,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12762,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x127621),x127621))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12769,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x127691),x127691))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12773,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x127731),f328(a116,x127731)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12776,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x127761),x127761))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12781,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x127811),x127811))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12784,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x127841),x127841))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12787,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x127871),x127871))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12790,plain, % 167.77/167.58 (E(f328(f328(f22(f879(x127901,a867)),f192(f879(x127901,a867))),x127902),f192(f879(x127901,a867)))), % 167.77/167.58 inference(rename_variables,[],[3549])). % 167.77/167.58 cnf(12791,plain, % 167.77/167.58 (P1(f328(f38(x127911),f192(f879(x127911,a867))))), % 167.77/167.58 inference(rename_variables,[],[3350])). % 167.77/167.58 cnf(12794,plain, % 167.77/167.58 (E(f328(f328(f22(f879(x127941,a867)),f192(f879(x127941,a867))),x127942),f192(f879(x127941,a867)))), % 167.77/167.58 inference(rename_variables,[],[3549])). % 167.77/167.58 cnf(12795,plain, % 167.77/167.58 (P1(f328(f38(x127951),f192(f879(x127951,a867))))), % 167.77/167.58 inference(rename_variables,[],[3350])). % 167.77/167.58 cnf(12798,plain, % 167.77/167.58 (E(f328(f328(f22(f879(x127981,a867)),f192(f879(x127981,a867))),x127982),f192(f879(x127981,a867)))), % 167.77/167.58 inference(rename_variables,[],[3549])). % 167.77/167.58 cnf(12799,plain, % 167.77/167.58 (P1(f328(f38(x127991),f192(f879(x127991,a867))))), % 167.77/167.58 inference(rename_variables,[],[3350])). % 167.77/167.58 cnf(12802,plain, % 167.77/167.58 (E(f328(f328(f22(f879(x128021,a867)),f192(f879(x128021,a867))),x128022),f192(f879(x128021,a867)))), % 167.77/167.58 inference(rename_variables,[],[3549])). % 167.77/167.58 cnf(12803,plain, % 167.77/167.58 (P1(f328(f38(x128031),f192(f879(x128031,a867))))), % 167.77/167.58 inference(rename_variables,[],[3350])). % 167.77/167.58 cnf(12807,plain, % 167.77/167.58 (E(f328(f259(x128071,x128071),f260(x128071,x128072)),x128072)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12812,plain, % 167.77/167.58 (E(f328(f328(f22(f879(x128121,a867)),f192(f879(x128121,a867))),x128122),f192(f879(x128121,a867)))), % 167.77/167.58 inference(rename_variables,[],[3549])). % 167.77/167.58 cnf(12813,plain, % 167.77/167.58 (P1(f328(f38(x128131),f192(f879(x128131,a867))))), % 167.77/167.58 inference(rename_variables,[],[3350])). % 167.77/167.58 cnf(12817,plain, % 167.77/167.58 (P1(f328(f38(x128171),f192(f879(x128171,a867))))), % 167.77/167.58 inference(rename_variables,[],[3350])). % 167.77/167.58 cnf(12820,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x128201),x128201))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12826,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x128261),x128261))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(12829,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x128291),f328(a116,x128291)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12832,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x128321),x128321))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12835,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x128351),f328(a116,x128351)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(12850,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x128501),x128501))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12853,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x128531),x128531))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(12856,plain, % 167.77/167.58 (~P1(f328(f328(f330(x128561),x128562),f192(f879(x128561,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12867,plain, % 167.77/167.58 (P1(f328(f328(f330(x128671),x128672),f251(f879(x128671,a867))))), % 167.77/167.58 inference(rename_variables,[],[3434])). % 167.77/167.58 cnf(12873,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x128731,a867)),x128732),x128732))), % 167.77/167.58 inference(rename_variables,[],[3576])). % 167.77/167.58 cnf(12879,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x128791),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12880,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x128801),x128801))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(12884,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x128841),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12885,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x128851),x128851))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(12894,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x128941),x128941))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12901,plain, % 167.77/167.58 (E(f328(f328(f16(x129011,x129012),x129013),x129014),x129013)), % 167.77/167.58 inference(rename_variables,[],[3265])). % 167.77/167.58 cnf(12904,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x129041,a867)),f328(f170(x129041),f174(x129041,x129042,x129043))),f328(f170(x129041),x129042)))), % 167.77/167.58 inference(rename_variables,[],[3979])). % 167.77/167.58 cnf(12908,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x129081),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12909,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),x129091),x129091))), % 167.77/167.58 inference(rename_variables,[],[3275])). % 167.77/167.58 cnf(12913,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x129131),f2(a872)))), % 167.77/167.58 inference(rename_variables,[],[4521])). % 167.77/167.58 cnf(12918,plain, % 167.77/167.58 (~P1(f328(f328(f243(f879(a872,a867)),f299(a872,f328(a116,x129181),f328(a116,x129181))),f299(a872,x129182,x129181)))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,12381,12506,3527,12141,12529,12531,3528,12208,3242,12537,12539,3243,12563,3209,12454,4489,4490,11664,4230,12577,12580,3246,12522,3084,3144,12498,4474,3578,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,12351,12485,12603,4471,10431,10524,3331,3294,12572,3487,3191,4466,2870,2871,2876,2877,2887,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2918,2924,2927,2933,2936,2950,2953,2954,2955,2968,2979,2982,2987,2990,2995,2996,3012,3013,3022,3024,3030,3034,3035,3036,3045,3052,4451,3063,3143,4452,3616,3844,11598,3116,11315,3256,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,12434,12487,12491,12496,12504,12514,12520,12535,12559,12561,12569,3857,3204,12329,12333,12337,3210,3217,3737,3976,3106,4468,3481,3829,11365,3330,3170,3135,3653,12584,3129,3950,3658,4435,3113,3114,3094,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,3380,4538,10401,3916,4481,10263,10428,11229,12293,12330,4488,12301,3265,11687,11690,4527,10978,11048,11276,11279,3678,3381,3602,3345,12518,3165,10330,10637,3166,3439,3158,3085,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,3570,4479,11346,3580,3619,3793,3549,12790,12794,12798,12802,12812,3839,12171,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,12425,12609,12667,12698,12710,12752,12773,12829,12835,3730,11584,3258,3354,11702,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,12320,12614,12617,12634,12637,12659,12711,12879,12884,12908,4533,11468,11499,11534,11564,12720,12724,3717,3488,3489,12640,12643,12646,12649,12679,3866,3302,3303,3277,4518,3164,4476,3669,4200,3985,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,12405,4027,3984,11855,12192,3928,10810,12036,12205,3979,10987,12074,12147,12204,12248,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,12431,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,12401,12660,12685,12762,12769,12776,12781,12784,12787,12820,12832,12850,12894,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,11958,12676,12826,12853,12880,12885,12909,3276,3350,12062,12740,12791,12795,12799,12803,12813,12817,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,12466,3434,10605,10869,10913,11183,11265,11426,11667,12296,12469,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,12460,12479,12739,12756,12759,3336,10634,10664,10673,11215,11766,12388,12402,12721,12725,12728,3376,3370,3797,3735,10309,11587,11615,12703,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,3296,10667,10818,10889,11616,11771,11963,12186,3758,11717,12656,4107,3494,4524,3769,3805,4507,4509,4510,3249,3250,4508,4511,4512,4416,4237,3776,3591,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,12216,3883,11304,11642,11646,11708,12304,12312,12394,3724,10929,10935,10950,11887,12016,12095,3576,11152,12121,12230,12240,12309,12360,12368,12476,3614,4061,3726,10670,11006,11158,11188,11202,12198,12308,3546,10591,10594,10676,10848,3545,4545,11581,4535,4540,12624,4546,10727,10827,11137,11423,11454,12180,12189,12236,12415,4167,10803,12201,12213,4068,3757,12482,3704,3705,4543,10282,10285,10622,10625,11465,11643,12424,4544,11561,11652,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6557,6562,6564,6569,6570,6578,6582,6595,6620,6621,6622,6623,6635,6640,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6792,6795,6831,6834,6835,6848,6849,6850,6851,6871,6872,6887,6913,6935,6946,6948,6949,6951,6953,6954,6987,6988,6993,6994,6995,6996,6998,7000,7025,7034,7035,7047,7057,7096,7106,7110,7117,7128,7134,7136,7142,7151,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7385,7399,7416,7448,7451,7477,7501,7518,7521,7522,7532,7550,7551,7553,7555,7557,7559,7587,7612,7613,7645,7647,7648,7649,7654,7676,7685,7695,7700,7706,7708,7714,7726,7727,7729,7760,7783,7850,7851,7898,7906,7907,7931,7932,7949,7950,8008,8009,8010,8035,8068,8075,8077,8087,8099,8130,8138,8145,8158,8180,8186,8213,8257,8285,8298,8316,8319,8349,8372,8433,8434,8437,8439,8544,8545,8546,8547,8576,8605,8636,8680,8698,8753,8798,8801,8814,8821,8858,8877,8905,8906,8924,8925,9065,9069,9089,9099,9122,9124,9127,9131,9134,9135,9148,9149,9169,9175,9187,9235,9253,9307,9308,9315,9376,9381,9417,9424,9427,9430,9431,9446,9462,9471,9483,9495,9496,9499,9501,9528,9653,9698,9699,9741,9786,9902,9959,10024,10098,10111,10116,3,2606,2609,2611,2612,2613,2614,2622,2628,2629,2630,2633,2634,2635,2636,2637,2639,2644,2645,2646,2647,2649,2651,2659,2660,2661,2669,2671,2672,2673,2675,2676,2677,2680,2681,2682,2692,2707,2708,2709,2711,2712,2714,2715,2719,2721,2723,2724,2725,2733,2735,2736,2737,2743,2746,2749,2750,2751,2775,2776,2777,2780,2781,2791,2793,2795,2796,2797,2821,2831,2832,5207,5267,5365,5451,5452,5453,5528,5626,5657,5691,5707,5709,5715,5778,5779,5780,5781,5787,5820,5950,5993,6016,6053,6093,6242,6249,6283,6284,6304,6307,6309,6316,6317,6318,6319,6320,6321,6322,6323,6402,6470,6471,6555,6589,6590,6632,6633,6771,6786,6860,6861,6868,6888,6911,6919,6921,6968,6991,6992,7008,7009,7010,7046,7090,7091,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7373,7375,7387,7419,7420,7421,7422,7567,7568,7574,7575,7577,7579,7791,7793,7794,7810,7848,7927,7966,8019,8040,8041,8056,8116,8228,8295,8296,8299,8334,8396,8397,8463,8482])). % 167.77/167.58 cnf(12919,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x129191),x129191))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12921,plain, % 167.77/167.58 (~P1(f328(f328(f242(f879(a872,a867)),f299(a872,f328(a116,x129211),f328(a116,x129211))),f299(a872,x129212,x129211)))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,12381,12506,3527,12141,12529,12531,3528,12208,3242,12537,12539,3243,12563,3209,12454,4489,4490,11664,4230,12577,12580,3246,12522,3084,3144,12498,4474,3578,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,12351,12485,12603,4471,10431,10524,3331,3294,12572,3487,3191,4466,2870,2871,2876,2877,2887,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2918,2924,2927,2933,2936,2950,2953,2954,2955,2968,2979,2982,2987,2990,2995,2996,3012,3013,3022,3024,3030,3034,3035,3036,3045,3052,4451,3063,3143,4452,3616,3844,11598,3116,11315,3256,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,12434,12487,12491,12496,12504,12514,12520,12535,12559,12561,12569,3857,3204,12329,12333,12337,3210,3217,3737,3976,3106,4468,3481,3829,11365,3330,3170,3135,3653,12584,3129,3950,3658,4435,3113,3114,3094,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,3380,4538,10401,3916,4481,10263,10428,11229,12293,12330,4488,12301,3265,11687,11690,4527,10978,11048,11276,11279,3678,3381,3602,3345,12518,3165,10330,10637,3166,3439,3158,3085,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,3570,4479,11346,3580,3619,3793,3549,12790,12794,12798,12802,12812,3839,12171,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,12425,12609,12667,12698,12710,12752,12773,12829,12835,3730,11584,3258,3354,11702,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,12320,12614,12617,12634,12637,12659,12711,12879,12884,12908,4533,11468,11499,11534,11564,12720,12724,3717,3488,3489,12640,12643,12646,12649,12679,3866,3302,3303,3277,4518,3164,4476,3669,4200,3985,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,12405,4027,3984,11855,12192,3928,10810,12036,12205,3979,10987,12074,12147,12204,12248,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,12431,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,12401,12660,12685,12762,12769,12776,12781,12784,12787,12820,12832,12850,12894,12919,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,11958,12676,12826,12853,12880,12885,12909,3276,3350,12062,12740,12791,12795,12799,12803,12813,12817,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,12466,3434,10605,10869,10913,11183,11265,11426,11667,12296,12469,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,12460,12479,12739,12756,12759,3336,10634,10664,10673,11215,11766,12388,12402,12721,12725,12728,3376,3370,3797,3735,10309,11587,11615,12703,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,3296,10667,10818,10889,11616,11771,11963,12186,3758,11717,12656,4107,3494,4524,3769,3805,4507,4509,4510,3249,3250,4508,4511,4512,4416,4237,3776,3591,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,12216,3883,11304,11642,11646,11708,12304,12312,12394,3724,10929,10935,10950,11887,12016,12095,3576,11152,12121,12230,12240,12309,12360,12368,12476,3614,4061,3726,10670,11006,11158,11188,11202,12198,12308,3546,10591,10594,10676,10848,3545,4545,11581,4535,4540,12624,4546,10727,10827,11137,11423,11454,12180,12189,12236,12415,4167,10803,12201,12213,4068,3757,12482,3704,3705,4543,10282,10285,10622,10625,11465,11643,12424,4544,11561,11652,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6557,6562,6564,6569,6570,6578,6582,6595,6620,6621,6622,6623,6635,6640,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6792,6795,6831,6834,6835,6848,6849,6850,6851,6871,6872,6887,6913,6935,6946,6948,6949,6951,6953,6954,6987,6988,6993,6994,6995,6996,6998,7000,7025,7034,7035,7047,7057,7096,7106,7110,7117,7128,7134,7136,7142,7151,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7385,7399,7416,7448,7451,7477,7501,7518,7521,7522,7532,7550,7551,7553,7555,7557,7559,7587,7612,7613,7645,7647,7648,7649,7654,7676,7685,7695,7700,7706,7708,7714,7726,7727,7729,7760,7783,7850,7851,7898,7906,7907,7931,7932,7949,7950,8008,8009,8010,8035,8068,8075,8077,8087,8099,8130,8138,8145,8158,8180,8186,8213,8257,8285,8298,8316,8319,8349,8372,8433,8434,8437,8439,8544,8545,8546,8547,8576,8605,8636,8680,8698,8753,8798,8801,8814,8821,8858,8877,8905,8906,8924,8925,9065,9069,9089,9099,9122,9124,9127,9131,9134,9135,9148,9149,9169,9175,9187,9235,9253,9307,9308,9315,9376,9381,9417,9424,9427,9430,9431,9446,9462,9471,9483,9495,9496,9499,9501,9528,9653,9698,9699,9741,9786,9902,9959,10024,10098,10111,10116,3,2606,2609,2611,2612,2613,2614,2622,2628,2629,2630,2633,2634,2635,2636,2637,2639,2644,2645,2646,2647,2649,2651,2659,2660,2661,2669,2671,2672,2673,2675,2676,2677,2680,2681,2682,2692,2707,2708,2709,2711,2712,2714,2715,2719,2721,2723,2724,2725,2733,2735,2736,2737,2743,2746,2749,2750,2751,2775,2776,2777,2780,2781,2791,2793,2795,2796,2797,2821,2831,2832,5207,5267,5365,5451,5452,5453,5528,5626,5657,5691,5707,5709,5715,5778,5779,5780,5781,5787,5820,5950,5993,6016,6053,6093,6242,6249,6283,6284,6304,6307,6309,6316,6317,6318,6319,6320,6321,6322,6323,6402,6470,6471,6555,6589,6590,6632,6633,6771,6786,6860,6861,6868,6888,6911,6919,6921,6968,6991,6992,7008,7009,7010,7046,7090,7091,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7373,7375,7387,7419,7420,7421,7422,7567,7568,7574,7575,7577,7579,7791,7793,7794,7810,7848,7927,7966,8019,8040,8041,8056,8116,8228,8295,8296,8299,8334,8396,8397,8463,8482,8483])). % 167.77/167.58 cnf(12922,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x129221),x129221))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(12925,plain, % 167.77/167.58 (~P1(f328(f328(f242(a872),f328(a116,x129251)),x129251))), % 167.77/167.58 inference(rename_variables,[],[4526])). % 167.77/167.58 cnf(12930,plain, % 167.77/167.58 (E(x129301,f540(f328(f5(x129302),f328(f5(x129302),x129301)),f5(x129302),x129302,x129302))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,12381,12506,12508,3527,12141,12529,12531,3528,12208,3242,12537,12539,3243,12563,3209,12454,4489,4490,11664,4230,12577,12580,3246,12522,3084,3144,12498,4474,3578,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,12351,12485,12603,4471,10431,10524,3331,3294,12572,3487,3191,4466,2870,2871,2876,2877,2887,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2918,2924,2927,2933,2936,2950,2953,2954,2955,2968,2979,2982,2987,2990,2995,2996,3012,3013,3022,3024,3030,3034,3035,3036,3045,3052,4451,3063,3143,4452,3616,3844,11598,3116,11315,3256,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,12434,12487,12491,12496,12504,12514,12520,12535,12559,12561,12569,3857,3204,12329,12333,12337,3210,3217,3737,3976,3105,3106,4468,3481,3829,11365,3330,3170,3135,3653,12584,3129,3950,3658,4435,3113,3114,3094,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,3380,4538,10401,3916,4481,10263,10428,11229,12293,12330,4488,12301,3265,11687,11690,4527,10978,11048,11276,11279,3678,3381,3602,3345,12518,3165,10330,10637,3166,3439,3158,3085,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,3570,4479,11346,3580,3619,3793,3549,12790,12794,12798,12802,12812,3839,12171,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,12425,12609,12667,12698,12710,12752,12773,12829,12835,3730,11584,3258,3354,11702,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,12320,12614,12617,12634,12637,12659,12711,12879,12884,12908,4533,11468,11499,11534,11564,12720,12724,3717,3488,3489,12640,12643,12646,12649,12679,3866,3302,3303,3277,4518,3164,4476,3669,4200,3985,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,12405,4027,3984,11855,12192,3928,10810,12036,12205,3979,10987,12074,12147,12204,12248,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,12431,4539,10758,11126,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,12401,12660,12685,12762,12769,12776,12781,12784,12787,12820,12832,12850,12894,12919,12922,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,11958,12676,12826,12853,12880,12885,12909,3276,3350,12062,12740,12791,12795,12799,12803,12813,12817,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,12466,3434,10605,10869,10913,11183,11265,11426,11667,12296,12469,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,12460,12479,12739,12756,12759,3336,10634,10664,10673,11215,11766,12388,12402,12721,12725,12728,3376,3370,3797,3735,10309,11587,11615,12703,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,12925,3296,10667,10818,10889,11616,11771,11963,12186,3758,11717,12656,4107,3494,4524,3769,3805,4507,4509,4510,3249,3250,4508,4511,4512,4416,4237,3776,3591,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,12216,3883,11304,11642,11646,11708,12304,12312,12394,12670,3724,10929,10935,10950,11887,12016,12095,3576,11152,12121,12230,12240,12309,12360,12368,12476,3614,4061,3726,10670,11006,11158,11188,11202,12198,12308,3546,10591,10594,10676,10848,3545,4545,11581,4535,4540,12624,4546,10727,10827,11137,11423,11454,12180,12189,12236,12415,4167,10803,12201,12213,4068,3757,12482,3704,3705,4543,10282,10285,10622,10625,11465,11643,12424,4544,11561,11652,3728,10588,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,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% 167.77/167.58 cnf(12931,plain, % 167.77/167.58 (P1(f328(f328(f330(x129311),f328(x129312,x129313)),f328(f307(x129314,x129311,x129312),f251(f879(x129314,a867)))))), % 167.77/167.58 inference(rename_variables,[],[3883])). % 167.77/167.58 cnf(12932,plain, % 167.77/167.58 (P26(x129321,x129321,f5(x129321),x129322)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12936,plain, % 167.77/167.58 (P1(f328(f328(f330(x129361),x129362),f251(f879(x129361,a867))))), % 167.77/167.58 inference(rename_variables,[],[3434])). % 167.77/167.58 cnf(12937,plain, % 167.77/167.58 (~P1(f328(f328(f330(x129371),x129372),f192(f879(x129371,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12941,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x129411,a867)),x129412),f251(f879(x129411,a867))))), % 167.77/167.58 inference(rename_variables,[],[3660])). % 167.77/167.58 cnf(12942,plain, % 167.77/167.58 (P26(x129421,x129421,f5(x129421),x129422)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12946,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x129461,a867)),x129462),f251(f879(x129461,a867))))), % 167.77/167.58 inference(rename_variables,[],[3660])). % 167.77/167.58 cnf(12947,plain, % 167.77/167.58 (P26(x129471,x129471,f5(x129471),x129472)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12951,plain, % 167.77/167.58 (P26(x129511,x129511,f5(x129511),x129512)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12954,plain, % 167.77/167.58 (~P1(f328(f328(f243(f879(x129541,a867)),x129542),f192(f879(x129541,a867))))), % 167.77/167.58 inference(rename_variables,[],[4539])). % 167.77/167.58 cnf(12957,plain, % 167.77/167.58 (P26(x129571,x129571,f5(x129571),x129572)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12960,plain, % 167.77/167.58 (P26(x129601,x129601,f5(x129601),x129602)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12963,plain, % 167.77/167.58 (P1(f328(f328(f330(x129631),x129632),f328(f328(f306(x129631),x129632),x129633)))), % 167.77/167.58 inference(rename_variables,[],[3591])). % 167.77/167.58 cnf(12971,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x129711,a867)),f192(f879(x129711,a867))),x129712))), % 167.77/167.58 inference(rename_variables,[],[3726])). % 167.77/167.58 cnf(12975,plain, % 167.77/167.58 (E(f328(f259(x129751,x129751),f260(x129751,x129752)),x129752)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(12979,plain, % 167.77/167.58 (~P1(f328(f328(f330(x129791),x129792),f192(f879(x129791,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12982,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x129821,a867)),x129822),f328(f328(f306(x129821),x129823),x129822)))), % 167.77/167.58 inference(rename_variables,[],[3724])). % 167.77/167.58 cnf(12983,plain, % 167.77/167.58 (P1(f328(f328(f330(x129831),f328(x129832,x129833)),f328(f307(x129834,x129831,x129832),f251(f879(x129834,a867)))))), % 167.77/167.58 inference(rename_variables,[],[3883])). % 167.77/167.58 cnf(12984,plain, % 167.77/167.58 (P26(x129841,x129841,f5(x129841),x129842)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(12987,plain, % 167.77/167.58 (P1(f328(f328(f330(x129871),x129872),f251(f879(x129871,a867))))), % 167.77/167.58 inference(rename_variables,[],[3434])). % 167.77/167.58 cnf(12994,plain, % 167.77/167.58 (~P1(f328(f328(f330(x129941),x129942),f192(f879(x129941,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(12997,plain, % 167.77/167.58 (~P1(f328(f328(f330(x129971),x129972),f192(f879(x129971,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(13001,plain, % 167.77/167.58 (E(f328(f328(f16(x130011,x130012),x130013),x130014),x130013)), % 167.77/167.58 inference(rename_variables,[],[3265])). % 167.77/167.58 cnf(13004,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x130041),f328(a116,x130041)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(13005,plain, % 167.77/167.58 (~E(f328(a116,x130051),x130051)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(13008,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x130081),f328(a116,f328(f328(f80(a872),x130082),x130081))))), % 167.77/167.58 inference(rename_variables,[],[3728])). % 167.77/167.58 cnf(13009,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x130091),f328(a116,x130091)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(13011,plain, % 167.77/167.58 (~E(f328(f328(f81(a872),f328(a116,f2(a872))),f33(x130111,x130112)),f328(f328(f81(a872),f328(a116,f2(a872))),f32(x130113,x130114)))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,12381,12506,12508,12932,12942,12947,12951,12957,12960,3527,12141,12529,12531,3528,12208,3242,12537,12539,3243,12563,3209,12454,4489,4490,11664,4230,12577,12580,3246,12522,3084,3144,12498,4474,3578,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,12351,12485,12603,12753,13005,4471,10431,10524,3331,3294,12572,3487,3191,4466,2870,2871,2876,2877,2887,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2918,2924,2927,2933,2936,2947,2950,2953,2954,2955,2968,2979,2982,2987,2990,2995,2996,3012,3013,3022,3024,3030,3034,3035,3036,3045,3052,4451,3063,3143,4452,3616,3844,11598,3116,11315,3256,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,12434,12487,12491,12496,12504,12514,12520,12535,12559,12561,12569,12807,3857,3204,12329,12333,12337,3210,3217,3737,3976,3105,3106,4468,3481,3829,11365,3330,3170,3135,3653,12584,3129,3950,3151,3658,4435,3113,3114,3094,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,3380,4538,10401,3916,4481,10263,10428,11229,12293,12330,12334,4488,12301,3265,11687,11690,12901,4527,10978,11048,11276,11279,3678,3260,3381,3602,3345,12518,3165,10330,10637,3166,4515,3439,3158,3085,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,11172,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,3570,4479,11346,3580,3619,3793,3549,12790,12794,12798,12802,12812,3839,12171,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,12425,12609,12667,12698,12710,12752,12773,12829,12835,13004,3730,11584,3258,3354,11702,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,12320,12614,12617,12634,12637,12659,12711,12879,12884,12908,4533,11468,11499,11534,11564,12720,12724,3717,3488,3489,12640,12643,12646,12649,12679,3866,3302,3303,3277,4518,3164,4476,3669,4200,3985,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,12405,4027,3984,11855,12192,3928,10810,12036,12205,3979,10987,12074,12147,12204,12248,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,12431,12941,12946,4539,10758,11126,12954,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,12401,12660,12685,12762,12769,12776,12781,12784,12787,12820,12832,12850,12894,12919,12922,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,11958,12676,12826,12853,12880,12885,12909,3276,3350,12062,12740,12791,12795,12799,12803,12813,12817,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,12466,3434,10605,10869,10913,11183,11265,11426,11667,12296,12469,12867,12936,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,12460,12479,12739,12756,12759,12856,12937,12979,12994,3336,10634,10664,10673,11215,11766,12388,12402,12721,12725,12728,3376,3370,3797,3735,10309,11587,11615,12703,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,12925,3296,10667,10818,10889,11616,11771,11963,12186,3758,11717,12656,4107,3494,4524,3769,3805,4507,4509,4510,3249,3250,4508,4511,4512,4416,4237,3776,3591,11580,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,12216,3883,11304,11642,11646,11708,12304,12312,12394,12670,12931,12983,3724,10929,10935,10950,11887,12016,12095,12365,3576,11152,12121,12230,12240,12309,12360,12368,12476,3614,4061,3726,10670,11006,11158,11188,11202,12198,12308,12354,3546,10591,10594,10676,10848,3545,4545,11581,4535,4540,12624,4546,10727,10827,11137,11423,11454,12180,12189,12236,12415,4167,10803,12201,12213,12239,4068,3757,12482,3704,3705,4543,10282,10285,10622,10625,11465,11643,12424,4544,11561,11652,3728,10588,10845,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5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% 167.77/167.58 cnf(13013,plain, % 167.77/167.58 (~E(f328(a116,x130131),x130131)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(13018,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),f2(a1)),f328(f104(a1),x130181)))), % 167.77/167.58 inference(rename_variables,[],[3376])). % 167.77/167.58 cnf(13021,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),f2(a872)),x130211))), % 167.77/167.58 inference(rename_variables,[],[3296])). % 167.77/167.58 cnf(13022,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x130221),x130221))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(13025,plain, % 167.77/167.58 (~E(f328(a116,x130251),f2(a872))), % 167.77/167.58 inference(rename_variables,[],[4466])). % 167.77/167.58 cnf(13030,plain, % 167.77/167.58 (P1(f328(f328(f330(x130301),x130302),f251(f879(x130301,a867))))), % 167.77/167.58 inference(rename_variables,[],[3434])). % 167.77/167.58 cnf(13034,plain, % 167.77/167.58 (~P1(f328(f328(f330(x130341),x130342),f192(f879(x130341,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(13037,plain, % 167.77/167.58 (P1(f328(f38(a872),f301(a872,x130371,x130372)))), % 167.77/167.58 inference(rename_variables,[],[3489])). % 167.77/167.58 cnf(13038,plain, % 167.77/167.58 (E(f328(f328(f240(a872),f328(a116,x130381)),f328(a116,x130382)),f328(a116,f328(f328(f240(a872),x130381),x130382)))), % 167.77/167.58 inference(rename_variables,[],[3451])). % 167.77/167.58 cnf(13041,plain, % 167.77/167.58 (P1(f328(f38(a872),f301(a872,x130411,x130412)))), % 167.77/167.58 inference(rename_variables,[],[3489])). % 167.77/167.58 cnf(13042,plain, % 167.77/167.58 (E(f328(f328(f241(a872),f328(a116,x130421)),f328(a116,x130422)),f328(a116,f328(f328(f241(a872),x130421),x130422)))), % 167.77/167.58 inference(rename_variables,[],[3452])). % 167.77/167.58 cnf(13045,plain, % 167.77/167.58 (P1(f328(f38(a872),f301(a872,x130451,x130452)))), % 167.77/167.58 inference(rename_variables,[],[3489])). % 167.77/167.58 cnf(13049,plain, % 167.77/167.58 (P1(f328(f38(a872),f301(a872,x130491,x130492)))), % 167.77/167.58 inference(rename_variables,[],[3489])). % 167.77/167.58 cnf(13053,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x130531,a867)),f328(f170(x130531),f328(f133(x130531,x130532),x130533))),f328(f170(x130531),x130533)))), % 167.77/167.58 inference(rename_variables,[],[3928])). % 167.77/167.58 cnf(13054,plain, % 167.77/167.58 (E(f328(f328(f16(x130541,x130542),x130543),x130544),x130543)), % 167.77/167.58 inference(rename_variables,[],[3265])). % 167.77/167.58 cnf(13057,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x130571,a867)),f328(f170(x130571),f328(f328(f173(x130571),x130572),x130573))),f328(f170(x130571),x130573)))), % 167.77/167.58 inference(rename_variables,[],[3973])). % 167.77/167.58 cnf(13058,plain, % 167.77/167.58 (E(f328(f328(f16(x130581,x130582),x130583),x130584),x130583)), % 167.77/167.58 inference(rename_variables,[],[3265])). % 167.77/167.58 cnf(13062,plain, % 167.77/167.58 (E(f328(f328(f16(x130621,x130622),x130623),x130624),x130623)), % 167.77/167.58 inference(rename_variables,[],[3265])). % 167.77/167.58 cnf(13075,plain, % 167.77/167.58 (P1(f328(f328(f242(a1),f2(a1)),f328(f104(a1),x130751)))), % 167.77/167.58 inference(rename_variables,[],[3376])). % 167.77/167.58 cnf(13078,plain, % 167.77/167.58 (~P1(f328(f328(f330(x130781),x130782),f192(f879(x130781,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(13081,plain, % 167.77/167.58 (~P1(f328(f328(f330(x130811),x130812),f192(f879(x130811,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(13082,plain, % 167.77/167.58 (E(f328(f259(x130821,x130821),f260(x130821,x130822)),x130822)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(13083,plain, % 167.77/167.58 (P26(x130831,x130831,f5(x130831),x130832)), % 167.77/167.58 inference(rename_variables,[],[3518])). % 167.77/167.58 cnf(13087,plain, % 167.77/167.58 (E(f328(f259(x130871,x130871),f260(x130871,x130872)),x130872)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(13093,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x130931),f328(a116,x130931)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(13095,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x130951),x130951))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(13096,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),f2(a872)),x130961))), % 167.77/167.58 inference(rename_variables,[],[3296])). % 167.77/167.58 cnf(13099,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),x130991),f328(a116,x130991)))), % 167.77/167.58 inference(rename_variables,[],[3342])). % 167.77/167.58 cnf(13101,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x131011),x131011))), % 167.77/167.58 inference(rename_variables,[],[3274])). % 167.77/167.58 cnf(13102,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),f2(a872)),x131021))), % 167.77/167.58 inference(rename_variables,[],[3296])). % 167.77/167.58 cnf(13106,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),f2(a872)),x131061))), % 167.77/167.58 inference(rename_variables,[],[3296])). % 167.77/167.58 cnf(13107,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),f2(a872)),f328(a116,x131071)))), % 167.77/167.58 inference(rename_variables,[],[3354])). % 167.77/167.58 cnf(13108,plain, % 167.77/167.58 (E(f328(f259(x131081,x131081),f260(x131081,x131082)),x131082)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(13111,plain, % 167.77/167.58 (P1(f328(f49(f328(f259(x131111,x131111),f260(x131111,f328(f328(f80(a872),f328(f328(f81(a872),f328(f262(a872,a872),f328(f328(f263(a872,a872),f2(a872)),x131112))),f328(a116,f328(f328(f80(a872),x131113),f328(f266(a872,a872),f328(f328(f263(a872,a872),f2(a872)),x131112)))))),f328(f266(a872,a872),f328(f328(f263(a872,a872),f2(a872)),x131112))))),f328(a116,f328(f328(f80(a872),x131113),f328(f266(a872,a872),f328(f328(f263(a872,a872),f2(a872)),x131112))))),f328(f328(f263(a872,a872),f2(a872)),x131112)))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,12381,12506,12508,12932,12942,12947,12951,12957,12960,12984,13083,3527,12141,12529,12531,3528,12208,3242,12537,12539,3243,12563,3209,12454,4489,4490,11664,4230,12577,12580,3246,12522,3084,3144,12498,4474,3578,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,12351,12485,12603,12753,13005,4471,10431,10524,3331,3294,12572,3487,3191,4466,12671,13025,2870,2871,2876,2877,2887,2888,2890,2891,2892,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2918,2924,2927,2933,2936,2947,2950,2953,2954,2955,2968,2969,2979,2980,2982,2987,2990,2995,2996,3012,3013,3022,3024,3030,3034,3035,3036,3045,3052,4451,3063,3143,4452,3616,3844,11598,3116,11315,3256,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,12434,12487,12491,12496,12504,12514,12520,12535,12559,12561,12569,12807,12975,13082,13087,13108,3857,3204,12329,12333,12337,3210,3217,3737,3976,3105,3106,4468,3481,3829,11365,3330,3170,3135,3653,12584,3129,3950,3151,3658,4435,3113,3114,3094,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,3380,4538,10401,3916,4481,10263,10428,11229,12293,12330,12334,4488,12301,3265,11687,11690,12901,13001,13054,13058,13062,4527,10978,11048,11276,11279,3678,3260,3381,3602,3373,3345,12518,3165,10330,10637,3166,4515,3439,3158,3085,3270,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,11172,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,3462,3570,4479,11346,3580,3619,3793,3549,12790,12794,12798,12802,12812,3839,12171,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,12425,12609,12667,12698,12710,12752,12773,12829,12835,13004,13009,13093,13099,3730,11584,3258,3354,11702,12602,13107,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,12320,12614,12617,12634,12637,12659,12711,12879,12884,12908,4533,11468,11499,11534,11564,12720,12724,3717,3488,3489,12640,12643,12646,12649,12679,12682,13037,13041,13045,3866,3451,13038,3452,13042,3302,3303,3277,4518,3164,4476,3669,4200,3985,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,12405,4027,3984,11855,12192,3928,10810,12036,12205,12428,13053,3973,13057,3979,10987,12074,12147,12204,12248,12904,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,12431,12941,12946,4539,10758,11126,12954,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,12401,12660,12685,12762,12769,12776,12781,12784,12787,12820,12832,12850,12894,12919,12922,13022,13095,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,11958,12676,12826,12853,12880,12885,12909,3276,3350,12062,12740,12791,12795,12799,12803,12813,12817,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,12466,3434,10605,10869,10913,11183,11265,11426,11667,12296,12469,12867,12936,12987,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,12460,12479,12739,12756,12759,12856,12937,12979,12994,12997,13034,13078,13081,3336,10634,10664,10673,11215,11766,12388,12402,12721,12725,12728,3376,13018,3370,3797,3735,10309,11587,11615,12703,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,12925,3296,10667,10818,10889,11616,11771,11963,12186,12749,13021,13096,13102,13106,3758,11717,12656,4107,3494,4524,3769,3805,4507,4509,4510,3249,3250,4508,4511,4512,4416,4237,4283,3776,3591,11580,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,12216,3883,11304,11642,11646,11708,12304,12312,12394,12670,12931,12983,3724,10929,10935,10950,11887,12016,12095,12365,3576,11152,12121,12230,12240,12309,12360,12368,12476,12873,3614,4061,3726,10670,11006,11158,11188,11202,12198,12308,12354,12971,3546,10591,10594,10676,10848,3545,4545,11581,4535,4540,12624,4546,10727,10827,11137,11423,11454,12180,12189,12236,12415,4167,10803,12201,12213,12239,4068,3757,12482,3704,3705,4543,10282,10285,10622,10625,11465,11643,12424,4544,11561,11652,3728,10588,10845,13008,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,528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387,7419,7420,7421,7422,7567,7568,7574,7575,7577,7579,7791,7793,7794,7810,7848,7927,7966,8019,8040,8041,8056,8116,8228,8295,8296,8299,8334,8396,8397,8463,8482,8483,8484,8485,8640,8851,8875,8876,8956,8970,9024,9025,9143,9179,9202,9236,9277,9469,9735,9928,9984,9986,6011,6385,6386,6473,6493,6494,6910,7126,8562,8595,8792,8982,8983,9052,9053,9325,9326,9327,9328,9531,9806,10107,10158,10159,6455,8387,8388,8841,8859])). % 167.77/167.58 cnf(13177,plain, % 167.77/167.58 (P1(f328(f328(f243(a1),f2(a1)),f328(f75(a1),f78(a1))))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,12381,12506,12508,12932,12942,12947,12951,12957,12960,12984,13083,3527,12141,12529,12531,3528,12208,3242,12537,12539,3243,12563,3209,12454,4489,4490,11664,4230,12577,12580,3246,12522,3084,3144,12498,4474,3578,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,12351,12485,12603,12753,13005,4471,10431,10524,3331,3294,12572,3487,3191,4466,12671,13025,2870,2871,2876,2877,2887,2888,2890,2891,2892,2893,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2918,2924,2927,2933,2936,2947,2950,2953,2954,2955,2968,2969,2979,2980,2982,2987,2990,2993,2995,2996,3012,3013,3022,3024,3030,3034,3035,3036,3045,3052,4451,3063,3143,4452,3616,3844,11598,3116,11315,3256,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,12434,12487,12491,12496,12504,12514,12520,12535,12559,12561,12569,12807,12975,13082,13087,13108,3857,3204,12329,12333,12337,3210,3217,3737,3976,3105,3106,4468,3481,3829,11365,3330,3170,3135,3653,12584,3129,3950,3151,3658,4435,3113,3114,3094,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,3380,4538,10401,3916,4481,10263,10428,11229,12293,12330,12334,4488,12301,3265,11687,11690,12901,13001,13054,13058,13062,4527,10978,11048,11276,11279,3678,3260,3381,3602,3373,3345,12518,3165,10330,10637,3166,4515,3439,3158,3085,3270,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,11172,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,3462,3570,4479,11346,3580,3619,3793,3549,12790,12794,12798,12802,12812,3839,12171,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,12425,12609,12667,12698,12710,12752,12773,12829,12835,13004,13009,13093,13099,3730,11584,3258,3354,11702,12602,13107,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,12320,12614,12617,12634,12637,12659,12711,12879,12884,12908,12913,4533,11468,11499,11534,11564,12720,12724,3717,3488,3489,12640,12643,12646,12649,12679,12682,13037,13041,13045,3866,3451,13038,3452,13042,3302,3303,3277,4518,3164,4476,3669,4200,3985,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,12405,4027,3984,11855,12192,3928,10810,12036,12205,12428,13053,3973,13057,3979,10987,12074,12147,12204,12248,12904,3980,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,12431,12941,12946,4539,10758,11126,12954,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,12401,12660,12685,12762,12769,12776,12781,12784,12787,12820,12832,12850,12894,12919,12922,13022,13095,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,11958,12676,12826,12853,12880,12885,12909,3276,3350,12062,12740,12791,12795,12799,12803,12813,12817,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,12466,3434,10605,10869,10913,11183,11265,11426,11667,12296,12469,12867,12936,12987,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,12460,12479,12739,12756,12759,12856,12937,12979,12994,12997,13034,13078,13081,3336,10634,10664,10673,11215,11766,12388,12402,12721,12725,12728,3376,13018,13075,3370,3797,3735,10309,11587,11615,12703,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,12925,3296,10667,10818,10889,11616,11771,11963,12186,12749,13021,13096,13102,13106,3758,11717,12656,4107,3494,4524,3769,3805,4507,4509,4510,3249,3250,4508,4511,4512,4416,4237,4283,3776,3591,11580,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,12216,3883,11304,11642,11646,11708,12304,12312,12394,12670,12931,12983,3724,10929,10935,10950,11887,12016,12095,12365,3576,11152,12121,12230,12240,12309,12360,12368,12476,12873,3614,4061,3726,10670,11006,11158,11188,11202,12198,12308,12354,12971,3546,10591,10594,10676,10848,3545,4545,11581,4535,4540,12624,4546,10727,10827,11137,11423,11454,12180,12189,12236,12415,4167,10803,12201,12213,12239,4068,3757,12482,3704,3705,4543,10282,10285,10622,10625,11465,11643,12424,4544,11561,11652,3728,10588,10845,13008,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6557,6562,6564,6569,6570,6578,6582,6595,6620,6621,6622,6623,6635,6640,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6792,6795,6831,6834,6835,6848,6849,6850,6851,6871,6872,6887,6913,6935,6946,6948,6949,6951,6953,6954,6987,6988,6993,6994,6995,6996,6998,7000,7025,7034,7035,7047,7057,7096,7106,7110,7117,7128,7134,7136,7142,7151,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7385,7399,7416,7448,7451,7477,7501,7518,7521,7522,7532,7550,7551,7553,7555,7557,7559,7587,7612,7613,7645,7647,7648,7649,7654,7676,7685,7695,7700,7706,7708,7714,7726,7727,7729,7760,7783,7850,7851,7898,7906,7907,7931,7932,7949,7950,8008,8009,8010,8035,8068,8075,8077,8087,8099,8130,8138,8145,8158,8180,8186,8213,8257,8285,8298,8316,8319,8349,8372,8433,8434,8437,8439,8544,8545,8546,8547,8576,8605,8636,8680,8698,8753,8798,8801,8814,8821,8858,8877,8905,8906,8924,8925,9065,9069,9089,9099,9122,9124,9127,9131,9134,9135,9148,9149,9169,9175,9187,9235,9253,9307,9308,9315,9376,9381,9417,9424,9427,9430,9431,9446,9462,9471,9483,9495,9496,9499,9501,9528,9653,9698,9699,9741,9786,9902,9959,10024,10098,10111,10116,3,2606,2609,2611,2612,2613,2614,2622,2628,2629,2630,2633,2634,2635,2636,2637,2639,2644,2645,2646,2647,2649,2651,2659,2660,2661,2669,2671,2672,2673,2675,2676,2677,2680,2681,2682,2692,2707,2708,2709,2711,2712,2714,2715,2719,2721,2723,2724,2725,2733,2735,2736,2737,2743,2746,2749,2750,2751,2775,2776,2777,2780,2781,2791,2793,2795,2796,2797,2821,2831,2832,5207,5267,5365,5451,5452,5453,5528,5626,5657,5691,5707,5709,5715,5778,5779,5780,5781,5787,5820,5950,5993,6016,6053,6093,6242,6249,6283,6284,6304,6307,6309,6316,6317,6318,6319,6320,6321,6322,6323,6402,6470,6471,6555,6589,6590,6632,6633,6771,6786,6860,6861,6868,6888,6911,6919,6921,6968,6991,6992,7008,7009,7010,7046,7090,7091,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7373,7375,7387,7419,7420,7421,7422,7567,7568,7574,7575,7577,7579,7791,7793,7794,7810,7848,7927,7966,8019,8040,8041,8056,8116,8228,8295,8296,8299,8334,8396,8397,8463,8482,8483,8484,8485,8640,8851,8875,8876,8956,8970,9024,9025,9143,9179,9202,9236,9277,9469,9735,9928,9984,9986,6011,6385,6386,6473,6493,6494,6910,7126,8562,8595,8792,8982,8983,9052,9053,9325,9326,9327,9328,9531,9806,10107,10158,10159,6455,8387,8388,8841,8859,9807,10157,4632,4634,4635,4690,4698,4835,4851,4852,4880,4881,4910,4965,5028,5087,5164,5200,5202,5210,5211,5237,5312,5333,5467,5533,5534,5535,5653])). % 167.77/167.58 cnf(13191,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),f328(a116,f328(f328(f80(a872),x131911),x131912))),f328(a116,x131912)))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,12381,12506,12508,12932,12942,12947,12951,12957,12960,12984,13083,3527,12141,12529,12531,3528,12208,3242,12537,12539,3243,12563,3209,12454,4489,4490,11664,4230,12577,12580,3246,12522,3084,3144,12498,4474,3578,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,12351,12485,12603,12753,13005,4471,10431,10524,3331,3294,12572,3487,3191,4466,12671,13025,2870,2871,2876,2877,2887,2888,2890,2891,2892,2893,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2918,2924,2927,2933,2936,2947,2950,2953,2954,2955,2968,2969,2979,2980,2982,2987,2990,2993,2995,2996,3012,3013,3022,3024,3030,3034,3035,3036,3045,3052,4451,3063,3143,4452,3616,3844,11598,3116,11315,3256,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,12434,12487,12491,12496,12504,12514,12520,12535,12559,12561,12569,12807,12975,13082,13087,13108,3857,3204,12329,12333,12337,3210,3217,3737,3976,3105,3106,4468,3481,3829,11365,3330,3170,3135,3653,12584,3129,3950,3151,3658,4435,3113,3114,3094,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,3380,4538,10401,3916,4481,10263,10428,11229,12293,12330,12334,4488,12301,3265,11687,11690,12901,13001,13054,13058,13062,4527,10978,11048,11276,11279,3678,3260,3381,3602,3373,3345,12518,3165,10330,10637,3166,4515,3439,3158,3085,3270,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,11172,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,3462,3570,4479,11346,3580,3619,3793,3549,12790,12794,12798,12802,12812,3839,12171,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,12425,12609,12667,12698,12710,12752,12773,12829,12835,13004,13009,13093,13099,3730,11584,3258,3354,11702,12602,13107,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,12320,12614,12617,12634,12637,12659,12711,12879,12884,12908,12913,4533,11468,11499,11534,11564,12720,12724,3717,3488,3489,12640,12643,12646,12649,12679,12682,13037,13041,13045,3866,3451,13038,3452,13042,3302,3303,3277,4518,3164,4476,3669,4200,3985,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,12405,4027,3984,11855,12192,3928,10810,12036,12205,12428,13053,3973,13057,3979,10987,12074,12147,12204,12248,12904,3980,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,12431,12941,12946,4539,10758,11126,12954,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,12401,12660,12685,12762,12769,12776,12781,12784,12787,12820,12832,12850,12894,12919,12922,13022,13095,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,11958,12676,12826,12853,12880,12885,12909,3276,3350,12062,12740,12791,12795,12799,12803,12813,12817,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,12466,3434,10605,10869,10913,11183,11265,11426,11667,12296,12469,12867,12936,12987,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,12460,12479,12739,12756,12759,12856,12937,12979,12994,12997,13034,13078,13081,3336,10634,10664,10673,11215,11766,12388,12402,12721,12725,12728,3376,13018,13075,3370,3797,3735,10309,11587,11615,12703,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,12925,3296,10667,10818,10889,11616,11771,11963,12186,12749,13021,13096,13102,13106,3758,11717,12656,4107,3494,4524,3769,3805,4507,4509,4510,3249,3250,4508,4511,4512,4416,4237,4283,3776,3591,11580,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,12216,3883,11304,11642,11646,11708,12304,12312,12394,12670,12931,12983,3724,10929,10935,10950,11887,12016,12095,12365,3576,11152,12121,12230,12240,12309,12360,12368,12476,12873,3614,4061,3726,10670,11006,11158,11188,11202,12198,12308,12354,12971,3546,10591,10594,10676,10848,3545,4545,11581,4535,4540,12624,4546,10727,10827,11137,11423,11454,12180,12189,12236,12415,4167,10803,12201,12213,12239,4068,3757,12482,3704,3705,4543,10282,10285,10622,10625,11465,11643,12424,4544,11561,11652,3728,10588,10845,13008,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6557,6562,6564,6569,6570,6578,6582,6595,6620,6621,6622,6623,6635,6640,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6792,6795,6831,6834,6835,6848,6849,6850,6851,6871,6872,6887,6913,6935,6946,6948,6949,6951,6953,6954,6987,6988,6993,6994,6995,6996,6998,7000,7025,7034,7035,7047,7057,7096,7106,7110,7117,7128,7134,7136,7142,7151,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7385,7399,7416,7448,7451,7477,7501,7518,7521,7522,7532,7550,7551,7553,7555,7557,7559,7587,7612,7613,7645,7647,7648,7649,7654,7676,7685,7695,7700,7706,7708,7714,7726,7727,7729,7760,7783,7850,7851,7898,7906,7907,7931,7932,7949,7950,8008,8009,8010,8035,8068,8075,8077,8087,8099,8130,8138,8145,8158,8180,8186,8213,8257,8285,8298,8316,8319,8349,8372,8433,8434,8437,8439,8544,8545,8546,8547,8576,8605,8636,8680,8698,8753,8798,8801,8814,8821,8858,8877,8905,8906,8924,8925,9065,9069,9089,9099,9122,9124,9127,9131,9134,9135,9148,9149,9169,9175,9187,9235,9253,9307,9308,9315,9376,9381,9417,9424,9427,9430,9431,9446,9462,9471,9483,9495,9496,9499,9501,9528,9653,9698,9699,9741,9786,9902,9959,10024,10098,10111,10116,3,2606,2609,2611,2612,2613,2614,2622,2628,2629,2630,2633,2634,2635,2636,2637,2639,2644,2645,2646,2647,2649,2651,2659,2660,2661,2669,2671,2672,2673,2675,2676,2677,2680,2681,2682,2692,2707,2708,2709,2711,2712,2714,2715,2719,2721,2723,2724,2725,2733,2735,2736,2737,2743,2746,2749,2750,2751,2775,2776,2777,2780,2781,2791,2793,2795,2796,2797,2821,2831,2832,5207,5267,5365,5451,5452,5453,5528,5626,5657,5691,5707,5709,5715,5778,5779,5780,5781,5787,5820,5950,5993,6016,6053,6093,6242,6249,6283,6284,6304,6307,6309,6316,6317,6318,6319,6320,6321,6322,6323,6402,6470,6471,6555,6589,6590,6632,6633,6771,6786,6860,6861,6868,6888,6911,6919,6921,6968,6991,6992,7008,7009,7010,7046,7090,7091,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7373,7375,7387,7419,7420,7421,7422,7567,7568,7574,7575,7577,7579,7791,7793,7794,7810,7848,7927,7966,8019,8040,8041,8056,8116,8228,8295,8296,8299,8334,8396,8397,8463,8482,8483,8484,8485,8640,8851,8875,8876,8956,8970,9024,9025,9143,9179,9202,9236,9277,9469,9735,9928,9984,9986,6011,6385,6386,6473,6493,6494,6910,7126,8562,8595,8792,8982,8983,9052,9053,9325,9326,9327,9328,9531,9806,10107,10158,10159,6455,8387,8388,8841,8859,9807,10157,4632,4634,4635,4690,4698,4835,4851,4852,4880,4881,4910,4965,5028,5087,5164,5200,5202,5210,5211,5237,5312,5333,5467,5533,5534,5535,5653,5654,5680,5684,5744,5755,5761,5833])). % 167.77/167.58 cnf(13199,plain, % 167.77/167.58 (~P1(f328(f38(x131991),f41(f879(x131991,a867),f251(f879(f879(x131991,a867),a867)))))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,12381,12506,12508,12932,12942,12947,12951,12957,12960,12984,13083,3527,12141,12529,12531,3528,12208,3242,12537,12539,3243,12563,3209,12454,4489,4490,11664,4230,12577,12580,3246,12522,3084,3144,12498,4474,3578,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,12351,12485,12603,12753,13005,4471,10431,10524,3331,3294,12572,3487,3191,4466,12671,13025,2870,2871,2876,2877,2887,2888,2890,2891,2892,2893,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2918,2924,2927,2933,2936,2947,2950,2953,2954,2955,2968,2969,2979,2980,2982,2987,2990,2993,2995,2996,3012,3013,3022,3024,3030,3034,3035,3036,3045,3052,4451,3063,3143,4452,3616,3844,11598,3116,11315,3256,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,12434,12487,12491,12496,12504,12514,12520,12535,12559,12561,12569,12807,12975,13082,13087,13108,3857,3204,12329,12333,12337,3210,3217,3737,3976,3105,3106,4468,3481,3829,11365,3330,3170,3135,3653,12584,3129,3950,3151,3658,4435,3113,3114,3094,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,3380,4538,10401,3916,4481,10263,10428,11229,12293,12330,12334,4488,12301,3265,11687,11690,12901,13001,13054,13058,13062,4527,10978,11048,11276,11279,3678,3260,3381,3602,3373,3345,12518,3165,10330,10637,3166,4515,3439,3158,3085,3270,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,11172,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,3462,3570,4479,11346,3580,3619,3793,3549,12790,12794,12798,12802,12812,3839,12171,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,12425,12609,12667,12698,12710,12752,12773,12829,12835,13004,13009,13093,13099,3730,11584,3258,3354,11702,12602,13107,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,12320,12614,12617,12634,12637,12659,12711,12879,12884,12908,12913,4533,11468,11499,11534,11564,12720,12724,3717,3488,3489,12640,12643,12646,12649,12679,12682,13037,13041,13045,3866,3451,13038,3452,13042,3302,3303,3277,4518,3164,4476,3669,4200,3985,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,12405,4027,3984,11855,12192,3928,10810,12036,12205,12428,13053,3973,13057,3979,10987,12074,12147,12204,12248,12904,3980,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,12431,12941,12946,4539,10758,11126,12954,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,12401,12660,12685,12762,12769,12776,12781,12784,12787,12820,12832,12850,12894,12919,12922,13022,13095,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,11958,12676,12826,12853,12880,12885,12909,3276,3350,12062,12740,12791,12795,12799,12803,12813,12817,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,12466,3434,10605,10869,10913,11183,11265,11426,11667,12296,12469,12867,12936,12987,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,12460,12479,12739,12756,12759,12856,12937,12979,12994,12997,13034,13078,13081,3336,10634,10664,10673,11215,11766,12388,12402,12721,12725,12728,3376,13018,13075,3370,3797,3735,10309,11587,11615,12703,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,12925,3296,10667,10818,10889,11616,11771,11963,12186,12749,13021,13096,13102,13106,3758,11717,12656,4107,3494,4524,3769,3805,4507,4509,4510,3249,3250,4508,4511,4512,4416,4237,4283,3776,3591,11580,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,12216,3883,11304,11642,11646,11708,12304,12312,12394,12670,12931,12983,3724,10929,10935,10950,11887,12016,12095,12365,3576,11152,12121,12230,12240,12309,12360,12368,12476,12873,3614,4061,3726,10670,11006,11158,11188,11202,12198,12308,12354,12971,3546,10591,10594,10676,10848,3545,4545,11581,4535,4540,12624,4546,10727,10827,11137,11423,11454,12180,12189,12236,12415,4167,10803,12201,12213,12239,4068,3757,12482,3704,3705,4543,10282,10285,10622,10625,11465,11643,12424,4544,11561,11652,3728,10588,10845,13008,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6557,6562,6564,6569,6570,6578,6582,6595,6620,6621,6622,6623,6635,6640,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6792,6795,6831,6834,6835,6848,6849,6850,6851,6871,6872,6887,6913,6935,6946,6948,6949,6951,6953,6954,6987,6988,6993,6994,6995,6996,6998,7000,7025,7034,7035,7047,7057,7096,7106,7110,7117,7128,7134,7136,7142,7151,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7385,7399,7416,7448,7451,7477,7501,7518,7521,7522,7532,7550,7551,7553,7555,7557,7559,7587,7612,7613,7645,7647,7648,7649,7654,7676,7685,7695,7700,7706,7708,7714,7726,7727,7729,7760,7783,7850,7851,7898,7906,7907,7931,7932,7949,7950,8008,8009,8010,8035,8068,8075,8077,8087,8099,8130,8138,8145,8158,8180,8186,8213,8257,8285,8298,8316,8319,8349,8372,8433,8434,8437,8439,8544,8545,8546,8547,8576,8605,8636,8680,8698,8753,8798,8801,8814,8821,8858,8877,8905,8906,8924,8925,9065,9069,9089,9099,9122,9124,9127,9131,9134,9135,9148,9149,9169,9175,9187,9235,9253,9307,9308,9315,9376,9381,9417,9424,9427,9430,9431,9446,9462,9471,9483,9495,9496,9499,9501,9528,9653,9698,9699,9741,9786,9902,9959,10024,10098,10111,10116,3,2606,2609,2611,2612,2613,2614,2622,2628,2629,2630,2633,2634,2635,2636,2637,2639,2644,2645,2646,2647,2649,2651,2659,2660,2661,2669,2671,2672,2673,2675,2676,2677,2680,2681,2682,2692,2707,2708,2709,2711,2712,2714,2715,2719,2721,2723,2724,2725,2733,2735,2736,2737,2743,2746,2749,2750,2751,2775,2776,2777,2780,2781,2791,2793,2795,2796,2797,2821,2831,2832,5207,5267,5365,5451,5452,5453,5528,5626,5657,5691,5707,5709,5715,5778,5779,5780,5781,5787,5820,5950,5993,6016,6053,6093,6242,6249,6283,6284,6304,6307,6309,6316,6317,6318,6319,6320,6321,6322,6323,6402,6470,6471,6555,6589,6590,6632,6633,6771,6786,6860,6861,6868,6888,6911,6919,6921,6968,6991,6992,7008,7009,7010,7046,7090,7091,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7373,7375,7387,7419,7420,7421,7422,7567,7568,7574,7575,7577,7579,7791,7793,7794,7810,7848,7927,7966,8019,8040,8041,8056,8116,8228,8295,8296,8299,8334,8396,8397,8463,8482,8483,8484,8485,8640,8851,8875,8876,8956,8970,9024,9025,9143,9179,9202,9236,9277,9469,9735,9928,9984,9986,6011,6385,6386,6473,6493,6494,6910,7126,8562,8595,8792,8982,8983,9052,9053,9325,9326,9327,9328,9531,9806,10107,10158,10159,6455,8387,8388,8841,8859,9807,10157,4632,4634,4635,4690,4698,4835,4851,4852,4880,4881,4910,4965,5028,5087,5164,5200,5202,5210,5211,5237,5312,5333,5467,5533,5534,5535,5653,5654,5680,5684,5744,5755,5761,5833,5911,6034,6057,6229])). % 167.77/167.58 cnf(13236,plain, % 167.77/167.58 (~E(f328(a116,x132361),x132361)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(13244,plain, % 167.77/167.58 (~P1(f328(f328(f242(a872),f328(a116,f328(f139(a872,a872,f80(a872),f2(a872)),f168(a872,f328(a116,f2(a872)),f328(a116,f2(a872)))))),f328(a116,f2(a872))))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,12381,12506,12508,12932,12942,12947,12951,12957,12960,12984,13083,3527,12141,12529,12531,3528,12208,3242,12537,12539,3243,12563,3209,12454,4489,4490,11664,4230,12577,12580,3246,12522,3084,3144,12498,4474,3578,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,12351,12485,12603,12753,13005,13013,4471,10431,10524,3331,3294,12572,3487,3191,4466,12671,13025,2870,2871,2876,2877,2887,2888,2890,2891,2892,2893,2898,2899,2900,2903,2904,2906,2907,2908,2910,2911,2914,2915,2918,2924,2927,2933,2936,2947,2950,2953,2954,2955,2968,2969,2979,2980,2982,2987,2990,2993,2995,2996,3012,3013,3022,3024,3030,3034,3035,3036,3045,3052,4451,3063,3143,4452,3616,3844,11598,3116,11315,3256,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,12434,12487,12491,12496,12504,12514,12520,12535,12559,12561,12569,12807,12975,13082,13087,13108,3857,3204,12329,12333,12337,3210,3217,3737,3976,3105,3106,4468,3481,3829,11365,3330,3170,3645,3135,3653,12584,3129,3950,3151,3658,4435,3113,3114,3094,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,3380,4538,10401,3916,4481,10263,10428,11229,12293,12330,12334,4488,12301,3265,11687,11690,12901,13001,13054,13058,13062,4527,10978,11048,11276,11279,3678,3260,3381,3602,3373,3345,12518,3165,10330,10637,3166,4515,3439,3158,3085,3270,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,11172,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,3462,3570,4479,11346,3580,3619,3793,3549,12790,12794,12798,12802,12812,3839,12171,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,12425,12609,12667,12698,12710,12752,12773,12829,12835,13004,13009,13093,13099,3730,11584,3258,3354,11702,12602,13107,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,12320,12614,12617,12634,12637,12659,12711,12879,12884,12908,12913,4533,11468,11499,11534,11564,12720,12724,3717,3488,3489,12640,12643,12646,12649,12679,12682,13037,13041,13045,13049,3866,3451,13038,3452,13042,3302,3303,3277,4518,3164,4476,3669,4200,3985,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,12405,4027,3984,11855,12192,3928,10810,12036,12205,12428,13053,3973,13057,3979,10987,12074,12147,12204,12248,12904,3980,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,12431,12941,12946,4539,10758,11126,12954,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,12401,12660,12685,12762,12769,12776,12781,12784,12787,12820,12832,12850,12894,12919,12922,13022,13095,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,11958,12676,12826,12853,12880,12885,12909,3276,3350,12062,12740,12791,12795,12799,12803,12813,12817,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,12466,3434,10605,10869,10913,11183,11265,11426,11667,12296,12469,12867,12936,12987,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,12460,12479,12739,12756,12759,12856,12937,12979,12994,12997,13034,13078,13081,3336,10634,10664,10673,11215,11766,12388,12402,12721,12725,12728,3376,13018,13075,3370,3797,3735,10309,11587,11615,12703,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,12925,3296,10667,10818,10889,11616,11771,11963,12186,12749,13021,13096,13102,13106,3758,11717,12656,4107,3494,4524,3769,3805,4507,4509,4510,3249,3250,4508,4511,4512,4416,4237,4283,3776,3591,11580,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,12216,3883,11304,11642,11646,11708,12304,12312,12394,12670,12931,12983,3724,10929,10935,10950,11887,12016,12095,12365,3576,11152,12121,12230,12240,12309,12360,12368,12476,12873,3614,4061,3726,10670,11006,11158,11188,11202,12198,12308,12354,12971,3546,10591,10594,10676,10848,3545,4545,11581,4535,4540,12624,4546,10727,10827,11137,11423,11454,12180,12189,12236,12415,4167,10803,12201,12213,12239,4068,3757,12482,3704,3705,4543,10282,10285,10622,10625,11465,11643,12424,4544,11561,11652,3728,10588,10845,13008,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6557,6562,6564,6569,6570,6578,6582,6595,6620,6621,6622,6623,6635,6640,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6792,6795,6831,6834,6835,6848,6849,6850,6851,6871,6872,6887,6913,6935,6946,6948,6949,6951,6953,6954,6987,6988,6993,6994,6995,6996,6998,7000,7025,7034,7035,7047,7057,7096,7106,7110,7117,7128,7134,7136,7142,7151,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7385,7399,7416,7448,7451,7477,7501,7518,7521,7522,7532,7550,7551,7553,7555,7557,7559,7587,7612,7613,7645,7647,7648,7649,7654,7676,7685,7695,7700,7706,7708,7714,7726,7727,7729,7760,7783,7850,7851,7898,7906,7907,7931,7932,7949,7950,8008,8009,8010,8035,8068,8075,8077,8087,8099,8130,8138,8145,8158,8180,8186,8213,8257,8285,8298,8316,8319,8349,8372,8433,8434,8437,8439,8544,8545,8546,8547,8576,8605,8636,8680,8698,8753,8798,8801,8814,8821,8858,8877,8905,8906,8924,8925,9065,9069,9089,9099,9122,9124,9127,9131,9134,9135,9148,9149,9169,9175,9187,9235,9253,9307,9308,9315,9376,9381,9417,9424,9427,9430,9431,9446,9462,9471,9483,9495,9496,9499,9501,9528,9653,9698,9699,9741,9786,9902,9959,10024,10098,10111,10116,3,2606,2609,2611,2612,2613,2614,2622,2628,2629,2630,2633,2634,2635,2636,2637,2639,2644,2645,2646,2647,2649,2651,2659,2660,2661,2669,2671,2672,2673,2675,2676,2677,2680,2681,2682,2692,2707,2708,2709,2711,2712,2714,2715,2719,2721,2723,2724,2725,2733,2735,2736,2737,2743,2746,2749,2750,2751,2775,2776,2777,2780,2781,2791,2793,2795,2796,2797,2821,2831,2832,5207,5267,5365,5451,5452,5453,5528,5626,5657,5691,5707,5709,5715,5778,5779,5780,5781,5787,5820,5950,5993,6016,6053,6093,6242,6249,6283,6284,6304,6307,6309,6316,6317,6318,6319,6320,6321,6322,6323,6402,6470,6471,6555,6589,6590,6632,6633,6771,6786,6860,6861,6868,6888,6911,6919,6921,6968,6991,6992,7008,7009,7010,7046,7090,7091,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7373,7375,7387,7419,7420,7421,7422,7567,7568,7574,7575,7577,7579,7791,7793,7794,7810,7848,7927,7966,8019,8040,8041,8056,8116,8228,8295,8296,8299,8334,8396,8397,8463,8482,8483,8484,8485,8640,8851,8875,8876,8956,8970,9024,9025,9143,9179,9202,9236,9277,9469,9735,9928,9984,9986,6011,6385,6386,6473,6493,6494,6910,7126,8562,8595,8792,8982,8983,9052,9053,9325,9326,9327,9328,9531,9806,10107,10158,10159,6455,8387,8388,8841,8859,9807,10157,4632,4634,4635,4690,4698,4835,4851,4852,4880,4881,4910,4965,5028,5087,5164,5200,5202,5210,5211,5237,5312,5333,5467,5533,5534,5535,5653,5654,5680,5684,5744,5755,5761,5833,5911,6034,6057,6229,6348,6503,6705,6706,6922,6961,7132,7359,7427,7767,7768,7864,8017,8799,9056,9291,9566,4865,4912,5053,5885])). % 167.77/167.58 cnf(13261,plain, % 167.77/167.58 (~E(f328(a116,x132611),x132611)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(13281,plain, % 167.77/167.58 (~E(f328(a116,x132811),x132811)), % 167.77/167.58 inference(rename_variables,[],[4456])). % 167.77/167.58 cnf(13320,plain, % 167.77/167.58 (P1(f328(f328(f243(a872),f2(a872)),f328(f328(f80(a872),f328(a116,f2(a872))),f2(a872))))), % 167.77/167.58 inference(scs_inference,[],[3518,11043,12077,12174,12269,12305,12313,12326,12381,12506,12508,12932,12942,12947,12951,12957,12960,12984,13083,3527,12141,12529,12531,3528,12208,3242,12537,12539,3243,12563,3209,12454,4489,4490,11664,4230,12577,12580,3246,12522,3084,3144,12498,4474,3578,4456,10205,10215,10226,10237,10338,10341,10344,10447,10560,10864,11028,11031,11232,11318,11325,11339,11391,11394,11438,11504,11551,11567,11866,11891,11903,11932,11938,12033,12137,12144,12297,12351,12485,12603,12753,13005,13013,13236,13261,13281,4471,10431,10524,3331,3294,12572,3487,3191,4466,12671,13025,2870,2871,2875,2876,2877,2878,2879,2880,2883,2887,2888,2889,2890,2891,2892,2893,2895,2898,2899,2900,2902,2903,2904,2906,2907,2908,2910,2911,2912,2914,2915,2918,2924,2927,2933,2936,2947,2950,2953,2954,2955,2968,2969,2979,2980,2982,2987,2990,2993,2995,2996,3012,3013,3022,3024,3025,3026,3030,3034,3035,3036,3037,3045,3047,3052,3055,3062,4451,3063,3143,4452,3616,3844,11598,3116,11315,3256,3232,10208,10272,10275,10365,10368,10661,11330,11333,11449,11491,11496,11593,12051,12245,12434,12487,12491,12496,12504,12514,12520,12535,12559,12561,12569,12807,12975,13082,13087,13108,3857,3204,12329,12333,12337,3210,3217,3737,3976,3105,3106,4468,3481,3829,11365,3330,3168,3170,3645,3135,3653,12584,3129,3950,3151,3658,4435,3113,3114,3094,3120,3150,3287,12384,12457,3332,10813,12138,3202,3203,3227,10472,10475,3380,4538,10401,3916,4481,10263,10428,11229,12293,12330,12334,4488,12301,3265,11687,11690,12901,13001,13054,13058,13062,4527,10978,11048,11276,11279,3678,3260,3381,3602,3373,3345,12518,3165,10330,10637,3166,4515,3439,3158,3085,3270,3187,11355,4063,12316,12446,3918,10984,11110,11161,12277,12283,12395,12398,12421,4550,10916,11115,11223,11248,11282,11288,12224,4551,11017,11118,11226,4552,11121,11172,4553,11175,4554,3186,3479,12177,12221,12300,3641,4346,4347,3462,3570,4479,11346,3580,3619,3793,3549,12790,12794,12798,12802,12812,3839,12171,3465,3719,3342,10349,10467,10538,10599,10602,10640,10734,10968,11194,11862,11925,12004,12042,12103,12106,12425,12609,12667,12698,12710,12752,12773,12829,12835,13004,13009,13093,13099,3730,11584,3258,3354,11702,12602,13107,3543,4521,10240,10243,10269,10742,10755,10874,11268,11358,11751,11759,11980,11983,12068,12227,12320,12614,12617,12634,12637,12659,12711,12879,12884,12908,12913,4533,11468,11499,11534,11564,12720,12724,3717,3488,3489,12640,12643,12646,12649,12679,12682,13037,13041,13045,13049,3490,3866,3451,13038,3452,13042,3302,3303,3277,4518,3164,4476,3669,4200,3985,3471,4534,4057,11243,3601,3315,11711,11714,12148,12249,12405,4027,3984,11855,12192,3928,10810,12036,12205,12428,13053,3973,13057,3979,10987,12074,12147,12204,12248,12904,3980,3642,11865,12011,12082,12128,4016,3660,10990,11053,11134,11197,12032,12096,12346,12418,12431,12941,12946,4539,10758,11126,12954,3274,10358,10454,10585,10647,10716,10761,10764,10797,10821,10858,10896,10932,11658,11705,11835,11890,11906,11909,11912,11915,12089,12109,12112,12115,12118,12185,12252,12357,12401,12660,12685,12762,12769,12776,12781,12784,12787,12820,12832,12850,12894,12919,12922,13022,13095,13101,3275,10387,10442,10652,10737,10861,11441,11547,11739,11742,11754,11841,11852,11873,11878,11918,11943,11958,12676,12826,12853,12880,12885,12909,3276,3350,12062,12740,12791,12795,12799,12803,12813,12817,4517,10306,10396,10509,10533,10779,10824,10834,11235,11513,11612,11633,11636,11639,11655,11797,11800,11803,11806,11902,11921,11924,11937,11992,11995,11998,12001,12069,12159,12162,12255,12258,12319,12350,12387,12466,3434,10605,10869,10913,11183,11265,11426,11667,12296,12469,12867,12936,12987,13030,4529,10788,10800,10905,10923,10926,10981,11067,11075,11091,11129,11146,11155,11191,11238,11256,11259,11262,11291,11298,11301,11684,11720,11986,11989,12023,12063,12092,12233,12274,12280,12369,12372,12391,12445,12451,12460,12479,12739,12756,12759,12856,12937,12979,12994,12997,13034,13078,13081,3336,10634,10664,10673,11215,11766,12388,12402,12721,12725,12728,3376,13018,13075,3370,3797,3735,10309,11587,11615,12703,4526,10260,10628,10631,11070,11088,11550,11603,11647,11668,11772,11809,11812,11815,11818,12925,3296,10667,10818,10889,11616,11771,11963,12186,12749,13021,13096,13102,13106,3758,11717,12656,4107,3494,4524,3769,3805,4507,4509,4510,3249,3250,4508,4511,4512,4416,4237,4283,3776,3591,11580,12963,4206,11448,4541,10231,10234,10490,10541,10544,10549,10955,11420,11671,11775,4548,11149,11273,11307,3993,12216,3883,11304,11642,11646,11708,12304,12312,12394,12670,12931,12983,3724,10929,10935,10950,11887,12016,12095,12365,12982,3576,11152,12121,12230,12240,12309,12360,12368,12476,12873,3614,4061,3726,10670,11006,11158,11188,11202,12198,12308,12354,12971,3546,10591,10594,10676,10848,3544,3545,4545,11581,4535,4540,12624,4546,10727,10827,11137,11423,11454,12180,12189,12236,12415,4167,10803,12201,12213,12239,4068,3757,12482,3704,3705,4543,10282,10285,10622,10625,11465,11643,12424,4544,11561,11652,3728,10588,10845,13008,4000,4565,4591,4640,4642,4672,4689,4696,4697,4736,4766,4772,4857,4882,4883,4918,4943,4944,4966,4967,4980,4984,5007,5014,5032,5035,5036,5037,5042,5043,5065,5090,5091,5101,5106,5112,5156,5157,5165,5174,5179,5181,5191,5193,5199,5203,5218,5225,5228,5229,5230,5234,5270,5283,5291,5293,5294,5298,5299,5300,5308,5311,5315,5316,5317,5324,5328,5329,5330,5338,5342,5343,5344,5349,5362,5371,5383,5385,5393,5394,5398,5402,5427,5433,5443,5444,5459,5471,5493,5499,5515,5516,5519,5538,5546,5547,5552,5553,5563,5565,5578,5582,5591,5592,5594,5609,5614,5624,5625,5637,5644,5658,5662,5665,5671,5672,5673,5676,5681,5719,5720,5723,5725,5728,5729,5730,5732,5734,5736,5741,5748,5763,5777,5782,5783,5796,5797,5802,5806,5808,5813,5854,5866,5875,5879,5890,5894,5895,5903,5916,5922,5940,5943,5953,5978,5992,6017,6037,6038,6041,6056,6058,6059,6061,6074,6075,6078,6080,6083,6084,6096,6102,6103,6104,6106,6108,6151,6152,6161,6168,6172,6208,6210,6212,6214,6223,6225,6227,6233,6235,6241,6244,6252,6259,6260,6261,6266,6288,6289,6290,6292,6298,6303,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6543,6545,6546,6599,6624,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6794,6845,6857,6859,6863,6880,6881,6915,6927,6958,6990,7044,7072,7127,7148,7157,7160,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7388,7398,7401,7417,7468,7469,7473,7516,7517,7535,7604,7623,7646,7669,7684,7699,7709,7718,7719,7746,7749,7751,7762,7800,7812,7837,7895,7929,7961,8000,8016,8032,8033,8109,8166,8185,8214,8235,8259,8356,8358,8364,8378,8382,8400,8422,8430,8432,8444,8450,8454,8475,8489,8490,8508,8510,8514,8515,8516,8517,8518,8540,8541,8542,8553,8567,8569,8581,8585,8587,8588,8589,8597,8602,8632,8633,8664,8677,8681,8699,8721,8722,8723,8724,8736,8737,8759,8769,8779,8780,8781,8782,8784,8805,8806,8817,8861,8867,8873,8884,8889,8891,8894,8895,8899,8909,8990,9021,9022,9023,9038,9055,9062,9091,9092,9133,9136,9162,9207,9208,9209,9224,9249,9263,9269,9272,9294,9295,9323,9384,9420,9421,9422,9447,9448,9466,9484,9489,9492,9506,9530,9552,9560,9561,9562,9563,9578,9580,9585,9616,9617,9623,9624,9626,9670,9671,9703,9712,9722,9725,9734,9748,9751,9779,9812,9814,9818,9875,9916,9917,9929,9930,9950,9955,9996,10047,10119,10120,10173,10189,2,8,9,4578,4579,4597,4628,4630,4631,4658,4664,4665,4676,4725,4727,4757,4771,4801,4897,4898,4911,4931,4987,4988,4991,4992,4994,4996,4997,5006,5010,5011,5021,5033,5034,5040,5060,5061,5078,5083,5084,5085,5086,5089,5097,5100,5107,5171,5177,5178,5185,5215,5226,5232,5248,5268,5269,5276,5277,5278,5287,5297,5304,5306,5307,5313,5320,5321,5334,5335,5336,5337,5339,5340,5345,5346,5347,5348,5379,5380,5381,5389,5390,5391,5392,5438,5440,5442,5478,5480,5481,5483,5484,5486,5487,5489,5498,5503,5505,5506,5507,5508,5509,5510,5517,5527,5530,5541,5557,5558,5561,5571,5574,5575,5576,5601,5611,5627,5628,5638,5639,5641,5643,5648,5683,5688,5690,5750,5784,5785,5789,5795,5798,5799,5800,5801,5807,5818,5819,5821,5822,5830,5851,5882,5898,5901,5902,5904,5913,5930,5933,5937,5938,5939,5955,5965,5966,5994,5995,5999,6019,6022,6026,6045,6050,6051,6076,6079,6087,6095,6101,6105,6112,6113,6114,6115,6154,6173,6226,6262,6264,6285,6286,6291,6294,6295,6299,6305,6314,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6557,6562,6564,6569,6570,6578,6582,6595,6620,6621,6622,6623,6635,6640,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6792,6795,6831,6834,6835,6848,6849,6850,6851,6871,6872,6887,6913,6935,6946,6948,6949,6951,6953,6954,6987,6988,6993,6994,6995,6996,6998,7000,7025,7034,7035,7047,7057,7096,7106,7110,7117,7128,7134,7136,7142,7151,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7385,7399,7416,7448,7451,7477,7501,7518,7521,7522,7532,7550,7551,7553,7555,7557,7559,7587,7612,7613,7645,7647,7648,7649,7654,7676,7685,7695,7700,7706,7708,7714,7726,7727,7729,7760,7783,7850,7851,7898,7906,7907,7931,7932,7949,7950,8008,8009,8010,8035,8068,8075,8077,8087,8099,8130,8138,8145,8158,8180,8186,8213,8257,8285,8298,8316,8319,8349,8372,8433,8434,8437,8439,8544,8545,8546,8547,8576,8605,8636,8680,8698,8753,8798,8801,8814,8821,8858,8877,8905,8906,8924,8925,9065,9069,9089,9099,9122,9124,9127,9131,9134,9135,9148,9149,9169,9175,9187,9235,9253,9307,9308,9315,9376,9381,9417,9424,9427,9430,9431,9446,9462,9471,9483,9495,9496,9499,9501,9528,9653,9698,9699,9741,9786,9902,9959,10024,10098,10111,10116,3,2606,2609,2611,2612,2613,2614,2622,2628,2629,2630,2633,2634,2635,2636,2637,2639,2644,2645,2646,2647,2649,2651,2659,2660,2661,2669,2671,2672,2673,2675,2676,2677,2680,2681,2682,2692,2707,2708,2709,2711,2712,2714,2715,2719,2721,2723,2724,2725,2733,2735,2736,2737,2743,2746,2749,2750,2751,2775,2776,2777,2780,2781,2791,2793,2795,2796,2797,2821,2831,2832,5207,5267,5365,5451,5452,5453,5528,5626,5657,5691,5707,5709,5715,5778,5779,5780,5781,5787,5820,5950,5993,6016,6053,6093,6242,6249,6283,6284,6304,6307,6309,6316,6317,6318,6319,6320,6321,6322,6323,6402,6470,6471,6555,6589,6590,6632,6633,6771,6786,6860,6861,6868,6888,6911,6919,6921,6968,6991,6992,7008,7009,7010,7046,7090,7091,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7373,7375,7387,7419,7420,7421,7422,7567,7568,7574,7575,7577,7579,7791,7793,7794,7810,7848,7927,7966,8019,8040,8041,8056,8116,8228,8295,8296,8299,8334,8396,8397,8463,8482,8483,8484,8485,8640,8851,8875,8876,8956,8970,9024,9025,9143,9179,9202,9236,9277,9469,9735,9928,9984,9986,6011,6385,6386,6473,6493,6494,6910,7126,8562,8595,8792,8982,8983,9052,9053,9325,9326,9327,9328,9531,9806,10107,10158,10159,6455,8387,8388,8841,8859,9807,10157,4632,4634,4635,4690,4698,4835,4851,4852,4880,4881,4910,4965,5028,5087,5164,5200,5202,5210,5211,5237,5312,5333,5467,5533,5534,5535,5653,5654,5680,5684,5744,5755,5761,5833,5911,6034,6057,6229,6348,6503,6705,6706,6922,6961,7132,7359,7427,7767,7768,7864,8017,8799,9056,9291,9566,4865,4912,5053,5885,5975,5986,6007,6021,6282,6708,7107,7317,7384,7460,7753,7822,7861,9407,9408,2607,2615,2618,2619,2620,2621,2623,2641,2643,2654,2663,2666,2704,2739,2753,2755,2823,2841,2854,5817,5864,6003,6088,6572,6573,5551,7852])). % 167.77/167.58 cnf(13348,plain, % 167.77/167.58 (~P1(f328(f328(f330(a872),x133481),f328(f249(a872),f2(a872))))), % 167.77/167.58 inference(rename_variables,[],[11732])). % 167.77/167.58 cnf(13351,plain, % 167.77/167.58 (~E(f328(f328(f80(a1),x133511),x133511),a101)), % 167.77/167.58 inference(rename_variables,[],[4479])). % 167.77/167.58 cnf(13378,plain, % 167.77/167.58 (~P1(f328(f328(f330(f878(x133781,x133781)),x133782),f260(x133781,f192(f879(x133781,a867)))))), % 167.77/167.58 inference(rename_variables,[],[10922])). % 167.77/167.58 cnf(13383,plain, % 167.77/167.58 (~E(f328(f328(f148(x133831),x133832),x133833),x133833)), % 167.77/167.58 inference(rename_variables,[],[4481])). % 167.77/167.58 cnf(13386,plain, % 167.77/167.58 (~E(f328(f328(f148(x133861),x133862),x133863),x133863)), % 167.77/167.58 inference(rename_variables,[],[4481])). % 167.77/167.58 cnf(13389,plain, % 167.77/167.58 (E(f328(f259(x133891,x133891),f260(x133891,x133892)),x133892)), % 167.77/167.58 inference(rename_variables,[],[3232])). % 167.77/167.58 cnf(13392,plain, % 167.77/167.58 (~P1(f328(f328(f192(f879(x133921,f879(x133922,a867))),x133923),x133924))), % 167.77/167.58 inference(rename_variables,[],[4546])). % 167.77/167.58 cnf(13410,plain, % 167.77/167.58 (P1(f328(f328(f243(a1),f328(f328(f22(a1),x134101),f78(a1))),x134101))), % 167.77/167.58 inference(rename_variables,[],[10736])). % 167.77/167.58 cnf(13423,plain, % 167.77/167.58 (~P1(f328(f328(f192(f879(x134231,f879(x134232,a867))),x134233),x134234))), % 167.77/167.58 inference(rename_variables,[],[4546])). % 167.77/167.58 cnf(13428,plain, % 167.77/167.58 (P1(f328(f328(f243(a1),f328(f328(f22(a1),x134281),f78(a1))),x134281))), % 167.77/167.58 inference(rename_variables,[],[10736])). % 167.77/167.58 cnf(13433,plain, % 167.77/167.58 (~P1(f328(f328(f330(f878(x134331,x134331)),x134332),f260(x134331,f192(f879(x134331,a867)))))), % 167.77/167.58 inference(rename_variables,[],[10922])). % 167.77/167.58 cnf(13441,plain, % 167.77/167.58 (~E(f328(f328(f148(x134411),x134412),x134413),x134413)), % 167.77/167.58 inference(rename_variables,[],[4481])). % 167.77/167.58 cnf(13444,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),x134441),f328(f328(f80(a872),x134441),x134442)))), % 167.77/167.58 inference(rename_variables,[],[3545])). % 167.77/167.58 cnf(13451,plain, % 167.77/167.58 (~P1(f328(f328(f330(a872),x134511),f328(f249(a872),f2(a872))))), % 167.77/167.58 inference(rename_variables,[],[11732])). % 167.77/167.58 cnf(13458,plain, % 167.77/167.58 (~P1(f328(f328(f330(x134581),x134582),f328(f308(x134581,x134583,x134584),f192(f879(x134583,a867)))))), % 167.77/167.58 inference(rename_variables,[],[10925])). % 167.77/167.58 cnf(13469,plain, % 167.77/167.58 (~P1(f328(f328(f330(x134691),x134692),f192(f879(x134691,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(13474,plain, % 167.77/167.58 (~P1(f328(f328(f330(f878(x134741,x134741)),x134742),f260(x134741,f192(f879(x134741,a867)))))), % 167.77/167.58 inference(rename_variables,[],[10922])). % 167.77/167.58 cnf(13479,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),f328(f328(f80(a872),x134791),x134792)),x134792))), % 167.77/167.58 inference(rename_variables,[],[4543])). % 167.77/167.58 cnf(13484,plain, % 167.77/167.58 (~P1(f328(f328(f192(f879(x134841,f879(x134842,a867))),x134843),x134844))), % 167.77/167.58 inference(rename_variables,[],[4546])). % 167.77/167.58 cnf(13497,plain, % 167.77/167.58 (P1(f328(f328(f242(f879(x134971,a867)),f328(f170(x134971),f174(x134971,x134972,x134973))),f328(f170(x134971),x134972)))), % 167.77/167.58 inference(rename_variables,[],[3979])). % 167.77/167.58 cnf(13505,plain, % 167.77/167.58 (~P1(f328(f328(f330(a872),x135051),f328(f249(a872),f2(a872))))), % 167.77/167.58 inference(rename_variables,[],[11732])). % 167.77/167.58 cnf(13508,plain, % 167.77/167.58 (~P1(f328(f328(f330(x135081),x135082),f328(f308(x135081,x135083,x135084),f192(f879(x135083,a867)))))), % 167.77/167.58 inference(rename_variables,[],[10925])). % 167.77/167.58 cnf(13515,plain, % 167.77/167.58 (~P1(f328(f328(f330(x135151),x135152),f192(f879(x135151,a867))))), % 167.77/167.58 inference(rename_variables,[],[4529])). % 167.77/167.58 cnf(13539,plain, % 167.77/167.58 (P1(f328(f328(f242(a872),f46(a872,x135391,x135392)),x135391))), % 167.77/167.58 inference(rename_variables,[],[3735])). % 167.77/167.58 cnf(13552,plain, % 167.77/167.58 (~E(f328(f328(f148(x135521),x135522),x135523),x135523)), % 167.77/167.58 inference(rename_variables,[],[4481])). % 167.77/167.58 cnf(13581,plain, % 167.77/167.58 (E(f328(f328(f125(x135811),x135812),f117(x135811)),x135812)), % 167.77/167.58 inference(rename_variables,[],[3204])). % 167.77/167.58 cnf(13586,plain, % 167.77/167.58 (~P1(f328(f328(f330(a872),x135861),f328(f249(a872),f2(a872))))), % 167.77/167.58 inference(rename_variables,[],[11732])). % 167.77/167.58 cnf(13589,plain, % 167.77/167.58 (~P1(f328(f328(f330(f878(x135891,x135891)),x135892),f260(x135891,f192(f879(x135891,a867)))))), % 167.77/167.58 inference(rename_variables,[],[10922])). % 167.77/167.58 cnf(13592,plain, % 167.77/167.58 (~P1(f328(f328(f243(a872),x135921),x135921))), % 167.77/167.58 inference(rename_variables,[],[4517])). % 167.77/167.58 cnf(13595,plain, % 167.77/167.58 (~P1(f328(f328(f330(a872),x135951),f328(f249(a872),f2(a872))))), % 167.77/167.59 inference(rename_variables,[],[11732])). % 167.77/167.59 cnf(13618,plain, % 167.77/167.59 (~E(f328(f328(f148(x136181),x136182),x136183),x136183)), % 167.77/167.59 inference(rename_variables,[],[4481])). % 167.77/167.59 cnf(13623,plain, % 167.77/167.59 (P1(f328(f328(f242(a872),x136231),f328(f328(f81(a872),x136231),x136231)))), % 167.77/167.59 inference(rename_variables,[],[3546])). % 167.77/167.59 cnf(13641,plain, % 167.77/167.59 (P1(f328(f328(f243(a872),x136411),f328(f328(f81(a872),f328(a116,x136411)),f328(a116,x136411))))), % 167.77/167.59 inference(rename_variables,[],[10590])). % 167.77/167.59 cnf(13644,plain, % 167.77/167.59 (~E(f328(f328(f148(x136441),x136442),x136443),x136443)), % 167.77/167.59 inference(rename_variables,[],[4481])). % 167.77/167.59 cnf(13649,plain, % 167.77/167.59 (P1(f328(f328(f242(a872),f2(a872)),x136491))), % 167.77/167.59 inference(rename_variables,[],[3296])). % 167.77/167.59 cnf(13652,plain, % 167.77/167.59 (~P1(f328(f328(f242(a872),f328(a116,x136521)),x136521))), % 167.77/167.59 inference(rename_variables,[],[4526])). % 167.77/167.59 cnf(13686,plain, % 167.77/167.59 (~P1(f328(f328(f192(f879(x136861,f879(x136862,a867))),x136863),x136864))), % 167.77/167.59 inference(rename_variables,[],[4546])). % 167.77/167.59 cnf(13700,plain, % 167.77/167.59 (~P1(f328(f328(f330(x137001),x137002),f192(f879(x137001,a867))))), % 167.77/167.59 inference(rename_variables,[],[4529])). % 167.77/167.59 cnf(13706,plain, % 167.77/167.59 (E(f328(x137061,f709(f328(x137061,x137062),f328(f235(x137063),x137062),x137061,x137064,x137063)),f328(x137061,x137062))), % 167.77/167.59 inference(rename_variables,[],[11101])). % 167.77/167.59 cnf(13721,plain, % 167.77/167.59 (P1(f328(f328(f330(x137211),f328(x137212,x137213)),f328(f307(x137214,x137211,x137212),f251(f879(x137214,a867)))))), % 167.77/167.59 inference(rename_variables,[],[3883])). % 167.77/167.59 cnf(13724,plain, % 167.77/167.59 (E(f328(x137241,f709(f328(x137241,x137242),f328(f235(x137243),x137242),x137241,x137244,x137243)),f328(x137241,x137242))), % 167.77/167.59 inference(rename_variables,[],[11101])). % 167.77/167.59 cnf(13734,plain, % 167.77/167.59 (~E(f328(a116,x137341),f2(a872))), % 167.77/167.59 inference(rename_variables,[],[4466])). % 167.77/167.59 cnf(13779,plain, % 167.77/167.59 ($false), % 167.77/167.59 inference(scs_inference,[],[3303,3717,4027,3866,4063,3063,4545,3277,3918,3350,4550,4508,3370,3730,4529,13469,13515,13700,3354,3979,13497,3376,3883,13721,3614,3757,3380,4471,4466,13734,4538,4481,13383,13386,13441,13552,13618,13644,4479,13351,3258,3275,3735,13539,3296,13649,3724,3576,3546,13623,3545,13444,3232,13389,3204,13581,4554,4517,13592,4526,13652,4546,13392,13423,13484,13686,4543,13479,4544,3487,11484,13011,10559,10346,11792,13177,13320,10590,13641,10574,11508,11033,12412,12448,10912,13111,10736,13410,13428,12468,11201,11157,11101,13706,13724,10271,12930,11250,10521,11180,12918,12921,13191,10693,12125,12229,11730,11732,13348,13451,13505,13586,13595,13244,12673,10922,13378,13433,13474,13589,10925,13458,13508,10675,11991,11255,12464,13199,11163,10937,2873,3830,9,2,5225,8518,8664,5211,6706,9623,6290,5625,7669,9560,5467,6454,6490,7401,5234,5591,7468,10189,6346,5298,5978,6337,4883,9055,5218,7283,8737,9917,7337,5563,5796,6172,6214,5230,5324,5916,8884,5730,5515,5534,5719,6229,5294,6083,4640,9162,9670,6106,6244,7746,9091,9291,8736,4697,4943,6347,9671,5665,7127,8378,5895,5755,5911,5312,5315,5802,8358,7535,9818,6790,6863,4910,5164,8553,9422,9624,5637,5940,5992,5228,5723,5797,6058,6453,5680,6506,6745,6857,8382,8588,7762,7516,9136,7398,5736,8585,6749,4736,4944,5953,6061,9552,5042,7157,7895,9484,7469,8780,6034,10119,5684,5329,6108,8214,9703,5734,5299,5383,6738,8508,5546,4965,6990,5519,8799,7308,4918,5720,6292,7217,7718,8540,5578,5594,6084,5035,5565,7961,9323,5398,5854,7517,6080,4882,6078,6546,8000,9384,6719,5101,4635,6235,7684,9092,6342,6718,8432,5744,8873,9023,5444,8602,8805,5300,9021,5036,5181,5202,5362,5875,9812,5808,9272,7473,9209,6059,5210,5499,5317,4672]), % 167.77/167.59 ['proof']). % 167.77/167.59 % SZS output end Proof % 167.77/167.59 % Total time :147.750000s %------------------------------------------------------------------------------